Monomer partitioning and composition drift in emulsion ...MONOMER PARTITIONING AND COMPOSITION DRIFT...
Transcript of Monomer partitioning and composition drift in emulsion ...MONOMER PARTITIONING AND COMPOSITION DRIFT...
Monomer partitioning and composition drift in emulsioncopolymerizationCitation for published version (APA):Verdurmen-Noël, E. F. J. (1994). Monomer partitioning and composition drift in emulsion copolymerization.Eindhoven: Technische Universiteit Eindhoven. https://doi.org/10.6100/IR426298
DOI:10.6100/IR426298
Document status and date:Published: 01/01/1994
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MONOMER PARTITIONING AND COMPOSITION DRIFT
IN EMULSION COPOLYMERIZATION
PROEFSCHRIFf
ter verkrijging van de graad van doctor aan de
Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof. dr. J .H. van Lint, voor een commissie aangewezen door bet College van Dekanen in het openbaar te verdedigen op
dinsdag 29 november 1994 om 16.00 uur
door
Elisabeth Fran~ois Johanna Verdurmen-Noel
geboren te Weert
druk. wfbro dissortatiodrukkorij. holmond.
Dit proefschrift is goedgekeurd door
de promotoren
en de copromotor
prof.dr.ir. A.L. German
prof.dr. J.M. Asua
dr. I.A. Maxwell
Het in dit proefschrift beschreven onderzoek werd gesteund door de Stichting Scheikundig
Onderzoek in Nederland (SON) met een subsidie van de Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO).
Summary
Summary
Emulsion copolymerization is a complex process due to the heterogeneity of the
system which consist of three distinct phases, i.e., the aqueous, polymer particle, and
monomer droplet phase. Nowadays, there is still a lack of knowledge on the basic processes
determining emulsion (co )polymerization kinetics. One of the aims of this investigation is
developing a correct and simple model to describe monomer partitioning of two monomers
with limited water solubility in an emulsion system in such a way as to avoid the use of
interaction parameters that are experimentally hard to determine and theoretically rather
vague. Such a model is forming a key barrier if one wants to predict emulsion
copolymerization using only parameters of physical significance.
It has been shown in previous work that the monomer ratios within the polymer
particle and monomer droplet phases are equal and independent of the copolymer
composition. However, no theoretical explanation was given. In chapter 5 the assumptions
required to modify the theory in order to explain this phenomenon are given. Furthermore,
simple equations are depicted to describe monomer partitioning in emulsion systems using
parameters of physical significance only, i.e., no adjustable or interaction parameters are used.
Model development based on the relationships described in chapter 5 provides a
better understanding of the effects of process parameters as for instance the monomer-to
water ratio and the polymer volume on monomer partitioning (chapter 6). A sensitivity
analysis showed that the reactivity ratios are the most important parameters affecting
composition drift. The effect of water solubility of the monomers on composition drift is only
significant in those cases were the amount of monomer in the aqueous phase is not negligible
as compared with the total monomer amount. The rate of polymerization mainly depends on
the maximum swellability of monomers in the polymer phase.
In principle the heterogeneity of the emulsion system can be used to influence the
chemical composition distribution of the copolymer. A second aim in this investigation is the
verification of the concept that minimum composition drift can be reached for monomer
combinations in which the more water soluble monomer also is the more reactive one. This
was tested for the monomer combinations methyl acrylate-indene (MA-Ind: chapter 7) and
methyl acrylate-vinyl esters (MA-VEst: chapter 8). lt was shown for the monomer
Summary
combination MA-Ind that minimum composition drift indeed could be obtained over a wide
range of initial monomer mole fractions, simply by adjusting the initial monomer-to-water
ratio. The strong effect of the ratio of the water solubilities of the monomers was illustrated
using a series of vinyl ester monomers in combination with MA. These MA-VEst monomer
combinations have similar reactivity ratios (chapter 3) and differ only in the water solubility
of the vinyl ester monomer. It was shown that minimum composition drift indeed could be
reached for MA-VEst combinations if the water solubility of the vinyl ester monomer was
low. The difference in water solubility of MA and V Ac was not large enough to compensate
the large difference in reactivity ratios between MA and V Ac. It becomes clear that, despite
of the similarity in reactivity ratios, the chemical composition distribution depends on the
selected monomer-to-water ratio and the water solubility of the vinyl ester monomer.
Apart from achieving a better understanding of composition drift and polymerization
rates through model development, in chapter 4 also efforts are made to monitor emulsion
copolymerization by on-line densimetry and on-line gas chromatography in order to improve
the quality and quantity of data on partial conversions of both monomers participating in the
emulsion polymerization. Using this combination of on-line techniques accurate information
of partial conversions was obtained as a function of time for the monomer combination MA
VAc.
Samenvatting
Samenvatting
Emulsiecopolymerisaties zijn complexe processen ten gevolge van het heterogene
karakter van het emulsiesysteem, dat bestaat uit een waterfase, een polymeerfase en
monomeerdruppels. Er bestaat er nog steeds een gebrek aan basiskennis ten aanzien van
kinetische processen in emulsie(co )polymerisaties. Een van de doelstellingen van dit onderzoek
is het ontwikkelen van een correct en eenvoudig model om de monomeerverdeling van twee
monomeren met een beperkte wateroplosbaarheid in een emulsiesysteem te beschrijven op een
dusdanige manier dat het gebruik van experimenteel moeilijk te bepalen en theoretisch
onduidelijk gedefmieerde interactieparameters vermeden kan worden. Een dergelijk model is
van groot belang indien men emulsiecopolymerisatieprocessen wil beschrijven met behulp van
parameters met fysische betekenis. In voorafgaand werk is aangetoond dat de molfracties
monomeer in de monomeerdruppels en polymeerdeeltjes identiek zijn en onafhankelijk van
de copolymeersamenstelling. Hiervoor is echter geen theoretische verklaring gegeven. In
hoofdstuk S worden de aannames besproken die gebruikt zijn om dit fenomeen te verklaren.
Verder worden eenvoudige relaties gegeven die de monomeer-verdeling in het emulsiesysteem
beschrijven met behulp van parameters met fysische betekenis, met andere woorden, bet
gebruik van interactie of variabele parameters kan vermeden worden.
Modellering gebaseerd op de relaties beschreven in hoofdstuk S geeft meer inzicht in
het effect van procesparameters zoals de monomeer-waterverbouding en bet polymeervolume
op de monomeerverdeling (hoofdstuk 6). Een gevoeligbeidsanalyse geeft aan dat de
reactiviteitsverboudingen de parameters zijn met de grootste invloed op het
samenstellingsverloop. De invloed van de wateroplosbaarheid van de monomeren is aileen
significant voor het samenstellingsverloop indien de boeveelheid monomeer opgelost in de
waterfase niet kan worden verwaarloosd ten opzicbte van de totale boeveelheid monomeer.
De polymerisatiesnelbeid is vooral afbankelijk van de maximale zwelbaarheid van polymeer
met monomeer.
In principe kan bet heterogene karakter van bet emulsiesysteem gebruikt worden om
de chemiscbe samenstellingsverdeling van bet gevormde copolymeer te beinvloeden. Een
tweede doelstelling van dit onderzoek is het verifieren van het concept dat een minimaal
Samenvatting
samenstellingsverloop bereikt kan worden voor monomeersystemen waarin bet beter oplosbare
monomeer tevens het meer reactieve monomeer is. Dit concept is experimenteel geverifieerd
voor de monomeercombinaties methylacrylaat-indene (MA-Ind: boofdstuk 7) en
methylacrylaat-vinylesters (MA-VEst: boofdstuk 8). Het is aangetoond dat een minimaal
samenstellingsverloop inderdaad bereikt kan worden over een breed traject van initiele
molfracties monomeer door simpelweg de monomeer-waterverhouding te varieren voor het
systeem MA-Ind. De sterke invloed van de verhouding van de wateroplosbaarheden van beide
monomeren wordt geYIJustreerd met bebulp van een serie van vinylesters in combinatie met
MA. Deze MA-VEst monomeercombinaties bezitten vergelijkbare reactiviteits-verhoudingen
(hoofdstuk 3) terwijl de wateroplosbaarheid van de vinyl esters sterk verschilt. Het is gebleken
dat een minimaal samenstellingsverloop behaald kan worden voor MA-VEst
monomeercombinaties waarin de wateroplosbaarheid van de vinyl ester laag is. V oor de
monomeercombinatie MA-V Ac is de afhankelijkheid van het samenstellingsverloop van de
monomeer-waterverhouding slecbts gering. In deze monomeercombinatie is het verschil in
wateroplosbaarheid blijkbaar niet groot genoeg om het grote verschil in reactiviteits
verhoudingen te compenseren. Duidelijk wordt dat, ondanks vergelijkbare reactiviteits
verhoudingen, de chemische samenstellingsverdeling van bet resulterende copolymeer
afhankelijk is van de geselecteerde monomeer-waterverhouding en de wateroplosbaarheid van
het vinylester monomeer.
Naast het verkrijgen van een dieper inzicht in samenstellingsverloop en
polymerisatiesnelheid door modellering en experimentele verificatie is in hoofdstuk 4 een
opstelling beschreven om kwalitatief en kwantitatief betere particle conversies van beide
monomeren in een emulsiecopolymerisatie te bepalen met behulp van on-line
gaschromatografie en on-line dichtheidsmetingen. Aangetoond is dat met behulp van deze
opstelling snel en accuraat partiele conversies als functie van de tijd bepaald kunnen worden.
Contents
Contents
Summary
Samenvatting
Chapter 1 Introduction
1.1 1.2 1.3 1.4
Short historic overview Background of the investigation Aim of the investigation Survey of this thesis References
Chapter 2 Theoretical background
2.1
2.2
Emulsion polymerization 2.1.1 Particle nucleation 2.1.2 Particle growth in emulsion polymerization Emulsion copolymerization References
Chapter 3 Experimental
3.1
3.2 3.3 3.4
Experimental (co )polymerization procedures 3.1.1 Purification of chemicals 3.1.2 Copolymerization reactions 3 .1.3 Determination of (partial) conversion Monomer partitioning Densimetry Determination of reactivity ratios by low conversion bulk polymerization References
Chapter 4 On-line gas chromatography and densimetry
4.1 4.2 4.3 4.4
Introduction Theory Experimental Results and Discussion 4.4.1 Density 4.4.2 Homopolymerization
1 2 3 4 6
1 1 8 9
II
13 13 14 15 16 18 19 26
27 29 31 33 33 34
4.5 4.4.3 Emulsion copolymerization of MA and V Ac Conclusions References
Chapter 5 Swelling of latex particles by two monomers
5.1 5.2
5.3
5.4
Introduction Theory 5.2.1 Saturation swelling of latex particles by two monomers 5.2.2 Partial swelling of latex particles by one monomer 5.2.3 Partial swelling of latex particles by two monomers Results and discussion 5.3.1 Monomer partitioning at saturation swelling of latex particles
by two monomers 5.3.2 Monomer partitioning at partial swelling of latex particles by
one monomer 5.3.3 Monomer partitioning at partial swelling of latex particles by
two monomers Conclusions References
Chapter 6 Model prediction of batch emulsion copolymerization
6.1 6.2
6.3
6.4
Introduction Theory 6.2.1 Saturation swelling of latex particles by two monomers:
determination of fpi 6.2.2 Partial swelling of latex particles by two monomers:
determination of fpi 6.2.3 Model calculations in emulsion copolymerization Results and discussion 6.3.1 General monomer partitioning considerations 6.3.2 Monomer partitioning of MA· V Ac monomer systems 6.3.3 Prediction of emulsion copolymerization composition Conclusions Appendix: sensitivity analysis
A-6.1 Introduction A-6.2 Results and discussion
A-6.2.1 Homo-monomer saturation concentrations A-6.2.2 Reactivity ratios A-6.2.3 Monomer and polymer densities
A-6.3 Conclusions References
Contents
39 43 44
45 47 52 54 54 56
57
59
60 63 64
65 67
68
70 73 75 76 78 82 84 86 86 87 88 93 94 95 96
Contents
Chapter 7
7.1 Introduction 7.2 Theory 7.3 Experimental
Monomer-to-water ratios as a tool in controlling emulsion copolymer composition
The methyl acrylate-indene system
7.4 Results and discussion 7.4.1 Optimization of recipe conditions 7.4.2 Model parameters 7.4.3 Composition drift in emulsion copolymerization of MA-Ind
7.5 Conclusions References
Chapter 8 The effect of water solubility of the monomers on composition drift in methyl acrylate-vinyl ester combinations
8.1 Introduction 8.2 Theory 8.3 Experimental 8.4 Results and discussion 8.5 Conclusions
References
Epilogue
List of sy~~~bols
Acknowledgement
Curriculum Vitae
97 99
101 102 102 103 105 112 114
115 117 118 119 124 126
127
130
133
134
Introduetion 1
Chapter 1 Introduction
1.1 Short historic overview
Emulsion polymerization is a free radical process starting from the dispersion of
a monomer in a continuous aqueous phase, commonly using an emulsifier and a water
soluble initiator. During an important part of the process the reaction system consists of
monomer droplets and monomer swollen polymer particles dispersed in the aqueous
phase. The fmal product, known as a latex, is a colloidal dispersion of polymer particles
in water.
The first attempts to perform emulsion copolymerization reactions were made
during World War I aiming at a synthetic substitute for natural rubber. Nowadays these
first attempts would be considered to be suspension polymerizations rather than
emulsion polymerizations. The first description of true emulsion polymerization
appeared in literature in 1927 in a patent granted to Dinsmore. 1 Luther and Heuck2•3
first described the use of emulsifier and initiator in emulsion polymerization. Good
overviews of early work in the field of emulsion polymerization are given by
Hohenstein and Mark4 and by Blacldey 5•
The commercial use of the emulsion polymerization process started in World
War II as a result of the Synthetic Rubber Program in the United States. Since then a
huge nmnber of papers have appeared on basic as well as applied aspects of emulsion
polymerization, indicating the general importance of the process.
Advantageous properties of the emulsion polymerization process include the good
heat transfer and, as a consequence good temperature control during reaction, the
possibility of reaching high conversions, the absence of toxic and flammable organic
solvents, and the possibility of producing high molecular weight copolymers at high
2 Chapter 1
polymerization rates. The resulting latices often can be used directly in coating, ink, and
adhesive applications. Application as elastomers, commodity and engineering plastics
becomes possible after polymer isolation. A disadvantage of the emulsion
polymerization process is the relatively poor film formation properties of the resulting
latex as compared with solvent based systems. Significant economic advantages can be
obtained by a better understanding of the basic principles of emulsion
(co)polymerization, since the latter will lead to better control of polymerization
reactions, in tum allowing fine-tuning of the process and the product performance in
terms of, amongst others, polymerization rates, molecular weight distributions, chemical
composition distributions, and particle morphology.
The first qualitative description of the kinetics of emulsion polymerization
reactions were reported by Harkins6 for the monomer styrene. Smith and Ewart7
developed a mathematical kinetic treatment that quantified the kinetic aspects of
emulsion polymerization for a number of limiting cases. After Smith and Ewart's early
work a large number of papers have been published dealing with modelling of emulsion
polymerization and copolymerization processes.
1.2 Background of the investigation
Although much research has been performed in order to achieve better
understanding of emulsion copolymerization, it is still relatively poorly understood.
Attempts to model emulsion copolymerization in terms of copolymer composition and
polymerization rates have been made by several investigators. 8•9•10
•11
•12
•13
•14
•15 For
this purpose existing basic theories for emulsion homopolymerization usually were
mathematically extended to emulsion copolymerization. The most widely used kinetic
model describing free radical copolymerization is the terminal model, also known as the
Mayo-Lewis16 or ultimate model. For most monomer combinations the copolymer
composition and the composition drift occurring during reaction can be fitted with this
terminal model. 17 Recently, however, many investigators mention the inability of the
terminal model to predict copolymerization rates. 18•19
•20
•21 .22 A model frequently
used to describe non-terminal behaviour of the kinetics is the penultimate model
developed by Fukuda et a/ .. 20 However, at least ten other models are also capable of
explaining the non-terminal behaviour. 16·'
8•22
•23
•24 Due to a lack of sufficiently accurate
experimental information model discrimination has not yet been possible.24•25
Furthermore, as a result of the complexity of the heterogeneous emulsion polymerization
Introduction 3
process until now most kinetic data are obtained from fitting semi·empirical models
resulting in values of the rate parameters that are nothing more than fitted estimations.
On behalf of correct model predictions of polymerization rates per particle in emulsion
homo·polymerization the values of all rate coefficients have to be known. In order to
predict overall polymerization rates also the number of particles needs to be known
since this overall polymerization rate is proportional to the particle number. In emulsion
copolymerization finding correct values for rate coefficients is even more complex.
As mentioned before, in most cases the copolymer composition can be well
predicted using the terminal model. However, the use of this model involves the
knowledge of the monomer concentrations of both monomers in the polymer particle
phase, where polymerization mainly occurs. These monomer concentrations in the
polymer phase can be calculated using relationships describing the monomer partitioning
over the polymer particle, the monomer droplet and the aqueous phases. In the literature,
an empirical and a thermodynamic approach have been proposed for describing
monomer partitioning.8•9
•10·u·12
•13
•14
•15 Disadvantages of these approaches are the lack of
theoretical background,8•9•10
•11
•12 and the use of interaction parameters 14
•15
.26 which are
experimentally hard to determine and theoretically rather vague.
From the above discussion follows the great importance of the availability of
simple relationships that correctly predict monomer concentrations in the polymer phase
since this forms the basis of all models predicting (instead of fitting) copolymer
composition and rates of copolymerization.
1.3 Aims of the investigation
After the above general introduction into the field of emulsion copolymerization
it will be clear that there is still a lack of knowledge of the basic processes governing
emulsion copolymerization kinetics. The first aim of this investigation is the
development of a reliable and simple model to describe monomer partitioning of two
monomers with limited water solubility in an emulsion system, in such a way as to
avoid the use of interaction parameters that are experimentally difficult to access and
theoretically rather vague. For the investigation of monomer partitioning between the
monomer droplet, polymer particle, and aqueous phases, the monomer combination
methyl acrylate-vinyl acetate was selected. In this system both monomers have a
relatively high water solubility making accurate water phase analysis by gas
chromatography possible for each monomer. Model development based on these new
4 Chapter 1
relationships opens possibilities of a better understanding of the effects of process
parameters, e.g. the monomer-to-water ratio and the polymer volume, on monomer
partitioning. A sensitivity analysis of the model will reveal the effects of varying model
parameters (maximum swellability, water solubility, reactivity ratios, and density values)
on the predictions of composition drift and polymerization rates.
In principle the heterogeneity of the emulsion system constitutes a new and
unique parameter to adjust the chemical composition distribution of the copolymer.
Theoretically, minimum composition drift can be obtained for those monomer
combinations in which the more water soluble monomer is also the more reactive one.
The second aim in this investigation is the experimental verification of this concept for
the monomer combination methyl acrylate-indene. Furthermore, the effect of different
monomer water solubilities on composition drift was investigated for the emulsion
copolymerization of methyl acrylate with a series of vinyl esters; viz. vinyl acetate, vinyl
2,2-dimethyl-propanoate, and vinyl 2-ethylhexanoate. These monomer combinations are
ideal for studying the effect of water solubility since the reactivity ratios· are very similar
for the three monomer combinations.
The third aim of this investigation . is increasing the quality and quantity of
experimental data by developing on-line techniques based on on-line densimetry and on
line gas chromatography, for detailed monitoring of emulsion copolymerization.
1.4 Survey of this thesis
In Chapter 2 the basic theoretical aspects of emulsion copolymerization are
briefly discussed.
In Chapter 3 experimental methods used in the study of emulsion
copolymerization are presented. The monomer partitioning experiments needed for
model development are described as well as the determination of the water solubility of
the monomers and of the maximum swellability of the monomers in polymer.
Furthermore, the determination of the relevant monomer reactivity ratios and of the
density of monomer and (co)polymer, needed for model predictions, are outlined.
In Chapter 4 the set-up for on-line densimetry and gas chromatography is given.
Also, the results obtained with these techniques are presented and evaluated.
Monomer partitioning relations for the swelling of two monomers in emulsion
systems at saturation swelling are described in Chapter 5. In addition, relationships for
partitioning of two monomers at partial swelling are derived.
Introduction 5
In Chapter 6 a model is developed to predict the course of emulsion
copolymerization as a function of conversion based on mass balance equations and
monomer partitioning relationships as described in Chapter 5. A sensitivity analysis for
this model is performed using the styrene-methyl methacrylate monomer combination as
an example. The sensitivity of the model to the various parameters is discussed.
The use of monomer-to-water ratios as a tool in controlling emulsion
copolymerizations is depicted in Chapter 7 for the monomer combination methyl
acrylate-indene. In this chapter theoretical predictions of minimum composition drift as a
function of monomer-to-water ratio are compared with experimentally observed data of
emulsion copolymerizations showing minimum composition drift.
In Chapter 8 the effect of different water solubility values of the monomers on
composition drift is presented for the copolymerization of methyl acrylate with a series
of vinyl esters of decreasing water solubilities, viz. vinyl acetate, vinyl 2,2-dimethyl
propanoate, and vinyl 2-ethylhexanoate.
In the Epilogue the results and their impact on future developments will be
evaluated against the background of the above aims.
Parts of this work have been presented at the Gordon Research Conference on
Polymer Colloids (Irsee, Germany, September 1992), the 8th International Conference
on Surface and Colloid Science (Adelaide, Australia, February 1994), and the 3th
International Symposium on Radical Copolymers in Dispersed Media (Lyon, France,
April 1994)
Parts of this thesis have been published or will be published soon: the
determination of the reactivity ratios presented in chapter 3,27•28 the determination of
partial conversion of two monomers in batch emulsion copolymerization by on-line
densimetry in combination with on-line gas chromatography described in chapter 4,29
the monomer partitioning work of chapter 5,30.3
1 the model development 32 and
sensitivity analysis33 described in chapter 6, the work in chapter 7 on achieving
minimum composition drift by adjusting monomer-to-water ratios,23 and the work in
chapter 8 on the effect of water solubility on composition drift in methyl acrylate-vinyl
.ester emulsion copolymerization.34 Furthermore, related work that was considered
beyond the scope of this thesis, viz. the determination of maximum swellabilities using
conductivity measurements/5 and work on the determination of the average number of
growing chains per particle for MMA-Sty emulsion copolymerizations as a function of
particle size, copolymer seed composition and initiator concentration, 36 has been
published or will be published soon.
6 References
I. US 1,732,795 (1929), The goodyear Tire & Rubber Co., lnv.: R. P. Dinsmore 2. US 1,860,681 (1932), !.G. Farbenindustrie A.G., Inv: M. Luther, C. Heuck 3. US 1,846,078 (1932), !.G. Farbenindustrie A.G., lnv: M. Luther, C. Heuck 4. W. P. Hohenstein, H. Mark, J Polym. Sci., 127, 549 (1946) 5. D.C. Blackley, In Emulsion Polymerisation - Theory and Practice, Applied
Publishers Ltd, London 1975, p 26-35 6. W.D. Harkins, J. Am. Chem. Soc., 69, 1428 (1947) 7. W.V. Smith, R.H. Ewart, J. Chem. Phys. 16, 592 (1948) 8. M. Nomura, K. Fujita, Macromol. Chem., Suppl., 10/11, 25 (1985) 9. M. Nomura, I. Rorie, M. Kubo, K. Fujita, J. Appl. Polym. Sci., 37, 1029 (1989) 10. G.H.J. van Doremaele, A.H. van Herk, A.L. German, Polymer International, 27,
95 (1992) 11. G.H.J. van Doremaele, F.H.J.M. Geerts, H.A.S. Schoonbrood, J. Kurja, A.L.
German, Polymer, 33, 1914 (1992) 12. G.H.J. van Doremaele, H.A.S. Schoonbrood, l Kurja, A.L. German, J Appl.
Polym. Sci., 45, 957 (1992) 13. M.J. Ballard, D.H. Napper, R.G. Gilbert, J Polym. Sci., Polym. Chem. Ed, 19,
939 (1981) 14. J. Guillot, Makromol. Chem., Suppl, 10111, 235 (1985) 15. J. Forcada, J. M. Asua, J. Polym. Sci., Polym. Chem. Ed, 28, 987 (1990) 16. F.R. Mayo, F.M. Lewis, JAm. Chem. Soc. 66, 1594 (1944) 17. J. Bandrup, E.H. lmmergut, Polymer Handbook, 3rd ed., Wiley, New York 1989 18. T. Fukuda, Y-D. Ma, H. Inagaki, Polym. J, 14, 705 (1982) 19. D.J.T. Hill, J.H. O'Donnell, P.W. O'Sullivan, Macromolecules, 17, 3913 (1982) 20. T. Fukuda, Y-D. Ma, H. Inagaki, Macromolecules, 18, 17 (1985) 21. T.P. Davis, K.F. O'Driscoll, M.C. Piton, M.A. Winnik, Macromolecules, 22,
2785 (1989) 22. H.J. Harwood, Makromol. Chem., Makromol. Symp., 10/11, 331 (1987) 23. J. Barton, E. Borsig, Complexes in Free Radical Chemistry, Elsevier, Amsterdam
1988 24. LA Maxwell, A.M. Aerdts, A.L. German, Macromolecules, 26, 1956 (1993) 25. G. Moad, D.H. Solomon, T.H. Spurling, R.A. Stone, Macromolecules, 22, 1145
(1989) 26. M. Morton, S. Kaizermann, M. W. Altier, J Colloid Sci., 9, 300 (1954) 27. L.F.J. Noel, J.L. van Altveer, M.D.F. Timmermans, A.L. German, in press by J
Polym. Sci., Polym. Chem. Ed., xx, xx (1994) 28. L.F.J. Noel, J.M.A.M. van Zon, A.L. German, J Appl. Polym. Sci., 51, 2073
(1994) 29. L.F.J. Noel, E.C.P. Brouwer, A.M. van Herk, A.L. German, to be submitted to J
Appl. Polym. Sci. 30. L.F.J. Noel, LA. Maxwell, A.L. German, Macromolecules, 26, 2911 (1993) 31. LA. Maxwell, L.F.J. Noel, H.A.S. Schoonbrood, A.L. German, Makromol. Chem.,
Theory Simul., 2, 269 (1993) 32. L.F.J. Noel, J.M.A.M. van. Zon, LA. Maxwell, A.L. German, J. Polym. Sci.,
Polym. Chem. Ed, 32, 1009 (1994) 33. L.F.J. Noel, I.A. Maxwell, W.J.M. van Well, A.L. German, J Polym. Sci.,
Polym. Chem. Ed. 32, 2161 (1994) 34. L.F.J. Noel, J.L. van Altveer, A.L. German, in preparation 35. L.F.J. Noel, R.Q.F. Janssen, W.J.M. van Well, A.M. van Herk, A.L. German, to
be submitted to J. Colloid Sci. 36. L.F.J. Noel, W.J.M. van Well, A.L. German, in preparation
Theoretical baekground 7
Chapter 2 Theoretical background
Abstraet: In this chapter the basic tbeoretieal aspects of emulsion (co)polymerization kineties relevant to this investigation are briefly discussed. It becomes clear that the emulsion process is essentially different from homogeneous processes. Important features are the kineties of emulsion (eo)polymerization, monomer partitioning and the terminal copolymerization modeL
2.1 Emulsion polymerization
The batch emulsion polymerization process can be divided into three distinct intervals
according to the Harkins-Smith-Ewart theory. 1.2 In interval I free radicals are generated
in the aqueous phase nucleating new particles until the end of interval I. In intervals II and
III ideally the particle number remains constant. During interval II the polymerization, which
is assumed to occur in the polymer particle phase, proceeds in the presence of monomer
droplets. In interval II the polymer particles are saturated with monomer leading to a
(sometimes) constant polymerization rate in emulsion homo-polymerizations. In interval III
the monomer concentration in the particle phase will decrease leading to increasingly lower
polymerization rates. Intervals II and III are known as the particle growth stages.
2.1.1 Particle nucleation
Particle nucleation in emulsion polymerization is a phenomenon that is still not well
understood although many investigations have been carried out on the subject. The theories
describing particle nucleation can be divided into two main categories depending on the main
locus of nucleation: (1) micellar nucleation involving the monomer swollen micelles, 1•2 and
(2) homogeneous or coagulative nucleation.3·45
·6
8 Chapter 2
According to the first mechanism radicals that are generated in the aqueous phase
enter monomer swollen micelles and initiate polymerization leading to mature monomer
swollen polymer particles. Due to the large total surface area of the micelles as compared
with the monomer droplets, normally no nucleation occurs in the monomer droplets. When
all micelles have disappeared the particle nucleation is ended approximately.
In case the emulsifier concentration is below the critical micelle concentration or in
the absence of emulsifier a stable latex can still be formed.5•7•8•9
•10
•11
•12 This can be
explained by the so-called homogeneous nucleation model5•6
•13 which states that radicals
generated in the aqueous phase react with solubilized monomer to form growing oligomeric
species. At a critical length at which the oligomers exceed their solubility or become surface
active, the oligomers will precipitate. The precipitated oligomeric chains absorb monomer
and emulsifier to form colloidally unstable precursor particles, which flocculate with each
other or with already existing mature latex particles.
2.1.2 Particle growth in emulsion polymerization
In interval II the polymeric particles have a constant and maximum monomer
concentration as a result of the presence of monomer droplets from which monomer diffuses
through the water as a medium towards the particles at a constant rate. In emulsion homo
polymerization this leads to constant polymerization rates during interval II. In interval III
the polymerization mte will decrease due to decreasing monomer concentration in the
polymer phase. However, increased polymerization rates can be observed due to the
Trommsdorff effect. The rate of polymerization (~ in mohhnw·3·s· 1) in emulsion homo
polymerization during intervals II and III is given by:
RP kP n N [MJP (2.1) N,.
where k., is the propagation rate coefficient (dm3·mol"1·s·1), ii the average number ofmdicals
per particle, [M]P the monomer concentration in the polymer particle phase {mol·dm-3), N
the number of particles per dm3 water and N.v is Avogadro's number (mol-1). The number
of particles, N, is mainly determined by the amount of initiator and emulsifier and dependent
on the kind of monomer. In ab initio reactions low reproducibility of the particle number
is obtained. Therefore, kinetic studies usually are started from a polymer seed, i.e.,
preformed polymer particles, in order to guarantee constant and known particle numbers.
Theoretical background 9
2.2 Emulsion copolymerization
The course of emulsion copolymerization depends mainly on the monomer reactivity
ratios and on the partitioning behaviour of the two monomers between the various phases
of the emulsion system. The knowledge of the concentrations of both monomers in the
polymer particle phase, where the polymerization is assumed to take place, is essential for
the correct use of kinetic models. As a result of monomer partitioning the monomer mole
fraction in the polymer particle phase can be different from the overall monomer mole
fraction. The terminal model14•15 is the model most often used to describe
copolymerization kinetics, the sequence distribution, and the chemical composition of the
copolymers prepared in homogeneous systems such as bulk and solution polymerization.
In this model the monomer addition rate depends on the nature of the terminal group only
and therefore obeys first order Markov Statistics. 16 The copolymerization scheme of the
terminal model is given in Table 2.1.
Table 2.1 Copolymerization scheme according to the terminal model
terminal group added monomer rate final
-M;• [M]; k;;[M•];[M]; -M;M,•
-M;• [M]; k;i[M•];[M]1 -M;Mj•
-Ml [M]; ki;[M•]JM]1 -M_M;•
-Mi• [M]i ~[M•]JM]1 -M_MJ•
The reactivity ratios of monomer i and j are defined as r; = k;/k;i and ri ~
respectively, where k;i is the propagation rate constant of the propagation step between
radical i and monomer j. The instantaneous copolymer composition in mole fraction of
monomer i units (F;) is given as a function of the reactivity ratios and the monomer
composition in the reaction mixture by the instantaneous copolymerization equation: 14•15
F, (2.2)
where ±: and ~ are the actual mole fractions of monomers i and j in the reaction mixture.
The average propagation rate constant (kp) is given by17
10
rJi + 2 JJ; + ri ./] r1 f/k11 + ri J]kjj
Chapter 2
(2.3)
It has been shown for most copolymer systems that the copolymer composition is well
predicted using this terminal model. 13 However, for several monomer systems the mean
propagation rate coefficient of copolymerization was found not to obey the terminal
model. 19•20 This deviation has been explained by invoking the penultimate model for
copolymerization,21 in which the penultimate group of the free radical chain end is
considered to affect its reactivity. In order to accommodate the fact that composition is well
predicted by the terminal model a 'restricted penultimate model' was adopted,22.23 which
reduces to the terminal model when considering copolymer composition only. However,
it should be noted that other models are also capable of explaining the non-terminal
behaviour of the rate of polymerization in copolymerization. 14•24
.25
When using the experimentally determined average propagation r;rte constant, ~.
instead of a homopolymerization rate coeffici~nt, ~in equation 2.1, the same relationship
may be used to describe the rate of polymerization in emulsion copolymerization. However,
it should be noted that theoretical predictions of the average number of growing chains per
particle in copolymerizations is even more complex than in the case ofhomopolymerization
since entry, exit, transfer and termination of radicals may depend on cross-transfer and cross
propagation coefficients which have to be taken into account. In emulsion copolymerizations
the polymerization rate does not have to remain constant in interval II since ~ ii, and [M]P
may change as a function of conversion if composition drift occurs.
