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Chain length dependence of the mean eld temperature in

poly(oxyethylene)poly(oxybutylene) diblock copolymers

J. Patrick A. Fairclough,a Anthony J. Ryan,a Simon Turner,a Ian W. Hamley,b Shaomin Mai,c

Colin Boothc and Richard C. Dennyd

a Department of Chemistry, University of Sheffield, Sheffield, UK S3 7HFb Department of Chemistry, University of L eeds, L eeds, UK L S2 9JT

c Department of Chemistry, University of Manchester, Manchester, UK M13 9PL

d CCL RC Daresbury L aboratory, Daresbury, W arrington, UK W A4 4AD

Received 18th December 1998, Accepted 5th March 1999

The mean eld behaviour of a series of short poly(oxyethylene)poly(oxybutylene) diblock copolymers with

50/50 volume fraction is discussed. The mean eld temperature is determined from small angle X-ray(TMF

)

scattering (SAXS). It is found to increase linearly with the volume normalised degree of polymerisation.rV

,

Introduction

Block copolymers comprise two or more chemically distinctpolymeric species joined by a covalent bond. Most commonlythe component chains are incompatible and will phaseseparate on a length scale comparable to the radius of gyra-tion of the polymer. They are said to microphase separate.Segregation is the term used to describe the three regions ofbehaviour within block copolymer melts. At strong segrega-tion (low temperature) the chains are appreciably stretchedand the interface between the blocks is sharp. At intermediatesegregation the interface adopts a sigmoidal shape and the

chains become less stretched. With increasing temperature theinterface breaks down and the chains mix. For weak segrega-tion the chains adopt a Gaussian conformation with chainsintimately mixed and mean eld behaviour is exhibited.Leibler1 developed a mean eld description of the behaviourof block copolymer melts for weak and intermediate segrega-tion. We have studied a series of diblock copolymers ofpoly(oxyethylene)poly(oxybutylene) in the semicrys-(E

nBm

)talline solid phase,2h4 ordered melt phases and disorderedmelt.5 Here we report further on the melt states and in partic-ular the behaviour above the order to disorder transition(ODT) and the transition to mean eld behaviour. Theoreticaland experimental aspects of microphase separation have beenreviewed and the reader is referred to these for a full descrip-

tion of the associated phenomena.6h9For a block copolymer chain of N total monomer units

comprising A monomer units and B monomer unitsNA

, NB

,the non-combinatorial Gibbs energy can be expressed as

*mix

Gnc\ kT(sr

V)/A/B

(1)

are the volume fractions of the A and B blocks, respec-/A/B

tively. Here

rV\N

A] N

B(lA/lB

) (2)

is a volume weighted degree of polymerisation, for andvA

vB

the respective monomer volumes.The function s, the FloryHuggins interaction parameter,

has empirically been observed to exhibit a temperature depen-

This work was carried out at the CCLRC, Daresbury Labor-atory, Daresbury, Warrington, UK WA4 4AD.

dence such as

s\a

T]b (3)

Where a and b are system dependant parameters, related tothe enthalpy and entropy of mixing, respectively. We havepreviously calculated the temperature dependence of s basedon a value of 10.5 at the ODT for symmetric volume fractioncopolymers.5 To take account of uctuation eects this hasbeen recalculated using Fredrickson and Helfands expressionfor a uctuating melt.10 This gives a value of at thesr

VB 15.5

ODT.Allowing for uctuation eects, the following param-eterisation has been obtained for poly(oxyethylene)poly(oxybutylene) diblock copolymers.

s\75.6

T[ 0.0929 (4)

The high value ofs for the EB system leads to short polymermolecules microphase separating and an expected deviationfrom mean-eld behaviour. The purpose of this study is toevaluate the eect of chain length on the mean eld behaviourwithin this system. The mean eld temperature, is theT

MF,

temperature below which deviation from the Leibler form ofthe small angle scattering intensity, I(q), is expected i.e. devi-

ation from I(q)~1PT~1. This deviation is primarily due tothe formation of density uctuations and chain stretching.Recent work by Maurer et al.,11 indicates that the form of sdescribing block copolymers is not sufficient to describe thebehaviour of blends. The authors ascribe this to the eects ofchain stretching and propose two separate forms of s forblock copolymers and blends.

