document: We deal with the intensity scattered by a random mixture of deuterated/hydrogenated PE chains. The algorithm used by us to evaluate the Kratky plots by sets of parallel polymer stems is very simplified. We checked it to be adequate in the reciprocal coordinate range under investigation [0<q(=4πsinθ/λ)≤0.25Å−1] comparing the results with more precise calculations. The scattering centres are identified with pseudo-atoms repeating after a constant distance of 1.27Å along straight lines coinciding with the stem axes, 100 scattering centres being placed on each stem; the scattering by atoms belonging to chain folds is neglected. The parallel stem axes are disposed according to a hexagonal setting – a rough approximation to the monoclinic, pseudo-hexagonal structure of PE – and the scattering centres have the same axial coordinates in all the stems. Defining an integer i going from 1 to the total number ns·100 of scattering centres, we have (q<1) [9](1A)q2·I(q)=C·(bH−bD)2∑i=1ns·100∑j=1ns·1004πqsin(q·dij)dij;dij2=Δij2+(zj−zi)2;q=2πsinθλwhere bH, bD respectively are the scattering lengths of hydrogen and deuterium, dij is the distance between C atoms, 2θ is the diffraction angle and λ the wavelength. The i-th C atom coordinate along the stem axis is zi and Δij is the distance between the stem axes where the atoms i and j belong. For all the stems we have the same set of zi coordinates. The sum in Eq. (1A) is extended to all the stems of the crystalline domain, see Figs. 2 and 10 for examples.
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