Electrical potentials of two identical particles with fixed surface charge density in a salt-free medium

The electrical potentials of two identical planar, cylindrical, and spherical particles immersed in a salt-free dispersion are solved analytically by a perturbation approach for the case of constant surface charge density. The system under consideration simulates, for example, micelles, where the ionic species in the liquid phase come mainly from the dissociation of the functional groups on the droplet surface. We show that for planar particles, the present zero-order perturbation solution is exact, and for cylindrical and spherical particles, the first-order perturbation solution provides sufficiently accurate results, with an averaged percentage deviation on the order of 1% under typical conditions. In general, the higher the surface charge density, the higher the valence of counterions, the smaller the separation distance between two particles, and the smaller the curvature of particle surface, the better the performance of the perturbation solution.     

Complexation of ferric oxide particles with pectins of different charge density

The effect of polyelectrolyte charge density on the electrical properties and stability of suspensions of oppositely charged oxide particles is followed by means of electro-optics and electrophoresis. Variations in the electro-optical effect and the electrophoretic mobility are examined at conditions where fully ionized pectins of different charge density adsorb onto particles with ionizable surfaces. The charge neutralization point coincides with the maximum of particle aggregation in all suspensions. We find that the concentration of polyelectrolyte, needed to neutralize the particle charge, decreases with increasing charge density of the pectin. The most highly charged pectin presents an exception to this order, which is explained with a reduction of the effective charge density of this pectin due to condensation of counterions. The presence of condensed counterions, remaining bound to the pectin during its adsorption on the particle surface, is proved by investigation of the frequency behavior of the electro-optical effect at charge reversal of the particle surface.     

Adsorption of novel thermosensitive graft-copolymers: Core-shell particles prepared by polyelectrolyte multilayer self-assembly

The adsorption properties of thermosensitive graft-copolymers are investigated with the aim of developing self-assembled multilayers from these copolymers. The copolymers consist of a thermoreversible main chain of poly(N-isopropylacrylamid) and a weak polyelectrolyte, poly(2-vinylpyridine), as grafted side chains. Zeta-potential, single particle light scattering and adsorption isotherms monitor the adsorption of the thermoreversible copolymers to precoated colloidal particles. The results show a smaller surface coverage for a larger density of grafted chains. The surface coverage is discussed in terms of surface charge density in the adsorbed monolayer. Taking into account the monolayer adsorption properties, conditions are developed for the multilayer formation from these copolymers. A low pH provides a sufficient charge density of the grafted chains to achieve a surface charge reversal of the colloids upon adsorption. The charge reversal after each adsorbed layer is monitored by zeta-potential and the increase of the thickness is determined by light scattering. Stable and reproducible multilayers are obtained. The results imply that the conformation of the thermosensitive component in multilayers depends strongly on the grafting density, where the polymer with a higher grafting density adsorbs in a flat conformation while that with a lower grafting density adsorbs with more loops.     

Density-functional theory of spherical electric double layers and zeta potentials of colloidal particles in restricted-primitive-model electrolyte solutions

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The theoretical predictions are in good agreement with the results from Monte Carlo simulations and from previous investigations using integral-equation theory for the ionic density profiles and the zeta potentials of spherical particles at a variety of solution conditions. Like the integral-equation approaches, the density-functional theory is able to capture the oscillatory density profiles of small ions and the charge inversion (overcharging) phenomena for particles with elevated charge density. In particular, our density-functional theory predicts the formation of a second counterion layer near the surface of highly charged spherical particle. Conversely, the nonlinear Poisson-Boltzmann theory and its variations are unable to represent the oscillatory behavior of small ion distributions and charge inversion. Finally, our density-functional theory predicts charge inversion even in a 1:1 electrolyte solution as long as the salt concentration is sufficiently high.     