Referenees 11
l. W.D. Harkins, J. Am. Chern. Soc., 69, 1428 (1947) 2. W.V. Smith, RH. Ewart, J. Chern. Phys., 16, 592 (1948) 3. W.J. Priest, J. Phys. Chern., 56, 1077 (1974) 4. G. Lichti, R.G. Gilbert, D.H. Napper, J. Polym. Chern., Polym. Chern. Ed, 21, 269
(1983) 5. A.R Goodall, M.C. Wilkinson, J. Hearn, J. Polym. Sci., 15, 2193 (1977) 6. R.M. Fitch, C.H. Tsai, In Polymer Colloids, Plenum Press, New York 1971 7. J.M. Willes, lndust. and Eng. Chern., 41(10), 2272 (1947) 8. J.W. Goodwin, J. Hearn, C.C. Ho, R.H. Ottewill, Br. Polym. J., 5, 347 (1973) 9. J.W. Goodwin, J. Hearn, C.C. Ho, RH. Ottewill, Col. Polym. Sci., 252, 464 (1974) 10. D. Munro, A.R. Goodall, M.C. Wilkinson, K. Randle, J. Hearn, J. Col. Interface. Sci.,
68, I (1979) 11. J.W. Goodwin, R.H. Ottewill, R. Pelton, G. Vianello, D.E. Yates, Br. Polym. J., 10,
173 (1978) 12. Z. Song, G.W. Poehlein, J. Col. Interface Sci., 128, 501 (1989) 13. P.J. Feeney, D.H. Napper, R.G. Gilbert, Macromolecules, 17, 2520 (1984) 14. F.R Mayo, F.M. Lewis, J. Am. Chern. Soc., 66, 1594 (1944) 15. T. Alfrey, G. Goldfinger, J. Chern. Phys., 12, 205 (1944) 16. J.L. Koenig, In Chemical Microstructure of Polymer Chains, John Wiley and Sons,
New York 1980 17. T. Fukuda, Y-D. Ma, H. Inagaki, Makromol. Chern., Suppl., 12, 125 (1985) 18. J. Bandrup, E.H. Immergut, Polymer Handbook, 3rd ed., Wiley, New York 1989 19. T. Fukuda, Y-D. Ma, H. Inagaki, Macromolecules, 18, 17 (1985) 20. T.P. Davis, K.F. O'Driscoll, M.C. Piton, M.A. Winnik, Macromolecules, 22, 2785
(1989) 21. E. Merz, T. Alfrey, G. Goldfinger, J. Polym. Sci., 1, 75 (1946) 22. T. Fukuda, Y-D. Ma, H. Inagaki, Polym. J., 14, 705 (1982) 23. T. Fukuda, Y-D. Ma, H. Inagaki, Makromol. Chern. Rapid Commun., 8, 495 (1987) 24. D.J.T. Hill, J.H. O'Donnell, P.W. O'Sullivan, Macromolecules, 17, 3913 (1982) 25. H.J. Harwood, Makromol. Chern., Makromol. Symp., 10/11, 331 {1987)
Experimental 13
Chapter 3 Experimental
Abstract: In this chapter the experimental procedures and set-up for 116 initio emulsion (co)polymerizations is described. The reactions were monitored by gravimetry and gas chromatography resulting in partial conversion data ofbotla monomers. The determination of the parameters needed for model predictions are described. These comprise the description of monomer partitioning experiments (water solubility and swellability of monomer in polymer), densimetry (monomer and polymer density) and low conversion balk polymerization (reactivity ratios).
3.1 Experimental (co)polymerization procedures.
3.1.1 Purification of chemicals
The following materials were used for emulsion (co )polymerization, monomer
partitioning experiments and for determination of the density: reagent-grade methyl aaylate
(MA, Janssen Chimica, Tilburg, The Netherlands), styrene (S, Merck, Darmstadt, Germany),
vinyl acetate (V Ac, Janssen Chimica, Tilburg, The Netherlands), vinyl 2,2-dimethyl
propanoate (VPV, product names VEOV A-5, Shell Research and Vynate NE0-5, Union
Carbide Corporation), vinyl 2-ethylhexanoate (V2EH, product name Vynate 2EH, Union
Carbide Corporation), and indene, tech., 90+% (lnd, Janssen Chimica, Tilburg, The
Netherlands), doubly distilled water, sodium persulphate (NaPS, p.a., Fluka AG, Buchs,
Switzerland) and 2,2'-azobis(2-methylpropionitrile) (AIBN, Janssen Chimica, Tilburg, The
Netherlands) as initiators, sodium dodecyl sulphate (SDS, Fluka AG, Buchs, Switzerland)
and Antarox C0-990 (Ant C0-990, C9HwC4H60(CH2CHP)100H, GAF, Delft, The
Netherlands) as surfactants, and sodium carbonate (Na2C03, p.a., Merck, Darmstadt,
Germany) as buffer. Before use, the MA, VAc, VPV, and V2EH were distilled under
reduced pressure to remove the inhibitor. The middle fraction was cut and stored at 4°C.
14 Chapter 3
The indene which was only 90% pure and contained some polymerizable components was
purified by shaking 0.5 dm3 indene with 0.4 dm3, 6M HCL for 24 h in order to remove basic
nitrogenous material, then refluxed with 40% NaOH for 2 h to remove benzonitrile.
Extraction by n-hexane was followed by washing with water (three times), drying with
MgS04 and evaporation of the n-hexane. Fractional distillation under reduced pressure is
repeated until gas chromatography showed that indene fractions of purities higher than 98%
were obtained. Gas chromatography in combination with mass spectroscopy (GC-MS)
showed that the amount of polymerizable impurities were negligible ( undecene concentration
< 0.03%). It was concluded that at this point the indene was sufficiently purified to be used.
The indene is stored under argon at 4°C. To prevent polymerization during the monomer
partitioning experiments, in these cases MA and V Ac were applied as received and some
inhibitor (hydroquinone) was added to the indene after its purification. The calibration of
the density cell was performed using doubly deionized water and toluene (p.a., Merck,
Darmstadt, Germany).
3.1.2 Copolymerization reactions
Emulsion polymerizations were performed under nitrogen atmosphere in a 1.3-dm3
stainless steel reactor equipped with four baffles at 90° intervals and with a six-bladed
turbine impeller. The impeller speed was between 200 and 300 rpm. In Figure 3.1 a cross
section of the reactor is shown. All batch emulsion (co )polymerizations for seed preparation
or for the study of copolymerization behaviour in terms of composition drift or
polymerization rate were performed in this or similar reactors.
Reactor dimensions in mm:
turbine position (from top) 120
turbine diameter 60
blade diameter 18
blade height 15
reactor diameter 96
baffle diameter 13.4
reactor height 205
Figure 3.1: Cross-section (}{the reactor used for emulsion (co)polymerizations
Experimental 15
All MA-VAc, MA-VPV, and MA-V2EH emulsion polymerizations were performed
at 50°C for 8 h using SDS as surfactant. On behalf of the application of the resulting seed
for monomer partitioning purposes, the temperature was raised to 80°C for 15 h to reach
high conversion and to dissociate any residual initiator. The MA-Ind copolymerizations were
performed at 70°C for 12 h using non-ionic Ant C0-990 as surfactant.
All reactions performed to study copolymerization behaviour in terms of composition
drift or polymerization rate were monitored by gravimetry to obtain conversion-time curves
and by gas chromatography to determine the overall monomer ratios as a function of time.
For off-line purposes a Hewlett Packard (HP) 5890A gas chromotograph was used in
combination with a HP 3393A integrator, a HP 7673A automatic sampler and a capillary
HP-5 column (crosslinked 5% Ph. Me. Silicone; 30m x 0.53 mm x 2.65 J.lm). Combining
results of gravimetry and gas chromatography yields the partial conversion of both
monomers in the copolymerization reaction. Monitoring emulsion reactions off-line at the
end of each reaction is a very laborious method. Although the results given in chapters 5-8
have been obtained off-line, effort has been put into developing an accurate and fast on-line
method to determine the partial conversions of the separate monomers in the emulsion
copolymerization. For this purpose the standard reactor shown in Figure 3.1 is equipped with
an on-line densimeter, capable of monitoring overall weight conversion, and an on-line gas
chromatograph, capable of monitoring the overall ratios of the residual monomers. The use
of this new combination of on-line teclmiques makes fast monitoring of the monomer
concentrations possible, thus allowing process control (e.g. reaction heat) as well as product
control (e.g. composition drift). The configuration developed for on-line monitoring and the
results obtained using this set-up are described in more detail in chapter 4.
3.1.3 Determination of (partial) conversion
The total overall conversion x101(t) can be determined by gravimetry using the
following equation:
x,.,(t) (3.1)
where DS(t) is the dry solids content at time t determined by weighing the latex mass of
a sample before and after drying (% ), M1 is the total mass of the emulsion mixture, Mmon
is the mass of the initially added monomers, and M., is the mass of the non-polymerizable
and non-evaporative components as the initiator, the buffer and the surfactant. Contrary to
homo-polymerizations where measuring the conversion is sufficient to describe the total
16 Chapter 3
course of the reaction, in copolymerizations two independent measuring techniques must
be used. For this purpose gas chromatography of a (diluted) sample taken during reaction
was used to determine the overall ratio of the residual monomers as a function of reaction
time. Combining the conversion and overall monomer ratio allows calculation of the partial
conversion of both monomers in emulsion copolymerization as a function of time or
conversion according to eqs 3.2 and 3.3.
x., = 1 - (Mio + Mio) . (1 - xto,,t ) J, Mjo(l + 1/qj/i,t)
(3.2)
x. = 1 - (Mio + Mi) . (1 - xtot,t ) 1,1
(3.3)
where xi.'' xi,t• and x..,.(t) represent the partial conversion of monomers j and i and the total,
overall conversion at timet, respectively, ~o and Mio represent the initial mass of monomers
i and j at the beginning of the reaction and qyi,t represents the overall ratio of monomer j
over i at timet. Combining conversion (X.01(t)) and gas chromatography (<Iy~J results in the
partial conversions of the separate monomers as a function of time. The residual monomer
concentrations in the reaction mixture can be determined directly from gas chromatography
by adding an internal standard to the reaction samples. This alternative approach to calculate
the partial conversion of both monomers was used to estimate the accuracy of the above
described method of determining partial conversions. Excellent agreement is obtained for
MA-Ind emulsion copolymerizations (chapter 7: Figure 7.3) when comparing conversion
results determined by gravimetry with those from gas chromatography.
3.2 Monomer partitioning
Seed preparation: The seed latices used in the monomer partitioning experiments were
prepared under conditions similar to the batch emulsion copolymerizations described in
section 3.1.2. The recipes for the MA-V Ac and MA-Ind seeds used in monomer partitioning
experiments with their respective monomers are given in Table 3.1. Before using the seed
latices for monomer partitioning experiments, the latices were dialysed in a membrane tube
to remove excess surfactant, initiator, buffer, and monomer. The dialysis water was changed
every 2 h until the conductivity of the water surrounding the membrane tube remained
constant in time at a value close to the value of distilled water. After this, the solids content
was determined by gravimetry, the mole fraction of monomer unit MA (FMA) in the polymer
Experimental 17
was determined by 1H-NMR, and the weight average particle diameter was determined using
dynamic light scattering (Malvern Autosizer lie 90° fixed angle at 25°C. The sample
preparation consisted of latex dilution followed by filtering). The particle size and solids
content of the latices used for monomer partitioning experiments are collected in Table 3.1.
Table 3.1: Emulsion copolymerization recipes (in grams), particle size (nm) and solids content (%) of latices used in monomer partitioning experiments.
Ingredient MA-VAc MA-Ind
MA 80 26.68 VAc 80 Ind 34.53
water 800 599.1
SDS 1.317
Ant C0-990 20.806
N~C03 0.141 0.660
NaPS 0.256 3.534
d,. 90 30
solids content 16.50 10.40
Monomer partitioning experiments: Monomer partitioning experiments were performed
using the ultracentrifuge method. 1•2 A latex with known solids content was mixed with
known amounts of monomer at the desired temperature in the absence of initiator.
Equilibrium was reached within 24 h of shaking. The polymer particle, monomer droplet
(at saturation swelling) and aqueous phases, were separated using an ultracentrifuge (45000
rpm Centrikon T-2060, 1-2 h, maximum centrifugal force is 2·107 mmin.2) at the desired
temperature (the maximum centrifugation temperature is 45°C). The concentrations of MA,
VAc, and Ind in the aqueous phase were determined by gas chromatography (GC) using
2-propanol as internal standard for MA and V Ac, and acetone as internal standard for Ind.
Assuming that (I) the volumes of monomer and polymer are additive, and (2) the copolymer
density is a linear function of the mole fraction of the monomer units, the monomer content
in the polymer particles was determined from mass balance calculations for partial swelling.
At saturation swelling a separate droplet phase prevents determination of the monomer
content in the polymer particles by mass balance considerations. Monomer concentrations
in the particles were then determined by GC after dissolving the monomer-swollen polymer
phase in toluene with 2-propanol as internal standard for MA-V Ac and MA-Ind.
18 Chapter 3
Determination of the dry solids content of the sample gave the polymer content, which was
needed to make corrections for the amount of aqueous phase within the polymer phase. The
monomer droplet phase was analyzed by GC in terms of monomer ratios for the MA-V Ac
monomer partitioning experiments.
Due to temperature limitations of the ultracentrifuge, the ultracentrifugation method
could not be used above 45°C. The maximum water solubilities at temperatures higher than
45°C where determined using a densimeter forMA and V Ac (see chapter 4), and using gas
chromatography for Ind. The Ind concentration at 70"C in the aqueous phase was determined
by taking a sample from the saturated aqueous phase of a thermostated water-indene mixture
at equilibrium with complete phase separation, using an acetone solution as internal standard.
The maximum swellabilities in the polymer phase ([M]p,sat(h) in mol'<inf3) and the water
solubility ([M].,sa~(h) in mol-dm'3) at various temperatures for several monomers in their
respective copolymers are shown in Table 3.2.
3.3 Densimetry
The measuring principle of the densimetry instrument is based on the change of the
frequency of a vibrating U-shaped sample tube, which is statically filled with sample liquid
or through which the sample flows continuously. The relationship between the period of
oscillation of the sample tube, T, and the density, p, is given by:
p _!_ (T2 - B) A
(3.4)
where A and B are the temperature dependent instrument constants which are determined
by calibration with fluids (toluene and water) of known density.
Densimetry was performed using a thermostated Anton Paar DMA 10 density cell.
The density of monomers or solutions can be calculated directly from the oscillation period
of the sample tube and the calibration constants using eq. 3.4. In order to obtain accurate
density values of (co)polymers all latices are diluted (to prevent coagulation) and degassed
at the same temperature as the statically density determination was performed. The
(co )polymer density can be calculated from the latex density and the solids content of the
diluted latex using the following equation: 3
(3.5)
where xP and x,. are the mass fractions of the polymer and serum (aqueous phase including
Experimental 19
dissolved initiator, surfactant, and buffer) which can be calculated from the solids content,
and p1, pP, and Ps represent the density of the total diluted latex, the (co)polymer, and the
serum, respectively.
Table 3.2: Homo-monomer saturation concentrations forMA, VAc, VPV, V2EH, and lnd detennined at several temperatures (C).
Monomer/(T'C)
MA (20°C) MA (50°C)
MA (70°C)
VAc (20°C)
VAc (50°C)
VPV (20°C)
V2EH (20°C)
Ind {20°C)
Ind (70°C)
7.05" 0.60" 0.55b
0.53b
6.11" 0.30" 0.28b
4d 7.3 •10"3 c
2.5d 0.23 •10"3 c
2.9" 2.8·10"3 •
2.8·10"3•
a determined by the ultracentrifugation method b determined by densimetry c = gas chromatography determination of the saturated aqueous phase of
a water-monomer mixture d solids content determination of the polymer phase
3.4 Determination of reactivity ratios by low conversion bulk polymerization
Accurate reactivity ratios are needed to predict the course of copolymer composition
in emulsion copolymerization as a function of conversion. For monomer combinations like
MA-Ind which have not been extensively studied, low conversion bulk copolymerizations
have to be performed to determine reliable reactivity ratios. The bulk copolymerizations were
carried out in 20 cm3 bottles thermostated at 70°C (MA-lnd). The reaction mixtures were
magnetically stirred. The reaction mixture consisted of 20 g of monomer with different
monomer mole fractions going from 10% to 90% MA, and 0.1 g AIBN as initiator. The
reactions were stopped at low conversion(< 3%) to prevent composition drift. The resulting
copolymer compositions were determined by 'H-NMR. Figure 3.2 depicts a typical example
of a 400-MHz 1H-NMR spectrum of low-conversion bulk MA-Ind copolymers dissolved
in CDC13 at 25°C. The average copolymer composition (mole fraction MA: FMA) can be
calculated with the following formula: FMA
2B- 2A 2B +A
(3.6)
20 Chapter 3
where A and B represent the total peak area of the aromatic (4 H oflnd) and aliphatic (4
H of lnd and 6 H of MA) protons, respectively.
A B
......... ---.----, -·-··~- .... ..,_......, "•·~--..--.. ·~~--·,-··~~.,
8 7 6 3 2
ppm
Figure 3.2: A 400 MHz 1 H-NMR spectrum typical of a MA-Ind copolymer dissolved in CDC/3 at 25°C. A and B stand for the total peak areas in the aromatic and aliphatic regions, respectively.
1.00
0.1S
J o.so
0.2S
0.00 0.00 0.2S o.so 0.1S 1.00
fMA
Figure 3.3: Comparison of the initial monomer composition-polymer composition data predicted with the instantaneous copolymer equation using the reactivity values of rw = 0.92 and r1nd 0.086 (- - -) and experimentally determined data from low conversion bulk polymerizations (o).
Experimental 21
Table 3.3: Low conversion bulk copolymerization data of MA-Ind copolymerizations at 7(J'C. F MA.cvk is calculated with the instantaneous copolymer equation using the reactivity ratios rMA = 0.92 and r1m~ 0.086
initial monomer fraction copolymer composition copolymer composition fMA F MA.experimenral FMA,calc
0.105 0.393 0.379 0.210 0.483 0.478
0.308 0.534 0.537
0.405 0.585 0.587
0.510 0.642 0.641
0.606 0.700 0.694
0.655 0.726 0.723
0.711 0.766 0.758
0.804 0.825 0.823
0.903 0.904 0.904
The reactivity ratios were determined by non-linear optimisation 4•5 of the initial monomer
mole fraction-copolymer composition data summarized in Table 3.3. When calculating
reactivity ratios with this non-linear optimisation method, errors in both the initial monomer
composition (estimated to be I%) and the copolymer composition (estimated to be 5%) are
taken into account. This results in the following reactivity data: rMA = 0.92 ± 0.16 and rind
0.086 ± 0.025. When using these reactivity ratios the initial monomer mole fraction
copolymer composition relation can be described theoretically using the instantaneous
copolymer equation (eq 2.2). Comparison of the experimental results with the theoretical
prediction of the instantaneous copolymer equation gives good agreement as can be seen
in Figure 3.3 and Table 3.3. This indicates that reliable values for the reactivity ratios for
MA-Ind have been obtained.
For more common monomer combinations like MA-V Ac and methyl methacrylate
styrene (MMA-S), the reactivity ratios may be found in the literature. 6.7 Although only
small differences in reactivity ratios have been observed in vinyl acetate-vinyl esters (V Ac
VEst) copolymerization reactions (rvAc "' rvEs1), composition drift occurring in
copolymerization reactions of an acrylic monomer such as MA with V Ac may be affected
by replacing V Ac by another vinyl ester. Since acrylic polymers are often used in various
applications, it is important to know whether or not the reactivity ratios of MA with vinyl
esters can be approximated by the reactivity ratios of MA and V Ac. For this reason the
reactivity ratios ofMA-VEst have been determined for V Ac, vinyl 2,2-dimethyl-propanaoate
(VPV), and vinyl 2-ethylhexanoate (V2EH) at 50°C in a similar way as described above for
22 Chapter 3
the system MA-Ind.
The general structure of the MA-VEst copolymers is given by:
-+rH-CH2-t-)x-+-( yH~CH2T
O=r ? 0 O=C I •• Rl
CH3
In this structural formula the left hand side group (x) represents the MA units and the right
hand side group (y) represents the vinyl ester units in the copolymer. The R-group in the
structural formula stands for the CH3, C4f4, and C7H15 group, respectively.
The reactivity ratios of MA-VAc copolymerizations have been determined before
by several investigators using different copolymer analysis methods, for example polymer
hydrolysis followed by acetic acid determinations, 8 infrared spectroscopy,9
interferometry,10 and 1H-NMR. 6 However, the initial monomer mole fraction-copolymer
composition data thus obtained may lack accuracy. 8 Furthermore, the reactivity ratios have
been calculated by traditional linearization procedures 11•12
•13 of the instantaneous
copolymer equation11•14 (eq 2.2) In this thesis, more accurate nonlinear optimisation
techniques have been used to determine reactivity ratios.4.s The MA-VEst reactivity ratios
are determined by the nonlinear optimisation technique described by Dube et al. 5 taking into
account the estimated experimental error in both initial monomer mole fraction and
copolymer composition.
A typical 400 MHz 1H-NMR spectrum of a low conversion bulk MA-V2EH
copolymer is given in Figure 3.4. The total peak area represented by A in Figure 3.4 is
generated as a result of the resonance of the V2EH proton marked by '*' in the above
structural formula of the copolymer. The peak area B is generated by the three methyl group
protons of MA in the copolymer. This methyl group is indicated by '**' in the structural
formula The peak area generated by all other protons is represented by C in Figure 3.4.
Note that the number of protons in the side group (and, therefore, the total peak area of C
as compared with A and B) will vary with the selected vinyl ester. Calculation of the
average copolymer composition of all MA-VEst copolymers (mole fraction MA: FMA) can
be determined from the peak areas A and Bin the 1H-NMR spectra by using the following
relationship:
Experimental 23
B (3.7) 3A + B
When calculating the reactivity ratios using a nonlinear optimisation method, from the initial
monomer mole fraction-copolymer composition data listed in Table 3.4, errors in both the
initial monomer composition (estimated to be 0.1%) and the copolymer composition
(estimated to be 3%) were taken into account.
B
5 4 3 2 0
ppm Figure 3.4: A typical 1 H-NMR spectrum of a MA-VEst copolymer. The total peak areas represented by A, B, and C result from 1 VEst proton, 3 MA protons, and all other protons, respectively.
The reactivity ratios resulting from nonlinear optimisation of the initial monomer
mole fraction-copolymer composition data (Table 3.4) are:
MA-VAc: rMA 6.9 ± 1.4 and rvAc = 0.013 ± 0.03;
MA-VPV: rMA 5.5 ± 1.2 and rvpv = 0.017 ± 0.035;
MA-V2EH: rMA 6.9 ± 2.7 and rvzEH 0.093 ± 0.23
On the basis of the 95% reliability interval depicted in Figure 3.5 it was concluded that the
reactivity of the three MA-VEst monomer systems can be described by one pair of reactivity
ratios. It should be mentioned that the large reliability interval on the reactivity ratio of
V2EH in the MA· V2EH monomer combination is a result of the lack of initial monomer
24 Chapter 3
mole fraction-copolymer composition data at low MA mole fractions. Bulk polymerizations
of MA-V2EH, performed at low MA mole fractions, were extremely sensitive to inhibition.
For this reason no reactions at low MA mole fractions could be performed.
Table 3.4 Initial monomer mole fractions (fu)-copolymer composition (Fu) dataofMAVAc, MA-VPV. and MA-V2EH, obtained by 1H-NMR of low conversion bulk copolymers.
fMA MA.VAc
0.100 0.181
0.200
0.300
0.600
0.700
0.800
i > 0 ·::: I'!! .t·s: .... I
FMA MA-VAc
0.616 0.704
0.71
0.803
0.935
0.924
0.979
0.40
0.20
fMA FMA fMA FMA MA-VPV MA-VPV MA-V2EH MA-V2EH
0.144 0.637 0.329 0.784 0.275 0.742 0.400 0.832
0.393 0.826 0.462 0.873
0.597 0.889 0.600 0.916
0.691 0.926 0.658 0.935
0.779 0.966 0.670 0.934
0.700 0.930
0.800 0.959
0.900 0.984
-0.20 L-----or-----.-----.----.---~ 0 2 4 6 8 10
reactivity ratio MA
Figure 3.5: The 95% reliability intervals are given for the reactivity ratios of MA-VAc, MA-VPV, MA-V2EH, and all MA-VEst combined
Due to the increased number of data points when combining all initial monomer mole
fraction-copolymer composition data, the reliability interval of the reactivity ratios has
decreased resulting in the following values:
rMA = 6.1 ± 0.6 and rvEst = 8.7·10"3 ± 23·10·3•
This result is in acceptable agreement with the reactivity ratios determined by Kulkarni et
Experimental 25
al. 6 for MA-VAc (rMA = 6.3 ± 0.4 and rvAc = 31·10·3 ± 6·10"3).
Comparison of the experimental results with the theoretical prediction given by the
instantaneous copolymer equation (eq 2.2) using the reactivity ratios rMA 6.1 and rVEst =
8.7·10·3, gives good agreement, as can be seen in Figure 3.6. From these results it can be
concluded that all three monomer combinations indeed can be described by one set of
reactivity mtios.
- 0.80 c:l 0 -.... u 0.60 Clll .::: 0 g 0.40
J 0.20
0.00 .!r-----.--......---....1 0.00 0.20 0.40 0.60 0.80 1.00
fMA (mol fraction)
Figure 3. 6: Comparison of the experimentally determined initial monomer mole fraction-copolymer composition data of MA with VAc (.t:.), VPV (o), and V2EH (D) with the theoretical instantaneous copolymer equation (- -
-) using the reactivity ratios r MA = 6.1 and r v&1 8. 7 ·10·3•
An advantage of the approximately equal reactivity mtios for V Ac, VPV, and V2EH
in MA-VEst monomer systems is that these systems are very suitable to study the important
effect of the monomer solubility in water on the course of emulsion copolymerization as
a function of the monomer-to-water ratio. This will be discussed in more detail in chapter
8. The reactivity ratios of the monomer combinations used in this thesis are summarized
in Table 3.5.
Table 3.5: Reactivity ratios of the monomer combinations MA-VEst, MA-lnd and MMA-S.
monomer 1-monomer 2 rl r2 references
MA-VEst (so•q 6.1 ± 0.6 8.7•10'3 ± 23·10'3 this work
MA-Ind (70°C) 0.92 ± 0.16 8.6•10'2 ± 2.5 •10'2 this work
MMA-S (4o•q 0.46 0.523 Fukuda et al. 7
26
I.
2.
3. 4.
5.
6.
7. 8. 9. 10. II. 12. 13. 14.
References
LA. Maxwell, J. Kurja, G.H.J. van Doremaele, A.L. German, Makromol. Chem., 193, 2065 (1992) LA. Maxwell, J. Kurja, G.H.J. van Doremaele, A.L. German, B.R. Morrison, Makromol. Chem., 193, 2049 (1992) F.J. Schork, W.H. Ray, AC'S Symp., 165, 505 (1981) F.L.M. Hautus, H.N. Linssen, A.L. German, J. Polym. Sci., Polym. Chem Ed., 22, 3487, 3661 (1984) M. Dube, A. Sanayei, A. Penlidis, K. F. O'Driscoll, P. M. Reilly, J. Polym. Sci., Polym. Chem. Ed., 29, 703 (1991) N.G. Kulkarni, N. Krishnamurti, P.C. Chatteljee, M.A. Sivasamban, Makromol. Chem, 139, 165 (1970) T. Fukuda, Y-D. Ma, H. lnagaki, Macromolecules, 18, 17 (1985) F.R. Mayo, C. Walling, F.M. Lewis, W.F. Hulse, J. Am. Chem. Soc., 70, 1523 (1958) T.A. Garrett, G.S. Park, J. Polym. &i., 4, A-1, 2714 (1966) I.S. Avetisyan, V.I. Eliseeva, O.G. Laronovo, Vysokomol. Soedin, 3, A 9, 570 (1967) F.R. Mayo, F.M. Lewis, J. Am. Chem. Soc., 66, 1594 (1944) M. Fineman, S.D. Ross, J. Polym. Sci., 5, 259 (1950) T. Kelen, F. Tiidos, J. Macromol. &i., Chem., A9, 1 (1975) T. Alfrey, G. Goldfinger, J. Chem. Phys., 12, 205 (1944)
On-line monitoring 1.7
Cbapter 4 On-line gas ebromatograpby and densimetry
Abstract: Monitoring and controlling composition drift is an important issue in emulsion copolymerization. Due to the heterogeneity of the polymerization system often combined with non-ideal kinetics, predicting copolymer composition and changes in monomer composition as a function of time is not straightforward. Therefore, accurate and fast on-line determination of partial conversions of the separate monomers is a key to understanding and controUing the copolymer system studied. For this reason on-line densimetry, resulting in overall weigllt conversion, is combined with on-line gas chromatography, resulting in the overall ratios of the residual monomer. Combining these two on-line data gives the partial conversion of each monomer as a function of time without the need of an internal standard. The determination of partial conversion of monomers in batch emulsion copolymerization from on-line gas chromatography and on-line densimetry is illustrated for the monomer system methyl acrylate-vinyl acetate.
4.1 Introduction
Composition drift is a typical aspect of (emulsion) copolymerization resulting in
chemically heterogeneous copolymers. Monitoring and controlling the occurrence of
composition drift is extremely important since copolymer properties strongly depend on,
among others, the chemical heterogeneity of the product. Prediction of copolymer composition
and changes in the composition of the reaction mixture as a function of time is often hampered
by non-ideal circumstances or the lack of parameters needed for model predictions. Therefore,
accurate and fast on-line determination of partial conversions of the separate monomers is
of great importance.
The use of on-line densimetry in obtaining conversion data for homopolymerizations
is already well established. Successful applications have been reported for the polymerization
of methyl methacrylate (MMA), 1•2
•3 vinyl acetate (VAc),4•
5•6 styrene (S),7 and even for
the gaseous monomer butadiene.3 Apart from the butadiene work that fitted the densimetry
data with gravimetry results at the end of each reaction, all other experiments have been based
28 Chapter 4
on the assumption that the volumes of monomer, polymer, and water are additive.
Furthermore, it is assumed that the specific volume of the (co )polymer is a linear function
of the homo-polymer specific volumes. As a consequence the specific volume of
heterogeneous and homogeneous copolymer of the same overall copolymer composition is
assumed to be equal. Using these assumptions in combination with pre-run data of the total
density difference going from I to 100% conversion, the on-line density signal can be
transformed into an on-line conversion signal. Note that, in cases where conversion
determination is based on calibration techniques or pre-run data, densimetry is a relative
method rather then an absolute one.
For copolymerization reactions the use of on-line densimetry becomes more complex
because composition drift will lead to changing specific volumes of the monomer and polymer
phase. Nevertheless, some attempts have been made to monitor batch emulsion
copolymerizations using a densimeter. One of the first attempts was made by Abbey1 for
the monomer combination butyl acrylate (BA)-MMA. Abbey made a rough estimation of
the resulting conversion-time curve for the BA-MMA emulsion copolymerization by simply
neglecting the occurrence of composition drift although he knew that this would lead to a
skewed conversion-time plot Canegallo et aC recently monitored emulsion copolymerizations
by densimetry for the monomer systems S-MMA, acrylonitrile-MMA and V Ac-MMA. They
accounted for composition drift by modelling this phenomenon and taking into account the
effect on density of changing monomer and polymer compositions as a function of conversion.
In order to obtain conversion from densimetry data Canegallo et al. 7 calculated the calibration
constants from a pre-run based on the theoretically calculated begin and end densities.
Although they were able to transform density into conversion data not only for
homopolymerization but also for copolymerization, care should be taken that the density
cell is calibrated at the same temperature and flow conditions as during reaction to ensure
that correct and absolute density values are obtained. The calibration constants used by
Canegallo et af were determined using density values of polymer and monomer at the reaction
temperature although the temperature in the density cell was approximately 6 oc lower. This
indicates that, although they were able to convert density into conversion successfully, the
density values obtained were not absolute ones.
Monitoring the partial conversion of both monomers as a function of time in emulsion
copolymerization instead of modelling the copolymerization, as Canegallo et al. 7 did, can
only be performed if additional information is available to convert density data into partial
conversion data. This extra information must be related to either the monomer ratio or the
copolymer composition.
On-line monitoring 29
Accurate ratios of residual monomers can be obtained by gas chromatography (GC).
Gas chromatography of the liquid phase is a well established method to obtain overall
monomer ratios in an emulsion system. Successful liquid phase on-line GC applications have
been reported by Rios eta/. 9 and van Doremaele. 10 Alternatively, on-line head space analysis
of the gas phase above the reactor content can be an option 11 although this method is not
straightforward since it involves the knowledge of monomer partitioning behaviour between
the reaction mixture and the gas above it, under the relevant reaction conditions. The complete
characterization in terms of absolute concentrations of both monomers as a function of time
during emulsion copolymerization is possible using only GC analysis, given the use of an
internal standard or a constant injection volume. However, the addition of an internal standard
to the reaction medium can influence polymerization kinetics and monomer partitioning12
leading to different conversion-time curves. Furthermore, the internal standard will remain
in the product. Accurate and reproducible injection volumes can only be obtained by taking
relatively large samples from the reaction mixture. Since injecting these large samples directly
into the GC-column leads to overload of the column and the use of a splitter does not give
reproducible absolute amounts of monomer, an approach has to be used in which an internal
standard must be added to the sample, followed by sample dilution and injection in the GC.
