Ja. Wesselingh et Am. Bollen, MULTICOMPONENT DIFFUSIVITIES FROM THE FREE-VOLUME THEORY, Chemical engineering research & design, 75(A6), 1997, pp. 590-602
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.