Functional data analysis techniques for the study of structural parameters in polymer composites

Abstract

This article presents a novel method, based on functional data analysis, to analyse measurements of structural parameters of polymers and polymer composites. The method is demonstrated using newly developed biodegradable conducting polymer composites prepared via a solution casting technique. The measurements of the macro- and microstructural parameters that are used in the characterization of these films are obtained using X-ray diffraction, an impedance analyser and a UV–vis spectrometer. A functional representation of the measured values of the parameters at different dopant concentrations is adopted by viewing them as realizations of a continuous-time stochastic process observed with measurement error. This allows one to estimate the mean functional relationship between a parameter and the dopant concentration. A functional version of principal component analysis is performed, by which the major modes of variation are discovered and the correlations of parameter values at different concentrations are estimated. This provides insight into local and global features of the relationship between these parameters. Some comments are made on how the parameters vary as a function of dopant concentration.