The stability of a salt-free colloidal dispersion

The electrical potential for the case of two identical, planar parallel particles immersed in a salt-free medium, where the ionic species in the counterions come solely from those that dissociated from the surfaces, is evaluated. Analytical expressions for the electrical potential, the concentration of counterions, and the electrical energy are derived. We show that in a salt-free dispersion, if the separation distance between two particles is sufficiently far, the electrical repulsive force dominates, that is, the total energy is positive and does not have a secondary minimum, which is not the case for a dispersion where both coions and counterions are present. Also, the conditions used to calculate the critical coagulation concentration in the classic Derjaguin-Landau-Verwey-Overbeek theory become inappropriate and the Derjaguin approximation is inapplicable. We show that if the surface charge density exceeds approximately 0.04 Cm(2), the stability of a salt-free dispersion remains essentially the same. If the surface charge density is sufficiently high, the maximum separation distance between two particles below which coagulation occurs is in the ranges of [0,1 nm] and [1,7 nm] for the cases where the Hamaker constant is 10(-20) and 10(-19) J, respectively.     

Hydrodynamic crossover in dynamic microparticle adhesion on surfaces of controlled nanoscale heterogeneity

This note documents the crossover from a regime where shear flow hinders microparticle adhesion on collecting surfaces to that where increased flow aids particle capture. Flow generally works against adhesion and successfully hinders particle capture when the net physicochemical attractions between the particles and collector are weak compared with hydrodynamic forces on the particle. Conversely, with strong attractions between particles and collector, flow aids particle capture by increasing the mass transport of particles to the interfacial region. Here, local hydrodynamics still generally oppose adhesion but are insufficient to pull particles off of the surface. Thus, flow actually increases the particle capture rate through the increased transport to the surface. These behaviors are demonstrated using 1 mum silica spheres flowing over electrostatically heterogeneous (length scales near 10 nm) collecting surfaces at shear rates from 22 to 795 s(-1). The net surface charge on the collector is varied systematically from strongly negative (pure silica) to strongly positive (a saturated polycationic overlayer), demonstrating the interplay between physicochemical and hydrodynamic contributions. These results clearly apply to situations where heterogeneous particle-surface interactions are electrostatic in nature; however, qualitatively similar behavior was previously reported for the effect receptor density on bacterial adhesion.     

On the role of electrostatic forces in the adhesion of polymer particles to solid surfaces

Simultaneous measurements have been made of the adhesive force and double electric charge of particles after their removal from a metal surface. For the systems investigated, the adhesive force and charge on the particles increase with particle diameter according to a power law with an exponent close to 2. Such dependence can be explained on the basis of the electrostatic nature of the adhesive forces. A double electric layer exists at the interface between the particles and the metal surface. A calculation was made of the surface density of charge for the polyvinyl chloride particle-steel system.     

Diffusiophoresis in a suspension of charge-regulating colloidal spheres

An analytical study of diffusiophoresis in a homogeneous suspension of identical spherical charge-regulating particles with an arbitrary thickness of the electric double layers in a solution of a symmetrically charged electrolyte with a uniform prescribed concentration gradient is presented. The charge regulation due to association/dissociation reactions of ionogenic functional groups on the particle surface is approximated by a linearized regulation model, which specifies a linear relationship between the surface charge density and the surface potential. The effects of particle-particle electrohydrodynamic interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations that govern the electric potential profile, the ionic concentration distributions, and the fluid flow field in the electrolyte solution surrounding the particle in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved with the equilibrium surface charge density (or zeta potential) of the particle as the small perturbation parameter. Closed-form formulas for the diffusiophoretic velocity of the charge-regulating sphere correct to the second order of its surface charge density or zeta potential are derived. Our results indicate that the charge regulation effect on the diffusiophoretic mobility is quite sensitive to the boundary condition for the electric potential specified at the outer surface of the unit cell. For the limiting cases of a very dilute suspension and a very thin or very thick electric double layer, the particle velocity is independent of the charge regulation parameter.     

