Electrostatic interaction between two spherical colloidal particles

Explicit exact analytic expressions are obtained in the form of infinite series for the potential distribution and the potential energy of the electrostatic interaction for the system of two dissimilar spheres in an electrolyte solution on the basis of the linearized Poisson—Boltzmann equation without recourse to Derjaguin's approximation. The leading term of the expression for the interaction energy (the zeroth order approximation) corresponds to the interaction energy that would be obtained if both spheres were ion-penetrable spheres (“soft” spheres). This term is a screened Coulomb interaction due to a simple linear superposition of the unperturbed potentials of the respective spheres, which is proportional to the product of their unperturbed surface potentials. The first-order approximation corresponds to the interaction energy that would be obtained if either sphere were a soft particle (the other being hard). The first-order correction term consists of two sub-terms, each of which is proportional to the square of the unperturbed surface potential of either sphere and does not depend on the unperturbed surface potential of the other sphere, can be interpreted as the interaction between the soft sphere and its image with respect to the hard sphere. This image interaction is attractive if the surface potential of the hard sphere is constant and repulsive if the surface charge density of the sphere is constant. It is shown that Derjaguin's method as well as its extension to the interaction of unequal spheres by Hogg, Healy and Fuerstenau (HHF) is quite a good approximation.     

Electrostatic Interaction between Two Dissimilar Spheres with Constant Surface Charge Density

Explicit exact analytic expressions are obtained in the form of infinite series for the potential energy of the electrostatic interaction for the system of two dissimilar hard spheres with constant surface charge density in an electrolyte solution on the basis of the linearized Poisson-Boltzmann equation. The effects of the particle polarization, that is, the internal fields induced within tim interacting spheres, which are found to be of the order of instead of 1/κa (where κ is the Debye-Hückel parameter and a is the sphere radius), are taken into account. As in the case of the interaction at constant surface potential, the zeroth-order approximation to the interaction energy corresponds to the interaction energy that would be obtained if both spheres were ion-penetrable spheres ("soft" spheres) and to that obtained by the linear superposition approximation. The first-order approximation corresponds to the interaction energy that would be obtained if either sphere were a soft sphere, with the other being a hard sphere with constant surface charge density. The first-order correction term can be interpreted as the image interaction between the soft sphere and its image with respect to the hard sphere.     

Ionic solvation at the solid/electrolyte interface: A statistical-mechanical approach

We have studied studied the influence of the size of ions on their adsorbability at a solid surface in the presence of a molecular solvent. Ions and molecules are represented respectively by charged hard spheres and dipolar hard spheres and the surface is just a neutral hard wall. We have found that the electrostatic interaction between ions and molecules can induce the exclusion of small ions from the surface. A pure MSA (mean spherical approximation) calculation would not give any effect of the solvation on the ionic density profile. The present calculation is limited to the case of infinite ionic dilution.     

球型胶粒间的相互作用能—Derjaguin法的改进

对求算球型胶体颗粒相互作用能的Ｄｅｒｊａｇｕｉｎ法进行了适当的修正，并由此得出简单的解析表达式，对低电位条件下等同和不等同球颗粒的计算结果表明，该法拓宽了Ｄｅｒｊａｇｕｉｎ公式的应用范围，提高了计算结果的精确度。     

Effect of attractions on the structure of polymer solutions confined between surfaces: a density functional approach

A density functional theory is presented to study the effect of attractions on the structure of polymer solutions confined between surfaces. The polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres, both having Yukawa-type attractions and the mixture being confined between attractive Yukawa-type surfaces. The present theory treats the ideal gas free energy functional exactly and uses weighted density approximation for the hard chain and hard sphere contributions to the excess free energy functional. The attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions on the density profiles of the polymer and the solvent molecules are found to agree quite well with the Monte Carlo simulation results for varying densities, chain lengths, wall separations, and different sets of interaction potentials.     

Internal electric field densities of metal nanoshells

The internal field patterns for gold shells filled with the same material as the surrounding medium are calculated with Mie theory and in the quasistatic approximation and their properties compared to the response of homogeneous spheres and metallic rings. One major difference between the sphere and shell case is that the areas of highest field enhancement in metallic shells are located perpendicular to the incident polarization, whereas for metallic spheres they are along the polarization direction. Recent results based on the discrete dipole approximation (DDA) are shown to be misleading, which might be due to the use of a too coarse grid size. We also show that the type of resonance and the associated internal field pattern (low or high energy) has a strong impact on the external fields.     

Macromolecule-Induced Clustering of Hard Spheres

The connectivity Ornstein-Zernike formalism, together with the polymer reference interaction site model (PRISM), is employed to describe connectivity and network formation in mixtures of spheres and polymers. Results are presented for the percolation of spheres induced by both flexible coil-like and rigid rod-like linear polymers; the Percus-Yevick (PY) approximation is used throughout. Our results are compared with predictions based on the adhesive hard sphere (AHS) model, and correlations with the polymer-mediated second virial coefficient between spheres are discussed. Copyright 2001 Academic Press.     

