Rheology of Filled Polymer Systems
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Rheology_of_Filled_Polymer_Systems/list.txtRheology of Filled Polymer Systems\32A99DE65D3E6ACD25105FB4C6C25EDD.pdf Rheology of Filled Polymer Systems\3B9F511318735E6747BBECB02D2A76.pdf Rheology of Filled Polymer Systems\491D9AD415512E721C0C5F1866FAC4.pdf Rheology of Filled Polymer Systems\5193A41BE8108AC099BA1D5D5013149.pdf Rheology of Filled Polymer Systems\64BCDB4C44B75C72AEB8B38EE9F7075.pdf Rheology of Filled Polymer Systems\751ED7D75AB8B14C89CA458A218FEC3.pdf Rheology of Filled Polymer Systems\822039F238FBDE7CA3ABC76199E4410.pdf Rheology of Filled Polymer Systems\827FA50595CDD83E60CAF26A82698B.pdf Rheology of Filled Polymer Systems\942495DBD71B38D66F7F83E55BB1B.pdf Rheology of Filled Polymer Systems\B353AAC08DC096E9FE89D04C28D116FF.pdf Rheology of Filled Polymer Systems\CED7CEC94F2EBA155ED35E5ECF36A19.pdf Rheology of Filled Polymer Systems\CFA2DE446054709C411E1B891E96E4E7.pdf Rheology of Filled Polymer Systems\E17DE202A55DBC74ACFE2A6ADA6ECD.pdf Rheology of Filled Polymer Systems\F6451D42A5EDECA8F8B369C41B387CD.pdf Rheology of Filled Polymer Systems\FDFC3FEE3972EF090A8DB2F74808211.pdf
Rheology_of_Filled_Polymer_Systems/Rheology of Filled Polymer Systems/32A99DE65D3E6ACD25105FB4C6C25EDD.pdfPreparation of. filled jr-
polymer systems O
In context with the preparation of filled polymer systems, there arethree terms, namely, compounding, blending and mixing, which areoften synonymously or interchangeably used and though variousresearchers have defined these terms, one is at times faced with thedilemma of terminology [I]. In the present case, definitions of the termsare given as applicable to the subject matter and hence exclude anyother connotations of the terms.
Compounding is the term used for those cases wherein polymers aresoftened, melted and intermingled with solid fillers and other liquidadditives to form filled polymer systems.
Blending is defined as a process in which two or more componentsor ingredients are physically intermingled without engendering anysignificant change in the physical state of the components. The com-ponents are, normally, polymers to form polymer blends, and hence inthe present context, will not be used to describe the intermingling offillers with polymers.
The word mixing is applied to both the processes of compoundingand blending, and describes the process of intimate intermingling ofpolymers with fillers/additives or two polymers without any specificrestrictions. It covers a broad spectrum of dispersion of variousingredients to form a homogeneous mixture on some definable smallscale.
5.1 GOODNESS OF MIXINGThe important aspect in mixing is to evaluate the quality of mixtures [2]or the goodness of mixing [3]. The most straightforward method ofcharacterizing the quality of the mixtures is to measure to what extentthe desired properties have been attained. Industrial quality controlfollows that route whenever feasible. However, this requires a detailed
description of the structure of the mixture and to theoretically establishthis, the spatial position of each ultimate minor particle in the matrixmust be determined. It is often not possible to predict the exact path ofindividual ultimate particles during the mixing process because mostcompounding equipments achieve the mixed state randomly, though,of course, there are some in which mixing progresses at least in a partlyordered fashion.
In the random mixed state there are more possible arrangements ofthe minor component than in the completely unmixed state. In thelatter state the probability is unity and in the former case it is very largeequal to
0 _ (N; + Nj)!mixed
~ N;!Ni! (5'1)
N; and N'2 are the number of ultimate particles of the major and minorcomponent respectively. A very great number of possible randomdistributions have to be considered [4] to be the most uniformdistribution which can be achieved with common random typecompounding equipments as shown in Figure 5.1. From the inspectionof Figures 5.1(d) and 5.1(e), it can be seen that in the case of filledpolymer systems, this type of regular random state would undoubtedlybe preferable to any other random state. In the case of small ultimateparticles which cluster together to form large agglomerates (blobs), theclusters have to be broken up into ultimate particles (aggregates) anduniformly distributed by the dispersive mixing action. The randomdistribution of a component 'A' in a component 'B' is achieved if theprobability of finding an ultimate particle of 'A' is the same at all pointsin the mixture and is equal to the volume fraction a of the component'A' in the mixture. In the completely unmixed state as shown in Figure5.1 (a), a sample of volume Vs will have a concentration of component Aof either 1 or O.
The probability to find XA = 1 is 'a' and to find XA = O is b, as shownin Figure 5.2 on the left-hand side. The mean is given by
M = * (5.2a)and the variance as
2 = d> (5.2b)
The probability distribution for finding a particular level ofconcentration in a sample after drawing a great number of samples canbe calculated [4] from the following expression
COMPONENT: A,BVOLUME FRACTION: a,b
ULTIMATE PARTICLE SIZE: a,0Figure 5.1 Number of possible random distributions of fillers in a polymer matrix which can be achieved with common random typecompounding equipments. (Reprinted from Ref. 4 with kind permission from John Wiley & Sons, Inc., New York, USA.)
m, it does not reduce to equation (4.1) when0^0. Further, the averaging process used for deriving equation (4.10)has been shown to be incorrect [101] and it has been argued that thedissipation in pair interactions is too small to explain the observedtrends. But since equation (4.10) does fit experimental data rather wellfor high solids concentrations, it can be simply considered as yetanother empirical equation.
Attempts [102-104] to fit the entire range of volume fraction from(j) -* O to 0 -> 0m have resulted in equations which give a unique curvethrough the use of a plot of relative viscosity versus the ratio of 4>/4>m.The work of Chong et al. [102] has shown a good fit betweenexperimental results and an equation of the following type:
'"Mi^fc)]'0m is normally determined from the experimental data. It is to be notedthat equation (4.11) reduces to equation (4.1) at low values of (/) when(J)n takes a value of 0.6.
One of the best available empirical expressions which fits the entirerange of volume fraction, is the Maron-Pierce type equation that was
carefully evaluated by Kitano, Kataoka and co-workers [103,104], andextensively tested by Poslinski et al [105,106].
rjr = [1 - 4>/(t>m}-2 (4.12a)For suspensions of smooth spheres, a value of 0m = 0.68 has been
suggested [107] and a value of 0m = 0.60-0.62 has been determinedthrough liquid displacement experiments [105,106]. In reality, of course,using ^1n as 0.6 or 0.62 or 0.68 does not improve the data fit appreciably.But at times it may be best to view m as an adjustable parameter andthen equation (4.12a) is rewritten as follows:
iyr = (1 - 1.Thus,
>7r = l + arl0 + ar22 (4.13)where
"=) + 2 --)SI-where Ji is an interaction parameter, /J0 is a rate constant for theequilibrium between free particles and floccules and Z0 is the degree offlocculation.
Hashin [120] used the flow-elasticity analogy to give the followingequation which was valid only for parallel, randomly placed infinitelylong fibers
^r = l+A (4-20)1-0Nielsen [121] used the same analogy, but his equation has not beentested for concentrated fiber suspensions.
The shape of the rod (whether straight or curved) does affect therelative viscosity of the suspension. The viscosity for curved fibersuspension is known to be higher than that for a straight fibersuspension and the difference increases with increasing concentration(Figure 4.4).
4.2.2 EFFECT OF SIZE DISTRIBUTION OF THE PARTICLES
Clarke [81] observed that mixed suspensions of mainly coarse particlesand relatively few fine particles showed a marked decrease in theviscosity compared to an all coarse suspension. Contrarily, suspensionswith mainly fine particles and few coarse particles showed very littlechange from an all fine suspension. It could thus be concluded that
Figure 4.4 Variation of the relative viscosity of suspensions with concentration for(a) curved fibers and (b) straight fibers.
smaller particles are interposed between larger particles, causing areduction in the interparticle impact resulting in a decrease in viscosity.Ward and Whitmore [122], Ting and Luebbers [123] and Moreland[124] also noticed similar results using different techniques ofmeasurement.
Shaheen [125] suggested that the addition of a little amount of smallparticles acts as a lubricant to facilitate the rotation of larger particles,leading to a reduction in the relative viscosity. Experimentally, it wasshown that the viscosity of a mixture of two different-sized particlesgoes through a minimum at about a volume fraction of small particlesequal to 0.25. Shaheen [125] wrote the modified form of Mooney'sequation (i.e. equation (4.8)) for a mixture of spherical particles of twodifferent sizes as follows:
/ 2/5a \ / 2.502 \'~
=Mr^Mi^^J (421)where
STRAIGHT FIBERSCURVED FIBERS
/r = l + aEs, the volume percent of the 15|im spheres, rangingfrom O to 100% of the total solids mixture as shown in Figure 7.6.Similar to the relative viscosity case in Figure 6.20, the relative primarynormal stress coefficient is also reduced when the two sizes of spheresare mixed together, and again the lowest values are obtained for0S = 10 to 30% of the smaller spheres, which happens to be the samerange when the maximum packing parameter is the highest.
