Far-infra-red absorption of non-polar liquids

A new conformal solution theory using a single pure fluid as a reference substance for the calculation of thermodynamic properties of fluid mixtures is developed. The perturbation theory developed by Weeks, Chandler and Andersen (WCA) and by Verlet and Weis (VW) is used to calculate the reference properties. The mean density approximation and corresponding state principle are used to eliminate the higher order terms in the mixture system and to derive the pseudo-parameters for the reference system. The mixture properties are obtained from the reference properties and their corresponding hard sphere excess functions defined as the properties of the mixture less the value of the properties for the hard sphere mixture.

The excess functions of mixing for several liquid mixtures of Lennard-Jones fluids, obeying the Lorentz-Berthelet rule, are calculated by the new method (VW-HSE). Comparison with the results of other theories and Monte Carlo data shows definite improvement. Since only the properties of a pure reference fluid are directly calculated, the method can be applied to more complicated multicomponent systems without additional computational effort as required by other theories.     

Monte Carlo values for the radial distribution function of a system of fluid hard spheres

The perturbation theory recently developed by Weeks, Chandler, and Andersen is applied to the solid phase of a rare gas near its melting line. The potential is separated into two parts: a reference part containing all the repulsive forces and a perturbation part containing all the attractions. We show that the expansion of the free energy in the perturbation potential is, as in the liquid phase, rapidly convergent for a temperature of the order of the triple-point temperature. On the contrary, the representation of the reference system by hard spheres with an appropriate diameter is less accurate than in the liquid phase. This representation requires the knowledge of the radial distribution functions of the hard-sphere solid for which we give a tabulation as well as an analytical representation. The perturbation theory is applied to the determination of the fluid-solid transition.     

Perturbation theory for mixtures of simple liquids

The perturbation approach developed by Weeks, Chandler, and Andersen (WCA) and by Verlet and Weis (VW) for pure systems is here generalized to the case of mixtures. We study binary mixtures of molecules interacting with the 12–6 Lennard-Jones potential, for which Monte Carlo simulations are available for comparison. The work is divided into two parts: The first part presents results of Monte Carlo calculations on mixtures of hard spheres of 864 and 1000 particles. The radial distribution functions generated are used to test the VW representation for the correlation functions of hard-sphere mixtures. This representation is found to work satisfactorily within the expected error limits. The second part deals with the two-step perturbation procedure for calculating the thermodynamic quantities of the Lennard-Jones system. The Lennard-Jones potential is divided into a reference potential, which is strictly repulsive, and an attractive part. The system of the reference potential is represented by a system of hard-sphere mixture with equivalent diameters determined by the WCA rule. Analytical expressions are given for evaluating these equivalent diameters. The Lennard-Jones system is then recovered to the first order by a λ expansion over the reference system. Comparison with Monte Carlo results for a mixture of Lennard-Jones molecules, obeying the Berthelot rule, shows that the total thermodynamic properties are reproduced by the perturbation theory to 1 per cent, while the agreement in excess properties is only moderately successful, similar to some other analytical theories compared here. To reproduce these excess properties, which are extremely small, a precision of 0·1 per cent in the theory is required. The present theory is estimated to be accurate to 1 per cent in view of the successive approximations made.     

A new integral equation for the radial distribution function of a hard sphere fluid

Based on a proposal by Shinomoto, a new integral equation is derived for the radial distribution function of a hard-sphere fluid using mainly geometric arguments. This integral equation is solved by a perturbation expansion in the density of the fluid, and the results obtained are compared with those from molecular dynamics simulations and from the Born-Green-Yvon (BGY) and Percus-Yevick (PY) theories. The present theory provides results for the radial distribution function which are intermediate in accuracy between those obtained from the BGY and from the PY theories.     

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.     

Andersen–Weeks–Chandler Perturbation Theory and One-Component Sticky-Hard-Spheres

We apply second order Andersen–Weeks–Chandler perturbation theory to the one-component sticky-hard-spheres fluid. We compare the results with the mean spherical approximation, the Percus–Yevick approximation, two generalized Percus–Yevick approximations, and the Monte Carlo simulations.     

