Generalized Rosenfeld scalings for tracer diffusivities in not-so-simple fluids: Mixtures and soft particles

TL;DR

This paper introduces a generalized Rosenfeld scaling law that relates tracer diffusivities to excess entropy in complex mixtures and soft particles, improving predictive accuracy over traditional theories.

Contribution

It develops a new empirical scaling law for tracer diffusivities in mixtures, extending Rosenfeld's original idea to more complex and soft particle systems.

Findings

The generalized Rosenfeld scaling accurately predicts tracer diffusivities across various mixture compositions.

It outperforms Enskog theory and pair-correlation based scalings in predictive accuracy.

Limitations include reduced accuracy for systems with significant diffusivity decoupling.

Abstract

Rosenfeld [Phys. Rev. A 15, 2545 (1977)] noticed that casting transport coefficients of simple monatomic, equilibrium fluids in specific dimensionless forms makes them approximately single-valued functions of excess entropy. This has predictive value because, while the transport coefficients of dense fluids are difficult to estimate from first principles, excess entropy can often be accurately predicted from liquid-state theory. Here, we use molecular simulations to investigate whether Rosenfeld's observation is a special case of a more general scaling law relating mobility of particles in mixtures to excess entropy. Specifically, we study tracer diffusivities, static structure, and thermodynamic properties of a variety of one- and two-component model fluid systems with either additive or non-additive interactions of the hard-sphere or Gaussian-core form. The results of the simulations demonstrate that the effects of mixture concentration and composition, particle-size asymmetry and additivity, and strength of the interparticle interactions in these fluids are consistent with an empirical scaling law relating the excess entropy to a new dimensionless (generalized Rosenfeld) form of tracer diffusivity, which we introduce here. The dimensionless form of the tracer diffusivity follows from knowledge of the intermolecular potential and the transport / thermodynamic behavior of fluids in the dilute limit. The generalized Rosenfeld scaling requires less information, and provides more accurate predictions, than either Enskog theory or scalings based on the pair-correlation contribution to the excess entropy. As we show, however, it also suffers from some limitations, especially for systems that exhibit significant decoupling of individual component tracer diffusivities.