The solid lines in Figure 7.6 represent the predictions of equation(7.1) with maximum packing fraction determined by equation (6.17)using the particle size distribution values of the bimodal componentslisted in Table 6.3. The agreement between theory and experiment isquite adequate. However, as discussed in section 7.3, there is a problemwith data interpretation because the curve of 60% by volume of totalspheres shows the highest elasticity which is incorrect.
7.5 EFFECT OF FILLER AGGLOMERATESAgglomerates occlude liquid in their interparticle voids and therebyleave a less volume fraction of the liquid around it. This would create
Figure 7.6 Variation of average relative primary normal stress coefficient as afunction of 0S, the volume percent of the 15^m glass spheres in the total mixturesuspended in a polybutene grade 24 matrix at 220C. (Reprinted from Ref. 72 with kindpermission from John Wiley & Sons, Inc., New York, USA.)
an apparent situation of higher filler loading than is actually present.Hence, the effect of filler agglomerates would be similar to that of fillerconcentrations; or, in other words, with larger number of filleragglomerates, the system would behave Theologically in a mannersimilar to a system with a higher filler concentration than what actuallyexists.
It can be thus expected that with increasing number of filleragglomerates when dealing with particulate fillers, the normal stressdifference would be lower. The extent of lowering of the normal stressdifference depends on the amount of occluded liquid by the agglomer-ates, the average number of particles in each agglomerate and hence thesize of the agglomerates. In an unagglomerated filled system, the extent
GLASS SPHERE FILLED POLYBDTENE
TQTALSPHERES
EQUATION CT. D
of normal stress difference lowering would be less if the particle size islarger. When an agglomerate is formed or present, it is as though theparticle size of the filler has increased throughout the system. Thus,with increasing number of particles in the agglomerates, the extent ofnormal stress difference lowering decreases. On the other hand, becauseof the occluded liquid in the interparticle voids of the agglomerates, theextent of normal stress difference lowering increases. It is basically thenet effect of these two opposing factors that determines exactly howmuch the normal stress difference would be lowered.
In the case of fiber-filled systems, too, the effect of agglomerateswould be to lower the normal stress difference. It has already beenshown in section 7.1 that fiber-filled systems show increases inelasticity. The extent of the increase would be thus reduced ifagglomerates are formed because the fibers that gather to make up theagglomerates are restrained and cannot orient during flow.
There are no experimental data specifically to support the intuitivethoughts put forth in this section. The reason is that determination ofnormal stress difference in the presence of agglomerates is extremelydifficult. The agglomerates interfere with the gap setting during coneand plate rheological measurements due to their increased size. Despitelack of actual data, the conclusions on the effect of agglomerates can bedrawn by carefully understanding the effect in analogous situations asdone here.
7.6 EFFECT OF FILLER SURFACE TREATMENTOne of the effective methods of reducing the number of filleragglomerates in a filled polymer system is through the use of surface-modifiers such as those listed in Table 1.5. Surface modifiers aregenerally bifunctional molecules with one end capable of adhering tothe filler and the other end compatible with the polymer, and at timeseven capable of reacting with it. Surface treatment basically helps thepolymer to wet the filler better and disperse it, thereby reducing andpreventing agglomeration because of promotion of filler-polymercontact as against filler-filler contact. Research work on the effect ofsurface treatment on the steady shear elastic properties of filledpolymer systems is limited [27,34] but good enough to draw adequateconclusions.
Figure 7.7 shows the effect of surface treatment on 30% calciumcarbonate filled polystyrene [27]. It can be seen that the data arepresented in both forms of representations. N1 vs. y (Figure 7.7(a)) andN1 vs. T12 (Figure 7.7(b)). In Figure 7.7(a), it appears that surfacetreatment reduces elasticity to a level even below that of the purepolymer. However, conclusions drawn from this type of representation
Figure 7.7(b) Variation of primary normal stress difference with shear stress forcalcium carbonate filled polystyrene containing 30% untreated and treated filler.(Reprinted from Ref. 27 with kind permission from Society of Plastics Engineers Inc.,Connecticut, USA.)
Figure 7.7(a) Variation of primary normal stress difference with shear rate forcalcium carbonate filled polystyrene containing 30% untreated and treated filler.(Reprinted from Ref. 27 with kind permission from Society of Plastics Engineers Inc.,Connecticut, USA.)
TKEKTEDUNTREATED
PASCALSUNITS
CALCIDH CARBONATE FILLED POLYSTYUENE
UNTREATED
TELEATED
UNITSPASCALS
CALCIUM CARBONATE FILLED POLYSTYRENE
would not be correct because the untreated 30% CaCO3 shows anincrease in elasticity, which is against intuition and logic as discussedin section 7.2. Thus, the representation given in Figure 7.7(b) is the trueone and shows that surface treatment increases the values of N1 asagainst that of the untreated system of a fixed filler loading at the samelevel of shear stress.
Figure 7.8 gives the plot of first normal stress difference vs. shearstress for CaCO3 filled polypropylene. Similar to the effect observed inFigure 7.7(b), the use of the surface modifiers, namely, silanes Y9187and AIlOO, shows an increase in the normal stress difference over thatof the untreated system irrespective of the temperature of measurement.Note that Y9187 is an N-octyltriethoxysilane while AIlOO is a y-aminopropyltriethoxysilane. The same effect is, however, not found tobe the case when considering a different filler such as glass beads in thepolypropylene.
CALCIUM CAEBONATE FILLED POLYPROPYLENE
UNITSPASCALS
Figure 7.8(a) Variation of primary normal stress difference with shear stress at20O0C for calcium carbonate filled polypropylene treated with silane surface modifiers.(Reprinted from Ref. 34 with kind permission from Society of Plastics Engineers Inc.,Connecticut, USA.)
Figure 7.8(b) Variation of primary normal stress difference with shear stress at24O0C for calcium carbonate filled polypropylene treated with silane surface modifiers.(Reprinted from Ref. 34 with kind permission from Society of Plastics Engineers Inc.,Connecticut, USA.)
Figure 7.9 shows that neither the silane Y9187 nor AIlOO is effectivein influencing the normal stress difference of the untreated glass beads-PP systems at 20O0C. However, at 24O0C, the surface modifier Y9187decreases the melt elasticity while AIlOO increases it. Note that the datain Figures 7.8 and 7.9 are all in the high shear rate range and obtainedusing the Han slit/capillary rheometer.
When the surface modifier is changed from the silane to a titanate inthe case of the CaCO3-PP system, as in Figure 7.10, the effects arequalitatively not different from those observed in Figure 7.7(a) or (b). Itis seen that the normal stress difference of the titanate KR-TTS treatedCaCO3-PP system is higher than that of the untreated CaCO3-PPsystem. In Figure 7.10, the low-shear data were obtained on theWeissenberg rheogoniometer and the high-shear data were got usingthe Han slit/capillary rheometer.
When the filler is changed to glass fiber and the same titanate KR-TTS is used as a surface modifier, it is seen that the untreated and
UOTTSPASCALS
CALCIUM CABBONATE FILLED POLYPROPYLENE
Figure 7.9(a) Variation of primary normal stress difference with shear stress at20O0C for glass bead filled polypropylene treated with silane surface modifiers.(Reprinted from Ref. 34 with kind permission from Society of Plastics Engineers Inc.,Connecticut, USA.)
Figure 7.9(b) Variation of primary normal stress difference with shear stress at24O0C for glass bead filled polypropylene treated with silane surface modifiers.(Reprinted from Ref. 34 with kind permission from Society of Plastics Engineers Inc.,Connecticut, USA.)
P?PP/GLASS BEADSPP/GLASS BEADS/Y9187PP/GLASS BEADS/Al 100
PASCALS
UNITS
GLASS BEADS FILLED POLYPROPYLENE
PPPP/GLASS BEADSPP/GLASS BEADS/Y9187PP/GLASS BEADS/AIlOO
UNITS
PASCALS
GLASS BEADS FILLED POLYPROPYLENE
Figure 7.10 Variation of primary normal stress difference with shear stress forcalcium carbonate filled polypropylene treated with titanate surface modifier TTS.Open symbols represent Weissenberg rheogoniometer data and closed symbolsrepresents Han slit/capillary rheometer data. (Reprinted from Ref. 34 with kindpermission from Society of Plastics Engineers Inc., Connecticut, USA.)
treated filled polypropylene systems do not show any difference in thenormal stress characteristics as shown in Figure 7.11.
The normal stress difference data in Figures 7.7-7.11 all go to showthat the effect of surface modifier is quite system specific. Hence,
CALCIUM CARBONATE FILLEDPOLYPROPYLENEUNTTS
PASCALS
Figure 7.11 Variation of primary normal stress difference with shear stress for fiberfilled polypropylene with 50% untreated and treated filler using titanate surfacemodifier TTS. Open symbols represent Weissenberg rheogoniometer data and closedsymbols represent Han slit/capillary rheometer data. (Reprinted from Ref. 81 with kindpermission from Academic Press Inc., New York, USA.)
extrapolation of information with regard to this effect can at times bedangerous. The efficiency of the surface modifiers will depend on thetype of filler, type of polymer, amount of modifier and method oftreatment as already discussed in section 6.6.
