Electrostatic attraction and/or repulsion between charged colloids: A (NVT) Monte-Carlo study

We have performed canonical Monte-Carlo simulation of the distribution of counter-ions between two uniformly charged colloids of different geometries (infinite slabs, discoids and spheres). We have calculated the net force (or the pressure) between the colloids as a function of the interparticle separation in order to determine their stability. Simulations were performed within the primitive model which describes short-ranged excluded volume effects and long-ranged electrostatic interactions. Long-ranged behavior of the Coulomb potential has been handle by different numerical procedures: Ewald summations, hypersphere's method or external self-consistent field's approximation. In all cases, the net force between a pair of colloids results from the balance between the electrostatic attraction and the contact repulsion exerted by the condensed counter-ions. In the case of two infinite slabs, both contributions are (in absolute value) of the same order of magnitude: the resulting net force depends on the so-called electrostatic coupling which is the ratio of the counter-ion/surface electrostatic term at contact divided by the thermal energy. At high coupling (high surface density, polyvalent ions and/or low dielectric constant), we have demonstrated the existence of an attractive domain responsible for the cohesion of various lamellar materials (calcic-clay, cement, organic dispersion...). At low coupling (monovalent counterions in water), we have only detected a monotonous swelling behavior (repulsion) of the charged interfaces. We discuss these results on the basis of ionic correlations within the double-layers of condensed counter-ions. In addition to the infinite-slab case, we present results for a pair of discoid and spherical colloids in order to evaluate finite-size effects. By contrast to infinite interfaces, the electrostatic attraction is found to be negligible for a pair of parallel discoids neutralized by monovalent counter-ions (weak coupling conditions); the net force is then repulsive and driven by the contact force. A net attraction is also Found in the case of divalent counter-ions (strong coupling conditions). No attractive regime is found in the case of interacting spheres neutralized by monovalent counter-ions.