Thermodynamics and structure of a two-dimensional asymmetric electrolyte by integral equation theory

Integral equation theories and Monte–Carlo simulations were used to determine the thermodynamic and structural properties of a two-dimensional asymmetric Coulomb system. We check correctness of different closures in integral equations and their ability to reproduce Kosterlitz–Thouless and vapour–liquid phase transitions of the electrolyte and critical points. Integral equation theory results were compared with Monte–Carlo data. Among selected closures, hypernetted-chain approximation results matched computer simulation data best, but these equations unfortunately break down at temperatures well above the Kosterlitz–Thouless transition. The Kovalenko-Hirata closure produces results even at very low temperatures and densities, but no sign of phase transition was detected.     

温稠密物质中不同价态离子分布对X-射线弹性散射光谱计算的影响

在天体物理和惯性约束聚变研究中涉及到的温稠密物质通常包含多种元素的混合,并且每种元素还被电离成多种离子价态,不同价态离子结构及其丰度将直接影响温稠密物质的诊断及其物理性质.同时,从电子结构计算出发来研究宏观物理性质时,还需要考虑温度、密度效应对离子结构的影响.本文从不同价态离子的电子结构计算出发,采用考虑了离子间相互作用的Saha方程获得了稠密环境下的离子丰度,并使用超网链(hypernetted-chain)近似对铝、金以及碳-氢混合物的径向分布函数进行了计算,结合离子周围电子的密度分布,最后获得X-射线汤姆逊散射的弹性散射谱.在X-射线散射谱计算中,计算了温稠密物质中同时存在不同离子价态时的电子结构和径向分布函数,发现在相同的等离子体环境下不同价态离子的径向分布函数和电子结构差别较大.这将对依赖于微观统计过程的物理性质,比如散射光谱,将产生较大的影响.     

Solution of the Ornstein-Zernike equation for a softcore Yukawa fluid. II. Numerical results

Numerical calculations are reported for the simplest case of the soft-core Yukawa fluid introduced in an earlier paper. Attention is given to the thermodynamic behavior, the correlation functions, and the interparticle potentials found by inverting the structural information using Percus-Yevick and hypernetted chain integration equation approximations.Supported by ARGC grant No. B7715646R.     

Variants of the optimised random phase approximation: from one direct correlation function to many different radial distribution functions

It is shown that there are an infinite number of radial distribution functions (RDFs), corresponding to only one direct correlation function (DCF) of the optimised random phase approximation (ORPA). This observation in the thermodynamic perturbation theory is in sharp contrast to that of integral equation theories in which they uniquely correspond. By devising a new method we will be able to introduce various perturbation theories of simple liquids all coming from one DCF. Among all, we will only present analytically seven variants of the ORPA in the thermodynamic perturbation theory of liquids. The DCF of hard-core potential for all variants is assumed to be the same as the ORPA. However, interestingly enough the resulted expressions for the Helmholtz free energies and the RDF are obtained very differently. Furthermore, the resulted thermodynamic properties come out somehow the same, whereas the structural functions of some variants are found to behave much better than the standard ORPA.     

Perturbation theory based direct correlation function for fluids with hard core potentials

Using second-order Barker–Henderson perturbation theory we are able to derive an explicit expression for the direct correlation function of fluids with hard core potentials. Using the obtained direct correlation function, one can explicitly calculate all thermodynamic properties of simple fluids with hard core potentials. Comparisons with computer simulation data show good agreement for both thermodynamic properties and the static structure factor of the hard core double Yukawa potential.     

