The Crossover Critical Behaviour In Ternary Liquid Mixtures Of [Ethanol+Water+Potassium Carbonate]

The phase diagrams for ternary solutions of water + ethanol + potassium carbonate were determined. It was found that when the mass ratio of ethanol to water (E/W) was small, the system had multiple critical points, and near the DCP (double critical point) and the CDP (critical double point) there existed two upper critical points and one lower critical point. However, as E/W≥0.3526, the DCP and CDP disappeared and there was only one upper critical point.The coexistence curves both in the single-critical-point region and multiple-critical-point region were determined by measurements of refractive indexes. The coexistence curves in the single critical point region were analyzed in terms of the spline fit to obtain the effective exponents β_eff for various τ. It was found that there existed crossover from the mean-field behavior to the 3D-Ising one and the crossover is nonmonotonic. We also discovered that the crossover critical behavior became more clear when E/W decreased and the concentration of potassium carbonate increased, which was consistent with the Sengers' crossover theory. The analysis of the parts of loops of coexistence curves above the lower critical points gave the values of critical exponents, which were between the values estimated by the Fisher model and the 3D-Ising theory. For the whole closed coexistence-curve loops, the corresponding filed variable τ_UL was used in analyses of data. It was found that the critical behavior was mean-field type, which was consistent with Jaffar's conclusion. Although good results of fits were also found for use of the Singers equations, the effective exponents β_eff calculated by using the optimized parameters in Singers equations were found almost to be a constant of 0.5, which is consistent with the predictions of mean-field theory.The light scattering measurements have been carried out at various temperatures and angles for a ternary critical solution of water + ethanol + potassium in one-phase region. The analyses of the light scattering data in terms of the Ornstein-Zernike and Debye theory gave the susceptibilities x and the correlation lengths ζ, and further to obtain the exponents γ and ν. It was found that there existed crossover from mean-field to 3D-Ising, and it belonged to nonmonotonic type and was consistent to the Sengers' prediction for complex fluids.The experimental data of susceptibilities χ, correlation lengths ζ and coexistence curves were fitted to the Singers crossover theory model and the same conclusion of nonmonotonic crossover from mean-field to 3D-Ising was obtained.