Curvature dependence of the interfacial tensions around nanoscale cylinder: Young's equation still holds

TL;DR

This study extends a theoretical framework to calculate nanoscale interfacial tensions around solid cylinders, confirming that Young's equation remains valid at the nanoscale despite curvature effects on local forces.

Contribution

It introduces a method to compute solid-liquid and solid-vapor interfacial tensions at the nanoscale using molecular dynamics, demonstrating the validity of Young's equation in such conditions.

Findings

Young's equation holds at the nanoscale for curved solid surfaces.

Curvature has a small effect on the contact angle but a large effect on local forces.

Interfacial tensions' curvature dependence differs from that of interfacial potential energies.

Abstract

By extending the theoretical framework derived in our previous study [Y. Imaizumi et al., J. Chem. Phys. 153, 034701 (2020)], we successfully calculated the solid-liquid (SL) and solid-vapor (SV) interfacial tensions of a simple Lennard-Jones fluid around solid cylinders with nanometer-scale diameters from single equilibrium molecular dynamics (MD) systems, in which a solid cylinder was vertically immersed into a liquid pool. The SL and SV interfacial tensions $\gamma_\mathrm{SL} - \gamma_\mathrm{S0}$ and $\gamma_\mathrm{SV} - \gamma_\mathrm{S0}$ relative to that for bare solid surface $\gamma_\mathrm{S0}$, respectively were obtained by simple force balance relations on fluid-containing control volumes set around the bottom and top of the solid cylinder, which are subject to the fluid stress and the force from the solid. % The theoretical contact angle calculated by Young's equation using these interfacial tensions agreed well with the apparent contact angle estimated by the analytical solution fitted to the meniscus shape, showing that Young's equation holds even for the menisci around solids with nanoscale curvature. % We have also found that the curvature effect on the contact angle was surprisingly small while it was indeed large on the local forces exerted on the solid cylinder near the contact line. In addition, the present results showed that the curvature dependence of the SL and SV interfacial free energies, which are the interfacial tensions, is different from that of the corresponding interfacial potential energies.