A perturbation density functional theory for hydrogen bonding cyclic molecules

Using the framework of Wertheim's thermodynamic perturbation theory, a new polyatomic density functional theory is developed to account for the intermolecular association of cyclic molecules in interfacial systems. To test the theory, Monte Carlo simulations in the canonical ensemble were performed for the specific case of an associating triatomic ring with one association site next to a hard wall. The theory and simulation results were found to be in good agreement.     

Dewetting in associating lattice gas model confined by hydrophobic walls

The phase behavior of a two dimensional fluid confined within hydrophobic walls is obtained by Monte Carlo simulations. The fluid is described by the associating lattice gas model which reproduces the density and diffusion anomalous behavior of water.The confined fluid exhibits a liquid-liquid critical temperature which decreases with the decrease of the distance between the confining walls. In contact with the wall a dewetting is observed. The thickness of this interfacial layer is independent of the distance between the two walls. Even for very small distances between the two walls no total depletion is observed and consequently no drying transition is present.     

Surface phase transitions of multiple-site associating fluids

Surface phase transitions of Lennard–Jones (LJ) based two- and four-site associating fluids have been studied for various associating strengths using grand-canonical transition matrix Monte Carlo simulations. Our results suggest that, in the case of a smooth surface, represented by a LJ 9-3-type potential, multiple-site associating fluids display a prewetting transition within a certain temperature range. However, the range of the prewetting transition decreases with increasing associating strength and increasing number of sites on the fluid molecules. With the addition of associating sites on the surface, a quasi-2D vapor–liquid transition may appear, which is observed at a higher surface site density for weaker associating fluids. The prewetting transition at lower associating strength is found to shift towards the quasi-2D vapor–liquid transition with increasing surface site density. However, for highly associating fluids, the prewetting transition is still intact, but shifts slightly towards the lower temperature range. Adsorption isotherms, chemical potentials and density profiles are used to characterize surface phase transitions.     

Pair approximation for polarization interaction: efficient method for Monte Carlo simulations of polarizable fluids

A new method is presented for the Monte Carlo simulations of polarizable models with induced dipole moments. This method updates induced dipole moments on all molecules when a single molecule is moved, without evaluating all pair interactions. Thus, depending on the number of molecules, it is 10–20 times faster than Monte Carlo simulations with full iteration. The efficiency makes it a powerful tool for the study of phase equilibria of polarizable models in grand canonical and Gibbs ensembles.     

Studies of a primitive model of mixtures of nonpolar molecules with water

The paper presents calculations of the properties of binary mixtures of hard spheres and directionally associating hard spheres, a simple model for mixtures of nonpolar molecules with water that was developed by Nezbeda and his coworkers. Extensive results from Monte Carlo simulations in the isobaric, isothermal ensemble are presented for the density, configurational energy and chemical potentials in the mixtures for fluid states over a range of temperatures, pressures and compositions. A species exchange technique is used to compute the chemical potential difference between components in the mixtures. The results obtained are compared with the predictions of first-order thermodynamic perturbation theory (TPT). It is found that this theory provides an accurate picture of the system over most of the conditions considered. Calculations are also made of vapour–liquid coexistence for the model using TPT and calculations of solid–fluid coexistence for the model using TPT and existing results for the free energy of the pure component solids. It is found that the vapour–liquid coexistence for the model is pre-empted by the solid–fluid coexistence, as had previously been found for the pure component directionally associating hard sphere system.     

A new simulation method for the determination of phase equilibria in mixtures in the grand canonical ensemble

A grand canonical Monte Carlo (GCMC) simulation method is presented for the determination of the phase equilibria of mixtures. The coexistence is derived by expanding the pressure into a Taylor series as a function of the temperature and the chemical potentials that are the independent intensive variables of the grand canonical ensemble. The coefficients of the Taylor series can be calculated from ensemble averages and fluctuation formulae that are obtained from GCMC simulations in both phases. The method is able to produce the equilibrium data in a certain domain of the (T, p) plane from two GCMC simulations. The vapour-liquid equilibrium results obtained for a Lennard-Jones mixture agree well with the corresponding Gibbs ensemble Monte Carlo data.     

