Interplay of complete wetting, critical adsorption, and capillary condensation

TL;DR

This study investigates the complex interplay of wetting, adsorption, and capillary condensation in two-dimensional Ising strips, revealing crossover behaviors, the existence of critical wetting transitions for specific boundary conditions, and the influence of confinement effects.

Contribution

It provides detailed analysis of the crossover between wetting and critical adsorption regimes, demonstrating the existence of critical wetting transitions for p=2 and mapping the wetting phase diagram.

Findings

Capillary condensation alters power law dependences along isotherms.

A broad crossover regime exists near the wetting temperature with non-power-law behavior.

Critical wetting transitions are confirmed for p=2, contrary to previous claims.

Abstract

The excess adsorption $\Gamma $ in two-dimensional Ising strips $(\infty \times L)$ subject to identical boundary fields, at both one-dimensional surfaces decaying in the orthogonal direction $j$ as $-h_1j^{-p}$, is studied for various values of $p$ and along various thermodynamic paths below the critical point by means of the density-matrix renormalization-group method. The crossover behavior between the complete wetting and critical adsorption regimes, occurring in semi-infinite systems, are strongly influenced by confinement effects. Along isotherms $T=const$ the asymptotic power law dependences on the external bulk field, which characterize these two regimes, are undercut by capillary condensation. Along the pseudo first-order phase coexistence line of the strips, which varies with temperature, we find a broad crossover regime where both the thickness of the wetting film and $\Gamma$ increase as function of the reduced temperature $\tau$ but do not follow any power law. Above the wetting temperature the order parameter profiles are not slab-like but exhibit wide interfacial variations and pronounced tails. Inter alia, our explicit calculations demonstrate that, contrary to opposite claims by Kroll and Lipowsky [Phys. Rev. B {\bf 28}, 5273 (1983)], for $p=2$ critical wetting transitions do exist and we determine the corresponding wetting phase diagram in the $(h_1,T)$ plane.