PPPP/GLASS FIBER/ITSPP/GLASS FIBER
UNITSPASCALS
GLASS FIBER FILLEDPOLYPROPYLENE
7.7 EFFECT OF POLYMER MATRIX
As already mentioned in section 6.7, the effect of polymer matrix on therheological properties of filled polymer systems would depend on thechemical nature of the polymer as well as its unfilled rheologicalproperties. In order to understand this effect, it would be essential toobserve normal stress difference response using different polymersystems but with the same filler of a fixed size/size distribution and ata fixed level of loading. This information is not available from onesource as in the steady shear viscous case [63]. Hence, this effect isexemplified by presenting data from different sources for differentpolymer systems but with the same fillers. Of course, the physicalcharacteristics of the chosen filler are unlikely to be the same and soalso, it is unlikely to find a particular filler loading as a commondenominator in all cases. Nevertheless, the data would give somegeneral idea of the effect of the polymer matrix.
Figure 7.12 Variation of primary normal stress difference with shear stress for glassfiber filled nylon 6,6 with 33 vol% of fiber. (Reprinted from Ref. 95 with kind permissionfrom Society of Plastics Engineers Inc., Connecticut, USA.)
NYLON 6,6/33% GLASS FIBERNYLON 6,6
GLASS FIBER FILLEDNYLON
UNITSPASCALS
Figures 7.12-7.14 show the effect of glass fibers at different loadinglevels on the normal stress difference behavior of nylon, polycarbonate(PC), and polystyrene (PS). Since the plots have been made as N1 vs. T12,they are independent of temperature. This is specifically clear fromFigure 7.12 which shows a uniqueness of data at the three temperaturesof 2750C, 2850C and 2950C [95].
In Figure 7.13 for polycarbonate [31], it is seen that N1 does not risesystematically with filler concentration at a fixed shear stress. The 30%loaded system coincides with the 10% loaded glass fiber filledpolycarbonate instead of lying between the 20% and the 40%. Noapparent explanation can be presented for such anomalous behavior.
In the case of glass fiber filled polystyrene [28], the loading level islimited to 10% and 22% and hence whether a reversal of the type thatwas observed in Figure 7.13 for PC takes place cannot be established.
Figure 7.11, which also gives the normal stress difference information
Figure 7.13 Variation of primary normal stress difference with shear stress for glassfiber filled polycarbonate of different grades of Makrolon. (Reprinted from Ref. 31 withkind permission from John Wiley & Sons, Inc., New York, USA.)
UOTTSPASCALS
MAKROLONGRADE
FILLER
GLASS FIBER FTTIED POLYCARBONATE
Figure 7.14 Variation of primary normal stress difference with shear stress for glassfiber filled polystyrene with different volume fraction. (Reprinted from Ref. 28 with kindpermission from John Wiley & Sons, Inc., New York, USA.).
on glass fiber filled systems [81] but using a different polymer, namelypolypropylene (PP), presents an unusual behavior. It is seen that this isthe lone case where a fiber filled system shows a decrease in elasticityof the polymer melt. The behavior is inexplicable considering the factthat even a Newtonian fluid containing fibers is known to show anincrease in elasticity [96].
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UOTTSPASCALS
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43. Bigg, D.M. (1982) Rheological analysis of highly loaded polymericcomposites filled with non-agglomerating spherical filler particles, Polym.Engg ScL1 22, 512-18.
44. Bigg, D.M. (1982) Rheological behavior of highly filled polymer melts,Polym. Engg Sc/., 23, 206-10.
45. Althouse, L.M., Bigg, D.M. and Wong, W.M. (1983) Evaluating theeffectiveness of filler surface treatments, Plastics Compounding, (March/April).
46. Lem, K.W. and Han, C.D. (1983) Rheological behavior of concentratedsuspensions of particulates in unsaturated polyester resin, /. Rheol., 27,263-88.
47. Daley, L.R. and Rodriguez, F. (1983) Flow properties of ethylene-propyleneterpolymer filled with silica modified by silane coupling agents, Ind. Eng.Chem. Prod. Res. Dev., 22, 695-8.
48. Mutsuddy, B.C. (1983) Influence of powder characteristics on therheology of ceramic injection molding mixtures, Proc. Brit. Ceram. Soc., 33,117-37.
49. Chaffey, C.E. (1983) Reinforced thermoplastics: through flow to use, Ann.Rev. Mater. Sa'., 13, 43-65.
50. Shenoy, A.V., Saini, D.R. and Nadkarni, V.M. (1983) Rheograms of filledpolymer melts from melt-flow index, Polym. Composites, 4, 53-63.
51. Shenoy, A.V. and Saini, D.R. (1983) Interpretation of flow data formulticomponent polymeric systems, Colloid Polym. ScL, 261, 846-54.
52. Suetsugu, Y. and White, J.L. (1983) The influence of particle size and surfacecoating of calcium carbonate on the rheological properties of its suspensionin molten polystyrene, /. Appl. Polym. ScL, 28,1481-501.
53. Luo, H.L., Han, C.D. and Mijovic, J. (1983) Effects of coupling agents in therheological behavior and physical mechanical properties of filled nylon 6, /.Appl. Polym. ScL, 28, 3387-98.
54. Bigg, D.M. (1984) Complex rheology of highly filled thermoplastic melts,Proc. IX Intl. Congress on Rheology in Mexico, Adv. in Rheology, 3, 429-37.
55. Kitano, T., Kataoka, T. and Nagatsuka, Y. (1984) Shear flow rheologicalproperties of vinylon and glass-fiber reinforced polyethylene melts, Rheol.Acta, 23, 20-30.
56. Kitano, T., Kataoka, T. and Nagatsuka, Y. (1984) Dynamic flow properties ofvinylon fiber and glass fiber reinforced polyethylene melts, Rheol. Acta, 23,408-16.
57. Suetsugu, Y. and White, J.L. (1984) A theory of thixotropic plasticviscoelastic fluids with a time-dependent yield surface and its comparisonto transient and steady state experiments on small particle filled polymermelts, /. Non-Newtonian Fluid Mech., 14,121-40.
58. Hinkelmann, B. and Mennig, G. (1985) On the rheological behavior of filledpolymer melts, Chem. Engg Comm., 36, 211-21.
59. Bretas, R.E.S. and Powell, R.L. (1985) Dynamic and transient rheologicalproperties of glass-filled polymer melts, Rheol. Acta, 24, 69-74.
60. Saini, D.R., Shenoy, A.V. and Nadkarni, V.M. (1985) Effect of surfacetreatment on the rheological and mechanical properties of ferrite-filledpolymeric systems, Polym. Engg ScL, 25, 807-11.
61. Saini, D.R. and Shenoy, A.V. (1986) Viscoelastic properties of highly loadedferrite-filled polymeric systems, Polym. Engg ScL, 26, 441-5.
62. Shenoy, A.V. and Saini, D.R. (1986) Quantitative estimation of matrix fillerinteractions in ferrite-filled styrene-isoprene-styrene block copolymersystems, Polym. Composites, 7, 96-100.
63. Saini, D.R., Shenoy, A.V. and Nadkarni, V.M. (1986) Melt rheology ofhighly loaded ferrite-filled polymer composites, Polym. Composites, 7,193-200.
64. Shenoy, A.V. and Saini, D.R. (1986) Wollastonite reinforced polypropylenecomposites: dynamic and steady state melt flow behavior, /. Reinf. PlasticsComp., 5, 62-73.
65. Mutel, A.T. and Kamal, M.R. (1986) Characterization of the rheologicalbehavior of fiber-filled polypropylene melts under steady and oscillatoryshear using cone-and-plate and rotational parallel plate geometry, Polym.Composites, 7, 283-94.
66. Edirisinghe, MJ. and Evans, J.R.G. (1987) Rheology of ceramic injectionmolding formulations, Br. Ceram. Trans. /., 86,18-22.
67. Sacks, M.D., Khadilkar, C.S., Scheiffele, G.W., Shenoy, A.V., Dow, J.H. andSheu, R.S. (1987) Dispersion and rheology in ceramic processing, Adv. inCeramics, 24, 495-515.
68. Dow, J. H., Sacks, M.D. and Shenoy, A.V. (1988) Dispersion of ceramicparticles in polymer melts, Ceram. Trans. (Ceram. Powder Sci. UA), 1, 380-8.
69. Hunt, K.N., Evans, J.R.G. and Woodthorpe, J. (1988) The influence of mixingroute on the properties of ceramic injection moulding blends, Br. Ceram.Trans. /., 17-21.
70. Takahashi, M., Suzuki, S., Nitanda, H. and Arai, E. (1988) Mixing and flowcharacteristic in the alumina/thermoplastic resin system, /. Am. Ceram. Soc.,17,1093-9.
71. Poslinski, A.J., Ryan, M.E., Gupta, R.K., Seshadri, S.G. and Frechette, FJ.(1988) Rheological behavior of filled polymer systems I. Yield stress andshear-thinning effects, /. Rheol, 32, 703-35.
72. Poslinski, AJ., Ryan, M.E., Gupta, R.K., Seshadri, S.G. and Frechette, FJ.(1988) Rheological behavior of filled polymeric systems II. The effect of abimodel size distribution of particulates, /. Rheol, 32, 751-71.
73. Ishigure, Y., Nagaya, K., Mitsumatsu, F., Otabe, S., Hayashi, K., Sobajima,A. and Murase, I. (1989) Relationship between the flow characteristics ofhighly filled alumina or zirconia-organic binder and the properties ofsintered products in injection molding processing, Rep. Gifu Pref. Ind. Res.Tech. Center, 21, 51-70.
