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Radial distribution functions of non-crystalline polymers and their application to the structural analysis of PMMA

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Abstract

The use of Radial Distribution Functions (RDFs) in the determination of the structure of non-crystalline polymers is briefly reviewed. Particular aspects of the procedure for preparing RDFs from X-ray scattering are discussed in detail; namely the employment of an energy dispersive detector to remove the Compton component of the scattered X-rays and the application of the method of sampled transforms. A RDF is presented for atactic polymethylmethacrylate (PMMA) and its precision and reliability are discussed. It is analysed by comparison with RDFs calculated from computer-generated atom co-ordinates for isolated lengths of PMMA chains in different conformations. Methods are introduced by which the calculated RDFs are smeared to account for random disorder in the real chain and normalized so that, despite the finite range of the model, they can be immediately compared with the difference RDF which is directly obtained by transforming the data. Comparison between experimental and calculated RDFs shows that reasonable agreement is only obtained for a very limited range of conformations corresponding to sequences of backbone bond rotation angles of (10‡, 10‡, −10‡, −10‡) and the bond angles alternately 110‡ and 128‡. The form of the RDF appears very sensitive to important aspects of the molecular structure. The results both confirm and refine an earlier proposal from this laboratory which was based on comparisons between experimental and calculated functions in reciprocal space.

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Author notes

  1. J. R. Waring

    Present address: British Railway Technical Centre, London Road, Derby, UK

Authors and Affiliations

  1. Department of Metallurgy and Materials Science, University of Cambridge, Pembroke Street, Cambridge, UK

    J. R. Waring, R. Lovell, G. R. Mitchell & A. H. Windle

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  1. J. R. Waring
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  2. R. Lovell
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  3. G. R. Mitchell
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  4. A. H. Windle
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Waring, J.R., Lovell, R., Mitchell, G.R. et al. Radial distribution functions of non-crystalline polymers and their application to the structural analysis of PMMA. J Mater Sci 17, 1171–1186 (1982). https://doi.org/10.1007/BF00543538

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