Zeta potential of colloidal particle in solvent primitive model electrolyte solution: a density functional theory study

A systematic study of zeta potential for a spherical double layer (SDL) around a colloidal particle in electrolyte solutions, is performed using density functional theory and Monte Carlo simulation. The usual recipe under the solvent primitive model is employed to model the system, where macroion, counterions, and coions are represented by charged hard spheres of uniform charge density and the presence of solvent is taken into account by modelling it as neutral hard spheres. All the components of the system are embedded in a dielectric continuum in order to consider the electrostatic effect of the solvent. The density functional theory employs a suitable weighted density approximation to calculate the hard-sphere contribution, whereas the residual electrostatic interactions are calculated as a small perturbation around the uniform fluid. The zeta potential profiles of a SDL in the presence of a number of electrolytes have been calculated and are found to be considerably influenced in the presence of solvent with an increase in the concentration of the electrolyte. The theory successfully predicts the maxima and sign reversal of the zeta potential profiles at high macroion surface charge density and in the presence of multivalent counterions, as obtained from the Monte Carlo simulation.     

Off-centre charge model of the planar electric double layer for asymmetric 2:1/1:2 valencies

ABSTRACT

Grand canonical Monte Carlo simulation results are reported for the structure and capacitance of a planar electric double layer containing off-centre charged rigid sphere cations and centrally charged rigid sphere anions. The ion species are assigned asymmetric valencies, +2:?1 and +1:?2, respectively, and set in a continuum dielectric medium (solvent) characterised by a single relative permittivity. An off-centre charged ion is obtained by displacing the ionic charge from the centre of the sphere towards its surface, and the physical double layer model is completed by placing the ionic system next to a uniformly charged, non-penetrable, non-polarizable planar electrode. Structural results such as electrode-ion singlet distribution functions, ionic charge density and orientation profiles are complemented by differential capacitance results at electrolyte concentrations of 0.2?mol/dm³ and 1?mol/dm³, respectively, and for various displacements of the cationic charge centre. The effect of asymmetry due to off-centre cations and valency asymmetry on the double layer properties is maximum for divalent counterions and when the cation charge is closest to the hard sphere surface.     

Effect of ionic size on the structure of spherical double layers: a Monte Carlo simulation and density functional theory study

The effect of ionic size on the diffuse layer characteristics of a spherical double layer is studied using Monte Carlo simulation and density functional theory within the restricted primitive model. The macroion is modelled as an impenetrable charged hard sphere carrying a uniform surface charge density, surrounded by the small ions represented as charged hard spheres and the solvent is taken as a dielectric continuum. The density functional theory uses a partially perturbative scheme, where the hard sphere contribution to the one particle correlation function is evaluated using weighted density approximation and the ionic interactions are calculated using a second-order functional Taylor expansion with respect to a bulk electrolyte. The Monte Carlo simulations have been performed in the canonical ensemble. The detailed comparison is made in terms of zeta potentials for a wide range of physical conditions including different ionic diameters. The zeta potentials show a maximum or a minimum with respect to the polyion surface charge density for a divalent counterion. The ionic distribution profiles show considerable variations with the concentration of the electrolyte, the valency of the ions constituting the electrolyte, and the ionic size. This model study shows clear manipulations of ionic size and charge correlations in dictating the overall structure of the diffuse layer.     

Towards a microscopic theory of wetting by ionic solutions. I. Surface properties of the semi-primitive model

As a first step towards a density functional theory (DFT) of wetting by ionic solutions we examine the density profiles of ions and solvent molecules confined near a charged wall, or between two walls, and the corresponding interfacial properties, including adsorption, surface tension, solvation force and electrostatic properties, within the semi-primitive model (SPM) of solutions made up of hard sphere solvent particles and charged hard spheres. Both monovalent and divalent cations with species-dependent diameters are considered. The density functional includes the best available Rosenfeld hard-sphere functional, as well as mean-field and Coulomb correlation contributions. The simpler mean-field functional is found to be adequate, at least for monovalent ions. The size differences lead to an interesting ‘fine structure’ of the density and charge density profiles. Cohesive interactions between all species are shown to lead to significant changes in the density profiles.     