Solvent density inhomogeneities and solvation free energies in supercritical diatomic fluids: a density functional approach

Density functional theory is used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute is modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The authors' approach is particularly suitable for thoroughly exploring the effect of different interaction parameters, such as solute-solvent interaction strength and range, solvent-solvent long-range interactions, and particle size, on the local solvent structure and the solvation free energy under supercritical conditions. Their results indicate that the behavior of the local coordination number in homonuclear diatomic fluids follows trends similar to those reported in previous studies for monatomic fluids. The local density augmentation is particularly sensitive to changes in solute size and is affected to a lesser degree by variations in the solute-solvent interaction strength and range. The associated solvation free energies exhibit a nonmonotonous behavior as a function of density for systems with weak solute-solvent interactions. The authors' results suggest that solute-solvent interaction anisotropies have a major influence on the nature and extent of local solvent density inhomogeneities and on the value of the solvation free energies in supercritical solutions of heteronuclear molecules.     

Long-Range Electrostatic Interaction between a Charged Wall and Two Similarly Charged Colloidal Spheres at Low Surface Potentials

The long-range electrostatic interaction between a pair of similarly charged colloidal spheres and a charged planar wall at low surface potentials is theoretically investigated. The linear Poisson-Boltzmann equation (PBE) and the point charge approximation of the charged sphere are used. The electrical potential distribution in the electrolyte solution is found from the PBE at the constant surface potentials using the image charge method. The electrostatic forces acting on the spheres are then calculated. The results show that the repulsive interaction between a pair of similarly charged colloidal spheres clearly decreases when a charged wall appears nearby, but it is impossible for an attractive force to emerge at the scaled surface potentials less than 1. There is, however, an attractive force between the charged wall and the similarly charged colloidal spheres, when the surface potential zetap on the wall is sufficiently higher than the surface potential zetas on the spheres to make zetap > zetasexp(kappah) (h is the distance from the wall to the sphere center). In this case, there are negative surface charges on the spheres at positive surface potential zetas. It is these negative charges that produce the above attraction. Copyright 1999 Academic Press.     

Ordering of amphiphilic Janus particles at planar walls: a density functional study

We investigate the structure formation of amphiphilic molecules at planar walls using density functional theory. The molecules are modeled as (hard) spheres composed of a hydrophilic and hydrophobic part. The orientation of the resulting Janus particles is described as a vector representing an internal degree of freedom. Our density functional approach involves fundamental measure theory combined with a mean-field approximation for the anisotropic interaction. Considering neutral, hydrophilic, and hydrophobic walls, we study the adsorption of the particles, focusing on the competition between the surface field and the interaction-induced ordering phenomena. Finally, we consider systems confined between two planar walls. It is shown that the anisotropic Janus interaction yields pronounced frustration effects at low temperatures.     

Electrostatic interaction between soft particles

Electrostatic interaction between two soft particles (i.e., polyelectrolyte-coated particles) in an electrolyte solution is discussed. An approximate analytic expression for the interaction energy between two dissimilar soft spheres is derived by applying Derjaguin's approximation to the corresponding interaction energy between two parallel dissimilar soft plates for the case where the density of fixed charges within the polyelectrolyte layer is low. The obtained expression covers various limiting cases that include hard sphere/hard sphere interaction, spherical polyelectrolyte/spherical polyelectrolyte interaction, soft sphere/spherical polyelectrolyte interaction, soft sphere/hard sphere interaction, and spherical polyelectrolyte/hard sphere interaction.     

Photoabsorption cross sections of sodium clusters: electronic and geometrical effects

We study the origin of the discrepancy between the photoabsorption cross sections of small jellium spheres calculated by the time dependent local density approximation (TDLDA) and experiments for small metallic clusters. We have specifically studied Na ₂₁ ⁺ . We conclude that both non-local exchange-correlation effects beyond the LDA and geometrical effects beyond the jellium approximation should be taken in the same calculation. We also present local and non-local calculations for Na _n ^? (n=19, 91 and 197) within the framework of the jellium model. The large anions show a fragmentation of the plasmon due to its interference with the ionization threshold. This feature is absent in the TDLDA results.     

Communication: lateral phase separation of mixed polymer brushes physisorbed on planar substrates

Here, we present a new method to model lateral phase separation in mixed polymer brushes physisorbed to a planar surface with mobile grafting points. The model is based on a local mean field theory that combines a Flory-Huggins approximation for interaction enthalpies with an Alexander-de Gennes brush entropy contribution. Using Monte Carlo sampling, the application of these two interactions to a lattice model yields a range of phase behavior consistent with previous theoretical and experimental work. This model will be useful for predicting mixed polymer brush morphologies on planar surfaces and in principle can be extended to other geometries (e.g., spheres) and polymer systems.     

