The Statistical Analysis of Light Scattering Data for Polymer Characterization

Abstract

<p> The models derived from classical light scattering theory for predicting Rayleigh light scattering contain useful parameters such as polymer weight average molecular weight, z-average radius of gyration and virial coefficients. The methods used to estimate these model parameters have not been based on sound statistical principles. It is with improved statistical estimation methods for these parameters that this thesis is concerned with. The methods of linear least squares, non-linear least squares and error propagation were applied to the analysis of wide angle and low angle laser light scattering data and the results compared.</p> <p> From the theory of dynamic light scattering, methods have been developed to reconstruct particle size distributions of unimodal, bimodal and polydisperse polymer solutions from the data accumulated in a single experiment. Some of these methods of reconstruction are based upon the estimation of the coefficients in a sum of exponentials. Estimating sums of exponentials is a highly ill-conditioned problem and the problems encountered thereof are examined in this thesis. Linear least squares, non-linear least squares and exponential sampling techniques were applied to experimental data from a number of simulated polymer distributions and the final results compared.</p>