It is obvious that this method can only be applied on-line if expensive robotics are included
in the system. In the approach presented herein the on-line gas chromatography is nsed only
to obtain the overall ratio of the monomers present in the batch emulsion copolymerization,
thus avoiding the complications of using an internal standard or a constant injection volume.
Combining on-line gas chromatography and on-line densimetry is then required to
obtain absolute monomer concentrations of both monomers as a function of time. The use
of this new combination of on-line techniques, in principle, makes fast monitoring of the
monomer concentrations possible, thus allowing product control (e.g. composition drift) as
well as process control (e.g. reaction heat).
4.2 Theory
Calculation of conversion based on density data obtained by on-line densimetry is
mostly based on the volume additivity assumption. 1·2.3.45
·13 When this assumption is valid,
the monomer conversion is a linear function of the specific volume of the emulsion. In these
cases the conversion can be calculated with:2
30 Chapter 4
0 t p~
t v. - v. Pe (4.1) X
o I v. - v.
0 I Pe Pe
where x, v (cm3/g), and p (glcm3} stand for the conversion, specific volume, and density
respectively, and where the subscript e stands for the total emulsion and the superscripts
o, t, and I stand for the conversion at the beginning of the reaction, time t, and complete
conversion, respectively. Note that the specific volume equals the reciprocal density value
for each component. The initial and final specific volumes of the reaction can be determined
experimentally from a pre-run or they can be approximated as weighted averages of the
component specific volumes:
(4.2a)
(4.2b)
where x stands for mass fraction and the subscripts m, p, and s stand for monomer, polymer,
and serum (the aqueous phase), respectively. Note that the initial mass fraction of monomer
in the reaction equals the mass fraction of polymer at complete conversion. The density values
(i.e., reciprocal specific volumes) of the monomers and polymers used in this chapter are
listed in Table 4.1. 14•15
Table 4.1 Densityvaluesofpurewater, monomers, and polymers used in the emulsion (co)polymerizations at the reaction temperature of 50"C.
density (glcm3)
Ingredient monomer polymer
styrene 0.8781 1.0438
vinyl acetate 0.8935 1.1696
methyl acrylate 0.9186 I.l987
water15 0.9881
toluene14 0.8375
On-line monitoring 31
4.3 Experimental
Emulsion (co)polymerization: For on-line monitoring of batch emulsion
(co )polymerizations the standard reactor depicted in Figure 3.1 was equipped with an on-line
densimeter and an on-line gas chromatograph. In Figure 4.1 the configuration of the batch
reactor system with on-line densimeter and on-line gas chromatograph is given. The reaction
volume in the sampling loops is approximately 21 em\ which normally is about 2% of the
total reaction volume. Since this volume is divided over two loops and since the flow through
each membrane piston pump is about 11.7 cm3/min, it takes approximately 1 minute for a
small sample volume to pass the loop for on-line measurements. Considering this relatively
small sample volume and the short residence time in the sampling loop the density and
monomer ratio values obtained from on-line measurements are assumed to be similar to the
conditions in the reactor itself. Furthermore, all effects of possible different reaction rates
(due to lower temperatures in the sampling loop) of the emulsion mixture in the sampling
loop as compared with the reaction mixture remaining in the reactor, are assumed to be of
negligible influence on the total reaction mixture in the reactor. The recipes of the emulsion
homo- and copolymerization reactions are depicted in Table 4.2.
N2
lie
lh
Air
I c
t [@l--<><1----<><J---+-------,
I B
[)I '
~----rr~,- M - ¥
~L(.)~r R
GC
.. .
Figure 4.1: Schematic representation of the configuration for on-line monitoring batch emulsion copolymerizations using densimetry and gas chromatography. The on-line densimeter (Dl). the on-line gas chromatograph (GC), the thermostatic baths (B), the reactor suited with baffles and a healing jacket (R), the on-line computer (C) and the double membrane piston pump (P). are indicated.
32 Chapter 4
Table 4.2 Batch emulsion polymerization recipes for the homopolymerization of Sand VAc and the copolymerization of MA-VAc.
Ingredients (g) homo-S homo-VAc co-MA-VAc
s 99.743
MA 50.454
VAc 50.193 50.411
SDS 2.299 0.296 0.299
NaPS 1.904 0.201 0.212
NaaC03 0.894 0.088 0.085
water 1031.96 979.37 992.34
The S and V Ac homopolymerizations and the MA-V Ac copolymerization were performed
under nitrogen at 50°C. Previous to the addition of the initiator solution. the rest of the
reaction mixture was stirred with ca. 800 rpm to ensure a relatively homogeneous reaction
mixture. At the moment of addition of the initiator solution the on-line monitoring is started.
All reactions were monitored by gravimetry and on-line densimetry yielding conversion-time
curves. The copolymerization reaction was also monitored by gas chromatography (both on
line and off-line) providing the overall monomer fractions as a function of time. Combining
both data gives the conversion of both monomers at the moment of sampling.
Densimetry: The on-line measurements described in this chapter were performed using an
Anton Paar DMA 512 density cell thermostated with a M3 LAUDA thermostatic bath and
an Anton Paar DMA 60 Densimeter. The DMA 512 remote cell can be used for high pressure
and high temperature applications. The U-shaped density cell (U-tube) is made of stainless
steel with an internal diameter of 2.4 mm and with an internal volume of approximately I
cm3• A membrane piston pump was used for continuous transport of the reaction mixture
through the on-line density cell. A pre-heater (length 15 em, internal diameter= 2 em)
was placed around the sampling tube just in front of the densimeter. The temperature of the
bath was set at such a temperature (53.0°C ± 0.1) that the reactor and the density cell where
at the same temperature (50.0°C). Contrary to the results of Canegallo et af.? the density-time
curves obtained from on-line densimetry were not sensitive to large scatter of density values
resulting from the formation of gas bubbles or coalescence of monomer droplets in the U-tube. 1
Therefore, in our set-up no phase separator was installed.
Gas chromatography: For on-line gas chromatography a Carlo Erba 8030 gas
chromatograph was used, equipped with an extra heated zone in which the on-line injection
On-line monitoring 33
system was installed. Continuous flow of helium for GC analysis and continuous flow of
the reaction mixture through a sampling disc valve 16 (diameter sampling hole= 1.56 mm;
thickness disc = 2.95 mm) was maintained during reaction. After the completion of each
GC analysis a new reaction mixture sample with a volume of approximately 5.6 l!l was
injected into the GC apparatus by simply rotating the sample disc. The GC sampling valve
could be operated either fully automatically by using a computer, or manually. The column
used for on-line GC analyses was a J & C Scientific Capillary DB5 column with a length
of 30m, an internal diameter of 0.53 mm and a film thickness of 1.5 lim. For the MA-V Ac
reactions consecutive samples could be taken every three minutes resulting in a sufficient
number of values of overall monomer ratios as a function of time. The on-line gas
chromatography values where compared to those obtained off-line to check the validity of
the system used. The apparatus for off-line purposes have been described in chapter 3.
4.4 Results and discussion
4.4.1 Density
Theoretically the conversion can be calculated from density measurements without
performing a pre-run if the specific volumes (i.e, reciprocal densities) of the components
in the three phases and mass fractions of the aqueous phase, the monomer phase, and the
polymer phase are known. However, small errors in density will lead to large deviations in
conversion determination for low solids reactions where the total density difference is small.
Therefore, on-line conversion determination from densimetry without the use of pre-run data
can only be performed accurately if the measured density value is an accurate and absolute
one. It should be noted that measuring absolute density in an on-line system as presented
herein is hampered by several complications. For instance, the density signal depends on
flow rate through the density cell, temperature, "homogeneity" of the heterogeneous system
(i.e., mixing to avoid phase separation in intervals I and II in emulsion polymerizations),
and pressure. The influence of each individual parameter on the density signal depends on
the sensitivity of the selected density cell towards these parameters. Extra complications will
occur as the viscosity will change as a function of conversion since this may lead to changing
flow rates and temperatures in the density cell. It should be noted that temperature control
in the density cell is difficult due to slow heat transfer between heating system and the U
shaped tube which is surrounded by vacuum. Good temperature control can only be obtained
by using a good pre-heater or using low flow rates. Conversion determination from absolute
34 Chapter 4
density values may be obtained if a flow controller is installed or by calibration of the density
cell under a series of(flow) conditions. Using the experimental set-up presented in this thesis,
the specific volume determined from on-line densimetry can deviate approximately 0.003
cm3/g from the absolute specific volume as a result of flow effects, the accuracy of the
measuring device, and scatter on the calibration constants. This implies that the method will
result in accurate conversion determinations for high solids content emulsion polymerizations
(40% solids; v. v."' 0.1; 3% error on conversion determinations), whereas, for very low
solids content reactions large errors in conversion determination may occur (5% solids; v.
v. "' 0.01; 300/o error on conversion determination). However, for two identical reactions
where flow and temperature fluctuations are approximately equal, the error on the specific
volume will be so small(< 0.0005 cm3/g) that the pre-run data of the frrst reaction can be
used for on-line determination of conversion in the second reaction. This can either be done
by measuring the total density difference and assuming volume additivity (eq 4.1), or
calculation of the calibration constants using the theoretical initial and final densities, 7 or
by using the aqueous phase density as a fitting pararneter,6 or by calibration of the density
data on conversion data. 8
From the above discussion it can be concluded that, as long as densimetry does not
result in accurate absolute density values, the quantitative use of densimetry during a reaction
is limited to high solids content reactions and to reactions for which a pre-run has been
performed. This makes densimetry a very useful method of on-line monitoring of standard
reactions, i.e., the method is extremely useful for industrial application in which pump
plugging can be avoided. In the literature it has been reported that solids contents at least
up to 30% are possible. 4 On-line densimetry always gives valuable qualitative information
during reaction, even if no direct information about absolute conversion is gained. Moreover,
it is a very quick and accurate method to gather much data from an experiment since as soon
as the reaction is finished a complete and detailed conversion-time curve can be determined.
4.4.2 Homopolymerization
For batch emulsion homopolymerization reactions on-line densimetry is sufficient
to monitor conversio.? as a function of time during reaction. In the case of homo
polymerizations transforming density values into conversion values is straightforward (eq
4.1).
Styrene: For S homopolymerizations the conversion-specific volume curve depicted
On-line monitoring 35
in Figure 4.2 shows that the specific volume indeed is a linear function of the conversion
of the reaction mixture. This justifies the use of eq. 4.1 to calculate conversion from the
density data. Comparison of conversion-time data resulting from gravimetry and densimetry
(using eq. 4.1) shows acceptable agreement as can be seen in Figure 4.3.
1.03
1.02
1.01
1.00
0.99 0.00 0.20 0.40 0.60 0.80 1.00
Conversion
Figure 4.2: Comparison of experimental and theoretically linear (fitted) conversion-specific volume results for the batch homopolymerization of styrene.
1.00 0
0.80
c:l 0 0.60 ... G!l
~ ~ c:l 0.40 0 u
0.20
0.00 0 so 100 150 200
Time (min)
Figure 4.3: Comparison of conversion results determined using on-line densimetry and gravimetry for the batch homopolymerization of styrene.
The bend in the density curve at 80% conversion is probably caused by fouling of the density
cell. Although membrane piston pumps are known as low shear pumps, the use of this type
of pump for on-line measurements of ab initio batch homo-polymerizations of S may cause
some pump plugging. Since this will influence the flow through the density cell and as a
direct consequence the value of the calibration constants, pump plugging will directly affect
36 Chapter 4
the density-time curve resulting from on-line densimetry. Less plugging can be expected
when using a peristaltic pump. However, finding proper tubing resistant to both monomers
needed in emulsion copolymerization is difficult. Furthermore, possible swelling of the tubes
and deposit of polymer on the tubing will also affect the flow and therefore the calibration
constants. Since monitoring emulsion copolymerization reactions is the main purpose of this
set-up, a membrane piston pump in combination with stainless steel tubing was selected.
Vinyl acetate: The specific volume-conversion results for a V Ac homopolymerization
depicted in Figure 4.4 show clearly that not one single linear relationship exists between
specific volume and conversion over the whole conversion range. This can only mean that
the assumption of additive volumes is not valid for the emulsion polymerization of V Ac,
i.e., eq. 4.1 cannot be used. The deviating behaviour is caused by volume contraction
occurring when V Ac is added to water. This volume contraction will lead to a density increase
(instead of the expected decrease in case the volumes where additive) when VAc is added
to water as can be seen in Figure 4.5 where the density of V Ac-water solutions is depicted
as a function of increasing amounts of V Ac (increasing monomer-to-water ratios MIW). The
volume contraction was determined off-line with a Anton Paar DMA I 0 density cell. All
density values depicted in Figure 4.5 are below the maximum water solubility of V Ac in
water. Higher MlW ratios lead to a separate aqueous phase, saturated with monomer, and
a separate monomer droplet phase. This immediately leads to phase separation and therefore
to huge scatter on the density values.
1.02 ..... 1:10 ~ saturated s u '-' C) g
1.01 -0 >
partially saturated u ;;:
l IZI
1.00 L.---...---=---.---....... -----.----"""'1 0.00 0.20 0.40 0.60 0.80 1.00
Conversion
Figure 4.4: Experimental (o) conversion-specific volume results for the batch homopolymerization ofVAc are fitted in two linear regions (saturated and below saturation; solid lines).
On-line monitoring 37
0.990
0.988 '------.-----,...-1--....----....--1---,
0.00 0.01 0.02 0.03 0.04 0.05
Monomer/water (gig)
Figure 4.5: Experimentally determined density values for VAc-water (!!.)and MA-water (o) solutions as a function of the MIW ratio. The data are fitted with two linear relations.
Due to the linearity between density and monomer-to-water ratio, the solubility of V Ac in
water at 50"C can be determined from measuring the density of the saturated aqueous phase.
This resulted in a water solubility for VAc of 0.28 moVdm3• That the volume additivity
assumption is not valid for other reasonably water soluble monomers either, is also illustrated
in Figure 4.5 for MA. The water solubility of MA at 50"C resulting from density
measurements is 0.55 moVdm3• The kink in linearity shown in Figure 4.4 is primarily caused
by the dissolved monomer in the aqueous phase. Due to the relatively high water solubility
of V Ac (0.28 moVdm3) in combination with the relatively low monomer-to-water ratio (M/W
= 0.051), a percentage of 48% of the VAc was dissolved in the aqueous phase at the
beginning of the reaction. The difference between the one linear line and two linear regions
situations will be smaller if a smaller percentage of the monomers is located in the aqueous
phase, i.e., for higher MIW ratios and/or for monomers with lower water solubilities. This
is illustrated by Penlidis et al. 4 who found reasonable agreement between gravimetry and
densimetry conversion results calculated using eq 4.1 for the batch emulsion
homopolymerization of VAc at a M/W ratio of 0.33 g/g (ca 8% of the V Ac is dissolved
in the aqueous phase at the start of the reaction).
During the homopolymerization of V Ac (Table 4.2) a substantial amount of the
monomer will be located in the aqueous phase (48%). Using eq. 4.1 to calculate the
conversion-time curve for this reaction will lead to a large difference between the conversion
data based on eq. 4.1 and gravimetry as can be seen in Figure 4.6 (top line and triangles).
38 Chapter 4
1.00
0.80
c:l 0.60 .9 U}
~ 0.40 > c:l 0
I;) 0.20
0.00
-0.20 0 so 100 150 200 250
Time (min)
Figure 4.6: For the batch homopolymerization ofVAc the calculated (3 methods) and gravimetry based conversion-time curves are compared; calculation based on one (top line) and two linear regions (middle line) between conversion and specific volume; gravimetry data (ll.); and calibration using gravimetry results (bottom line).
These problems can be solved in the following three ways:
1) Dividing the reaction into a saturated (Interval II) and partially saturated (Interval
III) region. By doing so we can assume that we have two linear regions in which we can
nse eq. 4.1 again. For the presented V Ac reaction the end of the saturation interval can be
calculated based on the water solubility value (0.28 molldm3) and the swellability of monomer
in the polymer phase (6.11 molldm3 swollen polymer phase) showing that Interval II is ended
at 26% conversion. The assumption of a linear region in the saturation region is quite
acceptable since the total amount of V Ac in the aqueous phase remains constant. Note,
however, that by assuming a linear region in interval II volume additivity between the polymer
and the monomer in the swollen particle phase is assumed. For the partially saturated region
the concentrations in both the aqueous phase and polymer particle phase will decrease.
Deviations of the linear behaviour will occur in this partially saturated region due to the fact
that the aqueous phase is always closer to saturation than the polymer particle phase. 12
However, the results of this approach are quite acceptable as can be seen by the reasonable
agreement between the conversion-time curve resulting from this approach and gravimetry
data (Figure 4.6; middle line and triangles).
2) Calibration of the density-time curve with a density-conversion relationship (fitted
with a polynomial of the 6th power) obtained by comparing on-line density values with
gravimetry results. 8 Using this approach accurate conversion-time curves can be obtained
On-line monitoring 39
after calibration of the results or, on-line by using the density-conversion relationship from
a pre-run. Using this approach excellent agreement between conversion-time curves resulting
from densimetry and gravimetry is obtained (Figure 4.6; bottom line and triangles).
3) Determining the specific volume of the monomer in the three phases and adjusting
eqs 4.1 and 4.2a.,b. However, this approach again only works when accurate absolute densities
are obtainable.
Conclusions about on-line densimetry in emulsion homopolymerization: In cases where more
than approximately 5% of the monomer is dissolved in the aqueous phase at the beginning
of the reaction, the volume additivity assumption cannot be used and the maximum water
solubility of the monomer has to be taken into account.
Note that in cases where conversion information is needed at the end of the reaction,
the calibration method is the most simple and accurate way to obtain conversion information
since temperature and flow deviations, and water solubility effects are all accounted for as
long as these phenomena are reproducible from one run to the other. Furthermore, this method
can be used in a similar way to obtain conversion data for emulsion polymerizations involving
two or more monomers.
4.4.3 Emulsion copolymerization of MA and V Ae
In emulsion copolymerization reactions the monomer and copolymer compositions
will also change as a function of conversion, probably leading to nonlinear conversion-specific
volume curves (unless both monomers and polymers have similar densities). For the emulsion
copolymerization of reasonably water soluble monomers as MA and V Ac even more
deviations from linearity of the conversion-specific volume curves can be expected. To avoid
these problems the gravimetry calibration method described in the previous section is used
to obtain accurate conversion-time curves.
A typical density-time curve resulting from on-line measurements of the batch emulsion
copolymerization ofMA and V Ac is shown in Figure 4. 7. Note that there is remarkably little
scatter on the density data, even at the beginning of the reaction (interval II) where phase
separation might occur. This can only be a result of the continuous pumping at turbulent
conditions that prohibits phase separation in the density cell. It also must be mentioned that
in case of V Ac homo- and MA-V Ac copolymerization hardly any pump plugging occurred
during reaction, i.e., a stable latex mixture is obtained. Transforming the density values into
specific volumes and thereafter combining the specific volume-time values with conversion-
40 Chapter 4
time values obtained gravimetrically, results in a nonlinear conversion·specific volume
relationship depicted in Figure 4.8.
1.01
1.00
0.99 .. ' . •
J 0.98 C....,.-~~ ....... --....-,..........--....-,..........--..,.....,
0 so 100 lSO 200
Time (min)
Figure 4. 7: Density-time curve typical of the batch emulsion copolymerization of VAc with MA.
1.02
1.01
1.00
0.99 L----..----...----......---....,.......--.., 0.00 0.20 0.40 0.60 0.80 1.00
Conversion
Figure 4.8: Experimentally determined relation (--)between specific volume and conversion for the batch copolymerization of MA-VAc; (o) conversion determined by gravimetry.
Using the relationship found by fitting the conversion·specific volume data, the
specific volume values where transformed into conversion values (Figure 4.9).
Similar, on-line results can be obtained if the conversion is calculated based on
the total difference in specific volume as a function of conversion from a pre-run.
On-line monitoring 41
As can be seen in Figure 4.9 good agreetnent is obtained between the densimetry
based and gravimetry-based conversion-time curve for this copolymerization of
MA and V Ac. From this it can be concluded that densimetry can be used as a
qualitative method to obtain on-line conversion in emulsion copolymerizations
if reactions are performed repeatedly. Note that at ca. 700/o conversion all MA
has reacted as a consequence of composition drift. The increased polymerization
rate at 700/o conversion can be explained by a different kinetic behaviour of V Ac
(different average number of radicals).
1.00
0.80
0.60
0.40
0.20 f • 0.00 YA--.-~-,.........--.....-,..----.--..--.--.--,
0 100 200 300 400
Time (min)
Figure 4. 9: Conversion as a function of time determined gravimetrically ( t:.) and calibrated using densimetry (line consisting of data point (small o)) for the batch copolymerization of MA-VAc.
The use of on-line gas chromatography to determine overall monomer ratios proved
to be a valuable method to monitor composition drift. Comparison of on-line gas -
chromatography with off-line monomer ratio results (qvAc/MA = overall concentration of
VAc/concentration ofMA) shows good agreement as can be seen in Figure 4.10. For the
monomer system MA-V Ac a complete on-line gas chromatographic analysis of the reaction
mixture could be performed every three minutes. Although total conversion was completed
only after approximately 9 hours, a considerable composition drift led to complete conversion
of MA within lh. Therefore, the number of samples was limited and no duplicate
measurements could be taken. Fitting the monomer ratio-time data enables one to calculate
the overall monomer ratio at any time during the copolymerization reaction.
Combining conversion-time values with overall monomer ratio-time values enables
one to calculate the partial conversion of the separate monomers as a function of time (or
42 Chapter 4
conversion) using eq 3.2 and 3.3.
30
20
10
ot=~==~~~~--~--~~ 0 SOO 1000 lSOO 2000 2SOO 3000 3SOO
Time (s)
Figure 4.10: On-line (o) and off-line ( .0.) monomer ratios determined .from gas chromatography for the emulsion copolymerization of MA-VAc are depicted as a jUnction of time together with a fit through both sets of data (line).
That this indeed results in very detailed information about the partial conversion of the
separate monomers MA and V Ac in a batch emulsion copolymerization (recipe Table 4.2)
can be seen in Figure 4.11. Comparison of theoretical predictions17 with experimental results
for the copolymerization ofMA and V Ac shows excellent agreement as can be seen in Figure
4.12 where the absolute numbers of moles of MA and VAc are depicted as a function of
conversion.
1.00
0.80
d .2 0.60 ... t I» g 0.40 u
0.20
0.00 0 5 10 15 20 25
(Thousands) Time (s)
Figure 4.11: Partial and total conversion calculated from on-line densimetry and on-line gas chromatography are shown for MA (top line) and VAc (bottom line) as a jUnction of time. The overall conversion is calculated from on-line measurements (middle line) and the gravimetry data (o).
On-line monitoring
0.60
~ 0.50 :>
1 0.40
< 0.30 ::s 'S 0.20 "' 0
1 0.10
0.00 0.0 0.2 0.4 0.6 0.8 1.0
conversion
Figure 4.12: Experimentally determined absolute monomer amounts ofMA and VAc (MA, bottom symbols; VAc, top symbols) resulting from on-line densimetry and on-line gas chromatography are compared with theoretical predictions (MA, bottom line; VAc, top line).
4.5 Conclusions
43
For relatively water soluble monomers such as VAc and MA it has been shown that
the specific volume of the monomers in the aqueous phase is different from the specific
volume of the pure (monomer droplets) monomers leading to two linear regions in the specific
volume-conversion curve of an emulsion homopolymerization. It was illustrated that for low
solids reactions of V Ac the volume additivity assumption no longer is valid. In these
complicated situations conversion can be calculated from densimetry data either by assuming
two linear regions for saturation and partial swelling and using the volume additivity
assumption in the separate regions, or by calibrating the specific volume values with
gravimetry values.
For the emulsion copolymerization of MA and V Ac the combination of on-line
densimetry with on-line gas chromatography proved to be a powerful method of determining
the partial conversion of both monomers as a function of time. Comparison of the on-line
data with off-line results and theoretical predictions gave satisfactory agreement. On-line
densimetry always can be used as a qualitative method to obtain on-line conversion data
for emulsion (co)polymerizations if reactions are performed repeatedly. It should be noted
that the approach presented in this thesis, viz. the on-line determination of partial conversions
of both monomers participating in the batch emulsion copolymerization reaction, can be used
for any desired monomer pair.
44 References
I. K.J. Abbey, ACS Symp. Ser., 165, 345 (1981) 2. F. J. Schork. W. H. Ray, ACS Symp., 165, 505 (1981) 3. C. H. M. Caris, R. P.M. Kuijpers, A.M. van Herk, A. L. German, Makromol. Chem.,
Macromol. Symp., 35136, 535 (1990) 4. A. Penlidis, J. F. MacGregor, A. E. Hamielec, Polym. Proc. Eng., 3(3), 185 (1985) 5. D. C. H. Chien, A. Penlidis, JMS-REV. Macromol. Chem. Phys., C30(l), I (1990) 6. P.D. Gossen, J.F. MacGregor, J. Colloid Inter. Sci., 160, 24 (1993) 1. S. Canegallo, G. Storti, M. Morbidelli, S. Carra, J. Appl. Polym. Sci., 47,961 (1993) 8. E.M. Verdurmen, E.H. Dohmen, J.M. Verstegen, I.A. Maxwell, A.L. German, R.G.
Gilbert, Macromolecules, 26, 268 (1993) 9. L. Rios, C Pichot, J. Guillot, Makromol. Chem., 181, 677 (1980) 10. G. H. J. van Doremaele, Ph.D. Thesis, Eindhoven University of Technology (1990) 11. M. Alonso, M. Alivers, L. Puigjaner, F. Recasens, Ind Eng. Chem. Res., 26,65 (1987) 12. L.F.J. Noel, I.A. Maxwell, A.L. German, Macromolecules, 26, 2911 (1993) 13. 0. Levenspiel, "Chemical Reaction Engineering", 2nd. ed. Wiley, New York 1972 14. E.W. Washburn, C.J. West, N.E. Dorsey, F.R. Bichowsky, A. Klemenc, International
Critical Tables of Numerical Data, Physics, Chemistry and Technology, Mcgraw-Hill Book Company, Inc, New York and London 1985
15. R.C. Weast, CRC Handbook of Chemistry and Physics, 66th Ed, NY, 1985 16. A.L. German, D. Heikens, J. Polym. Sci., Al, 9, 2255 (1971) 17. L.F.J. Noel, J.M.A.M. van Zon, I.A. Maxwell, A.L. German, J. Polym. Sci., Polym.
Chem. Ed., 32, 1009 (1994)
Monomer partitioning 45
Chapter 5 Swelling of latex particles by two monomers
Abstract: The swelling of polymeric latex particles with solvent and monomer is important for the emulsion polymerization process since it influences composition drift and rate of polymerization. For the monomer combination, methyl acrylatevinyl acetate, both saturation and partial swelling were determined experimentally. Theories for saturation swelling and partial swelling of the separate monomers are in good agreement with experimental results. Based on previous work an extended thermodynamic model for monomer partitioning at partial swelling of latex particles by two monomers with limited water solubility is developed. Results predicted by this model are in good agreement with observed monomer partitioning behaviour. ·
5.1 Introduction
Partitioning of two monomers between latex particles, monomer droplets, and the
aqueous phase in an emulsion polymerization is, amongst other things, important for modelling
both the composition drift occurring during reaction and the rate of polymerization. In order
to accurately describe emulsion copolymerization in terms of composition drift, monomer
partitioning between the different phases should be taken into account.
Morton et a/. 1 dealt with saturation swelling of latex particles primarily by monomers
indicating that the mixing of monomer and polymer (expressed in terms of the Flory-Huggings
theorf) together with the interfacial Gibbs free energy term (Gibbs-Thomson equation1•3
)
determines the monomer concentration in the polymer particles. For two monomer partitioning
it has been found experimentally for several monomer combinations45 that the monomer
mole fractions in the polymer particle and monomer droplet phases are equal. This phenomenon
is clearly illustrated in Figure 5.1 where experimental data on the partitioning of MA and
V Ac between the particle and the monomer droplet phases are displayed together with
experimental data from the literature for the monomer combinations MA-S, 6 BA-S, 6 MA-BA, 6
46 Chapter 5
MA-MMA, 11 and MMA-8,14 on a series of (co)polymer seeds varying in composition.
1.00
111-4~ 0.50
0.00 ~~~"--------.--------... 0.00 0.50 1.00
fd Figure 5. 1: Experimentally determined monomer fractions in latex particles (f) as a jUnction of the monomer fraction · in the droplet phase (f) for the monomer combination MA-VAc (O) on apoly-(MA-VAc) latex and for the monomer combinations MA-S (t:.);6 BA-S (0};6 MA-BA (•); 6 MA-MMA r-J; 11 MMA-S (e)14 on several (co)polymer seeds. The solid line represents the prediction given by eq 5.12a,b.
The results presented in Figure 5.1 imply that the entropy of mixing of the monomers must
be the main factor determining the monomer mole fractions. Note that even in these cases
the absolute monomer concentrations will depend on contributions of the mixing of monomer
and polymer and the interfacial Gibbs free energy. Based on these considerations Maxwell
et al.6•7 formulated three assumptions, that simplify existing thermodynamical relationships,
resulting in basic equations that confirm the experimental results represented in Figure 5.1.
Using this approach, simple relationships were developed dealing with saturation swelling
of a polymer latex by two monomers. The basic thermodynamic relationships will be presented
together with the three assumptions and the resulting simplified relationships in the theory
section (5.2).
At partial swelling of latex particles, however, occurring in the so-called interval III
of emulsion polymerization, there are no monomer droplets present in the system and the
monomer is solubilized in both the particle and the aqueous phases. Based on work done
by Vanzo et al.8 and Gardon,9 a simple model was developed by Maxwell et a/. 10 for the
estimation of monomer partitioning, for one monomer of limited water solubility. Both
models, describing saturation swelling and partial swelling, are tested for the monomer
combination MA-V Ac.
Based on the three assumptions previously formulated in the work of Maxwell et
al.,6•7•10 now in this thesis an extended model is developed to predict the partial swelling
Monomer partitioning 47
of latex particles with two monomers of limited water solubilities. The results predicted by
this extended model are compared with observed monomer partitioning results for the
monomer combination MA-V Ac. Note that the theoretical developments described here are
specific for the swelling of latex particles with monomers. However, the conclusions drawn
are quite general, and are valid for all partially water soluble solvents. Furthermore, the theory
can be trivially extended to take into account three or more solvents or monomers. 11
5.2 Theory
Morton et a/. 1 considered the saturation swelling of latex particles by a monomer
having limited solubility in the water phase. When the homogeneously swollen latex particle
phase is in equilibrium with the free-monomer phase the partial molar Gibbs free energy
of the monomer is given in terms of the Flory-Huggins theory2 and the Gibbs-Thomson
equation1•3
[ l l 2 2V ?{V
113
l1p. /(RT) = ln(1 - v \ + v 1 - - + xvP + ml P P P' P ]J R RT
n •
(5.1)
where AJlp is the partial molar Gibbs free energy (or chemical potential) of monomer in
polymer phase relative to the partial molar Gibbs free energy of pure monomer, vP is the
volume fraction of polymer in the latex particles, P';. the number-average degree of
polymerization, x the Flory-Huggins interaction parameter, R the gas constant, T the
temperature, y the particle-water interfacial tension, V mi is the molar volume of monomer
i, and R0 is the unswollen radius of the latex particle. The first two terms at the right hand
side in eq 5.1 represent the combinatorial entropy of mixing (denoted as the 'configurational
entropy' by Flory), the third expression represents the so-called 'residual' free energy
containing both enthalpic and entropic terms, and the fourth expression represents the
contribution from the latex particle-water surface interfacial Gibbs free energy. Note that.
since P';. is normally large, eq 5.1 may usually be written in a simpler form
.1. J.lp I(RT) = ln(l (5.2)
For simplicity, in the following theoretical development we use the form of eq 5.2 and not
eq 5.1 (i.e., we assume 1/P,. is small for the polymers of interest).
For two-monomer partitioning in an emulsion system the partial molar Gibbs free
energy of monomer i in the monomer droplet (e. J.id,) and polymer particle (A !lp;) phases can
48 Chapter 5
be calculated from the Flory-Huggins theory: 2•3
•12
Ll!J.d./(RD = lnv~, ,(r) + (l - m.)vd. 1(r) + xv~;sa~(r)
1 w,sa u !f,Sa '1 tt•
(5.3)
LlJ.!p; /(RD lnvP, + (1 (5.4)
where vdi, Vq;, vP, and vl!i are the respective volume fractions of monomers i andj in the
monomer droplets and latex particles, x,i is the interaction parameter between monomers i
and j, and X;p and ;ware the interaction parameters between each of the respective monomers
i andj and the polymer. The term mu is the ratio of the molar volumes of pure monomers
i andj (i.e., my= Vm/Vm;, where Vm, and Vm; are the molar volumes of monomers i andj,
respectively). The derivation of eq 5.3 involves the reasonable assumption3 that m;p and mlP,
the ratios of the respective molar volumes of monomers i and j and the molar volume of
polymer, are negligible as compared with all other terms. The use of the Flory-Huggins theory
in this case will be discussed later in this chapter. In this thesis the postscript (r) always
represents the saturation value of the quantity at a certain monomer mole ratio in the particle
or droplet phases, and the subscripts a, p, and d represent the aqueous phase, the polymer
particle phase, and the monomer droplet phase, respectively. Note that we are always dealing
with saturation swelling if there are monomer droplets present. The use of eq 5.3 assumes
that the lattice model is valid for mixtures of small molecules; this is valid for two organic
monomers of equal or similar molar volumes. Note also that due to the normally large size
of monomer droplets we have not considered contributions from the monomer droplet-water
interfacial free energy in eq 5.3 (this assumption may not be valid for a system containing
very small monomer droplets). An example of typical saturation values for all parameters
in eq 5.4 together with the resulting values for all terms in eq 5.4 is given in Table 5.1. Note
that the total sum of the expressions in eq 5.4 in the example given in Table 5.1, as in several
other situations, is dominated by the entropy of mixing monomer and polymer (the absolute
value of In vi>l + vP is much larger then the sum of all other terms).