Surface charge density and electrokinetic potential of highly charged minerals: experiments and Monte Carlo simulations on calcium silicate hydrate

In this paper, we are concerned with the charging and electrokinetic behavior of colloidal particles exhibiting a high surface charge in the alkaline pH range. For such particles, a theoretical approach has been developed in the framework of the primitive model. The charging and electrokinetic behavior of the particles are determined by the use of a Monte Carlo simulation in a grand canonical ensemble and compared with those obtained through the mean field theory. One of the most common colloidal particles has been chosen to test our theoretical approach. That is calcium silicate hydrate (C-S-H) which is the main component of hydrated cement and is known for being responsible for cement cohesion partly due to its unusually high surface charge density. Various experimental techniques have been used to determine its surface charge and electrokinetic potential. The experimental and simulated results are in excellent agreement over a wide range of electrostatic coupling, from a weakly charged surface in contact with a reservoir containing monovalent ions to a highly charged one in contact with a reservoir with divalent ions. The electrophoretic measurements show a charge reversal of the C-S-H particles at high pH and/or high calcium concentration in excellent agreement with simulation predictions. Finally, both simulation and experimental results clearly demonstrate that the mean field theory fails not only quantitatively but also qualitatively to describe a C-S-H dispersion under realistic conditions.     

The effect of surface modification on the stability characteristics of poly(N-isopropylacrylamide) latices under Brownian and flow conditions

The stability of thermoreversible microgel particles of poly(N-isopropylacrylamide) having carboxylate surface charge groups has been studied in the presence of electrolyte and non-adsorbing polymer. Methylation of the surface charge groups leads to a decrease in the electrophoretic mobility of the particles and also the interparticle electrostatic repulsive potential, resulting in the material becoming more susceptible to flocculation. The Hamaker constant of the microgel particles increases with the decrease in the hydrodynamic size of the particles following heating. This brings about an increase in the van der Waals attractive energy which results in the particles aggregating in the presence of sufficient electrolyte. Under conditions of flow through membranes, where shearing forces are operative, the flocculation observed following the heating of the dispersions results in the blockage of pores.     

Aggregation and dispersion of small hydrophobic particles in aqueous electrolyte solutions

The effect of salts on the solvent-induced interactions between hydrophobic particles dispersed in explicit aqueous solution is investigated as a function of the salt's ionic charge density by molecular dynamics simulations. We demonstrate that aggregates of the hydrophobic particles can be formed or dissolved in response to changes in the charge density of the ions. Ions with high charge density increase the propensity of the hydrophobic particles to aggregate. This corresponds to stronger hydrophobic interactions and a decrease in the solubility (salting-out) of the hydrophobic particles. Ions with low charge density can either increase or decrease the propensity for aggregation depending on whether the concentration of the salt is low or high, respectively. At low concentrations of low charge density ions, the aggregate forms a "micelle-like" structure in which the ions are preferentially adsorbed at the surface of the aggregate. These "micelle-like" structures can be soluble in water so that the electrolyte can both increase the solubility and increase aggregation at the same time. We also find, that at the concentration of the hydrophobic particles studied (approximately 0.75 m), the aggregation process resembles a first-order transition in finite systems.     

Preparation of ultrathin membranes by layer-by-layer (LBL) deposition of oppositely charged inorganic colloids

Nanofilms were prepared by alternating deposition of Mg–Al (2:1) NO ₃ ⁻ layered double hydroxide (LDH), hectorite and silica particles present study. The charge density of the oppositely charged materials strongly affect film properties like thickness and ordering. The specific charge of the colloidal particles was measured with the particle charge detector. The sequential build up of the thin films was followed by spectrophotometry and X-ray diffraction (XRD). The surface morphology of the formed multilayers was characterized and film thickness determination was performed by atomic force microscopy. The influence of the charge density of hectorite and silica particles on the LDH/hectorite, LDH/silica film thickness was studied. The results reveal that the LDH concentration has a significant effect on the film thickness while the hectorite and silica concentration were not important. Films prepared from the different types of negatively charged inorganic particles in the same concentration range (0.25–1.0%) have similar thickness because of the much higher surface charge relative to the LDH lamellae.     

