Evaluation of Concentration Dependence of χ-Parameter, Flory Temperature and Entropy Parameter for Polymer–Solvent System from Their Critical Solution Temperature and Concentration Data

Abstract

The critical polymer volume fraction vpc and the critical solution temperature Tc were estimated from the threshold cloud point (tcp) for polystyrene (PS) and polyethylene (PE) solutions in literature. The critical points thus obtained, together with those directly determined in literature, of PS in ten solvents and PE in sixteen solvents were analyzed, according to the Shultz–Flory (SF), Koningsveld et al. (KKS), and Kamide–Matsuda (KM) methods, to evaluate the Flory temperature θ and the entropy parameter ψ. The concentration dependence parameters p1 and p2 of the χ-parameter, as given by χ=χ0(1+P1vp+P2vp2)(χ0, a concentration-independent parameter, vp, polymer volume fraction) were determined by KKS and KM methods, which gave almost the same values of p1 and p2. Except for few solvents, p1 value for PS solutions can be regarded as constant, which is near to 2/3, theoretically predicted when A2=A3=0 at θ (A2 and A3, second and third virial coefficients). For lower critical solution point (LCSP), p2 is always negative, except for PS/cyclopentane and for upper critical solution point (UCSP) p2 is positive. The very wide variation of p1 and p2 with solvents was observed for PE. Application of KM method to the most reliable data on PE/diphenylether by Koningsveld et al. led to p1=0.61, which is not so far from the theoretical value. θ, obtained by three methods, is practically independent of the method used, if ψ estimated by KM method coincides with that by KKS method for a given polymer–solvent system, if ψ was found to be positive for UCSP and negative for LCSP, suggesting that the polymer solution should be athermal at a temperature between UCSP and LCSP. The effect of solvent nature on p1, p2 , θ, and ψ are discussed in some detail.