电解液中带电平板与带电胶体球之间的有效相互作用

用Poisson-Boltzmann方程，计算了在具有单价离子的电解质溶液中均匀地带同号电荷的两无限大平行平板间的有效相互作用，以及用Derjaguin近似研究了边界对带电胶体球的影响.不考虑微离子相互作用时，两带电平板只有排斥作用，而且边界条件(面电荷密度)的改变对它们之间的有效相互作用影响不大.带电平板与带电胶体球之间的相互作用也有类似规律. 关键词： Poisson-Boltzmann方程 Derjaguin近似 双电层 渗透压     

A self-consistent density-functional approach to the structure of electric double layer: charge-asymmetric electrolytes

A self-consistent density-functional approach has been employed to study the structure of an electric double layer formed from a charge-asymmetric (2:l) electrolyte within the restricted primitive model which corresponds to charged hard sphere ions and a continuum solvent. The particle correlation due to hard-core exclusions is evaluated by making use of the universality of the density functionals and the correlation function of the uniform hard sphere fluid obtained through the integral equation theory with an accurate closure relation whereas mean spherical approximation is employed for the electrical contribution. Numerical results on the diffuse layer potential drop, ionic density profile, and the mean electrostatic potential near the electrode surface at several surface charge densities are found to be in quantitative agreement with the available simulation data.     

Microscopic density functional theory of wetting and drying of a solid substrate by an explicit solvent model of ionic solutions

Classical density functional theory (DFT) of inhomogeneous fluids is applied to an explicit solvent ‘semi-primitive’ model (SPM) of ionic solutions to investigate the influence of ionic solutes on the wetting behaviour of a solvent in contact with a neutral or charged planar substrate. The SPM is made up of three species of hard sphere particles with different diameters, interacting via an attractive Yukawa potential to model excluded volume and cohesion. The solvent particles are neutral, while the monovalent anions and cations are oppositely charged. The polar nature of the solvent is modelled by a continuum dielectric permittivity linked to the local solvent density. All three species interact with the impenetrable substrate via an attractive external potential. While excluded volume effects are accurately described by a Rosenfeld ‘fundamental measure’ free energy functional, the short range Yukawa attraction and Coulombic interactions are treated within the mean-field approximation. The ionic solutes are found to have a significant impact on the wetting behaviour of the solvent, in particular on the wetting temperature. Strong electric fields, or long-ranged (weakly screened) Coulombic forces are shown to have the propensity to change the wetting transition from second to first order. The cation–anion size asymmetry leads to charge separation on the liquid–vapour interface of the solution, which in turn can induce a drying transition on the liquid side of liquid–vapour coexistence.     

A study on the distribution of adsorbed nanoparticles

We use Monte Carlo simulation to calculate the distributions of particles under adsorption force near planar and cylindrical surfaces, respectively. Both hard sphere interaction and repulsive Yukawa (screened coulomb) interaction are employed in our simulations. We study the influence of the inter-particle potentials. The difference between the MC simulation results and the analytical results of ideal gas model shows that the interaction between particles plays an important role in the density distribution under external fields. Moreover, the 2-dimensional constructions of particles close to the surface are studied and show relations of the interaction between particles. These results may indicate us how to improve the methods of building nanoparticle coatings and nano-scale patterns.     

A study on the distribution of adsorbed nanoparticles

We use Monte Carlo simulation to calculate the distributions of particles under adsorption force near planar and cylindrical surfaces,respectively.Both hard sphere interaction and repulsive Yukawa (screened coulomb) interaction are employed in our simulations.We study the influence of the inter-particle potentials.The difference between the MC simulation results and the analytical results of ideal gas model shows that the interaction between particles plays an important role in the density distribution under external fields.Moreover,the 2-dimensional constructions of particles close to the surface are studied and show relations of the interaction between particles.These results may indicate us how to improve the methods of building nanoparticle coatings and nano-scale patterns.     

Static polarizability effects on counterion distributions near charged dielectric surfaces: A coarse-grained Molecular Dynamics study employing the Drude model

Coarse-grained implicit solvent Molecular Dynamics (MD) simulations have been used to investigate the structure of the vicinal layer of polarizable counterions close to a charged interface. The classical Drude oscillator model was implemented to describe the static excess polarizability of the ions. The electrostatic layer correction with image charges (ELCIC) method was used to include the effects of the dielectric discontinuity between the aqueous solution and the bounding interfaces for the calculation of the electrostatic interactions. Cases with one or two charged bounding interfaces were investigated. The counterion density profile in the vicinity of the interfaces with different surface charge values was found to depend on the ionic polarizability. Ionic polarization effects are found to be relevant for ions with high excess polarizability near surfaces with high surface charge.     

