Heterogeneous Nucleation of a Droplet Pinned at a Chemically Inhomogeneous Substrate: A Simulation Study of the Two-dimensional Ising Case

TL;DR

This simulation study investigates how chemical inhomogeneities on a substrate influence droplet nucleation and growth in a two-dimensional lattice gas model, revealing regimes of droplet pinning and growth behavior.

Contribution

It provides a detailed analysis of heterogeneous nucleation at chemically inhomogeneous boundaries using Monte Carlo simulations and phenomenological theory, highlighting the effects of inhomogeneity size and bulk field.

Findings

Droplets can be pinned at the inhomogeneity for certain bulk fields.

The effective contact angle depends on the product of inhomogeneity size and bulk field.

Large bulk fields lead to droplets growing to system size.

Abstract

Heterogeneous nucleation is studied by Monte Carlo simulations and phenomenological theory, using the two-dimensional lattice gas model with suitable boundary fields. A chemical inhomogeneity of length b at one boundary favors the liquid phase, while elsewhere the vapor is favored. Switching on the bulk field favoring the liquid, nucleation and growth of the liquid phase starting from the region of the chemical inhomogeneity is analyzed. Three regimes occur: for small fields, the critical droplet radius is so large that a critical droplet having the contact angle required by Young's equation in the region of the chemical inhomogeneity does not yet fit there, since the baseline length of the circle-cut sphere droplet would exceed b. For an intermedium regime of bulk fields, such droplets fit inside the inhomogeneity, and are indeed found in simulations with large enough observation times, but these droplets remain pinned to the chemical inhomogeneity when their baseline has grown to the length b. On general grounds one can predict that the effective contact angle as well as the excess density of the droplets, scaled by b^2, are functions of the product b and the bulk field, but do not depend on both variables separately. For larger fields the droplets nucleated at the chemical inhomogeneity grow to the full system size.