Thermodynamic perturbation theory for the (12-6-n) fluids

A perturbation method in which attractive forces are taken as perturbation of the repulsive (reference) forces is applied to calculate the thermodynamic properties of (12-6-n) fluids in terms of the properties of hard-sphere fluid. The numerical values of the thermodynamic properties (free energy per particle, compressibility and excess internal energy) for a range of temperature and density are given for (12-6-8) fluids. Further, two perturbation schemes are adopted to evaluate the total radial distribution function using the EXP version of the optimized cluster theory (OCT). The numerical results are reliable as reported at two states (T* = 1·036,ρ* = 0·65 andT* = 0·719ρ* = 0·85) for the (12-6-8) fluid and the Lennard-Jones (12-6) fluid as well.     

Thermodynamic properties of liquid metals,temperature dependent hard-sphere model

An analytic solution of the Percus-Yevick equation for the hard-sphere model of a liquid is used to investigate the thermodynamic properties of liquid metals near the triple point. The temperature dependence of the packing fraction (or hard-sphere diameter) is introduced by the phenomenological method using the compressibility equation. Agreement between theory and experiment is improved for both the thermal pressure coefficient and specific heat.     

Equation of state and liquid–vapour equilibrium in a triangle-well fluid

The second-order thermodynamic perturbation theory formulation of Barker and Henderson is used to derive the equation of state of the triangle-well fluid. This is combined with the rational function approximation to the radial distribution function of the hard-sphere fluid. Results are obtained for the critical parameters and the liquid–vapour coexistence curve for various values of the range of the potential. A comparison with available simulation data is presented.     

Quantum perturbations to the radial distribution function of a hard-sphere fluid

Expressions derived in the previous paper for quantum corrections to the radial distribution function of a fluid are applied to the hard-sphere fluid. It is found that the perturbation theory given in the paper is valid only at very high values of temperatures when applied to calculate the correction to the distribution function of the hard-sphere fluid and is not valid at the temperatures at which Gibson and others have obtained numerical results for a given value of ?a³, where ? is the number density and a the hard-sphere diameter.     

广义Morse流体解析状态方程及对氮的应用

 根据Ross变分微扰理论以及硬球流体Percus-Yevick（PY） 径向分布函数表达式,建立了广义Morse势流体的解析状态方程。与模拟结果的比较一方面证实了广义Morse 势模型的合理性;另一方面表明了解析Ross变分微扰理论的精度相当或略好于非解析的Weeks-Chandler-Anderson （mWCA）理论,而优于复杂的优化超网络链积分方程理论（RHNC）。该解析状态方程被应用于拟合处于环境温度和压强小于1 GPa情形流体氮的实验数据,所得到的势能参数被用于预测高温高密度情形氮流体的压强,预测结果证实,该解析状态方程可以很好地适用于较宽的压强和温度范围。     

Lennard-Jones chain mixtures: radial distribution functions from Monte Carlo simulation

Radial distribution functions are calculated for binary Lennard-Jones chain mixtures from Monte Carlo simulation. Average and end-to-end inter- and intrachain radial distribution functions are calculated, ten for a binary mixture and four for a pure component. The effects of density, concentration, temperature, chain length, Lennard-Jones size and energy parameters are investigated. It is found that intrachain radial distribution functions are largely independent of density except at very high densities, where they start to take on a structure tending towards that of a crystal lattice. In addition, the effect of using different distribution functions to calculate the associating contribution in statistical associating fluid theory (SAFT) is examined. Further, the effect of using short chain fluids rather than the monomer unit as the reference system in the calculation of the pressure and free energy of chain fluids in first-order thermodynamic perturbation theory (TPT) is examined. It is found that the choice of reference radial distribution function has a marked effect on the calculation of thermodynamic properties through the use of SAFT and TPT.     

Second-order Percus-Yevick theory for a confined hard-sphere fluid

A fluid of hard spheres confined between two hard walls and in equilibrium with a bulk hard-sphere fluid is studied using a second-order Percus-Yevick approximation. We refer to this approximation as second-order because the correlations that are calculated depend upon the position of two hard spheres in the confined fluid. However, because the correlation functions depend upon the positions of four particles (two hard spheres and two walls treated as giant hard spheres), this is the most demanding application of the second-order theory that has been attempted. When the two walls are far apart, this calculation reduces to our earlier second-order approximation calculations of the properties of hard spheres near a single hard wall. Our earlier calculations showed this approach to be accurate for the single-wall case. In this work we calculate the density profiles and the pressure of the hard-sphere fluid on the walls. We find, by comparison with grand canonical Monte Carlo results, that the second-order approximation is very accurate, even when the two walls have a small separation. We compare with a singlet approximation (in the sense that correlation functions that depend on the position of only one hard sphere are considered). The singlet approach is fairly satisfactory when the two walls are far apart but becomes unsatisfactory when the two walls have a small separation. We also examine a simple theory of the pressure of the confined hard spheres, based on the usual Percus-Yevick theory of hard-sphere mixtures. Given the simplicity of the latter approach the results of this simple (and explicit) theory are surprisingly good.     

