Contact angle

The contact angle is the angle, conventionally measured through the liquid, where a liquid–vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation. A given system of solid, liquid, and vapor at a given temperature and pressure has a unique equilibrium contact angle. However, in practice a dynamic phenomenon of contact angle hysteresis is often observed, ranging from the advancing (maximal) contact angle to the receding (minimal) contact angle. The equilibrium contact is within those values, and can be calculated from them. The equilibrium contact angle reflects the relative strength of the liquid, solid, and vapor molecular interaction. The contact angle is the angle, conventionally measured through the liquid, where a liquid–vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation. A given system of solid, liquid, and vapor at a given temperature and pressure has a unique equilibrium contact angle. However, in practice a dynamic phenomenon of contact angle hysteresis is often observed, ranging from the advancing (maximal) contact angle to the receding (minimal) contact angle. The equilibrium contact is within those values, and can be calculated from them. The equilibrium contact angle reflects the relative strength of the liquid, solid, and vapor molecular interaction. The shape of a liquid–vapor interface is determined by the Young–Dupré equation, with the contact angle playing the role of a boundary condition via the Young equation. The theoretical description of contact arises from the consideration of a thermodynamic equilibrium between the three phases: the liquid phase (L), the solid phase (S), and the gas or vapor phase (G) (which could be a mixture of ambient atmosphere and an equilibrium concentration of the liquid vapor). (The 'gaseous' phase could be replaced by another immiscible liquid phase.) If the solid–vapor interfacial energy is denoted by γ S G {displaystyle gamma _{SG}} , the solid–liquid interfacial energy by γ S L {displaystyle gamma _{SL}} , and the liquid–vapor interfacial energy (i.e. the surface tension) by γ L G {displaystyle gamma _{LG}} , then the equilibrium contact angle θ C {displaystyle heta _{mathrm {C} }} is determined from these quantities by the Young equation: The contact angle can also be related to the work of adhesion via the Young–Dupré equation: where Δ W S L V {displaystyle Delta W_{mathrm {SLV} }} is the solid – liquid adhesion energy per unit area when in the medium V. The earliest study on the relationship between contact angle and surface tensions for sessile droplets on flat surfaces was reported by Thomas Young in 1805. A century later Gibbs proposed a modification to Young’s equation to account for the volumetric dependence of the contact angle. Gibbs postulated the existence of a line tension, which acts at the three-phase boundary and accounts for the excess energy at the confluence of the solid-liquid-gas phase interface, and is given as: cos ⁡ ( θ ) = γ S V − γ S L γ L V + κ γ L V 1 a {displaystyle cos( heta )={frac {gamma _{SV}-gamma _{SL}}{gamma _{LV}}}+{frac {kappa }{gamma _{LV}}}{frac {1}{a}}} where, κ is the line tension and a is the droplet radius. Although experimental data validates an affine relationship between the cosine of the contact angle and the inverse line radius, it does not account for the correct sign of κ and overestimates its value by several orders of magnitude. With improvements in measuring techniques such as AFM, confocal microscopy and SEM, researchers were able to produce and image droplets at ever smaller scales. With the reduction in droplet size came new experimental observations of wetting. These observations confirmed that the modified Young’s equation does not hold at the micro-nano scales. Jasper proposed that including a VdP term in the variation of the free energy may be the key to solving the contact angle problem at such small scales. Given that the variation in free energy is zero at equilibrium: