The generalized free volume theory is applied to the soft-core multiple-Yukawa solid, and the hard-core multiple-Yukawa is included in as a special case. The expressions for equation of state and internal energy are derived. The formalism developed is applied to the C60, C76, and C84 solids. The effective diameter of C60 molecule is taken as the experimental value; the parameters of the double Yukawa (DY) potential for carboncarbon atoms are determined through fitting the experimental data of cohesive energy, the lattice constant, and the compression curve of C60 solid at ambient temperature. The effective diameter of C76 and C84 molecules are determined through fitting the experimental lattice constants at ambient temperature. The numerical results of C60 solid from the soft-core DY potential are in good agreement with the experiments, including the lattice constant and compression curve. The lattice constant versus temperature relationship for C76 and C84 solids calculated from the DY potential is qualitatively in accordance with experimental data as same as the Girifalco potential. The compression curve of the C84 solid calculated from the DY potential deviates from and is softer than the experimental data available. The reason for deviation is discussed, and it is concluded that the influence of compressibility of fullerene molecules to thermophysical quantities is important at high-pressure conditions.

In this paper it is shown that the relationship of bulk modulus with pressure, BZf (P), should be linear both at low and high-pressure limiting conditions. Because most of present equations of state (EOS) for solids cannot satisfy such linear relationship at high pressure, a new function f (P) is proposed to satisfy the linearity. By integrating the bulk modulus, an EOS with three parameters and satisfying the quantum-statistics limitation is derived. It is shown that the EOS can be reduced to two-parameter EOS approximately satisfying the limiting condition. By applying the two EOSs and other three typical EOSs to 50 materials, it is concluded that for materials at low and middle-pressure regimes, the limiting condition does not operate, the Baonza EOS gives the best results, but it cannot provide analytic expression for cohesive energy. The Vinet and our second EOSs are slightly inferior, both EOSs can provide analytic expression for cohesive energy, and for materials at highpressure regimes our second EOS gives the best results. The Holzapfel and our first EOSs give the worst results, although they strictly satisfy the limiting condition. For practical applications, the limiting condition is not important because it only operates as V→0. © 2004 Elsevier Ltd. All rights reserved.

The analytic equations of state for the double Yukawa fluids with (GHCDY) and without (SDY) hard-core repulsion have been derived based on the Barker–Henderson and Ross perturbation theories, respectively, and the analytic expression of HS-RDF previously developed. The comparison of the numerical results with computer simulation data shows that the GHCDY potential should be divided into three types in terms of the values of parameters in GHCDY potential function. The first type is hard-core plus pure attraction. Second type is hard-core plus small part soft-repulsion and attraction. Third type is hard-core plus large part softrepulsion and attraction. The BH theory is applicable to first and second types but not to third type. The simple fluid is one of the most important prototypes of GHCDY fluid, and it belongs to second type. The charged protein molecules is another one, it belongs to third type. The GHCDY potential being appropriate to charged protein molecules is very similar to the SDY potential, and its thermodynamic properties can be alternatively described by using the Ross variational perturbation theory. © 2004 Elsevier B. V. All rights reserved.

A fitting procedure is proposed to establish two analytic approximate expressions for the complicated Rarker-Henderson (BH) diameter with Lennard-Joues potential in two temperature ranges. Considering that the differentiation is a process enlarging the errors and the integration decreasing the errors and that the derivative of BH diameter is important in the calculation of in ternal energy, we propose to tit the derivative directly, instead of usually fitting the original function and subsequently deriving its derivative. The simplicity and precision of two expressions developed are superior to the extensively deriving its derivative. The simplicity and precision of two expressions developed are superior to the extensively used expressions in literature. The one with following form only has an average fitting 0.0063% in the reduced temperature range (0.4≤Kt/S≤15), and can be extrapolated to a wider temperature range (0.4≤Kt/S≤50) with an average error 0.13%, which is d/ơ=1.1755+0.02878 In T -0.2072T1/4+0.00643T3/4.

A simple method is proposed to dispose the quantum effect and anharmonic effect at the same time. Considering the quantum effect is remarkable only at low temperature, and tends to zero at high temperature, the potential energy of an atom is expanded harmonically to consider the quantum effect of solids within the harmonic oscillator framework. The anharmonic effect is remarkable only at high temperature, and tends to zero at low temperature, it was disposed by using a classical approximation. The universal formalism is applied to the generalized Lennard-Jones solid. The comparison shows that the results with and without anharmonic effect are in agreement with cach other at some low temperature, to which the Einstein model is applicable. The results without anharmonic effect become divergent at slightly higher temperatures; however, the results including anharmonic effect are in good agreement with the experimental data of solid xenon. The method proposed in this paper can be extended on other potentials to develop practical molecular thermodynamic equations of state for solids.