A generalized scattering data decomposition framework for determining network process-structure-property relationships in polymer materials

摘要

In this work, we present an optimization-based methodology to identify network process-structure-property relationships in multiphase polymeric materials. A quantitative description of the material structure can be provided by x-ray and neutron scattering signatures, which are modeled as the weighted sum of linearly independent components. The profile of a component depends on the shape, aggregation, and extent of fundamental structural units present in the material, and the inherent modeling complexity can be reduced by extraction of these components from process-dependent scattering datasets using minimal a priori information. The decomposition methodology we develop is based on network component analysis (NCA), a nonlinear program used to generate a unique, globally optimal matrix decomposition. Using NCA, we conduct a case study of amphiphilic triblock copolymers in solution using simulated small-angle neutron scattering data. Component signatures are successfully recovered based solely on knowledge of a network topology specified by sample scattering length density contrast-matching conditions. Then, the approach is reformulated as a mixed-integer nonlinear program in order to study systems with unknown topology, and applied in the study of ethylene/alpha-olefin copolymer crystallization from the melt using wide- and small-angle x-ray scattering (WAXS/SAXS) data. For this system, the topology is specified by the number density of structural units, and the optimal components can be correlated to crystalline and amorphous regions for WAXS datasets, while the optimal SAXS components can be correlated to ordered and disordered crystalline lamellae.