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.     

Effects of electrostatic interactions and geometrical confinements on depletion interactions in charged colloidal system

In a charged colloidal system, the influence on depletion interaction between two like-charged macro-ions is studied through Monte Carlo simulation in this paper. The numerical results show that this depletion force is affected by both the electrostatic interactions between charged spheres and charged plates and by the geometrical factor of the two charged plates, and they further indicate that the influence of geometrical confinement on the depletion interaction is larger than that of electrostatic potential.     

Depletion interactions in cylindric pipeline

In a colloidal system confined by a small cylindric pipeline, the depletion interaction between two large spheres is different to the system confined by two plates, and the influence on depletion interaction from the pipeline is related to both the size and shape of it. In this paper, the depletion interactions in the systems confined by pipelines of different sizes or different shapes are studied by Monte Carlo simulations. The numerical results show that the influence on depletion force from the cylindric pipeline is stronger than that from two parallel plates, and the depletion force will be strengthened when the diameter of the cylinder is decreased. In addition, we also find that the depletion interaction is rather affected if the shape change of the pipeline is slightly changed, and the influence on depletion force from the shape change is stronger than that from the size change.     

Casimir and Surface Tension Forces on a Single Interacting Bose–Einstein Condensate in Canonical Ensemble

The forces on a single Bose–Einstein condensate confined between two parallel plates consist of two components, namely, surface tension force and Casimir force. In canonical ensemble, these forces are quite different from the one in grand canonical ensemble. In small region with distance $$\ell $$ between two parallel plates, using double parabola approximation, we find that surface tension force decreases as $${{\ell }^{{ - 3}}}$$, whereas the Casimir force, in one-loop approximation of the quantum field, is proportional to $${{\ell }^{{ - 13/2}}}$$. The total force is also considered and its veer is found.     

带电胶体系统中的排空作用

用Monte Carlo模拟研究弱带电胶体系统的性质.在四维超球面欧氏空间中严格表示库仑作用的基础上，通过接受率法计算带电胶球间的排空势和排空力.研究了受限于两块平行带电平板之间、淹没于带电小胶球之中的一个或两个带电大胶球系统的排空作用，并通过与不带电的硬球系统相应结果的分析、对比，发现静电势能增强带电胶球之间的排空作用. 关键词： 超球面法 接受率方法 排空作用 Monte Carlo模拟     

Disorder-induced stabilization of the pseudogap in strongly correlated systems

The interplay of strong interaction and strong disorder, as contained in the Anderson-Hubbard model, is addressed using two nonperturbative numerical methods: the Lanczos algorithm in the grand canonical ensemble at zero temperature and quantum Monte Carlo simulations. We find distinctive evidence for a zero-energy anomaly which is robust upon variation of doping, disorder, and interaction strength. Its similarities to, and differences from, pseudogap formation in other contexts, including perturbative treatments of interactions and disorder, classical theories of localized charges, and in the clean Hubbard model, are discussed.     

Simulation of phase equilibria and interfacial properties of binary mixtures on the liquid-vapour interface using lattice sums

Molecular dynamics simulations of Lennard-Jones binary mixtures were performed to obtain phase equilibria and thermodynamic properties for the liquid—vapour interface. The dispersion interactions were handled using the lattice sum method where the full interaction is obtained and there is no requirement for any long range correction to the properties. The application of the method using the Lorentz—Berthelot combining rule for unlike interactions is discussed. The coexisting densities, adsorption of molecules at the interface and surface tension are the main results of this work. Coexisting properties were compared with Gibbs ensemble Monte Carlo results and with those of the grand canonical Monte Carlo method combined with the histogram reweighting technique, and good agreement was found. The lattice sum method results were compared with those of the spherically truncated and shifted potential to analyse the truncation effect. The adsorption of molecules at the interface and surface tension increase with interaction.     

The grand canonical ensemble Monte Carlo method applied to electrolyte solutions

A grand canonical ensemble Monte Carlo method is developed for application to electrolyte solutions.

The method proves to be of comparable accuracy and speed to the conventional NVT Monte Carlo method for electrolytes but has the added advantage of being able to fix the chemical potential. This latter point is vital for the study of surface phenomena. Application of the method to 1:1 and 2:2 primitive model electrolytes is made as is a comparison with the results of approximate statistical mechanical treatments.     

