The macroscopic viscosity approximation: A first-principle relationship between molecular diffusion and viscosity

Abstract

In this article, a new relationship between viscosity and molecular diffusion at infinite dilution is proposed for better rationalization and prediction of these properties, based on a “macroscopic viscosity approximation” (MVA), i.e., by assuming viscosity around a solute as equal to the macroscopic, measurable viscosity of the solvent. This implies that activation energies of the viscous flow and diffusion process are equal. The hypothesis is validated by our correlation analysis (mean difference of 0.10 kcal/mol, R2 = 0.96). The new approach, named “Modified Stokes–Einstein” (MSE), achieves better performance than the widely used Wilke–Chang (WC) correlation both in organic solvents [mean relative error (MRE) of 15% vs 24%, respectively] and in water (MRE of 13% vs 21%, respectively). Contrary to the popular WC correlation as well as all other available approaches in the literature, the MSE approach can be used consistently for water, without requiring any ad hoc association parameter, and is not fitted on diffusion and/or viscosity data, making all of its underlying hypotheses explicit. Based on the MVA and the MSE, a simple atomic count estimation method for the activation energy of the flow allows us to simultaneously predict viscosity and diffusion coefficients with an MRE of 21%–22%, again slightly better than the WC correlation, but not requiring any experimental data as the input. This work provides rationalized and efficient means for prediction of diffusion coefficients at infinite dilution and pure liquid viscosities wherever such properties are required, for example, as inputs for mixing rules to predict flow and transport behavior of complex systems.