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 (RPM) 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 (MF) 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.Comment: 31 pages, 10 figure

Effects of confinement on pattern formation in two dimensional systems with competing interactions

Template-assisted pattern formation in monolayers of particles with competing short-range attraction and long-range repulsion interactions (SALR) is studied by Monte Carlo simulations in a simple generic model [N. G. Almarza et al., J. Chem. Phys., 2014, 140, 164708]. We focus on densities corresponding to formation of parallel stripes of particles and on monolayers laterally confined between straight parallel walls. We analyze both the morphology of the developed structures and the thermodynamic functions for broad ranges of temperature T and the separation L between the walls. At low temperature stripes parallel to the boundaries appear, with some corrugation when the distance between the walls does not match the bulk periodicity of the striped structure. The stripes integrity, however, is rarely broken for any L. This structural order is lost at T = T(L) depending on L according to a Kelvin-like equation. Above the Kelvin temperature T(L) many topological defects such as breaking or branching of the stripes appear, but a certain anisotropy in the orientation of the stripes persists. Finally, at high temperature and away from the walls, the system behaves as an isotropic fluid of elongated clusters of various lengths and with various numbers of branches. For L optimal for the stripe pattern the heat capacity as a function of temperature takes the maximum at T = T(L).Peer Reviewe

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 ito 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

Partial integration and local mean-field approach for a vector lattice model of microemulsions

A vector model on the simple cubic lattice, describing a mixture of water, oil, and amphiphile, is considered. An integration over the amphiphile orientational degrees of freedom is performed exactly in order to obtain an effective Hamiltonian for the system. The resulting model is a three-state (spin-1) system and contains many-site interaction terms. The analysis of the ground state reveals the presence of the water-oil-rich phase as well as the amphiphile-rich and the cubic phases. The temperature phase diagram of the system is analyzed in a local mean-field approach, and a triple line of water-rich, oil-rich, and microemulsion coexistence is obtained. For some values of the model parameters, lamellar phases also appear in the system, but only at finite temperature. The Lifshitz line is determined in a semianalytical way in order to locate the microemulsion region of the disordered phase

Mesoscopic theory for size- and charge- asymmetric ionic systems. I. Case of extreme asymmetry

A mesoscopic theory for the primitive model of ionic systems is developed for arbitrary size, $\lambda=\sigma_+/\sigma_-$, and charge, $Z=e_+/|e_-|$, asymmetry. Our theory is an extension of the theory we developed earlier for the restricted primitive model. The case of extreme asymmetries $\lambda\to\infty$ and $Z \to\infty$ is studied in some detail in a mean-field approximation. The phase diagram and correlation functions are obtained in the asymptotic regime $\lambda\to\infty$ and $Z \to\infty$, and for infinite dilution of the larger ions (volume fraction $n_p\sim 1/Z$ or less). We find a coexistence between a very dilute 'gas' phase and a crystalline phase in which the macroions form a bcc structure with the lattice constant $\approx 3.6\sigma_+$. Such coexistence was observed experimentally in deionized aqueous solutions of highly charged colloidal particles

Bistability in a self-assembling system confined by elastic walls: Exact results in a one-dimensional lattice model

© 2015 AIP Publishing LLC. The impact of confinement on self-assembly of particles interacting with short-range attraction and long-range repulsion potential is studied for thermodynamic states corresponding to local ordering of clusters or layers in the bulk. Exact and asymptotic expressions for the local density and for the effective potential between the confining surfaces are obtained for a one-dimensional lattice model introduced by J. Pękalski et al. [J. Chem. Phys. 138, 144903 (2013)]. The simple asymptotic formulas are shown to be in good quantitative agreement with exact results for slits containing at least 5 layers. We observe that the incommensurability of the system size and the average distance between the clusters or layers in the bulk leads to structural deformations that are different for different values of the chemical potential μ. The change of the type of defects is reflected in the dependence of density on μ that has a shape characteristic for phase transitions. Our results may help to avoid misinterpretation of the change of the type of defects as a phase transition in simulations of inhomogeneous systems. Finally, we show that a system confined by soft elastic walls may exhibit bistability such that two system sizes that differ approximately by the average distance between the clusters or layers are almost equally probable. This may happen when the equilibrium separation between the soft boundaries of an empty slit corresponds to the largest stress in the confined self-assembling system.Peer Reviewe