Thermodynamics of isotopic polymer mixtures: Significance of local structural symmetry

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Abstract
The dependence on composition (Φ) and degree of polymerization (N) of the effective segment–segment interaction parameter, χ̃=− 1/2 ∂2Γ/∂Φ2, has been determined for mixtures of perdeuterated and normal (protonated) poly(vinylethylene) and poly(ethylethylene) by small angle neutron scattering (SANS), where Γ represents the excess free energy of mixing. Owing to the small reduction in length and polarizability of carbon–hydrogen bonds with deuterium substitution, isotopic polymer mixtures are characterized by small positive χ̃ parameters. However, deuterium substitution does not significantly influence the local structural symmetry (i.e., the liquid structure or reduced thermodynamic properties) of polymer isotopes, consistent with the assumptions of Flory–Huggins (FH) lattice theory. Nevertheless, we find that χ̃ depends significantly on both Φ and N, contrary to the predictions of FH theory. A general theory, which corrects FH theory for monomer concentration fluctuations, is shown to closely account for these experimental results. In understanding the previous experimental investigations of χ̃ for mixing chemically different species, the monomer concentration fluctuations discussed here must be addressed in addition to the effects due to local structural asymmetry.