A universal coexistence curve for polymer solutions

Abstract

Coexistence curves for binary polymer/solvent solutions are asymmetric when volume fraction is used as the concentration variable. Coexistence curves for polystyrene/methylcyclohexane solutions can be symmetrized by a simple transformation of variables; in the new dimensionless variable ψ, all of the data satisfy a universal scaling law: ‖ψ−ψ c ‖=ψ0(εN 0.313)β; ε≡(T c −T)/T c , where N is the degree of polymerization and ψ c and ψ0 are constants independent of N. The experimental value of the critical exponent β (0.327±0.002) agrees well with recent renormalization group calculations for the Ising model. The exponent on N(0.102±0.002) may be universal and should be compared with its mean‐field value of 1/4; a calculation of its nonclassical value remains a challenging theoretical problem.