Interaction in colloidal systems: Buckling and melting

Melting Is Well-Known, but Is It Also Well-Understood?

Contrary to continuous phase transitions, where renormalization group theory provides a general framework, for discontinuous phase transitions such a framework seems to be absent. Although the thermodynamics of the latter type of transitions is well-known and requires input from two phases, for melting a variety of one-phase theories and models based on solids has been proposed, as a generally accepted theory for liquids is (yet) missing. Each theory or model deals with a specific mechanism using typically one of the various defects (vacancies, interstitials, dislocations, interstitialcies) present in solids. Furthermore, recognizing that surfaces are often present, one distinguishes between mechanical or bulk melting and thermodynamic or surface-mediated melting. After providing the necessary preliminaries, we discuss both types of melting in relation to the various defects. Thereafter we deal with the effect of pressure on the melting process, followed by a discussion along the line of type of materials. Subsequently, some other aspects and approaches are dealt with. An attempt to put melting in perspective concludes this review.

State diagram for the electrostatic adsorption of charged colloids on confining walls: simulation and theory

We study the structure of charged colloidal suspensions under confinement and determine a state diagram for the occurrence of electrostatic adsorption onto the confining walls, an effect that results in the accumulation of particles on the bounding surfaces and that could be relevant in experiments. We use Monte Carlo simulations to quantify this structural transition and perform theoretical calculations based on integral equations. Overall, our results provide a guide for experimentalists dealing with charged colloidal systems to determine the relevance of this purely electrostatic effect.

Monte Carlo study of crystalline order and defects on weakly curved surfaces

We numerically study the ground states of particles interacting via a repulsive Yukawa potential on two rigid substrates shaped as isolated and periodically arranged bumps characterized by a spatially varying Gaussian curvature. Below a critical aspect ratio that describes the substrate deformation, the lattice is frustrated, but defect free. A further increase of the aspect ratio triggers defect unbinding transitions that lower the total potential energy by introducing dislocations either in isolation or within grain boundaries. In the presence of very strong deformations, isolated disclinations are nucleated. We show that the character and spatial distribution of defects observed in the ground state reflect the symmetries and periodicity of the two model surfaces investigated in this study.

Electrical Double-Layer Interaction between Charged Particles near Surfaces and in Confined Geometries

The proximity effect of one or two flat surfaces on the double-layer interaction between two identically charged colloidal particles immersed in an electrolyte is examined. Simple analytical formulas are presented for the interaction of (i) two particles in the vicinity of a charged flat surface and (ii) two particles confined between two parallel plates. It is found that the surface(s) can strongly influence the pairwise interaction of the particles, leading to increase, decrease, or even elimination of the electrostatic interaction, in comparison to the corresponding result in an unbounded electrolyte. Copyright 1999 Academic Press.

On the difference in ionization properties between planar interfaces and linear polyelectrolytes

Ionizable planar interfaces and linear polyelectrolytes show markedly different proton-binding behavior. Planar interfaces protonate in a single broad step, whereas polyelectrolytes mostly undergo a two-step protonation. Such contrasting behavior is explained using a discrete-charge Ising model. This model is based on an approximation of the ionizable groups by point charges that are treated within a linearized Poisson-Boltzmann approximation. The underlying reason as to why planar interfaces exhibit mean-field-like behavior, whereas linear polyelectrolytes usually do not, is related to the range of the site-site interaction potential. For a planar interface, this interaction potential is much more long ranged if compared with that of the cylindrical geometry as appropriate to a linear polyelectrolyte. The model results are in semi-quantitative agreement with experimental data for fatty-acid monolayers, water-oxide interfaces, and various linear polyelectrolytes.