Poisson-Boltzmann study of the effective electrostatic interaction between colloids at an electrolyte interface

Abstract

The effective electrostatic interaction between a pair of colloids, both of them located close to each other at an electrolyte interface, is studied by employing the full, nonlinear Poisson-Boltzmann (PB) theory within classical density functional theory. Using a simplified yet appropriate model, all contributions to the effective interaction are obtained exactly, albeit numerically. The comparison between our results and those obtained within linearized PB theory reveals that the latter overestimates these contributions significantly at short inter-particle separations. Whereas the surface contributions to the linear and the nonlinear PB results differ only quantitatively, the line contributions show qualitative differences at short separations. Moreover, a dependence of the line contribution on the solvation properties of the two adjacent fluids is found, which is absent within the linear theory. Our results are expected to enrich the understanding of effective interfacial interactions between colloids.

Electrostatic interaction of particles trapped at fluid interfaces: effects of geometry and wetting properties

“…[11,12] in which κ 1 κ 2 . A similar discrepancy appeared while comparing the interactions within the linear and nonlinear theory for parallel flat surfaces [25]. Thus taking into account particle curvature does not significantly change this result.…”

“…Between the two systems considered below, the data for flat wall interactions for water-lutidine interfaces are taken from Ref. [25] and those for water-octanol interfaces are newly generated here. We mention that all numerical examples presented here have been chosen such that the conditions for applying the DA are satisfied.…”

“…It has been shown that in this case the linearization of the Poisson-Boltzmann (PB) theory is applicable [21]. Recent studies, directed towards the opposite limit of small inter-particle separations, have been performed within the linearized PB theory [22][23][24] or by considering a flat plate geometry [22,24,25] in order to simplify the problem. Whereas the former approximation is often violated at short separations, the latter represents the ideal situation of a contact angle of exactly 90 • and the absence of particle curvature.…”

“…As long as the size of the particles is sufficiently larger than both the length scale of the interaction and the inter-particle separation, which is usually the case for short inter-particle separations we are interested in, one can apply the Derjaguin approximation (DA) using results of the corresponding case of planar walls [27]. Having recently solved this two-plate problem exactly (i.e., without using the superposition approximation) within the nonlinear PB theory [25], we proceed one step further and compute the force between a pair of spheres or parallel cylinders. A similar approach has already been employed and proved to be valid in this context [28,29].…”

Mesoscopic electrohydrodynamic simulations of binary colloidal suspensions

“…For example, the commonly used DLVO potential is not directly applicable, as the electrostatic interaction between Debye layers is expected to be already resolved at large distances, although not when the separation between the colloids becomes small, ||r j − r k || < ∆x. Moreover, a more general description is needed for colloids at fluid interfaces, a topic of active research [39][40][41][42][43]. Finding a correction for electrostatic interactions, such as Eq.…”