Shear rate dependence of viscosity

The Rouse and Zimm models provide little direct help in dealing with t](y) since each predicts a viscosity which is independent of shear rate. The principal interest here is in concentrated systems where entanglement effects are prominent. Nevertheless, shear rate can influence the viscosity of polymer systems at all levels of concentration, including infinite dilution (307) and melts with M Mc (308, 315). It is therefore essential to identify the causes of shear rate dependence in systems of isolated or weakly interactions molecules in order to separate intramole- 

The effects of molecular structure on rj(y) are most conveniendy discussed in terms of reduced variables. The choice of form for reduced shear rate is guided both by the observation that the long relaxation times govern the onset of shear 

The reduced shear rate / retains a meaning over the entire range of concentration, becoming / = [r/] t]sMy/RT at infinite dilution and / =rj0My/cRT in concentrated solutions, where t]0 t]s. The corresponding reduced viscosities are [t/]/M0 and Reduced plots remove most of the observed variation among systems (Figs. 8.4-8.7), and simplify the empirical examination of residual 

7 Others have defined these variables slightly differently, using (1 — p)tjs in place of in Eqs.(8.2) and (8.3), where (p is the volume fraction of polymer in the solution. However, the practical effect is entirely negligible for all data examined in this review. The value of qo-tjs increases so rapidly with polymer concentration that tj0 — % and are 

Another alternative is to correlate data in terms of a reduced shear stress, —-, in 

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In steady shear flows, only the shear-rate dependence of viscosity is well documented in terms of molecular structure effects. Molecular theories are more... 

Viscoelastic behavior is classified as linear or non-linear according to the manner by which the stress depends upon the imposed deformation history (SO). Insteady shear flows, for example, the shear rate dependence of viscosity and the normal stress functions are non-linear properties. Linear viscoelastic behavior is obtained for simple fluids if the deformation is sufficiently small for all past times (infinitesimal deformations) or if it is imposed sufficiently slowly (infinitesimal rate of deformation) (80,83). In shear flow under these circumstances, the normal stress differences are small compared to the shear stress, and the expression for the shear stress reduces to a statement of the Boltzmann superposition principle (15,81) ... 

The effects of interaction on viscoelastic properties at low concentrations depend on the Simha parameter. For example, Ferry has pointed out the importance of c[jj] for the transition from Zimm-like to Rouse-like behavior in the dynamic properties and in the observed values of J (15). The shear rate dependence of viscosity undergoes a corresponding transition as a function of... 

Only a few non-linear viscoelastic properties have been studied with polymers of well-characterized structure. The most prominent of these is the shear-rate dependence of viscosity. Considerable data have now been accumulated for several polymers, extending over a wide range of molecular weights and concen-... 

Fig. 8.6. Shear rate dependence of viscosity as a function of concentration. Data were obtained on a single narrow distribution sample of polystyrene (Mw = 411000) in n-butyl benzene (155) at 30° C. (Reproduced from Transactions of the Society of Rheologie, Volume 11, Fig. 2, p. 273, New York Wiley Sons.)...

Fig. 8.7. Shear rate dependence of viscosity for undiluted polystyrenes of different molecular weights. Weight-average molecular weights are 48500 117000 G 179000 G 217000 242000. All data are reduced to 183° C the dashed line has a slope of -0.82 (324). (Reproduced from Journal of colloid and interfache science, Vol. 22, Fig. 1, p. 520. New York ...

Fig. 8.8. Shear rate dependence of viscosity in reduced formas a function of concentration. Data were obtained on one narrow distribution sample (Mw= 1820000) of poly(

Graessley, W.W., Hazleton,R.L., Lindeman,L.R, The shear-rate dependence of viscosity in concentrated solutions of narrow-distribution polystyrene. Trans. Soc. Rheol. 11,267-285 (1967). 

Graessley,W.W., Segal,L. Effect of molecular weight distribution on the shear rate dependence of viscosity in polymer systems. A-I.Ch.E. J. 16,261-267 (1970). 

The rheological properties of the polymers reported in Table A.l were measured with a capillary die with diameter of 0.030 in or 0.050 in, and with LID from 33 to 40. At processing temperatures, the effect of the entrance pressure could be neglected. The shear-rate dependence of viscosity is obtained by applying the Rabinowitsch correction. 

Morris, E. R., Cutler, A. N., Ross-Murphy, S. B., Rees, D. A., and Price, J. (1981). Concentration and shear rate dependence of viscosity in random coil polysaccharide solutions. Carbohydr. Polym. 1 5-21. 

The concept of polymer entanglements represents intermolecular interaction different from that of coil overlap type interaction. However, it is difficult to define the exact topological character of entanglements. The entanglements concept was aimed at understanding the important nonlinear rheological properties, such as the shear rate dependence of viscosity. However, viscoelastic properties could not be defined quantitatively as is possible with the reptation model. Because an entanglement should be... 

Figure 10.2. Shear rate dependence of viscosity for a high molecular weight PP at 180°C.

Figure 5. Effect of hydrophobe level on the shear rate dependence of viscosity. Solvent is 2.0 wt % NaCl. Hydrophobe monomer is N-n-octylacrylamide. Hydrolysis level is 18 mol %. Polymer concentration is 2000 ppm.

Hashmi, S.A.R. and Kitano, T. (2007) Shear rate dependence of viscosity and first normal stress difference of LCP/PET blends at solid and molten states of LCP.J. Appl. Polym. Sd 104 (4), 2212-2218. 

W. W. Graessley, R. L. Hazleton, and L. R. Lindeman, The Shear Rate Dependence of Viscosity in Concentrated Solutions of Narrow Distribution Polystyrene Trans. Soc. Rheol. 11, 267-285 (1967). 

The shear rate dependence of viscosity for pure PLA and various PLACNs measured at 175°C is plotted in Figure 6.9. Pure PLA exhibits almost Newtonian behavior at all shear... 

This section considers the behavior of polymeric liquids in steady, simple shear flows - the shear-rate dependence of viscosity and the development of differences in normal stress. Also considered in this section is an elastic-recoil phenomenon, called die swell, that is important in melt processing. These properties belong to the realm of nonlinear viscoelastic behavior. In contrast to linear viscoelasticity, neither strain nor strain rate is always small, Boltzmann superposition no longer applies, and, as illustrated in Fig. 3.16, the chains are displaced significantly from their equilibrium conformations. The large-scale organization of the chains (i.e. the physical structure of the liquid, so to speak) is altered by the flow. The effects of finite strain appear, much as they do when a polymer network is deformed appreciably. 

For most polymeric liquids, the shear-rate dependence of viscosity goes over to a power law beyond fo-... 

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