Self-diffusion and binary Maxwell-Stefan diffusion coefficients of quadrupolar real fluids from molecular simulation

TL;DR

This paper uses molecular dynamics simulations to accurately predict self- and binary Maxwell-Stefan diffusion coefficients of quadrupolar fluids, validating empirical models and improving understanding of diffusion in complex fluids.

Contribution

It provides the first comprehensive simulation-based predictions of diffusion coefficients for quadrupolar fluids and tests empirical equations against these results.

Findings

Self-diffusion coefficients predicted with less than 1% uncertainty.

Simulation results agree within 2-28% with experimental data.

Darken's empirical equation best estimates Maxwell-Stefan diffusion coefficients.

Abstract

Self- and binary Maxwell-Stefan diffusion coefficients were determined by equilibrium molecular dynamics simulations with the Green-Kubo method. This study covers self-diffusion coefficients at liquid states for eight pure fluids, i.e. F$_2$, N$_2$, CO$_2$, CS$_2$, C$_2$H$_6$, C$_2$H$_4$, C$_2$H$_2$ and SF$_6$ as well as Maxwell-Stefan diffusion coefficients for three binary mixtures N$_2$+CO$_2$, N$_2$+C$_2$H$_6$ and CO$_2$+C$_2$H$_6$. The fluids were modeled by the two-center Lennard-Jones plus point-quadrupole pair potential, with parameters taken from previous work of our group which were determined solely on the basis of vapor-liquid equilibrium data. Self-diffusion coefficients are predicted with a statistical uncertainty less than 1% and they agree within 2% to 28% with the experimental data. The correction of the simulation data due to the finite size of the system increases the value of the self-diffusion coefficient typically by 10%. If this correction is considered, better agreement with the experimental data can be expected for most of the studied fluids. Maxwell-Stefan diffusion coefficients for three binary mixtures were also predicted, their statistical uncertainty is about 10%. These results were used to test three empirical equations to estimate Maxwell-Stefan diffusion coefficients in binary mixtures, i.e. the equations of Caldwell and Babb, of Darken, and of Vignes. The equations of Caldwell and Babb and of Vignes show qualitatively different behavior of the Maxwell-Stefan diffusion coefficient than that observed in the simulations. In agreement with previous work, the best results are obtained in all cases with the equation of Darken.