Scaling of wetting and pre-wetting transitions on nano-patterned walls

TL;DR

This paper investigates how nano-patterned walls with alternating wet and dry stripes influence wetting transitions, revealing a first-order transition and universal scaling of pre-wetting phenomena using microscopic density functional theory.

Contribution

It demonstrates the first microscopic evidence of a logarithmic relation between stripe separation and wetting transition, confirming mesoscopic model predictions for finite-size effects.

Findings

Wetting transition occurs at a separation D_w proportional to ln L.

Pre-wetting lines exhibit universal scaling and data collapse.

Results confirm mesoscopic model predictions for finite-size effects.

Abstract

We consider a nano-patterned planar wall consisting of a periodic array of stripes of width $L$, which are completely wet by liquid (contact angle $\theta=0$), separated by regions of width $D$ which are completely dry (contact angle $\theta=\pi)$. Using microscopic Density Functional Theory we show that in the presence of long-ranged dispersion forces, the wall-gas interface undergoes a first-order wetting transition, at bulk coexistence, as the separation $D$ is reduced to a value $D_w\propto\ln L$, induced by the bridging between neighboring liquid droplets. Associated with this is a line of pre-wetting transitions occurring off coexistence. By varying the stripe width $L$ we show that the pre-wetting line shows universal scaling behaviour and data collapse. This verifies predictions based on mesoscopic models for the scaling properties associated with finite-size effects at complete wetting including the logarithmic singular contribution to the surface free-energy.