Effects of polydispersity in quenched-annealed fluids: An integral equation approach

An extension of the replica Ornstein-Zernike (ROZ) equations for partly quenched polydisperse systems is presented. Explicit calculations have been performed for a monodisperse hard sphere fluid confined by a polydisperse hard sphere disordered matrix by using Percus-Yevick and hypernetted chain (HNC) approximations. The chemical potential of adsorbed fluid species has been evaluated. A numerical solution of the ROZ equations makes use of the orthonormal polynomials with the weight function corresponding to the distribution function of the diameters of matrix species. We have also compared the results of theoretical predictions with Monte Carlo simulation in a canonical ensemble. The result of this comparison suggests that the HNC approximation performs slightly better in predicting the structural properties of the system.     

计算平均力势的理论方法

提出了一个用于计算平均力势的普适性的理论框架,方法克服了以前的方法的缺陷,仅仅需要溶剂粒子在单个溶质粒子附近的密度分布作为输入.计算了两个大尺寸溶质粒子浸在小尺寸硬球溶剂浴中的平均力势,理论预言与可能的模拟数据符合.调查了溶剂-溶质相互作用势、溶剂密度、溶质粒子尺寸对过量平均力势的影响.结论是:溶剂粒子在单个溶质粒子附近的减少导致吸引的过量平均力势,而溶剂粒子在单个溶质粒子附近的聚集导致排斥的过量平均力势,高溶剂密度与大溶质粒子尺寸能强化这种趋势.讨论了这种空耗吸引-聚集排斥与生物学中的疏水吸引-水化排斥的联系.     

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.     

Chemical potential of electrolytes adsorbed in porous media with charged obstacles: application of the continuum replica methodology

A theoretical study is reported of a quenched-annealed system where both components were modelled as size symmetric +1: ?1 primitive model electrolytes. The partly quenched system was studied by using the replica Ornstein-Zernike (ROZ) integral equation theory in the hypernetted chain (HNC) approximation and grand canonical Monte Carlo (GCMC) simulations. The primary interest was the excess Gibbs free energy (logarithm of the mean activity coefficient) of the adsorbed electrolyte and an expression for this quantity, valid within the ROZ/HNC formalism, was derived. The effects of the concentration of matrix ions, pre-quenching conditions, and the electrolyte and solvent conditions (concentration, temperature, dielectric constant) on the structure and thermodynamics of the adsorbed electrolyte were examined. The numerical results indicated that the mean activity of the adsorbed electrolyte differs substantially from the corresponding quantity for the bulk electrolyte. The excess chemical potential depends strongly on the concentration of charged obstacles and matrix preparation, and also on the temperature and dielectric constant of the annealed electrolyte solution. Newly generated computer simulation results for the structural and thermodynamic parameters, obtained by the grand canonical Monte Carlo method, were used to assess the validity of the ROZ/HNC approximation. It was shown that the ROZ/HNC theory yields good agreement with the computer simulations.     

Potentials of mean force for hydrophobic interactions between hydrocarbons in water solution: dependence on temperature,solute shape,and solute size

We carried out molecular dynamics (MD) simulations with the AMBER force field for four pairs of spherical dimers of different size (neopentane, bicyclooctane, adamantane, and fullerene‐C₆₀) using the TIP3P model of water as solvent. For comparison, we performed MD simulations for a linear molecule of n‐pentane at the same conditions. To assess the entropy contribution to the Gibbs free energy, MD simulations were run at three different temperatures of 273 K, 323 K, and 348 K, respectively, using umbrella‐sampling/the WHAM method. The stability of dimers is described by a potential of mean force (PMF). The shape of PMF curves for hydrophobic interactions is characteristic, and entails a contact minimum, a solvent‐separated minimum, and a desolvation maximum. The depth and position of the contact minimum for each pair change with the size of the nonpolar particle, and are consequently shifted to a larger distance for larger molecules. Additionally, the Lennard–Jones contribution to the PMF increases simultaneously with an increase in particle size. For a linear dimer, the contact minimum is shifted to a shorter distance than it is for spherical systems with the same number of carbon atoms. The contact minima on PMF curves increase with temperature, suggesting that the association entropy is positive. Dimensionless PMF curves showed a low dependency (near contact minima regions) on temperature, as the association entropy is low. Copyright © 2014 John Wiley & Sons, Ltd.     

Equilibrium partitioning of a simple fluid in a matrix-filled cylindrical pores with adsorbing walls: A grand canonical Monte Carlo study

We have studied a model of a hard sphere fluid adsorbed in a cylindrical pore filled with quenched disordered matrix of hard sphere particles using Grand canonical Monte Carlo simulations. The interactions between matrix species and pore walls are assumed of a hard sphere type. However, the pore walls exert a short-range attraction upon adsorbed fluid particles. We discuss the adsorption isotherms and the density profiles of fluid particles in pores with different microporosity for several values of the pore radius. We have observed that like in homogeneous microporous media the adsorption increases with increasing porosity. However, trends of behavior of the isotherms also reflect layering of adsorbed fluid. The data obtained in this study may serve as a benchmark for the development of the theory of confined quenched-annealed systems and for computer simulation investigation of models permitting phase transitions in pores. This project has been supported in parts by DGAPA of the UNAM under research grant IN111597, by the National Council for Science and Technology (CONACyT), grant No. 25301-E.     

