Quantifying the solid-fluid interfacial tensions depending on the substrate curvature: Young's equation holds for wetting around nanoscale cylinder.

Keitaro Watanabe,Hiroki Kusudo,Carlos Bistafa,Takeshi Omori,Yasutaka Yamaguchi

doi:10.1063/5.0079816

Keitaro Watanabe, Hiroki Kusudo + Show 3 more

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https://doi.org/10.1063/5.0079816

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Abstract

By extending the theoretical framework derived in our previous study [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 systems in which a solid cylinder was vertically immersed into a liquid pool. The SL and SV interfacial tensions γSL - γS0 and γSV - γS0 relative to that for bare solid surface γS0, respectively, were obtained by simple force balance relations on fluid-containing control volumes set around the bottom and top ends 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 to fit 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.

Highlights

IntroductionWhere γSL, γSV and γLV are solid-liquid (SL), solid-vapor (SV) and liquid-vapor (LV) interfacial tensions, respectively
As we see cap-shaped liquid droplets on solid surfaces almost everyday, wetting behavior is one of the most common physical phenomena in human life, and is a research target in various scientific and engineering fields.[1,2,3,4,5] By defining the interfacial tensions and the contact angle θ, wetting is usually described by Young’s equation:[6]γSL − γSV + γLV cos θ = 0, (1)where γSL, γSV and γLV are solid-liquid (SL), solid-vapor (SV) and liquid-vapor (LV) interfacial tensions, respectively
Going back to the relation between the SL or SV interfacial tension and the fluid stress in the interface via the mechanical routes, what we need is not the stress distribution but the stress integral. Considering this feature, in our previous study,[26] we provided a theoretical framework to extract the SL and SV interfacial tensions from a single molecular dynamics (MD) simulation by using the local forces and the local interaction potential exerted on a quasi-two-dimensional (2D) flat and smooth solid plate immersed into a liquid pool of a simple liquid, called the Wilhelmy plate, and verified through the comparison between the MD results and the interfacial works of adhesion obtained by the thermodynamic integration (TI)

Summary

Introduction

Where γSL, γSV and γLV are solid-liquid (SL), solid-vapor (SV) and liquid-vapor (LV) interfacial tensions, respectively. Young’s original idea of Eq (1) in 1805 was the wall-tangential force balance of interfacial tensions exerted on the contact line (CL) – before the establishment of thermodynamics7 –, but it is often explained from a thermodynamic point of view rather than from the mechanical balance.[1] Practically, the contact angle is used as a common measure of wettability. Various models have been proposed to capture the details of the CL, such as including the precursor film[1,8] or the microscopic contact angle,[9] or considering the effects of line tension due to the contact-line curvature in Eq (1).[10,11] it is difficult to experimentally validate these models mainly because measuring the interfacial tensions γSL and γSV, which include the solid surface, is difficult.[12,13]

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