(545a) A Modified Network Component Analysis (NCA) Methodology for the Decomposition of X-Ray Scattering Signatures from Polymers
In this work we present an optimization-based methodology to identify network structure-process relationships in polymeric materials in order to provide a robust understanding of how processing conditions affect their structural domains. The approach is largely inspired by Network Component Analysis (NCA), originally developed by Liao and co-workers (2003) to infer unobservable phenomena using large multivariate data sets. The fundamental assumption in NCA is that the connective relationship between desired unobservable phenomena and measured data is based on a largely known bipartite network topology. However in many such analyses, this topology is either partially or completely unknown. To address this issue, the original NCA problem is reformulated as a mixed integer nonlinear program (MINLP). Optimal solutions of the MINLP formulation provide network topologies and physically meaningful component signatures that correspond to the best possible data reconstruction. We demonstrate this approach for the analysis of wide angle X-ray scattering (WAXS) data from a branched copolymer system. The copolymer samples vary in side chain length and isothermal crystallization temperature. Employing our analysis we isolate crystalline and amorphous components and observe their temperature-dependent variation. Reasonable agreement is achieved between the degree of crystallinity calculated by this NCA-based decomposition and the experimentally reported values.