Order-parameter profile at long distances in an adsorbed binary liquid mixture near criticality

Abstract

Adsorption of a binary liquid mixture near criticality onto a solid glass substrate can be studied using light reflected off the glass/liquid boundary. Reflectivity data analyzed with a modified Landau-Ginzburg theory using a contact wall interaction are consistent with an exponential decay of the order parameter into the bulk. This analysis provides a measure of ${h}_{1}$, the effective glass/liquid interaction strength. The reflectivity can also be expressed as an expansion in the moments of the order-parameter profile. For the data presented and an exponential profile the expansion can be truncated at the first-order moment, ${M}_{1}$. We assume an exponential form of the profile to express the zeroth moment as a function of ${M}_{1}$. The first moment is fitted as a power law in t, the reduced temperature. Analysis of these preliminary data yields an exponent p=0.88\ifmmode\pm\else\textpm\fi{}0.10 that is consistent with the prediction p=2\ensuremath{\nu}-\ensuremath{\beta} from the scaling law of Fisher and de Gennes.