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.     

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 effective interactions between colloidal hard spheres in microporous media: Hypernetted chain approximation for replica Ornstein-Zernike equations

In this work, the effective interaction between hard sphere colloidal particles in the presence of a hard sphere solvent, both dispersed either in a disordered quenched matrix of hard spheres or in the random matrix of freely overlapping obstacles is analyzed, using the replica Ornstein-Zernike (ROZ) integral equations. The ROZ equations are supplemented by the hypernetted chain closure. The presence of either disordered or random matrix is manifested in the attractive minima of the colloid-colloid potential of mean force (PMF), in addition to a set of minima due to the presence of solvent species. The effects of matrix microporosity and solvent density on the PMF and the intercolloidal forces are investigated. This project has been supported in part by the National Council for Science and Technology of Mexico (CONACyT) under Grant 25301-E.     

Interaction between solute molecules in medium density solvents

Solvation properties of solutes in supercritical, medium density solvents have been analysed using hypernetted-chain theory with the emphasis on the solvent-mediated interaction between solute molecules. The solvent and solute molecules are Lennard-Jones particles, and the solute is present at infinite dilution. Also a pair of solute molecules separated by different distances has been considered using reference interaction site model theory. Mainly, solvents at two typical densities (1.09_pc and 2.91_pc; pc is the critical density) that are in medium and high density regions, respectively, are treated. The temperature is set at 1.04T_C (T_c is the critical temperature). When the solute size is larger than the solvent size and the strength of the solute-solvent attractive interaction is greater than that of the solvent-solvent in the medium density region, the solvent structure confined between a pair of solute molecules is largely different from that near a single solute molecule. The confined solvent becomes denser and more stabilized as the distance between the solute molecules decreases, and an attractive interaction is induced between them. The interaction becomes even more attractive as the strength of the solute-solvent attractive interaction increases. The observations are qualitatively different from those in the high density region. Another high density region, which is well below the critical temperature, has been considered, but the behaviour observed is similar to that in the high density region above the critical temperature.     

A classical density functional approach to depletion interaction of Lennard-Jones binary mixtures

In this article, we apply classical density functional theory to investigate the characteristics of depletion interaction in Lennard-Jones (LJ) binary fluid mixtures. First, to confirm the validity of our adopted density functional formalism, we calculate the radial distribution functions using a theoretical approach and compare them with results obtained by molecular dynamics simulation. Then, this approach is applied to two colloids immersed in LJ solvent systems. We investigate the variation of depletion interaction with respect to the distance of two colloids in LJ binary systems. We find that depletion interaction may be attractive or repulsive, mostly depending on the bulk density of the solvent and the temperature of the binary system. For high bulk densities, the repulsive barrier of depletion force is remarkable when the total excluded volume of colloids touches each other and reaches a maximum. The height of the repulsive barrier is related to the parameters of the LJ potential and bulk density. Moreover, the depletion force may exhibit attractive wells if the bulk density of the solvent is low. The attractive well tends to appear when the surface–surface distance of colloids is half of the size of the polymer and deepens with temperature lowering in a fixed bulk density. In contrast with the hard-sphere system, no oscillation of depletion potential around zero is observed.     

Effects of solute-solvent and solvent-solvent attractive interactions on solute diffusion

A study is reported on the diffusion process of a solute molecule in a Lennard-Jones-like liquid near the triple point by a molecular dynamics simulation. Systematic changes were made to the strength of the solute-solvent or solvent-solvent attractive interaction in order to elucidate its effects on the diffusion coefficient. When the solute-solvent attractive interaction is enhanced, the diffusion coefficient of the solute becomes much smaller than that predicted by the Stokes-Einstein relationship with a stick boundary condition. The generalized friction coefficient on the solute molecule was investigated, and the attractive force between solute and solvent is found to be the main cause for the enhancement of the friction. When the attractive interaction between solvent molecules is weakened, the diffusion coefficient of a solute does not change, whereas that of a solvent does. Compared with the shear viscosity of the solvent, the diffusion coefficient of the solute breaks the Stokes-Einstein relationship, whereas the Stokes-Einstein relationship appears to hold in the case of the solvent molecule.     

On the absence of charge symmetry in electrostatic interaction between charged drops and hard particles

It is shown that the analytical expressions for the energy and force of electrostatic interaction between charged conducting particles (drops), a point charge, and a finite-size particle, as well as between a particle (a drop or a point charge) and a conducting plane, are asymmetric with respect to the sign of one of the charges. This is because the polarization interaction is always attractive irrespective of the signs of interacting particles. The absence of this symmetry leads to the self-constriction of charged aerodispersed systems containing a condensed phase, for example, plasma or liquid-droplet systems.     

