A. Ionic liquids. In recent years, standard capacitors have largely been replaced by electric double layer capacitors, EDLCs, also called ``supercapacitors''. EDLCs are much more efficient devices. Here, charge separation is provided by the electric
double layer that forms at electrodes immersed in an electrolyte. The narrow width of the Debye length, combined with the large
area of nanoporous electrodes, can lead to an enormous capacitance. In this project, we use a combination of classical density functional theory, and MD+MC simulations, to elucidate structure, thermodynamics and capacitance of models of nanoporous electrodes, immersed in ionic liquids, or ionic liquid + solvent mixtures.
B. Many-body interactions. It is well-known that the addition of non-adsorbing polymers can destabilize a dispersion of colloidal particles. This is driven by the net attraction that results when polymers are depleted from the regions between particles. The classical model to study depletion effects is a suspension of inert hard sphere particles, immersed in a solution of ideal polymers. This model has attracted a lot of experimental and theoretical attention. Despite its apparent simplicity, the model is not easy to analyze theoretically. We have recently addressed this system from the point of view of an effective potential theory. Averaging over polymer configurations defines a many-body potential of mean force between the colloidal particles. We have recently developed a useful effective N-body potential between hard-sphere particles, immersed in an ideal polymer solution, which appears accurate to all-orders in N. Our theory utilizes a generalization of the Edwards-deGennes treatment of continuous chains. Thus, polymer configurations are appropriately accounted for. While promising, our theory still awaits direct comparisons with full-scale simulation treatments, of identical model systems. We are furthermore expanding the theory to treat interacting chains, which also will require extensive simulations, for a proper accuracy-evaluation.
C. Temperature-dependent polymer-mediated interactions. We have developed models for polymer solutions that display a lower critical solution temperature, LCST. In the presence of colloidal particles, these systems display a temperature response that often is counterintuitive and non-monotonic. We utilize classical polymer density functional theory to establish potential of mean forces, which are then imported to a Metropolis Monte Carlo code, permitting an implicit polymer approach. Nevertheless, the presence of long-ranged barriers and short ranged but deep minima, presents computational challenges. These can be alleviated by cluster moves, but the simulations remain computationally expensive. An interesting finding is the occurrence of equilibrium polymers, where the monomers are composed of colloidal particles, onto which polymers are grafted. Such structures can form through the combination of a deep but short-ranged free energy minimum, and a long-ranged repulsion. These interactions tend to cause particles in a cluster to align themselves linearly, as this will reduce the overall repulsion, yet retain the attraction. . This phenomenon is primarily observed at particle volume fractions that are low enough to prevent the polymers joining to form a 3-dimensional network (i.e. a gel).