Monte Carlo simulation of confined fluids of polarizable particles: an efficient iterative treatment of the local field in slab geometry using Ewald summation

We propose a method for treating in Monte Carlo simulations the problem of the induced dipoles for polarizable particle fluids confined in slab geometry and subject to an external field. In order to compute the local field in a reasonable time, a partial update of the induced dipole moments is performed by introducing a cut-off distance, as in bulk systems. This strategy is then combined with a slab adapted 3D-Ewald summation for treating the long-range interactions between the induced dipoles. The method is illustrated by simulations of confined binary mixtures in the canonical and grand canonical ensembles.     

Exchange monte carlo for molecular simulations with monoelectronic hamiltonians

We introduce a general Monte Carlo scheme for achieving atomistic simulations with monoelectronic Hamiltonians including the thermalization of both nuclear and electronic degrees of freedom. The kinetic Monte Carlo algorithm is used to obtain the exact occupation numbers of the electronic levels at canonical equilibrium, and comparison is made with Fermi-Dirac statistics in infinite and finite systems. The effects of a nonzero electronic temperature on the thermodynamic properties of liquid silver and sodium clusters are presented.     

Extension of the effective solid-fluid Steele potential for Mie force fields

Molecular simulation of fluid systems in the presence of surfaces require computationally expensive calculations due to the large number of solid–fluid pair interactions involved. Representing the explicit solid as a continuous wall with an effective potential can significantly reduce the computational time and allows exploring larger temporal and spatial scales. The well-known (10-4-3) Steele potential is one such analytic expression that faithfully represents the effective solid–fluid interactions for homonuclear crystalline solids with hexagonal lattice symmetry. However, this and most of the effective potentials found in the literature have been developed for fluids and solids interacting exclusively through Lennard-Jones potentials. In this work, we extend the Steele model to obtain the effective wall–fluid potentials for Mie force fields. We perform molecular dynamics simulations of coarse-grained fluids modelled via the SAFT force field approach in the presence of explicit and implicit surfaces to compare structural and dynamic properties in both representations. Also, we study the adsorption of ethane into slit-like pores with explicit and implicit surfaces via grand canonical Monte Carlo simulations. We explore the validity and the improvement in the simulation performance as well as the limitations of the proposed expression.     

Classical multicomponent fluid structure near solid substrates: Born-Green-Yvon equation versus density-functional theory

We report a study of adsorption of binary mixtures of hard spheres of different sizes on a hard wall by using a version of density-functional theory, the Born-Green-Yvon (BGY) equation and Monte Carlo simulations. Following the BGY approach introduced by Fischer and Methfessel for single-component fluids, the proposed extension uses coarse-grained densities to approximate the contact values of pair distribution function of hard spheres. A procedure for evaluation of the coarse-grained densities, leading to an exact theory in one dimension, is proposed. The density-functional theory employed here, however, uses the Meister-Kroll and Groot approach. Comparisons of theoretical calculations with Monte Carlo simulations, as well as with previous theoretical predictions, have shown that density-functional theory reproduces the pseudo-experimental data accurately, even for extremely large size ratios of molecules of both species. The accuracy of the predictions of the BGY approach is less satisfactory, and for higher bulk fluid densities discrepancies with numerical simulations have been found.     

The correlations in a star molecule fluid. Integral equation theory and Monte Carlo study

The structure of a starlike molecule (SLM) fluid with four arms of different length is studied by applying the associative Percus–Yevick integral equation (IE) theory and canonical Monte Carlo (MC) simulations. In the IE study the SLM fluid is modelled by a fluid of hard spheres with four associative sites on each sphere while the MC has been performed for a freely-joined tangent hard sphere fluid. The total radial distribution functions have been calculated in both approaches for different volume fraction regimes and different arm lengths. It is shown that the associative IE theory predicts the structure of SLM fluid best for relatively long arms and at high densities. Additionally, the dependence of the SLM centre–centre correlations on the functionality and fluid particle density has been analysed using the MC results.     

Molecular simulation study of triangle-well fluids confined in slit pores

Grand canonical Monte Carlo simulations are used to study the behaviour of triangle-well (TW) fluids with variable well widths confined inside slit pores. The effect of individual factors influencing the properties of confined fluids such as fluid–fluid interactions, pore size and pore wall–fluid interactions are obtained using simulations as it is difficult to experimentally determine the same. An interesting observation of this study is that inside the narrow pore of slit height h* = 5 at the high-pressure condition of P* = 0.8, for the TW fluid with long-range attraction or for the fluid at a low temperature for even a short-range attraction, the density profiles show layering such that there is a sticking tendency of the particles at centre, while there is a depletion of particles near the wall (as the layers at the centre have higher density peak heights than near the walls).     

