A. M. Somoza

Two-stage capillary condensation in pores with structured walls: A nonlocal density functional study

We present phase diagrams for capillary condensation in chemically structured slit pores characterized by two first-order transitions from the confined “gas” over “liquid bridges” to “liquid.” The split adsorption is produced by a complex periodic wall potential in one of the lateral directions that mimics inhomogeneities in real materials. After the previous condensation of liquid drops at the most attractive adsorption sites these may combine to form liquid bridges between opposite walls, separated between them by “gas gaps.” Nonlocal density functional theory is employed to investigate this stepwise mechanism and the stability of the liquid bridges phase in function of the thermodynamic conditions and the pore structure, especially the ratio of the two typical lengths, the corrugation period λ and the pore width H. Macroscopic predictions for the subcritical phase equilibria and the critical limit complete the study. The calculations confirm our previous results [P. Rocken and P. Tarazona, J. Chem. Phy...

Self-Assembled Triply Periodic Minimal Surfaces as Molds for Photonic Band Gap Materials

We propose systems with structures defined by self-assembled triply periodic minimal surfaces (STPMS) as candidates for photonic bandgap materials. To support our proposal we have calculated the photonic bands for different STPMS and we have found that, at least, the double diamond and gyroid structures present full photonic bandgaps. Given the great variety of systems which crystalize in these structures, the diversity of possible materials that form them and the range of lattice constants they present, the construction of photonic bandgap materials with gaps in the visible range may be presently within reach.

Scaling of the interfacial tension of microemulsions: A phenomenological description

Recent experiments revealed a striking scaling behavior of the low and ultralow interfacial tension of microemulsions. A description of this behavior based on the Helfrich elastic free energy, which is symmetric in the principal curvatures c1 and c2, appears to be inconsistent. We show that, within the phenomenological theory of membrane bending elasticity, symmetry breaking between the two principal curvatures seems to be required in order to explain the low, but nonzero, values of the interfacial tension and its temperature dependence. We propose two simple generalizations of the Helfrich free energy which describe the experimental results. The first considers a quadratic elastic free energy and anisotropy in the membrane which breaks the symmetry between the two principal curvatures. In the second, which is applicable to systems with positive saddle‐splay rigidities, the symmetry between the two principal curvatures is spontaneously broken by inclusion of higher‐order terms in the curvatures in order t...

LIQUID-CRYSTAL PHASE DIAGRAM OF THE GAY-BERNE FLUID BY PERTURBATION THEORY

A thermodynamic linear perturbation theory for the Gay–Berne intermolecular potential has been developed which is able to predict the occurrence of isotropic liquid‐vapour coexistence as well as the stability of a nematic phase. The theory can be regarded as a generalisation to molecular fluids of the Weeks, Chandler, Andersen (WCA) pertubative scheme for simple fluids. The reference system, a hard Gaussian overlap model, is analysed within density‐functional theory using a standard Onsager‐like approach, the ‘‘decoupling approximation,’’ where density correlations are treated to all orders (albeit approximately) whereas orientational correlations are approximated by the low density limit. We implement this idea by using an equivalent system of hard spheres to approximate the density‐dependent part of the excess free energy. The structure of the reference system is approximated by the radial distribution function of an equivalent system of hard spheres, scaled with the contact distance of the hard core. T...

Elastic constants from a microscopic model of bilayer membrane

A simple microscopic model for amphiphilic molecules dissolved in water allows us to obtain within the same scheme the molecular structure of membranes and micelles, the equilibrium thermodynamics for these aggregates and the elastic constants of the membranes. We present a study of vesicles with cylindrical geometry which, joined to previous results for spherical vesicles, gives the saddle-splay modulus and the bending rigidity. Finally, the constraint on the exchange of molecules between the inner and the outer monolayers is included in the model, calculating the nonlocal bending curvature.

Asymmetric water-oil-amphiphile mixtures: Lamellar phases and droplet microemulsions

A continuum microscopic model for symmetric amphiphilic mixtures, is generalized by considering explicitly water-oil asymmetry, through the interactions between amphiphiles and water and oil. The phase diagram, including lamellar phases, and the properties of water-oil interfaces are studied, using an approximate free energy density-functional, for a wide range of amphiphilic interactions. We also consider the structure and stability of spherical micelles and study the dilute micellar regime. By combining the microscopic density-functional description with the phenomenologic Helfrich elastic free energy, we calculate the elastic properties of the amphiphilic film. Our results for the elastic constant, ks=2k+k, are compared with experimental data.

Theoretical study of the anomalous surface tension properties of liquid crystals

We study the surface properties of a molecular model of a liquid crystal using a density functional theory. The intermolecular interaction includes a Maier-Saupe term as well as terms which break the orientational symmetry at the interface. These latter contributions prove to play an essential role in the explanation of some of the anomalous surface-tension features observed in experimental systems. In particular, a dramatic surface tension maximum above the clearing point TNI is seen to be associated with increased nematic order close to the nematic-vapor interface. In addition, further reduction of the surface tension with decreasing temperature below TNI is observed to be related either with rapidly increasing surface-enhanced order, in which case there is a surface tension minimum, or with growing surface smectic order above the nematic-smectic transition temperature.

3D loop models and the CP(n-1) sigma model.

Many statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and short-loop phases. We map them to CP(n-1) sigma models, where n is the loop fugacity. Using Monte Carlo simulations, we find continuous transitions for n=1, 2, 3, and first order transitions for n≥5. The results are relevant to line defects in random media, as well as to Anderson localization and (2+1)-dimensional quantum magnets.

Negative magnetoresistance in ultrananocrystalline diamond: Strong or weak localization?

Electronic transport of ultrananocrystalline diamond involves the interplay between disorder, Anderson localization, and phase coherence. We show that variable range hopping explains many key features of the conductivity including the large low temperature negative magnetoresistance. Our numerical studies suggest two regimes where the (negative) magnetoresistance varies with magnetic field B such as B2 or B1∕2, respectively, depending on the ratio of the cyclotron orbital radius and the hopping distance. This agrees with experiment, which also points to the expected T−1∕2 temperature dependence of the hopping distance at the critical field.

Length distributions in loop soups.

Statistical lattice ensembles of loops in three or more dimensions typically have phases in which the longest loops fill a finite fraction of the system. In such phases it is natural to ask about the distribution of loop lengths. We show how to calculate moments of these distributions using CP(n-1) or RP(n-1) and O(n) σ models together with replica techniques. The resulting joint length distribution for macroscopic loops is Poisson-Dirichlet with a parameter θ fixed by the loop fugacity and by symmetries of the ensemble. We also discuss features of the length distribution for shorter loops, and use numerical simulations to test and illustrate our conclusions.