Scaling behaviour of thin films on chemically heterogenous walls

TL;DR

This study compares microscopic density functional theory predictions with mesoscopic interfacial Hamiltonian theory for liquid droplet formation on chemically striped walls, confirming scaling laws and shape predictions for large stripe widths.

Contribution

It provides a microscopic validation of mesoscopic predictions for droplet height and shape on chemically heterogeneous surfaces, highlighting the accuracy and limitations of the interfacial Hamiltonian approach.

Findings

Droplet height scales as L^{1/2} for large stripes.

Excellent agreement between DFT and mesoscopic theory for L ≥ 50 molecular diameters.

Droplet height is lower than predicted for smaller stripes.

Abstract

We study the adsorption of a fluid in the grand canonical ensemble occurring at a planar heterogeneous wall which is decorated with a chemical stripe of width $L$. We suppose that the material of the stripe strongly preferentially adsorbs the liquid in contrast to the outer material which is only partially wet. This competition leads to the nucleation of a droplet of liquid on the stripe, the height $h_m$ and shape of which (at bulk two-phase coexistence) has been predicted previously using mesoscopic interfacial Hamiltonian theory. We test these predictions using a microscopic Fundamental Measure Density Functional Theory which incorporates short-ranged fluid-fluid and fully long-ranged wall-fluid interactions. Our model functional accurately describes packing effects not captured by the interfacial Hamiltonian but still we show that there is excellent agreement with the predictions $h_m\approx L^{1/2}$ and for the scaled circular shape of the drop even for $L$ as small as $50$ molecular diameters. For smaller stripes the droplet height is considerably lower than that predicted by the mesoscopic interfacial theory. Phase transitions for droplet configurations occurring on substrates with multiple stripes are also discussed.