The partial molar Gibbs energy of the monomer in the aqueous phase (c.J..L.;) is given
6!!., IRT =In a1 (5.5)
where the activity of monomer i, a,, is given by a1 = (y [M,].)/(y o [M,].0); where y is the
activity coefficient of the monomer; yo the activity coefficient of the monomer at some
Monomer partitioning 49
Table 5.1 The values of the terms in the Flory-Huggins expression for the polymer phase (eq. 5.4) are given for the following typical parameters values: vP = 0.3; vp; = 0.2; vPi = 0.4; m!i = 0.9; X!i = 0.5; X;p = 0.2; Xjp = 0.3; 'Y = 20·10-1 N·dm-1
; V.,; = 0.1 d1fl·mot1;
R0 = Ur dm; R = 83.1 N ·dm ·mot1 • K 1
; T = 300 K. The affect of deviations in the separate parameters on the total sum is illustrated by assuming X;p = 0.3; x!i = 0.4; and m9 = 1.
X.;p = 0.2
x.!i = 0.5
mr = 0.9
lnvp; -1.61 -1.61 -1.61 -1.61
(I - m!i)vw 0.04 0.04 0.04 0
vP 0.3 0.3 0.3 0.3
x.!ivw2 0.08 0.08 0.06 0.08
X.;pV/ 0.02 O.o3 0.02 0.02
vpjvp(x.9 + X.;p - x.~!i) 0.05 0.06 0.04 0.05
2V .rurvp•nfRoRT 0.01 0.01 0.01 0.01
total sum -1.11 -1.09 -1.14 -1.15
standard state, [M;]. the concentration of monomer in water, and [M;].o the concentration
of monomer in water at standard state. We chose the standard state to be just homo-saturation
of the monomer in water, i.e., [M;].o = [M;]._,.,(h). In this thesis the postscript (h) always
represents the saturation concentration in the absence of other monomers (homo-saturation).
The activity coefficients describe the solute-solute and the solute-solvent interactions; up
to a concentrations of a few molar solute the solute-solute interactions are insignificant; hence,
y = y 0• Therefore, eq 5.5 becomes
L\J.L IRT =In [ [MJ. ] ., [M J •.••• c h)
(5.6)
Equation 5.6 has been shown to be true for a variety of monomer-latex systems. 6•10
At equilibrium the partial molar Gibbs free energy of each monomer will be equal
in each of the three phases, i.e., the polymer particle, the monomer droplet, and the aqueous
phases.
(5.7)
Applying this condition to eqs 5.3-5.6, for saturation swelling the following equations
for monomer i are found: 6'7'2'3'12
lnvpi.sat(r) + (1 - mY)vpJ,salr) + vp,sat(r) + x.uv!1,,..(r) + X.;pv!,.a~(r) +
2V miyv~~.,(r) vpJ,s.lr)vp,sa.Cr)(X.# + X.;p 'X.;pmij) + RaRT (5.8a)
In v • ..,i'l • (I - m,)v•~(') • x,v~..(') " In [ i~~::;~;]
Similarly, for monomer j we find:
(5.8b)
where 1p is related to x.ij by 'X.ii = 'X.ii m1;. All other terms are as previously described, and the
subscript 'sat' combined with the term (r), indicates saturation values at a particular monomer
ratio, r.
At partial swelling (i.e., no droplet phase) the equations will be more simple because
the expression for the droplet phase can be neglected. For monomer i the equation will be
(5.8c)
Similarly, for monomer j
(5.8d)
Equation 5.8a-d can be used to predict monomer partitioning for latex systems containing
two monomers in both, saturation (eq 5.8a,b) and partial (eq 5.8c,d) swelling. There are,
however, difficulties in determining the values for the interaction parameters and the interfacial
tension because, amongst other things, both may be dependent upon the volume fraction of
polymer in the latex particles as well as on the monomer ratio. 2
The experimentally found result of equal monomer mole fraction in the polymer particle
and monomer droplet phase can also be obtained theoretically when using the following
assumptions which were formulated by Maxwell et al. 6 for saturation swelling:
Monomer partitioning 51
Assumption (1): The difference between the molar volumes of many pairs of monomers
is slight; therefore, the ratio of the molar volumes of monomer i and j is well approximated
by unity; i.e., mu = mji = L Note that in this case the interaction parameters Xu and Xji will
be equal. Note also that this assumption validates the use of eq 5.3 in what follows since
mole fraction is then equivalent to volume fraction. The mixing of two small molecules should,
in principle, be considered in terms of mole fraction. We adopt the form of eq 5.3 for simplicity
and note here that, because of assumption (I), further theoretical development utilizing this
simplification is validated.
Assumption (2): The contribution to the partial molar free energy of the terms containing
X;p are small as compared with all other terms. As a result slight changes in X;p are relatively
unimportant for monomer partitioning, as can be seen in Table 5.1.
At saturation swelling these assumptions lead to the following result for monomer i:6
(5.9a)
An analogous equation can be derived in a similar manner for monomer j.
(5.9b)
An analogous equation can be derived for monomer j at partial swelling.
Using eq 5.9a for monomer i together with a similar equation for monomer j, we find
for saturation swelling6
vdi.sat(r) l + ::dvd ..• (r) - v.,..,(r)) = v di_...(r) '' '·- ...
[M)._...(r) ]]
[M)._...(h) (5.10a)
and for partial swelling
In [ ::] • x,<vw - v,) • In
[M.J.
[MJ .... ,(h)
[ [M). l (5.10b)
[M) •. ,.,(h)
52 Chapter 5
Assumption (3): The contribution to the partial molar free energy arising from the residual
partial molar free energy of mixing of the two monomers is small relative to all other terms
in eq 5.4, i.e., all terms in eqs 5.9a,b and 5.10a,b containing xij, can be neglected.
5.2.1 Saturation swelling of latex particles by two monomers
For saturation swelling Maxwell et al.6 derived the following relationships when using
assumptions (1)-(3) in combination with the right hand equality of eqs 5.8a.,b:6
(M Ja,mt(r)
(M Ja,sat( h)
[M) •.• ir)
[M) • .sat(h)
(S.lla)
(S.llb)
where [M,].,.,,(r) and [MJla.sat(r) are the saturation solubility values for monomers i andj in
the aqueous phase at a certain monomer ratio, r. Equations 5.11 a.,b show that the concentrations
of monomer i and j in the aqueous phase are linear functions of the mole fraction of the
respective monomers in the monomer droplet phase.
Using eq 5.1 Oa with assumption (3) gives the following relationships between the
droplet phase and the particle phase: 6
(5.12a)
fpj,sat = f <ji,sat (5.12b)
where fp;.sat• fdi,sat• fw,sat• and f.y,sat represent successively the mole fraction of monomers i and
j in the monomer droplet and polymer particle phases at saturation swelling. Note that in
the particle phase the monomer mole fraction does not include the mole fraction of polymer
(fp; = vp/(vpi + vw)). We may state that eq 5.12a,b, which results from the use of the three
assumptions formulated in this thesis, gives a good approximation of the monomer partitioning
behaviour for the polymers and monomers studied, as can be seen in Figure 5.1. Furthermore,
it has been shown that eq 5.12a,b is approximately valid over a wide range of conditions
typical of emulsion polymer systems even when the three assumptions ((1)-(3)) utilized in
their derivation do not hold exactly. Numerical analysis of the full equation that results when
eq 5.8b is subtracted from eq 5.8a has shown that the mole fractions predicted by eq 5.12a,b
are almost always correct.7 Equation 5.12a,b appears to be insensitive to the validity of
assumptions (1)-(3), i.e., the three assumptions are of algebraic necessity only. This is an
Monomer partitioning 53
important result, since it points to the general applicability of eq 5.12a,b even if one or more
of the assumptions described above would not hold exactly. This implies that the entropy
of mixing of the monomers is the main factor determining the monomer mole fractions.
Polymer phase. Using eq 5.12a,b Maxwell et a/.6 also developed an empirical description
for the concentration of two monomers at saturation swelling within polymer latices. These
relations can be derived using eq 5.12a,b, the relation fpi,sat = [M;]p,sa1(r)/([M;]p,sa.(r) + [Mj]p.sa~.(r))
and the assumptions that (1) the total monomer concentration in the latex particles is just
equal to the sum of the concentrations of the individual monomers and (2) the total monomer
concentration in the latex particles is a linear function of the fraction of the monomers in
the droplet phase. For a particular seed latex the concentration of monomer i within the
particles, at a certain monomer ratio r ([M,]p.sat(r)), as a function of the fraction of monomer
i in the droplets is given by6
Similarly, for the monomer j
where [M;]p,sat(h) and [M1]p,sat(h) are the maximum saturation concentrations of monomers
i and j in the latex particles at homo-monomer saturation swelling. Note that the monomer
mole fraction in the droplets just equals the monomer mole fraction in the polymer particles;
hence, in eq 5.13a,b the monomer mole fractions can be replaced by fpi,sat and fl?i.sat if required.
Aqueous phase. Utilising the three assumptions described above, Maxwell et al.6 found from
eq 5.9a and its analogue for monomer j the following relationships:
(5.14a)
(5.14b)
Based on eq 5.14a,b, the following simple relationship between the mole fraction of monomer
i in the polymer phase (fp~,sat) and in the aqueous phase (fa;_,J can be developed:
f [I [M )._,.,(h) I + P•.sat ~ (M Ja,sat(h)
[M ).,""(h) (5.15)
[M J •. sat(h)
54 Chapter 5
An analogous equation for monomer j can also be developed, where the subscripts i and
j in eq 5.15 are replaced by j and i, respectively. Note that when [M;].,,11(h) "" [M1] ..... (h),
the mole fraction of monomer i in the aqueous phase is equal to that in the polymer phase,
i.e., fai,sat "" fpl,sat fdi,sat). Note also that when monomer j has a low water solubility, i.e.,
[MJ1a.sat<h) "" 0, the mole fraction of monomer i in the aqueous phase will be close to unity
( fai,.., "" I).
5.2.2 Partial swelling of latex particles by one monomer
Based on the Vanzo equation, Maxwell et a/. 10 derived a semi-empirical equation to
describe partial swelling of latex particles by one monomer. Maxwell et al. showed that
the dominant factor determining monomer partitioning of one monomer at partial swelling
is the Gibbs energy due to the entropy of mixing of monomer and polymer. All other terms
as the residual free energy and the polymer particle-water interfacial free-energy terms (see
eq 5.2) are relatively small and approximately constant (const.) as a function of the volume
fraction of polymer. 10•2 The partial swelling of latex particles by one monomer is then
described by
[ [M] l ln(l - v) + vP + const. = In •
p [MJ ..... (h) (5.16)
where [M]. and [M] .. ,..(h) are the respective concentrations of monomer in the aqueous phase
below saturation and at homo-saturation swelling. A similar relationship can be formulated
for saturation swelling when replacing the volume fraction of polymer and the monomer
concentration in the aqueous phase below saturation by those quantities at saturation swelling,
i.e., replacing vP by vp,sat and [M]. by [M].,.ih). Subtracting this eq from eq 5.16 results in
a semi-empirical relationship that describes partial swelling of latex particles by one monomer.
In (1 v) + v - v = In [ [MJ. I (1 - V ) p p,sat [MJ (h)
p,sat a.sat
(5.17)
5.2.3 Partial swelling of latex particles by two monomers
At partial swelling there is no droplet phase present so eq 5.10b must be used. If
the polymer fraction within the particles, vr. is relatively large, then vPJ- vP1 is small. In this
case the following inequality holds: abs(xy(vp~- vr1)) << abs(ln (vp/vp1)) in which abs means
Monomer partitioning 55
that the absolute values of these quantities should be used. Alternatively, if 'Xii < I, then this
inequality also holds. The assumptions used to derive this inequality will be discussed in
more detail in the Results and Discussion section in the light of the experimental results. 13
Using this inequality, the simplified eq 5.10b becomes:
[MJ.
[M).
[M) •. ,ih)
[M J •. sar(h) (5.18)
Note that for a certain ratio of monomers, r, at saturation [M;}. [M;]a,sa~(r) where [M,]a,sa~(r)
is the saturation value at that ratio of monomers. Hence, the saturation values in eq 5.18 must
be the saturation values for homo-monomer saturation swelling ([M;]a,sa~(h) and [Mj]a,sa~(h)).
This is an important result since the homo-monomer saturation values are readily accessible
parameters.
From saturation swelling we know that the volume fractions of monomer i over
monomer j in the droplet phase are equal to the volume fractions of monomer i over monomer
j in the polymer particles. Knowing this and combining eqs 5.1la,b and 5.18 gives the
following equation: [MJ.
[MJ.,, •• (r)
From eqs 5.1la,b, 5.18, and 5.19 we also find
[M).
[M) •. , •• (r)
[M)P
[M)p,sa~(r)
(5.19)
(5.20)
The use of eqs 5.19 and 5.20 is very convenient when realizing that with known mole
fractions of monomer i within the particle phase, fp1, the saturation concentrations at any
monomer ratio r can be calculated directly from the saturation swelling equations ( eqs 5 .16a,b
and 5.17a,b). Hence, eqs 5.19 and 5.20 give readily accessible relationships between the
concentrations of monomer i and monomer j in the aqueous phase ( eq 5 .19) and the polymer
phase (eq 5.20) at partial swelling of the latex particles.
The monomer concentrations in the particle phase and the aqueous phase at partial
swelling can be related in a manner similar to that used by Maxwell et a/. 10 when developing
the semi-empirical equation for the one-monomer situation (eq 5.17). The sum of all terms
containing interaction parameters and monomer molar volumes is assumed to be approximately
constant at all volume fractions of polymer. This assumption arises from the fact that the
dominant term for partial swelling of latex particles is the combinatorial entropy of mixing
monomer and polymer. All other terms have been shown to be small and approximately
56 Chapter 5
constant at partial swelling. 10 For two-monomer swelling, from eq 5.8c for monomer i we
find an equation similar to eq 5.17:
ln~+v V pi.sat(r) P
[M] v (r) = In I a
p,sat [M.] () I ll,Sllt r
(5.21)
Note that the saturation volume fractions can be calculated from eq 5.13a,b and molar volumes
and require only a knowledge of the homo-saturation concentrations of the monomers in
the particles (i.e., each monomer in the absence of the other). For monomer j analogous
relations can be derived where the subscripts i in eq 5.21 are replaced by the subscript j.
Rewriting eq 5.18 gives a similar relationship between the polymer and aqueons phases
at partial swelling to that developed for saturation swelling oflatex particles (i.e., eq 5.15).
fpi
f . [ 1 - [M) ..... (h) l + pi [M.] (h)
r a,sat
[M).,sa~(h)
[M ;)., ... (h)
(5.22)
From this we can conclude that eq 5.15 holds for both saturation and partial swelling oflatex
particles by two monomers with limited water solubility.
The important equations for partial swelling are eqs 5.18 and 5.22, because they relate
the concentration of one monomer in the aqueous phase with the concentration of the same
monomer in the polymer phase; eqs 5.19 and 5.20, because they give relationships for the
concentrations of monomer i and j in the aqueous phase ( eq 5 .19) and the polymer phase
(eq 5.20), respectively; and eq 5.21 since the partially saturated polymer phase is related
to the saturated polymer phase for each monomer in this equation.
5.3 Results and discussion
Jt has been shown6 that one-monomer partitioning between the polymer particle phase
and aqueous phase can be described with eq. 5.17 for a series of particle diameters (unswollen:
30-100 nm), temperatures (20-45"C), number average degrees of polymerization (P'. = 87-
15000), and copolymer compositions (S-MA: going from poly-MA to poly-(MA-S) and poly
S). Therefore, the use of one seed (Table 3.3: MA-V Ac seed) for the partitioning experiments
was sufficient to develop relationships predicting monomer partitioning at partial swelling
even though the particle size distribution may be broad and composition drift during seed
preparation may have led to different copolymer compositions.
For saturation swelling Maxwell et a/.6 made three assumptions to develop expressions
Monomer partitioning 57
for two-monomer partitioning. It seems reasonable to suggest that these assumptions should
also be valid for partial swelling. Based on these three assumptions described in section 5.2,
relationships were derived for two-monomer partitioning at partial swelling. Considering
these assumptions in regards to our experimental system, we note the following:
Assumption (1): The differences between molar volumes of monomers is generally
small. In the case of MA and V Ac the differences will be extremely small because the
molecular mass of MA is equal to the molecular mass of V Ac and also because the densities
of the monomers are nearly equal (VMA = 90.1 and VvAc = 92.2 cm3 mot·• at 20"C).
Assumption (2): It is hard to assess whether the contribution to the partial molar free
energy of the terms containing the interaction parameter between monomer and polymer are
indeed small as compared with all other terms since only few reliable values for these
parameters exist for any monomer-polymer system. This is because it is hard to measure
these parameters independently. Furthermore, the theoretical nature of these parameters is
rather vague since they are supposed to include both temperature-dependent enthalpic and
temperature-independent entropic terms. That the situation is even more complex has been
shown by Flory,2 who pointed out that the interaction parameters should also be polymer
concentration-dependent at high volume fractions of polymer. However, the justification of
the use of assumption (2) is supported by Table 5.1 where it is shown that the contribution
of the expressions containing lip to the partial molar free energy of monomer in polymer
is relatively small as compared with the sum of all other expressions.
Assumption (3): The contribution to the partial molar free energy arising from the
residual partial free energy of the mixing of two monomers is small relative to all other terms
in eq 5.l0b ifx.9 is small and/or if the polymer fraction within the particles, vp, is relatively
large (i.e., vPi- Vp; is small). In this case the following inequality holds: abs(x.!t(vPi- vp;)) <<
abs(ln (vp/vP.i)). The use of assumption (3) is supported by Table 5.1 where it is shown that
the contribution to the partial molar free energy of monomer in polymer of the terms
containing '4• is relatively small as compared with the sum of all other expressions.
5.3.1 Monomer partitioning at saturation swelling oflatex particles by two monomers.
As predicted by eq 5 .12a,b the fractions of monomer in the droplet and particle phases
are equal for several monomer combinations in a series of latex systems varying in copolymer
composition (see Figure 5.1). This suggests that the three assumptions used by Maxwell et
a/.6 in the derivation of this equation are (sufficiently) valid for all these combinations,
including the monomer combination MA-VAc in a poly-(MA-VAc) seed latex.
58 Chapter 5
That the concentrations of monomer i and j in the polymer phase and aqueous phase
can be described with eqs 5.13a,b and 5.14a,b is shown by the good agreement between
experiments and theory (Figure 5.2a,b) for the monomer combination MA-VAc. Equations
5.13a,b and 5.14a,b are very useful because they only require the individual homo-saturation
values in the polymer and aqueous phases to be known in order to calculate the relevant
monomer concentrations.
Based on the relationships developed for saturation swelling and based on experiments
performed, it can be concluded that the entropy of mixing of two monomers is the dominant
contribution to monomer partitioning, and as a result of this the presence of polymer has
no significant effect upon the ratio of the two monomers in the polymer phase. Although
the monomer ratio in the polymer phase is independent of the polymer composition, the
absolute monomer concentrations at saturation do depend upon the polymer and monomer
type (in terms of mixing of monomer and polymer and latex particle-water surface interfacial
energy). Knowing that the polymer composition has no effect on the monomer ratios,6•14
we can conclude that composition drift occurring during emulsion copolymerization as a
direct result of the monomer ratio within the polymer particles is independent of polymer
compositions. Different polymer compositions leading to other absolute concentrations in
the polymer particles will only influence the polymerization rates in the latex particles. Mass
balance shows that, for monomer systems where either one or both the monomers have a
high but still limited water solubility, changing the monomer-to-water ratio has an effect
on the monomer ratios within the particles. In this way composition drift and polymerization
rate will depend on the monomer-to-water ratio.
8 A 8 0.7
i ""' a:::' 0.6 6 6 -o a
:::=- T :::=-"' o.s 0 o:::r !. a o
1 '-'! 0.4
~ 4 T 4 ....... 18 0.3
.L ~ ! 2 2 ~~
0.2
~- 0.1 0 0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0
fp,MA
B
T T l .L
0.2 0.4 0.6 0.8
0.7 0.6 o.s 0.4 0.3 0.2 0.1
0.0 1.0
(!;'
.9 ;:::,. 0
! 8 I :i ~
Figure 5.2: Comparison of the predictions of eqs 5.13a,b and 5.14a,b (---:) with experimentally determined monomer concentrations ofMA (O) and VAc (D) inapoly-(MAVAc) particle phase (Fig. 5.2a; eq 5.13a,b) and in the aqueous phase (Fig. 5.2b; 5.14a,b) as a function of the monomer .fractions in the polymer phase.
Monomer partitioning 59
5.3.2 Monomer partitioning at partial swelling of latex particles by one monomer
For monomer partitioning at partial swelling by one monomer with limited water
solubility, Maxwell et al. 10 derived a semi-empirical relation where the value of the sum of
the residual free energy and the particle-water interfacial free energy terms are estimated
from the saturation swelling volume fraction of polymer (eq 5.17). To use this model, only
the saturation concentrations in the polymer and aqueous phases are needed. Experiments
were performed to determine whether there is good agreement between this semi-empirical
expression and experiments. As can be seen in Figure 5.3, good agreement for both MA
and V Ac is reached when taking experimental errors into account.
o.so ........ 0.00 r===trff=====4~..l..Q B -O.SO ! ~ -1.00
i -l.SO
:i -2.00
-2.50
-3.00 L....--..----.---.----..---,.---T-----1'-o 0.30 0.40 0.50 0.60 0. 70 0.80 0.90 1.00
v,
Figure 5.3: Comparison of the predictions of eq 5.17 and experimental measurements of MA ( o ) and VAc ( o ). The volume fraction of polymer at saturation swelling was 0.365 forMA (--) and 0.437 for VAc (- - -).
At partial swelling the relationship between the monomer concentration in the aqueous
phase and the polymer phase is nonlinear leading to a monomer concentration in the aqueous
phase that is closer to saturation than the monomer concentration in the polymer phase.
Therefore, it can be concluded that in interval III of an emulsion polymerization with a
monomer with relatively high (but still limited) water solubility, a significant amount of the
monomer will be located in the aqueous phase. In this way the monomer concentration in
the polymer phase will be reduced and the polymerization rate may be lowered as the
monomer-to-water ratio is reduced. Note that also other factors may affect the rate of
polymerization (e.g., the Trommsdorff-Norrish gel effect, initiator efficiency, diffusion
controlled propagation, etc.), but these considerations are outside the scope of this thesis
and are discussed elsewhere. 15
60 Chapter 5
5.3.3 Monomer partitioning at partial swelling of latex particles by two monomers
In Figure 5.4 the relationship derived between the concentration of MA and V Ac in
the aqueous phase and polymer particles (eq 5.18) is compared with experimental results.
From the good agreement between theory and experiments it can be concluded that assumptions
(1)-(3) seem to be justified during the development of eq 5.18. It is important to note that
a sensitivity analysis has shown, 7 for typical values of all interaction parameters and molar
volumes of monomers, that the three assumptions are of algebraic necessity only: numerical
solutions of the full equations for two-monomer swelling described by eq 5 .Sa-d almost always
verify the use of the three assumptions, and also the simplified equations that result from
the use of these assumptions (e.g., eq 5.18).
2.0
~ 1.5
>p,. 1.0 J 0.5
0.0 0.0 0.5 1.0 1.5 2.0
([MA]J[V Ac].)cx
Figure 5.4: Comparison of predicted (eq 5.18; --.)and experimentally determined volume fractions of MA and VAc in the polymer phase as a function of monomer ratios in the aqueous phase multiplied by a constant a (a= 0.3010.60 for MA-VAc).
1.00
........ 0.80 ~ !
'Q' 0.60
~ '"""' 0.40
~ r;... 0.20
0.00 ""---..----.----.----....-------. 0.00 0.20 0.40 0.60 0.80 1.00
[MA]J[MA]....,(r)
Figure 5.5: Comparison of the predictions ofeq 5.19 (---)with experimentally measured concentrations forMA and VAc in the aqueous phase ([MAla.-(h) = 0.60 mol/dm3 and [VAcJ •.. ,alh) = 0.30 mol/dm3
}.
Monomer partitioning
1.00
';::;- 0.80
:;0.60 > 5o.4o ~ :::. 0.20
0.00 ~---......----.----.---........ --..... 0.00 0.20 0.40 0.60 0.80 1.00
[MA],I[MA]...,...(r)
Figure 5. 6: Comparison oft he predictions of eq 5. 20 with experimentally measured concentrations forMA and VAc in the polymer particle phase ([MA ]p.sa~(h) = 7.05 mol/dm3 and [VAc]p,safh) = 6.11 molldm3
).
61
Based on eq 5.18 relationships between monomers i andj in the aqueous phase (eq
5.19) and in the polymer phase ( eq 5.20) were developed. Here also good agreement between
experiments and theory was found as shown in Figures 5.5 and 5.6. From these results it
can be concluded that at equilibrium at a certain monomer ratio, r, the concentrations of both
monomers in the aqueous phase are equally far away from saturation values at that ratio.
The concentrations of one monomer in both the polymer and aqueous phases can be
related by eq 5 .21. As can be seen in Figure 5. 7 experiments and theory show good agreement.
Equation 5.21 was developed in analogy with a similar equation developed for homo-saturation
swelling, utilizing the concept that the free energy of mixing is dominated by combinatorial
entropy at partial swelling.
0.0
-2.5
-3.0 1...--....--....--....----....----....----......-u..., 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
v, Figure 5. 7: Comparison between predictions of eq 5.21 forMA (top line; "pMA..Jr
0.618) = 0.409) and VAc (bottom line; "pvAc,wlr 0.382) = 0.409) with experimental measurements for MA ( o ) and VAc ( o ).
62 Chapter 5
That this assumption is valid is shown by the agreement between experiments and theory
in Figure 5.7. From eq 5.21 it can be concluded that the monomer concentration in the aqueous
phase is closer to saturation than the monomer concentration in the polymer phase. For
monomers with relatively high (but still limited) water solubility a significant amount of the
monomer will be located in the aqueous phase.
For partial swelling, as for saturation swelling, it may be concluded that the entropy
of mixing of two monomers is dominant in the equilibrium reached during monomer
partitioning. The monomer ratios within the polymer phase are independent of the polymer
composition. However, in a manner similar to saturation swelling, absolute monomer
concentrations in both the polymer and the aqueous phase do depend on the polymer
composition.
The relation between the mole fraction of monomer i in the aqueous phase and the
mole fraction of monomer i in the polymer phase for saturation swelling is given by eq 5.18.
The exact same expression was also found for partial swelling (eq 5.22). Using this simple
relation(s) for both saturation and partial swelling requires only the knowledge of the individual
homo-saturation concentrations of the monomers in the aqueous phase. To prove that this
relation indeed is valid for both partial and saturation swelling theory and experiments are
compared in Figure 5.8.
1.00
0.80
0.60
·~J 0.40
0.20
0.00 "----.-----....----........ --....-----. 0.00 0.20 0.40 0.60 0.80 1.00
fp.MA
Figure 5. 8: Comparison of the predictions of eqs 5. 15 and 5. 22 (----:) with experimentally determined mole fractions of MA in the aqueous phase as a jUnction of the mole .fraction ofMA in the polymer particle phase for MA-VAc in apoly(MAVAc) latex at saturation ( o ) and partial swelling ( o ).
Monomer partitioning 63
5.4 Conclusions
It has been shown for several monomer combinations (including MA-V Ac) that monomer
partitioning at saturation swelling can be predicted with the simplified relationships developed
by Maxwell et a/. 6 It became clear that the mixing of two monomers is independent of the
polymer type and that the ratios of monomers in the droplet and particle phases are equal.
Only the absolute value of the degree of swelling depends on the monomer and polymer
type. These results indicate that the entropy of mixing of two monomers is the dominant
contribution to the thermodynamic equilibrium reached.
Partial swelling of latex particles with one monomer can be described with the semi
empirical relation developed by Maxwell et a/. 10 This semi-empirical relation is based on
the findings that both the interfacial tension and the residual free energy terms are approximately
constant with the volume fraction of polymer and therefore can be estimated from the volume
fraction of polymer at saturation swelling. Monomer partitioning in these cases is dominated
by the contribution of the entropy of mixing of monomer and polymer.
For partial swelling with two monomers with limited water solubilities simple
relationships have been developed to predict the monomer concentrations and fractions within
the different phases. Comparison of experimental results with the developed relationships
showed excellent agreement. Similar to the saturation swelling theory, the entropy of mixing
of two monomers at partial swelling is the dominant contribution to the equilibrium.
The good agreement between experimental data and theory for monomer partitioning
at both saturation and partial swelling suggests that the theoretical development correctly
describes the thermodynamics oflatex particle swelling. Note that the use of these relationships
merely requires the individual homo-saturation values of the monomers in the polymer particles
and the aqueous phase, which are readily accessible parameters. With the relationships develo
ped for saturation and partial swelling the mole fraction of monomer i and the absolute
concentrations of monomers i and j within the particle phase can be determined. Knowledge
of the mole fraction of monomer i within the particle phase enables the prediction of
composition drift occurring in emulsion copolymerizations; the absolute concentrations of
monomers i and j in the particle phase play an essential role in better understanding and
predicting rates of polymerization. The latter is of paramount importance in determining optimal
addition rate profiles, which are indispensable in preparing compositionally homogeneous
copolymers in semi-batch processes.
64 References
I. M. Morton, S. Kaizerman, M.W. Altier, J Colloid Sci., 9, 300 (1954) 2. P.J. Flory, In Principles of Polymer Science, Cornell University Press, Ithaca, NY,
1953 3. J. Ugelstad, P.C. Mork, H.R. Mfutakamba, E. Soleimany, I. Nordhuus, R. Schmid,
A. Berge, T. Ellingsen, 0. Aune, K. Nustad, In Science and Technology of Polymer Colloids, G.W. Poehlein, R.H. Ottewill, J.W. Goodwin, Eds., NATO ASI Vol. 1, Ser. E, Plenum, NY, 1983
4. M. Nomura, K. Fujita, Makromol. Chern., Suppl., 10/11, 25 (1985) 5. G.H.J. van Doremaele, F.H.J.M. Geerts, H.A.S. Schoonbrood, J. Kurja, A.L. German,
Polymer, 33, 1914 (1992) 6. LA. Maxwell, J. Kurja, G.H.J. van Doremaele, A.L. German, Makromol. Chern., 193,
2065 (1992) 7. LA. Maxwell, L.F.J. Noel, H.A.S. Schoonbrood, A.L. German, Makromol.
Chern., Theory and Simulation, 2, 269 (1993) 8. E. Vanzo, R.H. Marchessault, V. Stannett, J Colloid Sci, 20, 62 (1965) 9. J.L. Gardon, J Polym. Sci., Polym. Chern. Ed, 6, 2859 (1968) 10. LA. Maxwell, J. Kurja, G.H.J. van Doremaele, A.L. German, B.R. Morrison,
Makromol. Chern., 193, 2049 (1992) II. H.A.S. Schoonbrood, M.A.T. van den Boom, A.L. German, J Pol. Sci., Polym. Chern.
Ed. XX, XX (1994) 12. J. Guillot, Acta Polym., 32, 593 (1981) 13. L.F.J. Noel, I.A. Maxwell, A.L. German, Macromolecules, 26, 2911 (1993) 14. A.M. Aerdts, M.M.W.A. Boei, A.L. German, Polymer, 34, 574 (1993) 15. I.A. Maxwell, E.M.F.J. Verdurmen, A.L. German, Mak:romol. Chern., 193,2677 (1992)
Model development
Chapter 6 Model prediction of batch
emulsion copolymerization
65
Abstract: Monomer partitioning in emulsion copolymerization plays a key role in determining composition drift and polymerization rates. The combination of thermodynamically based monomer partitioning relationships described in chapter 5 with mass balance equations, makes predictions of monomer partitioning in emulsion copolymerizations possible in terms of monomer mole fractions and monomer concentrations in the particle and aqueous phases. Using this approach, the effects of monomer-to-water ratios and polymer volumes on the monomer mole fraction within the polymer particle phase in a nonpolymerizing system at thermodynamic equilibrium can be determined. Comparison of these monomer partitioning predictions with experiments for the monomer system methyl acrylate-vinyl acetate (MA-VAc) shows good agreement. Furthermore, composition drift occurring in a polymerizing system as a function of conversion can be predicted if the reactivity ratios are known and if the assumption is made that equilibrium is maintained during reaction. Comparison of predictions with experimental results for emulsion copolymerizations of the monomer systems MA-VAc and MA-indene shows good agreement.
