Extended Gibbs Free Energy and Laplace Pressure of Ordered Hexagonal Close-Packed Spherical Particles: A Wettability Study

The wetting property of spherical particles in a hexagonal close-packed (HCP) ordering from extended Gibbs free energy (GFE) and Laplace pressure view points is studied. A formalism is proposed to predict the contact angle (theta) of a droplet on the HCP films and penetration angle (a) of the liquid on the spherical particles. Then, the extended Laplace pressure for the layered HCP ordering is calculated and a correlation between the wetting angle, sign of pressure, and pressure gradient is achieved. Our results show that the sign and the slope of pressure are important criteria for determining the wettability state and it is found that the contact angle is independent of the particle radius, as supported by various experimental reports. The pressure gradient for the HCP films with Young contact angle higher than (lower than) a critical contact angle, 135 degrees (45 degrees), is positive (negative), indicating the superhydrophobicity (superhydrophilicity) state of the surface. To validate the proposed formulation, theoretical calculations are compared with the reported experimental measurements, showing a good agreement.

Automated summary

This study investigates the wetting property of spherical particles in an HCP structure and proposes a formalism for predicting contact and penetration angles. The results show that the sign and slope of pressure are key criteria for determining the wetting state, and the contact angle is independent of particle radius. Additionally, the pressure gradient of HCP films can indicate their hydrophobic or hydrophilic nature.