Influence of Solvent-Solvent and Solute-Solvent Interaction Properties on Solvent-Mediated Potential

A recently proposed universal calculational recipe for solvent-mediated potential is applied to calculate excess potential of mean force between two large Lennard-Jones (LJ) or hard core attractive Yukawa particles immersed in small LJ solvent bath at supercritical state. Comparison between the present prediction with a hypernetted chain approximation adopted for solute-solute correlation at infinitely dilute limit and existing simulation data shows high accuracy for the region with large separation, and qualitative reliability for the solute particle contact region. The calculational simplicity of the present recipe allows for a detailed investigation on the effect of the solute-solvent and solvent-solvent interaction details on the excess potential of mean force. The resultant conclusion is that gathering of solvent particles near a solute particle leads to repulsive excess PMF, while depletion of solvent particles away from the solute particle leads to attractive excess PMF, and minor change of the solvent-solvent interaction range has large influence on the excess PMF.     

Influence of Solvent-Solvent and Solute-Solvent Interaction Properties on Solvent-Mediated Potential

A recently proposed universal calculational recipe for solvent-mediated potential is applied to calculate excess potential of mean force between two large Lennard-Jones （LJ） or hard core attractive Yukawa particles immersed in small LJ solvent bath at supercritical state. Comparison between the present prediction with a hypernetted chain approximation adopted for solute-solute correlation at infinitely dilute limit and existing simulation data shows high accuracy for the region with large separation, and qualitative reliability for the solute particle contact region. The calculational simplicity of the present recipe allows for a detailed investigation on the effect of the solute-solvent and solvent-solvent interaction details on the excess potential of mean force. The resultant conclusion is that gathering of solvent particles near a solute particle leads to repulsive excess PMF, while depletion of solvent particles away from the solute particle leads to attractive excess PMF, and minor change of the solvent-solvent interaction range has large influence on the excess PMF.     

Hydrophobic/hydrophilic solvation: inferences from Monte Carlo simulations and experiments

In this study Monte Carlo simulations are used to determine the solvation properties of model hydrophobic (xenon and hard sphere) and hydrophilic (dimethyl ether) solutes in SPC/E water. Various contributions to the experimental solvation entropy, including the solvent reorganization entropy, have been determined. The main conclusion drawn, which is in accord with solubility data, is that poor solubility correlates with poor solute-water interaction. At room temperature, energy dominates the aqueous solubility of both hydrophobic and hydrophilic solutes, rather than entropy. However, at higher temperatures the solubility can pass through a minimum, and then entropy becomes dominant. Another interesting finding is the presence of larger than expected cavities in water. Two different simulation results support this finding. This unexpected hollow structure in water explains why a hard sphere solute is more soluble in water than in a comparable hard sphere or Lennard-Jones solvent. Hydrogen bonding causes water to aggregate into clusters that produce a few large cavities rather than many smaller cavities. The propensity for clustering also explains why water gives the illusion of being a low density liquid. Sufficient theoretical apparatus is developed to connect theoretical solvation properties to those measured by simulation and experiment. Finally, based on gas solubility, an intuitive hydrophobic/hydrophilic scale is developed.     

Computer simulation model of the structure of ion implanted impurities in semiconductors

A system of ion implanted impurities in a semiconductor is described by a Monte Carlo simulation of a non-equilibrium system of random distributed hard spheres. The radial distribution function of this system is found. The comparison is made with the fluid hard sphere case. The assumption that the absence either of annealing or diffusion of the impurities after the implantation process is also made.     

约束条件下胶球间排空力的研究

用MonteCarlo方法对处于两平行硬板约束下三个浓度的大小胶球系统进行了模拟,通过对大胶球表面小胶球密度的统计,由密度积分公式获得了大胶球所受的排空力.研究结果显示,因为平行硬板的存在或当改变两平行硬板的距离时,同浓度下,排空力在硬板距离小的时候最明显;三个浓度中,浓度高的,排空力受硬板距离影响最大;有硬板约束比无该约束的时候,排空力效果更显著.     

Phase coexistence and interface structure of a two-component Lennard-Jones fluid in porous media: application of Born—Green—Yvon equation

The Born-Green-Yvon equation with smoothed density approximation is used to calculate the liquid-liquid density profiles of a symmetric Lennard-Jones fluid in a hard sphere disordered matrix. The phase diagrams are evaluated for model systems characterized by different matrix densities and compared with the results of theoretical predictions and the Monte Carlo simulations of Gordon, P. A., and Glandt, E. D., 1996, J. chem. Phys., 105, 4257. It was found that increasing the matrix packing fraction reduces the magnitude of the miscibility gap and smooths the density profiles between two coexisting phases.     