The solvophobic effect in simple fluid mixtures

The “solvophobic” effect is the tendency of solute particles to cluster as the attractive interaction between solvent particles is strengthened. The potentials of mean force in the hypernetted chain approximation have been obtained for a simple fluid mixture consisting of two hard spheres immersed in a hard core/Yukawa tail solvent. The results clearly exhibit features attributable to the “solvophobic” effect.     

A sphere-based model for the electrostatics of globular proteins

We propose a model for the electrostatics of globular proteins in which the low dielectric region is replaced by concentric spheres of the appropriate size. The method uses analytical formulas for the dielectric sphere and allows an efficient and accurate treatment of bulk charges. For surface charges, we propose a numerical determination of the sphere radius based on the solvent exposure of the individual atoms. The present implementation of the sphere model yields a good approximation of finite-difference Poisson solvation and interaction energies for a test set of 12 proteins.     

Effect of attractive interactions on the structure of polymer melts confined between surfaces: a density-functional approach

A density-functional theory is presented to study the structure of polymers, having attractive interactions, confined between attractive surfaces. The theory treats the ideal-gas free-energy functional exactly and uses weighted density approximation for the hard-chain contribution to the excess free-energy functional. The bulk interactions of freely jointed hard spheres are obtained from generalized Flory equation of state and the attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions are found to be in quite good agreement with the Monte Carlo simulation results for varying densities, chain lengths, and different interaction potentials. The results confirm important implications of using different approximations for the hard-sphere and attractive interactions.     

球胶体颗粒之间相互作用能的求解

根据线性迭加近似方法,定义了一个修正电位项,较详细地推导出用于中等电位条件下球形胶体颗粒相互作用能和力的公式,该公式较为简单、实用,然而,对其所做的改进主要是针对相互作用能而不是力,对其原因也作了简单的讨论.     

Thermodynamically consistent closure approximation for hard spheres systems

We present a new closure relation that is an extension of the Percus-Yevick approximation. In the proposed closure, we introduce an additional term and a mixing coefficient that can be determined by imposing a condition of thermodynamic self-consistency. Moreover, the mixing coefficient is calculated analytically within a linear approximation. In the case of a monodisperse system of hard spheres, we compare the results of our model to well-established thermodynamic expressions and also to the structural properties of fairly known closure approximations. In the second case, and using an equivalent scheme, the new closure relation is extended to the depletion potential between two large hard spheres immersed in a liquid of small hard spheres. In both cases, the results of our model are in good agreement with numerical simulations performed at intermediate concentrations.     

Prediction of collective diffusion coefficient of bovine serum albumin in aqueous electrolyte solution with hard-core two-Yukawa potential

A new method to predict concentration dependence of collective diffusion coefficient of bovine serum albumin (BSA) in aqueous electrolyte solution is developed based on the generalized Stokes-Einstein equation which relates the diffusion coefficient to the osmotic pressure. The concentration dependence of osmotic pressure is evaluated using the solution of the mean spherical approximation for the two-Yukawa model fluid. The two empirical correlations of sedimentation coefficient are tested in this work. One is for a disordered suspension of hard spheres, and another is for an ordered suspension of hard spheres. The concentration dependence of the collective diffusion coefficient of BSA under different solution conditions, such as pH and ionic strength is predicted. From the comparison between the predicted and experimental values we found that the sedimentation coefficient for the disordered suspension of hard spheres is more suitable for the prediction of the collective diffusion coefficients of charged BSA in aqueous electrolyte solution. The theoretical predictions from the hard-core two-Yukawa model coupled with the sedimentation coefficient for a suspension of hard spheres are in good agreement with available experimental data, while the hard sphere model is unable to describe the behavior of diffusion due to its neglect of the double-layer repulsive charge-charge interaction between BSA molecules.     

Hydrophobic interactions and osmotic second virial coefficients for methanol in water

A recent theory of the hydrophobic effect together with a simple model for an alcohol molecule is used to calculate the osmotic (McMillan-Mayer) second virial coefficientB ₂ for methanol dissolved in water. We use this calculation to study the validity of common arguments that try to draw microscopic structural information from experimental virial coefficient data. In disagreement with many workers, we find that the hydrophobic interaction between hard spheres in water is attractive and that its strength diminishes as temperature is raised. Models that have come to the opposite conclusions have neglected complications inherent to real solutes such as the role of the hydroxy groups in affecting the correlations between the apolar portions of neighboring alcohols. The calculations reported here indicate that this neglect is a poor approximation for methanol. Our calculations also show that osmotic virial coefficients are sensitive to subtle details in the potentials of mean force. Therefore, slowly varying (e.g., dispersion) interactions may also contribute significantly to the values of these coefficients without significantly changing the solvent structure near the solute molecules.