Lennard-Jones fluids confined in nanoscopic slits: Evidence for reentrant filling transitions

By using grand canonical and canonical ensemble Monte Carlo simulations, the structure and phase behavior of a Lennard-Jones (LJ) fluid confined between the parallel (100) planes of a face-centered cubic crystal are studied. Slit pores with a width which allows three adsorbate layers to form are used. It is shown that the filled pore consists of three commensurate layers over a wide range of the surface potential strength, while the pore-filling mechanism and the topology of the phase diagram change when the strength of this fluid-wall potential is varied. Condensation may occur in one step or via two layering-like transitions. The structure of monolayer films depends on the strength and corrugation of the surface potential, and the condensation of the middle layer may induce a reentrant first-order transition.Received: 16 January 2004, Published online: 23 March 2004PACS: 64.70.Nd Structural transitions in nanoscale materials - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 68.35.Rh Phase transitions and critical phenomena     

Nucleation on a sphere: the roles of curvature,confinement and ensemble

ABSTRACT

By combining Monte Carlo simulations and analytical models, we demonstrate and explain how the gas-to-liquid phase transition of colloidal systems confined to a spherical surface depends on the curvature and size of the surface, and on the choice of thermodynamic ensemble. We find that the geometry of the surface affects the shape of the free energy profile and the size of the critical nucleus by altering the perimeter–area ratio of isotropic clusters. Confinement to a smaller spherical surface results in both a lower nucleation barrier and a smaller critical nucleus size. Furthermore, the liquid domain does not grow indefinitely on a sphere. Saturation of the liquid density in the grand canonical ensemble and the depletion of the gas phase in the canonical ensemble lead to a minimum in the free energy profile, with a sharp increase in free energy for additional growth beyond this minimum.     

Structural properties of effective potential model by liquid state theories

This paper investigates the structural properties of a model fluid dictated by an effective inter-particle oscillatory potential by grand canonical ensemble Monte Carlo (GCEMC) simulation and classical liquid state theories.The chosen oscillatory potential incorporates basic interaction terms used in modeling of various complex fluids which is composed of mesoscopic particles dispersed in a solvent bath,the studied structural properties include radial distribution function in bulk and inhomogeneous density distribution profile due to influence of several external fields.The GCEMC results are employed to test the validity of two recently proposed theoretical approaches in the field of atomic fluids.One is an Ornstein-Zernike integral equation theory approach;the other is a third order + second order perturbation density functional theory.Satisfactory agreement between the GCEMC simulation and the pure theories fully indicates the ready adaptability of the atomic fluid theories to effective model potentials in complex fluids,and classifies the proposed theoretical approaches as convenient tools for the investigation of complex fluids under the single component macro-fluid approximation.     

A Monte Carlo Study of Influences on Depletion Force from Another Large Sphere in Colloidal Suspensions

According to the acceptance ratio method, the influences on the depletion interactions between a large sphere and a plate from another closely placed large sphere are studied by Monte Carlo simulation. The numerical results show that both the depletion potential and depletion force are affected by the presence of the closely placed large sphere; the closer the large sphere are placed to them, the larger the influence will be. Furthermore, the influences on the depletion interactions from another large sphere are more sensitive to the angle than to the distance.     

相互作用势对模拟计算单壁碳纳米管物理吸附储氢的影响

采用巨正则Monte Carlo方法模拟氢分子在单壁碳纳米管中的储存与分布,重点研究了Lennard-Jones势、Crowell-Brown势和Silvera- Goldman势对模拟计算单壁碳纳米管物理吸附储氢的影响.计算结果显示,碳纳米管与氢分子间的相互作用宜采用Lennard-Jones势描述;氢分子与氢分子间相互作用的描述则与碳纳米管的管径有关,管径较小时选Lennard-Jones势较佳,管径偏大时取七参数Silvera-Goldman 势更为合理,而三参数Silvera-Goldman势则不宜采用;并给出了相应的理论解释.     

微孔对单壁纳米碳管储氢性能的影响

用巨正则蒙特卡罗分子模拟方法研究了单壁纳米碳管中的微孔即单壁纳米碳管基本孔-内管腔和管间孔对单壁纳米碳管储氢性能的影响.与低温下氮气吸附实验结果的比较发现单壁纳米碳管的内管腔是吸附的主要位置.分析单壁纳米碳管内管腔中吸附势的叠加和利用效率，发现管径为2nm左右时单壁纳米碳管内管腔的储氢容量最高.当单壁纳米碳管阵列的管间距增加时，单壁纳米碳管的管间孔也会成为有效的氢吸附位. 关键词： Monte Carlo方法 单壁纳米碳管 储氢 微孔     

