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.     

Structural and thermodynamic properties of inhomogeneous fluids in rectangular corrugated nano-pores

Based on the free-energy average method, an area-weighted effective potential is derived for rectangular corrugated nano-pore. With the obtained potential, classical density functional theory is employed to investigate the structural and thermodynamic properties of confined Lennard-Jones fluid in rectangular corrugated slit pores. Firstly, influence of pore geometry on the adsorptive potential is calculated and analyzed. Further, thermodynamic properties including excess adsorption, solvation force, surface free energy and thermodynamic response functions are systematically investigated. It is found that pore geometry can largely modulate the structure of the confined fluids, which in turn influences other thermodynamic properties. In addition, the results show that different geometric elements have different influences on the confined fluids. The work provides an effective route to investigate the effect of roughness on confined fluids. It is expected to shed light on further understanding about interfacial phenomena near rough walls, and then provide useful clues for the design and characterization of novel materials.     

Density Functional Approach Based on Numerically Obtained Bridge Functional

The Ornstein Zernike equation is solved with the Rogers Young approximation for bulk hard sphere fluidand Lennard-Jones fluid for several state points. Then the resulted bulk fluid radial distribution function combinedwith the test particle method is employed to determine numerically the function relationship of bridge functional as afunction of indirect correlation function. It is found that all of the calculated points from different phase space statepoints for a same type of fluid collapse onto a same smooth curve. Then the numerically obtained curve is used tosubstitute the analytic expression of the bridge functional as a function of indirect correlation function required in themethodology [J. Chem. Phys. 112 (2000) 8079] to deterrnine the density distribution of non-uniform hard spherefluid and Lennard Jones fluid. The good agreement of theoretical predictions with the computer simulation data isobtained. The present numerical procedure incorporates the knowledge of bulk fluid radial distribution function intothe constructing of the density functional approximation and makes the original methodology more accurate and moreflexible for various interaction potential fluid.     

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.     

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.     

The thermodynamic properties of normal liquid helium 3

The thermodynamic properties of normal liquid helium 3 are calculated by using the lowest order constrained variational (LOCV) method. The Landau Fermi liquid model and Fermi-Dirac distribution function are considered as our statistical model for the uncorrelated quantum fluid picture and the Lennard-Jones and Aziz potentials are used in our truncated cluster expansion (LOCV) to calculate the correlated energy. The single particle energy is treated variationally through an effective mass. The free energy, pressure, entropy, chemical potential and liquid phase diagram as well as the helium 3 specific heat are evaluated, discussed and compared with the corresponding available experimental data. It is found that the critical temperature for the existence of the pure gas phase is about 4.90 K (4.45 K), which is higher than the experimental prediction of 3.3 K, and the helium 3 flashing temperature is around 0.61 K (0.50 K) for the Lennard-Jones (Aziz) potential.     

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.     

LJ模型的热力学特性、相平衡及用于真实分子的研究

结合描述硬球固体Helmholtz自由能的自由体积方法与描述硬球固体径向分布函数的拟合的分析表达式与一阶热力学摄动理论,用于描述Lennard Jones(LJ)固体的Helmholtz自由能.按照一个修正的WCA方法将LJ势分为短程排斥部分与长程吸引部分,将文献中一个用于求取液相的等价的硬球直径的简单的迭代法扩展到固相,用于求取固相的等价的硬球直径.在固体Helmholtz自由能的计算中,使用200壳层,以便获得精确的结果.体相LJ液体的热力学特性由一个最近提出的状态方程求取.该方法很好地描述了LJ固体的过量Helmholtz自由能与状态方程,满意地描述了Lennard Jones模型的相平衡;通过选取合适的LJ势参数,能很好地描述了真实分子的融化曲线.     

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.     

NpT-ensemble Monte Carlo calculations for binary liquid mixtures

A Monte Carlo method for the calculation of thermodynamic properties in the isothermal-isobaric ensemble is described. Application is made to the calculation of excess thermodynamic properties (enthalpy, volume and Gibbs free energy) of binary mixtures of Lennard-Jones 12-6 liquids. Comparison is made with the predictions of a number of theories of liquid mixtures; the so-called van der Waals one-fluid model and the variational theory of Mansoori and Leland are both found to give excellent results. The accuracy attainable in estimates of the excess properties is discussed in terms of statistical fluctuations in various calculated quantities and the advantages and disadvantages of the method are examined in relation to calculations by the more familiar constant-volume method.     

A core-softened fluid model in disordered porous media. Grand canonical Monte Carlo simulation and integral equations

We have studied the microscopic structure and thermodynamic properties of a core-softened fluid model in disordered matrices of Lennard-Jones particles by using grand canonical Monte Carlo simulation. The dependence of density on the applied chemical potential (adsorption isotherms), pair distribution functions, as well as the heat capacity in different matrices are discussed. The microscopic structure of the model in matrices changes with density similar to the bulk model. Thus one should expect that the structural anomaly persists at least in dilute matrices. The region of densities for the heat capacity anomaly shrinks with increasing matrix density. This behavior is also observed for the diffusion coefficient on density from independent molecular dynamics simulation. Theoretical results for the model have been obtained by using replica Ornstein-Zernike integral equations with hypernetted chain closure. Predictions of the theory generally are in good agreement with simulation data, except for the heat capacity on fluid density. However, possible anomalies of thermodynamic properties for the model in disordered matrices are not captured adequately by the present theory. It seems necessary to develop and apply more elaborated, thermodynamically self-consistent closures to capture these features.     

