A model dipolar ellipsoidal fluid

A theoretical method previously introduced in order to study the structure and thermodynamics of a charged ellipsoidal fluid is here applied to the study of a dipolar ellipsoidal fluid. To enable the strong-coupling (large dipole) form of the direct correlation function to be written analytically, the model employs ellipsoids with charges distributed over their surfaces. This implies that the electric field at a large distance from one molecule results from many multipoles although the dipole is the dominant one. A geometric ansatz for the direct correlation function containing a small number of parameters is then constructed and the parameters determined through the means of a variational principle based upon the mean spherical approximation. From the resultant direct correlation function it is possible to determine thermodynamic properties, including the relative permittivity of the fluid and the electrostatic energy. Within the model no ferroelectric transition is observed. Further the resultant direct correlation function is in a suitable analytic form for applications to the structure of an inhomogeneous fluid. The model is applied to fluids of ellipsoids with elongations ranging between 1/5 (oblate) and 5 (prolate). The range of dipole moments and densities allows relative permitivities up to approximately 80. The results are consistent with other studies of hard dipolar fluids although the model is not precisely the same except in the special case of hard spheres.     

Density functional approximation for van der Waals fluids： based on hard sphere density functional approximation

A universal theoretical approach is proposed which enables all hard sphere density functional approximations (DFAs) applicable to van der Waals fluids. The resultant DFA obtained by combining the universal theoretical approach with any hard sphere DFAs only needs as input a second-order direct correlation function (DCF) of a coexistence bulk fluid, and is applicable in both supercritical and subcritical temperature regions. The associated effective hard sphere density can be specified by a hard wall sum rule. It is indicated that the value of the effective hard sphere density so determined can be universal, i.e. can be applied to any external potentials different from the single hard wall. As an illustrating example, the universal theoretical approach is combined with a hard sphere bridge DFA to predict the density profile of a hard core attractive Yukawa model fluid influenced by diverse external fields; agreement between the present formalism's predictions and the corresponding simulation data is good or at least comparable to several previous DFT approaches. The primary advantage of the present theoretical approach combined with other hard sphere DFAs is discussed.     

Thermodynamic Limit for Polydisperse Fluids

We examine the thermodynamic limit of fluids of hard core particles that are polydisperse in size and shape. In addition, particles may interact magnetically. Free energy of such systems is a random variable because it depends on the choice of particles. We prove that the thermodynamic limit exists with probability 1, and is independent of the choice of particles. Our proof applies to polydisperse hard-sphere fluids, colloids and ferrofluids. The existence of a thermodynamic limit implies system shape and size independence of thermodynamic properties of a system.     

Statistical Mechanics Approach for Uniform and Non-uniform Fluid with Hard Core and Interaction Tail

One recently proposed self-consistent hard sphere bridge functional was combined with an exponential function exp(-cr) and a re-normalized indirect correlation function to construct the bridge function for fluid with hard core and interaction tail. In the present approach, the adjustable parameter α was determined by the thermodynamic consistency realized on the compressibility modulus, the re-normalization of the indirect correlation function was realized by a modified Mayer function with the interaction potential replaced by the perturbative part of the interaction potential. As an example, the present bridge function was combined with the Ornstein-Zernike (OZ) equation to predict structure and thermodynamics properties in very good agreement with the simulation data available for Lennard-Jones (L J). Based on the universality principle of the free energy density functional and the test particle trick, the numerical solution of the OZ equation was employed to construct the first order direct correlation function of the non-uniform fluid as a functional of the density distribution by means of the indirect correlation function. In the framework of the density functional theory, the numerically obtained functional predicted the density distribution of LJ fluid confined in two planar hard walls that is in good agreement with the simulation data.     

High momentum nucleons in the nucleus

Using Jastrow form for the nuclear wave function, single-particle distributions in the momentum space are extracted for the correlation functions corresponding to the Reid soft core, Hamada-Johnston and Ohmura-Morita-Yamada (OMY) hard core potentials. The correlations functions used for this purpose are the numerical solutions of the Schrödinger type equation for the realistic potentials and analytical form for the OMY potential. It is found that the calculated momentum distributions, with Woods-Saxon basis functions, differ significantly beyond 400 MeV/c. Comparison with the experimental proton momentum distribution from (γ, p) reaction suggests that while the OMY potential results are nearer to the experimental values, the realistic potentials do not introduce the high momentum components to the required extent.     

