On the role of the reference system in perturbation theory: An augmented van der Waals theory of simple fluids

In this study, we show that the inclusion of a short-range part of the total attractive interaction into a reference system allows a natural extension of the traditional first-order perturbation theory of simple fluids to practically all thermodynamic states. This theory is applied to the thermodynamic functions and the liquid–vapor coexistence curve of the Lennard-Jones-like medium range Yukawa fluid and to the Sutherland fluid. Comparison with computer simulation data and the second-order Barker–Henderson perturbation theory is discussed.     

Solid phase thermodynamic perturbation theory: test and application to multiple solid phases

A simple procedure for the determination of hard sphere (HS) solid phase radial distribution function (rdf) is proposed, which, thanks to its physical foundation, allows for extension to other crystal structures besides the fcc structure. The validity of the procedure is confirmed by comparing (1) the predicted HS solid phase rdf's with corresponding simulation data and (2) the predicted non-HS solid phase Helmholtz free energy by the present solid phase first-order thermodynamic perturbation theory (TPT) whose numerical implementation depends on the HS solid phase rdf's as input, with the corresponding predictions also by the first-order TPT but the required HS solid phase rdf is given by an "exact" empirical simulation-fitted formula. The present solid phase first-order TPT predicts isostructural fcc-fcc transition of a hard core attractive Yukawa fluid, in very satisfactory agreement with the corresponding simulation data and is far more accurate than a recent thermodynamically consistent density functional perturbation theory. The present solid phase first-order TPT is employed to investigate multiple solid phases. It is found that a short-ranged potential, even if it is continuous and differentiable or is superimposed over a long-ranged potential, is sufficient to induce the multiple solid phases. When the potential range is short enough, not only isostructural fcc-fcc transition but also isostructural bcc-bcc transition, simple cubic (sc)-sc transition, or even fcc-bcc, fcc-sc, and bcc-sc transitions can be induced. Even triple point involving three solid phases becomes possible. The multiple solid phases can be stable or metastable depending on the potential parameters.     

Phase behavior of colloids and proteins in aqueous suspensions: Theory and computer simulations

The fluid phase behavior of colloidal suspensions with short-range attractive interactions is studied by means of Monte Carlo computer simulations and two theoretical approximations, namely, the discrete perturbation theory and the so-called self-consistent Ornstein-Zernike approximation. The suspensions are modeled as hard-core attractive Yukawa (HCAY) and Asakura-Oosawa (AO) fluids. A detailed comparison of the liquid-vapor phase diagrams obtained through different routes is presented. We confirm Noro-Frenkel's extended law of scaling according to which the properties of a short-ranged fluid at a given temperature and density are independent of the detailed form of the interaction, but just depend on the value of the second virial coefficient. By mapping the HCAY and AO fluids onto an equivalent square-well fluid of appropriate range at the critical point we show that the critical temperature as a function of the effective range is independent of the interaction potential, i.e., all curves fall in a master curve. Our findings are corroborated with recent experimental data for lysozyme proteins.     

An application of mean-field perturbation theory for the adsorption of polar molecules in nanoslit-pores

In the present research study, we present the development of a model for characterizing and predicting the adsorption of polar molecules between two parallel plates based on mean-field perturbation theory. The electrostatic forces between fluid–fluid molecules in the slit shaped pore are modeled by considering permanent dipole–dipole interactions and permanent dipole-induced dipole moment interactions. The intermolecular potential for the electrostatic interactions was obtained by considering statistical averages over all possible orientations of the molecules. The proposed model is then used to study the sorption of water molecules in the slit shaped pore and an explicit equation for the Helmholtz free energy of the pore phase fluid is derived. Adsorption isotherms for different pore sizes are simulated and the relative contributions of fluid–wall and fluid–fluid interactions to the Helmholtz free energy are calculated as an illustration and compared with the results of existing models in the literature.AMS subject classification: 82B03, 82B05, 82B26, 82B30, 82D15, 31B10, 41A25     

Phase behavior of density-dependent pair potentials

Phase diagram is calculated by a recently proposed third-order thermodynamic perturbation theory (TPT) for fluid phase and a recently proposed first-order TPT for solid phases; the underlying interparticle potential consists of a hard sphere repulsion and a perturbation tail of an attractive inverse power law type or Yukawa type whose range varies with bulk densities. It is found that besides usual phase transitions associated with density-independent potentials, the density dependence of the perturbation tail evokes some additional novel phase transitions including isostructural solid-solid transition and liquid-liquid transition. Novel triple points are also exhibited which includes stable fluid (vapor or liquid)-face-centered cubic(fcc)-fcc and liquid-liquid-fcc, metastable liquid-body-centered cubic(bcc)-bcc. It also is found that the phase diagram sensitively depends on the density dependence and the concrete mathematical form of the underlying potentials. Some of the disclosed novel transitions has been observed experimentally in complex fluids and molecular liquids, while others still remain to be experimentally verified.     

