Interatomic distance functions obtained by electron diffraction from the polyethylene melt: Possible errors in the interpretation of radial distribution functions

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Abstract
These investigations were undertaken in order to study in more detail problems regarding the distribution of molecules in the polymer melt, specifically the question concerning the existence of short−range order. The specimens studied in greatest detail were high−density polyethylene. The technique employed was that of electron diffraction, using the sector apparatus now common in gas electron diffraction work. Photographic densities were transformed to intensities (Itot), interpolated on an s scale {s=4π sin[(1/2) ϑ]λ−1], divided by the theoretical atomic scattering Ib, and a smooth background IB(s) (chosen by applying the usual criteria, e.g., smoothness and a flat zero line in the radial distribution function), yielding a quantity defined as 1+i (s). A radial distribution function is obtained by Fourier sine transform of si (s): φ (r) = (2/π)1/2 ℱsmaxsmin si (s) exp(−bs2) sin(rs) ds, where the damping factor b is chosen to reduce the termination error due to the lacking intensity data beyond s=smax. Great emphasis has been placed in this investigation on improving the accuracy and objectivity of the method, regarding both the diffraction technique and estimation of the background as well as the calculating method. It was thus possible to obtain radial distribution curves with good resolution up to about 10 Å. The limitations set by the experimental method do not allow any conclusions to be drawn about molecular configuration beyond this value.