Scattering from Polydisperse Melts

Abstract

Effective isotropic pair potentials for polymer chains in a melt are derived from a phenomenological, coarse grained model of mixing on small distance scales, and the radial distribution functions of chain centers of mass and the scattering are calculated in the hypernetted chain approximation. The systems chosen for illustrative calculations are quasi-binary melts of deuterated and protonated polyethylene and polystyrene, both of which have been reported to exhibit anomalous composition dependence of neutron scattering. Quite large deviations from the Flory−Huggins picture of random spatial mixing of chains are found and the deviations decrease rather slowly with increasing molecular weights. However, nonrandom mixing gives rise to anomalous scattering of significant magnitude only if the mixture is asymmetric in particular ways. Differences in molecular weight (smaller for the deuterated polymer) and polydispersity (larger for the deuterated polymer) of about 10% are sufficient to exhibit anomalous scattering due to errors in the Flory−Huggins entropy of mixing. Smaller differences in the packing energies of the two different monomers, which are associated in the phenomenological model with composition dependent partial monomer volumes, reveal errors in the usual random phase analysis of scattering. Relative volumes of mixing deuterated and protonated polymer must range up to 1% in order to rationalize experimental anomalous scattering.