Self-consistent Ornstein-Zernike approximation for the Yukawa fluid with improved direct correlation function

Thermodynamic consistency of the mean spherical approximation as well as the self-consistent Ornstein-Zernike approximation (SCOZA) with the virial route to thermodynamics is analyzed in terms of renormalized gamma-ordering. For continuum fluids, this suggests the addition of a short-ranged contribution to the usual SCOZA direct correlation function, and the shift of the adjustable parameter from the potential term to this new term. The range of this contribution is fixed by imposing consistency with the virial route at the critical point. Comparison of the results of our theory for the hard-core Yukawa potential with the simulation data show very good agreement for cases where the liquid-vapor transition is stable or not too far into the metastable region with respect to the solid state. In the latter case for extremely short-ranged interactions discrepancies arise.     

On the fluid phase behaviour of fluid binary mixtures using the Yukawa fluid molecular model

By expanding Ginoza’s mean spherical approximation (MSA) results in an inverse-temperature expansion, Henderson et al. obtained explicit results for the thermodynamic functions of a pure Yukawa fluid. We have recently published explicit results for the coefficients in an inverse-temperature expansion of the thermodynamic functions for the MSA for mixtures of Yukawa fluids. Attention is drawn to the fact that the MSA in the Ginoza formulation, does not always yield a convergent solution. The expansion used in this paper will always yield a result. In this work we present our investigations of the fluid phase diagram of Yukawa binary mixtures by considering an expansion of the MSA Helmholtz free energy up to the fifth order of the inverse-temperature expansion. The calculated fluid phase diagrams for Yukawa binary mixtures are similar to those of real mixtures.     

Thermodynamic and structural properties of repulsive hard-core Yukawa fluid: integral equation theory, perturbation theory and Monte Carlo simulations

The thermodynamic and structural properties of purely repulsive hard-core Yukawa particles in the fluid state are determined through Monte Carlo simulation and modeled using perturbation theory and integral equation theory in the mean spherical approximation (MSA). Systems of particles with Yukawa screening lengths of 1.8, 3.0, and 5.0 are examined with results compared to variations of MSA and perturbation theory. Thermodynamic properties were predicted well by both theories in the fluid region up to the fluid-solid phase boundary. Further, we found that a simplified exponential version of the MSA is the most accurate at predicting radial distribution function at contact. Radial distribution function of repulsive hard-core Yukawa particles are also reported. The results show that methods based on MSA and perturbation theory that are typically applied to the attractive hard-core Yukawa potential can also be extended to the purely repulsive hard-core Yukawa potential.     

Yukawa流体的相平衡和界面张力研究

应用二阶微扰理论, Duh-Mier-Y-Teran状态方程和在平均球近似(mean spherical approximation, MSA)的基础上获得的直接相关函数, 建立了适用于均匀流体和非均匀流体的状态方程. 结合此状态方程, 重整化群理论(renormalization group theory, RG)和密度泛函理论(density functional theory, DFT), 分别研究了Yukawa流体的相平衡和界面张力. 结果与分子模拟数据吻合良好.     

Interactions of nanoscopic particles with phase-separating polymeric mixtures

Roughly 70% of all manufactured polymeric materials contain solid ‘filler’ particles. These filled systems exhibit increased strength and heat resistance, and decreased gas permeability as compared to the pure polymer matrix. While the solid additives are essential for providing the desired attributes, the influence of nanoscopic particles on the structural evolution of multicomponent polymeric fluids is still poorly understood. New research is revealing that a dynamic coupling between the fluid–fluid phase separation and fluid–particle wetting significantly affects the morphology and kinetic behavior of the system. In the case of diblock/filler mixtures, the particles can influence the orientation and size of lamellar domains. Thus, the emerging results provide guidelines for fabricating new composite materials.     