74. Dow, J.H., Sacks, M.D. and Shenoy, A.V. (1990) Dispersion of aluminaparticles in polyethylene melts, Ceram. Trans. (Ceram. Powder Sci. Ill), 12,431-42.
75. Edirisinghe, MJ., Shaw, H.M. and Tomkins, K.L. (1992) Flow behavior ofceramic injection moulding suspensions, Ceramics Int., 18,193-200.
76. Nielsen, L.E. (1974) Mechanical Properties of Polymers and Composites, MarcelDekker, New York, Vol. 2, Ch. 7, 379-86.
77. Han, C.D. (1976) Rheology in Polymer Processing, Academic Press, New York,7,182-8.
78. Nielsen, L.E. (1977) Polymer Rheology, Marcel Dekker, New York, Ch. 9,133-57.
79. Paul, D.R. and Newman, S. (1978) Polymer Blends, Academic Press, NewYork, 1, Ch. 7, 295-352.
80. Vinogradov, G.V. and Malkin, A.Y. (1980) Rheology of Polymers, MirPublishers, Moscow, 380-402.
81. Han, C.D. (1981) Multiphase Flow in Polymer Processing, Academic Press,New York.
82. Shenoy, A.V. (1988) Rheology of highly filled polymer melt systems, inEncyclopedia of Fluid Mechanics, (ed. N.P. Cheremisinoff), Gulf Publishing,Houston, TX, 7, 667-701.
83. Yanovsky, Yu.G. and Zaikov, G.E. (1990) Rheological properties of filledpolymers, in Encyclopedia of Fluid Mechanics, (ed. N.P. Cheremisinoff), GulfPublishing, Houston, TX, 9, 243-76.
84. Carreau, PJ. (1992) Rheology of filled polymeric systems, in TransportProcesses in Bubbles, Drops and Particles (eds R.P. Chhabra and D. Dekee),Hemisphere Publishing, New York, 165-90.
85. Advani, S.G. (ed.) (1994) Flow and Rheology in Polymer Composites Manu-facturing, Elsevier Science BV.
86. Boger, D.V. and Derm, M.M. (1981) Capillary and slit methods of normalstress measurements, /. Non-Newtonian Fluid Mech., 6,163-85.
87. Han, C.D. (1982) Polymer News, 8,111-14.88. Oda, K., White, J.L. and Clark, E.S. (1978) Correlation of normal stresses in
polystyrene melts and its implications, Polym. Engg ScL, 18,15-28.89. Minoshina, W., White, J.L. and Spruiell, J.E. (1980) Experimental
investigation of the influence of molecular weight distribution on therheological properties of polypropylene melts, Polym. Engg ScL, 20,1166-76.
90. White, J.L. and Tanaka, H. (1981) Comparison of a plastic-viscoelasticconstitutive equation with rheological measurements on a polystyrene meltreinforced with small particles, /. Non-Newtonian Fluid Mech., 8,1-10.
91. Hopper, J.R. (1967) Effect of oil and black on SBR rheological properties,Rubber Chem. TechnoL, 40, 463-75.
92. Gotten, G.R. (1968) Rubber Age, 100, 51.93. Medalia, A.T. (1970) Morphology of aggregates VI. Effective volume of
aggregates of carbon black from electron microscopy; application to vehicleabsorption and to die swell of filled rubber, /. Colloid Inter/. ScL, 32,115-31.
94. Vinogradov, G.V., Malkin, A.Ya., Plotnikova, E.P., Sabsai, O.Yu. andNikolayeva, N.E. (1972) Rheological properties of carbon black filledpolymers, Int. J. Polym. Mat., 2,1.
95. Pisipati, R. and Baird, D.G. (1981) Correlation of rheological properties offilled nylon melts with processing performance, SPE ANTEC, 27, 32-4.
96. Mewis, J. and Metzner, A.B. (1974) The rheological properties ofsuspensions of fibers in Newtonian fluids subjected to extensionaldeformations, /. Fluid Mech., 62, 593-600.
Front MatterTable of Contents7. Steady Shear Elastic Properties7.1 Effect of Filler Type7.2 Effect of Filler Size7.3 Effect of Filler Concentration7.4 Effect of Filler Size Distribution7.5 Effect of Filler Agglomerates7.6 Effect of Filler Surface Treatment7.7 Effect of Polymer MatrixReferences
AppendicesAuthor IndexIndex
Rheology_of_Filled_Polymer_Systems/Rheology of Filled Polymer Systems/5193A41BE8108AC099BA1D5D5013149.pdf v This page has been reformatted by Knovel to provide easier navigation.
Contents
Preface ............................................................................ ix
1. Introduction ............................................................. 1 1.1 Polymers ...................................................................... 1
1.1.1 Thermoplastics, Thermosets and Elastomers .................................................. 1
1.1.2 Linear, Branched or Network Polymers ....... 2 1.1.3 Crystalline, Semi-Crystalline or
Amorphous Polymers .................................. 5 1.1.4 Homopolymers ............................................ 6 1.1.5 Copolymers and Terpolymers ..................... 7 1.1.6 Liquid Crystalline Polymers ......................... 9
1.2 Fillers ............................................................................ 9 1.2.1 Rigid or Flexible Fillers ................................ 10 1.2.2 Spherical, Ellipsoidal, Platelike or
Fibrous Fillers ............................................. 10 1.2.3 Organic or Inorganic Fillers ......................... 11
1.3 Filled Polymers ............................................................ 11 1.4 Filler-Polymer Interactions ........................................... 16
1.4.1 Filler Geometry ........................................... 18 1.4.2 Volume Fraction .......................................... 19 1.4.3 Filler Surface ............................................... 19 1.4.4 Wettability ................................................... 19 1.4.5 Filler Surface Treatment .............................. 21
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1.5 Rheology ...................................................................... 39 References .......................................................................... 43
2. Basic Rheological Concepts .................................. 54 2.1 Flow Classification ....................................................... 55
2.1.1 Steady Simple Shear Flow .......................... 55 2.1.2 Unsteady Simple Shear Flow ...................... 59 2.1.3 Extensional Flow ......................................... 62
2.2 Non-Newtonian Flow Behavior .................................... 66 2.2.1 Newtonian Fluids ........................................ 66 2.2.2 Non-Newtonian Fluids ................................. 67 2.2.3 Viscoelastic Effects ..................................... 71
2.3 Rheological Models ..................................................... 79 2.3.1 Models for the Steady Shear Viscosity
Function ...................................................... 79 2.3.2 Model for the Normal Stress Difference
Function ...................................................... 84 2.3.3 Model for the Complex Viscosity
Function ...................................................... 86 2.3.4 Model for the Dynamic Modulus
Functions .................................................... 90 2.3.5 Models for the Extensional Viscosity
Function ...................................................... 93 2.4 Other Relationships for Shear Viscosity
Functions ..................................................................... 99 2.4.1 Viscosity-Temperature Relationships .......... 99 2.4.2 Viscosity-Pressure Relationship .................. 103 2.4.3 Viscosity-Molecular Weight
Relationship ................................................ 104 References .......................................................................... 104
Contents vii
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3. Rheometry ............................................................... 112 3.1 Rotational Viscometers ................................................ 113
3.1.1 Cone and Plate Viscometer ......................... 115 3.1.2 Parallel-Disc Viscometer ............................. 117
3.2 Capillary Rheometers .................................................. 118 3.2.1 Constant Plunger Speed Circular Orifice
Capillary Rheometer ................................... 119 3.2.2 Constant Plunger Speed Slit Orifice
Capillary Rheometer ................................... 124 3.2.3 Constant Speed Screw Extrusion Type
Capillary Rheometers .................................. 124 3.2.4 Constant Pressure Circular Orifice
Capillary Rheometer (Melt Flow Indexer) ....................................................... 126
3.3 Extensional Viscometers ............................................. 128 3.3.1 Filament Stretching Method ........................ 128 3.3.2 Extrusion Method ........................................ 130
References .......................................................................... 131
4. Constitutive Theories and Equations for Suspensions ........................................................... 136 4.1 Importance of Suspension Rheology .......................... 136 4.2 Shear Viscous Flow ..................................................... 137
4.2.1 Effect of Shape, Concentration and Dimensions on the Particles ........................ 137
4.2.2 Effect of Size Distribution of the Particles ...................................................... 147
4.2.3 Effect of the Nature of the Particle Surface ....................................................... 150
4.2.4 Effect of the Velocity Gradient ..................... 150
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4.2.5 Effect of Flocculation ................................... 151 4.2.6 Effect of the Suspending Medium ................ 153 4.2.7 Effect of Adsorbed Polymers ....................... 154 4.2.8 Effect of Chemical Additives ........................ 160 4.2.9 Effect of Physical and Chemical
Processes ................................................... 160 4.2.10 Effect of an Electrostatic Field ..................... 162
4.3 Extensional Flow .......................................................... 164 References .......................................................................... 167
5. Preparation of Filled Polymer Systems ................ 175 5.1 Goodness of Mixing ..................................................... 175 5.2 Mixing Mechanisms ..................................................... 183 5.3 Compounding Techniques .......................................... 186
5.3.1 Selection Criteria ......................................... 186 5.3.2 Batch Mixers ............................................... 189 5.3.3 Continuous Compounders ........................... 192 5.3.4 Dump Criteria .............................................. 218
5.4 Compounding/Mixing Variables .................................. 221 5.4.1 Mixer Type .................................................. 223 5.4.2 Rotor Geometry .......................................... 224 5.4.3 Mixing Time ................................................. 225 5.4.4 Rotor Speed ................................................ 229 5.4.5 Ram Pressure ............................................. 229 5.4.6 Chamber Loadings ...................................... 231 5.4.7 Mixing Temperature .................................... 232 5.4.8 Order of Ingredient Addition ........................ 236
References .......................................................................... 237
