Growth kinetics in a strained crystal film on a wavy patterned substrate.

We study the combination of the Asaro-Tiller-Grinfeld morphological instability of a strained film and the organizing effect of an underlying patterned substrate. We use a continuum description of surface diffusion accounting for elasticity, surface energy and wetting interactions. We solve both the mechanical equilibrium and the growth dynamics during annealing at linear order in the film modulation amplitude. We characterize the kinetic phase diagram as a function of time, the film thickness and the ratio between the substrate and the instability wavelengths. We find that the film surface can skip from a configuration in phase with the substrate to either an out-of-phase or a non-ordered configuration, depending on the pattern wavelength and annealing time.

Charge renormalization and other exact coupling corrections to the dipolar effective interaction in an electrolyte near a dielectric wall.

The aim of the paper is to study the renormalizations of the charge and screening length that appear in the large-distance behavior of the effective pairwise interaction w(alphaalpha') between two charges e(alpha) and e(alpha') in a dilute electrolyte solution, both along a dielectric wall and in the bulk. The electrolyte is described by the so-called primitive model in the framework of classical statistical mechanics and the electrostatic response of the wall is characterized by its dielectric constant. In a previous paper [Phys. Rev. E 68, 022133 (2003)] a graphic reorganization of resummed Mayer diagrammatics has been devised in order to exhibit the general structure of the 1/y3 leading tail of w(alphaalpha') (x,x',y) for two charges located at distances x and x' from the wall and separated by a distance y along the wall. When all species have the same closest approach distance b to the wall, the coefficient of the 1/y3 tail is the product Dalpha(x)Dalpha'(x') of two effective dipoles. Here we use the same graphic reorganization in order to systematically investigate the exponential large-distance behavior of w(alphaalpha') in the bulk. (We show that the reorganization also enables one to derive the basic screening rules in both cases.) Then, in a regime of high dilution and weak coupling, the exact analytical corrections to the leading tail of w(alphaalpha'), both in the bulk or along the wall, are calculated at first order in the coupling parameter epsilon and in the limit where b becomes negligible with respect to the Debye screening length. (Epsilon is proportional to the so-called plasma parameter.) The structure of corrections to the terms of order epsilon is exhibited, and the scaling regime for the validity of the Debye limit is specified. In the vicinity of the wall, we use the density profiles calculated previously [J. Stat. Phys. 105, 211 (2001)] up to order epsilon and a method devised [J. Stat. Phys. 105, 245 (2001)] for the determination of the corresponding correction in the auxiliary screened potential, which also appears in the linear-response theory. The first coupling correction to the effective dipole Dalpha(x) is a function (not a mere exponential decay) determined by the nonuniformity of the density profiles as well as by three- and four-body screened interactions in w(alphaalpha'). Though the effective screening length (beyond the Debye value) in the direction perpendicular to the wall is the same as in the bulk, the bare solvated charges are not renormalized by the same quantity as in the bulk, because of combined steric and electrostatic effects induced by the wall.

Dipolar effective interaction in a fluid of charged spheres near a dielectric plate.

Static correlations in a classical fluid of charged spheres at equilibrium are studied in the vicinity of an insulating wall characterized by its dielectric constant. It is well known that the deformations of screening clouds induced by the presence of the wall result into an effective f(alphaalpha('))(x,x('))/y(3) interaction in the pair distribution function between two charges e(alpha) and e(alpha(')) located at distances x and x(') from the wall and separated by a large distance y along the wall. We investigate the structure of f(alphaalpha('))(x,x(')). The method is based on systematic resummations in the Mayer diagrammatics, which are valid both in the bulk and in an inhomogeneous situation. The screened potential phi arising in the formalism happens to coincide with the linearized mean-field approximation for the immersion free energy of two external unit charges. Phi is shown to decay as a repulsive f(phi)(x,x('))/y(3) interaction, whatever the density profiles may be. f(phi)(x,x(')) takes a factorized dipolar structure f(phi)(x,x('))=D(phi)(x)D(phi)(x(')) for distances x and x(') larger than the maximum of the closest approach distances b(alpha)'s to the wall for every species alpha. Moreover, we devise a reorganization of resummed diagrammatics, which is adequate for the determination of the large-distance behavior of correlations, and we prove that, when all species have the same approach distance b to the wall, f(alphaalpha('))(x,x(');b)=D(alpha)(x)D(alpha('))(x(')). In this case, the leading tail of the effective electrostatic interaction between two like charges at the same distance x from a single wall is repulsive. Results are independent of charge magnitudes, of excluded-volume sphere sizes, and of the existence of a surface charge on the wall. It holds whether charges are concentrated at sphere centers or uniformly spread over their surfaces. Comparison is made with an experiment about dilute colloids where the linearized mean-field approximation proves to be relevant. At equilibrium attraction between like charges in confined geometry might arise from purely electrostatic charge-charge interactions only through correlation effects not taken into account in the latter approximation.