Interfacial morphology and correlations in adsorption at a chemically structured substrate - exact results in d=2

TL;DR

This paper derives exact results for the morphology and correlations of an interface adsorbed on a chemically structured substrate in two dimensions, revealing how inhomogeneities influence interfacial behavior at the wetting transition.

Contribution

It provides exact analytical expressions for probability distribution functions of the interface and demonstrates the equivalence of inhomogeneity effects to interface pinning in the macroscopic limit.

Findings

Exact formulas for one-point and two-point distribution functions.

Inhomogeneity effects are equivalent to pinning at boundaries for large inhomogeneities.

Comparison of interfacial structure with homogeneous substrate results.

Abstract

Adsorption at a 1-dimensional planar substrate equipped with a localized chemical inhomogeneity is studied within the framework of a continuum interfacial model from the point of view of interfacial morphology and correlation function properties. Exact expressions for the one-point and two-point probability distribution functions $P_\Gamma (l_\Gamma)$ and $P_{\Gamma_1, \Gamma_2}(l_{\Gamma_1},l_{\Gamma_2})$, $l_\Gamma$ being the interface position above a fixed point $\Gamma$ of the substrate, are derived for temperature corresponding to the inhomogeneity's wetting transition. It is demonstrated that in the limit of macroscopic inhomogeneity's size the net effect of the remaining homogeneous parts of the substrate on the interfacial morphology above the inhomogeneity is exactly equivalent to appropriate pinning of the interface at its boundaries. The structure of the average interfacial morphology and correlation function in this limit are discussed and compared to earlier results obtained for systems with homogeneous substrate.