Enrique Lomba

A reference hypernetted‐chain equation for soft potentials. Atomic and molecular Lennard‐Jones systems

A recently proposed reference hypernetted‐chain equation based on a semiphenomenological bridge function due to Verlet is reformulated for atomic and molecular Lennard‐Jones liquids. In this new approximation we treat the size of the reference‐system hard particles as a function of density and temperature through a functional relationship presented herein. The theory yields excellent results for the structure and thermodynamics of atomic Lennard‐Jones liquids over a wide range of temperature and density and is quite satisfactory for Lennard‐Jones homonuclear diatomics.

The solution of the reference hypernetted chain equation for the dipolar hard diatomic fluid

The reference hypernetted chain equation (RHNC) for a fluid of dipolar hard diatomics was solved numerically. Three choices for the reference bridge function B0(12), were examined. The simplest, B0(12)=0 (HNC) and B0(12) corresponding to the uncharged homonuclear hard diatomic fluid, computed from simulation data and by the Percus–Yevick approximation. The computed fluid structure [i.e., the g(12) expansion coefficients] showed a remarkable quantitative agreement with the structure obtained from a mean reaction field Monte Carlo simulation. The same applied to the configurational energy. The values for the dielectric constant, however, furnished only qualitatively indications of the density dependence of this quantity. The probable origin of this discrepancy is analyzed.

New aspects in the simulation and behaviour of polar molecular fluids

A Monte Carlo computer simulation study of a simple model for dipolar molecular fluids is reported. Long-range interactions are treated by the Reaction Field method. A detailed investigation of the density dependence of dielectric, structural and thermodynamic properties is presented. At moderately high densities the dielectric constant is found to exhibit a clear maximum. Special attention has also been addressed to the influence of sample size and cutoff radius on dielectric properties; unlike the case of dipolar hard sphere fluids, such properties are rather sensitive to changes in the sample size, whereas the cutoff radius seemingly plays a minor role.

Background and bridge functions for the homonuclear hard diatomic fluid

The Monte Carlo method has been used to compute the coefficients of the spherical harmonic expansion of the function y=g exp(βu) for a hard diatomic fluid. The ‘‘series’’ function S(12) is also computed from MC data by means of an integral equation procedure. Thus, the Bklm(r) terms of the harmonic series of the bridge function B(12) can be easily obtained. The spherical harmonic expansion has proved an efficient tool to deal with these angular functions since the series is very rapidly convergent. We also have investigated the Percus–Yevick approximation both for the S(12) and the B(12), and a remarkable qualitative agreement with our MC data is found.

HNCR — a program to calculate the structure and thermodynamics of binary mixtures of charged hard spheres

Abstract HNCR is a program to determine the structure and thermodynamics of the primitive model of electrolytes, i.e. binary mixtures of charged hard spheres with arbitrary sizes and charges. This is achieved by solving the hypernetted chain equation by means of a hybrid Newton-Raphson procedure. The algorithm used is both fast and stable, and it is particularly useful for calculations involving a wide range of temperatures or concentrations for a given system.

On the thermodynamics of quadrupolar two-centre Lennard-Jones fluids

Abstract Lombardero, M., Martin, C., Lomba, E. and Fernandez, A. 1992. On the thermodynamics of quadrupolar two-centre Lennard-Jones Fluids. Fluid Phase Equilibria , 74:95-108. The basic ideas of a non-spherical reference perturbation approach, recently applied with success to quadrupolar hard diatomic fluids, are extended to systems of molecules interacting via a two-centre Lennard-Jones potential plus a point quadrupole moment. In this work solely first order contributions to the Helmholtz free energy are considered. These can be obtained in a straightforward way by combining spherical harmonic expansions for the molecular pair distribution function of the unperturbed potential and the perturbative component, together with the RAM perturbation theory for the harmonic components of the reference system distribution function. On the other hand, in order to assess the theory, Monte Carlo calculations were performed for several densities at a given temperature and (very high) quadrupole moment.

A MC Study of the Influence of Electrostatic Interactions on the Orientational Structure of Heteronuclear Fluids

A fluid composed of HCl molecules is modelled by a system of two-centre Lennard-Jones particles. We have carried out several Monte Carlo simulations for this model, with and without long range electrostatic interactions in order to assess their effect on the microscopic structure of the fluid (especially its orientational order) and related properties as the Kirkwood factor and the configurational energy.

On the Non-Solution Region of the Hypernetted Chain and Related Equations for Ionic and Simple Fluids

It is well known that the numerical solution of the hypernetted chain equation (HNC) for systems like the primitive model of electrolytes breaks down at low ionic concentration for temperatures well above the expected coexistence region between dilute and highly concentrated phases. In a recent work the nature of this divergence was investigated, comparing it to a similar problem for sticky hard spheres in the. Percus-Yevick (PY) approximation. On the basis of our analysis we conclude that the failure of the HNC (which is also present in most approximations at low density) is of the same nature and is connected to the existence of two possible solutions. Our analysis is consistent with the results of a recent comprehensive numerical study by Belloni and shows that the divergence is not associated with the presence of a spinodal in the boundaries of the non-solution region, but is connected with the existence of a square root branch point in the solution. This is a general feature of the HNC equation, which under certain conditions, however, does not prevent the equation from predicting the phase coexistence in systems like the simple Lennard-Jones fluid. For completeness, we also analyze related approximations, such as the Reference Hypernetted Chain and hybrid approaches such as the crossover integral equation.