Interaction between electrical double layers of soil colloids and Fe/Al oxides in suspensions

Phyllosilicates with net negative surface charge and Fe/Al oxides with net positive surface charge coexist in variable-charge soils, and the interaction between these oppositely charged particles affects the stability of mixed colloids, aggregation, and even the surface chemical properties of variable-charge soils. The interaction of the diffuse layers of electrical double layers between the negatively charged soil colloidal particles and the positively charged particles of goethite or gamma-Al(2)O(3) was investigated in this article through the comparison of zeta potentials between single-soil colloidal systems and binary systems containing soil colloids and Fe/Al oxides. The results showed that the presence of goethite and gamma-Al(2)O(3) increased the zeta potential of the binary system containing soil colloids and Fe/Al oxides, which clearly suggests the overlapping of the diffuse layers in soil colloids and Fe/Al oxides. The overlapping of the diffuse layers leads to a decrease in the effective negative charge density on soil colloid and thus causes a shift of pH-zeta potential curves toward the more positive-value side. The interaction of the electrical double layers is also related to the charge characteristics on the Fe/Al oxides: the higher the positive charge density on Fe/Al oxides, the stronger the interaction of the electrical double layers between the soil colloid particles and the Fe/Al oxides.     

Simulation of secondary particle formation in seeded emulsion polymerization: The effect of surface charge density

Mathematical modeling and simulation were carried out to investigate the effects of the surface charge density of seed particles on secondary particle formation and the rate of polymerization in the early stage of emulsifier-free seeded emulsion polymerization of methyl methacrylate. Limited coagulation theory was applied to simulate new particle nucleation. The main factor influencing the capture rate of oligomeric radicals in a growing seed particle was assumed to be the electrostatic repulsion of seed particles. DLVO (Deryagiun-Landau-Verwey-Overbeek) theory was also introduced to estimate the electrical repulsion between seed particles and oligomeric radicals in the aqueous phase. In the case of highly charged seed particles, the adsorption rate of oligomeric radicals in the aqueous phase showed a strong effect on the polymerization rate. The low adsorption of oligomeric radicals results in a low value of the average number of radicals per particle. The surface charge density of seed particles was found to play an important role in limiting the polymerization rate at the beginning of the reaction and even in affecting the formation of secondary particles.     

Discrete charge effects on the Donnan potential and surface potential of a soft particle

The Donnan potential and surface potential of soft particles (i.e., polyelectrolyte-coated hard particles) in an electrolyte solution play an essential role in their electric behaviors. These potentials are usually derived via a continuum model in which fixed charges inside the surface layer are distributed with a continuous charge density. In this paper, for a plate-like soft particle consisting of a cubic lattice of fixed point charges, on the basis of the linearized Poisson–Boltzmann equation, we derive expressions for the electric potential distribution in the regions inside and outside the surface layer. This expression is given in terms of a sum of the screened Coulomb potentials produced by the point charges within the surface layer. We show that the deviation of the results of the discrete charge model from those of the continuous charge model becomes significant as the ratio of the lattice spacing to the Debye length becomes large.     

Effect of a surface charge on the halfwidth and peak position of cluster plasmons in colloidal metal particles

The optical response of colloidal particles depends on a variety of properties of the cluster, e.g., shape, size, size distribution and particle material. Since particles often are charged, also the surface charge may be a parameter which influences their optical properties. In this paper the effect of a surface charge on optical properties of spherical colloidal particles is studied and its magnitude is estimated by extended computations for silver clusters with surface plasmon in aqueous suspension. Two models are presented and discussed. The first model is based on the electrodynamic solution by Bohren and Hunt (Can. J. Phys. 55, 1930 (1977)), where a surface conductivity _S for a free surface charge yield an additional contribution _S to the dielectric constant of the particle material. In the second model, the surface charge contributes to the number density of free electrons in the cluster. Both models lead to a shift of the cluster plasmon peak, while an increase of the plasmon halfwidth could not be derived. The effect is quite small and limited on very small clusters.PACS 61.46+w 73.20.Mf 78.20.Dj     

