Maxwell–Stefan diffusivities in liquid mixtures: Using molecular dynamics for testing model predictions

Multicomponent diffusion is ubiquitous in (bio)chemical processes. The Maxwell–Stefan (M–S) framework provides a sound theoretical basis for describing transport diffusion as it correctly accounts for the gradient in chemical potential as driving force. Unfortunately, M–S diffusivities Đij cannot be measured directly in experiments. The use of predictive models based on easily measurable quantities like Fick- or self-diffusivities in diluted systems is therefore desirable. In this study, equilibrium molecular dynamics (EMD) simulations are used to study M–S diffusivities in liquid mixtures containing n-hexane, cyclohexane and/or toluene. Predictive models for estimating M–S diffusivities Đ i j x k → 1 in ternary systems are investigated. The following analysis are carried out. First, these predictive models are used to calculate the self-diffusivity in the infinite dilution limit using the well-known Vignes approximation. The predicted self-diffusivity is compared to the self-diffusivity directly calculated from EMD simulations. Second, we investigated the quality of the Vignes approximation using diffusivities obtained from EMD simulations. Third, we directly compared the predictive models for Đ i j x k → 1 with EMD simulations. Our results show that: (1) predicted self-diffusivities are not very sensitive to the choice of the predictive model for Đ i j x k → 1 ; (2) the Vignes equation results in only reasonable predictions for M–S diffusivities, yielding errors of 13% on average; (3) the interaction between solutes and solvent cannot be neglected in predictive models for Đ i j x k → 1 ; (4) present predictive models for calculating Đ i j x k → 1 from binary data results in errors of 8% for the systems under investigation.