Corrections to Scaling in the Hydrodynamic Properties of Dilute Polymer Solutions

TL;DR

This paper analyzes the corrections to the hydrodynamic radius of dilute polymer solutions, revealing an analytic correction term related to chain discretization and providing numerical estimates for the universal ratio of radii.

Contribution

It identifies the leading correction to the asymptotic hydrodynamic radius law as an analytic term and provides numerical estimates for the universal ratio R_G / R_H in good and theta solvents.

Findings

Leading correction term is of order N^{-(1 - ν)}

Universal ratio R_G / R_H is approximately 1.59 for good solvents

Ratio R_G / R_H is approximately 1.44 for theta solvents

Abstract

We discuss the hydrodynamic radius $R_H$ of polymer chains in good solvent, and show that the leading order correction to the asymptotic law $R_H \propto N^\nu$ ($N$ degree of polymerization, $\nu \approx 0.59$) is an ``analytic'' term of order $N^{-(1 - \nu)}$, which is directly related to the discretization of the chain into a finite number of beads. This result is further corroborated by exact calculations for Gaussian chains, and extensive numerical simulations of different models of good--solvent chains, where we find a value of $1.591 \pm 0.007$ for the asymptotic universal ratio $R_G / R_H$, $R_G$ being the chain's gyration radius. For $\Theta$ chains the data apparently extrapolate to $R_G / R_H \approx 1.44$, which is different from the Gaussian value 1.5045, but in accordance with previous simulations. We also show that the experimentally observed deviations of the initial decay rate in dynamic light scattering from the asymptotic Benmouna--Akcasu value can partly be understood by similar arguments.