We present a personal view on the current state of statistical mechanics of Coulomb fluids with special emphasis on the interactions between macromolecular surfaces, concentrating on the weak and the strong coupling limits. Both are introduced for a (primitive) counterion-only system in the presence of macroscopic, uniformly charged boundaries, where they can be derived systematically. Later we show how this formalism can be generalized to the cases with additional characteristic length scales that introduce new coupling parameters into the problem. These cases most notably include asymmetric ionic mixtures with mono-and multivalent ions that couple differently to charged surfaces, ions with internal charge (multipolar) structure and finite static polarizability, where weak and strong coupling limits can be constructed by analogy with the counterion-only case and lead to important new insights into their properties that cannot be derived by any other means. © 2013 AIP Publishing LLC. [http://dx

We reformulate the theory of strong electrostatic coupling in order to describe an asymmetric electrolyte solution of monovalent salt ions and polyvalent counterions using field-theoretical techniques and Monte Carlo simulations. The theory is based on an asymmetric treatment of the different components of the electrolyte solution. The weak coupling Debye-Hückel approach is used in order to describe the monovalent salt ions while a strong coupling approach is used to tackle the polyvalent counterions. This combined weak-strong coupling approach effectively leads to dressed interactions between polyvalent counterions and thus directly affects the correlation attraction mediated by polyvalent counterions between like-charged objects. The general theory is specifically applied to a system composed of two uniformly charged plane-parallel surfaces in the presence of salt and polyvalent counterions. In the strong coupling limit for polyvalent counterions, the comparison with Monte Carlo simulations shows good agreement for large enough values of the electrostatic coupling parameter. We delineate two limiting laws that in fact encompass all the Monte Carlo data.

We investigate the ion distribution and overcharging at charged interfaces with dielectric inhomogeneities in the presence of asymmetric electrolytes containing polyvalent and monovalent ions. We formulate an effective "dressed counterion" approach by integrating out the monovalent salt degrees of freedom and show that it agrees with results of explicit Monte-Carlo simulations. We then apply the dressed counterion approach within the framework of the strong-coupling theory, valid for polyvalent ions at low concentrations, which enables an analytical description for salt effects as well as dielectric inhomogeneities in the limit of strong Coulomb interactions on a systematic level. Limitations and applicability of this theory are examined by comparing the results with simulations.

We investigate theoretical models of room temperature ionic liquids, and find that the experimentally observed camel-shape of the differential capacitance is strongly related to dispersion interactions in these systems. At low surface charge densities, the loss of dispersion interactions in the vicinity of the electrodes generates depleted densities, with a concomitant drop of the differential capacitance. This behavior is not observed in models where dispersion interactions have been removed.

A simple approach is used to introduce effects of ion-ion correlations into the Poisson-Boltzmann theory. The mean-field character of the theory is retained and correlations are approximated by an effective interaction potential, which differs from the Coulombic at short range. In particular, the severe overestimation of the average interaction energy between ions of like charge inherent in the original Poisson-Boltzmann theory, is accounted for by this effective potential. We show that important phenomena due to ion-ion correlations, such as net attraction between surfaces of like charge and charge reversal in double layer systems, are qualitatively and semiquantitatively reproduced by this correlation-corrected theory, which contains no adjustable parameter. The response of net surface interactions to the addition of salt is also captured by the theory and satisfactory quantitative agreement is found with simulation results, even at molar concentrations of divalent salt and in the presence of highly charged surfaces. The mean-field theory is furthermore able to qualitatively predict the way in which bulk salt properties such as the osmotic coefficient and the excess chemical potential depend on the salt concentration. The quantitative performance is poorer than for electric double layer systems, but there is still a substantial improvement relative to the ordinary Poisson-Boltzmann theory.