用重整化群理论研究胶体模型体系的相行为

用yukawa势能函数表达胶体颗粒之间的吸引作用。用Duh-Mier-Y-Teran状态方 程表达液相Helmholtz自由能。用一阶微扰理论、固体硬球径向分布函数解析式和 改进的胞腔模型建立固相状态方程，结合建立的状态方程和重整化群理论。研究了 胶体模型体系的液-液相平衡和液-固相平衡。研究表明，颗粒之间色散作用量程参 数的变化对胶休到本世纪末茶杯 系的相行为有特殊需要影响。所得结果与分子模 拟数据吻合良好。     

High pressure phase equilibria in methane + waxy systems: 1. Methane + heptadecane

Fluid–fluid and fluid–solid phase equilibrium were experimentally determined under pressure on the system methane + heptadecane using a full visibility cell. Measurements were performed using the synthetic method on mixtures ranging from pure heptadecane to 99% of methane. The liquid–solid phase transitions were investigated up to 90 MPa and fluid phase boundary was studied in the temperature domain from 293 to 373 K. The appearance of a minimum in the three phase (V–L–S) equilibrium curve is discussed and it is shown that the difference in the solid phase structure and the presence of a solid–solid phase transition do not affect significantly the phase diagram determined.     

Further test of third order + second-order perturbation DFT approach: hard core repulsive Yukawa fluid subjected to diverse external fields

Grand canonical Monte Carlo simulation is used to investigate density profiles of hard-core repulsive Yukawa (HCRY) model fluid under the influence of various external fields and radial distribution function (RDF) of the bulk HCRY system. The aim of these extensive simulations is to provide exact data for purely repulsive interaction potential against which the validity of a third order + second-order perturbation DFT approach can be tested. It is found that a semiempirical parametrized bridge function due to Malijevsky and Labik performs very well for the RDF of the bulk HCRY fluid. Incorporation of a bulk second-order direct correlation function (DCF) of the HCRY fluid based on the Malijevsky-Labik bridge function into the third order + second-order perturbation DFT approach yields the resulting theoretical predictions for the density profiles of inhomogeneous HCRY fluid that are in a very good agreement with the simulation data, an exception being somewhat larger deviations appearing for the structure of the fluid around the center of a hard spherical cavity. Both theory and simulation predict layering transition and gas-liquid coexistence phenomena occurring with the HCRY model fluid under confined conditions. For the case of an inverse sixth-power repulsive potential under the influence of a flat stationary wall defined by an inverse twelfth-power repulsive potential, the present third order + second-order perturbation DFT approach is found to be superior to several existing weighted density approximations (WDA) and partitioned WDA.     

Use of the Yukawa fluid as the reference system in perturbation theory

The Weeks-Chandler-Anderson (WCA) perturbation theory is studied utilising recent results for the Yukawa model fluid. Replacing the attractive tail of the Lennard-Jones potential with a Yukawa tail, where the Yukawa parameters are chosen using a least squares fit, it is shown that accurates field dstribution functions can be generated via the EXP approximation of the WCA optimized cluster theory. The comparative case and accuracy with which the correlation functions for the Yukawa fluid can be compared render this a very useful method for studying the equilibrium properties of simple liquids.     

Effect of critical fluctuations on adsorption of van der Waals fluid in a spherical cavity

A recently proposed non-uniform fifth-order thermodynamic perturbation theory (TPT) is employed to investigate the adsorption of a hard core attractive Yukawa (HCAY) fluid in a spherical cavity. Extensive comparison with available simulation data indicate that the non-uniform fifth-order TPT is sufficiently reliable in calculating the density profiles of the HCAY fluid in the highly confining geometry, and generally is more accurate than a previous third-order?+?second-order perturbation density functional theory. The non-uniform fifth-order TPT is free from numerically solving an Ornstein–Zernike integral equation, and also free of any adjustable parameter; consequently, it can be applied to both supercritical and subcritical temperature regions. The non-uniform fifth-order TPT is employed to investigate critical adsorption of the HCYA fluid in a single spherical cavity – it is disclosed that the critical fluctuations near the critical point induce depletion adsorption – quantitative theoretical calculation on relationship between the critical depletion adsorption, parameters of coexistence bulk phase and the responsible external field is in agreement with qualitative physical analysis.     

Calculating thermodynamic properties from perturbation theory: Part III. The mixtures of square-well chain fluid

A completely analytic perturbation theory has been developed to calculate the Helmholtz energy, compressibility factor, internal energy and constant-volume heat capacity for square-well chain fluid mixtures. This theory is based on the improved Barker–Henderson macroscopic compressibility (mc) approximation proposed by Zhang, the first-order perturbation theory of Wertheim in which Zhang’s analytic monomer radial distribution function as the function of temperature and monomer density is used, and a simple mixing rule similar to that of Hino–Prausnitz. The validity of the perturbation theory is evaluated by comparing the calculated compressibility factor, internal energy and constant-volume heat capacity for the freely jointed square-well chain mixtures from the theory to MC simulation data. The results show that the theory predicts results in good agreement with simulation results.     