Adsorption thermodynamics of a lattice-gas model with non-additive lateral interactions on triangular and honeycomb lattices

Adsorption thermodynamics of a lattice-gas model with non-additive interactions between adsorbed particles for triangular and honeycomb lattices is discussed in the present study. The model used here assumes that the energy which links a certain atom with any of its nearest-neighbors strongly depends on the state of occupancy in the first coordination sphere of that adatom. By means of Monte Carlo simulations in the grand canonical ensemble the adsorption isotherms and isothermal susceptibility (or equivalently the mean square density fluctuations of adparticles) were calculated and their striking behavior was analyzed and discussed in terms of the low temperature phases formed in the system.     

H2的自由扩散和吸附状态的对比研究

运用巨正则Monte Carlo方法, 模拟了H₂在自由扩散状态下及碳纳米管吸附状态下的分布, 对H₂的自由扩散和吸附状态进行了对比研究. 研究表明: 77 K和2 MPa下, (30, 30)扶手椅型碳纳米管质量储氢密度为3.74%, 77 K和10 MPa下, 质量储氢密度为7.4%. 吸附状态的H₂分子主要汇聚在碳纳米管内外两个壁面. 关键词： 储氢 碳纳米管 巨正则Monte Carlo     

An efficientmethod to determine chemical potential of mixtures in the isothermal and isobaric bulk phase with kineticMonte Carlo simulation

A kinetic Monte Carlo (kMC) scheme in the NPT ensemble (constant number of molecules, pressure and temperature) has been developed to determine accurate chemical potentials for all components in a homogeneous mixture. The simulation requires two moves: (1) a displacement move and (2) a volume change move. In the former, the mobility rate of a selected molecule is determined by its interaction with all the other molecules in the system and is moved to a random position within the simulation box, according to the Rosenbluth algorithm, without any rejections (entropic sampling). The volume change move is decided by a comparison between either the instant pressure or the partial average pressure (with long-range correction) and the specified pressure and is carried out much less frequently than the displacement move. We applied this NPT scheme to a number of mixtures in both the gaseous and liquid phases, and show that the derived chemical potentials are accurate and reproducible. The method is recommended for obtaining chemical potentials in mixtures that are required as input in a grand canonical ensemble simulation.     

Adsorption thermodynamics of a lattice–gas model with non-additive lateral interactions

In the present paper, we study the adsorption thermodynamics of a lattice–gas model with non-additive interactions between adsorbed particles. We have assumed that the energy which links a certain atom with any of its nearest neighbors strongly depends on the state of occupancy in the first coordination sphere of that adatom. By means of Monte Carlo simulations in the grand canonical ensemble the adsorption isotherms, isothermal susceptibility (or equivalently the mean square density fluctuations of adparticles), and isosteric heat of adsorption were calculated and their striking behavior was analyzed and discussed in terms of the low temperature phases formed in the system.     

Adsorption of water—methanol mixtures in carbon and aluminosilicate pores: a molecular simulation study

A theoretical study is reported of the adsorption behaviour of water—methanol mixtures in slit carbon and in uncharged alumino-silicate micropores. The adsorption isotherms are obtained for a pore of width of 2 nm and at a temperature of 298 K from grand canonical ensemble Monte Carlo simulations. The results show that the graphite and uncharged silicate surfaces are covered by a dense layer of flatly adsorbed water and methanol molecules having weaker hydrogen bonding. In the interior of the pore, the fluid exhibits bulk-like behaviour with a stronger hydrogen bonded structure. Solvation forces are also calculated as a function of pore size. The positive values found for the solvation force for all pore sizes reflect the hydrophobic interactions of the mixture with the carbon and uncharged alumino-silicate walls.     

The adsorption of a hard sphere fluid in a slit-like pore filled with a disordered matrix of hard spheres: attractive wall-hard sphere interaction

The adsorption of a hard sphere fluid in a slit-like pore filled with a disordered hard sphere matrix is studied using the inhomogeneous Ornstein-Zernike equation with hypernetted chain closure. In contrast to previous studies, an attractive wall-hard sphere interaction is considered. The adsorption is affected by the attractive interaction both directly by the fluid-wall interaction and indirectly by the change in the structure of the matrix. Density profiles and pair distribution functions are reported. For comparison, grand canonical Monte Carlo simulation data are obtained. The agreement of the theoretical and simulation results is satisfactory but somewhat less pleasing than for the purely repulsive case.