Experimental

Five diblock copolymers of symmetric volume fraction wereprepared by sequential anionic polymerisation. The polydis-persity of all samples was below 1.07 as evaluated by(M

w/M

n)

gel permeation chromatography (GPC). The composition waschecked by NMR (see Table 1). These are the values used in

subsequent calculations. The presence of approximately 2%triblock copolymer was not felt to be sufficiently signicant towarrant inclusion in the analysis.

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8/3/2019 J. Patrick A. Fairclough et al- Chain length dependence of the mean eld temperature in poly(oxyethylene)-poly(ox

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Table 1 Characteristics of polymer studied

Composition Volume fraction (/E

) rV

E56

B27

0.52 107E60

B29

0.52 115E74

B37

0.51 148E85

B45

0.50 170E96

B47

0.52 185

Fig. 1 Typical plot of scattering vector (q) versus intensity versus

temperature for polymer The temperature range during thisE74B37 .run is reduced to show the ODT and the DOT.

Fig. 2 Typical data plot for T~1 versus I(q)~1 showing the meaneld temperature for copolymer Insert shows the variation inE

74B37

.d spacing (d\ 2p/q*) where q* is the position of the peak centre.

Fig. 3 Plot showing the variation in the mean eld temperaturewith chain length. The right hand axis shows the product for(T

MF) sr

Vs calculated at using eqn. (4).T

MF

The mean eld temperature was determined from the tem-perature dependence of the intensity of the correlation holepeak in the disordered melt via small angle X-ray scattering(SAXS). The SAXS experiments were carried out on Station8.2 of the CCLRC Daresbury Synchrotron Radiation Source(SRS). The optics, beamline geometry and data acquisition aredescribed elsewhere.12 The sample container comprises aLinkam single pan aluminium DSC pan, with a hole cut in thelid and base covered with thin mica sheet to allow the trans-mission of X-rays.5 The data were collected on a quadrant

linear detector, as the scattering from the samples was iso-tropic. The data were corrected for scattering from the samplepan and camera, for changes in transmission and decay in thebeam and nally for detector non-linearity. The data wereconverted to an absolute intensity scale by comparison with asecondary standard. The SAXS data were electronically corre-lated with the DSC data (sample temperature and inputheating power).

The sample was heated at a rate of 50 C min~1 to above itsODT and then cooled at 10 C min~1 to 70 C, then heated at10C min~1 to 40 C above the ODT to a maximum of220 C. This was found to be necessary as signs of degradationwere observed at 240 C. The scattering from the melt phasewas tted with a Pearson VII function by the CollaborativeComputing Project 13 (CCP13) t program.13 This func-tion is useful because it allows the shape of the peak to varyfrom a Gaussian to a Lorentzian prole. This is measured bya shape parameter, low values indicating a Lorentzian prole,high values a Gaussian. On cooling through the disorder toorder transition (DOT) there is a sharp transition from theweak Lorentzian uctuation peak to a strong, sharp Gaussiancharacteristic of the instrument resolution function. The dataare collected as a series of time frames and the tting routinetakes the results of the previous t as a rst step in tting thenext data set. As the data are electronically correlated, tem-perature versus intensity plots can readily be created.

Results and discussion

Fig. 1 shows the scattering as the ODT is crossed. The scat-tering peak transforms within 2 C from a sharp Gaussian, inthe lamella ordered phase to a weak Lorentzian in the disor-dered melt. During this transition the intensity, width andshape of the peak change dramatically. The peak centre doesnot change. This is a characteristic of the transition as it is acritical phenomenon, whereby on cooling from the disorderedmelt a single dominant wavelength is selected from the rangeof uctuation wavelengths above the ODT. This becomes thedomain period within the ordered structure. From the Leiblertheory,1 the scattering from a diblock copolymer can bedescribed as

S(q)\

N

F(x)[ 2sN (5)

where F(x) is a correlation function depending on the numberof segments, N is the total number of segments and(N

