Free-energy landscapes of intrusion and extrusion of liquid in truncated and inverted truncated conical pores: implications to the Cassie-Baxter to Wenzel transition

TL;DR

This paper analyzes the free-energy landscapes of liquid intrusion and extrusion in truncated conical pores to understand the stability and transition mechanisms between superhydrophobic Cassie-Baxter and Wenzel states, using classical capillary theory.

Contribution

It provides a detailed analysis of free-energy landscapes for liquid transitions in conical pores, revealing different behaviors based on pore geometry and liquid manipulation.

Findings

Different free-energy landscapes for truncated and inverted truncated cones.

Gradual and abrupt destruction of Cassie-Baxter state depending on conditions.

Simple Laplace pressure criterion is insufficient for stability prediction.

Abstract

As the simplest model of transition between the superhydrophobic Cassie-Baxter (CB) and Wenzel (W) states of a macroscopic droplet sitting on a microscopically rough or corrugated substrate, a substrate whose surface is covered by identical truncated or inverted truncated conical pores is considered. The free energy landscapes of the intrusion and extrusion processes of a liquid into single pore are analyzed when the liquid is compressed or stretched so that the liquid phase is either stable or metastable relative to the vapor phase. Therefore, this model is also relevant to the stability of the superhydrophobic submerged substrates. In this study, the macroscopic classical capillary theory is adopted. Even within this simplified model, two simple geometries of truncated and inverted truncated cones lead to completely different free-energy landscapes. A simple criterion for the stability of the CB state based on Laplace pressure is shown not to be sufficient to understand the destruction and recovery of the CB state. The free-energy landscapes indicate that a gradual and an abrupt destruction of CB state is possible, which depends on the orientation of the conical pore and whether the liquid is compressed or stretched. The extensions of these theoretical results to more complex geometries are briefly discussed.