# Comparative study of a solid film dewetting in an attractive substrate potentials with the exponential and the algebraic decay

Mikhail Khenner

Arxiv ID: 0805.3545•Last updated: 12/3/2020

We compare dewetting characteristics of a thin nonwetting solid film in the
absence of stress, for two models of a wetting potential: the exponential and
the algebraic. The exponential model is a one-parameter (r) model, and the
algebraic model is a two-parameter (r,m) model, where r is the ratio of the
characteristic wetting length to the height of the unperturbed film, and m is
the exponent of h (film height) in a smooth function that interpolates the
system's surface energy above and below the film-substrate interface at z=0.
The exponential model gives monotonically decreasing (with h) wetting chemical
potential, while this dependence is monotonic only for the m=1 case of the
algebraic model. Linear stability analysis of the planar equilibrium surface is
performed. Simulations of the surface dynamics in the strongly nonlinear regime
(large deviations from the planar equilibrium) and for large surface energy
anisotropies demonstrate that for any m the film is less prone to dewetting
when it is governed by the algebraic model. Quasiequilibrium states similar to
the one found in the exponential model (M. Khenner, Phys. Rev. B 77, 245445
(2008)) exist in the algebraic model as well, and the film morphologies are
similar.

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