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

Measurements of osmotic compressibility (near the lower consolute point, $T_L$) 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 ($\Delta$T)=250 mK. Analyzing the data by means of the conventional field variable $t[=|(T_c-T)/T_c|]$ yielded an exact doubling of the critical exponent (CE) $\gamma$ for a $\Delta$T=250 mK. The approach to double criticality (for intermediate $\Delta$T) is described by a crossover of the CE from the doubled to its single limit as $t\rightarrow 0$. Recourse to a more appropriate field variable, $t_{UL}[=|(T_U-T)(T_L-T)/T_UT_L|]$, restores the Ising value of $\gamma$(=1.24) for any $\Delta$T. The salt-doped mixtures permitted us to observe a doubling of the extended scaling exponent ($\Delta$) 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 $t^\prime_{UL}[=\mid(T_U-T)(T_L-T)/T^2\mid]$ 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 $\gamma$ as $T_D$ (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