6.1 Introduction
Attempts to model emulsion copolymerization have been made by several
investigators. 1•2
•3
•4
•5
•6
•7
•8 For this purpose, basic theories for emulsion
homopolymerization were mathematically extended to emulsion copolymerization. Due to
the complexity of the emulsion polymerization process, most data on kinetics have been
fitted with empirical models. Based on this, the values of many rate parameters have been
fitted. For correct model predictions of emulsion homopolymerization the values for the rate
parameters for entry, exit, termination, transfer and propagation of oligomeric radicals have
66 Chapter 6
to be known, in addition to the number of particles. For emulsion copolymerization, finding
correct values for rate parameters is much more complex than in the case of
homopolymerizations. The use of emulsion copolymerization models also incorporates the
knowledge of monomer ratios in the particle phase, where the reaction takes place. For
describing monomer partitioning behaviour that determines the concentration of both
monomers in the polymer phase, both empirical and a thermodynamic approaches have been
reported in the literature. 1•2•3
•45
•6
•7
•8 In the first approach empirical relationships describing
monomer partitioning were developed often based on questionable assumptions, e.g.,
assuming constant concentrations of monomers in the polymer phase during interval II of
emulsion copolymerization6 or neglecting the monomer in the aqueous phase. 1•2 Another
approach is the experimental determination of monomer partitioning coefficients3•4
•5 fitted
with empirical relationships. The thermodynamic approach developed by Morton9 for
emulsion homopolymerizations and later extended to emulsion copolymerizations 7•8
•12 is a
fundamental and promising approach. However, it involves many parameters of which the
values are often not known. Furthermore, the physical significance of the interaction
parameters used is rather vague since they often include enthalpic and entropic effects -
parameters that often depend on the polymer concentration. It is of great importance to have
(simple) relationships that correctly predict monomer concentrations in the polymer phase
since this is the basis of all models for predicting (instead of fitting) copolymer composition
and rates of polymerization.
Recently, generally accepted thermodynamic relationships9•10
'11
'12
'13 have been
simplified by Maxwell et a/. 14 for saturation swelling and by Noel et al. 15 for partial
swelling of particles by two monomers, see chapter 5. The use of these novel and simple
relationships that will be summarized in the theory part of this chapter is very convenient
since they only require the homo-monomer saturation values of the water solubility and . maximum swell ability in the polymer phase of the individual monomers to be known. It is
very important to realize that the use of these relationships does not involve the use of
ambiguous interaction parameters.
Based on these novel relationships for monomer partitioning, combined with mass
balance equations, monomer mole fractions and absolute concentrations of monomers in the
particle and aqueous phases can be calculated. Using this approach the effects of monomer
to-water ratios (M/W) and polymer volume (V po) on monomer partitioning in a certain
mixture of water, monomer, and polymer can be determined in terms of the mole fraction
of monomer i in the polymer particle phase, fr,. In this chapter results of these experiments
are compared with model predictions for the monomer system MA-VAc. From these static
Model development 67
partitioning experiments, a better understanding of monomer partitioning occurring m
emulsion polymerizations can be gained, leading to better control of copolymer formed
during reactions. The effects of water solubility of the monomers, maximum swellability
of the monomers in the polymer, and different overall monomer mole fractions on monomer
partitioning are described herein.
Apart from predicting monomer partitioning under nonpolymerizing conditions,
predictions under polymerizing conditions are also possible if the assumption is made that
thermodynamic equilibrium is maintained during emulsion copolymerization. This will be
valid if the resistance against mass transport is much lower than the resistance against
reaction. Although model predictions are compared with experimental results of emulsion
copolymerization reactions for only a couple of monomer systems, i.e., MA-vinyl esters
(VEst, this chapter and chapter 8), MA-Ind (chapter 7), and MMA-S, 16 the model in
principle covers any given monomer pair where the polymer swells with the monomer and
of which the monomers have a limited water solubility. For monomer combinations in which
the more water soluble monomer is also the more reactive one, the heterogeneity of the
emulsion system in theory can be used to minimize composition drift occurring during batch
emulsion copolymerization. The monomer system MA-Ind is chosen because it meets these
requirements. Results of these copolymerizations will be discussed in detail in chapter 7.
6.2 Theory
In emulsion systems (co )polymerization is assumed to occur mainly within the
polymer particle phase. Therefore, predictions of composition drift and/or rates of
polymerization can only be performed in a correct manner if the mole fraction of monomer
i in the polymer particle phase is known as a function of conversion. In chapter 5 the
following basic equation for two monomer partitioning in emulsions has been derived14•1s· 17
[MJ.(r)
= In ( [MJ._sa~(h) ) [Mi].(r)
[M) •. ,.lh)
(6.1)
The use of the left hand side of this equation directly results in equal mole fractions in the
polymer and monomer droplet phase (eq 5.12a,b).
With eq 6.1, relationships for saturation and partial swelling were derived describing
monomer partitioning in latex systems with two monomers. However, to predict monomer
68 Chapter 6
concentrations in all phases for a given monomer-water-polymer mixture, the monomer mole
fraction in the polymer phase must be known. These monomer mole fractions in the polymer
phase can be calculated when combining monomer partitioning relationships with mass
balance equations for each component. When using this combination, predictions of
monomer mole fractions in the polymer phase can be made in nonpolymerizing monomer
partitioning experiments using parameters with physical significance (water solubilities,
maximum swellabilities of monomer in polymer) only. Moreover, this procedure can be
extended to model predictions of emulsion copolymer composition and polymerization rate
if thermodynamic equilibrium in monomer partitioning is assumed during reaction. Since
different relationships are valid for saturation and partial swelling, separate model
developments are described in the next two sections.
6.2.1 Saturation swelling of latex particles by two monomers: determination of t;u.
In chapter 5 the following eqs are given to describe the monomer concentration in
the polymer phase, 14
(6.2a)
(6.2b)
and in the aqueous phase,
(6.3a)
(6.3b)
and the relation between the mole fraction of monomer i in the polymer and aqueous
phases Is
(M J.,,.,(r) (6.4a) fpi.sat (I - a) + a
where a is the ratio of the water solubilities of monomer j over monomer i (a =
[M;la.sat(h)/[M.J •. , • .(h)). The self evident relationship between the monomer mole fractions
and the monomer mole ratios (q, [M;]/[M;D is given by:
Model development 69
(6.4b)
where qpl,sat is the mole ratio of monomer i over monomer j in the polymer phase at
saturation swelling. Using eq 6.4b to rewrite eq 6.4a gives:
(6.4c)
where lk,sat is the mole ratio of monomer i over monomer j in the aqueous phase at
saturation swelling. The result shown in eq 6.4c is consistent with the right hand side of eq
6.1. Eqs 6.4a-c have been shown to be valid for both partial and saturation swelling~ in
chapter 5. In case of partial swelling the subscript sat and the extension (r) should be
removed from relationships 6.4a-c.
Using eqs 6.3-6.4 enables one to predict monomer partitioning for known mole
fractions of monomer i in the polymer phase. However, for model development this mole
fraction of monomer i in the polymer phase needs to be predicted for known monomer
water-polymer mixtures. This can be done by taking mass balance equations for monomers
i and j at saturation swelling into account. For this reason the following mass balance
equations were formulated and used for the first time in this context:
M1,, [M Ja,sat(r) V a + [M Jp,sa,(r) V P + [M Jd,sat(r) V d (6.Sa)
(6.5b)
where M1,, and Mj,t are the total moles of monomers i and j in the system; V •' V P' and V d
are the volumes of the saturated aqueous phase (the volume of water+ monomer dissolved
in it), the monomer swollen polymer phase (the volume of the polymer + monomer in the
saturated polymer), and the monomer droplet phase. Using eq 5.l2a and rewriting fdi,sat in
terms of monomer ratios we find for [Mj]d:
(6.6)
Combining eqs 6.5a-b and 6.6 leads to a more simple equation in which the monomer
droplet phase does not appear any more. Using this simplified expression together with eqs
6.2a-b and 6.3a-b yields:
M,,, M,,, = V. ([MJ •. ,.,(h) - [M) •. ,ih))
( 1 - fpi.sat) (6.7)
70 Chapter 6
in which fpi,sat and V. are the two unknowns.
A second expression of V • as a function of fpi,sat can be determined from the mass
balance equation of the aqueous phase when volume additivity of water and monomer
dissolved in the aqueous phase is assumed. This will result in a relationship between v. (volume of the aqueous phase including monomer) and V w (volume of the aqueous phase
without monomer):
v. (6.8)
in which MW1 and MWj are the molecular masses of monomers i and j and P; and pj are
the densities of monomers i and j. Using eqs 6.3a-b to replace the unknowns [M;] .. 581 and
[MJ .... , by a relationship in fp;,sat in eq 6.8, and thereafter combining eqs 6.7 and 6.8, will
lead to a second-order equation in fpi.sat' This can be solved to yield fpi,sat·
Solving the resulting relation for saturation swelling gives the mole fraction of
monomer i in the polymer phase for a certain monomer-water-polymer mixture at saturation
swelling. This prediction can be used to describe monomer partitioning in interval I and II
situations in emulsion copolymerization reactions.
6.2.2 Partial swelling of latex particles by two monomers: determination of t;,..
At partial swelling there is no droplet phase present so the middle expression in eq
6.1 is redundant, resulting in the following equality:
[MJ. [M) •. 581(h)
[M). [M J .. ,.,(h) (6.9)
Note that below saturation the subscript ,..(r) is removed. Rewriting eq 6.9 in terms of
monomer mole ratios will give similar relationships to eqs 6.4a and 6.4c. As stated before
it can be concluded from this that eqs 6.4a-c hold for both saturation and partial swelling
of latex particles by two monomers with limited water solubility. Furthermore, it has been
shown15 that at equilibrium and at a certain monomer ratio, r, the concentrations of both
monomers in the aqueous phase and also in the polymer phase are equally far away from
saturation values at that ratio. For the aqueous phase this leads to:
[MJ. F,., • (6.10)
and for the polymer phase:
Model development
[MJP
[M Jp.sat(r)
[M)P
[M .1 sat(r) jJp,
71
= F, .. P (6.11)
where the degree of saturation of the aqueous and polymer phases is expressed by Fsat. and
F sat P' respectively.
In chapter 5 the relationship between the volume fraction of monomer i in the
polymer and the concentration in the aqueous phase is given by: 15
v. ln __ P_'_ + v
v pi,sat(r) P ( ) 1
[M J. v r = n-:::-::-::---,-.,-
p,sat [M .] (r) 1 a,sat
(6.12)
Using eqs 6.9-6.12 allows one to predict monomer partitioning for known mole
fractions of monomer i in the polymer phase. However, for model development this mole
fraction of monomer i in the polymer phase needs to be predicted for known monomer
water-polymer mixtures. This again can be done by taking mass balance equations for
monomers i andj at partial swelling into account. For this reason the mass balance eqs 6.5a
b were reduced to 6.13a-b:
(6.13a)
(6.13b)
Note that in the following model development for partial swelling the monomer mole ratio
(~) replaces the mole fraction (fp~) of monomer i in the polymer phase. With eq 6.4b a
direct relationship between the monomer ratio and fraction is given. From eqs 6.13a-b and
6.4b we find for [M;]. and [M1],:
(6.14a)
(6.14b)
(6.1Sa)
(6.15b)
Assuming volume additivity of water and monomers dissolved in the aqueous phase the
72 Chapter 6
volume of the aqueous phase v. (water+ monomers), can be calculated with a mass balance
equation similar to eq 6.8:
v. (6.16)
The volume of the swollen polymer phase can be calculated by a mass balance
equation of the polymer phase assuming volume additivity of polymer and monomer located
in the polymer phase:
vpo (6.17)
where Vpo is the volume of the polymer in the polymer phase (i.e., without monomer).
Combining eqs 6.l4a-b and 6.16 results in a relation for v. (aqueous phase +monomer)
with qp; as the only unknown parameter. A similar relation in <~p1 can be found for V P when
combining eqs 6.1 5a-b with eq 6.17. With known monomer mole ratio in the polymer phase,
the volume of the aqueous phase including dissolved monomer (V.) and the swollen volume
of the polymer phase (V p) can be calculated. Using eqs 6.2a-b and 6.3a-b gives the aqueous
and polymer phase monomer concentrations at saturation at that monomer mole ratio, r (i.e.
[M,].,sa~(r}, [M1]a,sat(r), [M;]p,,alr), and [Mj]p,sat(r)). Using the values for V. and VP, [M,]. and
[M1]p the degree of saturation in the aqueous (F,.t.) and polymer (F,at p) phases can be
calculated using eqs 6.14a, 6.15a, and 6.1 0-6.11.
Combining eqs 6.10, 6.11, 6.12, and knowing that vp/vp,,sat(r) equals [M1]/[M1]p,sat(r)
we find: F
In (~) = v ""(r) - v F p, P sat a
(6.18)
6.15b and 6.18 yields:
(6.19)
where qpi,catc stands for the calculated mole ratio of monomer i in the polymer phase at partial
swelling. With known qP, (or fp,) the right-hand term of eq 6.19 can be calculated resulting
in qp;,catc· Continued iteration until abs.(qp,- qpi.catc) reaches a small tolerance value gives the
correct mole ratio of monomer i in the polymer phase.
Based on the model for partial swelling presented in this section, the mole fraction
of monomer i in the polymer phase can be calculated for a certain monomer-water-polymer
Model development 73
mixture. The results of these calculations can be used to describe monomer partitioning at
partial swelling, i.e., in interval III situations in emulsion copolymerization reactions.
6.2.3 Model calculations in emulsion copolymerization.
Since polymerization in emulsions is assumed to occur in the polymer particle phase,
the monomer mole fraction in the polymer phase, fp;, has to be used instead of the overall
monomer mole fraction (f0; MA/(M11 + M~) to calculate the instantaneous copolymer
composition. In the previous two sections, models have been developed to predict the
monomer mole fraction in the polymer phase for a given monomer-water-polymer mixture
at both saturation and partial swelling. Using the models for saturation and partial swelling
a computer program has been written to predict the course of emulsion copolymerization.
A flow diagram of this program is presented in Figure 6.1.
Based on the homo-monomer saturation values of monomers i and j in the polymer
([M;]p.salh), [M1]p,sa,(h)) and aqueous ([M;].,,m(h), [MJ.,, • .(h)) phases it can be determined in
a quite straightforward way whether the model for saturation or partial swelling should be
applied to a given monomer-water-polymer mixture (V., VP, M11, and M;J. From the water
solubility and maximum polymer swellability values combined with recipe conditions, the
monomer mole fractions can be calculated using eqs 6.2-6.8 in the case of saturation
swelling, and eqs 6.9-6.19 and repeated iteration in the case of partial swelling. The
instantaneous copolymerization equation 18•19 (eq 2.2; fp; instead of f;) will give the
copolymer composition in mole fraction of monomer i (F;) as a function of the reactivity
ratios and the mole fraction of monomer i in the polymer particle phase.
Assuming that monomer partitioning equilibrium is maintained despite
polymerization, complete emulsion polymerization can be predicted in the following manner,
provided that small successive conversion steps are taken until complete conversion. The
conversion steps taken need to be small enough to ensure a nearly constant mole fraction
of monomer i in the polymer, and as a consequence an also almost constant copolymer
composition during this conversion step. As a result of polymerization the total monomer
(M;., MJt) and polymer (V po) quantities will change slightly during each conversion step. The
monomer mole fraction in the polymer phase at the next small conversion step can then be
calculated with slightly different monomer and polymer concentrations, again using eqs 6.2-
6.8 for saturation swelling and eqs 6. 9-6.10 for partial swelling. Based on this approach,
prediction is possible of inter alia, fP;' F" [M;]., and [Mj]P as a function of conversion.
74
X:= X +0.01
YES
recalculate Mit , MJ1 , V po for x: = x + 0.01 using eq 2.2
x: =X+ 0.01
NO
recalculate M;1 , Mjt , V po for x: = x + 0.01 using eq 2.2
if x:= I then prediction of emulsion copolymerization as
function of x is complete
Chapter 6
Gpi,in: = qpi,in • C2
Figure 6. 1: Flow diagram of the program used for predictions of emulsion copolymerization. Tol stands for a small tolerance value, CJ and C2 are constants, x is conversion, and qp;,,.1, qP'·"' and qpi,caii· are the mole ratios of monomer i at the end of saturation swelling, and the start value and resulting value of consecutive conversions steps at partial swelling, respectively.
Model development 75
The use of the models presented herein for saturation swelling and partial swelling
only require that the homo-monomer saturation values in the polymer and aqueous phases
are known for a given monomer-water-polymer mixture. Predictions of monomer partitioning
experiments for a given monomer-water-polymer mixture in terms of mole fraction of
monomer i in the polymer phase and based on this predictions of complete emulsion
copolymerizations as a function of conversion now can be made quite easily.
6.3 Results and discussion
Monomer partitioning in latex systems at partial swelling with one or two monomers
can be described by eq 6.18 as can be concluded from Figure 6.2 where monomer
partitioning predictions are successfully compared with experimental results for homo-MA
and MA-V Ac combinations if the experimental error resulting from gas chromatography
is taken into account. Furthermore, from Figure 6.2, it can be concluded that at partial
swelling the aqueous phase is closer to saturation than the polymer phase, i.e. F sat. > F sat p·
Thus, for monomers with a relatively high but limited water solubility a considerable amount
of the monomer can be located in the aqueous phase. Note that the curvature of lines
predicted with eq 6.18 depends upon the volume fraction of polymer at saturation swelling
and therefore also on the maximum swellabilities of monomer in polymer. However, the
difference in volume fraction of polymer at saturation swelling for homo-monomer swelling
of MA compared with V Ac is relatively small (0.3 7 for MA and 0.44 for V Ac ), and
therefore all monomer partitioning results for homo-monomer as well as for co-monomer
experiments can be compared with one theoretical line.
1.00
= .g, 0.80
~ ~ 0.60 0 Q,
~ 0.40 .I :: 0.20
0.00 l!t-:........--r-~--.-~--r--~-.--~-. 0.00 0.20 0.40 0.60 0.80 1.00
% saturation aqueous phase Figure 6. 2: Comparison of the predictions of eq 6.18 (line) with experiments for homo-saturation of MA (D), and two monomer (MA-VAc) experiments at several overall monomer fractions forMA (.1) and VAc (o).
76 Chapter 6
6.3.1 General monomer partitioning considerations.
In this thesis monomer i has been chosen to be the monomer with the higher water
solub~lity. Adding more water to a certain monomer-water-polymer mixture will especially
withdraw monomer i from the polymer phase into the aqueous phase leading to lower values
of the mole fraction of monomer i in the polymer phase. In general this means that by
choosing a monomer-to-water ratio or polymer volume one is able to control the monomer
composition in the polymer particle phase. This is the main issue in the following section.
Two extreme monomer partitioning situations may occur in emulsion polymerization
resulting in a maximum and a minimum value for the mole fraction of monomer i in the
polymer particle phase.
The maximum value of the mole fraction of monomer i in the polymer phase is
reached if all monomer is located in the monomer droplet and polymer particle phases. In
this case, the mole fraction of monomer i in the polymer phase equals the overall mole
fraction of monomer i, i.e., fJ>i,max f01• This will occur at saturation swelling when the
amount of monomer dissolved in the aqueous phase is negligible as compared with the total
amount of monomer (large monomer droplet and polymer particle phases as compared with
aqueous phase) or if the water phase concentration is too low to significantly affect the
monomer amounts within the monomer droplet and polymer particle phases.
The minimum value for the mole fraction of monomer i in the polymer particle phase
is reached when all monomer is dissolved in the aqueous phase. In this case the mole
fraction of monomer i in the aqueous phase equals the overall mole fraction of this
monomer, fa~ = f01• From this mole fraction of monomer i in the aqueous phase, the minimum
mole fraction of monomer i within a hypothetical polymer phase, fpi,min• can be determined
with eqs 6.4a-c if the ratio of the water solubilities of monomer j over monomer i, i.e., if
a = [Mj].,, .. (h)/[M J.,,.,(h) is known. In the absence of polymer the minimum mole fraction
of monomer i in the polymer phase is only a hypothetical quantity. However, if there would
be a small amount of polymer in the monomer-water-polymer mixture, with a negligible
effect on monomer partitioning, the mole fraction in the polymer phase would be very close
to the hypothetical minimum mole fraction. The value of fpi,min strongly depends upon the
a-value as can be seen in Figure 6.3 where it is clearly shown that the difference between
fpi,max and fpl,min is larger for smaller a-values. This fpi.min can be reached only if the monomers
have high water solubilities, if the monomer-to-water ratio is low and if the amount of
polymer phase is too small to affect monomer partitioning.
Model development
1.0
-C+-40. 0.5
0.0 0.0 0.5 1.0
Figure 6.3: The extreme values of the mole fraction of monomer i in the polymer phase (t;,) are given by the maximum, J;,,,max (all monomers in the polymer porticle and monomer droplet phases), and the minimum, J;,;,mm (all monomers in the aqueous phase) monomer mole fraction in the polymer phase for several values of a = [M}a.salh)I[MJa..mlh), a = 0.5; 0.267 and 0.005.
77
For a nonpolymerizing monomer partitioning experiment with an arbitrary monomer
water-polymer mixture, the value of the mole fraction of monomer i in the polymer phase
can be calculated using the relationships presented in the "Theory" section of this chapter
for saturation or partial swelling. Depending on mixture conditions, e.g., monomer-to-water
ratio (M/W) and the polymer volumes (V po), the value for the mole fraction of monomer
i in the polymer phase will vary between fP'·"""' and fp;,min· From Figure 6.3, we can conclude
that the effect of different monomer-water-polymer mixture conditions on monomer
partitioning is the largest for small values of a. Furthermore, in Figure 6.3 the effect of
overall monomer mole feed fractions (f01), on fp;,max and fpl,min and the maximum difference
between this maximum and minimum value for the mole fraction of monomer i in the
polymer phase, i.e., fp;,m"" - fpl,min• can be seen. Note that if a= I there will be no effect of
different monomer-to-water ratios and polymer volumes on the mole fraction of monomer
i in the polymer phase, i.e., fp;,mll>< fpi,min· However, if a= 1, and if the monomer amount
is kept constant, the volume of the droplet phase will decrease with increasing water amount
(i.e., decreasing monomer-to-water ratio) or increasing polymer volume at saturation
swelling. At partial swelling the absolute concentrations of monomers in both the polymer
78 Chapter 6
particle and aqueous phase will decrease with increasing water content (decreasing monomer
to-water ratio} and increasing polymer volume due to dilution effects.
6.3.2 Monomer partitioning of MA-VAc monomer systems.
The effect of different monomer-water-polymer mixture conditions, e.g., the
monomer-to-water ratio and the polymer volume, upon the monomer mole fractions in the
polymer phase can be predicted by the models developed herein. In the MA-V Ac monomer
system, MA will be the monomer with higher water solubility resulting in a ratio of water
solubilities of V Ac and MA of 0.5. The extreme values of the monomer mole fractions in
the polymer phase for MA-VAc with an overall monomer mole fraction ofMA equal to 0.5,
are fp;,max=O.S and fp;,min=0.333 as can be seen in Figure 6.3. For the MA-VAc monomer
system the effect of increasing monomer-to-water ratio in the absence and presence of
polymer at an overall monomer mole fraction of 0.5 was investigated.
If there is no polymer phase present at an overall monomer mole fraction of 0.5 and
if the aqueous phase is kept constant at a volume of V w = I dm3, the effect of different
monomer-to-water ratios on the mole fraction of MA in the hypothetical polymer phase
is the largest, i.e., going from the hypothetical minimum monomer mole fraction at low
monomer-to-water ratios (f~.min
monomer-to-water ratios (f~ ...... )
o.so
0.45
.._.'& 0.40
0.35
0.33) to the maximum monomer mole fraction at high
0.5, as shown in Figure 6.4.
saturation
0.30 '-~-~--.---.....--.--....----....-....--....----. 0.00 0.20 0.40 0.60 0.80 1.00
M/W (gjg)
Figure 6.4: Predictions for saturation and partial swelling of the mole fraction of MA in the polymer phase if;,AvJ as a jUnction of the monomer-to-water ratio (MIW) for the MA-VAc monomer combination at an overall monomer mole fraction of /,,MA = 0.5 in the absence of polymer.
Model development 79
At similar overall monomer mole fractions of 0.5, in the presence of polymer with
a volume of V PO that can swell with MA and V Ac, the minimum value for the mole fraction
·of MA in the polymer phase, ~ 0.33, will not be reached at similar values for the
aqueous phase volume (V w) and the monomer-to-water ratio, due to monomer partitioning
between the polymer and aqueous phase. In Figure 6.5 (Vw = 1 dm3, VPO = 0.05 dm3,
varying M/W) one can see that in the presence of a polymer with volume V PO 0.05 L, the
lowest value for the monomer mole fraction of MA in the polymer phase is indeed higher
than fpMA,min 0.33. The presence of polymer makes the maximum difference in mole fraction
of MA in the polymer phase (t;,i,max - fpi,min) smaller. Furthermore, the saturation swelling
region will start at higher monomer-to-water ratios (Figure 6.4 as compared with Figure 6.5)
in the presence of polymer.
0.50
0.45
..._., 0.40 saturation
0.3S
0.30 L...--+--.----.....----..-----.r-----. 0.00 0.20 0.40 0.60 0.80 1.00
MfW (gig)
Figure 6.5: Comparison of model predictions (line) with experimental (o) values of the mole fraction of MA in the polymer phase (f,uJ for partial and saturation swelling as a function of the monomer-to-water. ratio (MIW) for the MA-VAc monomer combination at overall fractions of MA of /.,MA 0.5, in the presence of polymer with a volume of 50 cm3 polymer I dm1 water.
The effects of different monomer-water-polymer mixtures, i.e., different monomer-to
water ratios and polymer volumes, on the monomer mole fraction in the polymer phase, are
based on withdrawing monomer from the monomer droplet and polymer particle phase into
the aqueous phase. Therefore, changing of these monomer-water-polymer mixture conditions
will have the largest effect on the monomer mole fraction in the polymer if only one of the
monomers has a relatively high but limited homo-monomer saturation concentration in the
aqueous phase. For monomer systems in which monomer i is the more water soluble
monomer, the effects of increasing monomer (at constant volumes of polymer and water),
polymer (at constant volumes of water and monomer) and water (at constant volumes of
80 Chapter 6
monomer and polymer) volumes on the mole fraction of monomer i in the polymer phase
at constant overall monomer mole fractions are combined in Table 6.1. The increasing,
decreasing, or constant mole fraction of monomer i in the polymer phase as a result of
different water (V w), polymer (V po) and monomer (M11 and M.J are represented in Table 6.1
by +,, • and o respectively.
Table 6.1 The efficts of increasing water, polymer or monomer volumes on J;,,; - = decrease, + = increase and o = no effect (constant fo)
constant fo; at saturation swelling partial swelling
increasing volume of: fpi,sal fpi
water: Vw -/o monomer: M;t, M;t + + polymer: V po 0 +
It is trivial that increasing the volume of the aqueous phase at partial swelling in the absence
of polymer in the monomer-water-polymer mixture will have no effect on the, in this case
hypothetical mole fraction of monomer i in the polymer phase (see also Figure 6.4}, while
in the presence of polymer a decrease in the mole fraction of monomer i in the polymer
phase will appear for an increased volume of the aqueous phase (see also Figure 6.5).
Furthermore, in Table 6.1 it is shown that increasing the polymer volume at saturation
swelling will lead to more saturated polymer phase and a smaller volume of monomer
droplet phase leaving the mole fraction of monomer i in the polymer phase unaffected.
However, one should realize that, starting at saturation swelling, a large increase in polymer
volume will lead to a shift from saturation towards partial swelling resulting in a constant
mole fraction of monomer i in the polymer phase at saturation swelling followed by an
increase in mole fraction of monomer i in the polymer phase at partial swelling. Using the
results represented in Table 6. I one can see the effects on the mole fraction of monomer
i in the polymer phase of different monomer, polymer, and water volumes and combinations
of these quantities such as monomer-to-water ratios at constant overall monomer mole
fractions. Knowing whether the mole fraction of monomer i in the polymer phase will
increase or decrease, predictions of monomer concentrations in the polymer phase and
aqueous phase can be made using eqs 6.2a-b and 6.3a-b at saturation swelling and 6.14a-b
and 6.15a-b at partial swelling.
The models developed in this chapter for saturation and partial swelling are compared
Model development 81
with experimental monomer partitioning results for MA-VAc in Figure 6.5. From the good
agreement between predictions and experiments it can be concluded that the models are
. capable of correctly predicting monomer mole fractions in the polymer phase for static
monomer partitioning experiments including a certain polymer volume.
From chapter 5 we known that the monomer mole fraction is equal in the polymer
and monomer droplet phase, fpi,sat = fdi,sat· The maximum swellability of monomer in the
polymer is determined by an equilibrium between the interfacial tension and the mixing of
monomer with polymer. Nomura et a/.20 found that the maximum swellabilities were
independent of copolymer composition for MMA-S. However, Maxwell et a/. 14 and van
Doremaele et a/. 4 showed that copolymer composition does have an effect on the homo
monomer swellabilities of monomer in the polymer phase for MA-S. Van Doremaele4
concludes, however, that this small effect of copolymer composition on homo-monomer
saturation values is negligible in practical situations. Furthermore, Maxwell et a/.21 pointed
out that temperature effects upon monomer partitioning are within experimental error for
MA-S in the temperature range from 20-45°C. However, it is known that water phase
concentrations of monomers are temperature dependent. From model predictions and theory
it can be concluded that at partial swelling the water solubilities (i.e., homo-monomer
saturation concentrations in the aqueous phase), the ratio of the water solubilities of both
monomers (a-value), the maximum swellabilities in the polymer phase (homo-monomer
saturation concentrations in the polymer phase) of monomers i and j, and the presence and
volume of polymer, will affect the monomer mole fraction in the particle phase. The point
where saturation swelling should be used instead of partial swelling depends on the same
parameters - namely the water solubilities, the maximum swellabilities, and the polymer
volume. At saturation swelling, the water solubility of the monomers and the ratio of these
water solubilities (a-value) affect the monomer mole fraction in the polymer phase, while
the maximum swellabilities of monomer in the polymer phase will only affect the absolute
concentrations of monomers i and j in the polymer phase and the volume of the monomer
droplet phase, leaving the monomer mole fraction in the polymer phase unchanged. Since
equal monomer mole fractions are found in the monomer droplet and polymer particle phase
at saturation swelling, i.e., fp; = fd;• the use of polymer volume in the case of saturation
swelling only affects the volume of the polymer and the monomer droplet phases and
certainly not the monomer mole fraction in the polymer phase. This result, already
represented in Table 6.1 is also illustrated by the similarity between Figures 6.4 and 6.5 at
saturation swelling.
82 Chapter 6
6.3.3 Prediction of emulsion copolymerization composition.
To predict the course of emulsion polymerizations using the models for saturation
and partial swelling presented herein, the homo-monomer saturation values in the polymer
and aqueous phases and the reactivity ratios for the chosen monomer system must be known.
For the MA-V Ac monomer combination, the reactivity ratios can be found in the
literature22 (r~ = 6.3 ± 0.4, rvAc = 0.031 ± 0.006). The homo-monomer saturation values
in the polymer and aqueous phase are listed in Table 3.5. In predictions of complete
emulsion copolymerization reactions, it is important to have accurate data on homo-monomer
saturation data and reactivity ratios since the calculations are sensitive to the values of these
quantities. Typical confidence intervals for homo-monomer saturation swelling are in the
range of 5-10% accuracy, while the accuracy in reactivity values strongly depends on the
calculation method used23 in combination with the number of experiments, and also on the
accuracy of the experimental method used. The influence of deviations in model parameters
will be discussed in the sensitivity analysis presented in the appendix.
For reactions with high monomer-to-water ratios starting in interval II, the homo
monomer saturation concentrations in the polymer phase only affect the absolute monomer
concentrations in the polymer phase leaving the monomer mole fraction in the polymer phase
(fp; . ..J unaffected. The large effect of the o:-value can be taken into account when using
homo-monomer saturation values in the aqueous phase determined at reaction temperature
(values are listed in Table 3.5). Predictions of the course of emulsion polymerization in
terms of monomer mole fractions in the polymer phase as a function of conversion, or
numbers of mole of monomers i and j as a function of conversion result in important
composition drift data. Since gas chromatography of reaction samples will give overall
values of the mole fraction of monomer i, experimental values for this overall monomer
mole fraction as a function of conversion will be compared with model predictions.
For the MA-V Ac ·monomer system experimental and predicted results of the overall
monomer mole fraction as a function of conversion are compared in Figure 6.6 (initial
reaction recipe is shown in Table 6.2). As can be seen by the strong decrease in the overall
monomer mole fraction with increasing conversion, there is strong composition drift. This
could be expected since the reactivity values in MA-V Ac copolymerizations are very far
apart (by a factor of200). Gas chromatography yields, as well as the overall monomer mole
fractions, the total moles in the reaction mixture, i.e., MMA.< and MvAc.1, as a function of
conversion. The number of moles as a function of conversion are presented in Figure 6.7.
Again a strong composition drift occurs leading to faster reaction ofMA (stronger decrease)
Model development 83
due to the higher reactivity ratio of MA Table 6.2 MA-VAc recipe for a kinetic batch
(rMA = 0.63) as compared with VAc (rvAc polymerization with a monomer-to-water ratio (MIW) of 0.1.
= 0.03). At 70% conversion the MA has
completely disappeared resulting m
homopolymerization of V Ac.