Modified equation of state for pure and hard sphere mixtures in mean ionic activity coefficient calculations by mean spherical approximation model

A hard sphere equation of state (EOS) based on tetrakaidecahedron cell geometry (instead of spherical shape) and highly optimized molecular dynamic simulation data is proposed. The EOS is extended to hard sphere mixture and its performance for compressibility factor calculation at different diameter size of hard sphere mixtures by using various mixing rule is compared with Monte Carlo simulation data. The results indicated that for all mixing rules, the proposed EOS has minimum error comparing with computer simulation data. Also the residual prosperities are derived by using the proposed EOS. The residual properties are used in mean spherical approximation model (MSA) to evaluate the mean ionic activity coefficient of aqueous electrolyte solutions. The results are compared with those obtained by similar hard sphere equations of state and it is shown that the proposed EOS has a better performance in predicting the mean ionic activity coefficient.     

Condensation of states at the Landau levels and disorder-independent transport in a random system

I consider an electron on a square lattice, formed by random strenght point potentials, in the presence of a magnetic field, orthogonal to the lattice. When the number of magnetic flux quanta per unit cell is less than one, then an infinite density of extended disorder independent states condenses at each Landau level and provides the possibility for resistivity minima in a disordered system.     

Noncollinear magnetic structure in a random system of densely packed hard spheres

For an amorphous model system consisting of a random set of 100 identical hard sphere densely packed in a cube with periodical boundary conditions the energies of spiral magnetic structures are investigated. It is shown for a simple model with exponentially decaying antiferromagnetic interaction that a spiral structure may exist displaying a minimum energy. The wavevector of the spiral minimizing the interaction energy depends on the range of interaction: for the short range one the pitch of the spiral is twice as high as that for the longer range of interactions The calculated energies are compared with the interaction energies in s.c., f.c.c., and b.c.c. lattices. It is found that the energy gain in the topologically random system with respect to the magnetically disordered state may be higher than that corresponding to the antiferromagnetic arrangement in a crystal.One of the authors (S. K.) thanks Dr. J. L. Finney for a valuable discussion concerning the computer generation of the random set of hard spheres.     

Forces between charged surfaces in a solvent primitive model electrolyte

Grand canonical Monte Carlo (GCMC) simulations have been performed to investigate the components of the force between parallel charged surfaces in an electrolyte. The solvent primitive model (SPM) was used to investigate the effect of neutral hard sphere solvent particles on the force between the surfaces. The effects of particle size, wall charge density, charge valency of the electrolyte, and the exclusion of neutral hard sphere are discussed. When solvent particles are considered, the total force between the charged surfaces is always repulsive, even for divalent counterions. This is different from the earlier conclusion reached with a restricted primitive model electrolyte. The repulsive force decreases in going from monovalent counterions to divalent counterions.     

Light-scattering cross section as a function of pair distribution density

This paper presents a simple method of approximation for calculating the scattering cross section for a random orientated convex particle illuminated by a non polarized electromagnetic wave. This method is proved efficient for sphere and spheroids as the scattering efficiency is smaller than one and as the material is optically either soft or hard.     

Fluid–fluid phase equilibria in disordered porous media. Nonadditive hard sphere mixture

We report a computer simulation and integral equation study of fluid–fluid phase equilibria of nonadditive hard sphere binary mixture adsorbed in disordered hard sphere matrix. The mixture exhibits phase separation with critical density ρ_c^f lower than its bulk counterpart. It is found that ρ_c^f decreases with increasing both porosity and nonadditivity parameter.     

Longitudinal Optical Fields in Light Scattering from Dielectric Spheres and Anderson Localization of Light

Recent research has shown that coupling between point scatterers in a disordered medium by longitudinal electromagnetic fields is harmful for Anderson localization of light. However, it has been unclear if this feature is generic or specific for point scatterers. The present work demonstrates that the intensity of longitudinal field outside a spherical dielectric scatterer illuminated by monochromatic light exhibits a complicated, nonmonotonous dependence on the scatterer size. Moreover, the intensity is reduced for a hollow sphere, whereas one can adjust the parameters of a coated sphere to obtain a relatively low longitudinal field together with a strong resonant scattering efficiency. Therefore, random arrangements of structured (hollow or coated) spheres may be promising three‐dimensional disordered materials for reaching Anderson localization of light.     

Configurational effects of templating on the adsorption isotherms of templated porous materials

The porosity and pore geometry of disordered materials can be influenced by employing a removable template during synthesis. A theoretical and simulation study is reported of the configurational effects of template size and density on the adsorption isotherms of templated porous materials. To isolate the configurational (entropic) contributions, the adsorbate, matrix and template components are modelled as hard spheres. The replica Ornstein-Zernike equations proposed by Zhang, L. and Van Tassel, P. R. (2000) J. chem Phys., 112, 3006 are used within the Percus-Yevick approximation to calculate adsorption isotherms for differently sized adsorbate and template components. These theoretical results are compared with results from Monte Carlo simulation. It is found that adsorption is most enhanced whenever the size of the template is equal to or slightly larger than that of the adsorbate. Also, for systems of constant matrix density or constant matrix plus template density, increasing the density of template enhances the adsorption.