Thermodynamic properties of a hard-core Lennard-Jones fluid from computer simulation and the coupling parameter series expansion

ABSTRACT

The thermodynamic properties of a fluid with an interaction potential consisting in a hard-sphere core plus a Lennard-Jones tail have been obtained by Monte Carlo (MC) NVT simulation as a function of the density along several isotherms. In addition, the liquid–vapour coexistence has been determined by means of histogram-reweighting MC. These data have been used to analyse the performance of perturbation theory. To this end, the first three perturbation terms of the inverse temperature expansion of the Helmholtz free energy have been obtained by means of MC NVT simulations to test the convergence of the perturbation series and to compare with the predictions of the coupling parameter series expansion. Then, the predictions of the latter theory for the thermodynamic properties have been compared with the simulations, revealing the overall excellent performance of this perturbation theory for this model fluid, except in the vicinity of the critical point.     

Interfacial and co-existence properties of the Lennard-Jones system at the triple point

A molecular dynamics simulation of the three phases of the Lennard-Jones system in co-existence is reported. The triple-point properties are compared with bulk-phase Monte-Carlo results, with experimental data on argon, and with the results of a preliminary simulation of this system.

Thermodynamic properties of the crystal-liquid and liquid-vapour interfaces are reported and difficulties in calculating interfacial excess properties are discussed. The crystal-liquid and liquid-vapour interfacial tensions are in accord with previous predictions.

It is suggested that the direct simulation of co-existing phases is a potentially practical route to the phase diagram if the thermodynamic equations of state of the individual phases are known.     

扩展桥密度泛函近似于非匀一非硬球流体

为了将非匀一硬球流体的桥密度泛函近似扩展到非匀一非硬球流体,提出了一个理论方案．所得的LJ流体的密度泛函近似计算简单,精确．特别是密度泛函近似仅仅需要共存体相流体的二阶直接相关函数作为输入,因而可以应用于超临界与亚临界温度．所提出的理论方案可以认为是热力学理论的非匀一对应物．     

Excess properties of Lennard-Jones binary mixtures from computer simulation and theory

Monte Carlo simulation and theory are used to calculate the excess thermodynamic properties of binary mixtures of spherical Lennard-Jones molecules. We study the excess functions of three binary mixtures characterized by the following size and dispersive energy ratios: (1) (σ₂₂/σ₁₁)³ = 2 and ?₂₂/?₁₁ = 2; (2) (σ₂₂/σ₁₁)³ = 1 and ?₂₂/?₁₁ = 1/2 and (3) (σ₂₂/σ₁₁)³ = 1/2 and ?₂₂/?₁₁ = 2. In all cases, the unlike size parameter, σ₁₂, is kept constant and equal to the value given by the Lorentz combining rule (σ₁₂ = (σ₁₁ + σ₂₂)/2). However, different unlike dispersive energy parameter values are considered through the following combining rules: (a) ?₁₂ = (?₁₁?₂₂)^1/2 (Berthelot rule); (b) ?₁₂ = ?₁₁ (association); and (c) ?₁₂ = ?₂₂ (solvation). The pressure and temperature dependence of the excess volume and excess enthalpy is studied using the NpT Monte Carlo simulation technique for all the systems considered. Additionally, the simplest conformal solution theory is used to check the adequacy of this approach in predicting the excess properties in a wide range of thermodynamic conditions and variety of binary mixtures. In particular, we have applied the van der Waals one-fluid theory to describe Lennard-Jones binary mixtures through the use of the Johnson et al. [1993, Molec. Phys., 78, 591] Helmholtz free energy. Agreement between simulation results and theoretical predictions is excellent in all cases and thermodynamic conditions considered. This work confirms the applicability of the van der Waals one-fluid theory in predicting excess thermodynamic properties of mixtures of spherical molecules. Furthermore, since binary mixtures of spherical Lennard-Jones molecules constitute the reference fluid to be used in perturbation theories for complex fluids, such as the statistical association fluid theory (SAFT), this work shows clearly the applicability of the conformal solution theory within the framework of SAFT for predicting excess functions.     

Effect of the attractive forces on the density change melting of 2D LJ fluids

The Weeks-Chandler-Andersen perturbation theory of fluids can be considered as a modern version of van der Waals'. Whereas in the old van der Waals theory the effect of the attractive forces on the thermodynamic properties is introduced through a constant, a, in Weeks-Chandler-Andersen theory this constant is replaced by a function of temperature and density α(β, ϱ). This function has been determined by means of Molecular Dynamics simulation of a two-dimensional Lennard-Jones fluid, and here is used to analyse the effect of attractive forces on the density change in melting. The influence is found to be slightly greater than the predictions of van der Waals theory.     

Equation of state for the Lennard-Jones truncated and shifted fluid with a cut-off radius of 2.5 σ based on perturbation theory and its applications to interfacial thermodynamics

ABSTRACT

An equation of state is presented for describing thermodynamic properties of the Lennard-Jones truncated and shifted (LJTS) potential with a cut-off radius of 2.5 σ. It is developed using perturbation theory with a hard-sphere reference term and labelled with the acronym PeTS (perturbed truncated and shifted). The PeTS equation of state describes the properties of the bulk liquid and vapour and the corresponding equilibrium of the LJTS fluid well. Furthermore, it is developed so that it can be used safely in the entire metastable and unstable region, which is an advantage compared to existing LJTS equations of state. This makes the PeTS equation of state an interesting candidate for studies of interfacial properties. The PeTS equation of state is applied here in two theories of interfaces, namely density gradient theory (DGT) and density functional theory (DFT). The influence parameter of DGT as well as the interaction averaging diameter of DFT are fitted to data of the surface tension of the LJTS fluid obtained from molecular simulation. The results from both theories agree very well with those from the molecular simulations.