Microscopical justification of Solid-State Wetting and Dewetting

TL;DR

This paper rigorously derives a continuum model for solid-state wetting and dewetting from atomistic interactions using $ ext{Gamma}$-convergence, characterizing regimes and effective parameters for crystalline drops on substrates.

Contribution

It provides a rigorous discrete-to-continuum derivation of the Winterbottom model for crystalline drops, including explicit conditions for wetting and dewetting regimes based on atomistic potentials.

Findings

Explicit characterization of wetting and dewetting regimes.

Effective expressions for surface anisotropy and adhesion parameter.

Convergence of atomistic minimizers to continuum solutions.

Abstract

The continuum model related to the Winterbottom problem, i.e., the problem of determining the equilibrium shape of crystalline drops resting on a substrate, is derived in dimension two by means of a rigorous discrete-to-continuum passage by $\Gamma$-convergence of atomistic models taking into consideration the atomic interactions of the drop particles both among themselves and with the fixed substrate atoms. As a byproduct of the analysis effective expressions for the drop surface anisotropy and the drop/substrate adhesion parameter appearing in the continuum model are characterized in terms of the atomistic potentials, which are chosen of Heitmann-Radin sticky-disc type. Furthermore, a threshold condition only depending on such potentials is determined distinguishing the wetting regime, where discrete minimizers are explicitly characterized as configurations contained in a layer with a one-atom thickness, i.e., the wetting layer, on the substrate, from the dewetting regime. In the latter regime, also in view of a proven conservation of mass in the limit as the number of atoms tends to infinity, proper scalings of the minimizers of the atomistic models converge (up to extracting a subsequence and performing translations on the substrate surface) to a bounded minimizer of the Winterbottom continuum model satisfying the volume constraint.