The Thermodynamics of High-Polymer Solutions: I. The Free Energy of Mixing of Solvents and Polymers of Heterogeneous Distribution

Abstract

The theories of Flory and Huggins for the free energy of mixing of a homogeneous chain polymer of uniform molecular weight with a single uniform solvent have been extended to the case of a polymer mixture of varying chain lengths with a mixture of solvents. By making the similar assumptions as those of Huggins, and utilizing familiar statistical mechanical methods, the partial molal free energy of mixing of the solvent is found to be $$\overline{{\mathrm{\Delta F}}_0}\mathrm{=RT[}\ln {\phi }_0{\text{+(1−φ}}_0{\text{)(1–1/m̄}}_N{\text{)+μ(1−φ}}_0{)}^2\mathrm{],}$$ where φ₀ is the volume fraction of solvent, m̄_N a simple function of the number average molecular weight, and μ a constant characteristic of the polymer‐solvent mixture (consisting largely of a heat term, but also including γ, the coordination number of the rubber segments). By assuming that a mixture of two solvents behaves like a new homogeneous liquid a method of calculating μ for such mixtures is developed. Applications of these formulas to solubility and fractionation are shown in a subsequent article.