Measurement of the adsorption at solid-liquid interfaces from the pressure dependence of contact angles

Earlier studies have indicated that in an isothermal three-phase system, the liquid-phase pressure at the three- phase line, x(3)(L), may be viewed as the independent variable of the contact angle, theta, and that adsorption at the solid-liquid interface is the mechanism relating them. When the liquid-vapor interface is axi-symmetric, we show that theta can be predicted as a function x(3)(L) and that by measuring theta(x(3)(L)), the amount adsorbed at the solid-liquid interface can be determined. We consider water in differently sized borosilicate glass cylinders. For progressively larger cylinders, x(3)(L) increases with cylinder radius, but when a particularly sized cylinder is rotated about it longitudinal axis, x(3)(L) is decreased. The observed value of theta in each case is found to be in close agreement with that predicted. A Gibbs model of the interphase is used, and the Gibbs adsorption at the solid-liquid interface is found to be negative. As x(3)(L) increases above its value at wetting, the amount adsorbed at the solid-liquid interface becomes progressively more negative. Negative adsorption is shown to mean that the concentration of the fluid component is greater in the bulk liquid than in the interphase and that the difference in concentration increases as x(3)(L) is increased. The data is used to investigate the hypothesis that the curvature of the three-phase line affects theta through line tension, but we find no relation between line tension and theta. There is an apparent relation between the curvature of the liquid-vapor interface, C-LV and theta, but this is shown to be because C-LV affects x(3)(L).