Polymer size in dilute solutions in the good-solvent regime

TL;DR

This paper analyzes how polymer sizes such as radius of gyration, hydrodynamic radius, and end-to-end distance vary with concentration in dilute and semidilute solutions, providing extrapolated predictions and error estimates.

Contribution

It introduces a method to extrapolate low-density polymer size expansions into the semidilute regime, including scaling corrections and comparison with field theory.

Findings

Predicted polymer radii for any concentration in the semidilute region.

Relative error in radius of gyration prediction is at most 5% at high concentrations.

Validated extrapolation method against theoretical predictions.

Abstract

We determine the density expansion of the radius of gyration, of the hydrodynamic radius, and of the end-to-end distance for a monodisperse polymer solution in good-solvent conditions. We consider the scaling limit (large degree of polymerization), including the leading scaling corrections. Using the expected large-concentration behavior, we extrapolate these low-density expansions outside the dilute regime, obtaining a prediction for the radii for any concentration in the semidilute region. For the radius of gyration, comparison with field-theoretical predictions shows that the relative error should be at most 5% in the limit of very large polymer concentrations.