Ellipsometric study of undersaturated critical adsorption

Abstract

At the liquid-vapor surface of a critical AB binary liquid mixture, if the surface energies ${\ensuremath{\sigma}}_{A}\ensuremath{\ll}{\ensuremath{\sigma}}_{B},$ then component A completely saturates the surface and one is in the regime of strong critical adsorption where the local volume fraction at the surface is solely a function of $z/\ensuremath{\xi}$ where \ensuremath{\xi} is the bulk correlation length and z is the depth into the liquid. If, however, ${\ensuremath{\sigma}}_{A}\ensuremath{\approx}{\ensuremath{\sigma}}_{B}$ then the surface composition is a sensitive function of the surface energy difference $\ensuremath{\Delta}\ensuremath{\sigma}={\ensuremath{\sigma}}_{A}\ensuremath{-}{\ensuremath{\sigma}}_{B}$ and the surface is ``undersaturated.'' We study this undersaturated critical adsorption regime using a homologous series of critical binary liquid mixtures. Component B (methyl formate) is fixed, while component A is varied from n-undecane to n-tetradecane. With increasing carbon chain length \ensuremath{\Delta}\ensuremath{\sigma} changes systematically from a negative to a positive value. We find that the experimental results, in both the one- and two-phase regions, are well described by a universal surface scaling function $G(z/\ensuremath{\xi},{\mathbf{h}}_{1}{t}^{\ensuremath{-}{\ensuremath{\Delta}}_{1}}),$ where ${\mathbf{h}}_{1}\ensuremath{\sim}\ensuremath{\Delta}\ensuremath{\sigma},$ $t=|{T}_{c}\ensuremath{-}T|{/T}_{c}$ is the reduced temperature relative to the critical temperature ${(T}_{c}),$ and ${\ensuremath{\Delta}}_{1}$ is a universal surface critical exponent. These results are in conformity with theoretical predictions.