On the Relative Roles of Free Volume and Activation Energy in the Viscosity of Liquids

Abstract

The rate‐theory approach of Eyring and the free‐volume theory of Cohen and Turnbull for liquid viscosities have been reconsidered. The rate theory has been reformulated using the Cohen and Turnbull expression for the probability of finding a vacant site and yields an equation of the form $${\mathrm{\eta =A}}_0\exp {\mathrm{[E}}_v^{*}{\mathrm{/RT+\gamma V}}_0{\mathrm{/V}}_f\mathrm{].}$$ This result has been applied to many liquids ranging from fused silica to liquid argon and including polyatomic van der Waals as well as hydrogen‐bonded liquids. Consistent fits to both temperature and pressure dependence of viscosity were obtained. A significant conclusion is that the free volume of liquids is considerably higher than that suggested by the WLF and Cohen and Turnbull equations.