On deviations from Young's equation

Abstract

Although Young's equation, γ_S=γ_SL+γ_L cos θ_C, is one of the oldest and most-used equations of classical physics and chemistry, it is in a rather delicate position scientifically, in that it is virtually impossible to prove experimentally. This is due, of course, to the uncertainties in the measurement of γ_S and γ_SL, the solid–air and solid–liquid surface tensions. Recently the validity of Young's equation has been questioned as the result of a theoretical analysis of the three-phase contact region where the liquid–air surface tension, γ_L, may be modified by interaction with the nearby substrate.

The present paper argues that Young's equation is a “macroscopic” equation which does not concern itself with the microscopic shape of the liquid surface in the vicinity of the three-phase contact region. The concept of a microscopic contact angle θ_P is introduced. θ_P is the angle that the free liquid surface makes with the substrate when the liquid thickness is ≪∼ 10 Å, i.e., microscopically near the three-phase contact line. The contact angle θ_C given by Young's equation is shown to be the angle that the liquid surface makes with the substrate at microscopically large distances from the contact line where the modification of surface tensions by interaction is negligible (> 10 Å). The connection between θ_P and θ_C is established by making only very general statements about the nature of this interaction and does not impose the unphysical restrictions on the profile shape in the neighbourhood of the three-phase contact line which lead to the conclusions of Jameson and del Cerro.