Monte Carlo and theoretical calculations of the first four perturbation coefficients in the high temperature series expansion of the free energy for discrete and core-softened potential models

Abstract

The first four perturbation coefficients in the expansion of the Helmholtz free energy in power series of the inverse of the reduced temperature for a number of potential models with hard-sphere cores plus core-softened and discontinuous tails are obtained from Monte Carlo simulations. The potential models considered include square-well, double square-well, and square-shoulder plus square-well, with different potential parameters. These simulation data are used to evaluate the performance of a traditional macroscopic compressibility approximation (MCA) for the second order coefficient and a recent coupling parameter series expansion (CPSE) for the first four coefficients. Comprehensive comparison indicates the incapability of the MCA for the second order coefficient in most non-stringent situations, and significance of the CPSE in accurately calculating these four coefficients.

Bending and Gaussian rigidities of confined soft spheres from second-order virial series

“…When the pair interaction between particles is defined as φ(r ≤ σ) = +∞ and by the IPL given in Eq. (19) for…”

“…[13][14][15] Several studies focused on elucidating the relation between core-softness and thermodynamic properties. [16][17][18][19] Basic research about bulk transport and virial coefficients was started by Rainwater and others, [20][21][22][23][24][25] and continues up to present. [18,[26][27][28] Analytic equations of state of the soft-sphere fluid were found using as input the known bulk virial coefficients using resummation, by * iurrutia@cnea.gov.ar adapting the Carnahan Starling equation of state for HS to soft-spheres and utilizing Padé approximants.…”

Excellence of numerical differentiation method in calculating the coefficients of high temperature series expansion of the free energy and convergence problem of the expansion

“…Approximate estimation of a 2 is implemented in the macroscopic compressibility approximation and local compressibility approximation, 14 but their validities have been questioned recently. 15,2,3,7,10 The CPSE offers a novel route for calculations of all a i of the HTSE in principle. The CPSE is characterized by the following two equations only involved with numerically available two-particle rdf of the reference fluid and imaginary fluid and derivatives of the latter with respect to a coupling parameter ξ…”

“…the coupling parameter ξ evaluated at ξ = 0, here ξ serves to link a reference potential to a target potential under consideration. In literatures, [2][3][4][5][6][7]9,10 one uses numerical differentiation to calculate the derivatives. Due to the unavoidable errors associated with the numerical differentiation, accurate calculation of the higher-order derivatives requires experience and skill.…”