A model for the Magill-Li viscosity-temperature relation

Abstract

A simple model has been developed to account for the viscosity‐temperature dependence of liquids. It is predicated upon the valid assumption that the activation energy for flow is Arrhenius‐like at sufficiently high temperatures, and that this activation energy varies inversely as the probability of finding sufficient local volume for transport at lower temperatures. The model yields a viscosity reducing equation very similar to the Magill‐Li empirical equation for the zero shear viscosity η as the function of temperature T. The relation is ln ( η η s ) =A ( exp [B (x+φ−1) −1 ] x − exp (B/2 φ) 1+φ ) ,where A = 2.68, B = 0.432, φ = 0.238, x = T/Tg , ηS is the reference viscosity at the reference temperature Ts , and Tg is the glass temperature. This relation has been successful in reducing data for several viscous materials unto a single master curve which extends over about 16 orders of magnitude in viscosity and encompasses a broad temperature range extending from Tg to about 2.5Tg in some instances.