Contents ix
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6. Steady Shear Viscous Properties .......................... 243 6.1 Effect of Filler Type ...................................................... 244 6.2 Effect of Filler Size ....................................................... 246 6.3 Effect of Filler Concentration ....................................... 248 6.4 Effect of Filler Size Distribution .................................... 262 6.5 Effect of Filler Agglomerates ....................................... 272 6.6 Effect of Filler Surface Treatment ................................ 273 6.7 Effect of Polymer Matrix .............................................. 279 6.8 Unification of Steady Shear Viscosity Data ................. 287 References .......................................................................... 303
7. Steady Shear Elastic Properties ............................ 312 7.1 Effect of Filler Type ...................................................... 313 7.2 Effect of Filler Size ....................................................... 315 7.3 Effect of Filler Concentration ....................................... 317 7.4 Effect of Filler Size Distribution .................................... 321 7.5 Effect of Filler Agglomerates ....................................... 321 7.6 Effect of Filler Surface Treatment ................................ 323 7.7 Effect of Polymer Matrix .............................................. 330 References .......................................................................... 332
8. Unsteady Shear Viscoelastic Properties .............. 338 8.1 Effect of Filler Type ...................................................... 344 8.2 Effect of Filler Size ....................................................... 344 8.3 Effect of Filler Concentration ....................................... 345 8.4 Effect of Filler Size Distribution .................................... 350 8.5 Effect of Filler Agglomerates ....................................... 356 8.6 Effect of Filler Surface Treatment ................................ 360 8.7 Effect of Polymer Matrix .............................................. 372
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8.8 Effect of Matrix Additives ............................................. 387 References .......................................................................... 390
9. Extensional Flow Properties .................................. 395 9.1 Effect of Filler Type ...................................................... 396 9.2 Effect of Filler Size ....................................................... 400 9.3 Effect of Filler Concentration ....................................... 402 9.4 Effect of Filler Surface Treatment ................................ 405 References .......................................................................... 409
10. Concluding Remarks .............................................. 416
Appendices .................................................................... 425 Appendix A Glossary .......................................................... 425 Appendix B ASTM Conditions and Specifications for
MFI ............................................................................... 430 Appendix C Data Details and Sources for Master
Rheograms .................................................................. 433 Appendix D Abbreviations .................................................. 439 Appendix E Nomenclature ................................................. 441 Appendix F Greek Symbols ............................................... 449
Author Index .................................................................. 455
Index ............................................................................... 469
Front MatterPrefaceTable of Contents1. Introduction1.1 Polymers1.2 Fillers1.3 Filled Polymers1.4 Filler-Polymer Interactions1.5 RheologyReferences
2. Basic Rheological Concepts2.1 Flow Classification2.2 Non-Newtonian Flow Behavior2.3 Rheological Models2.4 Other Relationships for Shear Viscosity FunctionsReferences
3. Rheometry3.1 Rotational Viscometers3.2 Capillary Rheometers3.3 Extensional ViscometersReferences
4. Constitutive Theories and Equations for Suspensions4.1 Importance of Suspension Rheology4.2 Shear Viscous Flow4.3 Extensional FlowReferences
5. Preparation of Filled Polymer Systems5.1 Goodness of Mixing5.2 Mixing Mechanisms5.3 Compounding Techniques5.4 Compounding/Mixing VariablesReferences
6. Steady Shear Viscous Properties6.1 Effect of Filler Type6.2 Effect of Filler Size6.3 Effect of Filler Concentration6.4 Effect of Filler Size Distribution6.5 Effect of Filler Agglomerates6.6 Effect of Filler Surface Treatment6.7 Effect of Polymer Matrix6.8 Unification of Steady Shear Viscosity DataReferences
7. Steady Shear Elastic Properties7.1 Effect of Filler Type7.2 Effect of Filler Size7.3 Effect of Filler Concentration7.4 Effect of Filler Size Distribution7.5 Effect of Filler Agglomerates7.6 Effect of Filler Surface Treatment7.7 Effect of Polymer MatrixReferences
8. Unsteady Shear Viscoelastic Properties8.1 Effect of Filler Type8.2 Effect of Filler Size8.3 Effect of Filler Concentration8.4 Effect of Filler Size Distribution8.5 Effect of Filler Agglomerates8.6 Effect of Filler Surface Treatment8.7 Effect of Polymer Matrix8.8 Effect of Matrix AdditivesReferences
9. Extensional Flow Properties9.1 Effect of Filler Type9.2 Effect of Filler Size9.3 Effect of Filler Concentration9.4 Effect of Filler Surface TreatmentReferences
10. Concluding RemarksAppendicesAppendix A: GlossaryAppendix B: ASTM Conditions and Specifications for MFIAppendix C: Data Details and Sources for Master RheogramsAppendix D: AbbreviationsAppendix E: NomenclatureAppendix F: Greek Symbols
Author IndexIndex
Rheology_of_Filled_Polymer_Systems/Rheology of Filled Polymer Systems/64BCDB4C44B75C72AEB8B38EE9F7075.pdfRheometry O
Rheometry is the measuring arm of rheology and its basic function is toquantify the rheological material parameters of practical importance.
A rheometer is an instrument for measuring the rheologicalproperties and can do one of the following two things:1. It can apply a deformation mode to the material and measure the
subsequent force generated, or2. It can apply a force mode to a material and measure the subsequent
deformation.The best designs of rheometers use geometries so that the forces/
deformation can be reduced by subsequent calculation to stresses andstrains, and so produce material parameters. It is very important thatthe principle of material independence is observed when parametersare measured on the rheometers. The flow within the rheometersshould be such that the kinematic variables and the constitutiveequations describing the flow must be unaffected by any rigid rotationof both body and coordinate system - in other words, the response ofthe material must not be dependent upon the position of the observer.When designing rheometers, care is taken to see that the rate ofdeformation satisfies this principle for simple shear flow or viscometricflow. The flow analyzed can be considered as viscometric (simpleshear) flow if sets of plane surfaces (known as shear planes) are seento exist and each is moving past the other as a solid plane, i.e. thedistance between every two material points in the plane remainsconstant.
The importance of viscometric flows becomes apparent when oneappreciates that the equation of motion for most viscometric flows canbe solved analytically. This is the reason why viscometric flows havebeen used for evaluating the viscosity function from viscometric dataand this fact has brought about the alternative name for simple shear
flows. All flows that do not conform to the viscometric behavior asdescribed above are termed non-viscometric flows. All rheometershave viscometric flows or at least 'near-viscometric' flows in them andhence are amenable to produce reliable material functions.
Rheometers used for determining the material functions of filledpolymer systems can be divided into two broad categories - (a) rotationaltype and (b) capillary type. Further subdivisions are possible andthese are shown in Table 3.1. In what follows only thoserheometers which are popularly used for rheological characterizationof filled polymer systems are described and discussed in detail. Forexample, though the bob and cup rotational viscometer has been used[1] in the fifties for polyethylene melts, it has not been included infurther detail. This is because this geometry is not at all popular evenfor unfilled thermoplastic melt studies, though Cogswell [2] didsuggest it in the seventies for measuring shear viscosities underconditions of controlled pressure. Similarly, other rheometers whichwere developed for rheological measurements of filled systems,particularly suspensions such as cement [3], red mud [4] or otherslurries [5,6], sealants [7], paints, foodstuffs or greases [8], dentalcomposites [9-11], propellants [12], etc. are also not described here, asthey are considered to be beyond the scope of this book. For a generaldiscussion on rheometry, as applicable to various types of fluids, it isadvisable to refer to some of the excellent monographs on this subject[13-18].
3.1 ROTATIONAL VISCOMETERSFor filled polymer studies, rotational viscometers with either the cone-plate or parallel-disc configuration are used.
The major advantages of cone and plate viscometers are:(i) a constant shear rate is maintained throughout the melt sample,
(ii) a small quantity of sample is required for measurement.On the other hand, the chief advantage of the parallel disc
configuration is that it can be used for filled polymer systems ofextremely high viscosity and elasticity.
The basic limitation in rotational viscometers is that they arerestricted in their use only to low shear rates for unidirectional shearand low frequency oscillations during oscillatory shear.
At higher shear rates as well as at higher frequencies, a flowinstability normally sets in the polymer sample which then begins toemerge out of the gap between the cone and plate or parallel-disc[19,20], thereby giving erroneous results. As a consequence of theabove, the measured material functions do not actually conform to the
Table 3.1 Rheometers for filled polymer systemsCapillary
Constantpressure
Plungertype
Circularorifice
Melt flowindexer(a) Kayeness*(b) Ceast*(c) Davenport*
(a) Haake rheocord*(b) Brabender plasticorder*
Slitorifice
Screwextrusion
type
Constantspeed
Circularorifice
Plungertype
Slitorifice
Han'sslitrheometer
(a) Monsantoautomaticrheometer*
(b) lnstroncapillaryrheometer*
Circularorifice
(a) Rheometrics mechanicalspectrometer*
(b) Sangamo Weissenbergrheogoniometer*
* Commercial instrument.