Effective Electrostatic Interactions Between Two Overall Neutral Surfaces with Quenched Charge Heterogeneity Over Atomic Length Scale

Using Monte Carlo results as a reference, a classical density functional theory (CDFT) is shown to reliably predict the forces between two heterogeneously charged surfaces immersed in an electrolyte solution, whereas the Poisson–Boltzmann (PB) theory is demonstrated to deteriorate obviously for the same system even if the system parameters considered fall within the validity range of the PB theory in the homogeneously charged surfaces. By applying the tested CDFT, we study the effective electrostatic potential of mean force (EPMF) between two face–face planar and hard surfaces of zero net charge on which positive and negative charges are separated and considered to present as discontinuous spots on the inside edges of the two surfaces. Main conclusions are summarized as follows: (i) strength of the EPMF in the surface charge separation case is very sensitively and positively correlated with the surface charge separation level and valency of the salt ion. Particularly, the charge separation level and the salt ion valency have a synergistic effect, which makes high limit of the EPMF strength in the surface charge separation case significantly go beyond that of the ideal homogeneously charged surface counterpart at average surface charge density similar to the average surface positive or negative charge density in the charge separation case. (ii) The surface charge distribution patterns mainly influence sign of the EPMF: symmetrical and asymmetrical patterns induce repulsive and attractive (at small distances) EPMF, respectively; but with low valency salt ions and low charge separation level the opposite may be the case. With simultaneous presence of both higher valency cation and anion, the EPMF can be repulsive at intermediate distances for asymmetrical patterns. (iii) Salt ion size has a significant impact, which makes the EPMF tend to become more and more repulsive with the ion diameter regardless of the surface charge distribution patterns and the valency of the salt ion; whereas if the 1:1 type electrolyte and the symmetrical patterns are considered, then the opposite may be the case. All of these findings can be explained self-consistently from several perspectives: an excess adsorption of the salt ions (induced by the surface charge separation) serving to raise the osmotic pressure between the plates, configuration fine-tuning in the thinner ion adsorption layer driven by the energy decrease principle, direct Coulombic interactions operating between charged objects on the two face-to-face plates involved, and net charge strength in the ion adsorption layer responsible for the net electrostatic repulsion.     

Change of electrostatic potential of mean force between two curved surfaces due to different salt composition,ion valence and size under certain ionic strength

Change of an electrostatic potential of mean force (EPMF) between two cylindrical rod surfaces with salt composition, ion valence, and ion size at a constant ionic strength of 0.3 M is studied by a classical density functional theory (CDFT) in a primitive model electrolyte solution. Several novel observations are made: (i) strength of a so-called like charge attraction (LCA) reduces in an invariable manner with the salt solution changing from single 2:1 electrolyte to mixture of 2:1 and 1:1 type electrolytes of varying concentration ratios; the change is even over entire range of the composition variation under low surface charge strength, and tends to be insensitive to the composition variation in the presence of the divalent counter-ion, and more and more drastic at a critical point the divalent counter-ion disappears, respectively, as the surface charge strength becomes big enough. (ii) Both monovalent counter-ion and co-ion diameters have only a marginal effect on both the LCA strength and equilibrium distance, and the former “abnormally” affects less than the latter. (iii) Depending on the surface charge strength considered, the divalent counter-ion diameter influences the LCA strength in solution comprised of 2:1 type and 1:1 type electrolytes, monotonously or non-monotonously. All of these findings provide forceful support for a recently proposed hydrogen-bonding style mechanism explaining the LCA.     

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.     

Electrophoresis of a charge-inverted macroion complex: Molecular-dynamics study

We have performed molecular-dynamics simulations to study the effect of an external electric field on a macroion in the solution of multivalent Z : 1 salt. To obtain plausible hydrodynamics of the medium, we explicitly make the simulation of many neutral particles along with ions. In a weak electric field, the macroion drifts together with the strongly adsorbed multivalent counterions along the electric field, in the direction proving inversion of the charge sign. The reversed mobility of the macroion is insensitive to the external field, and increases with salt ionic strength. The reversed mobility takes a maximal value at intermediate counterion valence. The motion of the macroion complex does not induce any flow of the neutral solvent away from the macroion, which reveals screening of hydrodynamic interactions at short distances in electrolyte solutions. A very large electric field, comparable to the macroion unscreened field, disrupts charge inversion by stripping the adsorbed counterions off the macroion. Received 5 December 2001 and Received in final form 10 April 2002     

Measuring inter-DNA potentials in solution

Interactions between short strands of DNA can be tuned from repulsive to attractive by varying solution conditions and have been quantified using small angle x-ray scattering techniques. The effective DNA interaction charge was extracted by fitting the scattering profiles with the generalized one-component method and inter-DNA Yukawa pair potentials. A significant charge is measured at low to moderate monovalent counterion concentrations, resulting in strong inter-DNA repulsion. The charge and repulsion diminish rapidly upon the addition of divalent counterions. An intriguing short range attraction is observed at surprisingly low divalent cation concentrations, approximately 16 mM Mg2+. Quantitative measurements of inter-DNA potentials are essential for improving models of fundamental interactions in biological systems.     

