Tendency toward crossover of the effective susceptibility exponent from its doubled Ising value to its doubled mean-field value near a double critical point

Critical behavior on approaching a special critical point in a complex fluid

The critical behavior of osmotic susceptibility is investigated in the re-entrant complex mixture 1-propanol (P)+water (W)+potassium chloride (KCl) through light-scattering measurements. The measurements are performed on approaching a special critical point [i.e., the double critical point (DCP)] in this mixture, along the line of upper critical solution temperatures (T(U)'s), by varying t from the high temperature one-phase region. The light-scattering data analysis emphasizes the need for corrections to the asymptotic Ising behavior and yields very large magnitudes for the correction-to-scaling amplitudes A(1) and A(2), with the first-correction amplitude A(1) being negative, signifying a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the T(U) closest to the DCP, the effective susceptibility exponent gamma(eff) displays a nonmonotonic crossover from its nearly doubled three dimensional (3D)-Ising value toward its nearly double mean-field value with an increase in t. While for that far away from the DCP, it displays a nonmonotonic crossover from its single-limit Ising value toward a value slightly lower than its mean-field value of 1 with an increase in t. This feature of the effective susceptibility exponent is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values in the nonasymptotic high t region. The renormalized Ising regime extends over a larger t range for the sample (or T(U)) closest to the DCP when compared to that far away from it. The in-between T(U)'s display a trend toward shrinkage in the renormalized Ising regime as T(U) shifts away from the DCP. Nevertheless, the crossover to the mean-field behavior is completed only beyond t>10(-2) for the T(U)'s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques, while the observed unique trend in the crossover behavior is discussed in terms of the varying influence of the DCP on the critical behavior along the T(U) line. The crossover behavior for the T(U)'s is pronounced and more sharp compared to the T(L)'s (lower critical solution temperatures) [U. K. Pradeep, J. Chem. Phys. 129, 134506 (2008)] in this mixture, although there exists no difference in the growth of the mesoscale clusters in the lower and upper one-phase regions in this mixture. Our observations suggest the need to look at the crossover behavior probably from two perspectives, namely, the dielectric effect and the clustering effect. The effective susceptibility exponent as a function of the field variable t(UL), instead of the conventional variable t, displays a sharp nonmonotonic crossover from its asymptotic 3D-Ising value ( approximately 1.24) toward a value slightly lower than its nonasymptotic mean-field value of 1, as that observed in the t analysis for the T(U) far away from the influence of the DCP.