Jean-Michel Caillol

A Monte Carlo study of the classical two-dimensional one-component plasma

We present results from extensive Monte Carlo simulations of the fluid phase of the two-dimensional classical one-component plasma (OCP). The difficulties associated with the infinite range of the logarithmic Coulomb interaction are eliminated by confining the particles to the surface of a sphere. The results are compared to those obtained for a planar system with screened Coulomb interactions and periodic boundary conditions; in this case the infinite tail of the Coulomb interaction is treated as a perturbation. The “exact” simulation results are used to test various approximate theories, including a semiempirical modification of the hypernetted-chain (HNC) integral equation. The OCP freezing transition is located at a couplingγ= e2/kBT−140.

Theoretical calculation of ionic solution properties

A model system of electrolyte solution is studied by molecular dynamics simulation. The results show how the polarizability of the molecules and the ratio of the molecular diameters of the ions and solvent molecules affect the properties of the system. The computation of the frequency dependent dielectric constant and conductivity in terms of correlation functions of the electrical current and microscopic polarization is discussed. A general solution of this problem is given for systems of arbitrary shape composed of nonpolarizable ions and solvent molecules. Three particular cases are considered in detail: the infinite system; a spherical system in contact with a dielectric and conducting continuum; a system with periodic boundary conditions. The zero frequency limit of the dielectric constant and conductivity is investigated.

Search of the gas-liquid transition of dipolar hard spheres

We present results of Monte Carlo simulations in the isothermal–isobaric ensemble and the Gibbs ensemble for the fluid of dipolar hard spheres. These results preclude the existence of a gas–liquid transition for a wide range of densities and temperatures.

A Monte Carlo study of the liquid–vapor coexistence of charged hard spheres

We determine the liquid–vapor coexistence curve of the restricted primitive model of electrolytes by means of Monte Carlo simulations in the Gibbs ensemble. Our results confirm earlier findings of Panagiotopoulos [Fluid Phase Equilibria 76, 97 (1992)]. A study of the electrical properties of the two coexisting phases reveals that the second Stillinger–Lovett condition is verified in the liquid but not in the vapor. This means that the latter could be dielectric.

Critical behavior of the restricted primitive model revisited

Reassessment of the critical temperature and density of the restricted primitive model of an ionic fluid by Monte Carlo simulations performed for system sizes with linear dimension up to L/σ=34 and sampling of ∼109 trial moves leads to Tc*=0.049 17±0.000 02 and ρc*=0.080±0.005. Finite size scaling analysis based in the Bruce–Wilding procedure gives critical exponents in agreement with those of the three-dimensional Ising universality class. An analysis similar to that proposed by Orkoulas et al. [Phys. Rev. E 63, 051507 (2001)], not relying on an a priori knowledge of the universality class, leads to an inaccurate estimate of Tc* and to unexpected behavior of the specific heat and value of the critical exponent ratio γ/ν.

Electrical properties of polarizable ionic solutions. I: Theoretical aspects

We generalize previous work [J. Chem. Phys. 85, 6645 (1986)] on the relation between the frequency‐dependent dielectric constant and conductivity and time correlation functions of electrical current and polarization in electrolyte solutions by allowing the ions and solvent molecules to be polarizable. Detailed results are given for the infinite system (no boundary), spherical system embedded in a continuum and periodic boundary conditions. The Stillinger–Lovett (SL) sum rules are derived for these geometries. It is shown, in particular, that they provide a means of calculating the high frequency dielectric constant in a molecular dynamics simulation. A test of the phenomenological coefficient‐susceptibility relations and the SL conditions is presented in part II by performing molecular dynamics simulations on a model electrolyte solution with different boundary conditions.

Electrical properties of polarizable ionic solutions. II. Computer simulation results

We present molecular dynamics simulations for two limiting models of ionic solutions: one where the solvent molecules are polar, but nonpolarizable; the other where they are only polarizable (but have no permanent dipole moment). For both models, the static two‐body correlation functions, the frequency‐dependent dielectric constant and conductivity are calculated and the statistical uncertainty on these quantities estimated for molecular dynamics runs of the order of 105 integration steps. For the case of the polar solvent, the accuracy of the computed static interionic correlation functions allows a valuable test of the hypernetted chain integral equation theory at an ionic concentration of 0.04. The quantitative variation of the fluctuations of polarization and electrical current with change of boundary conditions is evaluated within the context of the second model (polarizable nonpolar solvent). Applying the relationships derived in Part I between the phenomenological coefficients and susceptibilities,...

Some applications of the Lambert W function to classical statistical mechanics

We apply the recently defined Lambert W function to some problems of classical statistical mechanics, i.e. the Tonks gas and a fluid of classical particles interacting via repulsive pair potentials. The latter case is considered both from the point of view of the standard theory of liquids and in the framework of a field theoretical description. Some new mathematical properties of the Lambert W function are obtained by passing.

Numerical simulations of homogeneous and inhomogeneous ionic systems : an efficient alternative to the Ewald method

A new method for the numerical simulation of ionic systems is proposed; it is a very efficient alternative to the well‐known Ewald method for the study of homogeneous and inhomogeneous phases of Coulomb systems. Its main feature is the use of a simulation cell which is the three dimensional surface of a four dimensional sphere. When the ionic interaction is the potential solution of the Poisson’s equation in this non‐Euclidean space, it is established by simulations that the results of the Ewald method and of the proposed method are identical for an homogeneous phase. The comparison with previous simulations for inhomogeneous systems demonstrates also the reliability and efficiency of the method.

A new potential for the numerical simulations of electrolyte solutions on a hypersphere

We propose a new way of performing numerical simulations of the restricted primitive model of electrolytes—and related models—on a hypersphere. In this new approach, the system is viewed as a single component fluid of charged bihard spheres constrained to move at the surface of a four dimensional sphere. A charged bihard sphere is defined as the rigid association of two antipodal charged hard spheres of opposite signs. These objects interact via a simple analytical potential obtained by solving the Poisson–Laplace equation on the hypersphere. This new technique of simulation enables a precise determination of the chemical potential of the charged species in the canonical ensemble by a straightforward application of Widom’s insertion method. Comparisons with previous simulations demonstrate the efficiency and the reliability of the method.