Theory and simulation of diffraction by disordered polycrystalline fibers
Abstract
X-ray diffraction patterns from oriented polymer fibers depend both on the conformations of the polymers, and the manner in which they pack. Existing methods for determining structures from diffraction patterns effectively assume that the packing is either random, or is ideally crystalline over small domains. However, the presence of both sharp reflections and diffuse intensity on diffraction patterns from some polymer fibers indicates that the polymers are packed as disordered crystallites. An understanding of disorder and its relationship to diffraction aids in characterizing disorder in these fibers and in accurate structure determination. The effects that various forms of disorder have on fiber diffraction patterns are investigated by mathematical and computational modeling. A fiber is modeled as an ensemble of disordered crystallites, and expressions for the cylindrically averaged layer line intensities derived that include the effects of finite crystallite size, molecular structure, uncorrelated lattice distortions, and rotational, screw and directional disorder. Computer software based on these expressions permits the calculation of diffracted intensities and characterization of the effects of disorder. Comparison of calculated patterns with a representative observed pattern shows that a model with uncorrelated disorder may account for some, but not all features of the observed pattern. The model of disorder is extended to include correlations between lattice distortions, using the formalism of perturbed lattices with imposed correlation fields. Expressions for the diffracted intensity are derived in real space that lead to an efficient algorithm for computing diffraction patterns. Software that implements the algorithm is used to examine the effects of correlated disorder. Patterns calculated for correlated lattice disorder show better agreement with a representative diffraction pattern than do those calculated for uncorrelated disorder.
Degree
Ph.D.
Advisors
Millane, Purdue University.
Subject Area
Polymers
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