WLF model for the pressure dependence of zero shear viscosity of polycarbonate

Abstract

Zero shear viscosity data of an amorphous polycarbonate (PC) were obtained by pressure-sweep tests at seven pressures from 1 to 700 bar, at 160, 180, 200, 220, and 240 °C above the glass transition temperature T_g. Independent shifts of the logarithmic zero shear viscosity and of the pressure were performed in order to build an empirical master curve at the reference temperature T₀ = 240 °C. On the basis of a Vogel-type model, analytical expressions which fit the empirical logarithmic zero shear viscosity and the pressure shift factors were obtained. Additionally, a general equation of the zero shear viscosity as a function of pressure at any reference temperature was deduced. It is shown that the temperature dependence of the zero shear viscosity follows the Williams-Landel-Ferry (WLF) equation, with a pressure dependence parameter B(P) = B(0)1−4.4×10−41barP\[ \left(1-4.4\times {10}^{-4}\frac{1}{\mathrm{bar}}P\right) \], B(0) = 02.87 from which it is obtained that the pressure dependence of fractional free volume of PC at the glass transition temperature is f(T_g, P) = 0.022 B(P).