Paralleldisc
Oscillatoryshear
Rotational
Unidirectionalshear
Cone-n-plate
higher deformation rates which are normally prevalent in processingoperations.
Commercially available rotational instruments, such as theMechanical Spectrometer (Rheometrics Inc., Piscataway, NJ, USA) andWeissenberg Rheogoniometer (Carri-Med Ltd, Dorking, England)can be used for unidirectional rotational shear as well as oscillatoryshear and come with interchangeable cone and plate/parallel-discconfigurations.
3.1.1 CONE AND PLATE VISCOMETER
The cone and plate viscometer is a widely used instrument for shearflow rheological properties of polymer systems [21-32]. The principalfeatures of this viscometer are shown schematically in Figure 3.1. Thesample whose rheological properties are to be measured is trappedbetween the circular conical disc at the bottom and the circularhorizontal plate at the top. The cone is connected to the drive motorwhich rotates the disc at various constant speeds while the plate is
AXIAL IHKUSTMEASDHWGDEVICE
TORQUEMEASDWNGDEVICE STATIONARY
FLAT DISK POLYMERMELT
RQTA3TNGCONICALDISK
Figure 3.1 Schematic diagram showing the principal features of a cone and platerotational viscometer.
connected to the torque-measuring device in order to evaluate theresistance of the sample to the motion. The cone is truncated at the top.The gap between the cone and plate is adjusted in such a way as torepresent the distance that would have been available if theuntruncated cone had just touched the plate. The angle of the conesurface is normally very small (O0 < 4 or 0.0696 radius) so as tomaintain [14] cosec2 O0 = 1. The cone angles are chosen such that forany point on the cone surface, the ratio of angular speed and distanceto the plate is constant. This ensures that the shear rate is constant fromthe cone tip to the outer radius of the conical disc. Similarly, the shearrate can be assumed to be constant for any point within the gap becauseof the predesigned method of gap adjustment as described earlier.
The flow curve for a sample held between the cone and plate isgenerated from measurements of the torque experienced by the platewhen the cone is rotated unidirectionally at different speeds. Thevarious parameters of relevance are determined as follows.
A. Shear rateFor a constant speed of rotation of N rpm, the linear velocity (v = cor) is27rrN/60m/sec where co is the angular velocity (rad/sec) and r is theradial position in meters. The gap height at r is rtan90 where 90 is thecone angle. Hence shear rate in reciprocal seconds at r can be writtenas, _ __ __
. _ 2nrN _ nN ^ nNy ~ 60rtan00 ~ 30tan00 ^ 306^ '
Since the cone angle is always maintained to be very small, theapproximation of tan O0 = O0 does hold good.
B. Shear stressThe following expression defines the relationship between themeasured torque and the shear stress:
- f* -*T = 2TiT21 / r2 dr = f nRi2l (3.2)Jo
Thus,Tf
T2I=-Z5 (3-3)2nRThe shear stress is then obtained in pascals when T is expressed in
newtons.m and R in meters. The ratio of equation (3.3) to equation(3.1) results in the apparent viscosity expressed in Pa.sec.
C. Normal stress differenceThe cone and plate configuration can be used for estimating theprimary normal stress difference of the sample. If p is the pressure at apoint on the plate in excess of that due to the atmospheric pressure,then it can be shown [14] that the total normal force NF on the plate isgiven by,
Np = f 2nrpdr (3.4)JO
which on integration gives
nR2NF=-J-Ni (3,5)
Thus
N,=^ (3.6)nR
Using equations (3.1) and (3.6), a plot of primary normal stress vs. shearrate can be generated.
The shear stress and primary normal stress measurements can bedone simultaneously on the sample when it is subjected tounidirectional rotational shear in the gap of a cone and plateviscometer.
D. Oscillatory shearThe cone and plate viscometer can be used for oscillatory shearmeasurements as well. In this case, the sample is deformed by anoscillatory driver which may be mechanical or electromagnetic. Theamplitude of the sinusoidal deformation is measured by a straintransducer. The force deforming the sample is measured by the smalldeformation of a relatively rigid spring or tension bar to which isattached a stress transducer. On account of the energy dissipated by theviscoelastic polymer system, a phase difference develops between thestress and the strain. The complex viscosity behavior is determinedfrom the amplitudes of stress and strain and the phase angle betweenthem. The results are usually interpreted in terms of the materialfunctions, */', G', G" and others [33-4O].
3.1.2 PARALLEL-DISC VISCOMETER
The parallel-disc viscometer used for measuring the shear stress andnormal stress difference of filled polymer systems is similar in principle
to the cone and plate viscometer except that the lower cone is replacedby a smooth circular disc. This type of viscometer was initiallydeveloped for measuring the rheological properties of rubber [41-45]and hence made use of serrated discs placed in a pressurized cavity toprevent rubber slippage. When it was adapted for other polymericsystems [27,46,47], measurements were performed using smooth discsand without pressure.
The rheological properties in the parallel-disc viscometer are basedon the shear rate at the outer radius of the disc. Thus,
ya = coR/H (3.7)where co is the angular velocity (rad/sec), R is the radius of the disc (m)and H is the gap between the two parallel discs (m).
Shear stress and normal stress differences are given by the followingrelationships:
,R=jr/1+^I) (3.8)2nR\ 3 dln yJ
(,,-) -(*- *>=SH^g) MOscillatory shear measurements can be done with the parallel-disc
arrangement in a similar manner as in the case of the cone and plateviscometer and similarly the material functions, r\ ,G, G" and otherscan be generated. However, a slightly different technique [48] is attimes used wherein the polymer sample is deformed between twooscillating parallel eccentric discs as shown in Figure 3.2. In this case,too, it has been shown that the fluid elements undergo a periodicsinusoidal deformation and the forces exerted on the disc are thusinterpreted in terms of G and G" [14].
3.2 CAPILLARY RHEOMETERS
Capillary rheometers of various types are used for determining therheological properties of polymer melts as can be seen from Table 3.1.The principal feature is that these rheometers are capable of extrudingpolymer samples at different speeds through the capillary ofappropriate size. They are broadly categorized as
(i) those operating at constant speed and(ii) those operating at constant pressure.
A further categorization is possible based on the melt transportmechanism being of the plunger or the screw type and on the orifice
Figure 3.2 Schematic diagram showing the principal features of a parallel eccentricdiscs rotational viscometer.
shape, through which the melt is extruded, being of the circular or slittype. Each type of capillary rheometer is discussed in detail in thefollowing subsections.
3.2.1 CONSTANT PLUNGER SPEED CIRCULAR ORIFICE CAPILLARYRHEOMETER
Commercially available instruments such as the Monsanto AutomaticRheometer and the Instron Capillary Rheometer are examples ofequipment which extrude the polymer through a capillary with acircular orifice using a plunger at constant speeds. The principalfeatures of this rheometer are shown schematically in Figure 3.3.
The major advantage of this type of capillary rheometer is thathigher shear rate levels than those attainable in rotational viscometerscan be achieved. In fact, the achievable shear rates are within therealistic ranges that are actually observed in processing operations,thus making the rheological data more meaningful for simulatingprocessing behavior. Of course, the highest attainable shear rate data
AXIALIHRUSTMEASDMNGDEVICE
STAUQNARYFLATDISK
TORQUEMEASURINGDEVICE
ROTAUNGFLATDISK
POLYMERMELT
Figure 3.3 Schematic diagram of a constant plunger speed circular orifice capillaryrheometer.
are limited due to the occurrence of flow instabilities resulting inextrudate distortion or melt fracture at die wall shear stress levelsgreater than 1O5Pa [49-53]. The die wall shear stress TW can be easilycalculated by taking a force balance across the capillary die as,
7^APdie = 27TRN/NTW (3.10)
or
TW = ^ ^ (3.11)^N
where RN and /N are the radius and length of the capillary die, whileAPdie is the pressure drop required to extrude the polymer melt. Sincethe polymer flows from a wide reservoir into a capillary die in aconverging stream and then exits into open air or another widereservoir in a divergent stream, it is necessary to correct the shear stressvalue for these entrance and end effects. The use of long capillaries inthe vain hope that the end effects might be negligible is notrecommended and in fact, should be discouraged. In capillaries longer
V-CONSTANT
PLUNGER.
