Volume-term theories, Sogami-Ise potential, and the Langmuir model for phase separation in macroion systems: a resolution

Long-range forces and charge inversions in model charged colloidal dispersions at finite concentration

In charged colloidal dispersion systems the interest is in finding their stability conditions, phase transitions, and transport properties, either in bulk or confinement, among other physicochemical quantities, for which the knowledge of the dispersions' molecular structure and the associated macroion-macroion forces is crucial. To investigate these phenomena simple models have been proposed. Most of the theoretical and simulation studies on charged particles suspensions are at infinite dilution conditions. Hence, these studies have been focused on the electrolyte structure around one or two isolated central particle(s), where phenomena as charge reversal, charge inversion and surface charge amplification have been shown to be relevant. However, experimental studies at finite volume fraction exhibit interesting phenomenology which imply very long-range correlations. A simple, yet useful, model is the Colloidal Primitive Model, in which the colloidal dispersion is modeled as a mixture of size (and charge) asymmetrical hard spheres, at finite volume fraction. In this paper we review recent integral equations solutions for this model, where very long-range attractive-repulsive forces, as well as new long-range, giant charge inversions are reported. The calculated macroions radial distribution functions, charge distributions, and macroion-macroion forces are qualitatively consistent with existing experimental results, and Monte Carlo and molecular dynamics simulations.

Nonlinear Poisson-Boltzmann equation in spherical symmetry

The Poisson-Boltzmann problem in spherical symmetry has been considered using the distribution of a self-consistent potential around a charged grain in a thermal collisional plasma as an example. The qualitative patterns of all possible solutions have been presented and a study of their asymptotics has been carried out. It has been demonstrated that for large potentials it is possible to neglect the curvature of the grain surface and to use the solution of the plane problem. It has also been demonstrated that the electrical interaction of the grains is possible only at distances smaller than eight screening lengths.

Electro-osmotic equilibria for a semipermeable shell filled with a solution of polyions

The authors study theoretically the electrostatic equilibria for a shell filled with a suspension of polyions (e.g., colloids, polyelectrolytes, etc.) and immersed in an infinite salt-free reservoir. The shell is treated as impermeable for polyions, but allowing free diffusion of counterions. From the solution of the linearized Poisson-Boltzmann equation we obtain the distribution of the potential and concentration profiles for polyions. The authors then derive explicit formulas for the excess electro-osmotic pressure of a polyion solution exerted by the shell. This is shown to be due to a concentration of polyions at the inner shell boundary and can be very different from the pressure of a corresponding bulk polyion solution.

Heterogeneous structure in colloidal systems: the role of the microion disposition

Under certain conditions colloidal systems exhibit a heterogeneous structure sometimes referred to as a "two state" structure, "spinodal instability," or a "phase separation." The present study focuses on the "orbital model" for the description of two geometries of colloidal clusters: a 7-particle diamond shape array and an 8-particle simple cubic array. The orbital model envisions the distribution of the microions as being dictated by the specific configuration of all the macroions in the system, in much the same way that electron distributions in molecules are determined by the array of atoms. Brownian dynamics simulations were performed as two similar clusters approached each other in rectangular cells at the volume fraction of phi(p)=0.01. The number distributions of both the counterion and coion species were determined three ways: the one-dimensional projection along the long axis of the computations cell; the three-dimensional number distributions in "real" space; and a "constant concentration" contour profile. It was found that as the two clusters approached each other the diamond cluster system became less stable whereas the simple cubic cluster system became more stable. This difference in behavior is attributed to the relative abilities of these structures to "share" counterions and the exclusion of the coions.