Theory of Polymer Chains in Poor Solvent: Single-Chain Structure, Solution Thermodynamics, and Θ Point

Using the language of the Flory χ parameter, we develop a theory that unifies the treatment of the single-chain structure and the solution thermodynamics of polymers in poor solvents. The structure of a globule and its melting thermodynamics is examined using the self-consistent filed theory. Our results show that the chain conformation involves three states prior to the globule-to-coil transition: the fully collapsed globule, the swollen globule, and the molten globule, which are distinguished by the core density and the interfacial thickness. By examining the chain-length dependence of the melting of the swollen globule, we find universal scaling behavior in the chain properties near the Θ point. The information on density profile and free energy of the globule is used in the dilute solution thermodynamics to study the phase equilibrium of polymer solution. Our results show different scaling behavior of the solubility of polymers in the dilute solution compared to the F–H theory, both in the χ dependence and in the chain-length dependence. From the perspectives of single chain structure and solution thermodynamics, our results verify the consistency of the Θ point defined by different criteria in the limit of infinite chain length: the disappearance of the effective two-body interaction, the abrupt change in chain size, and the critical point in the phase diagram of the polymer solution. Our results show χ_Θ = 0.5 (for the case of equal monomer and solvent volume), which coincides with the value predicted from the F–H theory.