13C hyperfine splitting in the benzene negative ion

A method is developed to calculate the coefficients appearing in the Høye, Stell and Waisman analytic solution of the Ornstein-Zernike equation for a hard core potential with a direct correlation function of the two Yukawa form. The method is simple and makes the choice of a physical solution easy. The compressibility, energy and virial pressures are calculated in the vicinity of the liquid-gas transition region and their dependence on changing K ₂, the amplitude of the repulsive Yukawa part, is analysed. This method offers promising possibilities for the application of the hard core, two Yukawa (HCTY) system in the theory of fluids.     

Structural and thermodynamic properties of a multicomponent freely jointed hard sphere multi-Yukawa chain fluid

The product-reactant Ornstein-Zernike approach, represented by the polymer mean-spherical approximation (PMSA), is utilized to describe the structure and thermodynamic properties of the fluid of Yukawa hard sphere chain molecules. An analytical solution of the PMSA for the most general case of the multicomponent freely jointed hard sphere multi-Yukawa chain fluid is presented. As in the case of the regular MSA for the hard sphere Yukawa fluid, the problem is reduced to the solution of a set of nonlinear algebraic equations in the general case, and to a single equation in the case of the factorizable Yukawa potential coefficients. Closed form analytical expressions are presented for the contact values of the monomer-monomer radial distribution function, structure factors, internal energy, Helmholtz free energy, chemical potentials and pressure in terms of the quantities, which follows directly from the PMSA solution. By way of illustration, several different versions of the hard sphere Yukawa chain model are considered, represented by one-Yukawa chains of length m, where m = 2, 4, 8, 16. To validate the accuracy of the present theory, Monte Carlo simulations were carried out and the results are compared systematically with the theoretical results for the structure and thermodynamic properties of the system at hand. In general it is found that the theory performs very well, thus providing an analytical route to the equilibrium properties of a well defined model for chain fluids.     

TPT2 and SAFTD equations of state for mixtures of hard chain copolymers

We present the second-order thermodynamic perturbation theory (TPT2) and the dimer statistical associating fluid theory (SAFTD) equations of state for mixtures consisting of hetero-nuclear hard chain molecules based on extensions of Wertheim's theory for associating fluids. The second-order perturbation theory, TPT2, is based on the hard sphere mixture reference fluid. SAFTD is an extension of TPT1 (= SAFT) and is based on the non-spherical (hard disphere mixture) reference fluid. The TPT2 equation of state requires only the contact values of the hard sphere mixture site-site correlation functions, while the SAFTD equation of state requires the contact values of site-site correlation functions of both hard sphere and hard disphere mixtures. We test several approximations for site-site correlation functions of hard disphere mixtures and use these in the SAFTD equation of state to predict the compressibility factor of copolymers. Since simulation data are available only for a few pure copolymer systems, theoretical predictions are compared with molecular simulation results for the compressibility factor of pure hard chain copolymer systems. Our comparisons show a very good performance of TPT2, which is found to be more accurate than TPT1 (= SAFT). Using a modified Percus-Yevick site-site correlation function SAFTD is found to represent a significant improvement over SAFT and is slightly more accurate than TPT2. Comparison of SAFTD with generalized Flory dimer (GFD) theory shows that both are equivalent at intermediate to high densities for the compressibility factor of copolymer systems investigated here.     

Pertubation theory for systems with strong short-ranged interactions

We propose a variant of thermodynamic perturbation theory based on the Mayer f-function which is applicable to strongly repulsive, and even singular interactions. The expansion of the free energy is successfully tested against known ‘exact results’ for hard-sphere fluids, and then applied to binary mixtures of particles with non-additive hard cores or shouldered potentials. The resulting phase diagrams agree well with existing simulation data and theoretical predictions.     

