Solid--on--Solid Model for Adsorption on Self--Affine Substrate: A Transfer Matrix Approach

TL;DR

This paper investigates a 2D solid-on-solid model for adsorption on a self-affine rough substrate using a transfer matrix method, revealing how the wetting behavior depends on the substrate's roughness exponent.

Contribution

It introduces a transfer matrix approach to analyze adsorption on self-affine substrates, extending understanding of wetting exponents for different roughness regimes.

Findings

For ta_s  1/2, the wetting exponent ta=1/3 matches flat substrates.

Numerical verification of a zero temperature fixed point for ta_s > 1/2.

Asymptotic behavior shows slow convergence, but confirms theoretical predictions.

Abstract

We study a $d=2$ discrete solid--on--solid model of complete wetting of a rough substrate with random self--affine boundary, having roughness exponent $\zeta_s$. A suitable transfer matrix approach allows to discuss adsorption isotherms, as well as geometrical and thermal fluctuations of the interface. For $\zeta_s\leq 1/2$ the same wetting exponent $\psi=1/3$ as for flat substrate is obtained for the dependence of the coverage, $\theta$, on the chemical potential, $h$ ($\theta\sim h^{-\psi}$ for $h\to 0$). The expected existence of a zero temperature fixed point, leading to $\psi=\zeta_s /(2-\zeta_s)$ for $\zeta_s>1/2$, is verified numerically in spite of an unexpected, very slow convergence to asymptotics.