Monolayer instability: An upper bound for the wetting and nonwetting of a substrate by a solid monolayer

Continuum mechanics and computer simulations are used to study the elastic stability of solid monolayers. We observe microscopically the upper limits of the ratio of adsorption to cohesive energies that allow for the wetting of the substrate by a solid monolayer using molecular dynamics. Also, structural instabilities are found analytically in nonlinear elastic continuum models by solving the nonlinear von K\'arm\'an equations for a thin circular system (an adsorbed island) undergoing planar compression. The instability occurs as a bifurcation at the first eigenvalue. A series of simulations over a range of adsorbate energies versus temperature demonstrates the existence of a stability boundary.