A completely analytic equation of state for the square-well chain fluid of variable well width

A completely analytic perturbation theory equation of state for the freely-jointed square-well chain fluid of variable well width (1 ≤ λ ≤ 2) is developed and tested against Monte Carlo simulation data. The equation of state is based on second-order Barker and Henderson perturbation theory to calculate the thermodynamic properties of the reference monomer fluid, and on first-order Wertheim thermodynamic perturbation theory to account for the connectivity of monomers to form chains. By using a recently developed real function expression for the radial distribution function of hard spheres in perturbation theory, we obtain analytic, closed form expressions for the Helmholtz free energy and the radial distribution function of square-well monomers of any well width. This information is used as the reference fluid in the perturbation theory of Wertheim to obtain an analytic equation of state, without adjustable parameters, that leads to good predictions of the compressibility factors and residual internal energies for 4-mer, 8-mer and 16-mer square-well fluids when compared with the simulation results. Further, very good results are obtained when this equation of state with temperature-independent parameters is used to correlate the vapor pressures and critical points of the linear alkanes from methane to n-decane.     

Thermodynamic properties of model solids with short-ranged potentials from Monte Carlo simulations and perturbation theory

Monte Carlo simulations have been performed to determine the excess energy and the equation of state of fcc solids with Sutherland potentials for wide ranges of temperatures, densities, and effective potential ranges. The same quantities have been determined within a perturbative scheme by means of two procedures: (i) Monte Carlo simulations performed on the reference hard-sphere system and (ii) second-order Barker-Henderson perturbation theory. The aim was twofold: on the one hand, to test the capability of the "exact" MC-perturbation theory of reproducing the direct MC simulations and, on the other hand, the reliability of the Barker-Henderson perturbation theory, as compared with direct MC simulations and MC-perturbation theory, to determine the thermodynamic properties of these solids depending on temperature, density, and potential range. We have found that the simulation data for the excess energy obtained from the two procedures are in close agreement with each other. For the equation of state, the results from the MC-perturbation procedure also agree well with the direct MC simulations except for very low temperatures and extremely short-ranged potentials. Regarding the Barker-Henderson perturbation theory, we have found that in general the second-order approximation does not provide significant improvement over the first-order one.     

Phase behavior of aqueous solutions containing dipolar proteins from second-order perturbation theory

Due to the interplay of Coulombic repulsion and attractive dipolar and van der Waals interactions, solutions of globular proteins display a rich variety of phase behavior featuring fluid-fluid and fluid-solid transitions that strongly depend on solution pH and salt concentration. Using a simple model for charge, dispersion and dipole-related contributions to the interprotein potential, we calculate phase diagrams for protein solutions within the framework of second-order perturbation theory. For each phase, we determine the Helmholtz energy as the sum of a hard-sphere reference term and a perturbation term that reflects both the electrostatic and dispersion interactions. Dipolar effects can induce fluid-fluid phase separation or crystallization even in the absence of any significant dispersion attraction. Because dissolved electrolytes screen the charge-charge repulsion more strongly than the dipolar attraction, the ionic strength dependence of the potential of mean force can feature a minimum at intermediate ionic strengths offering an explanation for the observed nonmonotonic dependence of the phase behavior on salt concentration. Inclusion of correlations between charge-dipole and dipole-dipole interactions is essential for a reliable calculation of phase diagrams for systems containing charged dipolar proteins and colloids.     

Improvement on macroscopic compressibility approximation and beyond

A numerical procedure is proposed to extend the thermodynamic perturbation expansion (TPE) to a higher order. It is shown that the present second order term is superior to that due to a macroscopic compressibility approximation (MCA), a local compressibility approximation, and a superposition approximation by Barker and Henderson [Rev. Mod. Phys. 48, 587 (1976)]. Extensive model calculation and comparison with simulation data available in literature and supplied in the present report indicate that the present third order TPE is superior to a previous second order TPE based on the MCA, two previous perturbation theories, which are respectively based on an analytical mean spherical approximation for an Ornstein-Zernike equation, and an assumed explicit functional form for the Laplace transform of radial distribution function multiplied by radial distance, and a recent generalized van der Waals theory. The present critical temperature for a hard core attractive Yukawa fluid of varying range is in very good agreement with that due to a hierarchical reference theory. The present third order TPE is computationally far more modest than the self-consistent integral equation theory, and therefore is a viable alternative to use of the latter.