Polymer size in dilute solutions in the good-solvent regime

Area of Science:

• Polymer physics
• Solution thermodynamics

Background:

• Understanding polymer behavior in solution is crucial for materials science and biophysics.
• Existing models often struggle to accurately predict polymer dimensions across all concentration regimes.

Purpose of the Study:

• To determine the density expansion of key polymer dimensions (radius of gyration, hydrodynamic radius, end-to-end distance).
• To extrapolate these expansions to predict polymer radii in the semidilute regime for any concentration.

Main Methods:

• Analysis of density expansion for polymer radii under good-solvent conditions.
• Consideration of the scaling limit with leading scaling corrections.
• Extrapolation of low-density expansions using expected large-concentration behavior.

Main Results:

• Derived density expansions for radius of gyration, hydrodynamic radius, and end-to-end distance.
• Developed predictions for polymer radii applicable to the semidilute concentration region.
• Showed a maximum 5% relative error for the radius of gyration at very high polymer concentrations.

Conclusions:

• The study provides a robust method for predicting polymer dimensions in solution.
• The findings are particularly valuable for understanding polymer behavior in the semidilute regime.
• The accuracy of the predictions, especially for the radius of gyration, is validated against field-theoretical models.