Maximum-Entropy Analysis of Photon Correlation Spectroscopy Data

The maximum-entropy formalism is briefly reviewed and then applied as a data analysis tool to estimating characteristic line-width distributions from photon correlation spectroscopy data. Two methods for solving the nonlinear maximum-entropy constrained optimization problem for maximal entropy characteristic line-width distributions are described. The reliability of the formalism is then tested by analyzing several sets of numerically simulated correlation data, which correspond to very broad unimodal characteristic line-width distributions, bimodal distributions, and a negatively skewed unimodal distribution. Experimental data of semidilute ternary solutions consisting of a four-arm star polystyrene (PS) and a linear poly(methyl methacrylate) (PMMA) in toluene are analyzed by the maximum-entropy formalism. From the behavior of the reconstructed characteristic line-width distributions, we can show a definite influence of the invisible (isorefractive) but entangled PMMA on the visible PS coils.