Theory of Polymers in Poor Solvent: Phase Equilibrium and Nucleation Behavior

We study the phase equilibrium and nucleation behavior of polymers in poor solvent by accounting for the large, localized fluctuations in the form of single-chain globules and multichain clusters. The density profile and free energy of the single-chain globule and multichain clusters are obtained by self-consistent-field theory. This information is then used in the dilute solution thermodynamics to investigate the equilibrium cluster size distribution, solubility limit, and nucleation in the supersaturated state. Our results show that the solubility of the polymer in the dilute side of the solution is enhanced by several orders of magnitude relative to the prediction of the Flory-Huggins (F-H) theory, which scales with the chain length to the 2/3 power rather than a linear power as predicted from the F-H theory. Our results also suggest a higher critical value of chi, consistent with computer simulation and experiment results. In the supersaturated state, we work out an effective spinodal where the nucleation barrier to phase separation via growth of the clusters becomes comparable to the thermal energy k(B)T. For a given supersaturation, we find that the nucleation barrier is quadratic in the chain length, suggesting a much slower precipitation rate for longer polymer chains.