BESERVOIR
POLYMERMELTCAPILLARY DEB
than D0, pressure dependence effects become significant. Hence, endeffects can never be assumed to be negligible. The customary method ofincorporating end effects correction is through the use of an effectivecapillary length (/N + RN) as suggested by Bagley [54]. It must beemphasized here that basically there is no alternative but to carry outthe Bagley procedure to make end corrections. The wall shear stress forfully developed flow over the length (/N + #N) is then written as,
_ ^NAPdiew
~~ in _i_rj? ^t ^ >A'N + C^N)The shear rate at the die wall is expressed by the Rabinowitsch-
Weissenberg [55] equation for steady laminar flow of a time-independent fluid as,
, 4 Q T 3 ldln(4Q/^N)1w
" ^3N [4 4 dlnrw J (6'L6)
The term d In (^Q/nR^)/d In TW is basically equal to l/n where n isthe power-law index depicting the non-Newtonian character of thepolymer system. Thus, from equations (3.12) and (3.13), the followingrelationship is written
RNAPdie /4Q\2(/^Ki^=H^J (3'14a)
or,
'N
r . &Pdie /oi / iu\^
=
~
c 57M ( }/cnUy
The above equation is a straight line when a plot of /N/KN vs. APdieis constructed at different constant values of (4Q/nR^) as shown inFigure 3.4(a). This is done using dies of various /N/#N ratios and theintercept on the /N/^N ordinate at APdie = O determines the value of(. There are possibilities of observing slight non-linearity in the plotsas can be seen for data at 3.6 and 10.8 s'1 in Figure 3.4(a). These areprobably due to the breakdown of the assumptions made during thederivation of equation (3.14) of time-independence and no wall slip.True mechanical wall slip can occur during polymer flow when theshear stresses are large enough to overcome the static friction betweenthe wall and the flowing material [56-62]. Mechanical slip can occur aseither a steady-state phenomenon or as an unsteady phenomenonknown as 'stick-slip' [62-64]. This wall slip may induce the slight non-linearity in the plots shown in Figure 3.4(a). It must be shown that theBagley plot is linear before any capillary viscometry data are regarded
Figure 3.4(a) Plot for determination of the Bagley correction term during polymermelt flow through a capillary rheometer.
as meaningful. Hence, only those plots which are basically linear inFigure 3.4(a) are to be used. Once the plots have been shown to belinear for a particular capillary length and class of material, it is onlythen the capillary can be selected for viscometric measurements. Froma linear regression of these plots, the correction term is determined.Using equation (3.12), the corrected shear stress value at the wall isestimated. It should be noted that, since polymers are viscoelastic, theentrance effect needs an elastic-energy correction too. This is becausewhen the melt converges into the capillary, elastic stresses developand begin to relax inside the capillary. This effect is taken into account[65] by modifying equation (3.12) to include the recoverable shear termas follows:
APdie ,gjgx^ 2(/N/RN + C + SR/2) ^1DJ
Thus, the elastic energy stored at the capillary entrance is related to thecorrection term by the following expression [65].
ec = C + y (3.16a)Assuming Hooke's law in shear, TW = G x SR where G is the apparentmelt shear modulus, the correction term is rewritten as
INTERCEPT
PRESSUREDROP
(1O6PASCAIS)
Figure 3.4(b) Variation of capillary correction term with true wall shear stress forglass bead filled polypropylene. (Reprinted from Ref. 66 with kind permission fromSociety of Plastics Engineers Inc., Connecticut, USA.)
ec = C + ^ (3.16b)
This suggests that when ec is plotted against TW, a straight lineshould emerge with a slope of ^G. When such a plot is prepared in thecase of filled polymer systems, an interesting behavior is observed [66]as can be seen from Figure 3.4(b). The corrections for variousconcentrations of glass beads in polypropylene have been plotted. Itcan be seen that the correction term decreases with increasing fillervolume concentration at constant shear, with the exception of the filledpolypropylene system containing 26 vol.% of glass beads. Thedecreasing trend of the correction term with increasing glass beads isconsistent with studies such as the one using glass bead filled styreneacrylonitrile (SAN) systems [67]. The decreasing trend indicates thatthe amount of stored energy must be decreasing and hence therecovered energy or die swell would also decrease with increasingglass bead volume fraction. This was indeed found to be the case [66]when a few measurements of die swell were qualitatively compared.The slope ec vs. TW lines are seen to be constant, except for = 0.21and hence can be assumed to be independent of glass bead
GLASS BEAD FILLEDPOLYPROPYLENE
UNITS
concentration [66]. In the case of glass bead filled SAN systems,however, the ec vs. TW lines are highly non-linear [67].
The capillary rheometer can be used for estimating the normal stressdifference using the total ends pressure loss [65,68] and the exitpressure loss [69-71], wherein the latter has a more rigoroustheoretical basis. However, the assumption of fully developed flowexisting up to the tube exit may not hold true, especially in slow flows[72] and the errors introduced by the velocity field distortions at theexit may prove significant.
3.2.2 CONSTANT PLUNGER SPEED SLIT ORIFICE CAPILLARYRHEOMETER
This rheometer is similar in all respects to that discussed in section 3.2.1except for the fact that it has a slit orifice cross-section rather than acircular one. The major credit for the development of the concept anduse of this rheometer goes to Han [69,71,72] though others [73] havealso used it for polymer melt studies. The instrument makes use of aseries of flush mounted transducers located along the flow channel wallwhich measure the pressure gradients along the flow direction. Theseare then converted into wall shear stress values [69] as follows:
TW = fro ^ (3.17)dXwhere b0 = half thickness of the channel.
The wall shear rate is determined from the following expressiongiven in Refs 14 and 69:
y 3Q T2 lln(3Q/4^)17w
~4fl0*d3 + 3 lnrw J (3'18)
where U0 is the half width of the channel.In general, this instrument is capable of providing data in the higher
shear rate ranges comparable to those obtainable from the circularorifice capillary rheometer described in section 3.2.1. Using exitpressure losses, this instrument can also be used for determination ofnormal stresses. However, the probable velocity-profile distortions atthe exit may introduce errors that may not be negligible thoughexperimental evidence based on limited data [26,71] suggests otherwise.
3.2.3 CONSTANT SPEED SCREW EXTRUSION TYPE CAPILLARYRHEOMETERS
These capillary rheometers are principally the same as those describedin sections 3.2.1 and 3.2.2 except for the melt transport system which is
Figure 3.5 Schematic diagram showing the principal features of a constant speedscrew extrusion type capillary rheometer.
of the screw extrusion type rather than the plunger type discussedearlier. A schematic diagram of an extrusion capillary rheometer isshown in Figure 3.5. Commercially available extrusion capillaryrheometers are the Haake Rheocord (Haake Buchler Instruments Inc.,Saddle Brook, NJ, USA) and the Brabendar Plasticorder (Brabendar,Duisburg, Germany). The rheological property measurements can bedone using a circular or slit orifice as these are separate attachments forthe miniaturized single screw extruder.
These types of capillary rheometer are capable of generatingrheological data from medium-to-high shear rates. The applicableequations for shear stress and shear rate are the same as thosediscussed in sections 3.2.1 and 3.2.2. The data generated are auto-matically corrected for the Bagley correction and the Rabinowitsch-Weissenberg correction through a computer software program[74].
The screw extrusion type capillary rheometers have been used forrheological studies of polymers [75,76] but have not become aspopular as the plunger type capillary rheometers because they need amuch larger quantity of feed. Care has to be taken that the materialcompletely fills the extruder screw during transportation in order toavoid cavitation and erroneous results. Nevertheless, the utility ofthese types of instrument cannot be undermined. The single screwextrusion capillary rheometer is only one of the functions performedby the commercially available Haake Rheocord and BrabendarPlasticorder. They come with a number of other accessories such asthe miniaturized internal mixer and miniaturized twin screw extruderas well. In fact, the miniaturized internal mixer too has at times beenused for assessing the rheological properties of polymer systems. The
HOPPER POLYMERMELTPOLYMEEt POWDEROIL PELLETS
MELT TEMPERATDRSTHERMOCOUPLE
EXTJLUSlDN SCREW CAPULARy BODY
POLYMER MELT
PRESSURETRANSDUCER
CAPILLARYDIE
torque vs. rpm data generated by internal mixer can be easilyconverted [77-79] to shear stress vs. shear rate data. A more detailedunderstanding of torque rheometry and instrumentation can beobtained from the excellent article by Chung [74].
3.2.4 CONSTANT PRESSURE CIRCULAR ORIFICE CAPILLARYRHEOMETER (MELT FLOW INDEXER)
This rheometer is also similar to the one described in section 3.2.1except for two differences. Firstly, the capillary used is of very shortlength and secondly, the polymer is extruded by the use of deadweights (i.e. constant pressure) rather than constant plunger speed. Thisinstrument, popularly known as the Melt Flow Indexer, is very popularin the thermoplastics industry due to its ease of operation and low cost,which more than compensates for its lack of sophistication. Theparameter measured through the melt flow indexer contains mixedinformation of the elastic and viscous effects of the polymer. Further,no end loss corrections have been developed for this capillaryequipment nor can the melt flow index be easily related to theWeissenberg-Rabinowitsch shear rate expression.
In most monographs and texts on polymer rheology, the Melt FlowIndexer has been treated in a very brief manner because it hasgenerally been considered as an instrument meant only for qualitycontrol. It was specified as a standard rheological quality control testin the ASTM, BS, DIN, ISO and JIS (see Appendix D, Abbreviationslist for complete forms of these standards). However, it has beenshown in the recent past [80] that the Melt Flow Indexer providesmore than just a quality control rheological parameter. In fact the bookon Thermoplastic Melt Rheology and Processing [81] shows the multipleuses of the data from the Melt Flow Indexer, and treats this particularinstrument in the utmost detail. Hence, in the present book the MeltFlow Indexer and the Melt Flow Index are discussed rather briefly;and readers are encouraged to refer to the other book [81] for morecomprehensive discussion on the subject.
