On what Terms and why the Thermodynamic Properties of Polymer Solutions Depend on Chain Length up to the Melt

TL;DR

This study develops and tests a simple theoretical model for how the thermodynamic interaction parameter chi in polymer solutions depends on chain length and solvent quality, validated through extensive experiments.

Contribution

It introduces a universal relation for chi(N, phi) that applies across different solvents and chain lengths, surpassing traditional models limited to good solvents.

Findings

Chi depends on chain length and solvent quality.

Model accurately predicts chi across various conditions.

Long chains show increased chi in good solvents, decreased in poor solvents.

Abstract

Theoretical considerations based on chain connectivity and conformational variability of polymers have lead to an uncomplicated relation for the dependence of the Flory-Huggins interaction parameter, chi, on the volume fraction of the polymer, phi, and on its number of segments, N. The validity of this expression is being tested extensively by means of vapor pressure measurements and inverse gas chromatography (complemented by osmotic and light scattering data from literature) for solutions of poly(dimethylsiloxane) in the thermodynamically vastly different solvents n-octane (n-C8), toluene (TL), and methylethylketone (MEK) over the entire range of composition for at least six different molecular masses of the polymer. The new approach is capable to model the measured chi (phi, N) very well, irrespective of the thermodynamic quality of the solvent, in contrast to traditional expressions, which are often restricted to good solvents but fail for bad ones and vice versa. At constant polymer concentration the chi values result lowest for n-C8 (best solvent) and highest for MEK (theta solvent); the data for TL fall between. The influences of N depend strongly on the thermodynamic quality of the solvent and are not restricted to dilute solutions. For good solvents chi increases with rising N. The effect is most pronounced for n-C8, where the different curves for chi (phi) fan out considerably. The influences of N become less distinct for TL, and for MEK they vanish at the (endothermal) theta temperature. For worse than theta conditions, the chi values of the long chains become less than that of short ones. This change in the sign of N-influences is in agreement with the present concept of conformational relaxation.