Zero-shear-rate viscosity molar mass dependence

Flow properties are very strongly dependent on molecular architecture, i.e. molar mass and chain branching. Figures 6.13 and 6.14 illustrate the effect of molar mass on the zero-shear-rate viscosity (//q) and on the steady-state recoverable shear compliance. 

The Rouse theory is clearly not applicable to polymer melts of a molar mass greater than (M ) for which chain entanglement plays an important role. This is obvious from a comparison of eqs (6.40)-(6.42) and experimental data (Figs 6.13 and 6.14) and from the basic assumptions made. However, for unentangled melts, i.e. melts of a molar mass less than (M ), both the zero-shear-rate viscosity and recoverable shear compliance have the same molar mass dependence as was found experimentally (Figs 6.13 and 6.14). The Rouse model does not predict any shear-rate dependence of the shear viscosity, in contradiction to experimental data. 

Fig. 6.14. Molar mass dependence of the zero shear rate viscosity of PI. The lower figure indicates for Mw > 2 x 10 gmon a power law rjo oc M. The critical molar mass as determined by the location of the break is = 1.3 x 10 gmol . Prom Pyckhout-Hintzen et al. [72]...

Polymers in solution or as melts exhibit a shear rate dependent viscosity above a critical shear rate, ycrit. The region in which the viscosity is a decreasing function of shear rate is called the non-Newtonian or power-law region. As the concentration increases, for constant molar mass, the value of ycrit is shifted to lower shear rates. Below ycrit the solution viscosity is independent of shear rate and is called the zero-shear viscosity, q0. Flow curves (plots of log q vs. log y) for a very high molar mass polystyrene in toluene at various concentrations are presented in Fig. 9. The transition from the shear-rate independent to the shear-rate dependent viscosity occurs over a relatively small region due to the narrow molar mass distribution of the PS sample. 

Viscosity is defined as the ratio of shear stress to shear rate. The viscosity of a Newtonian fluid is a material constant that depends on temperature and pressure but is independent of the rate of shear that is, the shear stress is directly proportional to the shear rate at fixed temperature and pressure. Low molar-mass liquids and aU gases are Newtonian. Complex liquids, such as polymers and suspensions, tend to be non-Newtonian in that the shear stress is a nonlinear function of the shear rate. Some typical melt viscosities are shown in Figure 1.7. The viscosity approaches a constant value at low shear rates, known as the zero-shear viscosity and denoted... 

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