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A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of fex - ref, chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established. [ABSTRACT FROM AUTHOR]

A hard sphere+triangle-well potential is employed to test a recently proposed thermodynamic perturbation theory (TPT) based on a coupling parameter expansion. It is found that the second-order term of the coupling parameter expansion surpasses by far that of a high temperature series expansion under a macroscopic compressibility approximation and several varieties. It is also found that the fifth-order version displays best among all of the numerically accessible versions with dissimilar truncation orders. Particularly, the superiority of the fifth-order TPT from other available liquid state theories is exhibited the most incisively when the temperature of interest obviously falls. We investigate the modification of the phase behavior of the hard sphere+triangle-well fluid resulting from a density dependence imposed on the original potential function. It is shown that (1) the density dependence induces polymorphism of fluid phase, particularly liquid-liquid transition in metastable supercooled region, and (2) along with enhanced decaying of the potential function as a function of bulk density, both the liquid-liquid transition and vapor-liquid transition tend to be situated at the domain of lower temperature, somewhat similar to a previously disclosed thumb rule that the fluid phase transition tends to metastable with respect to the fluid-solid transition as the range of the attraction part of a density-independence potential is sufficiently short compared to the range of the repulsion part of the same density-independence potential. [ABSTRACT FROM AUTHOR]

Abstract The coupling parameter series expansion (CPSE) is used to calculate coefficients a i (i = 1,2,3,…7) of the high temperature series expansion (HTSE) for two hard sphere ＋ square well models and two hard sphere ＋ square well ＋ square shoulder models, the four sets of coefficients are used to construct 28 Padé approximant variants P n ∕ d for the four models. Based on the 28 Padé variants, six common thermodynamic functions for the four models are calculated and compared with corresponding results based on MC simulations reported in the literature and the HTSE truncated to seventh order in the present work, respectively. Several conclusions are generalized from the comparisons: (i) the commonly used rule of the minimum value for n − d to choose the best Padé approximation may not select the best one, which depends on the model and relevant parameters values and has to be determined in advance by reference to simulations. (ii) From the whole table of 28 Padé approximants, reliable (throughout the text, by “reliable” we mean the results are at least qualitatively correct) variants always can be singled out, which not only provides an improvement over the raw HTSE truncated at the optimal order but also is free of pole(s) and consequently applicable over reasonably wide phase space of interest; particularly, the improvement can be immense for most but not all of the models considered when the excess heat capacity is being considered. (iii) Among the reliable P n ∕ d approximations picked, some have high values of n + d indicating that the higher-order HTSE coefficients calculated by the CPSE provide important and reliable information for the unknown excess Helmholtz free energy, and the conventional Padé summation indeed provides an effective method to utilize the information. (iv) The Padé summation can be a resort in statistical mechanics perturbation theories of simple potential fluids because of its simplicity in the actual application and possibility in improving the raw HTSE ; however, to ensure the use reliably, one comprehensive pre-research should be carried out. Highlights • Coefficients of high temperature series expansion for four models are calculated. • Padé approximant variants for four models are constructed. • Higher-order perturbation coefficients provide important information. [ABSTRACT FROM AUTHOR]

Using the TL (Tang and Lu, 1993) method, Ornstein-Zernike integral equation is solved perturbatively under the mean spherical approximation ( MSA ) for fluid with potential consisting of a hard sphere plus square-well plus square-shoulder ( HS + SW + SS ) to obtain first-order analytic expressions of radial distribution function ( RDF ), second-order direct correlation function, and semi-analytic expressions for common thermodynamic properties. A comprehensive comparison between the first-order MSA and high temperature series expansion ( HTSE ) to third-, fifth- and seventh-order is performed over a wide parameter range for both a HS + SW and the HS + SW + SS model fluids by using corresponding “exact” Monte Carlo results as a reference; although the HTSE is carried out up to seventh-order, and not to the first order as the first-order MSA the comparison is considered fair from a calculation complexity perspective. It is found that the performance of the first-order MSA is dramatically model-dependent: as target potentials go from the HS + SW to the HS + SW + SS , (i) there is a dramatic dropping of performance of the first-order MSA expressions in calculating the thermodynamic properties, especially both the excess internal energy and constant volume excess heat capacity of the HS + SW + SS model cannot be predicted even qualitatively correctly. (ii) One tendency is noticed that the first-order MSA gets more reliable with increasing temperatures in dealing with the pressure, excess Helmholtz free energy, excess enthalpy and excess chemical potential. (iii) Concerning the RDF , the first-order MSA is not as disappointing as it displays in the cases of thermodynamics. (iv) In the case of the HS + SW model, the first-order MSA solution is shown to be quantitatively correct in calculating the pressure and excess chemical potential even if the reduced temperatures are as low as 0.8. On the other hand, the seventh-order HTSE is less model-dependent; in most cases of the HS + SW and the HS + SW + SS models, the seventh-order HTSE improves the fifth- and third-order HTSE in both thermodynamic properties and RDF , and the improvements are very demonstrable in both the excess internal energy and constant volume excess heat capacity; for very limited cases, the seventh-order HTSE improves the fifth-order HTSE only within lower density domain and even shows a bit of inadaptation over higher density domain. [ABSTRACT FROM AUTHOR]

