Control Parameter Dependence of Transport Coefficients near the Glass Transition

The master curves for transport coefficients, such as self-diffusion coefficient D, shear viscosity eta, and electrical conductivity sigma, near the glass transition are studied based on the fact recently proposed by the present author that the long-time self-diffusion coefficients in both fragile and strong liquids are well described by the following two types of master curves, depending on whether the control parameter is an intensive one (X) or an extensive one (Y); f (x) = (1 - x)(2+epsilon) exp[62x(3+epsilon)(1 - x)(2+epsilon)] and g(y) = (1 - y)(2)/y, where x = X/X-f and y = Y/Y-f, X-f and Y-f being fictive singular points to be determined. Here epsilon = 4/3 for fragile liquids and 5/3 for strong liquids. The thermodynamic function Y = h(X) is then used to relate f (x) with g(y) and vice versa. The experimental data and the simulation results for the shear viscosity and the electrical conductivity are also analyzed by using the master curves f (x) and g(y). Thus, it is shown that any transport coefficients are well described by those master curves up to the deviation point, above which all the data start to deviate from the master curves and the system becomes out of equilibrium.