From the good agreement shown
in Figures 6.6 and 6.7 between model
predictions and experimental results for
the overall monomer mole fraction (f0MA)
and the numbers of moles (MMA,t and
Ingredients (g)
MA
VAc
Water
NaPS
SDS
Na2C03
Kinetic run
45
45
917.4
0.219
1.313 0.098
M_,,) as a function of conversion, it can be concluded that the relationships used to predict
the monomer mole fractions in the polymer phase are indeed capable of correctly predicting
the course of emulsion polymerization for saturation swelling and partial swelling. Note that
the reactivity ratios and the homo-monomer saturation values used for model predictions
are accurate enough to obtain good agreement between experimental results and model
predictions.
Comparison of model predictions of emulsion copolymerization composition as a
function of conversion with experimental results for the MA-Ind monomer system show
good agreement as can be seen in Figure 7.7 (initial reaction recipes are shown in Table 7.1).
From this, it can be concluded that the above described approach can be used not only for
MA-V Ac, but also for other monomer systems. The reactivity ratios of the monomer system
MA-Ind (rMA = 0.92 and r100 = 0.086) are less far apart than those of MA-VAc (a factor of
10 for MA-Ind as compared with a factor of200 for MA-VAc) leading to less composition
drift. The large effect of different monomer-to-water ratios on composition drift shown in ,._ Figure 7.7 is typical for a system like MA-Ind where one of the monomers (MA) is very
water soluble. This effect will be discussed in more detail in chapter 7.
From the good agreement shown in Figures 6.6, 6.7 and 7.7 between experimental
results and model predictions it can be concluded that the models for saturation and partial
swelling developed in this chapter provide a good description of the course of emulsion
copolymerization. Furthermore, it can be concluded that the reactivity ratios (Table 3.7) and
homo-monomer saturation values (Table 3 .5) used in the model predictions of MA-V Ac and
MA-Ind emulsion copolymerizations were determined accurately enough to obtain good
agreement between predicted and experimental results.
84
0.60
o.so
0.40
~0.30 ..... 0.20
0.10
0.00 1--.----,,.-------.---....-'+-<,..... ...... ~~ 0.00 0.20 0.40 0.60 0.80 1.00
Conversion
Chapter 6
Figure 6. 6: Comparison of predictions (line) with experimentally determined values (o) of the overall mole fraction of MA (f~ as a function of conversion for the monomer system MA-VAc (Initial recipe: MIW 0.1, Vpo = O,f.MA = 0.5).
::::: 0
0.60
o.so
a o.4o .._
-~ 0.30 :I ,0.20
0.10
0.00 L-~-...----.-----...__;:--------4P 0.00 0.20 0.40 0.60 0.80 1.00
Conversion
Figure 6. 7: Comparison of predictions for the number of moles of MA and VAc (lines) with experimentally determined results for MA (o) and VAc (D) as a function of conversion (Initial batch recipe: MIW = 0.1, V"', = 0, f.,MA 0.5).
6.4 Conelusions
Combining thermodynamically-based monomer partitioning relationships for
saturation14 and partial swelling 15 with mass balance equations results in a model for
saturation and a model for partial swelling, in either case predicting the mole fraction of a
certain monomer i in the polymer phase. The effect of monomer-to-water ratio and polymer
volume on the monomer mole fraction in the polymer phase can be well predicted with the
Model development 85
relationships described in this chapter.
The ratio of homo-monomer saturation concentrations in the aqueous phase of
monomer j over monomer i (monomer i being the more water soluble monomer) has shown
to play a key role in determining the resulting mole fraction of monomer i in the polymer
phase.
With the models presented in this chapter it is possible to predict emulsion
copolymerization in terms of monomer mole fractions within the particle phase (composition
drift) and absolute monomer concentrations as a function of conversion. Predicted emulsion
polymerization behaviour compares quite acceptably with experimental results forMA-V Ac
and MA-Ind especially when considering that these predictions were made without any
adjustable parameters. The approach presented in this chapter is valid for all monomer
systems that have equal monomer mole fractions in the polymer and droplet phase at
saturation swelling. It has been shown experimentally 14•15 and theoretically17 that this
condition is met for several monomer systems. Possible exceptions are monomers that do
not swell their polymer and monomers that are fully miscible with water. It must be realized
that the approach presented here is very convenient since it only requires the homo-monomer
saturation values in the polymer and aqueous phase, which can easily be obtained from
experiments. This means, the copolymer composition in a batch emulsion copolymeriza!ion
can be predicted, a priori, without the use of any adjustable parameters!
86 Chapter 6
Appendix: sensitivity analysis
A-6.1 Introduction
In chapter 6 a model has been developed capable of predicting absolute monomer
concentrations and their ratios in the polymer, aqueous, and monomer droplet phases as a
function of conversion in batch emulsion copolymerizations. This model will be referred
at as "the model" in the rest of this thesis. In this appendix the sensitivity of model
predictions of composition drift toward deviations up to 1 0% in all model parameters is
estimated using the monomer combination MMA-S as an example.
Assuming the formation of homogeneous particles, model predictions can be
performed if the reactivity ratios, water solubilities, maximum swellabilities, monomer and
polymer densities, and the recipe conditions (monomer amounts and water volume) are
known. Although the model has been shown to give good agreement between theory and
experiments,24 it is of great importance to know the sensitivity of the model predictions
to the various parameters. For this reason, this appendix investigates the effects of deviations
in water solubilities, swellabilities, reactivity ratios, and monomer and polymer densities on
the predicted course of emulsion copolymerization in terms of composition drift and absolute
monomer concentrations. The effect on copolymer composition can be seen by studying the
change of the monomer mole fraction in the polymer phase for different parameter values
as a function of conversion. Note that any effects of model parameters on the monomer mole
fraction in the polymer phase can be linked directly with copolymer composition by the well
known instantaneous copolymer equation (eq 2.2). 18'19 The MMA-S monomer system was
selected since it has been the subject of several investigations, l,20.2S,l6.27
•28
•29
·3ti.JI.32
resulting in many known parameters.
For model predictions of MMA-S, amongst others, the maximum swellability and
water solubility need to be known. Comparing results of Nomura et al. 20 who found that
the maximum swellabilities of S and MMA in the copolymer MMA-S were independent
of the copolymer composition at so•c, with results of other investigators 33•4 indicates that
maximum swellabilities are temperature independent in the range of20-so•c. Based on these
data we adopted for the present sensitivity analysis the copolymer independent maximum
swellabilities: [MMA]p.sat 6.3 ± 0.6 mol/dm3 and [S]p.sat 5.5 ± 0.6 mol/dm3• These values
were validized by Noel et a!. by comparing monomer partitioning results with conductivity
Appendix: sensitivity analysis 87
measurements.24 All other model parameter values were either found in the literature or have
been determined experimentally at 40"C by using densimetry for density values and gas
chromatography analysis of monomer-saturated water for the determination of the water
solubility of MMA. 24 All standard parameters used for model predictions are listed in Table
A-6.1.
The sensitivity of model predictions is estimated for deviations up to I 0% in the
model parameters shown in Table A-6.1 (total deviation is 20%). The 10% deviation in
model parameters is selected since it represents the estimated precision in some of the model
parameters. For convenience this 10% deviation has been used for all model parameters that
have been the subject of this sensitivity analysis.
Table A-6.1: Model parameters used for model predictions of MMA-S copolymerizations at 4(J'C
model parameter MMA s swellability (mol/dm 3) 6.3 5.5
water solubility (mol/dm3) 0.12. 3.8•10'3 b
monomer density (kg/dm3) 0.918. 0.887<
polymer density (kg/dm3) l.l49" 1.046c
reactivity ratiosd 0.46 0.523
A-6.2 Results and discussion
a these values were determined experimentally by densimetry or gas chromatography. b value determined by Lane et al. 34
c values determined by Patnode et al.Js d values determined by Fukuda et a/. 26
On behalf of the sensitivity analysis, a standard recipe was adopted for the model
predictions of MMA-S copolymerizations with a monomer-to-water ratio of 0.2 and an
overall monomer mole fraction of fo,MMA = 0.5 (SM4: Tables A-6.2 and A-6.3). All possible
deviations in model predictions resulting from the use of other model parameters were
compared with this standard recipe. The deviating model parameters are shown in Tables
~-6.2 and A-6.3. Deviations in changing homo-monomer saturation concentrations and
reactivity ratios are expected to depend on the monomer-to-water ratio. For this reason, the
effects of deviations in model parameters on the mole fraction of MMA in the polymer
phase, fp.MMA> is also studied as a function of changing monomer-to-water ratios (SMI-SM6}.
88 Chapter 6
Table A-6.2: Standard (SM4) and deviating model parameters (SM1-SM12) used to perform a sensitivity analysis of the theoretical batch emulsion copolymerization model: the sensitivity ofhomo-monomer saturation concentrations, monomer-to-water ratios and overall monomer mole fractions are tested All other parameters as in Table A-6.1.
name MJW fo,MMA [MMA].,,.,(h) [SJ .... ,(h) ( ·1 o·3) [MMA]p,sat(h) [ s ]p,sat(h)
SM1 0.02 0.5 0.12 3.8 6.3 5.5 SM2 0.05 0.5 0.12 3.8 6.3 5.5 SM3 0.1 0.5 0.12 3.8 6.3 5.5 SM4 0.2 0.5 0.12 3.8 6.3 5.5 SM5 0.4 0.5 0.12 3.8 6.3 5.5
SM6 1.0 0.5 0.12 3.8 6.3 5.5
SM7 0.2 0.5 0.132 3.4 6.3 5.5 SM8 0.2 0.5 0.108 4.2 6.3 5.5
SM9 0.2 0.5 0.12 3.8 6.93 6.05
SMIO 0.2 0.5 0.12 3.8 5.67 4.95
SM11 0.2 0.25 0.12 3.8 6.3 5.5 SM12 0.2 0.75 0.12 3.8 6.3 5.5
Table A-6.3: Standard (SM4) and deviating model prediction parameters (SM13-SM18) used to perform a sensitivity analysis of the theoretical model: the sensitivity of reactivity ratios (rMMA and r.J and monomer and polymer densities (SM13-SM18) are tested All other parameters as in Table A-6.1.
name rMMA rs PMMA,m Ps,m PMMA,p Ps,m
SM4 0.46 0.523 0.918 0.886 1.149 1.046
SM13 0.506 0.471 0.918 0.886 1.149 1.046
SM14 0.414 0.575 0.918 0.886 1.149 1.046 SM15 0.46 0.523 0.826 0.797 1.149 1.046
SM16 0.46 0.523 1.010 0.975 1.149 1.046
SM17 0.46 0.523 0.918 0.886 1.264 1.151
SM18 0.46 0.523 0.918 0.886 1.034 0.941
A-6.2.1 Homo-monomer saturation concentrations
The effects of deviations up to 10% in homo-monomer saturation concentrations in
both the aqueous phase (water solubility) and the polymer phase (swellability) were
investigated by comparing model predictions with deviating model parameters with the
standard prediction (SM4). For this purpose the water solubility of both monomers was
varied separately and also simultaneously. The predictions leading to the strongest deviations
Appendix: sensitivity analysis 89
in composition drift and/or absolute monomer concentrations are depicted in Table A-6.2
(SM7 and SM8). A similar approach was adopted for deviations in the maximum
swellabilities of monomer in the polymer phase (Table A-6.2: SM9 and SMIO). The
predictions of the monomer mole fraction in the polymer phase do not noticeably depend
on the 10% deviation in homo-monomer saturation concentrations in both the polymer and
the aqueous phase (all predicted curves coincide; SM4, SM7, SM8, SM9, and SMIO). The
effects of changing homo-monomer saturation concentrations (both aqueous and polymer
particle phases) on the absolute monomer concentration can be seen in Figure A-6.1.
7 1------'~t.!Wt.-.,._
61----.....::::; .......
s J 4
! 3
2
0 ~----r-----r-----~----~--~ 0.00 0.20 0.40 0.60 0.80 1.00
Conversion
Figure A-6.1: The absolute monomer concentration in the polymer phase is depicted as a function of conversion for model predictions in which the water solubility and the maximum swellabi/ity was changed (SM4 and SM7-SMJO: the model parameters can be seen in Table A-6.2).
Water solubility: The negligible effect of changing water solubility values on the
predictions of monomer mole fractions and total monomer concentration in the polymer
phase as a function of conversion is a result of the negligible amount of monomer located
in the aqueous phase ( 6 g) as compared to the total monomer amount (200 g). Increasing
the water solubility value of the more water soluble monomer will lead to an increase of
the total amount of monomer dissolved in the aqueous phase. However, the maximum
experimental difference of 10% will not make the amount of monomer located in the
aqueous phase considerable compared to the total amount of monomer present in the
predicted reaction.
Swellability: The effects of varying swellabilities on model predictions of composition drift
and absolute monomer concentrations in the polymer phase (Figure A-6.1) can be described
by dividing the model prediction into a saturated interval II region and an unsaturated
interval III region. Since the monomer mole fractions in the polymer particle phase and
90 Chapter 6
monomer droplet phase are equal, changing swellability values will only affect the total
monomer concentration in the polymer phase and the amount of monomer droplet phase at
saturation swelling. This results in monomer mole fractions in the polymer phase totally
independent of the swellability values of both monomers in the polymer phase at saturation
swelling.33 In other words, at saturation swelling composition drift is not at all influenced
by maximum swellability values.
At partial swelling it has been shown that monomer partitioning between the polymer
particle and aqueous phases depends only on the maximum swellability of the monomers
in the polymer phase. Different maximum swellabilities will affect the curvature of the
relationship between the degree of saturation of the aqueous and polymer phases. In Figure
A-6.2, the relation between the degree of saturation in the aqueous and polymer phases is
presented for several maximum swellability values, illustrating that even the largest
deviations in maximum swellability have only a small effect on the curvature of the line.
Furthermore, the different curvature can lead to deviating monomer mole fractions only if
the amount of monomer in the aqueous phase cannot be neglected compared to the total
monomer amount. For MMA-S predictions with monomer-to-water ratios of MIW = 0.2,
the amount of monomer in the aqueous phase is negligible as compared with the total
amount of monomer (6 g to 200 g). From this it can also be concluded that at partial
swelling the maximum swellability has a negligible effect on composition drift.
1.00
0.80
... 0.60
J 0.40
0.20
0.00 0.00 0.20 0.40 0.60 0.80 1.00
F .... Figure A-6.2: The degree of saturation in the polymer (F,01 ,) is depicted as a function of the degree of saturation in the aqueous phase (F sm J. The lines depict the maximum swellability of MMA (6.3 molldm3
), S (5.5 molldm3), and the
minimum and maximum swellabilities on the MMA and S (minimum: 4.95 mol!dm3 and maximum: 6.93 molldm3
) taking 10% deviation into account.
From Figure A-6.1 it can be seen that the maximum swellability of monomers in the
polymer phase will affect the absolute monomer concentration in the polymer particle phase
Appendix: sensitivity analysis 91
at saturation swelling. Although the absolute monomer concentrations are quantities that are
not important for composition drift (only the mole fraction in the polymer is relevant), it
is an important parameter affecting polymerization rates at saturation swelling. As can be
seen in Figure A-6.1, the disappearance of droplets at the end of interval II is strongly
affected by the maximum swell ability. At partial swelling, the monomer concentration in
the polymer particle decreases with conversion in an approximately linear relationship. At
partial swelling the use of different swellability values does not lead to large differences
between the absolute monomer concentrations in the polymer phase as a function of
conversion.
It should be noted that the deviations in monomer mole fraction and absolute
monomer concentrations in the polymer phase depend on the monomer-t~rwater ratio and
on the water solubility of the selected monomer combination. In case the amount of
monomer in the aqueous phase is not negligible as compared with the total amount of
monomer, the monomer mole fraction in the polymer phase will deviate more from the
standard prediction. This implies directly that, for monomer combinations with lower water
solubility values as compared with MMA (< 0.12 mol/dm3), the effect of water solubility
on composition drift can be neglected. Furthermore, it can be expected that, for monomers
with higher water solubility values than MMA, the monomer amount in the aqueous phase
may no longer be negligible as compared to the total monomer amount. In these cases the
effect of water solubility on composition drift may be significant even at higher monomer-ttr
water ratios.
5
""' * 4 ._,
j 3
8 8 2
'::1 .l!l > &
Figure A -6. 3: The predicted maximum deviations in the monomer mole fraction in the polymer phase resulting from different water solubility (top line) and swellability (lower line) values are depicted as a function of the monomer-towater ratio.
92 Chapter 6
For the monomer combination MMA-S the deviations in monomer mole fraction and
absolute monomer concentrations in the polymer phase as a function of the monomer-to
water ratio are estimated by comparison between predictions with standard model parameters
and deviating parameters. From Figure A-6.3 it can be seen that the maximum deviations
in predicted monomer mole fractions are larger at low monomer-to-water ratios. Note that
the effect of deviations in the maximum swellability can be neglected even at low monomer
to-water ratios, while the effect of deviations in water solubility can no longer be neglected
for monomer-to-water ratios below MIW = 0.02.
Comparing standard with deviating model parameters results in large, significant
deviations in the absolute monomer concentrations in the polymer phase at saturation
swelling, as can be seen in Figure A-6.4. Note, however, that these large deviations in
monomer concentration in the polymer phase are only present at saturation swelling. At the
end of interval II these deviations will quickly reduce to negligible effects of maximum
swellability values on the maximum concentrations in the polymer phase. The deviations
in monomer concentrations in the polymer phase caused by deviating water solubilities
increase with decreasing monomer-to-water ratios (Figure A-6.4). At monomer-to-water
ratios lower then MIW = 0.1 these deviations can no longer be neglected.
10
€ 8 ! ~ 6
8 c:l 0
4 ·= .. ·;;: 2 0
Q
M/W
Figure A-6.4: The predicted maximum deviations in the absolute monomer concentration in the polymer phase resulting from diffirent water solubility (lower line) and swellability (top line) values are depicted as a function of the monomer-to-water ratio.
The most important conclusions from the above discussion about the effect of
deviating homo-monomer saturation concentrations on model predictions are:
In MMA-S copolymerization reactions the effect of changing water solubilities on
the monomer mole fraction in the polymer phase, i.e, on composition drift and
Appendix: sensitivity analysis 93
copolymer composition distributions, is limited to low monomer-to-water ratios (MIW
< 0.02), since in these cases the amount of monomer located in the aqueous phase
is not negligible compared to the total amount of monomer.
2 Composition drift in copolymerization reactions is virtually independent of the
maximum swellability of monomer in polymer for monomer systems in which the
monomer mole fractions in the polymer and monomer droplet phase at saturation
swelling are equal.
3 In MMA-S copolymerizations, the effect of deviations in water solubility on the
absolute monomer concentrations is limited to low monomer-to-water ratios (MIW
< 0.1).
4 The maximum swellability will have a large effect on the absolute monomer
concentrations in the polymer phase.
The most important aim of the model described in Chapter 6 is the prediction of composition
drift occurring in batch emulsion copolymerization reactions. Taking this into account, it
should be noted that conclusions 3 and 4 are not relevant since the absolute monomer
concentrations will only affect the polymerization rate, leaving composition drift unchanged.
A-6.2.2 Reactivity ratios
The effect of deviations up to 1 0% in reactivity ratios on the predicted monomer mole
fraction increases with increasing conversion, as can be seen in Figure A-6.5.
0.80
0.70
~ 0.60 ,J
0.40 '-------..,,....-----.---....----.---~ 0.00 0.20 0.40 0.60 0.80 1.00
Conversion
Figure A -6.5: The monomer mole fraction in the polymer phase is depicted as a function of conversion for several reactivity ratios. The model parameters of the reactions represented SM4, SM13 and SM14 can be seen in Table A-6.3.
94 Chapter 6
Due to small deviations in consecutive conversion steps (of 1%) taken in the model
prediction, accumulation of the deviation occurs leading to the largest deviations at 1 00%
conversion. Note that although larger conversion steps would reduce the accumulation of
small deviations, this would make the approximation of constant monomer and copolymer
composition during that conversion step dubious. Changes of 1 0% in only one of the
reactivity ratios will already lead to deviations of 5% at 90% conversion and to deviations
of l 0% at I 00% conversion. Deviations in both reactivity ratios may even double the
deviations in monomer mole fractions in the polymer phase. The reactivity ratios are,
therefore, the most important parameters for model predictions of composition drift. This
is in sharp contrast with the negligible effect of deviations in reactivity ratios on the total
monomer concentration in the polymer phase(< 2%). This is probably due to the relatively
small difference in maximum swellability values of MMA and S. Performing similar model
predictions -at different overall monomer mole fractions results in approximately the same
deviations in monomer mole fractions and absolute monomer concentrations in the polymer
phase, as could be expected since the reactivity ratios are an intrinsic property of the
copolymer system.
A-6.2.3 Monomer and polymer densities
Recipe conditions, such as the amount of monomers and the volume of the aqueous
phase, are known within small deviations of I%. A sensitivity analysis shows that both
composition drift and absolute monomer concentrations in the polymer phase are not
significantly affected by these small deviations, leading to experimentally inobservable
differences. Other important parameters needed for model predictions are the density values
of both monomers and homo-polymers participating in the simulated batch emulsion
polymerization. These density values are often known in the literature within a small
reliability interval of approximately I%. A sensitivity analysis of small errors of I% on both
the monomer and polymer densities showed that here also predictions of composition drift
and absolute monomer concentrations are within experimental error. For monomers of which
the monomer and polymer densities are not known, a rough estimation of both values already
results in reliable predictions of composition drift. This was concluded from model
predictions in which first the monomer and then the polymer densities were changed with
10"/o (Table A-6.3: SM15-SM18), resulting in almost identical monomer mole fractions as
a function of conversion. The effects of changing monomer and polymer densities on the
absolute monomer concentrations in the polymer phase can be seen in Figure A-6.6,
Appendix: sensitivity analysis 95
indicating that the predicted end of interval II is influenced by the monomer and polymer
densities. The maximum deviations in the absolute monomer concentrations in the polymer
phase resulting from different monomer and polymer density values are approximately 6%
(at ca. 40% conversion) and 8% (at 100% conversion) for deviating monomer and polymer
densities respectively.
7
61----~"""""./
s ! 4
!3 2
1
0~--~----~----~--~----~
0.00 0.20 0.40 0.60 0.80 1.00 Conversion
Figure A-6.6: The absolute monomer concentration in the polymer phase is depicted as a jUnction of conversion for model predictions performed with deviating monomer and polymer density values. The model parameters of the reactions represented SM4 and SMJ5 to SM18 can be seen in Table A-6.3.
A-6.3 Conclusions
From the sensitivity analysis it can be concluded that composition drift predicted in
the modelling of batch emulsion copolymerizations strongly depends on the reactivity ratios.
Due to accumulation of small deviations in consecutive conversion steps, the final deviation
at high conversion (> 90%) then can no longer be neglected. The effect of water solubility
of the monomers on composition drift is significant only when the amount of monomer
dissolved in the aqueous phase cannot be neglected as compared with the total monomer
amount. For the monomer combination MMA-S, this effect becomes important only at very
low monomer-to-water ratios (< 0.02). For monomer combinations with water solubilities
lower than MMA ( < 0.12 mol/L) this effect of water solubility on composition drift can be
neglected, whereas this effect may be significant even at higher monomer-to-water ratios,
for monomers with higher water solubility values. The effects of maximum swellability
values and monomer and polymer densities on composition drift can usually be neglected.
96 References
1. M. Nomura, K. Fujita, Macromol. Chern., Suppl., 10/11, 25 (1985) 2. M. Nomura, I. Horie, M. Kubo, K. Fujita, J. Appl. Polym. Sci., 37, 1029 (1989) 3. G.H.J. van Doremaele, A.H. van Herk, A.L. German, Polym. Int., 27, 95 (1992) 4. G.H.J. van Doremaele, F.H.J.M. Geerts, H.A.S. Schoonbrood, J. Kurja, A.L. German,
Polymer, 33, 1914 (1992) 5. G.H.J. van Doremaele, H.A.S. Schoonbrood, J. Kurja, A.L. German, J. Appl. Polym.
Sci., 45, 957 (1992) 6. M.J. Ballard, D.H. Napper, R.G.Gilbert, J. Polym. Sci., Polym. Chern. Ed., 19, 939
(1981) 7. J. Guillot, Makromol. Chern., Suppl, 10/11 235 (1985) 8. J. Forcada, J. M. Asua, J. Polym. Sci., Polym. Chern. Ed, 28, 987 (1990) 9. M. Morton, S. Kaizermann, M.W. Altier, J Colloid Sci., 9, 300 (1954) 10. J.L. Gardon, J. Polym. Sci., Polym. Chern. Ed, 6, 2859 (1968) 11. J. Ugelstad, P.C. Mork, H.R. Mfutakamba, E. Soleimany, I. Nordhuus, R. Schmid,
A. Berge, T. Ellingsen, 0. Aune, K. Nustad, in Science and Techno/ow o(Polymer Colloids, Vol.l, G.W. Poehlein, R.H. Ottewill, J.W. Goodwin, Eds., NATO ASI Series, 1983
12. J. Guillot, Acta Polym., 32, 593 (1981) 13. C.M. Tseng, M.S. El-Aasser, J.W. Vanderhoff, Org. Coat. Plast. Chern., 45, 373
(1981) 14. I.A. Maxwell, J. Kurja, G.H.J. van Doremaele, A.L. German, Makromol. Chern., 193,
2065 (1992) 15. L.F.J. Noel, I.A. Maxwell, A.L. German, Macromolecules, 26, 2911 (1993) 16. L.F.J. Noel, W.J.M. van Well, A.L. German, to be submitted 17. I.A. Maxwell, L.F.J. Noel, H.A.S. Schoonbrood, A.L. German, Makromol.
Chern., Theory Simul., 2, 269 (1992) 18. T. Alfrey, G. Goldfmger, J Chern. Phys., 12, 205 (1944) 19. F.R. Mayo, F.M. Lewis, JAm. Chern. Soc., 66, 1594 (1944) 20. M. Nomura, K. Yamamoto, I. Horie, K. Fujita, M. Harada, J. Appl. Polym. Sci., 27,
2483 (1982) 21. I.A. Maxwell, J. Kurja, G.H.J. van Doremaele, A.L. German, B.R. Morrison,
Makromol. Chern, 193, 2049 (1992) 22. N.G. Kulkarni, N. Krishnamurti, P.C. Chatterjee, M.A. Sivasamban, Makromol.
Chern., 139, 165 (1970) 23. F.L.M. Hautus, H.N. Linssen, A.L. German, J Polym. Sci., Polym. Chern. Ed, 22,
3487 (1984) 24. L.F.J. Noel, R.Q.F. Janssen, W.J.M. van Well, A.L. German, to be submitted 25. H.K. Mahabadi, K.F. O'Driscoll, J Macromol. Sci, Chern. Ed, Al1(5), 967 (1977) 26. T. Fukuda, Y -D Ma, H. Inagaki, Macromolecules, 18, 17 (1985) 27. T. Fukuda, Y-D rna, H. Inagaki, Makromol. Chern., Rapid Commun., 8, 495 (1987) 28. T.P. Davis, K.F. O'Driscoll, M.C. Piton, M.A. Winnik, J Polym. Sci., Polym. Letters,
27, 181 (1989) 29. K. O'Driscoll, J. Huang, Eur. Polym. J, 7/8, 629 (1989) 30. T.P. Davis, Polym. Comm., 31, 442 (1990) 31. I.A. Maxwell, A.M. Aerdts, A.L. German, Macromolecules, 26, 1956 (l993) 32. J. Schweer, Makromol. Chern., Theory Simul., 2, 485 (1993) 33. A.M. Aerdts, M.M.W.A. Boei, A.L. German, Polymer, 34, 574 (1993) 34. W.H. Lane, Ind. Eng. Chern. Anal. Ed., 18, 295 (1946) 35. W. Patnode, W.J. Schreiber, J Am. Chern. Soc., 61, 3449 (1939)
Monomer-to-water ratios as a tool 97
Chapter 7 Monomer-to-water ratios as a tool
in controlling emulsion copolymer composition
The methyl acrylate-indene system
Abstract: Most copolymerizations typically exhibit drifting copolymer composition as a function of conversion. Reducing this so-called composition drift will lead to a decrease in chemical heterogeneity of the copolymers formed. For monomer systems in which the more water soluble monomer is also the more reactive one, theory predicts that composition drift in batch emulsion copolymerization can be reduced or even minimized by optimizing the monomerto-water ratio. To verify these theoretical considerations, emulsion copolymerizations have been performed with varying monomer-to-water ratios, for the monomer combination MA-Ind. This monomer combination bas been chosen as the model system since it meets the basic requirements needed to obtain minimum composition drift. From the good agreement between experiments and theoretical predictions for MA-Ind, it was concluded that control and even minimization of composition drift in batch emulsion copolymerization for monomer systems in which the more water soluble monomer is also the more reactive is indeed possible by adjusting the initial monomer-to-water ratio of the reaction mixture.
7.1 Introduction
Composition drift occurring in batch emulsion copolymerization will lead to
chemically heterogeneous copolymers. To control composition drift, semi-continuous
emulsion copolymerization processes have been developed. The various addition strategies
used in semi-continuous processes include (1) the addition of a given monomer mixture at
a constant rate lower than the polymerization rate (starved conditions) '·v·4•5
•6
•7
•8
•9 and
(2) the addition of monomer(s) at an optimal addition profile with addition rates higher than
the polymerization rate (flooded conditions). 10•11
•12
•13
•14 Disadvantages of these
98 Chapter 7
strategies are the relatively long reaction times, especially under starved conditions, and the
time consuming determination of the optimal addition profile or rate coefficients (in case
a theoretical model is used), which, furthermore, requires an immediate start of reaction since
inhibition hampers the addition procedure. For monomer systems in which at least one of
the monomers has a relatively high but limited water solubility, a different approach can
be used to influence composition drift. When a monomer has a relatively high but still
limited water solubility, a certain amount of that monomer will be located in the aqueous
phase, thus influencing the monomer ratio and concentrations within the polymer particle
phase. Since this polymer particle phase is considered to be the main locus of reaction, the
monomer ratio and monomer concentrations within the polymer phase control both,
copolymer composition and polymerization rate. Depending on the amount of water in the
reaction mixture, i.e., depending on the monomer-to-water ratio (MIW), more or less
monomer will be dissolved in the aqueous phase. It should be noted that efforts to raise the
final solids content of a latex will change the monomer-to-water ratio and thus, in many
cases, the copolymer composition of the product. By adding more water to the reaction
mixture, the more water soluble monomer can be withdrawn from the particles and thus from
reaction. If the monomer with the higher water solubility is also the less reactive one,
composition drift can be enhanced by decreasing the monomer-to-water ratio. A system that
illustrates this is the system MA-8. 15 In principle it should be possible to lower or even
minimize composition drift for monomer combinations where the more water soluble
monomer also is the more reactive one. Since the water solubilities of the monomers MA
and indene (Ind) differ by two orders of magnitude and since MA is not only the more water
soluble but also the more reactive monomer, the somewhat unusual monomer combination
MA-Ind is chosen as an example to show that minimization of composition drift is indeed
possible just by changing monomer-to-water ratios (M/W). The structural formula of indene
(CqH8) is shown in Figure 7.1. Note that although the monomer system MA-lnd is an ideal
monomer combination to verify theoretical predictions other monomer combinations in which
the more water soluble monomer is also the more reactive one also comply with the theory.
However, it is important to realise that for reactivity ratios that are far apart composition
drift can only be minimized if the water solubility of the monomers is also very far apart.
Otherwise unrealistic and impractical monomer-to-water ratios will be required or, in
extreme situations, minimum composition drift cannot be achieved in batch emulsion
copolymerization by simply changing the monomer-to-water ratio.
In this chapter, effects of increasing both the initiator and surfactant concentrations
upon the MA-Ind conversion-time curves are discussed. Based on homo-monomer saturation
Monomer-to-water ratios as a tool
concentrations and reactivity ratios
(Chapter 3) model predictions of
minimum composition drift are
performed for the monomer system
MA-Ind using the theory and model
presented in this thesis. In this way the
effect of changing monomer-to-water
ratios in ab initio batch emulsion
copolymerizations with similar initial
overall monomer mole feed ratios can
be studied. Theoretical predictions of
99
Figure 7.1: The structural formula of the monomer indene.
minimum composition drift will be compared with experimental results for the monomer
combination MA-Ind.
7.2 Theory
The copolymerization equation (eq 2.2) relates the instantaneous copolymer
composition with the reactivity ratios and monomer feed composition for solution and bulk
polymerizations. 16•17 In solution and bulk copolymerization of a given monomer system
i-j with reactivity ratios lower than unity, conditions can be reached where the monomer
mole fraction equals the copolymer composition of the instantaneously formed copolymer
(f; = F;). At these so-called azeotropic conditions, there will be no composition drift, i.e.,
the instantaneous copolymer composition remains constant during conversion.
