Origin of attraction between likely charged hydrophobic and hydrophilic walls confining near-critical binary aquaeous mixture with ions

Effect of ionic solute on a near-critical binary aqueous mixture confined between charged walls with different adsorption preferences is considered within a simple density functional theory. For the near-critical system containing small amount of ions a Landau-type functional is derived based on the assumption that the correlation, $\xi$, and the Debye screening length, $\kappa^{-1}$, are both much larger than the molecular size. The corresponding approximate Euler-Lagrange equations aresolved analytically for ions insoluble in the organic solvent. Nontrivial concentration profile of the solvent is found near the charged hydrophobic wall as a result of the competition between the short-range attraction of the organic solvent and the electrostatic attraction of the hydrated ions. Excess of water may be present near the hydrophobic surface for some range of the surface charge and $\xi\kappa$. As a result, the effective potential between the hydrophilic and the hydrophobic surface can be repulsive far from the critical point, then attractive and again repulsive when the critical temperature is approached, in agreement with the recent experiment [Nellen at.al., Soft Matter {\bf 7}, 5360 (2011)]

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

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

Correlation functions in ionic liquid at coexistence with ionic crystal. Results of the Brazovskii-type field theory

Correlation functions in the restricted primitive model are calculated within a field-theoretic approach in the one-loop self-consistent Hartree approximation. The correlation functions exhibit damped oscillatory behavior as found before in the Gaussian approximation [Ciach at. al., J. Chem. Phys. {\bf 118}, 3702 (2003)]. The fluctuation contribution leads to a renormalization of both the amplitude and the decay length of the correlation functions. The renormalized quantities show qualitatively different behavior than their mean-field (MF) counterparts. While the amplitude and the decay length both diverge in MF when the $\lambda$-line is approached, the renormalized quantities remain of order of unity in the same dimensionless units down to the coexistence with the ionic crystal. Along the line of the phase transition the decay length and the period of oscillations are independent of density, and their values in units of the diameter of the ions are $\alpha_0^{-1}\approx 1$ and $2\pi/\alpha_1\approx 2.8$ respectively.Comment: 21 pages including 9 figure

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

Phase behavior of hard spheres confined between parallel hard plates: Manipulation of colloidal crystal structures by confinement

We study the phase behavior of hard spheres confined between two parallel hard plates using extensive computer simulations. We determine the full equilibrium phase diagram for arbitrary densities and plate separations from one to five hard-sphere diameters using free energy calculations. We find a first-order fluid-solid transition, which corresponds to either capillary freezing or melting depending on the plate separation. The coexisting solid phase consists of crystalline layers with either triangular or square symmetry. Increasing the plate separation, we find a sequence of crystal structures from n triangular to (n+1) square to (n+1) triangular, where n is the number of crystal layers, in agreement with experiments on colloids. At high densities, the transition between square to triangular phases are intervened by intermediate structures, e.g., prism, buckled, and rhombic phases.Comment: 9 pages, 4 figures. Accepted for publication in J. Phys.: Condens. Matte

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

Thermodynamics and Phase Transitions of Electrolytes on Lattices with Different Discretization Parameters

Lattice models are crucial for studying thermodynamic properties in many physical, biological and chemical systems. We investigate Lattice Restricted Primitive Model (LRPM) of electrolytes with different discretization parameters in order to understand thermodynamics and the nature of phase transitions in the systems with charged particles. A discretization parameter is defined as a number of lattice sites that can be occupied by each particle, and it allows to study the transition from the discrete picture to the continuum-space description. Explicit analytic and numerical calculations are performed using lattice Debye-H\"{u}ckel approach, which takes into account the formation of dipoles, the dipole-ion interactions and correct lattice Coulomb potentials. The gas-liquid phase separation is found at low densities of charged particles for different types of lattices. The increase in the discretization parameter lowers the critical temperature and the critical density, in agreement with Monte Carlo computer simulations results. In the limit of infinitely large discretization our results approach the predictions from the continuum model of electrolytes. However, for the very fine discretization, where each particle can only occupy one lattice site, the gas-liquid phase transitions are suppressed by order-disorder phase transformations.Comment: Submitted to Molecular Physic

X-Ray Scattering at FeCo(001) Surfaces and the Crossover between Ordinary and Normal Transitions

In a recent experiment by Krimmel et al. [PRL 78, 3880 (1997)], the critical behavior of FeCo near a (001) surface was studied by x-ray scattering. Here the experimental data are reanalyzed, taking into account recent theoretical results on order-parameter profiles in the crossover regime between ordinary and normal transitions. Excellent agreement between theoretical expectations and the experimental results is found.Comment: 9 pages, Latex, 1 PostScript figure, to be published in Phys.Rev.