On the nature of the coexistence surface and the critical double point in a polymer plus poor solvent system

Abstract

We observe a critical double point (CDP) in a polystyrene (molecular weight=13 000) plus acetone mixture when a small amount of water is added to it instead of varying the molecular weight or the pressure. A very close access to CDP has been achieved, as exemplified by a sample with a miscibility gap, ΔT_E (the difference between the upper and lower extremum temperatures, T_EU and T_EL, respectively) as small as 194 mK. The critical exponent (β) for the phase diagram exhibits a twofold increase in its 3-D Ising value for a sample with ΔT_E=194 mK, when the usual field variable (the reduced temperature, t) is used. The universal value of β(=0.325) is retrieved for any ΔT_E with the aid of the field variable t_UL[=‖(T_EU-T)(T-T_EL) /T_EU/BTEL‖]. Our evidence shows that, at least for the order parameter, ΔT_E is preferable to ΔT_c (the difference between the upper and lower critical temperatures, T_U and T_L, respectively) as a measure of the distance from CDP in this system. The critical line and the locus of the extremum temperatures are similar and are nearly parabolic in shape. Most of our observations can be understood in terms of the geometric picture of phase transitions as well as the Landau-Ginzburg theory, as applied to reentrant phase transitions. A microscopic understanding of the role of water in reducing the miscibility gap (Δ T_E) in these complex systems remains to be achieved.