Virial coefficients and osmotic pressure in polymer solutions in good-solvent conditions

TL;DR

This paper calculates virial coefficients for polymer solutions in good solvents and develops an accurate expression for osmotic pressure across dilute and semidilute regimes, validated by theory and experiments.

Contribution

It provides a novel extrapolation method for osmotic pressure from low to high concentrations in polymer solutions under good-solvent conditions.

Findings

Virial coefficients accurately determined up to the fourth order.

Osmotic pressure expression valid across dilute and semidilute regimes.

Error margins of 1-2% below overlap concentration, up to 10% at high concentrations.

Abstract

We determine the second, third, and fourth virial coefficients appearing in the density expansion of the osmotic pressure of a monodisperse polymer solution in good-solvent conditions. Using the expected large-concentration behavior, we extrapolate the low-density expansion outside the dilute regime, obtaining the osmotic pressure for any concentration in the semidilute region. Comparison with field-theoretical predictions and experimental data shows that the obtained expression is quite accurate. The error is approximately 1-2% below the overlap concentration and rises at most to 5-10% in the limit of very large polymer concentrations.