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

## TL;DR

This paper presents a mean-field approach to diffusion in binary mixtures, clarifying how the thermodynamic factor influences tracer and intrinsic diffusion coefficients, with findings supported by experimental data.

## Contribution

It introduces a method that extends the Darken equation, allowing separate dependence of diffusion coefficients on the thermodynamic factor, which was not previously distinguished.

## Key findings

- $D_A^*$ depends on the thermodynamic factor $\
- $D_A$ is independent of $\
- Experimental data supports the theoretical predictions.

## Abstract

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 $\Phi$ (a function of the derivative of the activity coefficient against 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 $\Phi$ appears in the expression for $D_A^*$, but the intrinsic diffusivity $D_A$ turns out to be independent of $\Phi$. Experimental results taken from the literature on diffusion in metal alloys are consistent with this theoretical prediction.