Thermodynamic scaling and corresponding states for the self-diffusion coefficient of non-conformal soft-sphere fluids

Abstract

In this work, we explore transport properties of a special type of repulsive spheres that exhibit remarkable scaling of their thermodynamic properties. In order to accomplish that we propose a new way to derive and express effective hard-sphere diameters for transport properties of simple fluids. The procedure relies on mapping the system's transport properties, in the low density limit, to the hard-sphere fluid. We have chosen a set of soft-sphere systems characterised by a well-defined variation of their softness. These systems represent an extension of the repulsive Lennard-Jones potential widely used in statistical mechanics of fluids and are an accurate representation of the effective repulsive potentials of real systems. The self-diffusion coefficient of the soft-sphere fluids is obtained by equilibrium molecular dynamics. The soft-sphere collision integrals of different systems are shown to follow quite simple relationships between each other. These collision integrals are incorporated, through the definition of the effective hard-sphere diameter, in the resulting equation for the self-diffusion coefficient. The approach followed exhibits a density rescaling that leads to a single master curve for all systems and temperatures. The scaling is carried through to the level of the mean-squared displacement.

Hidden Scale Invariance in Condensed Matter

“…In terms of hidden scale invariance, quasiuniversality is the statement that the function Φ̃ of eq is quasiuniversal: Φ̃( R̃ ) ≅ Φ̃ 0 ( R̃ ) . Recent works confirming quasiuniversality include studies of quasiuniversal melting criteria, various LJ-type potentials, plastic flow-event statistics, and universally growing length scales upon supercooling. ,, The standard argument for quasiuniversality is based on representing the system in question by a HS reference system. ,,− A recent alternative argument for quasiuniversality refers to the so-called NVU dynamics, which is geodesic dynamics on the constant-potential-energy hypersurface …”

Simple liquids’ quasiuniversality and the hard-sphere paradigm

“…How to determine the effective HS packing fraction of a given simple liquid at a given state point? The literature gives many different answers to this question, for instance those of [99], [145][146][147][148][149][150][151][152]. The simplest of these criteria determines the effective HS radius from the equation ( ) = v r k T HS B [150], but after half a century of research there is still no recipe for calculating the HS packing fraction that is generally agreed upon.…”

Effect of chain flexibility on master curve behavior for diffusion coefficient

“…1,2 The diffusion coefficient of non-atomic and non-hard sphere fluids can also, to a degree, be described as a D*[η] if the packing fraction can be properly defined. [3][4][5][6] This amounts to mapping the system structure and interaction potentials onto an "effective" hard site diameter that, in general, would be a function of temperature and pressure. There is no rigorous manner for performing such a mapping; however, it is essential that D not be used to define η.…”