Molecular weight distribution viscosity versus shear rate

Figure 2-30. Melt-flow rates as a function of molecular weight distribution, a) Molecular weight distribution (MWD) curves b) viscosity versus shear rate, as related to MWD and c) factors influencing viscosity.

Tuminello, W.H. and Cudre-Mauroux, N. (1991) Determining molecular weight distributions from viscosity versus shear rate flow curves. Polymer Engineering and Science, 31, 1496-1507. 

A typical viscosity versus shear rate curve would be like the one shown in Fig. 1.6. There is a Newtonian region in the low shear where the viscosity does not change with shear rate. At some critical shear rate, there is a continuous drop off of viscosity with shear rate. The drop-off of viscosity wifli shear rate would occur sooner if the molecular-weight distribution is widened. This is because the shorter molecular chains are of lower viscosity and cause the vis-... 

Quantitative comparisons were made by fitting the Williamson model to the flow curve data. The zero-shear viscosity and rate index are two parameters obtained from the Williamson model fits. The zero-shear viscosity is the viscosity valne extrapolated to infinitely low shear rate, while the rate index is the slope of the viscosity versus shear rate relationship in the shear-thinning region at high shear rates. These two parameters are very sensitive to differences in the molecular weight distributions of the resins. Table 15-Tl lists the zero-shear viscosities and rate indexes of the two resin samples. 

This blending rule is used in Chapter 8 as the basis for one method for inferring the molecular weight distribution from the curve of viscosity versus shear rate. 

Of the viscometric functions, the viscosity is by far the easiest to measure and is thus the most often reported. As in the case of Newtonian fluids, the viscosity of a polymer depends on temperature and pressure, but for polymeric fluids it also depends on shear rate, and this dependency is quite sensitive to molecular structure. In particular, the curve of viscosity versus shear rate can be used to infer the molecular weight distribution of a linear polymer as is explained in Chapter 8. And in certain cases it can also tell us something about the level of long-chain branching. This curve is also of central importance in plastics processing, where it is directly related to the energy required to extrude a melt. 

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