Energetics of Colloids: Do Oppositely Charged Particles Necessarily Attract Each Other?

Abstract

The electrostatic free energy of two oppositely charged macroions, suspended in ionic solution is calculated for different distances between the macroions. This is done by using a lattice field theory formulation of the statistical mechanics of Coulomb gas particles of finite size interacting with a fixed charge distribution (J. Chem. Phys. 1995, 102,4584). In many cases, it is found that, regardless of the size of the mobile ions, the minimum of the free energy is at a separation between the macroions corresponding to a noncontact configuration. Illustrative examples, which emphasize the source of the repulsion at near-touching configurations are presented and discussed. The intriguing experimental study of oppositely charged colloidal particles,’ the development of novel theoretical approaches to these and a thorough examination of the need for a long-range attraction-repulsion rather than the commonly used repulsion-only potential between negatively charged macro ion^,^ all of which have emerged during the last couple of years, are drawing the attention of the scientific community to colloid sciences. Since the beginning of colloid sciences in the early 1800s the vast majority of systems of interacting macroions which have been studied (both experimentally and the~retically)~,’ have been composed of macroions with the same sign charge. For fluids and crystals of charged polystyrene spheres (“polyballs”), for example, the case with all polyballs negatively charged has received by far the most attention. These systems are relatively easy to prepare. In addition, like charges on all the polyballs keep these macroions from aggregating. Indeed, these systems can, under appropriate conditions (mainly associated with the ionic strength of the aqueous environment), order into stable crystalline arrays. Nevertheless, positively charged polyballs have been synthesized, and the possibility that under appropriate conditions a stable & polyball system can be prepared is currently under study.’ It certainly motivates more detailed studies of the interactions between oppositely charged macroions suspended in ionic solutions. Recently we used a lattice field theory (LlT) formulation of the statistical mechanics of interacting macroions to carry out a theoretical study of the effect of the dielectric constant on the energetics of oppositely charged p~lyballs.~~ Throughout our study, simple (mobile) ions were assumed to be infinitesimal. The most important (perhaps surprising) result of our study was that in many cases the minimum of the free energy was at a separation between the polyballs corresponding to a noncontact rather than a near-touching configuration. Very recently the LFT formalism has been generalized to treat mobile ions having a finite The present letter extends our theoretical studies of systems of two oppositely charged polyballs, having different charges and dielectric constants, with different ionic strengths for mobile ions which have finite sizes. The formalism will be briefly introduced, followed by results of our calculations. The results, which will be presented, emphasize the physical origin of the repulsive forces between oppositely charged polyballs.