Studies of short-range order in amorphous polymers by radial distribution functions derived from X-ray diffraction

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Abstract
Interatomic and intermolecular ordering in amorphous polymers can be characterized by radial distribution functions (RDF) derived from radiation scattering measurements (X-rays, neutrons, etc.). The type of information which may be derived from RDF data in monatomic systems is illustrated by measurements on a sample of vitreous carbon, which is shown to consist of graphite-like sheets of hexagonally packed carbon atoms with no true graphitic registration between the sheets. As an example of the type of information available in polyatomic systems, an RDF study of aluminum phosphate is given to show that the basic atomic arrangement is very similar to vitreous silica with aluminum and phosphorous stoms occupying positions in aluminum phosphate similar to silicon atoms in silica. RDF methods have been applied to investigate short-range ordering in amorphous bisphenol A polycarbonate which has been reported to exhibit a grainy or nodular structure under electron microscopy. Two samples with different thermal histories were examined. Both had been rapidly quenched from the melt, and subsequently one was annealed below Tg to produce a marked change in impact properties. Most of the intramolecular distances in the polymer repeat unit were successfully resolved in the RDF patterns in the region 1< r< 6 Å. However, there were only suggestions of broad peaks at r < 5.5 Å and r < 10 Å, attributable to inter-molecular ordering, indicating that little intermolecular ordering had occurred in either sample. The RDF patterns were virtually identical, indicating that the short-range order (0 to 10 Å) in the samples has been essentially unaffected by the annealing procedures. In order to assess the sensitivity of the RDF method to short-range intermolecular ordering, a more highly annealed sample was examined. In addition to the intramolecular distances which were very similar to those resolved in the previous samples, the RDF plot showed a marked periodicity peaking at intervals of ∼ 5.5 Å which was attributable to intermolecular ordering, thus confirming the sensitivity of the RDF technique to intermolecular ordering in amorphous polymers. Similar studies have been made on polyethylene terephthalate films, both “quenched amorphous” and one annealed near Tg (100 hr at 65[ddot]C) to provide complementary structural information on structures reported in electron micrographs under similar conditions. Again, all intramolecular peaks of the polymer repeat unit were resolved in the RDF's for both samples for r < 6 Å. However, there were only suggestions of broad peaks at ∼5 and ∼8 Å which might be attributed to intermolecular ordering, and there was no detectable increase in intermolecular ordering on annealing. It is not necessary to assume intermolecular ordering over much greater than ∼ 10 Å to explain the RDF data for either polycarbonate or polyethylene terephthalate, and the relevance of this finding to proposed models of polymer...