If there is a separate aqueous phase present as in emulsion copolymerization, the
simple theory predicting azeotropic conditions becomes complicated. For monomers with
relatively high, but still limited water solubility, a considerable amount of the monomer can
be dissolved in the aqueous phase. This will affect the monomer mole fractions in the
particle phase. In these emulsion copolymerizations, the copolymerization equation (eq 2.2)
can still be used, but instead of the overall monomer mole fraction, f0 ;. the monomer mole
fraction in the polymer phase, fp;• should be used. For monomer combinations in which at
least one of the monomers has a relatively high, but still limited water solubility,
composition drift will occur with increasing conversion, even if conditions are chosen in
which the pre-requisite for azeotropic conditions, i.e., instantaneous copolymer composition
equals the overall monomer mole composition, is met. The reason that azeotropic conditions
cannot be maintained over a wide range of conversion in emulsion copolymerization is
100 Chapter 7
caused by the effect of changing monomer-to-water ratios and increasing polymer volumes
on the monomer mole fraction in the polymer particles as conversion increases. In emulsion
copolymerizations, where at least one of the monomers in the selected monomer combination
has a relatively high, but limited water solubility, composition drift cannot be avoided; it
can only be minimized. Theoretically, this minimum composition drift can be obtained for
several overall monomer mole fractions by using the heterogeneity of the emulsion system.
This is in contrast with solution or bulk polymerization, where azeotropic conditions can
only be obtained at one overall monomer mole fraction. Exact azeotropic behaviour in
emulsion copolymerization can be obtained only in the following cases: (I) if both
monomers in the chosen monomer combination have low water solubility, leading to
negligible amounts of monomer in the aqueous phase as compared to the amount of
monomers in the organic (monomer droplet and polymer particle) phase, or, (2) if the ratio
of the water solubilities is equal to unity, leading to identical monomer mole ratios in the
aqueous phase and in the polymer particle phase. Note that in the above cases changing the
monomer-to-water ratios has no effect on the course of emulsion polymerization.
As stated above, theoretically, it should be possible to control and minimize
composition drift for monomer combinations where the more water soluble monomer also
is the more reactive one. Based on the water solubility of the monomers, an amount of
monomer is withdrawn from the monomer droplets and polymer particles, thus affecting the
monomer ratio within the polymer phase and therefore having an effect on the copolymer
formed. If monomer i is chosen to be the monomer with the highest water solubility, the
mole fraction of monomer i in the copolymer will reach a maximum value when all the
monomer is located in the polymer particle and monomer droplet phase (comparable with
solution and bulk polymerizations), and it will reach a minimum value when all monomer
is located in the aqueous phase. The value for the minimum mole fraction of monomer i
strongly depends upon the ratio of the water solubility of monomer j over the water
solubility of monomer i, denoted as the a-value. It has been shown in Chapter 6 that the
difference between maximum and minimum monomer mole fractions will be the largest for
small a-values. In such cases, changing the monomer-to-water ratio or polymer volume will
have the strongest effect upon the monomer mole fraction in the polymer phase. It is in these
cases that, for monomer systems in which the more reactive monomer is also the more water
soluble one, minimum composition drift can be obtained by changing the monomer-to-water
ratio.
Monomer-to-water ratios as a tool 101
7.3 Experimental
The emulsion copolymerizations described in this chapter can be divided into two
categories: 1) polymerizations to determine optimum concentrations of surfactant (Ant C0-
990) and initiator (NaPS) resulting in stable latices and reasonable polymerization rates, and
2) polymerizations to study composition drift .
. Emulsion copolymerizations to determine optimum concentrations of surfactant and
initiator were carried out in 100 ml reactors thermostated at 1o•c and mixed with a magnetic
stirrer. Since our main interest was obtaining reasonable polymerization rates, these reactions
were followed by gravimetry only. For the MA-Ind copolymerization high initiator
concentrations were needed to give reasonable polymerization rates, resulting in unstable
latices. The use of non-ionic Ant C0-990 instead ofSDS gave satisfying results. The recipes
used to determine optimum concentrations for the emulsion copolymerizations are shown
in Table 7.1
Table 7.1: MA -Ind copolymerization recipes to achieve optimum reaction conditions (optimize) and to study the effict of monomer-to-water ratio on composition drift (MIW = 0.4, 0.3 and 0.1).
Ingredients optimize MIW = 0.4 MIW = 0.3 MIW 0.1
MA (g) 3.8 165.47 144.87 62.09 Ind (g) 5.2 74.41 64.46 27.83
Water (g) 90 600.1 700.3 898.8 NPS (l o-3 molldmw3
) 10-25 26.31 25.05 24.90 Ant C0-990 (10'3 molldmw3
) 2.5-12.5 7.449 7.498 7.539
Na:zC0 3 (10'3 mol/rlmw3) 10 9.968 9.916 10.035
Emulsion polymerizations to study composition drift were performed as described
in Chapter 3 and Figure 3.1. The recipes for these emulsion copolymerizations, which were
performed using the same overall monomer mole fraction of foMA 0.75 and varying
monomer-to-water ratios are given in Table 7.1. All reactions concerning composition drift
were monitored by gravimetry, yielding conversion-time curves, and by GC providing the
overall monomer fractions as a function of time. An indication of the accuracy of data
analyses was obtained by adding known amounts of n-butanol as internal standard to the
GC samples in order to obtain extra conversion-time data. Combining both data gives the
overall conversion of both monomers at each moment during the reaction.
102 Chapter 7
7.4 Results and discussion
7.4.1 Optimization of recipe conditions
To achieve reasonable polymerization rates in MA-Ind emulsion copolymerization
reactions, high initiator concentrations were needed. Reactions performed with surfactant
SDS, frequently used in emulsion polymerization, did not result in colloidally stable latices
for any SDS concentration (going from 10·10·3 to 75·10"3 mol/dm3). The use of the non
ionic surfactant Ant C0-990 instead of SDS resulted in colloidally stable latices. The
surfactant and initiator concentrations were optimized resulting in concentrations of 7.5·10·3
and 10·10'3 mol/dm\ respectively.
Some typical conversion-time curves for the emulsion copolymerization of MA-Ind
can be seen in Figure 7.2 for several initiator (NaPS) concentrations. From Figure 7.2 it can
be concluded that the overall polymerization rate increases with increasing NaPS
concentrations as can be expected from emulsion polymerization theory.
1.00 0 0
0 0 0 0
0.75 0 0 0 _..... 0 0 . 0 0 0 '-'
c:l 0
·~ 0 D 0 l>
l>
0.50 D 0 l> 0 l> ., 0 l>
> D l> c:l
0 0 0 l> <.1 0.25 D
0 l> 0 €l "
l>
0.00 0 3 6 9
time (hours)
Figure 7. 2: Conversion-time curves of MA -Ind emulsion copolymerizations for initiator (NaPS) concentrations of 10·}()"3 (il), 15 ·J0·3 (o), 20 ·10·3 (D), and 25 ·10·3 molldm,/ ( 0 ).
Experiments performed with increasing surfactant (Ant C0-990) concentrations showed a
slight increase in polymerization rate. Particle size analysis by dynamic light scattering
(Malvern Autosizer lie) showed that the particle size decreased with increasing initiator and
surfactant concentrations. This behaviour is typical of emulsion polymerization, 18 since by
using more surfactant, more particle surface can be stabilized. Increasing the initiator
concentration leads to higher radical concentrations in the beginning of the reaction and,
Monomer-to-water ratios as a tool 103
·therefore, more particles can be nucleated.
Comparison of gravimetry and GC results is shown in Figure 7.3 for the MA-Ind
reaction at a monomer-to-water ratio of 0.1 kg/kg (recipe: Table 7.1). For the reaction
depicted in Figure 7.3 it can be concluded that the polymerization rate of Ind is higher than
the polymerization rate of MA, resulting in a copolymer composition that is more Ind-rich
in the beginning and more MA-rich towards the end of the polymerization as compared with
the initial overall monomer mole fraction. The accuracy of the experimental results is
illustrated by the good agreement when comparing the total conversion-time curves obtained
from gravimetry with the data obtained from GC analysis using an internal standard,
enabling the determination of not only monomer ratios but also conversion data of the
separate monomers. Note that the internal standard was added afterwards to samples taken
from the reaction since, otherwise, monomer partitioning during reaction would have been
affected by the internal standard. All MA-Ind emulsion copolymerization experiments
performed to study composition drift behaviour were analyzed in the above manner.
1.00 lJ. B ~ Q a lJ.
~ lJ. ~
,..... 0.1S '
lJ. 8 0
0 lJ. ~ ...... 0
d .5! o.so lJ.
"' 0 .. 0 4) 0 > d 6
~ 0
0 tJ. ~ B ... 0.2S tJ.8 ~@
0.00 0 2 4 6
time (hours)
Figure 7.3: Experimental conversion-time results for MA-lnd emulsion copolymerization at MIW = 0.1 and foMA = 0. 7 5. The total conversion was determined by gravimetry ( 0) and GC (o); the partial conversion of both monomers was determined by GC (MA: D ; !nd .t.}.
7.4.2 Model parameters
Predictions of the course of emulsion copolymerizations can be made by using the
model described in Chapter 6. The use of this model is very convenient since it only requires
the reactivity ratios and the homo-saturation values of the monomers in the aqueous and
104 Chapter 7
polymer phase to be known. For this reason these model parameters have been determined
experimentally for the current work. The determination procedure and the results are
described in full detail in Chapter 3.
Although the absolute concentrations of monomers in the particle phase strongly
depend upon the homo-saturation concentrations of the monomers in the polymer particle
phase, it has been shown in previous sections that the monomer ratio within the polymer
phase is independent of the maximum swellability of both monomers in the polymer phase,
i.e., independent of the copolymer composition at saturation swelling. Therefore, it can be
concluded that changing copolymer composition as a function of conversion occurring at
saturation swelling, may affect the rate of polymerization (changing absolute concentrations)
but certainly not the composition drift (constant monomer ratio within the particles).
At partial swelling monomer partitioning between the aqueous and polymer phase
depends upon the volume fraction of polymer (eq 6.18), i.e., depends on the maximum
swellability in the polymer of the monomers. The change in maximum swellability as a
function of copolymer composition has been shown to be negligible 19•20 for several
monomer systems. The effect of changing monomer composition on the (maximum) volume
fractions of polymer is taken into account in model predictions in eq 6.2a-b, whereas the
effect of changing copolymer composition can be estimated using eq 6.18 by assuming
maximum swellabilities of a monomer mixture (50% MA-50% Ind; normal swellability of
5 mol/dm3) in the homopolymer-Ind of 4 mol/dm3 and in the homopolymer-MA of 6
mol/dm3• From Figure 7.4 where the degree of saturation in the polymer phase is depicted
as a function of the degree of saturation in the aqueous phase, it can be concluded directly
that the effects of changing copolymer composition going from poly-Ind to poly-MA has
a relatively small influence on monomer partitioning at partial swelling. These results agree
very well with the results of the sensitivity analysis presented in the appendix of Chapter
6. In practical situations, all effects of changing maximum swellabilities will even be smaller
since the change in copolymer composition is less drastic than presented in Figure 7.4.
Based on the above discussion, all effects of changing maximum swellabilities of
monomer in the polymer phase as a result of changing copolymer composition are neglected
for saturation and partial swelling. All model predictions are carried out using one set of
homo-saturation concentrations of MA and ]nd that have been determined by monomer
partitioning experiments in a 50% MA-50% Ind seed (Chapter 3).
As shown in the sensitivity analysis, the water solubility of both monomers in the
aqueous phase may have a large effect on monomer partitioning in cases where the absolute
monomer amount in the aqueous phase cannot be neglected compared to the total amount
Monomer-to-water ratios as a tool 105
of monomers. For some of the reactions presented in this Chapter the amount of monomer
(MA has a relatively high water solubility) in the aqueous phase cannot be neglected. For
this reason, accurate water solubility values of the both monomers in the aqueous phase at
reaction temperature have been determined (Chapters 3 and 4).
0.75
Qo
r:s.ti 0.50
0.25
0.00 w::;_ _________ ___J
0.00 0.25 o.so 0.75 1.00
Figure 7. 4: Model predictions of the degree of saturation in the polymer phase, F,at P' as a fimction of the degree of saturation in the aqueous phase, F sat, using eq 6. 18 with maximum swellabilities of monomer in the polymer phase of 4 and 6 molldm3
•
7.4.3. Composition drift in emulsion copolymerization of MA-Ind
The monomer mole fraction in the polymer phase is determined by monomer
partitioning. Changing the monomer-to-water ratio or the polymer volume in a monomer
water-polymer mixture will lead to different monomer mole fractions in the polymer phase.
This effect will be especially large if one of the monomers has a relatively high but still
limited water solubility, as, for instance, MA.
Assuming monomer i to be the more water soluble monomer, two extreme values
for the monomer mole fraction in the polymer phase can be obtained, i.e., a maximum value
fpi.max which is reached if all monomer is located in the polymer phase and a minimum value
fp;,min which is reached if all monomer is dissolved in the aqueous phase. As was shown in
Chapter 6, the value of fp;,min strongly depends upon the a-value leading to larger differences
between fp;,max and fpi,min for smaller a-values (see eq 6.4a). This t;,;,min can be reached only
if at least one of the monomers has a relatively high water solubility and if the monomer-to
water ratio is low and if the amount of polymer phase is too small to affect monomer
106 Chapter 7
partitioning. It is important to realise that although the minimum monomer mole fraction
in the polymer only depends on the ratio of the water solubilities, a, the absolute water
solubility values are determining the monomer-to-water ratio needed to obtain this minimum
monomer mole fraction in the polymer phase. This is illustrated by the following example:
if a = 0.1 and the water solubilities are 0.5 and 0.05 mol/dm3 then less water is needed to
dissolve all these monomers than in case of water solubilities of 0.05 and 0.005 moVdm3•
This obviously results in different monomer-to-water ratios needed to obtain a minimum
monomer mole fraction in the polymer phase.
Depending on recipe conditions, like monomer-to-water ratio (MIW) and polymer
volumes (V po), the value for the mole fraction of monomer i in the polymer phase will vary
between fp;,max and fpi,min· In Figure 7.5 the maximum and minimum values for the monomer
mole fraction in the polymer phase as a function of the overall monomer mole fraction are
given for the monomer system MA-Ind in which a 0.0053. Due to the large difference
in water solubility of MA as compared with Ind, expressed in the low a-value, the monomer
mole fraction in the polymer phase is strongly affected by changing monomer-to-water
ratios. This effect of MIW on the mole fraction of monomer i in the polymer phase in the
absence of polymer is also clearly shown in this Figure 7.5.
1.00
i 0.50 '-"<
0.25
0.016
0.25 0.50 0. 75 1.00 fo.MA
Figure 7.5: Monomer mole fractions in the polymer phase, J;,.MA• as a function oft he overall monomer male fraction for the monomer system MA-Ind: minimum (min), maximum (max) and monomer-to-water ratio dependent (MIW = 0.0/, 0.02, 0.05, 0.1. 0.3).
Monomer-to-water ratios as a tool
1.00 ,..----------~
0.78 ~~----------£.-' 0.75
rs..i o.so
0.25
0.00 0.00 0.25 o.so 0. 75 1.00
fo,MA
Figure 7. 6: Monomer mole fractions in the copolymer, F MA• (resulting from J;,MA data presented in Figure 7.5) as afimction of the overall monomer mole fraction, f.MA, for the monomer system MA-Ind: instantaneous copolymer compositions resulting from the minimum (min), maximum (max) and MIW dependent mole fractions (MIW = 0.0/, 0.02, 0.05, 0./, 0.3).
107
The copolymer composition resulting from the maximum and minimum values for
the monomer mole fraction in the polymer phase can be calculated with the instantaneous
copolymer equation (eq 2.2) using the reactivity values rMA = 0.92 and r1nd = 0.086 (Chapter
3). These copolymer compositions, which are typical of each monomer system with given
a.-value and reactivity ratios, are depicted in Figure 7.6 together with the diagonal line
representing azeotropic conditions, i.e., overall monomer mole fraction equal to instantaneous
copolymer composition. From Figure 7.6 one can see directly the minimum and maximum
instantaneous copolymer compositions obtainable when starting from a given overall
monomer mole fraction in an emulsion copolymerization of MA-Ind. The strong effect of
varying monomer-to-water ratios on the instantaneous copolymer composition is also
depicted in Figure 7.6. To illustrate the minimum and maximum mole fractions of monomer
i and the resulting instantaneous copolymer compositions an example is shown in Figures
7.5 and 7.6 for an overall monomer mole fraction offoMA 0.75. For low monomer-to-water
ratios without polymer (almost all monomers located in the aqueous phase), one can see that
the minimum monomer mole fraction in the polymer phase is reached, fpMA,min = 0.016,
(Figure 7.5) resulting in a copolymer composition ofF MA 0.13 (Figure 7.6), whereas at
high monomer-to-water ratios, the maximum monomer mole fraction is reached, fpMA.max =
0.75 (Figure 7.5), resulting in a copolymer composition ofFMA = 0.78 (Figure 7.6). We have
108 Chapter 7
already seen that azeotropic conditions occur only if the instantaneous copolymer
composition equals the overall monomer mole fraction. Knowing this, one can see in Figure
7.6 that the intersection of the lines representing minimum, maximum and MIW-dependent
values for the instantaneous copolymer composition with the diagonal gives the conditions
needed to obtain azeotropic conditions, i.e., instantaneous copolymer composition equals
overall monomer mole fraction. Calculation shows that these azeotropic conditions can be
found by varying the MIW ratio for fllM4 values between 0 and 0.91 at low conversion.
However, the aim of this work is to achieve minimum composition drift over a wider range
of conversion, and is not restricted to low conversion. Therefore, the overall monomer mole
fraction needed for minimum composition drift over the entire range of conversion may
deviate slightly from the conditions represented by the intersections of the diagonal and the
copolymer compositions shown in Figure 7.6.
Experimental results of emulsion copolymerization composition as a function of
conversion have been compared with predictions of the model presented in Chapter 6 for
MA-Ind systems. The large effect of different monomer-to-water ratios on the system MA
Ind, with a relatively water soluble monomer like MA, can be seen in Figure 7.7 where
theory and experiment are compared resulting in very good agreement (initial reaction
recipes are shown in Table 7.1). To enlighten the maximum span of composition drift, a
theoretical prediction of extreme high monomer-to-water ratios (MIW oo) is depicted in
Figure 7.7.
1.00
0.90
0.80
0.60
oo
/9/' M/W •0.1 9-
MfW- 00
solution, bulk
o.so '---~-...,-----...--~--,--~---,-~__._, 0.00 0.20 0.40 0.60 0.80 1.00
Conversion
Figure 7. 7: Comparison of predicted and experimentally determined overall mole fractions for the monomer system MA-lnd, with initial overall monomer mole fraction off,,MA 0. 75 and different monomer-to-water ratios (MIW) ofO.J, 0.3 and 0.4 (predictions lines, experiments symbols).
Monomer-to-water ratios as a tool 109
Note that the composition drift behaviour in this extreme case is equal to the composition
drift behaviour in homogeneous systems as bulk and solution (i.e., fP = f.) for similar initial
mole fractions. Note furthermore that increasing the monomer-to-water ratios to extreme
high values may result in phase inversion. However, this phenomenon is not discussed here.
In case of MA-Ind emulsion copolymerizations more of the more water soluble MA will
be buffered in the aqueous phase at lower monomer-to-water ratios as compared with higher
monomer-to-water ratios. As can be seen in Figure 7.7, minimum or even reversed
composition drift can be achieved by simply changing the monomer-to-water ratio in a batch
emulsion copolymerization of MA-Ind.
J
1.00
0.90
0.80
0.60
0
0 M/W•O.l
o.so L..---..----..----..------~__;;..__._, 0.00 0.20 0.40 0.60 0.80 1.00
Conversion
Figure 7.8: Comparison of model prediction (lines) with experimental results (symbols) of the mole fraction of MA in the polymer phase as a function of conversion, with an initial overall monomer mole fraction of /.,MA 0. 75 and different MIW ratios.
What exactly happens in the emulsion copolymerizations of MA-Ind at an overall
monomer ratio of MA with varying monomer-to-water ratios is depicted more clearly in
Figure 7.8, where theoretical and experimental mole fractions ofMA in the polymer phase
are compared. In case of MA-Ind emulsion copolymerizations, a larger part of the more
water soluble MA will be buffered in the aqueous phase at lower monomer-to-water ratios,
resulting in lower mole fractions of MA in the polymer phase at the beginning of the
reaction. Composition drift at low M/W ratios (Figure 7.8, foMA = 0.75, MIW = 0.1) shifts
from instantaneous copolymer compositions with higher Ind contents than the initial overall
feed in the beginning of the reaction, to instantaneous copolymer compositions with higher
MA contents than the initial overall feed at the end of the reaction. At higher monomer-to
water ratios (Figure 7.8, t;,A-M = 0.75, M/W = 0.4 to oo) less MA is buffered in the aqueous
110 Chapter 7
phase, leading to composition drift shifting from higher mole fractions ofMA in the polymer
phase in the beginning of the reaction {higher MA content in instantaneous copolymer than
in the initial overall feed) to lower mole fractions of MA in the end of the reaction {higher
Ind content in the instantaneous copolymer than in the initial overall feed). From Figures
7. 7 and 7 .8, we can conclude that composition drift can indeed be minimized by varying
the monomer-to-water ratio in MA-Ind emulsion polymerization. For overall mole fractions
of MA of foAM = 0. 75 minimum composition drift is achieved for monomer-to-water ratios
ofMJW = 0.3.
The course of emulsion copolymerization at minimum composition drift is shown
in more detail in Figure 7.9, where model predictions of fpAM and foMA and resulting from
this the mole fraction of MAin the copolymer {FMA) are compared with experiments (fpMA
and F AM are calculated from foMA and overall conversion using monomer partitioning
relationships and the instantaneous copolymer equation). As could be expected at minimum
composition drift conditions, all three compositions, fpMA, foMA, and F MA are more or less
constant as a function of conversion. Another important result of Figure 7.9 is that the
prerequisite for minimum composition drift, i.e., f.MA equal to FA« (see Figure 7.6), is
apparently approximated during reaction. In Figures 7.5 and 7.6, it is illustrated that by
simply changing initial reaction conditions like the monomer-to-water ratio, one can reach
minimum composition drift, if desired. In case the occurrence of composition drift is desired,
one can change the monomer-to-water ratio in such a way as to achieve composition drift
in the desired direction and to the desired extent.
1.00
0.90
f;l,i 0.80
J fp,MA
J 0.70
0.60
0.50 L----.....---.....-~-.--~---,.--~--. 0.00 0.20 0.40 0.60 0.80 1.00
Conversion
Figure 7. 9: Comparison of model predictions (lines) and experimental results (symbols) of!;..~« (o), /,,.~« (0) and F.~« (!J.) as a function of conversion for the emulsion copolymerization of MA-Ind with MIW = 0.3 andf.MA = 0. 75, resulting in minimum composition drift.
Monomer-to-water ratios as a tool 111
As can be seen in Figure 7.6, minimum composition drift conditions can also be
achieved for other overall monomer mole fractions. From the good agreement between
predictions and experimental results shown in Figure 7.7, it can be concluded that the model
used to predict the course of emulsion copolymerization can provide good simulations of
copolymer composition in emulsion copolymerization, even under conditions as critical as
those leading to minimum composition drift. Therefore, the presented model can be used,
in combination with the experimentally determined homo-monomer saturation values and
reactivity ratios, to predict the monomer-to-water ratio needed to achieve minimum
composition drift for several overall monomer mole fractions for the monomer system MA
Ind. The monomer-to-water ratios needed to obtain this minimum composition drift at given
overall monomer mole fractions in MA-Ind emulsion copolymerization are shown in Figure
7.10. From these predicted results, we can conclude that minimum composition drift indeed
can be achieved for other overall monomer mole fractions as welL Note, however, that
realistic monomer-to-water ratios for batch emulsion copolymerizations normally are between
0.1 < MIW < 2.
1.00
]1 ~ 0.75
~ 0.50
.I 0.25 8
0.00 0.00 0.25 0.50 0.75 1.00
fo,MA (-)
Figure 7.10: Model prediction of the monomer-to-water ratio as a .function of the overall mole fraction of MA needed to achieve minimum composition drift. The parameters used in the model predictions are listed in Tables 3.2 and 3.5.
Note also that the assumption of negligible polymerization in the aqueous phase may not
longer be valid at low monomer-to-water ratios. In this case, a considerable percentage of
the polymerization might occur in the aqueous phase. One way to avoid this from happening
might be the use of an oil soluble initiator in combination with an aqueous phase free radical
scavenger or retarder as an alternative of the water soluble initiator NaPS.
112 Chapter 7
It is important to realise that minimizing composition drift in MA-Ind reactions is
possible due to the moderate difference in reactivity values of the monomers (a factor of
10) combined with a large difference in homo-monomer saturation concentrations (factor
a. 0.05). In this case, the water phase can buffer a sufficient amount of the more reactive
monomer to minimize composition drift.
The intrinsic possibility of achieving minimum composition drift in batch emulsion
copolymerization for other monomer systems can be determined directly when the water
solubilities of the monomers (a.) and the reactivity values are known for a given monomer
system. The maximum monomer mole fraction in the polymer phase always equals the
overall monomer mole fraction. If the reactivity ratios of the chosen monomer systems are
known, the copolymer composition resulting from the maximum monomer mole fraction
in the polymer phase can be calculated with eq 2.2. It was shown that the minimum
monomer mole fraction in the polymer phase is reached when the monomer mole fraction
in the aqueous phase was equal to the overall monomer mole fraction. From this monomer
mole fraction in the aqueous phase, the minimum monomer mole fraction in the polymer
phase can be calculated directly with eq 6.4a if the ratio of the water solubilities of the
monomers, the a.-value, is known for the chosen monomer system. The copolymer
composition resulting from this minimum monomer mole fraction in the polymer phase again
can be calculated using eq 2.2 if the reactivity ratios are known. If the copolymer
compositions resulting from the minimum and maximum monomer mole fractions in the
polymer phase are higher and lower, respectively, than the overall monomer mole fraction,
the prerequisite for minimum composition drift, i.e., equal overall monomer mole fraction
to instantaneous copolymer composition, can be achieved for the selected overall monomer
mole fraction. The approach presented in this Chapter will always give information about
the span of control of the composition drift even in those cases where minimum composition
drift carmot be achieved. The procedure described here can be used for any monomer system
at every desired overall monomer mole fraction, giving similar results as shown in Figures
7.5 and 7.6 for MA-Ind emulsion copolymerizations.
7.5 Conclusions
Theoretical considerations are leading to the concept that for monomer systems in
which the water solubility of the monomers is sufficiently far apart (low a-values) minimum
composition drift can be achieved by properly adjusting the initial monomer-to-water ratio
in a batch emulsion copolymerization in which the more reactive monomer is also the more
Monomer-to-water ratios as a tool 113
water soluble one. Experimental verification of this prediction has shown that minimum
composition drift could be achieved for the monomer system MA-Ind where MA is the more
reactive as well as the more water soluble monomer. Model predictions show that
composition drift can be minimized for MA-Ind emulsion copolymerization over a wide
range of initial monomer feed fractions, simply by choosing different initial monomer-to
water ratios.
114 Chapter 7
1. K. Chujo, Y. Harada, S. Tokuhara, K. Tanaka, J. Polym. Sci., Part C, 27, 321 (1969) 2. J. Snuparek, Angew. Makromol. Chern., 25, 113 (1972) 3. R.A. Wessling, D.S. Gibbs, J. Macromol. Sci., Chern., A-7, 647 (1973) 4. J. Snup;irek, F. Krska, J. Appl. Polym. Sci., 20, 1753 (1976) 5. J. Snuparek, F. Krska, J. Appl. Polym. Sci., 21, 2253 (1977) 6. J. Snuparek, K. Ka5par, J. Appl. Polym. Sci., 26, 4081 (1981) 7. M.S. El-Aasser, T. Makgawinita, J.W. Vanderhoff, J. Polym. Sci., Polym. Chern. Ed,
21, 2363 (1983) 8. S.C. Misra, C. Pichot, M.S. El-Aasser, J.W. Vanderhoff, J. Polym. Sci., Polym. Chern.
Ed, 21, 2383 (1983) 9. T. Makgawinata, M.S. El-Aasser, A. Klein, J.W. Vanderhoff, J. Dispersion Sci.
Techno/., 5, 301 (1984) 10. G. Arzamendi, J.M. Asua, J. Appl. Polym. Sci., 38, 2019 (1989) 11. G. Arzamendi, J.M. Asua, Makromol. Chern., Macromol. Symp., 35/36, 249 (1990) 12. G. Arzamendi, J.M. Asua, Ind Eng. Chern. Res., 30, 1342 (1991) 13. G.H.J. van Doremaele, H.A.S. Schoonbrood, J. Kurja, A.L. German, J. Appl. Polym.
Sci., 45, 957 (1992) 14. G. Arzamendi, J.C. de Ia Cal, J.M. Asua, Angew. Makromol. Chern., 194, 47 (1992) 15. G.H.J. van Doremaele, Ph.D. Thesis, Eindhoven University of Technology,
Eindhoven, the Netherlands (1990) 16. T. Alfrey, G. Goldfinger, J. Chern. Phys., 12, 205 (1944) 17. F.R. Mayo, F.M. Lewis, J. Am. Chern. Soc., 66, 1594 (1944) 18. R.M. Fitch, C.H. Tsai, Polymer Colloids, Plenum, New York, 1971 19. G.H.J. van Dorernaele, F.H.J.M. Geerts, H.A.S. Schoonbrood, J. Kurja, A.L. German,
Polymer, 33, 1914 (1992) 20. M. Nomura, K. Yarnarnoto, I. Horie, K. Fujita, J. Appl. Polym. Sci., 27,2483 (1982)
The effect of water solubility on composition drift
Chapter 8 Tbe effect of water solubility of tbe monomers on
composition drift on metbyl acrylate-vinyl ester combinations
115
Abstract: It has been shown theoretically that composition drift mainly depends on reactivity ratios and water solubilities. Minimum composition drift can be obtained by lowering the monomer-to-water ratio in monomer systems where the more reactive monomer is also the more water soluble one. Investigating the effect of water solubility on composition drift while keeping the reactivity ratios constant can elucidate the importance of the water solubility. The monomer combinations methyl acrylate-vinyl acetate (MA-V Ac), methyl acrylate-vinyl 2,2-dimethylpropanoate (MA-VPV), and methyl acrylate-vinyl 2-ethylhexanoate (MA-V2EH) are ideal monomer combinations for studying the effect of water solubility on composition drift since the reactivity ratios for this series of monomer systems are approximately equal. Solution copolymerizations are performed to elucidate maximum composition drift at extremely high monomerto-water ratios. From comparing theoretical predictions with experimental results it could be concluded that composition drift for the monomer combination MA-V Ac could only be reduced since the difference in water solubility was not large enough to compensate the effects of the large difference in reactivity ratios. However, for the monomer combinations MA-VPV and MAV2EH the difference in water solubility was large enough to make minimum composition drift possible for low monomer-to-water ratios even for monomer combinations with reactivity ratios as far apart as in the MA-vinyl ester case.
8.1 Introduction
Vinyl acetate copolymers are widely used in interior architectural waterborne
coatings. Due to the poor hydrolytic stability of these copolymers, their use as exterior
coatings is limited. Vinyl ester monomers of the C9-Cll versatic acids, as produced by
Shell, have been available in Europe for about 25 years. 1•2
·3 As a result of recently
116 Chapter 8
developed large scale transvinylation methods, new vinyl ester monomers also have been
produced by the Union Carbide Corporation.4 Due to neighbouring group steric effects, the
use of these monomers in emulsion copolymerization results in improved hydrolytic stability
and water resistance when compared with vinyl acetate. 1•2
•3 Furthermore, glass transition
temperatures of (co)polymers will strongly depend on the vinyl ester used. In this way
copolymers can be designed over a wide range of glass transition temperatures.
Next to resistance against hydrolysis and glass transition temperatures, the product
properties are also determined by the heterogeneity of the copolymer. In the sensitivity
analysis (appendix chapter 6) it was shown that the course of composition drift in
copolymerization reactions is mainly determined by the water solubility of the contributing
monomers and their reactivity ratios. 5 For the monomers VAc, VPV, and V2EH the
reactivity ratios with MA have been determined by nonlinear optimisation6•7 of monomer
feed-copolymer composition data, indicating that for practical purposes the three MA-VEst
monomer systems can be described with one set of reactivity data (chapter 3: rMA = 6.1 ±
0.6 and rvEst = 8.7·10-3 ± 23·10-3).
8 An advantage of the approximately equal reactivity
ratios for VAc, VPV, and V2EH in MA-VEst monomer systems is that these systems can
be used as a tool in studying the important effect of the monomer solubility in water on the
course of emulsion copolymerization reactions of MA-VEst, especially as a function of the
monomer-to-water ratio.
As described in chapter 7,9 minimum composition drift can be obtained for monomer
combinations in which the more water soluble monomer is also the more reactive monomer.
In this chapter it will be discussed whether or not this statement still holds for monomer
combinations with reactivity ratios as far apart as in the MA-VEst case (where they differ
by a factor of 700!). Intuitively one can see that minimum composition drift in these cases
can only be reached if the monomer-to-water ratio is very low and if the difference between
the water solubility of the monomers is large enough to counteract the difference in the
reactivity ratios. Based on homo-monomer saturation concentrations and reactivity ratios
(Chapter 3) model predictions of minimum composition drift are performed for the monomer
systems MA-VEst using the theory and model presented in this thesis. In this way the effect
of changing monomer-to-water ratios in ab initio batch emulsion copolymerizations with
similar initial overall monomer mole ratios can be predicted for a series of monomer
combination with approximately equal reactivity ratios and covering a wide range of water
solubilities (listed in Tables 3.2 and 3.5). Some of the predictions of composition drift will
be compared with experimental results to validate the theoretical model for the MA-VEst
monomer systems.
