Inverse problems in polymer characterization: Direct analysis of polydispersity with photon correlation spectroscopy

Abstract

Abstract A method is presented for inverting the Fredholm integral equations of the first kind that arise in many experimental determinations of molecular weight distributions of high polymers. The well known problems of instability and nonuniqueness are minimized by constraining the distribution to be the smoothest nonnegative one that is consistent with the data. Analyses of simulated photon correlation spectroscopy data show that good accuracy can be obtained for unimodal distributions and fair accuracy for certain bimodal ones, provided that systematic errors are kept below the random noise level. The method is completely automatic in that no initial estimate or prior information about the distribution is needed. However, if there happens to be a priori knowledge that the distribution is unimodal or that it is bimodal, constraining the distribution accordingly can further improve the stability and accuracy.