A modified soft-core fluid model for the direct correlation function of the square-shoulder and square-well fluids

We propose a simple analytical expression of the direct correlation function for the square-shoulder and square-well fluids. Our approximation is based on an ansatz for the direct correlation function of a modified soft-core fluid, whose parameters are adjusted by fitting the data obtained from Monte Carlo computer simulations. Moreover, it is complemented with a Wertheim-like parametrization to reproduce correctly the direct correlation inside the hard-core. We demonstrate that this approach is in quantitative agreement with the numerical solution of the Ornstein–Zernike equation within the Percus–Yevick approximation. We also show that our results are accurate in a large regime of densities for different interaction ranges and potential strengths. Therefore, this opens up the possibility of introducing the square-shoulder or the square-well potentials as new reference systems in advanced theoretical approximations.     

The thermodynamics of molecules with discrete potentials

Fluids formed by molecules interacting with discrete potentials are examined in the context of perturbation theory and the reference hypernetted chain equation (RHNC) solution to the Ornstein—zernike equation. A perturbation theory for discrete-potential fluids (DPT) is presented, which only requires one to know the properties of a square-well fluid of variable range. Several potentials are studied: square-shoulder, a combination of a square-well and square-shoulder, and a discrete representation of a continuous potential model. We have found that the DPT approach reproduces the RHNC predictions in most of the cases.     

Heat capacity of square-well fluids of variable width

We have obtained by Monte Carlo NVT simulations the constant-volume excess heat capacity of square-well fluids for several temperatures, densities and potential widths. Heat capacity is a thermodynamic property much more sensitive to the accuracy of a theory than other thermodynamic quantities, such as the compressibility factor. This is illustrated by comparing the reported simulation data for the heat capacity with the theoretical predictions given by the Barker-Henderson perturbation theory as well as with those given by a non-perturbative theoretical model based on Baxter's solution of the Percus-Yevick integral equation for sticky hard spheres. Both theories give accurate predictions for the equation of state. By contrast, it is found that the Barker-Henderson theory strongly underestimates the excess heat capacity for low to moderate temperatures, whereas a much better agreement between theory and simulation is achieved with the non-perturbative theoretical model, particularly for small well widths, although the accuracy of the latter worsens for high densities and low temperatures, as the well width increases.     

The role of higher-order terms in perturbation approaches to the monomer and bonding contributions in a SAFT-type equation of state for square-well chain fluids

A perturbation theory for square-well chain fluids is developed within the scheme of the (generalised) Wertheim thermodynamic perturbation theory. The theory is based on the Pavlyukhin parametrisations [Y. T. Pavlyukhin, J. Struct. Chem. 53, 476 (2012)] of their simulation data for the first four perturbation terms in the high temperature expansion of the Helmholtz free energy of square-well monomer fluids combined with a second-order perturbation theory for the contact value of the radial distribution function of the square-well monomer fluid that enters into bonding contribution. To obtain the latter perturbation terms, we have performed computer simulations in the hard-sphere reference system. The importance of the perturbation terms beyond the second-order one for the monomer fluid and of the approximations of different orders in the bonding contribution for the chain fluids in the predicted equation of state, excess energy and liquid–vapour coexistence densities is analysed.     

Gibbs ensemble simulation of the vapour-liquid equilibrium of square well spherocylinders

Gibbs ensemble Monte Carlo simulations have been performed for systems of square-well spherocylinders of different length-to-breadth ratio. The results are used to test a recent perturbation theory proposed for this kind of system. In addition, the results are compared to similar simulations performed for a Kihara fluid of elongated molecules. An unexpected good agreement is found for the coexistence thermodynamic and structural properties of both model fluids, hence suggesting that the hard spherocylinder plus square-well interaction should be considered as a reference potential for a perturbative treatment of more complex fluid models.     

