Double-critical-point phenomena in three-component liquid mixtures: Light-scattering investigations.

Abstract

Measurements of osmotic compressibility (near the lower consolute point, ${\mathrm{T}}_{\mathrm{L}}$) in two reentrant liquid mixtures [3-methylpyridine (MP)+water (W)+heavy water (HW) and MP+W+NaCl] are presented. The closest approach to the double critical point (DCP) was marked by a sample of loop size (\ensuremath{\Delta}T)=250 mK. Analyzing the data by means of the conventional field variable t[=|(${\mathrm{T}}_{\mathrm{c}}$-T)/${\mathrm{T}}_{\mathrm{c}}$|] yielded an exact doubling of the critical exponent (CE) \ensuremath{\gamma} for a \ensuremath{\Delta}T=250 mK. The approach to double criticality (for intermediate \ensuremath{\Delta}T) is described by a crossover of the CE from the doubled to its single limit as t\ensuremath{\rightarrow}0. Recourse to a more appropriate field variable, ${\mathrm{t}}_{\mathrm{UL}}$[=|(${\mathrm{T}}_{\mathrm{U}}$-T)(${\mathrm{T}}_{\mathrm{L}}$-T)/${\mathrm{T}}_{\mathrm{U}}$${\mathrm{T}}_{\mathrm{L}}$|], restores the Ising value of \ensuremath{\gamma}(=1.24) for any \ensuremath{\Delta}T. The salt-doped mixtures permitted us to observe a doubling of the extended scaling exponent (\ensuremath{\Delta}) and also to scrutinize the ionic critical phenomena. The range of simple scaling in MP+W+HW was found to be extremely large. Switching to a modified variable ${\mathrm{t}}_{\mathrm{UL}}^{\ensuremath{'}}$[=|(${\mathrm{T}}_{\mathrm{U}}$-T)(${\mathrm{T}}_{\mathrm{L}}$-T)/${\mathrm{T}}^{2}$|] led to a remarkable enhancement in the weight of the extended scaling term in both the mixtures---in apparent disagreement with the earlier findings that reported a widening of the asymptotic region. Non-phase-separating samples of MP+W+HW showed the expected saturating divergence preceded by a region of doubled \ensuremath{\gamma} as ${\mathrm{T}}_{\mathrm{D}}$ (DCP temperature) was neared. Most of the facets of our investigations can be comprehended in terms of the geometrical picture of phase transitions as well as the Landau-Ginzburg theory as applied to the reentrant phase transitions.