Effect of charge-density fluctuations on the order-disorder transition in the lattice restricted primitive models of electrolytes

Lattice Model Results for Pattern Formation in a Mixture with Competing Interactions

A monolayer consisting of two types of particles, with energetically favored alternating stripes of the two components, is studied by Monte Carlo simulations and within a mesoscopic theory. We consider a triangular lattice model and assume short-range attraction and long-range repulsion between particles of the same kind, as well as short-range repulsion and long-range attraction for the cross-interaction. The structural evolution of the model upon increasing temperature is studied for equal chemical potentials of the two species. We determine the structure factor, the chemical potential-density isotherms, the specific heat, and the compressibility, and show how these thermodynamic functions are associated with the spontaneous formation of stripes with varying degrees of order.

Field theory for size- and charge-asymmetric primitive model of ionic systems: mean-field stability analysis and pretransitional effects

The primitive model of ionic systems is investigated within a field-theoretic description for the whole range of diameter-, lambda , and charge, Z ratios of the two ionic species. Two order parameters (OP) are identified. The relation of the OP's to physically relevant quantities is nontrivial. Each OP is a linear combination of the charge density and the number-density waves. Instabilities of the disordered phase associated with the two OP's are determined in the mean-field approximation (MF). In MF a gas-liquid separation occurs for any Z and lambda is not equal to 1 . In addition, an instability with respect to various types of periodic ordering of the two kinds of ions is found. Depending on lambda and Z , one or the other transition is metastable in different thermodynamic states. For sufficiently large size disparity we find a sequence of fluid-crystal-fluid transitions for the increasing volume fraction of ions, in agreement with experimental observations. The instabilities found in MF represent weak ordering of the most probable instantaneous states, and are identified with structural loci associated with pretransitional effects.

Simulation of symmetric tricritical behavior in electrolytes

Despite extensive experimental, theoretical, and simulation efforts, a unified description of ionic phase transitions and criticality has not yet emerged. In this work, we investigate the phase behavior of the restricted primitive model of electrolyte solutions on the simple cubic lattice using grand canonical Monte Carlo simulations and finite-size scaling techniques. The phase diagram of the system is distinctly different from its continuum-space analog. We find order-disorder transitions for reduced temperatures T* < or approximately 0.51, where the ordered structures resemble those of the NaCl crystal. The order-disorder transition is continuous for 0.15 < or approximately T* < or approximately 0.51 and becomes first order at lower temperatures. The line of first-order transitions is a line of three-phase coexistence between a disordered and two ordered phases. The line of continuous, second-order transitions meets this line of triple points at a tricritical point at T* approximately equal to 0.1475. We locate the line of continuous transitions, and the line of triple points using finite-size scaling techniques. The tricritical temperature is estimated by extrapolation of the size-dependent tricritical temperatures obtained from a sixth-order Landau expansion of the free energy. Our calculated phase diagram is in qualitative agreement with mean-field theories.

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.

Phase behavior of the lattice restricted primitive model with nearest neighbor exclusion

The global phase behavior of the lattice restricted primitive model with nearest neighbor exclusion has been studied by grand canonical Monte Carlo simulations. The phase diagram is dominated by a fluid (or charge-disordered solid) to charge-ordered solid transition that terminates at the maximum density rho*(max)= sqrt 2 and reduced temperature T* approximately equal to 0.29. At that point, there is a first-order phase transition between two phases of the same density, one charge-ordered, and the other charge-disordered. The liquid-vapor transition for the model is metastable, lying entirely within the fluid-solid phase envelope.