Phase separation in polymer solutions near the critical point

The Edwards path-integral description of chain statistics is used to derive an effective $\phi^4$ field theory of polymer solutions that is applicable near the temperature of critical phase separation $T_c$. The present formalism, an extension of the mean-field approach discussed in paper I [R. E. Goldstein and B. J. Cherayil, J. Chem. Phys. 90,7448 ( 1989)], makes use of standard results from the theory of continuous phase transitions to account for the effects of previously neglected density fluctuations, and to obtain thereby, among other results, estimates for the temperature and molecular weight-scaling exponents of the coexistence curve in the vicinity of $T_c$. The critical monomer volume fraction $\rho_c$ of the solution is shown to scale as the osmotic second virial coefficient below the theta point, providing a rigorous approach to the calculation of the molecular weight dependence of $\rho_c$. Experimental data on the phase separation of solutions of polystyrene in methylcyclohexane are shown to lie on a single universal curve when expressed in terms of the scaling variables suggested by the present analysis