Development of a Theory Describing the Radius of Gyration of Polymers in Solution Based on the Integral Equation Theory of Molecular Liquids

A novel theoretical framework has been developed to predict the radius of gyration of polymers in solution. The approach is based on the mean-field theory proposed by Flory, which formulates the free energy as a function of the radius of gyration, incorporating both short-range intrachain correlations and long-range intermonomer interactions. The persistence length, representing the local chain flexibility, is evaluated using the three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) method, based on the solvent-dependent dihedral free energy profiles obtained from poly(ethylene glycol) (PEG) model compounds. The excluded volume, accounting for long-range interactions between distant monomer pairs, is calculated using the polymer RISM (PRISM) theory. The excluded volume contribution is further decomposed into the direct and indirect terms, and their behavior is analyzed using solvent distribution functions. The method was applied to PEG in aqueous and methanolic solutions. The predicted radius of gyration was found to be larger in water than in methanol, reflecting the existence of stronger polymer-solvent interactions in the former. The results are compared with previous experimental and theoretical studies, and the reliability of the proposed methodology is considered.