Diffusion in binary mixtures: An analysis of the dependence on the thermodynamic factor

We study the diffusion process in binary mixtures using transition probabilities that depend on a mean-field potential. This approach reproduces the Darken equation, a relationship between the intrinsic and the tracer diffusion coefficients, D_{A} and D_{A}^{*}, through the thermodynamic factor Φ (a function of the derivative of the activity coefficient against the molar fraction). The mean-field approach allows us to go beyond the Darken equation and separately specify the dependence of D_{A} and D_{A}^{*} on the thermodynamic factor. We obtain that Φ appears in the expression for D_{A}^{*}, but the intrinsic diffusivity D_{A} turns out to be independent of Φ. Experimental results taken from the literature on diffusion in metal alloys are consistent with this theoretical prediction.