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.

An angle dependent site-renormalized theory for the conformations of n-butane in a simple fluid.

The angular dependent site-renormalized integral equation theory is developed to compute the dihedral conformation distribution and intermolecular pair distributions of n-butane at infinite dilution in a Lennard-Jones solvent. The equations take advantage of the topological diagrammatic expansion of the full angular dependent molecular system by resumming the series in conjunction with the intramolecular degree of freedom. To first order in an angular basis set, the numerical results of these site-renormalized equations are a systematic quantitative improvement over previous methods. In particular, the thermodynamics and conformational distribution of the solute are essentially indistinguishable from simulation.

Criticality, tricriticality, and crystallization in discretized models of electrolytes.

The Restricted Primitive Model of ionic systems is studied within a field-theoretic approach in order to provide a theoretic basis for the qualitative difference in the phase diagrams obtained in simulations for sigma/a=1,sigma/a=2, and sigma/a>/=3 ( a is the lattice constant and sigma is the ion diameter). The evolution of the phase diagrams from the case sigma/a=1 to the case sigma/a=square root[2] [nearest-neighbor ( NN ) occupancy excluded] is studied in the model with NN repulsion, 0/= J0 increases. We argue that this transition corresponds to formation of a bcc ionic crystal. For high densities the ions form an fcc crystal, for which we find a fluctuation-induced first-order charge-ordered-charge-disordered transition, in agreement with recent simulation studies. Our results also shed light on the simulation results obtained for an off-lattice ionic system, for which a schematic phase diagram is constructed.

Effect of space discretization on phase diagrams in ionic systems: a field-theoretic approach.

Using Landau-Ginzburg-Wilson field-theoretic methods we determine for what kind of space discretization the transition between charge-disordered and charge-ordered phases in the restricted primitive model is fluctuation-induced first order. We identify this transition with ionic-crystal formation. We predict four types of generic phase diagrams in ionic systems for various kinds of space discretization for low and intermediate densities of ions. Our results also shed light on the simulation results obtained for an off-lattice ionic system over a wide range of densities, including the fcc crystal.

Complex phase behavior induced by repulsive interactions

For a solid in which the interactions have a hard core plus a simple soft repulsive tail we show, using a perturbation theory, that the possible stable crystalline structures give rise to a rich phase behavior. We find two concomitant critical points each corresponding to phase transitions separating bcc and fcc structures, respectively, and the occurrence of a transition between fcc and bcc phases without change in density. This novel phenomenology may be relevant to the behavior of some metallic systems, colloids, and to water.

Thermodynamically self-consistent theories of fluids interacting through short-range forces.

The self-consistent Ornstein-Zernike approximation (SCOZA), the generalized mean spherical approximation (GMSA), the modified hypernetted chain (MHNC) approximation, and the hierarchical reference theory (HRT) are applied to the determination of thermodynamic and structural properties, and the phase diagram of the hard-core Yukawa fluid (HCYF). We investigate different Yukawa-tail screening lengths lambda, ranging from lambda=1.8 (a value appropriate to approximate the shape of the Lennard-Jones potential) to lambda=9 (suitable for a simple one-body modelization of complex fluids like colloidal suspensions and globular protein solutions). The comparison of the results obtained with computer simulation data shows that at relatively low lambda's all the theories are fairly accurate in the prediction of thermodynamic and structural properties; as far as the phase diagram is concerned, the SCOZA and HRT are able to predict the binodal line and the critical parameters in a quantitative manner. At lambda=4 some discrepancies begin to emerge in the performances of the different theoretical approaches: the MHNC remains, on the whole, reasonably accurate in predicting the energy and the contact value of the radial distribution function; the SCOZA predicts well the equation of state up to the highest lambda values investigated. The GMSA and the MHNC underestimate and overestimate, respectively, the liquid coexisting density, while the SCOZA and HRT yield liquid branches that fall between the two former theoretical predictions, although both appear to overestimate the critical temperature somewhat. At higher lambda's the GMSA and MHNC binodals further worsen, while the SCOZA appears to remain usefully predictive. In general, the predictions of all the theories tend to slightly worsen at low temperatures and high density. The determination of the freezing line, performed by means of a one-phase "freezing criterion" (due to other authors) is not particularly satisfactory within either the SCOZA or the MHNC; the GMSA prediction for the freezing line at lambda=7 and 9 is instead able to follow in a qualitative manner the pattern of the solid-vapor coexistence line as determined through computer simulation studies. The necessity of further assessments of the freezing predictions is also discussed. Finally, versions of the GMSA, SCOZA, and HRT that can be expected to be more accurate for interactions with extremely short-ranged attractions are identified.

The donnan equilibrium: a theoretical study of the effects of interionic forces.

We investigate the conditions under which nonideality in solution influences the Donnan equilibrium. Of the various parameters that characterize this equilibrium, the osmotic pressure established across the Donnan membrane is found to be particularly sensitive to intermolecular interactions between the diffusible and nondiffusible ionic species. Under physiologically appropriate conditions, we find that it is almost never valid to use Debye-Hückel theory to calculate ionic activities: it is important to take proper account of ion size. When the diffusible species is a 1-1 electrolyte, this can be done using the mean spherical approximation (MSA) for a mixture of ions of different diameters. For 2-2, or higher-valent, electrolytes one should also include the effects of the second ionic virial coefficient, which the MSA omits.