Density Profiles in a Quantum Coulomb Fluid Near a Hard Wall

Journal of Statistical Physics - Equilibrium particle densities near a hard wall are studied for a quantum fluid made of point charges which interact via Coulomb potential without any...     

Growth of hexagonal quantum dots under preferential evaporation

We perform numerical simulations of hexagonal quantum dots of AlGaN semiconductors. We show that the competition between surface mass diffusion and evaporation rules the morphology of the quantum dots. The system displays three different behaviors: presence of separated islands without a wetting layer, islands dissolving into the wetting layer, or islands that do not evolve. The first behavior is of special interest because its optoelectrical properties are significantly improved in comparison with quantum dots with a wetting layer.     

Classical and Quantum Algebraic Screening in a Coulomb Plasma near a Wall: A Solvable Model

The static position correlation in a quantum Coulomb plasma near a wall is studied by means of a model where two quantum charges are embedded in a classical plasma at equilibrium. Three kinds of walls are considered: a wall without electrostatic properties, a dielectric, and an ideal conductor. At large separations y along the wall, the correlation exactly decays as 1/y ³, though no algebraic tail exists for classical charges near an ideal conductor. This tail originates from thermal statistical and purely quantum fluctuations of polarization clouds which are deformed by the geometric constraint due to the wall and by the charges induced by influence inside a wall with electrical properties. The coefficient of the 1/y ³ tail can be calculated explicitly in a weak-coupling and low-delocalization regime. Then classical, diffraction, and purely quantum contributions are disentangled.     

Density Profiles in a Classical Coulomb Fluid Near a Dielectric Wall. I. Mean-Field Scheme

The equilibrium density profiles in a classical multicomponent plasma near a hard wall made with a dielectric material characterized by a relative dielectric constant ∈_w are studied from the first Born–Green–Yvon (BGY) equation combined with Poisson equation in a regime where Coulomb coupling is weak inside the fluid. In order to prevent the collapse between charges with opposite signs or between each charge and its dielectric image inside the wall when ∈_w>1, hard-core repulsions are added to the Coulomb pair interaction. The charge-image interaction cannot be treated perturbatively and the density profiles vary very fast in the vicinity of the wall when ∈_w≠1. The formal solution of the associated inhomogeneous Debye–Hückel equations will be given in Paper II, together with a systematic fugacity expansion which allows to retrieve the results obtained from the truncated BGY hierarchy. In the present paper the exact density profiles are calculated analytically up to first order in the coupling parameter. The expressions show the interplay between three effects: the geometric repulsion from the impenetrable wall; the electrostatic effective attraction (∈_w>1) or repulsion (∈_w<1) due to its dielectric response; and the Coulomb interaction between each charge and the potential drop created by the electric layer which appears as soon as the system is not symmetric. We exhibit how the charge density profile evolves between a structure with two oppositely-charged layers and a three-layer organization when ∈_w varies. (The case of two ideally conducting walls will be displayed elsewhere).     

Ionic criticality: an exactly soluble model

Gas-liquid criticality in ionic fluids is studied in exactly soluble spherical models that use interlaced sublattices to represent hard-core multicomponent systems. Short-range attractions in the uncharged fluid drive criticality, but charged ions do not alter the universality class. Debye screening remains exponential at criticality in fully ion-symmetric 1:1 models. However, ionic asymmetry couples charge and density fluctuations in a direct manner: The charge correlation length then diverges precisely as the density correlation length and the Stillinger-Lovett rule is violated at criticality.     

How multivalency controls ionic criticality

To understand how multivalency affects criticality in z:1 ionic fluids, we report an ion-cluster association theory embodying ionic solvation and excluded volume for equisized hard-sphere models with z=1-3. In accord with simulation but contradicting integral equation and field theories, the reduced critical temperature falls when z increases while the density rho(c) rises steeply. These trends can be explained semiquantitatively by noting that 80%-90% of the ions near T(c) are bound in neutral or charged clusters, depleting the ionic strength. For z not equal 1, predicted interphase Galvani potentials vanish at T(c).     

Density Profiles in a Classical Coulomb Fluid Near a Dielectric Wall. II. Weak-Coupling Systematic Expansions

In the framework of the grand-canonical ensemble of statistical mechanics, we give an exact diagrammatic representation of the density profiles in a classical multicomponent plasma near a dielectric wall. By a reorganization of Mayer diagrams for the fugacity expansions of the densities, we exhibit how the long-range of both the self-energy and pair interaction are exponentially screened at large distances from the wall. However, the self-energy due to Coulomb interaction with images still diverges in the vicinity of the dielectric wall and the variation of the density is drastically different at short or large distances from the wall. This variation is involved in the inhomogeneous Debye–Hückel equation obeyed by the screened pair potential. Then the main difficulty lies in the determination of the latter potential at every distance. We solve this problem by devising a systematic expansion with respect to the ratio of the fundamental length scales involved in the two coulombic effects at stake. (The application of this method to a plasma confined between two ideally conducting plates and to a quantum plasma will be presented elsewhere). As a result we derive the exact analytical perturbative expressions for the density profiles up to first order in the coupling between charges. The mean-field approach displayed in Paper I is then justified.