Molecular dynamic simulations and global equation of state of square-well fluids with the well-widths from λ = 1.1 to 2.1

We present the results of extensive new molecular dynamic (MD) simulations in the one-phase region for square well fluids with well widths λ?=?1.10, 1.15, 1.20, 1.25, 1.375, 1.50, 1.75, 1.90, 2.0, and 2.10. These data have been used in developing a crossover equation of state (CR EOS) for square-well fluids with well widths 1.1?≤?λ?≤?2.1. The CR EOS incorporates non-analytic scaling laws in the critical region, and in the limit of low densities yields the exact second and third virial coefficients. Also in the high-temperature region, it reproduces first-order perturbation theory results. The CR EOS was tested against our new MD simulations, and earlier MD and Monte-Carlo (MC) simulations reported by other authors as well. Excellent agreement between calculated values and simulation data for all SW fluids is observed. In combination with the density-functional theory, the CR EOS is also capable of reproducing surface tension simulations with high accuracy. Application of the CR EOS for solid–liquid equilibrium calculations in combination with the Lennard–Jones and Devonshire cell model for the solid phase, is also discussed.     

Molecular dynamical calculations of the transport properties of a square-well fluid: V. The coefficient of self-diffusion

The diffusivity of a system, consisting of square-well molecules, has been determined by means of the dynamical computer simulation technique. The calculations offer a systematic investigation of the diffusivity covering almost the whole fluid region. It is found that at low and intermediate densities, the addition of a square negative potential on hard spheres lowers the diffusion coefficient but that at high densities, an increase can also be found, depending on the choice of the potential parameters. A negative first-order and a positive second-order density dependence of the product of density and diffusion coefficient has been found, which is in qualitative correspondence with results of real experiments.     

Structural and thermodynamic properties of the restricted primitive model electrolyte in a mixture with uncharged hard spheres: a grand canonical Monte Carlo simulation and integral equation study

A restricted primitive model electrolyte in a mixture with uncharged hard spheres was studied at room temperature using grand canonical Monte Carlo computer simulation and Ornstein–Zernike integral equation theory in the hypernetted chain approximation (HNC). The mean spherical approximation results are also presented for a few cases. We obtained the pair distribution functions of species of the system, the dependencies of the total fluid density and the ionic fraction on the chemical potentials, the excess internal energy and the heat capacity at constant volume for a wide range of chemical potentials of the species from the simulations and HNC theory. In the majority of cases, good agreement between the theoretical predictions and simulation data is obtained. The composition of the mixture is determined by the chemical potentials of both species. The pair distribution functions have a Debye-like shape at low densities for various values of the ion fraction. By increasing the chemical potential of the uncharged component, weak trends for structuring of the solution are observed with the formation of ion-hard sphere-ion complexes. At high densities, a tendency for in-phase oscillations of ion–ion functions is observed similar to the pure electrolyte in the restricted primitive model. We analysed the chemical potential–density and the chemical potential–ion fraction projections of the equation of state in detail. Also, the heat capacity at constant volume has been calculated for the first time. The model and the results are useful for the development of the theory of inhomogeneous fluid mixtures.     

Perturbation theory for mixtures of discrete potential fluids

A thermodynamic perturbation theory for mixtures of fluids composed of particles interacting via discrete potentials is presented, based on previous work for pure component systems. Square-well and square-shoulder mixtures are accurately described by this theory, giving the necessary information for studying a wide range of discrete potential fluids. As an example of this, the theory is applied to a discrete Lennard-Jones mixture, obtaining very good results when compared against computer simulation values. The scope of this work is to implement perturbation theory for discrete potential systems in modern theories for complex fluids.     

Liquid–vapour equilibrium of multipolar square-well fluids.Gibbs ensemble simulations and equation of state

Simulation results for a system comprising a square well plus either a point dipole or a point quadrupole are presented. The properties obtained are the vapour–liquid equilibrium densities and the critical properties. Critical densities are not very sensitive to the values of dipole or quadrupole, while critical temperatures increase significantly when the multipole strength rises. A comparison with a perturbation theory for multipolar square-well systems is presented. Overall agreement between simulated and theoretical values is good when comparison is restricted to quadrupoles or dipoles corresponding to the most relevant real polar substances but is only moderate for the largest multipolar strengths considered.     

