The refinement of the crystal and molecular structures of polymers using X-ray data and stereochemical constraints

Abstract A general method is described for the automatic determination of the positions, orientations and conformations of molecules in crystals which best correspond to observed X-ray diffraction. The molecular conformations are described in terms of chain parameters, and standard bond lengths and angles are maintained during the refinement. For this reason the method is particularly suitable for establishing structures of polymers in crystalline fibres where the poor quality diffraction data requires to be supplemented by stereochemical information. Additional constraints which ensure that successive monomer units are linked appropriately are achieved by means of Lagrange multipliers. Refinement of the structures of Terylene and α- poly - l - alanine are used to illustrate successful application of this approach in the analysis of polymer structure.