A]N

B)

the copolymer architecture and being the radiusx\ q2Rg2 , R

gof gyration. Thus s is proportional to S(q)~1 and hence I(q)~1,as such the reciprocal of intensity should be proportional toreciprocal temperature in the mean eld region. A plot ofreciprocal intensity versus reciprocal temperature can be seenin Fig. 2 with an indication of the mean eld temperature.This is the temperature below which the linear relationship nolonger holds.14 Characteristically at this temperature (T

MF),

the peak centre also shows a discontinuity in the temperaturedependence as indicated in Fig. 2. Other authors have report-

ed that d ln(q*)/dT changes faster than below thed ln Rg/dTmean eld temperature.14,15 This indicates that the blockcopolymer is undergoing an increasing amount of stretching

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8/3/2019 J. Patrick A. Fairclough et al- Chain length dependence of the mean eld temperature in poly(oxyethylene)-poly(ox

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as the temperature is lowered. Sakimoto and Hashimoto14observe the gradient of the d spacing increasing discontin-uously on heating at thus indicating the onset of chainT

MFstretching. The range of mean eld temperatures exhibited, forour EB copolymer is plotted in Fig. 3. This shows a linearvariation with chain length Plotting versus pro-(r

V). T

MFsrV

duces no discernible trend with chain length, indicating amean eld value of of approximately 10.2, this indepen-sr

Vdence is a consequence of assuming a T~1 dependence of sfrom eqn. (4).

Conclusions

Temperature correlated SAXS data have been used to calcu-late the transition to mean eld behaviour in a series of blockcopolymer melts. This is seen to vary linearly with ther

V,

volume normalised degree of polymerisation.

Acknowledgements

was provided for JPAF and RCD under EPSRCFundingContract GR/K05982 and BBSRC Contract 28/X04460,respectively. The authors are grateful for the help of B.U.Komansheck for the setting up of the SAXS experiment.

References

1 L. Leibler, Macromolecules, 1980, 13, 1602.2 A. J. Ryan, J. P. A. Fairclough, I. W. Hamley, S-M. Mai and C.

Booth, Macromolecules, 1997, 30, 1723.

3 S-M. Mai, J. P. A. Fairclough K. Viras, P. A. Gorry, I. W.Hamley, A. J. Ryan and C. Booth, Macromolecules, 1997, 30,8392.

4 I. W. Hamley, M. L. Wallwork, D. A. Smith, J. P. A. Fairclough,A. J. Ryan, S-M. Mai, Y-W. Yang and C. Booth, Polymer, 1998,39, 3321.

5 S-M. Mai, J. P. A. Fairclough, I. W. Hamley, M. W. Matsen,R. C. Denny, B-X. Liao, C. Booth and A. J. Ryan, Macromolecules,1996, 29, 6212.

6 I. W. Hamley, T he Physics of Block Copolymers, Oxford Uni-versity Press, Oxford, 1998.

7 F. S. Bates and G. H. Fredrickson, Annu. Rev. Phys. Chem., 1990,

41, 525.8 R. A. Brown, A. J. Masters, C. Price, X-F. Yuan, in Com-

prehensive Polymer Science, ed. C. Booth and C. Price, Pergamon,Oxford, 1989, ch. 6.

9 M. Matsen and F. S. Bates, Macromolecules, 1996, 29, 1091.10 G. H. Fredrickson and E Helfand, J. Chem. Phys., 1987, 87, 697.11 W. W. Maurer, F. S. Bates, T. P. Lodge, K. Almdal, K. Morten-

sen and G. F. Fredrickson, J. Chem. Phys., 1998, 108, 2989.12 W. Bras, G. E. Derbyshire, A. J. Ryan, G. R. Mant, A. Felton, R.

A. Lewis, C. J. Hall and G. N. Greaves, Nucl. Instrum. MethodsPhys. Res., 1993, 29, 1091.

13 The program is available from the Fibre and Polymer DiractionCollaborative Computing Project, CCP13, web site at http://wserv1.dl.ac.uk/SRS/CCP13/software.html.

14 N. Sakamoto and T. Hashimoto, Macromolecules, 1995, 28, 6825.15 J. H. Rosedale, F. S. Bates, K. Almdal, K. Mortensen and G. D.

Wignall, Macromolecules, 1995, 28, 1429.

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