Thermodynamic properties for the triangular-well fluid

The thermodynamic properties of the triangular-well fluid with a well range of up to twice the hard sphere diameter were studied by means of a new developed equation of state and molecular simulation. This EoS is based on the perturbation theory of Barker and Henderson with the first and second-order perturbation terms evaluated by molecular simulation and then a fit with a simple function based on the radial distribution function of the reference fluid. The thermodynamic properties for the triangular-well fluid were also obtained directly by Gibbs ensemble and NPT Monte Carlo simulations. Good agreement is observed between the proposed EoS and the molecular simulation results. A model for the triangular-well solid is also presented; this has been used to calculate the solid–liquid transition line. Very good agreement is obtained with previously report values for this line and for the triple point temperature and pressure.     

Extension of Compressibility-Route Cubic Equations of State and the Radial Distribution Functions at Contact to Multi-Component Hard-Sphere Mixtures

The equation of state(EOS) for hard-sphere fluid derived from compressibility routes of Percus-Yevick theory(PYC) is extended. The two parameters are determined by fitting well-known virial coefficients of pure fluid.The extended cubic EOS can be directly extended to multi-component mixtures, merely demanding the EOS of mixtures also is cubic and combining two physical conditions for the radial distribution functions at contact(RDFC) of mixtures.The calculated virial coefficients of pure fluid and predicted compressibility factors and RDFC for both pure fluid and mixtures are excellent as compared with the simulation data. The values of RDFC for mixtures with extremely large size ratio 10 are far better than the BGHLL expressions in literature.     

Extension of Compressibility-Route Cubic Equations of State and the Radial Distribution Functions at Contact to Multi-Component Hard-Sphere Mixtures

The equation of state (EOS) for hard-sphere fluid derived from compressibility routes of Percus-Yevick theory (PYC) is extended. The two parameters are determined by fitting well-known virial coefficients of pure fluid. The extended cubic EOS can be directly extended to multi-component mixtures, merely demanding the EOS of mixtures also is cubic and combining two physical conditions for the radial distribution functions at contact (RDFC) of mixtures. The calculated virial coefficients of pure fluid and predicted compressibility factors and RDFC for both pure fluid and mixtures are excellent as compared with the simulation data. The values of RDFC for mixtures with extremely large size ratio 10 are far better than the BGHLL expressions in literature.     

Analytic solution of Percus-Yevick equation for fluid of hard spheres

A new method of analytic solution of the Percus-Yevick equation for the radial distribution functiong(r) of hard-sphere fluid is proposed. The original non-linear integral equation is reduced to non-homogeneous linear integral equation of Volterra's type of the second order. The kernel of this new equation has a polynomial form which allows to find analytic expression forg(r) itself without using the Laplace transformation. In addition, the first three moments of the total correlation function can be found.     

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.     

Analysis of the liquid structure of 3d transition metals from the Wills-Harrison model

Calculations of the liquid structure of 3d transition metals from the effective pair interactions of Wills and Harrison are performed by using the optimized random phase approximation in order to point out the influence of thes-electron pseudopotential on the repulsive and attractive forces governing the liquid structure. Our results are compared to those obtained in the Weeks, Chandler Andersen approximation and in the thermodynamic variational method.     

Shear viscosity of a simple fluid over a wide range of strain rates

The shear viscosity of the Weeks—Chandler—Andersen (WCA) fluid at the Lennard-Jones triple point has been calculated over a wide range of strain rates using the transient time correlation function (TTCF) formalism. It has been demonstrated that these calculations can be carried out at arbitrarily low strain rates with the precision of the Green—Kubo calculations. At high strain rates, the calculated data agree within the error bars with more precise data acquired using the computationally less demanding steady state (SS) non-equilibrium molecular dynamics (NEMD) method. The linear variation of viscosity with the square root of the strain rate is discussed.