Universal Ratios of Characteristic Lengths in Semidilute Polymer Solutions

TL;DR

This paper identifies universal ratios among five characteristic lengths in semidilute polymer solutions, enabling inference of various solution properties from a single measurement, supported by experimental, simulation data, and theoretical analysis.

Contribution

It introduces and calculates universal ratios of characteristic lengths in semidilute polymer solutions, combining experimental, simulation, and theoretical approaches.

Findings

Five characteristic length ratios are universal constants.

Ratios are estimated for theta and good-solvent conditions.

Simulation data supports the universality of these ratios.

Abstract

We use experimental and simulation data from the literature to infer five characteristic lengths, denoted $\xi_s$, $\xi_f$, $\xi_\Pi$, $\xi_\phi$, and $\xi_D$ of a semidilute polymer solution. The first two of these are defined in terms of scattering from the solution, the third is defined in terms of osmotic pressure, the fourth by the spatial monomer concentration profile, and the last by co-operative diffusion. In a given solution the ratios of any of these five lengths are expected to be universal constants. Knowing these constants thus allows one to use one measured property of a solution as a means of inferring others. We calculate these ratios and estimate their uncertainties for solutions in theta as well as good-solvent conditions. The analysis is strengthened by use of scattering properties of isolated polymers inferred from computer simulations.