We implement a variational iteration method for solving a Poisson–Boltzmann equation (PBE) describing a spherical colloid immersed in a general electrolyte solution. In this method, a general Lagrange multiplier is introduced to construct correction functional for the problem, and the multiplier is identified optimally via a variational method; a linearization solution of the original PBE is chosen as an initial approximation for the iteration. To proceed with the iteration analytically, we approximate the highly nonlinear term of the PBE by a polynomial of proper order. Due to presence of an exponent integral function in the first-order iteration solution, higher-order iteration solutions are analytically unavailable currently. Based on the first-order iteration solution, analytic expression for surface charge density/surface potential relationship is acquired. The present analytic solution contrasts sharply with previous ones by two striking features: (1) the present one surpasses well beyond previous approximate solutions in that general electrolyte type can be dealt with in a unified way, and (2) valid application scope of the present expression is in small κadomain and thus is complementary with those of previous ones. [ABSTRACT FROM AUTHOR]

Thefirst three coefficients of the high temperature series expansion(HTSE) of the Helmholtz free energy for a number of simple potentialmodels with hard-sphere cores plus continuous tails are obtained forthe first time from Monte Carlo simulations. The potential modelsconsidered include Square-well, Sutherland, attractive Yukawa, andtriangle-well with different potential ranges, as well as a modelpotential qualitatively resembling the depletion potential in colloidaldispersions. The simulation data are used to evaluate performanceof a recent coupling parameter series expansion (CPSE) in calculatingfor these coefficients, and a traditional macroscopic compressibilityapproximation (MCA) for the second-order coefficient only. A comprehensivecomparison based on these coefficients from the two theoretical approachesand simulations enables one to conclude that (i) unlike one commonexperience that the widely used MCA usually underestimates the second-ordercoefficient, the MCA can both overestimate and underestimate the second-ordercoefficient, and worsens as the range of the potential decreases;and (ii) in contrast, the CPSE not only reproduce the trends in thedensity dependence of the perturbation coefficients, even the thirdone, observed in the simulations, but also the agreement is quantitativein most cases, and this clearly highlights the potential of the CPSEin providing accurate estimations for the higher-order coefficients,thus giving rise to an accurate higher-order HTSE. [ABSTRACT FROM AUTHOR]

We have extended the Raveché–Mountain–Streett one-phasecriterion that governs the freezing of Lennard-Jones systems to a hard-core repulsive Yukawa-model (HCRYM) system. We find in the framework of the Rogers–Young (RY) approximation for an Ornstein–Zernike integral equation that an HCRYM fluid freezes when the ratio α = g(rmin)/g(rmax), where rmax is the distance corresponding to the maximum in the radial distribution function g(r) and rmin is the distance corresponding to the subsequent minimum in g(r), is approximately 0.215. To describe the freezing of charge-stabilized colloidal dispersions in electrolytes, which consist of colloidal macroions,electrolyte small ions, and solvent molecules, we employ the single-component model in which the colloidal particles interact through the effective screened Coulomb potential of Belloni. Whenthe macroion surface effective charge number is taken as an adjustable parameter, the theoretical freezing line predicted by the RY g(rmin)/g(rmax) = 0.215 Raveché–Mountain–Streett one-phase criterion is in very good agreement with the corresponding experimental data.PACS Nos.: 61.25.Em, 61.20.Gy [ABSTRACT FROM AUTHOR]

Functional expansion of non-uniform first-order direct correlation function (DCF) around bulk density is rewritten with the concept of weighted density, it is found that the resulting first-order expansion term is actually the first-order expansion term of the Taylor series expansion of the uniform first-order DCF with weighted density as its density argument, the higher-order terms are incorporated into the first-order expansion approximation by Lagrangian theorem. Based on the functional integration view, the present Letter devises a numerical procedure to predict excess Helmholtz free energy from the approximation for the non-uniform first-order DCF. The physical foundation of the present discussion also applies to electronic density functional theory. [Copyright &y& Elsevier]