The effect of water solubility on composition drift 117
8.2 Theory
As stated above, theoretically it should be possible to control and minimize
composition drift for monomer combinations where the more water soluble monomer also
is the more reactive one. As described in chapter 7, the mole fraction of the better water
soluble monomer i in the copolymer will reach a maximum value when all the monomer
is located in the polymer particle and monomer droplet phase, and it will reach a minimum
value when all monomer is located in the aqueous phase. The value for the minimum mole
fraction of monomer i strongly depends upon the a-value, i.e., the ratio of the water
solubility of monomer j over the water solubility of monomer i according to eq. 6.4a. For
the three monomer combinations at hand the minimum mole fractions can be calculated
using the water solubility values listed in Table 3.2 resulting in a-values of 51·10·2, 13 ·10-3,
and 0.41·10·3 for the monomer combinations MA-VAc, MA-VPV, and MA-V2EH,
respectively. Using other vinyl ester monomers as for instance vinyl propionate (VP),
different a-values will be found (a= 0.11). Although the MA-VP monomer combination
has not been studied here, its a-value will be used to show the effect of different a-values /
on the minimum mole fraction in the polymer phase. The minimum and maximum mole
fraction MA in the polymer particle phase is depicted in Figure 8.la as a function the overall
mole fraction MA for the monomer combinations MA-VAc, MA-VP, MA-VPV, and MA
V2EH. Using the instantaneous copolymer equation (eq 2.2)10•11 in combination with the
reactivity ratios of rMA = 6.1 and rve,1 = 8.7·10·3, the resulting copolymer composition can
be calculated. The minimum and maximum copolymer composition resulting from these
mole fractions are elucidated as a function of overall monomer mole fraction in Figure 8.1 b.
Note that for the calculation of the instantaneous copolymer composition from the mole
fraction MA in the polymer phase the same reactivity ratios are used for the monomer
combination MA-VP as for the other MA-VEst combinations. From Figure 8.lb we can see
directly that composition drift can not be suppressed completely by lowering the monomer
to-water ratio for MA-V Ac as a result of the a-value which is too close to l (the water
solubilities are too close together). From Figure 8.1 b we can also see that for MA-VP (a
= 0.11) and MA-VPV (a = 13 ·10'3), composition drift theoretically can be minimized for
overall mole fraction of MA ranging from 0.65 to 1 and 0.28 to 1, respectively. For the
monomer combination MA-V2EH (a 0.41·10.3) minimum composition drift can be
obtained over the whole range of overall monomer mole fractions going from 0 to I. Note
that although it is theoretically possible to obtain minimum composition drift, very low (i.e.,
118 Chapter 8
impractical) monomer-to-water ratios may have to be used.
A
0.80
0.60
0.40
0.20
0.00 Wi:O.o::::;::::;...-==;;.,_.....;o.a
0.00 0.20 0.40 0.60 0.80 1.00
0.80
0.60
0.40
0.20
0.00 !!:.---..===--....:.:....-=..;.~~ 0.00 0.20 0.40 0.60 0.80 1.00
Figure 8.1 (A) Maximum ff;,,,.d and a-value dependent mmtmum mole fractions of MA in the polymer phase, and (B) instantaneous copolymer composition resulting from these mole fractions MA in the polymer phase, as a jUnction of the overall mole fraction of MA. The a values correspond with the monomer combinations MA-VAc (0.51), MA-VP (0.11), MA-VPV (0.013), and MA-V2EH (0.00041), respectively.
8.3 Experimental
The emulsion copolymerizations to study composition drift were performed as
described in Chapter 3 at a temperature of 50°C. The recipes for these emulsion
copolymerizations, which were performed using the same overall monomer mole fraction
of foMA 0.75 and varying monomer-to-water ratios are collected in Table 8.1.
Solution polymerizations of MA-V Ac and MA-V2EH were performed at 70"C and
of MA-VPV at 60°C in the same reactor as the emulsion polymerization reactions (Figure
3.1). The initial overall mole fraction of MA was similar to the emulsion situation (fo,AM =
0.75), toluene was used as solvent, and AIBN was used as initiator. The recipes of the
solution copolymerizations are collected in Table 8.2. Note that the temperature of the
solution copolymerizations was higher than for the emulsion copolymerization reactions in
order to obtain reasonable polymerization rates. It has been assumed that the reactivity ratios
do not significantly vary with temperature, within the range of 50-70°C. This assumption
will be discussed in more detail in the light of the experimental results.
All reactions concerning composition drift were monitored by gravimetry, yielding
conversion-time curves and by gas chromatography providing the overall monomer fractions
The effect of water solubility on composition drift 119
as a function of time. Combining both data gives the overall conversion of both monomers
at each moment during the reaction.
Table 8.1 Emulsion copolymerization recipes for MA-VEst reactions with varying monomer-to-water ratios at 50"C. All masses are in grams.
I VAc VPV V2EH
MIW 0.02 0.3 0.02 0.02 0.1 0.3 0.02 0.02 0.1 0.3
MA 13.50 202.4 12.03 11.91 59.90 180.4 10.81 10.78 53.79 162.6 VAc 4.50 67.43
VPV 6.04 5.91 30.01 89.52
V2EH 7.12 7.11 35.47 107.2
water 895 900 900 901 897 901 899 900 907 900 SDS 1.31 1.30 1.30 1.30 2.58 7.77 1.30 1.32 2.61 7.79
NaPS 0.20 0.21 0.12 1.07 1.06 1.06 1.06 0.12 0.48 1.07
N~~:zC03 0.10 0.10 0.48 0.48 0.42 0.47 0.48 0.49 0.20 0.48
Table 8.2 Solution copolymerization reactions of MA-VAc and MA-V2EH at 7fJ'C and MA-VPV at 6(f'C.
Ingredients (g)
MA
VAc
VPV
V2EH
AIBN
toluene
8.4 Results and discussion
MA-VAc
75.53
24.92
0.99
891
MA-VPV
66.36
32.90
0.99
904
MA-V2EH
60.03
40.72
1.00
900
Using the reactivity ratios and water solubility values of the monomers given in
chapter 3, the course of composition drift in emulsion copolymerizations can be predicted
with the model described in chapter 6. Note that it was shown in the sensitivity analysis that
the maximum swel!ability of monomer in polymer has a negligible effect on composition
drift. Therefore, model predictions can be performed using rather rough determinations of
swellability values. These estimations were determined by monomer partitioning experiments
similar to the ones described in chapter 3. However, instead of determining the amount of
water (and monomer dissolved in it), in the polymer-monomer samples only the solids
120 Chapter 8
content was calculated. From this the maximum swellability of monomer in polymer was
determined. The results of these estimations are listed in Table 3.2.
The large effect of different monomer-to-water ratios on the monomer mole fraction
in the polymer phase and as a result of this on the instantaneous copolymer composition
can be seen in Figure 8.2 where the monomer combination MA-VPV is used as an example.
Similar results are obtained for the monomer combination MA-V2EH. As a result of the
high a-value of the MA-VAc monomer system only a small influence of the monomer-to
water ratio on the monomer composition in the polymer particle phase and thus on the
instantaneous copolymer composition has been observed.
~ ......
1.00 1.00 A B
M/W. 0.1 0.75 0.75
0.50 J 0.50
0.25 0.25
0.00 0.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75
fo,MA fo,MA
Figure 8.2 (A) Influence of the monomer-to-water ratio on the mole fraction of MA in the polymer phase, and (B) instantaneous copolymer composition resulting from these mole fractions MA, both as a function of the overall mole fraction of MA for the MA-VPV monomer combination (ex = 0.013).
1.00
The results of the reactions with varying M/W ratios are depicted in Figures 8.3-8.5
for the three monomer combinations. The maximum possible span of control in emulsion
copolymerization can be obtained when comparing very high monomer-to-water ratios with
very low ones. The high-limit case will exhibit composition drift behaviour equal to that
in reactions performed in homogeneous systems (bulk or solution copolymerizations). In
order to study this maximum monomer-to-water situation, solution copolymerizations were
performed using toluene as solvent. Note that the assumption is made that the reactivity
ratios are independent of the solvent toluene. The theoretical and experimental results of
these reactions are also depicted in Figures 8.3 to 8.5. Note that in solution
copolymerizations the reactivity ratios are the only determining model parameters. Therefore,
it can be concluded from the agreement between predicted and experimental solution
copolymerization results that the reactivity ratios which were determined by low conversion
The effect of water solubility on composition drift 121
bulk polymerization at 50°C are also valid in solution polymerization using toluene as
solvent at temperatures up to 70°C. In other words, the reactivity ratios seem to be rather
temperature independent in the range of 50-70°C. In the low monomer-to-water situations
more of the better water soluble MA will be buffered in the aqueous phase leading to
different composition drift behaviour since MA is partly and temporarily withdrawn from
reaction. For the monomer combination MA-V Ac the effect of varying the monomer-to
water ratio is relatively small even for low monomer-to-water ratios as a result of the small
difference in water solubility between MA and VAc (a= 0.5).
1.00
0.80
~ ...: 0.60
0.40
0.20
0.00 0.00 0.20 0.40 0.60 0.80 1.00
conversion Figure 8.3 Overall MA mole fraction as a function of conversion for MA-VAc solution (o) and emulsion copolymerization reactions with monomer-to-water ratios of0.02 (~>)and 0.3 (D).
1.00
0.80
.. 0.60
j 0.40
0.20
0.00 0.00 0.20 0.40 0.60 0.80 1.00
conversion
Figure 8.4 Overall MA mole fraction as a function of conversion for MA-VPV emulsion copolymerization reactions with monomer-to-water ratios of0.02 (with initiator concentrations of0.13 gdm/ (o), and 1.2 gdm.,·3
(•)}, 0.1 (D), and 0.3 (6).
122 Chapter 8
1.00
0
j 0.40
0.20
0.00 L---.----.------,.------,__.l...!ll....~ 0.00 0.20 0.40 0.60 0.80 1.00
conversion
Figure 8.5 Overall MA mole fraction as a function of conversion forMAV2EH solution ( 11.) and emulsion copolymerization reactions with monomer-towater ratios of0.02 (with initiator concentrations of 1.2 grlmw-3 (.i), and 0.13 grlm,._3 (v)), 0.1 (D), and 0.3 (o).
From Figures 8.4 and 8.5 it becomes clear that the ratio of the water solubilities of both
monomers indeed has a large effect on composition drift in MA-VPV and MA-V2EH
monomer systems as was expected from the theoretical predictions depicted in Figure 8.1-
8.2. Furthermore, from Figures 8.3-8.5 it becomes clear that there is reasonable agreement
between experimental results of emulsion copolymerization reactions and theoretical
predictions of the overall monomer mole fraction as a function of conversion for monomer
to-water ratios larger than approximately 0.1.
It is important to realise that minimizing composition drift in MA-VPV and MA
V2EH reactions is only possible due to the large difference in water solubility values of the
monomers (a factor of 80 and 2400, respectively) which is necessary to counteract the large
difference in reactivity ratios (factor 700). In this case the water phase can buffer a sufficient
amount of the more reactive monomer to minimize composition drift.
The deviations observed between theory and experiment for low monomer-to-water
ratios may have two possible causes: 1) water phase polymerization of the better water
soluble MA can not be neglected, and 2) the model predictions are sensitive towards
deviations in model parameters for low monomer-to-water ratios, where the amount of
monomer in the aqueous phase cannot be neglected as compared with the total amount of
monomer.
The water phase polymerization has been examined by performing two reactions
differing only in initiator concentration. In those cases where water phase polymerization
plays an important role, more MA-rich oligomers will be formed in the aqueous phase at
The effect of water solubility on composition drift 123
higher concentrations of the water soluble initiator. It is expected that, as a result of more
homogeneous nucleation, the MA will disappear faster as a function of conversion at higher
initiator concentrations. However, the composition drift behaviour in the two reactions is
equal within experimental error (see Figures 8.4 and 8.5), strongly suggesting that the
discrepancy between theory and experiment cannot be explained by water phase
polymerization alone. The occurrence of insignificant aqueous phase polymerization of MA
in the MA-VPV reactions was confirmed by 1H-NMR and HPLC analyses. The 1H-NMR
analyses of low conversion samples showed that the overall copolymer composition was
equal to the theoretically predicted copolymer composition within experimental error, while
in HPLC analysis no homo-polymer of MA was found.
For the MA-V2EH reactions significant deviations were found between the
theoretically predicted (pred) and experimentally (exp) determined copolymer compositions
(M/W = 0.02, 1H-NM~red = 0.73, 1H-NMI\xp = 0.87; M/W 0.3, 1H-NM~ = 0.94, 1H
NMR,xp = 0.98). Furthermore, some homopolymer of MA was found with HPLC in this
case, indicating that water phase polymerization has occurred in the MA-V2EH emulsion
copolymerizations.
The effect of intentionally imposed deviations in the model parameters on
composition drift has been discussed in detail in the appendix of chapter 6 for MMA-S,
indicating that the effect of deviations only can be neglected if the amount of monomer in
the aqueous phase is negligible as compared with the total monomer amount. In the MA
VEst polymerizations with low monomer-to-water ratios, the amount of monomer located
in the aqueous phase cannot be neglected. Therefore, the (in)accuracy of the model
parameters may lead to deviations between experimental results and model predictions. As
can be seen in Figures 8.4 and 8.5, in the present cases the deviations indeed are larger for
low monomer-to-water ratios. Performing model predictions with different parameters for
the MA-VPV combination at low monomer-to-water ratios of 0.02 (see Table 8.3; 10%
deviation on reactivity ratios, water solubility, and swellability of polymer with monomer)
indicates that predictions in these low monomer-to-water cases indeed are sensitive towards
deviations in model parameters (Figure 8.6).
Summarizing the above discussion on water phase polymerization and the sensitivity
of predictions towards the accuracy of model parameters, the following can be concluded:
1) Accurate model predictions at low monomer-to-water ratios in both MA-VPV and MA
V2EH emulsion copolymerization are prohibited by the sensitivity of predictions towards
(in)accuracies of the model parameters.
2) The discrepancy between theory and experiment in the MA-VPV copolymerization can
124 Chapter 8
solely be attributed to (in)accuracy of the model parameters, since in that case no significant
water phase polymerization has occurred.
3) The discrepancy between theory and experiment of the MA-V2EH copolymerizations is
most probably caused by both, inaccuracy of the model parameters and aqueous phase
polymerization.
Table 8.3 Standard parameters (VPVJ) and intentionally introduced deviating parameters (VPV2-4), used in MA-VPV model predictions at 5(J'C. All concentrations are in mol/dm3
•
fMA
fypy
VPVl VPV2 VPV3 VPV4
6.7 1-10'5
[MA].,sat(h) [VPV] .. ,01(h)
[MA]p,sat(h) [VPV)p,sat(h)
6.1 8.7·10'3
0.55
7.3•10'3
7.05
4.0
6.7 1•10'5
0.55 7.3•10'3
7.05
4.0
6.7 1·10"5
0.49 8·10"3
7.05
4.0
0.49 8·10'3
7.7
4.4
VPVl
0.40 VPV4
0.20
0.00 '-----.,-----..-----..-----..,..---0.00 0.20 0.40 0.60 0.80 1.00
conversion
Figure 8. 6 Model predictions of the overall MA mole fraction as a jUnction of conversion using the series of model parameters listed in Table 8.3 for a MAVPV copolymerization (MIW 0.02), and comparison with experimental data (o).
8.5 Conclusions
Theory predicts that for monomer systems in which the water solubility of the
The effect of water solubility on composition drift 125
monomers is very far apart (low a-values) the effect of differences in reactivity ratios on
copolymer heterogeneity can be compensated. In principle, composition drift can be reduced
by changing the initial monomer-to-water ratio in batch emulsion copolymerizations in which
the more reactive monomer is also the more water soluble one. Experimental verification
of this concept has shown that minimum composition drift could be achieved for the
monomer system MA-VPV and MA-V2EH, where MA is the more reactive and more water
soluble monomer. For the monomer combination MA-V Ac composition drift could only be
slightly reduced by lowering the monomer-to-water ratios since the difference in water
solubility of the two monomers is too small in this system.
An important conclusion that can be drawn when comparing the composition drift
behaviour of the three MA-VEst monomer combinations is that, although the reactivity ratios
are approximately equal for the three systems, the chemical composition distribution of each
of the resulting copolymers will definitely change if one vinyl ester monomer is replaced
by another one, as a result of their differing water solubilities. Such a replacement would
therefore also immediately affect copolymer heterogeneity and hence properties.
126 Chapter 8
1. H.P.H. Scholten, J. Vermeulen, "A new versatile building Block for HighPerformance Polymeric Binders", XIX Fatipec Conference, Aachen, 18-24, 1988
2. W.C. Aten, "Effect of Composition and Molecular Weight on the Performance of Latices Based on Vinyl Ester of Versatile Acid in Modern Emulsion Paints", XVIIth Fatipec Congress, Lugano, 1984 .
3. M.M.C.P. Slinckx, H.P.H. Scholten, "Veova 9/(Meth) acrylates, A new Class of Emulsion Copolymers", 19th Water-Borne, Higher Solids and Powder Coating Symposium, New Orleans, La., 1992
4. R.E. Murray, US 4, 981, 973 to Union Carbide, 1991 5. L.F.J. Noel, LA. Maxwell, W.J.M. van Well, A.L. German, J Polym. Sci., Polym.
Chem. Ed., 32, 2161 (1994) 6. F.L.M. Hautus, H.N. Linssen, A.L. German, J Polym. Sci., Polym. Chem. Ed., 22,
3487, 3661 (1984) 7. M. Dube, R. Amin Sanayei, A. Penlidis, K.F. O'Driscoll, P.M. Reilly, J. Polym. Sci.,
Polym. Chem., 29, 703 (1991) 8. L.F.J. Noel, J.L. van Altveer, M.D.F. Timmennans, A.L. German, in press by J
Polym. Sci., Polym. Chem. Ed., xx, xx (1994) 9. L.F.J. Noel, J.M.A.M. van Zon, A.L. German, J Appl. Polym. Sci., 51, 2073 (1994) 10. F.R. Mayo, F.M. Lewis, J Am. Chem. Soc., 66, 1594 (1944) 11. T. Alfrey, G. Goldfinger, J Chem. Phys., 12, 205 (1944)
Epilogue 127
Epilogue
The primary goal of the research described in this thesis was gaining basic insight in
copolymerization taking place in heterogeneous media, in particular emulsion copolymerization.
It was hoped that these insights, combined with the development of enhanced methods
of on-line process monitoring, would contribute to a better control of composition drift in
emulsion copolymerization, and hence to the preparation of well-defined emulsion copolymers.
In order to reach this goal, the following more specific aims were formulated:
(1) Development of a reliable and simple model to describe monomer partitioning of two
monomers with limited water solubility, in such a way as to avoid the use of interaction
parameters that are experimentally difficult to access and theoretically rather vague.
(2) Investigation and evaluation of the (theoretical) concept that minimum composition drift
could be obtained by adjusting the monomer-to-water ratio for those monomer combinations
in which the more water soluble monomer is also the more reactive one.
(3) Development and evaluation of reaction monitoring techniques that provide a large
number of high-quality· data over the entire conversion range.
In the following a summary will be given of the strategies followed to reach these aims,
and some selected results will be shortly highlighted:
ad(1) Based on earlier work an extended model has been developed capable of describing
monomer partitioning at partial swelling oflatex particles by two monomers with limited water
solubility. The most important and striking feature of this partitioning model is that the only
parameters required are the individual homo-saturation values of the monomers in the polymer
particles and the aqueous phase, which are readily accessible. Experimental verification of the
model predictions for the monomer combination methyl acrylate-vinyl acetate shows excellent
agreement.
The availability of the present model solves one of the major problems in modelling
emulsion copolymerization, and allows the prediction of i.a. the compositional heterogeneity
of emulsion copolymers.
128 Epilogue
In addition, the present model also allows prediction of the absolute monomer
concentrations in the particle phase, which det~rmine the rate of (co)polymerization. This is
of great importance in determining optimal addition rate profiles, needed when preparing
compositionally homogeneous copolymers in semi-continuous processes. The latter, however,
is beyond the scope of this thesis.
ad(2) The reactivity-solubility concept was first tested for the emulsion copolymerization of
methyl acrylate-indene, where methyl acrylate is the more reactive as well as the more water
soluble monomer. It appears, when starting from any initial value within a wide range of
monomer feed compositions, that indeed the composition drift can be minimised (almost zero)
over the entire conversion range, simply by adjusting the monomer-to-water ratio.
A most rigorous test of the validity of the above concept is performed in a study of
the effect of the monomer-to-water ratio on the copolymerization of methyl acrylate with a
series of vinyl esters of strongly varying water solubility. The large difference in reactivity
(for all these systems a factor of ca. 700), cannot be compensated by the small difference in
water solubility between methyl acrylate and vinyl acetate, but it can be compensated by the
larger difference in water solubility between methyl acrylate and the other (more hydrophobic)
vinyl esters. The results clearly show that in essence the concept remains valid: i.e., in all cases
the composition drift is suppressed when decreasing the monomer-to-water ratio. Depending
on the specific monomer combination some intrinsic or practical limitations may occur,
however, preventing the composition drift to become (almost) zero.
These investigations provide and allow the utilization of a new handle on the
compositional control in emulsion copolymerization; a tool that is unique in the sense that it
does not exist in homogeneous (bulk or solution) copolymerization.
The present findings on the effects of monomer-to-water ratio and of monomer
solubility in water are having important practical implications as well. For example, in those
cases where the solids content in the reactor is changed, or where one of the monomers in the
recipe is replaced (even by an equimolar amount of another monomer of equal reactivity), a
copolymer product of different heterogeneity and thus different properties can be expected.
ad(3) The accurate and rapid determination of the partial conversion of the separate monomers
is of key importance to understanding, modelling, and controlling emulsion copolymerization.
The physical complexity of the systems (e.g., the heterogeneity leading to monomer
Epilogue 129
partitioning), calls for the combination of two on-line techniques: densimetry yielding the
overall weight conversion, and gas chromatography providing the overall ratios of the residual
monomers. Combination of these two data sets allows the calculation of the partial conversion
of each monomer as a function of time, most importantly, without the need of an internal
standard.
Adequate solutions have been proposed for non-ideal behaviour, as observed e.g. in
the system methyl acrylate-vinyl acetate, where the specific volume of the monomers in the
aqueous phase is different from that in the mono~er droplet phase.
Even for this rather complex, non-ideal system comparison of the on-line data with
off-line results and theoretical predictions gave satisfactory agreement, which validates this
powerful combination of techniques, indispensable in monitoring emulsion copolymerization.
The method developed is certainly not restricted to the present systems, but could be
applied, in principle, to any monomer combination. Extension of the method to monitor
terpolymerization seems quite well feasible. Future developments also may include the
instantaneous control of monomer addition, based on on-line measurements of monomer
conversion data, allowing the preparation of tailor made copolymers in a single run. For
example, the composition drift could be controlled in any desired manner by on-line
measurement of the instantaneous monomer concentrations, and feed-back control of the
addition rate of the more reactive monomer.
130
symbol
A
B
DS(t)
List of symbols
temperature dependent densimeter instrument constant
temperature dependent densimeter instrument constant
dry solids content at time t determined by weighing the latex mass
of a sample before and after drying
mole fraction of monomer i
copolymer composition in mole fraction of monomer i
degree of saturation of the polymer phase
F sat. degree of saturation of the aqueous phase
propagation rate coefficient
average propagation rate coefficient
propagation rate constant of the propagation step between radical i
and monomer j
number average molecular weight
List of symbols
units
%
-I%
--1%
dm3mol"l-s·l
dm3 mol"1 -s·1
dm3mol"1-s"1
gmol"1
mass of the non-polymerizable and non-evaporative components in emulsion
mass of the initially added monomers to an emulsion
g
g
g
g
total mass of the emulsion mixture
initial mass of monomers i at the beginning of the reaction
m9 ratio of the molar volumes of monomers i and}, (my = VmfVm}
Mx,t total moles of monomer x in the system
N.. avogadro's number
N number of particles per litre water
ii average number of radicals per particle
P. number-average degree of polymerization
R gas constant
%''·' overall ratio of monomer j over i at time t
r1 reactivity ratio of monomer i defined as r, = k;/k1i
ri reactivity ratio of monomer j defined as ri = kjki1
unswollen radius of the latex particle
rate of polymerization
List of symbols
t time
T temperature
T period of oscillation of the sample tube
xto.Ct) total overall conversion determined by gravimetry
x,,, partial conversion of monomer i at time t
X mass fraction, subscripts m, p and s stand for monomer, polymer
and serum (the aqueous phase), respectively
vpo polymer volume
vp volumes of the monomer swollen polymer phase (the volume of the
polymer+ monomer in the saturated polymer)
v. volume of the saturated aqueous phase (the volume of water+ monomer
dissolved in it)
vw volume of the aqueous phase (without monomer)
vd volume of the monomer droplet phase
vmx molar volume monomer x
v specific volume
Greek symbols
p
ratio of the water solubilities of monomer j over monomer i
density, subscripts l, p, and s represent the density of the total
diluted latex, the (co)polymer and the serum, respectively
A~ partial molar Gibbs free energy or chemical potential
v P volume fraction of polymer in the latex particles
vx_vCz) volume fraction in phase x of monomer y at homo saturation swelling
(z=h) or at a certain monomer ratio (z=r), at saturation swelling
subscript 'sat' is added
x Flory-Huggins interaction parameter
xii interaction parameter between monomers i and j
X;p. x1P interaction parameters between each of the respective monomers
i and j and the polymer
y particle-water interfacial tension
131
s
K
s
--I%
--1%
--fOAl
dm3
dm3
dm3
dm3
dm3
dm3mo1"1
dm3-Jcg-l
132
Concentrations
[M] monomer concentration
[M]p,i concentration of monomer i in the polymer phase
[M] • .; concentration of monomer i in the aqueous phase
[M •] free radical concentration
Subscripts, superscripts, and abbreviations
o start of the reaction
at 1 00% conversion
a aqueous phase
e total emulsion
List of symbols
mol-dm-3
mol-dm-3
mol-dm"3
mol-dm-3
h homo saturation swelling; saturation concentration of monomer in the absence of other
monomers
monomer i
j monomerj
m monomer droplet phase
MIW monomer to water ratio
p polymer particle phase
r mole ratio of monomers i and j
sat saturated
timet
Acknowledgement 133
Acknowledgement
The work presented in this thesis has been carried out in the Polymer Chemistry Group
of Prof. A.L. German. I wish to express my gratitude towards the members of this group, who
have contributed to this thesis.
More specifically I thank my first promoter Ton German, for his confidence in me and
for his pleasant way of coaching. My copromoter, Ian Maxwell (Memtec Limited, Sydney,
Australia), is gratefully acknowledged for his invaluable contributions to and discussions on
this work especially in the field of thermodynamics and modelling, and for the correction of
papers and this thesis. Alex van Herk is acknowledged for his contributions in the discussions,
especially on the on-line measurements.
I wish to thank all students who contributed with experimental work and useful
discussions: Jan van Zon, Menno Timmermans, Dirk van Wasbeek, Frank Riswick, Eric
Brouwer, Willy van Well, Erwin Goosen, and Jeroen van Altveer. I also like to thank Herman
Ladan (TEM), Wieb Kingma (GC), Alfons Franken and Paul Cools (HPLC).
Of the people outside the polymer group who have helped me during my Ph.D. work,
wish to thank my second promoter, Prof. J.M. Asua (San Sebastian, Spain) for our
discussions and his comments on the manuscript of this thesis. Denis Heymans (Shell Research
S.A., Louvain-la-Neuve, Belgium), and David R. Bassett and Martha J. Collins (Union Carbide
Corporation, South Charleston, USA) are gratefully acknowledged for supplying me with
samples of the vinyl ester monomers.
The investigations were supported by the Netherlands Foundation for Chemical
Research (SON) with financial aid from the Netherlands Organization for Scientific Research
(NWO). Further financial contributions from the Foundation ofEmulsion Polymerization (SEP)
and Shell Nederland B.V. are also gratefully acknowledged.
Finally I wish to express my gratitude towards everybody who has shown interest in
me and my Ph.D.-work.
134 Currieulum vitae
Currieulum vitae
Lilian Verdurmen-Noel was born in Weert, The Netherlands, on the lllh of August,
1965. After graduation from secondary school at the Philips van Horne Scholen Gemeenschap
in 1985 she started her academic study in chemistry and chemical technology at the Eindhoven
University ofTechnology. She graduated (ir-diploma) on August 28, 1990 on a project entitled:
duplex stability and protein degradation of natural and fosforothioate DNA, in the group of
Prof.Dr. H.M. Buck of the organic chemistry department.
In the same year she started her Ph.D. project on monomer partitioning and composition
drift in emulsion copolymerization in the polymer chemistry group ofProf.dr.ir. A.L. German.
Stellingen
behorende bij het proefschrift
Monomer partitioning and composition drift
in emulsion copolymerization
van
Elisabeth, Franr,:ois, Johanna Verdurmen-Noel
1. Thermodynamische evenwichtsrelaties kunnen, ondanks sterke vereenvoudiging door
het gebruik van rigoureuze aannamen, leiden tot nauwkeurige voorspellingen van de
verdeling van monomeren over de verschillende fasen in emulsies. I.A. Maxwell, J. KU1ja, G.H.J. van Doremaele, A.L. German, Makromol. Chem., 193, 2065 (1992);
I.A. Maxwell, L.F:J. Noel, H.A.S. Schoonbrood, A.L. German, Makromol. Chem., Theory and
Simulation, 2, 269 (1993); Hoofdstuk 5 uit dit proefschrift.
2. De bewering van Ballard et a/. dat het einde van interval II in
emulsiecopolymerisaties voor de twee afzonderlijke monomeren bij verschillende
overall conversies zou liggen, duidt op een gebrek aan inzicht in de
monomeerverdeling in emulsiecopolymerisatie. M.J. Ballard. D.H. Napper, RG. Gilbert, J. Polym. Sci .. Polym. Chem. Ed., 19, 939 (1983)
3. Conversie in emulsiepolymerisatie kan met behulp van on-line dichtheidsmetingen
nauwkeurig bepaald worden, ondanks grote afwijkingen tussen afgelezen dichtheid
en absolute dichtheid. P.D. Gossen, J.F: MacGregor, J. Colloid 1nter, Sci., 160, 24 (1993); S. Canegallo, G. Storti, M.
Morbidelli, S. Carra, J. Appl. Polym. Sci., 47, 961 (1993); Hoofdstuk 4 uit dit proefschrift.
4. In de literatuur beschreven bepalingen van de reactiviteitsverhoudingen met behulp
van achterhaalde, onjuiste en onnauwkeurige methoden, blijven een onnodig en
hardnekkig verschijnsel.
M. Charreyre. V, Razaftndrakoto, L. Veron, T. Delair, C. Pichot, Macromol. Chem. Phys .. 195, 2141
(1994); B. Suthar, J. Joshi, J. Indian Chem. Soc., 70, 180 (1993); M. Ada/, P. Flodin, E. Gottberg
Klingskog, K. Holmberg, Tenside Surf Det., 31, 9 (1994).
5. Vergeleken met traditionele monomeerverdelingsevenwichtsexperimenten is het
verrichten van geleidbaarheidsmetingen aan emulsiepolymerisaties een relatief
simpele en directe methode om maximale zwelbaarheden van polymeer met
monomeer te bepalen.
R.Q.F. Janssen. A.M. van Herk, AL German, Surface Coatings International (JOCCA), 76(11), 455
(!993); L.F.J. Noel, R.Q.F. Janssen, W.J.M. van Well, A.M. van Herk, A.L. German, to be submitted
6. Het gebrek aan experimented bepaalde kinetische parameters van copolymerisaties
verhindert vooralsnog de experimentele verificatie van theoretische modellen voor
emulsiecopolymerisaties.
L.F.J. Noel, W.J.M. van Well, A.L. German, to be submitted
7. Het in 1994 publiceren van een uitgebreide beschrijving van de reeds in 1950
gepubliceerde Finemann-Ross methode om reactiviteitsverhoudingen te bepalen is
overbodig, ongewenst en duidt op een kritiekloze houding van de referees.
M. Ada/, P. Flodin, E. Gottberg-Klingskog, K. Holmberg, Tenside Surf Det., 31, 9 (1994).
8. Het aanduiden van een land (Nederland) met de naam van een van de provincies
(Holland) dient vermeden te worden onder andere omdat het kan leiden tot
verwarring en verkeerde statistieken betreffende aantallen deelnemers en hun land
van herkomst. Conference book, 8'• International Conference on Surface and Colloid Science, Adelaide, South
Australia, /3-/8 February 1994
9. Het vermelden dat uiteindelijke conclusies ondanks redeneerfouten toch geldig zijn
is eerder lachwekkend dan wetenschappelijk overtuigend.
H. Akisada, J. Colloid Interface Sci., 97, 105 (1985); Handout bij poster "CMC and Micellar
Composition of Ionic surfactant, Nonionic that, and Salt System" gepresenteerd door H. Akisada
tijdens: "8'" International Conference on Surface and Colloid Science'~ Adelaide, South Australia,
13-18 February 1994
10. De verdraagzaamheid van buren kan op eenvoudige wijze getest worden door het
nemen van een kat.
11. Aangezien het idee van nieuwbouw voor de faculteit Scheikundige Technologic al
bijna twintig jaar geleden werd geopperd, zou bij een snelle besluitvorming de dan
tot stand gekomen "nieuw"-bouw nu al weer sterk verouderd zijn.
Eindhoven, 29 november 1994