[15] Correlation Function Profile Analysis of Polydisperse, Macromolecular Solutions and Colloidal Suspensions

This chapter presents the detailed descriptions of five methods of obtaining information about the characteristic linewidth distribution function G(F) from measured photocount autocorrelation functions, each with its own advantages and disadvantages. The cumulants and nonlinear double exponential approaches require no a priori information about G(F), but are severely limited in the form of the distribution functions they can adequately represents. Both the methods discussed in the chapter are useful in providing starting estimates for the other techniques. The linear multiexponential and histogram approaches with singular value decomposition, and the regularized inversion, address the ill conditioning and may therefore be capable of more detailed dcscription of G(F). The singular value decomposition methods requires a value for the range of G(F) in order to set up the model, are not constrained to physically reasonable distributions, and requires an interactive rank reduction stop to achieve a meaningful solution. The results of the histogram and multiexponential singular value decomposition and regularization techniques are illustrated in the chapter.