Light scattering near a double critical point: Evidence for crossover behavior.

Abstract

We report measurements of osmotic compressibility in a quasibinary liquid mixture of 3-methylpyridine, water, and heavy water. The measurements probed the lower consolute point (${\mathit{T}}_{\mathit{L}}$) for samples of varying loop sizes (\ensuremath{\Delta}T). An exact doubling of the critical exponent (\ensuremath{\gamma}) was observed over the entire experimental temperature range (${\mathit{T}}_{\mathit{L}}$-T) for a sample with \ensuremath{\Delta}T as small as 250 mK. For intermediate \ensuremath{\Delta}T 's (22\ensuremath{\ge}\ensuremath{\Delta}T\ensuremath{\ge}1 \ifmmode^\circ\else\textdegree\fi{}C), a smooth crossover from the double (2\ensuremath{\gamma}) to the single exponent (\ensuremath{\gamma}) was noticed, as t [=\ensuremath{\Vert}(${\mathit{T}}_{\mathit{L}}$-T)/${\mathit{T}}_{\mathit{L}}$\ensuremath{\Vert}]\ensuremath{\rightarrow}0. The universal value of \ensuremath{\gamma} (=1.24) was recovered for experimen- tal paths terminating in ${\mathit{T}}_{\mathit{L}}$ for any \ensuremath{\Delta}T, provided the field variable used was ${\mathit{t}}_{\mathit{U}\mathit{L}}$ [=\ensuremath{\Vert}(${\mathit{T}}_{\mathit{U}}$-T)(${\mathit{T}}_{\mathit{L}}$-T)/${\mathit{T}}_{\mathit{U}}$${\mathit{T}}_{\mathit{L}}$\ensuremath{\Vert}] instead of t. This field variable (${\mathit{t}}_{\mathit{U}\mathit{L}}$) follows naturally from the geometrical picture as well as the Landau-Ginzburg theory, as applied to the reentrant phase transitions.