Molecular dynamics simulations of polyelectrolyte adsorption

We have performed molecular dynamics simulations of polyelectrolyte adsorption at oppositely charged surfaces from dilute polyelectrolyte solutions. In our simulations, polyelectrolytes were modeled by chains of charged Lennard-Jones particles with explicit counterions. We have studied the effects of the surface charge density, surface charge distribution, solvent quality for the polymer backbone, strength of the short-range interactions between polymers and substrates on the polymer surface coverage, and the thickness of the adsorbed layer. The polymer surface coverage monotonically increases with increasing surface charge density for almost all studied systems except for the system of hydrophilic polyelectrolytes adsorbing at hydrophilic surfaces. In this case the polymer surface coverage saturates at high surface charge densities. This is due to additional monomer-monomer repulsion between adsorbed polymer chains, which becomes important in dense polymeric layers. These interactions also preclude surface overcharging by hydrophilic polyelectrolytes at high surface charge densities. The thickness of the adsorbed layer shows monotonic dependence on the surface charge density for the systems of hydrophobic polyelectrolytes for both hydrophobic and hydrophilic surfaces. Thickness is a decreasing function of the surface charge density in the case of hydrophilic surfaces while it increases with the surface charge density for hydrophobic substrates. Qualitatively different behavior is observed for the thickness of the adsorbed layer of hydrophilic polyelectrolytes at hydrophilic surfaces. In this case, thickness first decreases with increasing surface charge density, then it begins to increase.     

A Monte Carlo study of spherical electrical double layer of macroions-polyelectrolytes systems in salt free solutions

A canonical Monte Carlo simulation is performed to investigate the microstructure and the electrical double layer (EDL) of polyelectrolytes around macroions in the bulk systems based on the primitive model. We explore the influences of particles size, chain length, and charge density of polyelectrolytes on the microscopic behavior of the macroions-polyelectrolytes systems. The simulation results show that the surface charge density and the chain length of the polyelectrolytes are two key factors that affect the microstructure of polyelectrolytes around the macroions and potential of mean force between the macroions as well as the zeta potential of the spherical EDL constructed by polyelectrolytes. The high surface charge density of a polyelectrolyte leads to the polyelectrolyte acting as a bridge for the aggregation of macroions, causing the presence of the attraction between macroions. The polyelectrolytes with a long chain length present a cooperativity effect for the adsorption of the polyelectrolytes on the surface of the macroions. Furthermore, the two key factors both induce the overcharge of the macroions. The longer the chain length and the higher surface charge density of the polyelectrolytes, the stronger is the overcharge.     

Synthesis and characterization of sulphonated core-shell latices in the size range between 30 and 80 nm

The objective of the current work was the synthesis of sulphonated core-shell nanolatices and to investigate to which extend it is possible to control the final surface charge of such latices. For this purpose differently sized polystyrene seed latices with average diameters in the size range between 30 and 80 nm were synthesized by emulsion polymerization. To obtain the final latices, a sulphonated comonomer was incorporated in the outer surface shell of the particles by further reaction of the seed latices with styrene and sodium styrene sulphonate (NaSS). In a first test series the seed latex surface was modified with four different amounts of NaSS. In a second test series four different seed latices were reacted with the same amount of NaSS. In the last set of reactions the seed latices were reacted with different amounts of NaSS and in these reactions the ratio of added NaSS to the specific surface area of the seed latex was kept constant to obtain differently sized latices of the same surface charge density. The yield of sulphonic acid groups in the particle shell was found between 57 and 74% after an intensive cleaning step by ion exchange. The results show possibilities for a reproducible synthesis of small sulphonated latex particles with a desired surface charge density.     

胶体粒子表面有效电荷的实验测量

胶体溶液中带电胶粒的有效电荷是计算粒子间相互作用势的一个重要参数. 在本文中用电导率-粒子数密度关系法和电导滴定法分别研究了七种粒径及表面带电情况均不相同的聚苯乙烯粒子, 结果显示两种测量方法得到的有效电荷数值具有较好的一致性, 误差在7%以内. 同时发现, 经验公式计算的有效电荷差不多是实验值的2倍, 表明文献中的经验公式对于本文所研究的胶体粒子体系不适用.