Comparing kinetic Monte Carlo and Thin-Film Modeling of Transversal Instabilities of Ridges on Patterned Substrates

TL;DR

This study compares kinetic Monte Carlo simulations and thin-film continuum models to analyze the transverse instability of ridges on patterned substrates, revealing qualitative agreement in instability evolution and characteristic scales.

Contribution

It introduces a comparative analysis of KMC and thin-film models for ridge instability, highlighting their qualitative agreement and scale differences.

Findings

Instability evolution qualitatively agrees between models.

Characteristic length and time scales differ significantly.

Dispersion relations are similar for linear instability modes.

Abstract

We employ kinetic Monte Carlo (KMC) simulations and a thin-film continuum model to comparatively study the transverse (i.e., Plateau-Rayleigh) instability of ridges formed by molecules on pre-patterned substrates. It is demonstrated that the evolution of the occurring instability qualitatively agrees between the two models for a single ridge as well as for two weakly interacting ridges. In particular, it is shown for both models that the instability occurs on well defined length and time scales which are, for the KMC model, significantly larger than the intrinsic scales of thermodynamic fluctuations. This is further evidenced by the similarity of dispersion relations characterising the linear instability modes.