Numerical solution of a modified Poisson-Boltzmann equation for 1 : 2 and 2 : 1 electrolytes in the diffuse layer

A modified Poisson-Boltzmann (MPB) equation for an unsymmetrically charged electrolyte in the diffuse part of the electric double layer at a plane charged wall is solved numerically using a quasi-linearization procedure. Computations are carried out for 1 : 2 and 2 : 1 restricted primitive model electrolytes with no imaging and for a metallic wall and the results compared with the classical Gouy-Chapman-Stern theory. Except for negligible surface charge, the system with a divalent counter ion is the most sensitive to any change in its physical parameters. In general the MPB mean electrostatic potential, in contrast to the Gouy-Chapman-Stern potential, is not a monotonic decreasing function. The asymptotic behaviour of the MPB equation implies charge oscillations above a critical electrolyte concentration (?0·23 M) while below this concentration imaging or surface charge-ion interactions can produce a charge inversion. Charge separation is found for no surface charge with a metallic wall. The point ion limit is briefly considered.     

Disappearance of the gas-liquid phase transition for highly charged colloids

We calculate the full phase diagram of spherical charged colloidal particles using Monte Carlo free energy calculations. The system is described using the primitive model, consisting of explicit hard-sphere colloids and point counterions in a uniform dielectric continuum. We show that the gas-liquid critical point becomes metastable with respect to a gas-solid phase separation at colloid charges Q > or =20 times the counterion charge. Approximate free energy calculations with only one and four particles in the fluid and solid phases, respectively, are used to determine the critical line for highly charged colloids up to Q=2000. We propose the scaling law T*(c) approximately Q(1/2) for this critical temperature.     

Finite size effect of ions and dipoles close to charged interfaces

The modified dipolar Poisson-Boltzmann(MDPB) equation,where the electrostatics of the dipolar interactions of solvent molecules and also the finite size effects of ions and dipolar solvent molecules are explicitly taken into account on a mean-field level,is studied numerically for a two-plate system with oppositely charged surfaces.The MDPB equation is solved numerically,using the nonlinear Multigrid method,for one-dimensional finite volume meshes.For a high enough surface charge density,numerical results of the MDPB equation reveal that the effective dielectric constant decreases with the increase of the surface charge density.Furthermore,increasing the salt concentration leads to the decrease of the effective dielectric constant close to the charged surfaces.This decrease of the effective dielectric constant with the surface charge density is opposite to the trend from the dipolar Poisson-Boltzmann(DPB) equation.This seemingly inconsistent result is due to the fact that the mean-field approach breaks down in such highly charged systems where the counterions and dipoles are strongly attracted to the charged surfaces and form a quasi two-dimensional layer.In the weak-coupling regime with the electrostatic coupling parameter(the ratio of Bjerrum length to Gouy-Chapman length) Ξ 1,where the MDPB equation works,the effective dielectric constant is independent of the distance from the charged surfaces and there is no accumulation of dipoles near the charged surfaces.Therefore,there are no physical and computational advantages for the MDPB equation over the modified Poisson-Boltzmann(MPB) equation where the effect of dipolar interactions of solvent dipoles is implicitly taken into account in the renormalised dielectric constant.     

Measurement of long-range repulsive forces between charged particles at an oil-water interface

Using a laser tweezers method, we have determined the long-range repulsive force as a function of separation between two charged, spherical polystyrene particles (2.7 microm diameter) present at a nonpolar oil-water interface. At large separations (6 to 12 microm between particle centers) the force is found to decay with distance to the power -4 and is insensitive to the ionic strength of the aqueous phase. The results are consistent with a model in which the repulsion arises primarily from the presence of a very small residual electric charge at the particle-oil interface. This charge corresponds to a fractional dissociation of the total ionizable (sulfate) groups present at the particle-oil surface of approximately 3 x 10(-4).     

Effect of geometrical confinement on the interaction between charged colloidal suspensions

The effective interaction between charged colloidal particles confined between two planar like-charged walls is investigated using computer simulations of the primitive model describing asymmetric electrolytes. In detail, we calculate the effective force acting onto a single macroion and onto a macroion pair in the presence of slitlike confinement. For moderate Coulomb coupling, we find that this force is repulsive. Under strong-coupling conditions, however, the sign of the force depends on the distance to the plates and on the interparticle distance. In particular, the particle-plate interaction becomes strongly attractive for small distances which may explain the occurrence of colloidal crystalline layers near the plates observed in recent experiments.