Weighted-density approaches for polymer structure at solid–polymer interfaces

Weighted-density approximations (WDAs), which are based on the weighting function for the second-order direct correlation functions (DCFs) of the uniform polymeric fluids, have been developed to investigate the structural and thermodynamic properties of polymer melts at interfaces. The advantage is the simplicity of calculation of the weighting functions and their accuracies in the applications. They were applied to study the local density distributions and adsorption isotherms of the freely jointed tangent hard-sphere chain, Yukawa chain, and hard-sphere chain mixture in slit pores. The polymer reference interaction model (PRISM) integral equation with the Percus–Yevick (PY) closure has been used to calculate the second-order DCF of the polymeric fluids required as inputs. The mean-field approximation (MFA) has been used to calculate the weighting function for the attractive contribution of a freely jointed tangent Yukawa chain fluid, having attraction among the beads. The calculated results show that (i) for the freely jointed tangent hard-sphere chain, the present theory is in excellent agreement with the computer simulations over a wide range of chain lengths and bulk densities, (ii) the WDA approach for the attraction provides an accurate method for the local density distributions of a freely jointed tangent Yukawa chain fluid, and that (iii) the present theory also yields a reasonably good result for the structural properties of the freely jointed hard-sphere chain mixtures composed of the chain and monomer.     

Thermodynamic properties of two-dimensional Yukawa systems

The simple analytical approximation for the energy densities in two-dimensional Yukawa systems is proposed for the wide range of parameters of non-ideal fluids. The use of this approach allows determining all thermodynamic functions and characteristics on the base of general thermodynamic relationships. The comparisons of obtained results with the numerical study of thermodynamic properties are presented. Simulations were performed for parameters typical for the laboratory dusty plasma experiments.     

Paired-phonon analysis of impurities in bose fluids

Summary The paired-phonon analysis for boson mixtures is employed in conjunction with the hypernetted-chain approximation to study the ground-state properties of an impurity embedded in liquid⁴He. Chemical potentials, volume coefficients and other thermodynamic quantities as well as some of the most interesting optimal correlation functions are calculated for various impurities interacting with the⁴He background atoms via Lennard-Jones potentials of differing strength. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Influence of size of solvent molecules on structural and thermodynamic properties of the electrode/electrolyte interface

The influence of size of solvent molecules on the structural and thermodynamic properties of the interface between the electrode and electrolyte, using the solvent primitive model, was studied by grand canonical Monte Carlo (GCMC) simulations. The computer simulation results are compared with those obtained from the modified Poisson–Boltzmann (MPB) theory. The ionic singlet distribution functions show that the solvent molecules of low diameter favour the counter ion adsorption on the electrode. With increasing diameter of the solvent molecules, the mean electrostatic potential increases, while the integral and differential capacitances decrease. The integral capacitance curves obtained by MPB theory are in qualitative agreement with those obtained by the GCMC simulation although the theoretical results are overestimated.     

Integral equation approximations for fluids of hard spheres with linear quadrupoles

In this paper we solve numerically several integral equation theories for the dense quadrupolar hard-sphere fluid. Closure approximations obtained by expanding the hypernetted-chain equation are shown to give pair-correlation functions and internal energies in good agreement with Monte Carlo calculations. The mean spherical approximation, however, is found to be extremely poor.     

The relationship between kinetic and thermodynamic fragilities in metallic glass-forming liquids

The correlation between the temperature dependence of the kinetic and thermodynamic properties of a series of metallic glass-forming liquids is investigated using the concept of fragility. The results indicate a correlation between the kinetic fragility and thermodynamic fragility in these liquids. The correlation depends critically on the approach used to evaluate the thermodynamic fragility. Two distinct correlation lines are found for the metal–metalloid and for the all-metallic-constituents glass-forming liquids. For the same thermodynamic fragility the metal–metalloid liquids exhibit a distinctively larger kinetic fragility than the pure-metallic liquids. From the evaluation of the Gibbs free-energy difference between the undercooled liquid and the crystalline phase mixture, a correlation between the kinetic fragility and the driving force for nucleation is found, showing that for glass formation in metallic alloys the thermodynamic and kinetic contributions act together.     

Linear-response theory for partly quenched systems

Summary The matrix of linear density response functions is constructed within density functional theory for a monatomic fluid adsorbed in a quenched material. The structural Ornstein-Zernike relations obtained by Given and Stell with the replica method are regained in the appropriate limit. The usefulness of the present reformulation of their theory is illustrated by deriving from it the free-energy functional and the structural closure relations in the hypernetted-chain approximation. The extension to dynamical properties of partly quenched systems is indicated.     

