Anisotropic lattice models of electrolytes

Anomaly of the dielectric function of water under confinement and its role in van der Waals interactions

We present a theoretical calculation of the changes in the Hamaker constant due to the anomalous reduction of the static dielectric function of water. Under confinement, the dielectric function of water decreases from a bulk value of 80 down to 2. If the confining walls are made of a dielectric material, the Hamaker constant reduces by almost 90%. However, if the confinement is realized with metallic plates, there is little change in the Hamaker constant. Additionally, we show that confinement can be used to decreases the Debye screening length without changing the salt concentration. This in turn is used to change the Hamaker constant in the presence of electrolytes.

The one-dimensional Coulomb lattice fluid capacitor

The one-dimensional Coulomb lattice fluid in a capacitor configuration is studied. The model is formally exactly soluble via a transfer operator method within a field theoretic representation of the model. The only interactions present in the model are the one-dimensional Coulomb interaction between cations and anions and the steric interaction imposed by restricting the maximal occupancy at any lattice site to one particle. Despite the simplicity of the model, a wide range of intriguing physical phenomena arise, some of which are strongly reminiscent of those seen in experiments and numerical simulations of three-dimensional ionic liquid based capacitors. Notably, we find regimes where over-screening and density oscillations are seen near the capacitor plates. The capacitance is also shown to exhibit strong oscillations as a function of applied voltage. It is also shown that the corresponding mean-field theory misses most of these effects. The analytical results are confirmed by extensive numerical simulations.

Field-theoretic description of ionic crystallization in the restricted primitive model

Effects of charge-density fluctuations on a phase behavior of the restricted primitive model are studied within a field-theoretic formalism. We focus on a lambda line of continuous transitions between charge-ordered and charge-disordered phases that is observed in several mean-field theories, but is absent in simulation results. In our study the RPM is reduced to a phi(6) theory, and a fluctuation contribution to a grand thermodynamic potential is obtained by generalizing the Brazovskii approach. We find that in a presence of fluctuations the lambda -line disappears. Instead, a fluctuation-induced first-order transition to a charge-ordered phase appears in the same region of a phase diagram, where the liquid-ionic-crystal transition is obtained in simulations. Our results indicate that the charge-ordered phase should be identified with an ionic crystal.

Universality class of the critical point in the restricted primitive model of ionic systems

A coarse-grained description of the restricted primitive model is considered in terms of the local charge- and number-density fields. Exact reduction to a one-field theory is derived, and exact expressions for the number-density correlation functions in terms of higher-order correlation functions for the charge-density are given. It is shown that in continuum space the singularity of the charge-density correlation function associated with short-wavelength charge-ordering disappears when charge-density fluctuations are included by following the Brazovskii approach. The related singularity of the individual Feynman diagrams contributing to the number-density correlation functions is cured when all the diagrams are segregated into disjoint sets according to their topological structure. By performing a resummation of all diagrams belonging to each set a regular expression represented by a secondary diagram is obtained. The secondary diagrams are again segregated into disjoint sets, and the series of all the secondary diagrams belonging to a given set is represented by a hyperdiagram. A one-to-one correspondence between the hyperdiagrams contributing to the number-density vertex functions, and diagrams contributing to the order-parameter vertex functions in a certain model system belonging to the Ising universality class is demonstrated. Corrections to scaling associated with irrelevant operators that are present in the model-system Hamiltonian, and other corrections specific to the RPM are also discussed.

Thermodynamics of electrolytes on anisotropic lattices

The phase behavior of ionic fluids on simple cubic and tetragonal (anisotropic) lattices has been studied by grand canonical Monte Carlo simulations. Systems with both the true lattice Coulombic potential and continuous-space 1/r electrostatic interactions have been investigated. At all degrees of anisotropy, only coexistence between a disordered low-density phase and an ordered high-density phase with the structure similar to ionic crystal was found, in contrast to recent theoretical predictions. Tricritical parameters were determined to be increasing functions of anisotropy parameters which is consistent with theoretical calculations based on the Debye-Hückel approach. At large anisotropies a two-dimensional-like behavior is observed, from which we estimated the dimensionless tricritical temperature and density for the two-dimensional square lattice electrolyte to be T*(tri)=0.14 and rho*(tri)=0.70.