Theory of Polymer Chains in Poor Solvent: Single-Chain Structure,   Solution Thermodynamics and Theta Point
  Using the language of the Flory chi 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 Theta point. The information of 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 chi dependence and the chain-length dependence. From the perspectives of single chain structure and solution thermodynamics, our results verifies the consistency of the Theta point defined by different criteria in the limit of infinite chain length: the disappearance of the second viral coefficient, the abrupt change in chain size and the critical point in the phase diagram of the polymer solution. Our results show the value of chi at the Theta point is 0.5 (for the case of equal monomer and solvent volume), which coincides with the value predicted from the F-H theory. 
Rui Wang and Zhen-Gang Wang
cond-mat.soft