Nonlinear dielectric effect of dipolar fluid mixtures

The linear and nonlinear dielectric effect for two- and three-component dipolar fluid mixtures are studied within the framework of the mean spherical approximation (MSA) of dipolar hard sphere mixtures. In our approach, equally sized dipolar hard spheres with different dipole moments are considered. Based on earlier results for the electric field dependence of the polarization our analytical equations show the so-called normal saturation effects, which are in good agreement with corresponding canonical ensemble Monte Carlo simulation data. Comparisons between the MSA based theoretical results and the corresponding Langevin and Debye-Weiss theories are also made.     

Equation of state of long chain molecules and rings

An equation of state for long chain molecules has been proposed using statistical associating fluid theory (SAFT). The formalism derived here is based on the assumption that the chain is formed by the pairs of trimers. The equations of state for 48-mers and 192-mers are formulated and compared with Monte Carlo results. The theory has been developed to treat hard sphere molecules with two attraction sites to form a ring molecule. The equations of state for trimer, hexamer and 12-mer ring molecules have been formulated. There is excellent agreement with available Monte Carlo results. Second virial coefficients of tangent chain molecules and ring molecules have been determined numerically and compared with simulation results.     

Monte Carlo simulation of quantum statistical lattice models

In this article we review recent developments in computational methods for quantum statistical lattice problems. We begin by giving the necessary mathematical basis, the generalized Trotter formula, and discuss the computational tools, exact summations and Monte Carlo simulation, that will be used to examine explicit examples. To illustrate the general strategy, the method is applied to an analytically solvable, non-trivial, model: the one-dimensional Ising model in a transverse field. Next it is shown how to generalized Trotter formula most naturally leads to different path-integral representations of the partition function by considering one-dimensional fermion lattice models. We show how to analyze the different representations and discuss Monte Carlo simulation results for one-dimensional fermions. Then Monte Carlo work on one- and two-dimensional spin-$\text{1}\text{2}$ models based upon the Trotter formula approach is reviewed and the more dedicated Handscomb Monte Carlo method is discussed. We consider electron-phonon models and discuss Monte Carlo simulation data on the Molecular Crystal Model in one, two and three dimensions and related one-dimensional polaron models. Exact numerical results are presented for free fermions and free bosons in the canonical ensemble. We address the main problem of Monte Carlo simulations of fermions in more than one dimension: the cancellation of large contributions. Free bosons on a lattice are compared with bosons in a box and the effects of finite size on Bose-Einstein condensation are discussed.     

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.     

Configurational entropy of adsorbed rigid rods: Theory and Monte Carlo simulations

The configurational entropy of straight rigid rods of length k (k-mers) adsorbed on square, honeycomb, and triangular lattices is studied by combining theory and Monte Carlo (MC) simulations in grand canonical and canonical ensembles. Three theoretical models to treat k-mer adsorption on two-dimensional lattices have been discussed: (i) the Flory-Huggins approximation and its modification to address linear adsorbates; (ii) the well-known Guggenheim-DiMarzio approximation; and (iii) a simple semi-empirical model obtained by combining exact one-dimensional calculations, its extension to higher dimensions and Guggenheim-DiMarzio approach. On the other hand, grand canonical and canonical MC calculations of the configurational entropy were obtained by using a thermodynamic integration technique. In the second case, the method relies upon the definition of an artificial Hamiltonian associated with the system of interest for which the entropy of a reference state can be exactly known. Thermodynamic integration is then applied to calculate the entropy in a given state of the system of interest. Comparisons between MC simulations and theoretical results were used to test the accuracy and reliability of the models studied.     

A dynamical mean field theory for the study of surface diffusion constants

We present a combined analytical and numerical approach based on the Mori projection operator formalism and Monte Carlo simulations to study surface diffusion within the lattice-gas model. In the present theory, the average jump rate and the susceptibility factor appearing are evaluated through Monte Carlo simulations, while the memory functions are approximated by the known results for a Langmuir gas model. This leads to a dynamical mean field theory (DMF) for collective diffusion, while approximate correlation effects beyond DMF are included for tracer diffusion. We apply our formalism to three very different strongly interacting systems and compare the results of the new approach with those of usual Monte Carlo simulations. We find that the combined approach works very well for collective diffusion, whereas for tracer diffusion the influence of interactions on the memory effects is more prominent.     

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