MULTICOMPONENT DIFFUSIVITIES FROM THE FREE-VOLUME THEORY

In this paper the free volume theory of diffusion is extended to multi component mixtures. The free volume is taken to be accessible for any component according to its surface. fraction. The resulting equations predict multicomponent (Maxwell-Stefan) diffusivities in simple liquid mixtures from pure component data such as molar masses, densities and viscosities. They can also be used together with an equation of state . For simple Liquid mixtures, the results agree closely with experimen t. For viscous liquids, rubbery polymers and glasses, orders of magnit ude and the main trends of diffusivities of small permeants are predic ted correctly. The equations follow many of the empirical rules known for diffusion coefficients. In non-viscous liquids they almost coincid e with an empirical modification of the Einstein-Stokes equation. They predict an Arrhenius type of temperature dependence with correct acti vation energies. In mixtures with similar components, they predict tha t MS-diffusivities should be Linear functions of composition (the Dark en rule). In mixtures with larger (but not-too-large) differences betw een the components, the MS-diffusivities are logarithmic functions of composition (the Vignes rule). In viscous mixtures and polymers, diffu sivities vary sharply (in a roughly exponential manner) with the conce ntration of the viscous component. The theory is not perfect, It fails for mixtures of molecules differing greatly in size or chemical struc ture. It can only be made to work with water and polymers with a few d ubious assumptions.