Exact results and mean field approximation for a model of molecular aggregation

We present a simple one-dimensional model with molecular interactions favouring the formation of clusters with a defined optimal size. Increasing the density, at low temperature, the system goes from a nearly-ideal gas of independent molecules to a system with most of the molecules in optimal clusters, in a way that resembles the formation of micelles in a dilution of amphiphilic molecules, at the critical micellar concentration. Our model is simple enough to have an exact solution, but it contains some basic features of more realistic descriptions of amphiphilic systems: molecular excluded volume and molecular attractions which are saturated at the optimal cluster. The comparison between the exact results and the mean field density functional approximation suggests new approaches to study the more complex and realistic models of micelle formation; in particular it addresses the long-standing controversy surrounding separation of internal degrees of freedom in the formulation of cluster association phenomena.Comment: 7 pages, 5 figures, some minor correction

Dynamic Density Functional theory for steady currents: Application to colloidal particles in narrow channels

We present the theoretical analysis of the steady state currents and density distributions of particles moving with Langevin dynamics, under the effects of an external potential displaced at constant rate. The Dynamic Density Functional (DDF) formalism is used to introduce the effects of the molecular interactions, from the equilibrium Helmholtz free energy density functional. We analyzed the generic form of the DDF for one-dimensional external potentials and the limits of strong and weak potential barriers. The ideal gas case is solved in a closed form for generic potentials and compared with the numerical results for hard-rods, with the exact equilibrium free energy. The results may be of relevance for microfluidic devices, with colloidal particles moving along narrow channels, if external driving forces have to compete with the brownian fluctuations and the interaction forces of the particles

Simple model for the phase coexistence and electrical conductivity of alkali fluids

We report the first theoretical model for the alkali fluids which yields a liquid-vapor phase coexistence with the experimentally observed features and electrical conductivity estimates which are also in accord with observations. We have carried out a Monte Carlo simulation for a lattice gas model which allows an integrated study of the structural, thermodynamic, and electronic properties of metal-atom fluids. Although such a technique is applicable to both metallic and nonmetallic fluids, non-additive interactions due to valence electron delocalization are a crucial feature of the present model.Comment: RevTex, 11 pages, 2 ps figure files appended, submitted to PR

Study of theoretical models for the liquid-vapor and metal-nonmetal transitions of alkali fluids

Theoretical models for the liquid-vapor and metal-nonmetal transitions of alkali fluids are investigated. Mean-field models are considered first but shown to be inadequate. An alternate approach is then studied in which each statistical configuration of the material is treated as inhomogeneous, with the energy of each ion being determined by its local environment. Nonadditive interactions, due to valence electron delocalization, are a crucial feature of the model. This alternate approach is implemented within a lattice-gas approximation which takes into account the observed mode of expansion in the materials of interest and which is able to treat the equilibrium density fluctuations. We have carried out grand canonical Monte Carlo simulations, for this model, which allow a unified, self-consistent, study of the structural, thermodynamic, and electronic properties of alkali fluids. Applications to Cs, Rb, K, and Na yield results in good agreement with observations.Comment: 13 pages, REVTEX, 10 ps figures available by e-mail

Growth in systems of vesicles and membranes

We present a theoretical study for the intermediate stages of the growth of membranes and vesicles in supersaturated solutions of amphiphilic molecules. The problem presents important differences with the growth of droplets in the classical theory of Lifshitz-Slyozov-Wagner, because the aggregates are extensive only in two dimensions, but still grow in a three dimensional bath. The balance between curvature and edge energy favours the nucleation of small planar membranes, but as they grow beyond a critical size they close themselves to form vesicles. We obtain a system of coupled equations describing the growth of planar membranes and vesicles, which is solved numerically for different initial conditions. Finally, the range of parameters relevant in experimental situations is discussed.Comment: 13 pages and 5 postscript figures. To appear in Phys. Rev

Density functional for hard hyperspheres from a tensorial-diagrammatic series

We represent the free energy functional by a diagrammatic series with tensorial coefficients indexed by powers of length scale. For hard cores, we obtain Percus' exact functional in one dimension and the Kierlik-Rosinberg form of fundamental measures theory in three dimensions. In five dimensions, the functional describes bulk fluids better than Percus-Yevick theory does. At planar walls density profiles oscillate with smaller periods than in lower dimensions. Our findings open up avenues for treating both more general high-dimensional systems, as well as three-dimensional mixtures via dimensional reduction.Comment: 12 pages, 4 figure

The structure of ionic aqueous solutions at interfaces: An intrinsic structure analysis.

We investigate the interfacial structure of ionic solutions consisting of alkali halide ions in water at concentrations in the range 0.2-1.0 molal and at 300 K. Combining molecular dynamics simulations of point charge ion models and a recently introduced computational approach that removes the averaging effect of interfacial capillary waves, we compute the intrinsic structure of the aqueous interface. The interfacial structure is more complex than previously inferred from the analysis of mean profiles. We find a strong alternating double layer structure near the interface, which depends on the cation and anion size. Relatively small changes in the ion diameter disrupt the double layer structure, promoting the adsorption of anions or inducing the density enhancement of small cations with diameters used in simulation studies of lithium solutions. The density enhancement of the small cations is mediated by their strong water solvation shell, with one or more water molecules anchoring the ion to the outermost water layer. We find that the intrinsic interfacial electrostatic potential features very strong oscillations with a minimum at the liquid surface that is ∼4 times stronger than the electrostatic potential in the bulk. For the water model employed in this work, SPC/E, the electrostatic potential at the water surface is ∼-2 V, equivalent to ∼80 kBT (for T = 300 K), much stronger than previously considered. Furthermore, we show that the utilization of the intrinsic surface technique provides a route to extract ionic potentials of mean force that are not affected by the thermal fluctuations, which limits the accuracy of most past approaches including the popular umbrella sampling techniqueThe following article appeared in Journal of Chemical Physics 137.11 (2012): 114706 and may be found at http://scitation.aip.org/content/aip/journal/jcp/137/11/10.1063/1.4753986Financial support for this work was provided by The Royal Society and the Dirección General de Investigación, Ministerio de Ciencia y Tecnología of Spain, under Grant No. FIS2010-22047-C05, and by the Comunidad Autónoma de Madrid under the R&D rogram of activities MODELICO-CM/S2009ESP-1691. F.B. would like to thank the EPSRC for the award of a Leadership Fellowshi