A Bayesian inversion method for estimating the particle size distribution of latexes from multiangle dynamic light scattering measurements

Abstract

A statistical Bayesian method is proposed for estimating the particle size distribution (PSD) of polymeric latexes from multiangle dynamic light scattering (MDLS) measurements. The procedure includes two main steps: 1) the calculation of the angle-dependent average diameters of the PSD from the MDLS autocorrelation measurements, and 2) the PSD estimation through a Bayesian method (that is solved with a Markov chain Monte Carlo sampling strategy implemented in the form of a Metropolis–Hasting algorithm). First, the method was evaluated through two simulated examples that involved unimodal and bimodal PSDs of different shapes. Then, the method was employed for estimating two bimodal PSDs obtained by mixing two narrow polystyrene standards. For comparison, all examples were also solved by numerical inversion of the raw MDLS autocorrelation measurements through a classical regularization technique typically used for inverting ill-conditioned linear problems. The proposed method appears as an effective and robust tool for characterizing unimodal or multimodal PSDs without requiring any a priori assumption on the number of modes or on their shapes. For unimodal PSDs exhibiting high asymmetries and for bimodal PSDs with modes of different particle concentration, the Bayesian method produced more accurate results than those obtained with the classical regularization technique.