An integral equation theory for the dense dipolar hard-sphere fluid

An integral equation theory based upon a simple linearization of the hypernetted-chain closure approximation is solved numerically for dipolar hard spheres. The pair-correlation function and thermodynamic properties are found to be in excellent agreement with Monte Carlo results. The dielectric constant in this approximation is larger than that predicted by previous theories.     

Wavelet method for solving integral equations of simple liquids

A new algorithm is developed to solve integral equations for simple liquids. The algorithm is based on the discrete wavelet transform of radial distribution functions. The Coifman 2 basis set is employed for the wavelet treatment. Using the algorithm, we have calculated structural and thermodynamic properties of a Lennard–Jones fluid in a wide range of energy and size parameters of the fluid.     

Structure of the square-shoulder fluid

The structural properties of square-shoulder fluids are derived from the use of the rational function approximation method. The computation of both the radial distribution function and the static structure factor involves mostly analytical steps, requiring only the numerical solution of a single transcendental equation. The comparison with available simulation data and with numerical solutions of the Percus–Yevick and hypernetted-chain integral equations shows that the present approximation represents an improvement over the Percus–Yevick theory for this system and a reasonable compromise between accuracy and simplicity.     

Phase diagram of two-dimensional binary Yukawa mixtures

We have used Ramakrishnan–Yussouff (RY) density functional theory (DFT) to explore the topology of the phase diagram of two-component charge stabilised colloidal suspensions confined to a two-dimensional plane. The particles of the system interact via purely repulsive soft core Yukawa potential. Pair correlation functions (PCFs) used as input informations in DFT were calculated by solving both the hypernetted chain (HNC) and Percus–Yevick (PY) integral equation theories. To test the relative performance of the HNC and PY theories in the context of phase transitions, we have also studied the corresponding one-component systems. We found that RY DFT with HNC PCFs does not stabilise solid in both the one- and two-component cases, whereas the PY theory does. By considering the freezing into the substitutionally disordered triangular solid, we found that the temperature-composition phase diagrams of the binary mixture are narrow spindles whose thickness depends on the symmetry of the mixture components and the value of the screening constant of the Yukawa potential. Although the phase diagram obtained by RY DFT with structural inputs calculated by the PY theory is found to be shifted to higher temperature region in the temperature-composition plane, however, it captures qualitatively all the essential features of the phase diagram. Our results are in principle verifiable through computer simulations and experiments.     

Thermodynamic aspects of the glass transition of silicates

The marked increase in second-order thermodynamic properties observed at the glass-transition signals the onset of configurational changes in viscous liquids. Experimental determinations in the glass-transition range will illustrate this point for thermal expansivity and demonstrate that the kinetics of volume, enthalpy and structural relaxation are identical for silicate liquids. Within the framework of the Adam–Gibbs theory, heat capacity and viscosity data may be combined to calculate configurational entropies and gain insights into the potential energy barrier to viscous flow. Finally, the considerable effect of water on the glass transition temperature of geologically relevant silicates is presented.     

液体-液体相变与反常特性

绝大多数物质的液态密度随温度降低而增大,即常见的热胀冷缩现象.但存在一类物质,如水及第四主族的硅、锗等,其液态密度在一定温度范围内随温度的升高而增大,即密度反常现象.此外,该类物质还存在动力学反常(密度越大粒子运动越快)、热力学反常(热力学量的涨落随温度降低而升高)等其他反常特性.这类材料的化学性质千差万别,但却具有相似的物理反常特性.进一步的理论研究发现部分材料具有两种液态,即高密度液态和低密度液态,两者之间存在一级相变.因此,反常特性与液体-液体相变是否有直接关联是一个值得深入研究的课题.本文主要介绍了具有液体-液体相变的一类材料及其反常特性,包括高温高压下氢的液体-液体相变及其超临界现象,镓的反常特性及其与液体-液体相变的关联等.