Transport coefficients of soft sphere fluid at high densities

Abstract

320Knowledge of transport properties of matter at high pressures and high temperatures is extremely impor tant. One of obvious examples of liquid at high pres sure and high temperature is Earth outer core which is supposed to be liquid. However, nowadays it is not possible to carry out any experiments at such extreme conditions. The extreme conditions region is also hard for theoretical investigations and simulation studies. Importantly, all theoretical models are developed for normal conditions, and we can never be sure that the same models are applicable at high pressure and tem perature. Basing on this speculation it becomes impor tant to carry out a systematic study of some simple model in wide range of pressures and temperatures in order to see the most important effects induced by pressure and temperature. Such investigation will give a solid base for studies of more complex and more realistic systems.In this work we choose a soft spheres system as a generic model for high pressure atomic systems. This system is defined by the interaction potential (1) where ε and σ are energy and length scales. This sys tem is convenient for our goals since its thermody namic quantities follow well known scaling laws [1][2][3][4][5]). An important consequence of this scaling is that the soft spheres phase diagram is one dimensional, and it is known at all temperatures. This allows us to carry out simulations up to very high temperatures and pres sures being sure that the system is in stable liquid phase. ¶ The article is published in the original.Obviously, soft sphere system is a toy model of a real liquid. However, at high pressures and tempera tures the behavior of substances is mostly governed by repulsive cores atoms. This makes soft spheres one of the simplest qualitative models of matter at extremely high temperatures and pressures.It is well known that the thermodynamic properties of the soft sphere system can be expressed in terms of a reduced parameter, γ = ρσ 3 (k B T/ε) -3/n , where ρ is the reduced number density (ρ = N/V, for N particles in volume V), k B is the Boltzmann constant and T is the temperature (Klein theorem [1-3]). It may be shown [1-5] that the following scaling laws are valid along the melting line (we skip the Boltzmann con stant in the formulas below for the sake of brevity):(2)where V 0 , T 0 , and P 0 are some arbitrary values of vol ume, temperature and pressure.The exponents in (2) and (3) were known before (see, for example, [3]). However, in [5] the method was developed which can be applied to any physical quantity of the form F = under the trans formation which preserves the form of Hamiltonian equations. This transformation conserves geometric relations on a phase trajectory, thereby preserving the scaling of the individual trajectories of each of the N particles and, hence, it conserves the multiphase nature of the whole system. The simplest example of a phase equilibrium curve is the two phase meltingMolecular dynamics computer simulation has been used to compute in wide pressure te...

Properties of liquid iron along the melting line up to Earth-core pressures

“…As it was mentioned in the introduction we are interesting in the behavior of the transport coefficients of liquid iron along the melting line. In our previous publications we analyzed the behavior of simple liquids along the melting curve [14,15]. Two simple models were studied -soft spheres (Φ(r) = ε( σ r ) n with n = 12) and Lennard-…”

Probing the link between residual entropy and viscosity of molecular fluids and model potentials

“…in which n = (2/n) + (1/2). The simulation for the IPP potential is carried out at specified pairs of ρ * = ρ N σ 3 and T * = T k B /ε, for which the simulation data are expressed in terms of η * /(T * ) n as a function of the scaling variable γ (see [59] and Section 3.C.2). For the n = 12 IPP potential, the residual entropy is obtained from integration of the convergent virial expansion given by [57].…”

“…Rosenfeld's curve of "universal" scaling might not have been quite right, but with the appropriate caveats, most repulsive-dominated potentials are remarkably consistent in the Rosenfeld scaling framework. [70,71,72,55,73,74,75]; black : IPP with n = 12 [59]; red : repulsive WCA potential; yellow : Lennard-Jones data from Ashurst and Hoover [69] considered by Rosenfeld [1]; orange dashed curve: hard sphere (Enskog theory plus correction of [76]); black dashed line: correlation from Rosenfeld [4]). A larger version of this figure is available in the SI (Fig.…”

Viscosity Measurements of Three Base Oils and One Fully Formulated Lubricant and New Viscosity Correlations for the Calibration Liquid Squalane

“…Ashurst and Hoover [66] were the first to point out this insight for viscosity and showed that the viscosity of the purely repulsive soft sphere potential can be expressed as a monovariate function of the parameter (T/  ), defined with the absolute temperature T, density  , and the exponent   which is directly related to the strength of the repulsive potential. In 2012, Fomin et al gave an empirical monovariate formulation for the viscosity of soft spheres in terms of this parameter [67].…”