Solutions of the Yvon-Born-Green equation for a system of square-well molecules at a temperature below the triple point

The Yvon-Born-Green equation (with superposition approximation) is solved numerically for the pair correlation function for a system of molecules interacting via the square-well potential (with σ₂/σ₁ = 1·85), for an isotherm below the triple point, and over a broad range of densities. The correlation function data and attendant thermodynamics generated for this isotherm are compared with results reported previously by the authors for several supercritical and subcritical isotherms of the square-well fluid. To facilitate the interpretation of these results, particularly in those regions of (T, ρ) space where phase transitions may occur, a geometrical representation of the data is presented (motivated, in part, by recent work by René Thom), and the location of the triple point is discussed in terms of this construction. The differences anticipated between results reported here and those that would be obtained in an exact statistical mechanical analysis, are identified.     

Vapour—liquid equilibrium of the square-well fluid of variable range via a hybrid simulation approach

The equilibrium between vapour and liquid in a square-well system has been determined by a hybrid simulation approach combining chemical potentials calculated via the Gibbs ensemble Monte Carlo technique with pressures calculated by the standard NVT Monte Carlo method. The phase equilibrium was determined from the thermodynamic conditions of equality of pressure and chemical potential between the two phases. The results of this hybrid approach were tested by independent NPT and μPT calculations and are shown to be of much higher accuracy than those of conventional GEMC simulations. The coexistence curves, vapour pressures and critical points were determined for SW systems of interaction ranges λ = 1.25, 1.5, 1.75 and 2. The new results show a systematic dependence on the range λ, in agreement with results from perturbation theory where previous work had shown more erratic behaviour.     

The phase behaviour of a fluid in a slitlike pore with permeable walls

The confinement of a lattice fluid in a set of slitlike pores separated by semipermeable walls with a finite width has been studied. The walls are modelled by a square-well repulsive potential with a finite height. The thermodynamic properties and the phase behaviour of the system are evaluated by means of Monte Carlo simulations. For some states theoretical calculations have been made using a mean-field-type theory. These investigations confirm previous findings for confined Lennard-Jones fluids, obtained from a density functional approach. For intermediate and low potential barriers that separate the pores, the isotherms exhibit two hysteresis loops and the liquid-vapour coexistence curve divides into two branches describing condensation inside the pore and inside the permeable wall. These two branches are separated by a triple point. At temperatures lower than the triple point temperature, the condensation takes place instantaneously in both the pore and inside the permeable wall. It was found that when the temperature is scaled by the bulk critical temperature, the phase diagram emerging from this simple mean-field treatment is close to the phase diagram obtained from simulation.     

方阱链流体在固液界面分布的密度泛函理论研究

应用Yethiraj的加权密度近似泛函理论研究平板狭缝中方阱链流体的密度分布，系统的Helm holtz自由能泛函分为理想气体的贡献利剩余贡献两部分，其中剩余贡献部分分别采用刘洪 来等人建立的基于空穴相关函数的方阱链流体状态方程和Gil-Villegas等人提出的统计缔合 流体理论状态方程(SAFT-VR)结合简单加权密度近似计算.考察了不同链长、温度、系统密度 和壁面吸引强度下平板狭缝中方阱链流体的密度分布，并与Monte Carlo(MC)模拟结果进行 了比较.结果表明采用不同的状态方程对密度分布的计算有明显的影响，对于受限于硬壁狭 缝中的方阱链流体，温度和密度比较高时，两种状态方程计算的结果均与MC模拟符合得比较 好，在低温和低密度下效果变差，SAFT-VR方程的计算结果更接近于MC模拟结果.对于受限于 方阱壁狭缝中的方阱链流体，由于系统密度分布的非均匀性加强，采用两种状态方程计算的 结果均与MC模拟结果有一定偏差，寻找更合适的权重函数是进一步改进的关键. 关键词： 密度泛函理论 非均匀流体 密度分布 固液界面 方阱链     

A parametrisation of the direct correlation function for the square-shoulder fluid

We introduce a parametrisation of the direct correlation function for the square-shoulder fluid and demonstrate that this parametrisation is in quantitative agreement with the numerical solution of the Ornstein–Zernike equation within the Percus–Yevick approximation. Moreover, the radial distribution function obtained from the parametrisation reproduces quantitatively Monte Carlo simulation data. Our results show that the parametrisation is accurate over a large regime of densities for different interaction ranges and potential strengths.     