Mechanism of particle thermophoresis in pure solvents

The thermophoresis of particles suspended in a pure solvent is theoretically examined. Thermophoresis is related to the temperature-induced pressure gradient in the solvent surrounding the particle and the resulting relative motion of the particle and the surrounding liquid. The excess pressure is produced by the particle-solvent interaction. As the interaction potential, London-van der Waals forces are considered. Using the known dependence of the interaction potential on the distance between the particle and the solvent molecule, an expression for the thermophoretic mobility (TM) (the particle velocity in a unit temperature gradient) is obtained. The resulting expressions are used to calculate the TM values for silica particles in several organic solvents and water. The calculated TM values for silica particles are of the same order as those reported in the literature. The model is consistent with laboratory measurements of particle thermophoresis, which is weak in water compared with organic solvents. This can be explained by the very low cubic thermal expansion coefficient for water. The calculated retention values for silica particles in thermal field-flow fractionation experiments performed in three organic solvents also follow the order known from literature.     

Phase diagram of highly asymmetric binary mixtures: A study of the role of attractive forces from the effective one-component approach

The phase diagram of an asymmetric solute-solvent mixture is investigated at the level of the effective one-component fluid. The solvent is taken into account by computing the potential of mean force between solute particles at infinite dilution for different models of solvent-solvent and solute-solvent short range interactions. Fluid-fluid and fluid-solid coexistence lines are determined from the free energy in the reference hypernetted chain theory for the fluid branch and from a variational perturbation theory for the solid one. The phase boundaries so determined compare well with recently published Monte Carlo data for mixtures of pure hard spheres. The influence of solute-solvent and solvent-solvent short range attractive forces is then investigated. When compared with pure hard core interactions, these forces are found to produce dramatic changes in the phase diagram, especially on the solvent packing fractions at which a dense fluid of solutes can be stable and on the separation of the fluid-fluid and fluid-solid coexistence lines. Finally, the connection of these results with the behavior of some colloidal suspensions is emphasized.     

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.     

Effect of acceleration by internal and external force fields on particle motion in intermediate regimes between the hydrodynamic and free-molecular limits

The kinetic theory of gases is applied to analyze slow translational motion of low-concentration particles driven by an external force in a homogeneous gas. The analysis takes into account the diffusion due to the difference in acceleration between particles and molecules in internal and external force fields. A general expression is derived for the particle drag force in hydrodynamic, free-molecular, and intermediate regimes. This expression reduces to a simple relation between the drag force and its values in the hydrodynamic and free-molecular limits and the force of intermolecular interaction between particles and gas molecules. In the case of spherically symmetric potential of interaction between the particle and molecules, the drag force is the harmonic mean of its limit values.     

Behavior of a wetting phase near a solid boundary: vapor near a weakly attractive surface

Density profiles of a LJ vapor near a weakly attractive surface with long-range fluid wall potential was studied along the pore coexistence curve. There are two localized density maxima near the pore wall: the first one is caused by localization of the molecules in the minimum of the fluid-wall potential, and the second one reflects adsorption of molecules at the first layer at higher densities. In addition, a third, weak density maximum is observed close to the critical temperature due to the competition between the long-range attractive tail of the fluid-wall potential and the effect of missing neighbors. This maximum separates the region of a gradual density depletion toward the surface due to the missing neighbor effect and the adsorption region further from the surface, where the density gradually increases toward the surface due to the attractive fluid-wall potential. When approaching the bulk critical temperature, this maximum moves away from the surface due to the divergence of the bulk correlation length. Applicability of various equations to describe the vapor density profiles is examined. Excess adsorption of vapor at low temperatures turns into excess depletion at higher temperatures. The crossover temperature increases with increasing pore size and strengthening fluid-wall interaction. The problems of the theory of the surface critical behavior of Ising models in a case of a non vanishing surface field and its mapping on a fluid is discussed.     

The effects of size,shape, and surface composition on the diffusive behaviors of nanoparticles at/across water–oil interfaces via molecular dynamics simulations

We have employed molecular dynamics simulations to systematically investigate the effects of nanoparticles’ structural and chemical properties on their diffusive behaviors at/across the water–benzene interface. Four different nanoparticles were studied: modified hydrocarbon nanoparticles with a mean diameter of 1.2 nm (1.2HCPs), modified hydrocarbon nanoparticles with a mean diameter of 0.6 nm (0.6HCPs), single-walled carbon nanotubes (SWCNTs), and buckyballs. We found that the diffusion coefficients of 0.6 and 1.2HCP were larger than the corresponding values predicted using the Stokes–Einstein (SE) equation and attributed this deviation to the small particle size and the anisotropy of the interface system. In addition, the observed directional diffusive behaviors for various particles were well-correlated with the derivative of the potential of mean force (PMF), which might indicate an effective driving force for the particles along the direction perpendicular to the interface. We also found that nanoparticles with isotropic shape and uniform surface, e.g., buckyballs, tend to have smaller diffusion coefficients than those of nanoparticles with comparable dimensions but anisotropic shapes and non-uniform surface composition, e.g., SWCNT and 0.6HCP. One possible hypothesis for this behavior is that the “perfect” isotropic shape and uniform surface of buckyballs result in a better-defined “solvation shell” (i.e., a shell of solution molecules), which leads to a larger “effective radius” of the particle, and thus, a reduced diffusion coefficient.     