The basic principle employed in the MFI test by any of thestandards is that of determining the rate of flow of molten polymerthrough a closely defined extrusion plastometer whose important partsare shown in Figure 3.6. The cylinder is of hardened steel and is fittedwith heaters, lagged, and controlled for operation at the requiredtemperature with an accuracy of 0.5C. The piston is made of steeland the diameter of its head is 0.075 0.015 mm less than that of theinternal diameter of the cylinder, which is 9.5mm. The die (or 'jet')has an internal diameter of 2.095 0.005 mm or 1.180 0.005 mm(depending on the procedure used) and is made of hardened steel. All
Figure 3.6 Schematic diagram of the melt flow index apparatus showing a cross-sectional view of the important parts.
surfaces of the apparatus which come into contact with the moltenpolymer are highly polished.
MFI is basically defined as the weight of the polymer (g) extrudedin lOmin through a capillary of specific diameter and length bypressure applied through dead weight under prescribed temperatureconditions. ASTM D1238 specifies the details of the test conditions assummarized in Appendix B for commonly used polymers. The testconditions include temperatures between 125 and 30O0C and differentapplied dead loads from 0.325 to 21.6kg giving pressures from 0.46 to30.4kgf/cm2. The specifications have been selected in such a way as to
PISTON
BARBEL
HEATER A 3NSUIATEQN
REMOVABLE DIE
POLYMER
LOAD
give MFI values between 0.15 and 25 for reliable results. ASTM D1238gives the accuracy of the MFI value obtainable from a single measure-ment as carried out by different operators at different locations to bein the range of 9 to 15% depending upon the magnitude of theMFI.
3.3 EXTENSIONAL VISCOMETERSThe rotational viscometers and the capillary rheometers described insections 3.1 and 3.2 are those applicable for shear flows. However, thereare processing operations that involve extensional flows. These flowshave to be treated differently for making measurements of extensionalviscosity. The extensional viscosity of a material is a measure of itsresistance to flow when stress is applied to extend it. In general,measurement of steady-state extensional viscosity has proven to beextremely difficult. Steady extensional rate would be achieved bypulling the ends of the sample apart such that / = I0 exp(ef) or in otherwords, at a rate that increases exponentially with time. Steady-state isreached when the force is constant. However, often the sample breaksbefore steady-state is achieved or the limits of the equipment areexceeded or at the other extreme, the forces become too small for thetransducer to differentiate between noise and response signal.Nevertheless, there have been various methods attempted for themeasurement of extensional viscosity.
3.3.1 HLAMENT STRETCHING METHOD
The most common method for measurement of extensional viscosity isto stretch the filament of material shown in Figure 3.7 vertically as doneby Ballman [82] or horizontally as done by Meissner [83]. The polymermust have a high enough melt viscosity of 104 Pa.sec or greater in orderto be amenable for such extensional experiments.
Hence such data are restricted to high viscosity polyolefins such aspolyethylene and polypropylene rather than low viscosity nylon andpolyester. Further, the deformation rates are to be maintained at lowvalues to prevent breakage of filament and hence the deformationrates are limited to 5 sec"1 or less.
In the method of Ballman [82], which has been used by others[84,85], a vertical thermostated filament is clamped at both ends andstretched at the rate dl/dt such as to maintain a constant deformationrate. Thus,
,-i*
CB) HORIZONTAL FILAMENT STKCTCHINO
Figure 3.7 Schematic diagram showing the principal features of the filamentstretching method for extensional viscosity measurements: (a) vertical filamentstretching; (b) horizontal filament stretching.
(a) VERTICAL FILAMENT STKBTCHING
In the method of Meissner [83], a horizontal filament immersed inthermostated immiscible oil is held at both ends between pairs oftoothed wheels rotating with a linear velocity of V/2. Thus,deformation rate is written as,
V/2 Vi=ik=J (3-20)There are other variations of the filament stretching technique. For
example, filaments are clamped at one end and taken up on a rotatingroll [86,87]. This reduces the amount of filament stretching to a moreuniform level and produces a more constant extensional rate. In fact,when the following filament is taken up on a cold roll [87] a betterconstancy in the extensional rate is obtained.
Extensional viscosity based on constant stress measurements [88]has also been reported [89,9O]. In one case [89], the filament isextended vertically on top of a bath whereas in the other case [90], thevertical sample is immersed in the bath. The commercial equipmentavailable for the measurement of extensional viscosity fromrheometrics is based on the latter [9O].
A new universal extensional rheometer for polymer melts has beendescribed by Munstedt [91]. It was specifically designed with the ideaof making measurements on small samples possible in researchlaboratories under a variety of physical conditions, e.g. at constantstress or constant stretching rate, as well as relaxation and recoilexperiments.
The rotary clamp consisting of a pair of gears is a basic constructionelement for the design of various types of extensional rheometerdescribed earlier. The fact that the design is amenable for use inuniaxial and biaxial extensional rheometry has been shown byMeissner et al. [92]. Other biaxial extensiometers have also beendescribed [93,94] by other researchers.
A method for measurement of viscoelastic properties of polymers inthe prestationary extensional flow has been investigated by Leitlands[95]. A special experimental device using a vibrorheometer withautomatic control has been suggested. Some other methods of experi-mental studies with regard to the extension of polymer melts havebeen discussed by Prokunin [96]. In terms of uniform extensional flowof polymers, a rather comprehensive review is that of Petrie and Dealy[97] which may be referred to for further information on the subject.
3.3.2 EXTRUSIONMETHOD
A typical example of extensional flow is the flow at the entrance of acapillary die. Besides the converging flow analysis of Cogswell [98,99],
there have been other analyses [100,101] in more recent times which areimproved versions of the same ideas, and these can be used as betteralternatives especially when dealing with filled polymer systems.Cogswell [102] has shown that the pressure losses through such diescan be used as a measure for the extensional viscosity. This method hasnot gained popularity because of the skepticism in accepting thecomplex converging flow patterns at the die entrance as representativeof true extensional flow with constant extensional rate. Cogswell [103]did suggest later that the die ought to be lubricated to reduce the shearflow and the profile of the die wall should vary at all cross-sections insuch a way as to ensure constant extensional rate along the die axis.Such a rheometer has been known to be developed and used forextensional viscosity data of polystyrene melt [104].
The extrusion method using a lubricated die [104,105] allows themeasurements of systems with viscosity levels as low as 102Pa.sec.Thus, it can be used for extensional viscosity determinations in thecase of nylon and polyester which are often spun to make syntheticfibers. Higher extensional rates, even 200 sec"1 are also achievable inthis apparatus [104,105], thus making the information relevant for thepolymer processing industries involved in fiber spinning.
REFERENCES1. Philippoff, W. and Gaskins, F.H. (1956) Viscosity measurements on molten
polyethylene, /. Polym. ScL, 21, 205-22.2. Cogswell, F.N. (1973) The influence of pressure on the viscosity of polymer
melts, Plastics & Polymer, 41, 39-43.3. Kalousek, G.L. (1973) A new instrument for measuring thixotropy, Cement
and Concrete Res., 3, 315-23.4. Sarmiento, G., Crabbe, P.G., Boger, D.V. and Uhlherr, P.H.T. (1979)
Measurement of the rheological characteristics of slowly settling flocculatedsuspensions, Ind. Eng. Chem. Process Des. Dev., 18, 746-51.
5. Horie, M. and Pinder, K.L. (1979) Time-dependent shear flow of artificialslurries in coaxial cylinder viscometer with a wide gap, Can. J. Chem. Engg,57,125-34.
6. Tuft, P. (1977) A tube viscometer for slurry investigations, 6th AustralasianHydraulics and Fluid Mech. Conf., Adelaide, Australia (5-9 Dec.).
7. Lippe, RJ. (1980) Rheological parameters: a versatile tool for the sealantformulator, Plastics and rubber: Processing, 51-54 (June).
8. Hodgetts, G.B. and Freestone, A.R.L (1977) Extrusion rheometer forcharacterising thixotropic materials, Rev. Sd. Instrum., 48, 411-13.
9. Jacobsen, P.H., Whiting, R. and Richardson, P.C.A. (1977) Viscosity ofsetting anterior restorative materials, Brit. Dent. /., 143, 393-6.
10. Whiting, R. and Jacobsen, P.H. (1979) The evaluation of non-Newtonianviscosity using a modified parallel-plate plastometer, /. Mat. ScL, 14,307-11.
11. Vermilyea, S.G., Huget, E.F. and De Simon, L.B. (1979) Extrusion rheometryof fluid materials, /. Dental Research, 58,1691-5.
12. Baker, F.S., Carter, R.E. and Warren, R.C. (1980) The rheological assessment ofpropellants, Paper presented at the 8th Int. Congr. Rheol., Naples (1-5 Sept.).
13. Van Wazer, J.R., Lyons, J.W., Kim, K.Y. and Colwell, R.E. (1963) Viscosityand Flow Measurement: A Laboratory Handbook of Rheology, Interscience, NewYork.
14. Walters, K. (1975) Rheometry, Chapman & Hall, London; (1980) Rheometry:Industrial Applications, Research Studies Press, Chichester, England.
15. Whorlow, R.W. (1980) Rheological Techniques, Ellis Horwood, Chichester,England.
16. Schramm, G. (1981) Introduction to Practical Viscometry, Gebruder HAAKEGmbH, Karlsruhe, Germany.
17. Dealy, J.M. (1982)