Thermodynamic properties of square-well fluids from a new coordination number model

A new coordination number model is proposed for square-well fluids at λ?=?1.5. The model modifies the theory previously developed for the coordination number of square-well fluids derived on the basis of the generalized Van der Waals theory by Largo and Solana. The present work proposes a new formula for the maximum reduced density and a new method to solve the integral corresponding to coordination number of hard sphere fluids. Thermodynamic quantities such as pair correlation function at contact, excess internal energy and constant volume excess heat capacity are determined employing the model. Good agreement is achieved between theoretical results and Monte Carlo (M.C.) data. As expected, the results of the excess heat capacity are poor at low temperatures.     

Mean spherical model-structure of liquid argon

A new formulation forS(k), the structure factor, has been obtained, treating the square-well potential as a perturbation on the hard-core in the mean spherical model approximation. The potential parameters have been varied not only to get a satisfactory peak height at the fitted temperature but also over a wide range of temperatures and densities. The agreement between the computed and experimental structure factor values shows that the representation of the attractive tail by a square-well potential yields a satisfactory method in understanding the structure of liquid argon.     

Monte Carlo and cell model calculations for the solid—fluid phase behaviour of the triangle-well model

Monte Carlo simulations and cell model calculations are reported for the vapour-liquid and solid-liquid phase behaviour of the triangle-well model system. The behaviour is examined as a function of the range of the triangle-well attraction, from 1.05 to 2.5 times the diameter of the hard core of the potential. Cell model calculations indicate that the stable solid is almost always face-centred cubic (fcc), except for a small set of conditions where hexagonal close-packed (hcp) is favoured. This outcome differs markedly from a much earlier study performed for the square-well model potential, where a much richer phase diagram was observed, with significant regions of stability for hep and body-centred cubic (bcc) phases. Monte Carlo simulations indicate that the cell model calculations represent well the true phase behaviour for this model system. The differing behaviour between the triangle-well and square-well models indicates an important role for the flatness of the potential well in governing the stability of hcp and bcc phases relative to the fcc phase.     

On the signs of fluorine spin coupling constants

From an exact expression for the free energy of a non-uniform fluid mixture a closure approximation for the inhomogeneous direct correlation functions is used to develop a theory of solvation forces in charged fluids based upon non-linear equations for the equilibrium ion number densities. In the limit of point ions, the expressions obtained reduce to those of the Poisson-Boltzmann theory of electrolytes. The numerical results obtained for a restricted primitive model electrolyte are compared with those of earlier work based on linear response theory and Poisson-Boltzmann theory with a simple Stern layer modification. At low electrolyte concentrations the agreement between all three theories is good. But at high electrolyte concentrations the Poisson-Boltzmann theory with a simple Stern layer correction fails to display the oscillations in the solvation force which characterize both the linear and non-linear theories.     

Diffusion within a near-critical nanopore fluid

Results are presented for grand canonical Monte Carlo (GCMC) and both equilibrium and non-equilibrium molecular dynamics simulations (EMD and NEMD) conducted over a range of densities and temperatures that span the two-phase coexistence and supercritical regions for a pure fluid adsorbed within a model crystalline nanopore. The GCMC simulations provided the low temperature coexistence points for the open pore fluid and were used to locate the capillary critical temperature for the system. The equilibrium configurational states obtained from these simulations were then used as input data for the EMD simulations in which the self-diffusion coefficients were computed using the Einstein equation. NEMD colour diffusion simulations were also conducted to validate the use of a system averaged Einstein analysis for this inhomogeneous fluid. In all cases excellent agreement was observed between the equilibrium (linear response theory) predictions for the diffusivities and non-equilibrium colour diffusivities. The simulation results are also compared with a recently published quasi-hydrodynamic theory of Pozhar and Gubbins (Pozhar, L. A., and Gubbins, K. E., 1993, J. Chem. Phys., 99, 8970; 1997, Phys. Rev. E, 56, 5367.). The model fluid and the nature of the fluid wall interactions employed conform to the decomposition of the particle–particle interaction potential explicitly used by Pozhar and Gubbins. The local self-diffusivity was calculated from the local fluid–fluid and fluid wall hard core collision frequencies. While this theory provides reasonable results at moderate pore fluid densities, poor agreement is observed in the low density limit.