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

Abstract

Rosenfeld [Phys. Rev. A 15, 2545 (1977)] originally noticed that casting the transport coefficients of simple monatomic equilibrium fluids in a specific dimensionless form makes them approximately single-valued functions of excess entropy. This observation has predictive value because, while the transport coefficients of dense fluids can be difficult to estimate from first principles, the excess entropy can often be accurately predicted from liquid-state theory. In this work, we use molecular simulations to investigate whether Rosenfeld's observation is a special case of a more general scaling law relating the tracer diffusivities of particles in mixtures to the excess entropy. Specifically, we study the tracer diffusivities, static structure, and thermodynamic properties of a variety of one- and two-component model fluid systems with either additive or nonadditive 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 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.

Structural and dynamical anomalies of a Gaussian core fluid: A mode-coupling theory study

“…A deep connection between structural and dynamical anomalies uncovered in earlier studies [9][10][11] has been reconfirmed by noting that both density and mole fraction anomalous behavior of diffusion could be described via a short-time ansatz for a time-dependent friction, with the latter constructed from structural data only. One remaining open question concerns the mole fraction dependence of shear viscosity of a GC mixture, it will be the subject of future research.…”

Thermodynamic and structural properties of the high density Gaussian core model

“…Recently, thermodynamic and transport anomalies of the fluid phase in the vicinity of the reentrant peaks are investigated. 10,[12][13][14][15][16] Microscopic and structural properties such as the static structure factor in the fluid phase are also reported and documented. 6,7,9,11 These studies revealed that, as the density increases beyond the reentrant peak but at a fixed temperature, thermodynamic and structural properties of GCM becomes more ideal-gas-like, signaled by the lowering of the peak of the structure factors and the better agreement with simple approximations such as the random phase approximation (RPA).…”

“…GCM was first introduced by Stillinger 4 and has been studied by many groups. [5][6][7][8][9][10][11][12][13][14][15][16] Despite of its simple form of the pair potential, GCM exhibits many typical thermodynamic behaviors of the ultra-soft particles. According to thermodynamic phase diagram obtained by numerical simulations, 4,8 GCM basically behaves such as hard spheres at very low densities and temperatures; the crystalline structure in the solid phase is fcc and the freezing/melting temperatures sharply increase with density.…”

Predicting the structure of fluids with piecewise constant interactions: Comparing the accuracy of five efficient integral equation theories

“…Excess entropy, its two-body approximation, and p 0 have been shown to correlate with various dynamic properties of equilibrium fluids, e.g. diffusivity or viscosity [8,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Mode-coupling theory also predicts that dynamic phenomena can be directly estimated from knowledge of the static structure factor [32].…”