Towards a unified view of fluids

It has traditionally been believed that, unlike normal fluids whose structural properties are determined primarily by the intermolecular short-range repulsive interactions, the properties of polar and associating fluids are strongly affected by the long-range Coulombic interactions. In the course of investigations to determine the primary driving forces governing the behaviour of various (non-simple) fluids, and hence to gain a deeper understanding of the molecular mechanisms leading to the development of theoretically based simple models and theory, extensive and systematic computer simulations have been performed on typical quadrupolar (carbon dioxide), dipolar (acetone and acetonitrile), and associating (hydrogen fluoride, methanol, and water) fluids using the available realistic effective pair potentials and their variants involving forces of different ranges. In addition to the main structural characteristics (one- and two-dimensional site–site correlation functions, local g factors, and radial slices through the full pair correlation function), the dielectric constants and the thermodynamic properties (internal energy and pressure) of both the homogeneous liquid and supercritical fluid phases, and vapor–liquid equilibria have also been considered. Furthermore, in the case of water, the diffusion coefficient and viscosity have also been considered along with water at the interface. All the obtained results lead to the unambiguous conclusion that the structure, defined in terms of the complete set of site–site correlation functions, for both polar and associating pure fluids is governed by the same molecular mechanism as for normal fluids, i.e. by the short-range interactions (which, however, may be both repulsive and attractive), whereas the long-range part of the electrostatic forces, regardless of their strength, plays only a marginal role and may be treated as a perturbation only. The consequences of these findings for theory and applications are also discussed.     

A hard sphere fluid model for superionic conductors

We develop a theory for the mobile constituent of a superionic conductor using the Ornstein-Zernike integral equation for the pair correlation function of an inhomogeneous fluid. We solve this equation in the Percus-Yevick approximation using a simple decoupling procedure and hard core potentials. Comparison is made with molecular dynamics calculations on α-AgI.     

Phase transition in gas of hard core spheres

We present a new method of analyzing the gas of hard core spheres. We investigate analytic properties of the thermodynamic function over the circle of convergence of the cluster expansion and describe the way in which phase transition occurs.     

Density functional study of the pressure tensor for inhomogeneous Lennard—Jones fluids

Based on classical density functional theory,an expression of the pressure tensor for inhomogeneous fluids is presented.This takes into account greater correlation between particles,especially for systems that are geometrically confined or involve an interface.The density and pressure components of Lennard-Jones fluids confined in hard and softened nano-cavities are calculated.A comparison between the results of this work and IK expression suggests that the agreement depends on temperature.The interfacial tension for hard sphere fluids agrees well with the Monte Carlo result when the bulk density is not too large.The results of the solid-fluid interfacial tension for Lennard-Jones fluids demonstrate that different types of external potentials modulate the interfacial tension in different manners.     

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 radial distribution function of a soft-repulsive hard core particle system

The system of hard core particles interacting via slowly decreasing repulsions of a finite range is investitated both theoretically and experimentally. The exponential (EXP) approximation of simple fluids is extended to pure repulsive potentials and is found as an accurate and rapid method to obtaining the radial distribution function. While the results based on the blip-function approximation are accurate only for a short interaction range and/or very low densities, agreement between the EXP results and Monte Carlo simulation data is excellent for all the interaction ranges and densities considered.     

A lattice-gas model with Coulomb interactions: Application to α-AgI

The pair correlation function g(r) for diffusing ions has been calculated within a lattice-gas model using the tetrahedral sites of α-AgI as lattice sites and the Ag ions as particles. The Coulomb and hard core interactions between the ions have been taken into account in the hypernetted chain approximation. Using parameters appropriate for α-AgI we find that g(r) exhibits many well pronounced oscillations extending up to about 10 nearest neighbor distances. Furthermore the direct correlation function approaches the Debye—Hückel form very rapidly beyond second nearest neighbor sites. Using g we have calculated the configurational entropy and its contribution to the specific heat as functions of the temperature. Our results are compared with experiment and computer simulations.     

The use of a non-spherical reference potential in statistical mechanical perturbation theory

A statistical mechanical perturbation theory for the pair correlation function and thermodynamic properties of molecular fluids is presented in which the reference potential function is non-spherical. With this choice the short-range molecular repulsive forces can be properly taken into consideration and attractive forces, such as those resulting from electric moments, treated as the perturbation. Calculations are presented for the first-order perturbation term to the Helmholtz free energy due to quadrupolar forces in models of liquid nitrogen and chlorine, and due to dipolar forces in liquid hydrogen chloride. For these calculations the rigid diatomic model and its modification appropriate to heteronuclear molecules were used for the reference potentials. It is found that the lowest-order perturbation terms here are proportional to the second power of the dipole or quadrupole moments, and not the fourth power as had been found previously using a spherical reference potential function. This second-order dependence on the electric moment is especially important in the case of mixtures, where it leads to an explanation for the occurrence of negative azeotropes in binary mixtures of species with quadrupole moments of opposite sign.