Effects of asperities on the van der Waals and electric double-layer interactions of two parallel flat plates

Electrostatic interactions between diffuse soft multi-layered (bio)particles: beyond Debye-Hückel approximation and Deryagin formulation

We report a steady-state theory for the evaluation of electrostatic interactions between identical or dissimilar spherical soft multi-layered (bio)particles, e.g. microgels or microorganisms. These generally consist of a rigid core surrounded by concentric ion-permeable layers that may differ in thickness, soft material density, chemical composition and degree of dissociation for the ionogenic groups. The formalism allows the account of diffuse interphases where distributions of ionogenic groups from one layer to the other are position-dependent. The model is valid for any number of ion-permeable layers around the core of the interacting soft particles and covers all limiting situations in terms of nature of interacting particles, i.e. homo- and hetero-interactions between hard, soft or entirely porous colloids. The theory is based on a rigorous numerical solution of the non-linearized Poisson-Boltzmann equation including radial and angular distortions of the electric field distribution within and outside the interacting soft particles in approach. The Gibbs energy of electrostatic interaction is obtained from a general expression derived following the method by Verwey and Overbeek based on appropriate electric double layer charging mechanisms. Original analytical solutions are provided here for cases where interaction takes place between soft multi-layered particles whose size and charge density are in line with Deryagin treatment and Debye-Hückel approximation. These situations include interactions between hard and soft particles, hard plate and soft particle or soft plate and soft particle. The flexibility of the formalism is highlighted by the discussion of few situations which clearly illustrate that electrostatic interaction between multi-layered particles may be partly or predominantly governed by potential distribution within the most internal layers. A major consequence is that both amplitude and sign of Gibbs electrostatic interaction energy may dramatically change depending on the interplay between characteristic Debye length, thickness of ion-permeable layers and their respective protolytic features (e.g. location, magnitude and sign of charge density). This formalism extends a recent model by Ohshima which is strictly limited to interaction between soft mono-shell particles within Deryagin and Debye-Hückel approximations under conditions where ionizable sites are completely dissociated.

A modeling approach to describe the adhesion of rough, asymmetric particles to surfaces

A combined theoretical and experimental study of the adhesion of alumina particles and polystyrene latex spheres to silicon dioxide surfaces was performed. A boundary element technique was used to model electrostatic interactions between micron-scale particles and planar surfaces when the particles and surfaces were in contact. This method allows quantitative evaluation of the effects of particle geometry and surface roughness on the electrostatic interaction. The electrostatic interactions are combined with a previously developed model for van der Waals forces in particle adhesion. The combined model accounts for the effects of particle and substrate geometry, surface roughness and asperity deformation on the adhesion force. Predictions from the combined model are compared with experimental measurements made with an atomic force microscope. Measurements are made in aqueous solutions of varying ionic strength and solution pH. While van der Waals forces are generally dominant when particles are in contact with surfaces, results obtained here indicate that electrostatic interactions contribute to the overall adhesion force in certain cases. Specifically, alumina particles with complex geometries were found to adhere to surfaces due to both electrostatic and van der Waals interactions, while polystyrene latex spheres were not affected by electrostatic forces when in contact with various surfaces.

Interactions between a solid spherical particle and a chemically heterogeneous planar substrate

The Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction forces between a chemically heterogeneous substrate and a spherical particle approaching the surface are calculated using a simple model. This model decomposes the heterogeneous substrate into nanoscale subunits and applies a pairwise summation of forces between each subunit and the approaching particle to determine the net DLVO force. This approach leads to a three-dimensional description of the forces arising from the chemical heterogeneity of the surface. In this three-dimensional realm, we observe the emergence of a substantial lateral force at specific separation distances from the substrate. More specifically, the lateral forces become significantly larger than the normal forces at separation distances between those of the repulsive barrier and the secondary minimum of the DLVO interaction energy curve. These lateral forces are most pronounced at high electrolyte concentrations, particularly at biological salt concentrations of approximately 0.1 M. Furthermore, the lateral forces are found to be significantly higher when the particle is near the edge of a heterogeneous region of the substrate. On the basis of the evidence of this study, and depending on the characteristics of the system, both the physical roughness and the chemical heterogeneity of a surface can significantly affect how a particle will interact with it.

Electrostatic interactions between double layers: influence of surface roughness, regulation, and chemical heterogeneities

Electrostatic interactions between two surfaces as measured by atomic force microscopy (AFM) are usually analyzed in terms of DLVO theory. The discrepancies often observed between the experimental and theoretical behavior are usually ascribed to the occurrence of chemical regulation processes and/or to the presence of surface chemical or morphological heterogeneities (roughness). In this paper, a two-gradient mean-field lattice analysis is elaborated to quantifying double layer interactions between nonplanar surfaces. It allows for the implementation of the aforementioned sources of deviation from DLVO predictions. Two types of ion-surface interaction ensure the adjustment of charges and potentials upon double layer overlap, i.e., specific ionic adsorption at the surfaces and/or the presence of charge-determining ions for the surfaces considered. Upon double layer overlap, charges and potentials are adjusted via reequilibrium of the different ion adsorption processes. Roughness is modeled by grafting asperities on supporting planar surfaces, with their respective positions, shapes, and chemical properties being assigned at will. Local potential and charge distributions are derived by numerically solving the nonlinear Poisson-Boltzmann equation under the boundary conditions imposed by the surface profiles and regulation mechanism chosen. Finite size of the ions is taken into account. A number of characteristic situations are briefly discussed. It is shown how the surface irregularities are reflected in the Gibbs energy of interaction.

