J. Torres-Arenas

Discrete perturbation theory for the hard-core attractive and repulsive Yukawa potentials

In this work we apply the discrete perturbation theory [A. L. Benavides and A. Gil-Villegas, Mol. Phys. 97, 1225 (1999)] to obtain an equation of state for the case of two continuous potentials: the hard-core attractive Yukawa potential and the hard-core repulsive Yukawa potential. The main advantage of the presented equation of state is that it is an explicit analytical expression in the parameters that characterize the intermolecular interactions. With a suitable choice of their inverse screening length parameter one can model the behavior of different systems. This feature allows us to make a systematic study of the effect of the variation in the parameters on the thermodynamic properties of this system. We analyze single phase properties at different conditions of density and temperature, and vapor-liquid phase diagrams for several values of the reduced inverse screening length parameter within the interval kappa( *)=0.1-5.0. The theoretical predictions are compared with available and new Monte Carlo simulation data. Good agreement is found for most of the cases and better predictions are found for the long-range ones. The Yukawa potential is an example of a family of hard-core plus a tail (attractive or repulsive) function that asymptotically goes to zero as the separations between particles increase. We would expect that similar results could be found for other potentials with these characteristics.

Discrete perturbation theory for continuous soft-core potential fluids

In this work, we present an equation of state for an interesting soft-core continuous potential [G. Franzese, J. Mol. Liq. 136, 267 (2007)] which has been successfully used to model the behavior of single component fluids that show some water-type anomalies. This equation has been obtained using discrete perturbation theory. It is an analytical expression given in terms of density, temperature, and the set of parameters that characterize the intermolecular interaction. Theoretical results for the vapor-liquid phase diagram and for supercritical pressures are compared with previous and new simulation data and a good agreement is found. This work also clarifies discrepancies between previous Monte Carlo and molecular dynamics simulation results for this potential.

Multiply associating electrolytes in the binding mean spherical approximation: Thermodynamic properties and speciation

Ionic solutions exhibiting multiple association are described within the binding mean spherical approximation (BiMSA). This model is based on the Wertheim formalism, in the framework of the primitive model at the McMillan-Mayer level. The cation and the anion form the various complexes according to stepwise complexation-equilibria. Analytic expressions for the Helmholtz energy, the internal energy, the speciation, and for the osmotic and activity coefficients are given considering a binary solution with an arbitrary number of association sites on one type of ion (polyion) and one site on the ions of opposite sign (counterions). As an alternative, mean field expressions, as developed in SAFT-type theories, are also presented. The result obtained from the latter approximate method exhibits a reasonable agreement with those from BiMSA for the speciation, and a remarkable one for the osmotic coefficient.

Properties of a hard-core Yukawa fluid in a uniform gravitational field obtained by a hybrid DFT-Monte Carlo method

A hybrid self-consistent method using a Density Functional Theory (DFT) and Monte Carlo (MC) simulations has been applied to obtain the density profiles of a hard-core monocomponent Yukawa fluid under the action of a gravitational field. In this method the properties of a N-particles fluid are obtained from a one-particle MC simulation in the presence of a N − 1 particles effective field, which is calculated by DFT within a local density approximation. The combined DFT/MC calculation is repeated in a self-consistent way until a desirable degree of accuracy is obtained. Two different approximations are used to feed the DFT approach, the mean spherical approximation (MSA) and the statistical associating fluid theory of variable range (SAFT-VR). Results compare very well with direct N-particles MC simulations in the NVT ensemble, for 3000 particles, with a significant reduction in the computing time.

Microcanonical ensemble simulation method applied to discrete potential fluids.

In this work we extend the applicability of the microcanonical ensemble simulation method, originally proposed to study the Ising model [A. Hüller and M. Pleimling, Int. J. Mod. Phys. C 13, 947 (2002)0129-183110.1142/S0129183102003693], to the case of simple fluids. An algorithm is developed by measuring the transition rates probabilities between macroscopic states, that has as advantage with respect to conventional Monte Carlo NVT (MC-NVT) simulations that a continuous range of temperatures are covered in a single run. For a given density, this new algorithm provides the inverse temperature, that can be parametrized as a function of the internal energy, and the isochoric heat capacity is then evaluated through a numerical derivative. As an illustrative example we consider a fluid composed of particles interacting via a square-well (SW) pair potential of variable range. Equilibrium internal energies and isochoric heat capacities are obtained with very high accuracy compared with data obtained from MC-NVT simulations. These results are important in the context of the application of the Hüller-Pleimling method to discrete-potential systems, that are based on a generalization of the SW and square-shoulder fluids properties.

Statistical thermodynamics for a self-gravitating fluid of rotating particles

Systems with long-range interactions (those which decay at large distances as r-l, with l ≥ d, where d is the dimensionality of the considered space), like gravitational or charged ones, present difficulties when treated by conventional statistical mechanics perturbation methods. In this work a self-gravitating fluid of rotating spherical particles is considered. The corresponding inter-particle potential model is a long-ranged one and was obtained from the application of the Newtonian limit to the Kerr metric. This potential has been expressed as a finite sum of hard-core Yukawa potentials. This new potential mimics the original long-ranged one and can be treated with conventional statistical mechanics methods. The first-order mean spherical approximation is applied to this potential to obtain the thermodynamic response functions.