NEUTRON-SCATTERING FROM SOLUTION-GROWN POLYMER CRYSTALS - A STATISTICAL-MODEL

An earlier statistical model for the spatial arrangement of isotopical ly labelled 'stems' (single molecular traverses) within single crystal s has been extended, with the probability of deposition of a labelled stem following another labelled stem (P-A), the probability of labelle d stem deposition after an unlabelled one (P-U) and the number of labe lled stems per 'sheet' (the crystallographic plane containing the labe lled stems) (sigma) as variables. Analytical expressions have been der ived for the dilution of one isotopic species with the other and for t he size distribution for clusters of labelled stems for a one-dimensio nal sheet of labelled stems. This opens the possibility of comparison with predictions from different possible crystallisation mechanisms. C alculations for the neutron scattering intensity from this model, with 'superfolding' (folding from one crystallographic fold plane to its n eighbour) occurring after a specified number of labelled stems, show g ood agreement with those based on the earlier model for a set of varia bles appropriate to solution-crystallised polyethylene. Experimental d ata are also well fitted. Conversely, a model with superfolding occurr ing at random along the molecular length is shown to provide a poor fi t to experimental data. A test is demonstrated for the number of compu ter simulations required to obtain adequate statistics.