Incipient CdS thin film formation

The quality of a final thin film is essentially determined by the processes taking place at incipient CdS deposition, which in turn are strongly influenced by the physicochemical properties of the substrate and liquid in contact. SEM pictures of deposits formed through steady flow of a supersaturated (with respect to CdS) solution suggest that initially nuclei are continuously generated on the substrate and grow as discrete "surface" particles. With time, these particles tend to "coalesce" with neighboring ones, while new nuclei keep forming and growing, leading to the formation of a coherent film. There is evidence that similar growth patterns prevail in CdS deposition via the chemical bath deposition (CBD) process. Based on experimental observations, a simple model is developed, which is capable of predicting macroscopically determined film characteristics such as the temporal thickness evolution including the "induction period." Two cases of the growth pattern are examined theoretically; one based on instantaneous surface nucleation (due to its simplicity) and another with a constant surface nucleation rate, which appears to be closer to experimental observations.

Cation-induced collapse of low-molecular-weight polyacrylic acid in the dispersion of barium titanate

Observations on the steric layers formed by the adsorption of low-molecular-weight polyacrylic acid (PAA) were taken using the colloidal probe method in an atomic force microscope. The effects of divalent barium ions and of monovalent potassium ions at varying concentrations were observed on the repulsive interaction profiles. High ionic concentrations screened double-layer forces to small distances, whereby the acting forces were reduced to steric interactions. De Gennes scaling theory was used to model the effect of electrolyte on an aqueous barium titanate system, which was stabilized with PAA. The brush model was found to represent the force curves better than the mushroom model. The collapse of PAA layers with increasing salt approximated a grafted polymer brush in monovalent electrolyte, but the addition of barium ions caused markedly less steric collapse. It is suggested that the formation of a Ba(2+)-PAA complex in the adsorbed layer increases its compressibility parameter.

Microflotation Suppression and Enhancement Caused by Particle/Bubble Electrostatic Interaction

The processes of attachment and detachment of small or medium-sized particles to relatively large bubbles during microflotation are considered in terms of the heterocoagulation theory. Calculations are made for the conditions that the surface potentials are of similar sign and constant, that one of the surface potentials is small, that hydrophobic attraction is absent, and that there are no surface deformations. Under these conditions bubble-particle aggregates may form as a result of an electrostatic attraction which exceeds the repulsive van der Waals force at intermediate distances. Next to electrostatic and van der Waals forces, hydrodynamic and gravitational forces are considered. These forces may overcome the electrostatic repulsion at large distances and promote particle bubble attachment. Strong electrostatic attraction at small distances, arising at a large difference of the surface potentials of the bubble and the particle and of low electrolyte concentrations, can prevent subsequent detachment by hydrodynamic and gravitational forces. With increasing electrolyte concentration the electrostatic barrier increases and the attractive electrostatic force diminishes. As a result, a critical electrolyte concentration for microflotation exists. Above this concentration attachment may still occur but it is followed by detachment. At lower electrolyte concentrations the electrostatic attractive force prevents the detachment. The dependence of the critical electrolyte concentration on the values of the bubble and particle potentials and the Hamaker constant is calculated. The critical concentration does not depend on particle or bubble size if the absolute values of the total detachment force and the total pressing force coincide, which is the case for Stokes and potential flow. For every electrolyte concentration lower than the critical value there are two critical particle sizes that limit the flotation possibility. For small particle sizes attachment is impossible because the pressing force is smaller than the electrostatic barrier. For large particle sizes detachment cannot be prevented because the detachment force exceeds the maximum electrostatic attraction. A microflotation domain of intermediate particle sizes exists in which irreversible heterocoagulation occurs. Copyright 2001 Academic Press.

A Model for Calculating Electrostatic Interactions between Colloidal Particles of Arbitrary Surface Topology

A numerical model for calculating the electrostatic interaction between two particles of arbitrary shape and topology is described. A key feature of the model is a generalized discretization program, capable of simulating any desired analytical shape as a set of flat, triangular elements. The relative sizes of the elements are adjusted using a density function to better match the desired shape and the spatial variation of the electrical surface properties on each particle. The distribution of either surface potential or surface charge density is then calculated using a boundary element approach to solve the linearized Poisson-Boltzmann equation. Example interaction energy profiles are calculated for three different types of roughness-bumps, pits, and surface waves. It is found that the interaction energy between rough particles remains different from that between two equivalent smooth spheres at all separations, even for gap widths much larger than either the solution Debye length or the characteristic roughness size. This behavior at large gap widths arises from the nature of the decay of the electric potential away from each particle. In addition, the magnitude of the roughness effect is found to depend greatly on the size and shape of the nonuniformity as well as the electrostatic boundary conditions. For example, for a sphere containing asperities of height equal to 0.2 times the particle radius, the interaction energy can be as much as 50% greater than that between two equivalent spheres under the condition of constant surface potential. At constant surface charge density, the ratio of the interaction energies between rough and smooth spheres was found to either diverge or become zero as contact between the two particles is approached, depending on the nature of the roughness. Changes of this magnitude could clearly have a substantial impact on the stability behavior of a dispersion of such particles. Copyright 2001 Academic Press.

Part II: Theoretical Analysis

Three phenomena involved in the perikinetic coagulation process were studied with regard to their ability to account for the influence of gravity on the coagulation rate: (1) surface charge effects on the pressure in the gap between two approaching particles, through the streaming potential generated by the squeezing flow; (2) free convection induced by temperature changes in the surroundings; (3) surface roughness and hydration force effects on the interaction force between two particles. In a separate paper flow interactions between two identical spheres are shown to be insufficient to explain the influence of gravity on coagulation rate. Of these phenomena studied, a combination of surface roughness and free convection can explain the influence of gravity on coagulation. Copyright 1998 Academic Press.