The effect of the relative permittivity on the tactoid formation in nanoplatelet systems. A combined computer simulation, SAXS, and osmotic pressure study.

The structural properties, and the intracrystalline swelling of Na+-, and Ca2+-montmorillonite (Na-, and Ca-mmt) have been investigated as an effect of decreasing the relative permittivity of the solvent, i.e. from water to ethanol (EtOH), utilizing the experimental techniques; small angle X-ray scattering (SAXS) and osmotic pressure measurements. The experimental data were compared with the continuum model, utilizing coarse-grained molecular dynamics bulk simulations, Monte Carlo simulations of two infinite parallel surfaces corresponding to two clay platelets, and the strong coupling theory. It was found that it is possible to tune the electrostatic interactions to obtain a transition from a repulsive to an attractive system for the Na-mmt by increasing the EtOH concentration, i.e. the Bjerrum length increases, and hence, the attractive ion-ion correlation forces are enhanced. A qualitative agreement was observed between the simulations and the experimental results. Moreover, a non-monotonic behavior of the intracrystalline swelling of Ca-mmt as a function of EtOH concentration was captured experimentally, where an increase in the osmotic pressure, and hence, an increase in the d-spacing was found at low concentrations, indicating that repulsive short-ranged interactions dominate in the system. Theoretically, the non-monotonic behavior could not be captured with the continuum model, probably due to the limitation that the electrostatic interactions solely enters the Hamiltonian via the Bjerrum length.

Dielectric response from lattices of dipoles with fixed orientation.

The properties of dipolar cubic lattices are studied and the paradox of how to obtain a long range polarization in such lattices is resolved by choosing a proper shape of the total system. It has been shown that large but finite number of aligned dipoles prefer to exist as needle shaped macroscopic particles [M. Yoon and D. Tománek, J. Phys.: Condens. Matter 22, 455105 (2010)]. The total energy for a particle in such a system has one short range contribution depending on the packing (the chosen lattice) and one long range term depending on the dipole density of the system. We show that the latter term corresponds exactly to the polarization term from a dielectric medium embedding a sphere of the considered system. There is no need to include a dielectric medium in this modeling and the "dielectric stabilization" is generated solely by the dipoles of the system.

Interaction and aggregation of charged platelets in electrolyte solutions: a coarse-graining approach.

A coarse-graining approach has been developed to replace the effect of explicit ions with an effective pair potential between charged sites in anisotropic colloidal particles by optimizing a potential of mean force against the results of simulations of two such colloidal particles with all ions in a cell model. More specifically, effective pair potentials were obtained for charged platelets in electrolyte solutions by simulating two rotating parallel platelets with ions at the primitive model level, enclosed in a cylindrical cell. One-component bulk simulations of many platelets interacting via the effective pair potentials are in excellent agreement with the corresponding bulk simulations with all mobile charges present. The bulk simulations were mainly used to study the effects of platelet size, flexibility, and surface charge density on platelet aggregation in an aqueous 2:1 electrolyte, but systems in a 1:1 electrolyte were also investigated.

Monte Carlo simulations of parallel charged platelets as an approach to tactoid formation in clay.

The free energy of interaction between parallel charged platelets with divalent counterions has been calculated using Monte Carlo simulations to investigate the electrostatic effects on aggregation. The platelets are primarily intended to represent clay particles. With divalent counterions, the free energy for two platelets or two tactoids (clusters of parallel platelets) shows a minimum at a short separation due to the attraction caused by ion-ion correlations. In a salt-free system, the free energy of interaction has a long-range repulsive tail beyond the minimum. The repulsion increases for tactoids with larger aggregation numbers, whereas the depth of the free-energy minimum is gradually reduced. For large enough aggregation numbers, the repulsion is dominating and the minimum is no longer a global free-energy minimum. This is an effect of the depletion of counterions free in solution (outside tactoids) as counterions and platelets aggregate into tactoids and the resulting redistribution of counterions in the system changes the effective interactions between platelets and tactoids. The difference in tactoid-tactoid interactions as a function of aggregation number can be removed by adding enough salt to mask the depletion. Adding salt also reduces the repulsive tail of the free energy of interaction and enhances the minimum. No dependence on the aggregation number suggests that an isodesmic model with a monotonically decaying distribution of aggregation numbers can be used to describe a clay system. This may help to explain the experimental observations of low average numbers of platelets in tactoids, although factors not included in the simulation model may also play an important role.