Compressibility effects in the analysis and interpretation of neutron scattering data from polymer blends

A thermodynamically consistent procedure, based on statistical mechanical fluctuation theory, has been developed for the analysis and interpretation of small-angle neutron scattering (SANS) data for compressible polymer blends. The development was motivated by inconsistencies between the interaction parameter obtained with an analysis based on the incompressible Flory-Huggins model, which is a function of composition, and the Flory-Huggins model itself, in which the interaction parameter is independent of composition. An expression is obtained that connects the forward scattering intensity with the curvature of the Gibbs energy for a binary blend of arbitrary compressibility. This expression, which forms the basis of the data analysis procedure, permits the contributions of various effects of compressibility to be estimated without the introduction of specific models. We show that contributions from both density fluctuations and excess volumes of mixing can safely be neglected in the analysis of SANS data for polymer blends. We illustrate the methodology with the lattice fluid model, which expresses the Gibbs energy curvature in terms of microscopic properties, thereby relating to the SANS intensity. A parameter characterizing system interactions can then be defined in terms of three energetic quantities, two of which can be evaluated from pure component PVT data. The remaining quantity, when treated as a system-specific constant, independent of temperature and blend composition, can quantitatively and self-consistently describe SANS data for weakly interacting blends, such as mixtures of saturated hydrocarbon polymers and isotopically substituted species.