On what terms and why the thermodynamic properties of polymer solutions depend on chain length up to the melt

Theoretical considerations based on chain connectivity and conformational variability of polymers have led to an uncomplicated relation for the dependence of the Flory–Huggins interaction parameter (χ) on the volume fraction of the polymer (ϕ) and on its number of segments (N). The validity of this expression was tested extensively with vapor-pressure measurements and inverse gas chromatography (complemented by osmotic and light scattering data from the literature) for solutions of poly(dimethylsiloxane) in thermodynamically vastly different solvents such as 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 of modeling the measured χ (ϕ, N), regardless of the thermodynamic quality of the solvent, in contrast to traditional expressions, which are often restricted to good solvents but fail for bad mixtures and vice versa. At constant polymer concentration, the χ values were lowest for n-C8 (best solvent) and highest for MEK (Θ solvent); the data for TL fell between them. The influences of N depended strongly on the thermodynamic quality of the solvent and were not restricted to dilute solutions. For good solvents, χ increased with rising N. The effect was most pronounced for n-C8, where the different curves for χ (ϕ) fanned out considerably. The influences of N were less distinct for TL, and for MEK they vanished at the (endothermal) θ temperature. For worse than θ conditions, the χ values of the long chains were less than that of the short ones. This change in the sign of N agreed with this concept of conformational relaxation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1601–1609, 2004