On equivalence of high temperature series expansion and coupling parameter series expansion in thermodynamic perturbation theory of fluids

Abstract

The coupling parameter series expansion and the high temperature series expansion in the thermodynamic perturbation theory of fluids are shown to be equivalent if the interaction potential is pairwise additive. As a consequence, for the class of fluids with the potential having a hardcore repulsion, if the hard-sphere fluid is chosen as reference system, the terms of coupling parameter series expansion for radial distribution function, direct correlation function, and Helmholtz free energy follow a scaling law with temperature. The scaling law is confirmed by application to square-well fluids.

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

“…When the HS is used as reference system in the HTSE, the HTSE is an expansion in powers of 1/T * n , in other words, the coefficient a n is not dependent on the temperature argument; by being aware of this point, Zhou further concludes that the HS-HTSE coefficients a n can be easily determined by evaluating the nth-order term of the CPSE at T * = 1 given that the HS is used as reference system in the CPSE, i.e., a n = F per −n /N kT T * =1 . In literature, 11 by proving an equivalence of the CPSE and the HTSE in thermodynamic perturbation theory of fluids by the help of language of the distribution function, the equation a n = F per−n /N kT T * =1 is developed into a scaling law with temperature valid for situations wherein the HS is used as reference system; as an important special case of the scaling law, a n = F per−n /N kT T * =1 is used to evaluate a n for years. 2,3,7,10 As regards the equivalence mentioned above, a further discussion is necessary.…”

Thermodynamic Properties of Ar, Kr and Xe from a Monte Carlo- Based Perturbation Theory with an Effective Two-Body Lennard-Jones Potential

“…The first-order term f 1 in the HTE ( 14) can be obtained accurately from the HS radial distribution function and higherorder terms can be obtained with quite good accuracy from the numerical solution of the so-called coupling parameter series expansion [34][35][36][37], based on a combination of perturbation theory with integral equation theory. Alternatively, several of the first terms in the series can be obtained from computer simulation, as done in the present work.…”

An Orbital‐Free Quantum Hypernetted Chain Model Based Perturbation Theory for Equation of State of Hydrogen and Helium in Warm Dense Regime

“…Recently, we developed a thermodynamic perturbation theory for classical fluids which combines the classical integral equation theory with the perturbation theory [13][14][15]. Recently, we developed a thermodynamic perturbation theory for classical fluids which combines the classical integral equation theory with the perturbation theory [13][14][15].…”

“…The problem of non-existence of solutions to Ornstein Zernike equation is also there in classical fluids. Recently, we developed a thermodynamic perturbation theory for classical fluids which combines the classical integral equation theory with the perturbation theory [13][14][15]. Using this method, both the structural and thermodynamic properties of fluids with particles interacting with pair potentials can be calculated to any order of the perturbation series.…”