Influence of the long-range forces in non-Gaussian random-packing dynamics

In this paper, we perform molecular dynamics (MD) simulations to study the random packing of spheres with different particle size distributions. In particular, we deal with non-Gaussian distributions by means of the Lévy distributions. The initial positions as well as the radii of five thousand non-overlapping particles are assigned inside a confining rectangular box. After that, the system is allowed to settle under gravity towards the bottom of the box. Both the translational and rotational movements of each particle are considered in the simulations. In order to deal with interacting particles, we take into account both the contact and long-range cohesive forces. The normal viscoelastic force is calculated according to the nonlinear Hertz model, whereas the tangential force is calculated through an accurate nonlinear-spring model. Assuming a molecular approach, we account for the long-range cohesive forces using a Lennard-Jones (LJ)-like potential. The packing processes are studied assuming different long-range interaction strengths.     

非线性晶体产生的空心光束中大尺寸粒子囚禁与导引

提出了一种基于非线性ZnSe晶体产生的空心光束与光泳力的大尺寸粒子二维囚禁与一维导引、三维囚禁方案.理论上分析并计算了单个非线性ZnSe晶体产生的空心光束内粒子受到的横向与纵向光泳力,纵向光泳力的大小同粒子尺寸与光束尺寸比例的四次方成正比,与空心光束功率成正比,方向与光束传播方向一致.粒子尺寸与空心光束尺寸越接近时,横向光泳力的大小越大.结果表明该光泳力可以实现对大尺寸粒子的二维囚禁,同时可对粒子进行长距离(米量级)一维定向导引;理论上分析并计算了基于双非线性ZnSe晶体产生的局域空心光束内粒子所受横向与纵向光泳力情况,光泳力与系统参数的依赖关系与单个非线性晶体产生的空心光束中的粒子受力情况类似,不同的是该条件下纵向光泳力指向光束中心.结果表明该局域空心光束可以实现大尺寸粒子的三维有效囚禁.基于非线性ZnSe晶体产生的空心光束或者局域空心光束可以作为大尺寸粒子非接触式有效操控的工具,在现代光学以及生物医学中有潜在的应用.     

低密度溶液中溶剂的重组织性质

分析了溶液的微观结构 ,结果表明 ,单个溶质粒子影响其周围的溶剂的结构 ,溶质粒子间的相互作用也将影响溶剂的结构 ,溶质对溶剂结构的影响称作溶剂的重组织 .提出了二阶重组织能及二阶重组织熵等概念 ,可以描述在两个溶质粒子发生碰撞时对其周围溶剂结构的影响 .利用二元系的集团展开理论 ,给出了溶剂的一阶、二阶重组织能和重组织熵的表达式 .统计热力学分析给出了溶剂 溶剂径向分布函数与溶质和溶剂化学势之间的关系 ,给出了无限稀溶液模型是否成立的宏观判据 .提出的理论可用于低密度的二元溶液 .     

Asymmetric mixture of hard particles with Yukawa attraction between unlike ones: a cluster algorithm simulation study

The influence of a Yukawa attraction between unlike species on the structure of an asymmetric mixture of hard particles is investigated. A recently proposed cluster algorithm for the simulation of hard particle fluids is extended in order to treat the Yukawa tail. Starting with nonoverlapping hard core configurations generated by the cluster algorithm, the attractive tail is treated according to a standard Metropolis scheme. Preliminary results on the effect of the Yukawa attraction on the pair distribution of the larger particles and the potential of mean force at infinite dilution confirm important changes in comparison with pure hard sphere mixtures.     

Interaction of charged dust particles in clouds of thermodynamically equilibrium charges

The solution of the Poisson-Boltzmann equation for a cloud of charges surrounding two charged dust particles treated as Debye atoms forming a Debye molecule is investigated numerically using Cassini coordinates. The electric force exerted on a dust particle by the other dust particle was determined by integrating the electrostatic pressure on the surface of the dust particle. It is shown that attractive forces appear when the following two conditions are satisfied. First, the Debye radius (corresponding to the electron density at half the mean distance between the dust particles) must be approximately equal to half the mean distance between the dust particles. Attraction between the dust particles emerges at a distance equal approximately to half the mean distance between the dust particles. Second, attraction takes place when like charges are concentrated predominantly on the dust particles. If the particles carry a small fraction of charge of the same polarity, repulsion between the particles takes place at all distances.     

A gas of Brownian particles in statistical dynamics

We consider a large number of particles on a one-dimensional latticel Z in interaction with a heat particle; the latter is located on the bond linking the position of the particle to the point to which it jumps. The energy of a single particle is given by a potentialV(x), x∈Z. In the continuum limit, the classical version leads to Brownian motion with drift. A quantum version leads to a local drift velocity which is independent of the applied force. Both these models obey Einstein's relation between drift, diffusion, and applied force. The system obeys the first and second laws of thermodynamics, with the time evolution given by a pair of coupled non linear heat equations, one for the density of the Brownian particles and one for the heat occupation number; the equation for a tagged Brownian particle can be written as a stochastic differential equation.