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Microscopical Justification of Solid-State Wetting and Dewetting.

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Summary

This study rigorously derives the Winterbottom problem continuum model from atomistic interactions, defining wetting and dewetting regimes based on atomic potentials. It provides effective expressions for surface anisotropy and adhesion parameters in crystalline drops.

Keywords:
AdhesionAnisotropyAtomistic modelsCapillarity problemsCrystallizationDiscrete-to-continuum passageIsland nucleationSurface energyWettingWinterbottom shapedewetting

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Area of Science:

  • Materials Science
  • Mathematical Physics
  • Surface Science

Background:

  • The Winterbottom problem addresses the equilibrium shape of crystalline drops on substrates.
  • Understanding these shapes is crucial for materials science and nanotechnology.
  • Existing models often lack rigorous grounding in atomic interactions.

Purpose of the Study:

  • To derive the two-dimensional continuum model for the Winterbottom problem using rigorous discrete-to-continuum methods.
  • To characterize effective expressions for surface anisotropy and adhesion parameters from atomistic potentials.
  • To establish a threshold condition for distinguishing between wetting and dewetting regimes.

Main Methods:

  • Utilizing Gamma-convergence of atomistic models to bridge discrete and continuum scales.
  • Considering interatomic interactions within the drop and between the drop and substrate.
  • Employing Heitmann-Radin sticky-disk potentials to model atomic interactions.

Main Results:

  • Successful derivation of the continuum model for crystalline drops on substrates.
  • Characterization of surface anisotropy and adhesion parameters in terms of atomistic potentials.
  • Determination of a potential-dependent threshold distinguishing wetting (thin wetting layer) from dewetting regimes.

Conclusions:

  • The study provides a rigorous mathematical foundation for the Winterbottom problem.
  • Effective parameters in continuum models can be directly linked to underlying atomic interactions.
  • The derived wetting/dewetting condition offers insights into thin film formation and stability.