Point tension in adsorption at a chemically inhomogeneous substrate in two dimensions

TL;DR

This paper investigates how the excess free energy associated with a chemical inhomogeneity on a substrate varies with its width and temperature, revealing different divergence behaviors and interactions in two temperature regimes.

Contribution

It provides an exact continuum transfer-matrix calculation of point free energy in a 2D adsorption system with chemical inhomogeneity, highlighting temperature-dependent behaviors.

Findings

Logarithmic divergence of excess free energy at large inhomogeneity width for high temperatures.

Convergence to twice the point tension at large widths for low temperatures.

Comparison of inhomogeneity interactions with earlier mean-field theory predictions.

Abstract

We study adsorption of liquid at a one-dimensional substrate composed of a single chemical inhomogeneity of width $2L$ placed on an otherwise homogeneous, planar, solid surface. The excess point free energy $\eta (L,T)$ associated with the adsorbed layer's inhomogeneity induced by the substrate's chemical structure is calculated within exact continuum transfer-matrix approach. It is shown that the way $\eta (L,T)$ varies with $L$ depends sensitively on the temperature regime. It exhibits logarithmic divergence as a function of $L$ in the limit $L\to\infty$ for temperatures such that the chemical inhomogeneity is completely wetted by the liquid. In the opposite case $\eta (L,T)$ converges for large $L$ to $2\eta_0$, where $\eta_0$ is the corresponding point tension, and the dominant $L$-dependent correction to $2\eta_0$ decays exponentially. The interaction between the liquid layer inhomogeneities at $-L$ and $L$ for the two temperature regimes is discussed and compared to earlier mean-field theory predictions.