Size Distribution of Nanoparticles by Dynamic Light Scattering. Comparison of Bayesian and Tikhonov Inversion Methods

Abstract

The diameter distribution of nanometric particles is estimated from multiangle dynamic light scattering (MDLS) measurements by solving an ill-conditioned nonlinear inverse problem through Tikhonov and Bayesian methods. For both methods, the data inputs are the angle-dependent average diameters of the particle size distribution (PSD), which are in turn calculated from the measured autocorrelation functions of the light intensity scattered by a dilute sample of particles. The performance of both methods were tested on the basis of: (i) three simulated polymer latexes that involved PSDs of different shapes, widths, and diameter ranges; and (ii) two real polystyrene latexes obtained by mixing two well-characterized standards of narrow PSDs (of known nominal diameters and standard deviations). For PSDs exhibiting highly-asymmetric modes, or modes of quite different relative concentrations, the Bayesian method produced PSD estimates better than those obtained through Tikhonov regularization.