A model for the Magill-Li viscosity-temperature relation

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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(ηηs)=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.