Particle sizing by dynamic light scattering: non-linear cumulant analysis

TL;DR

This paper evaluates non-linear cumulant analysis for dynamic light scattering data, demonstrating its robustness and accuracy in particle sizing, especially for mean and variance estimation, using computer simulations with realistic noise.

Contribution

It shows that non-linear cumulant analysis is feasible and advantageous over linear methods for particle sizing, with improved accuracy and robustness.

Findings

Non-linear analysis is straightforward with modern computers.

Mean and variance of diffusion constants are accurately estimated for distributions with width up to 0.6.

Higher moments are difficult to determine reliably.

Abstract

We revisit the method of cumulants for analysing dynamic light scattering data in particle sizing applications. Here the data, in the form of the time correlation function of scattered light, is written as a series involving the first few cumulants (or moments) of the distribution of particle diffusion constants. Frisken (2001 Applied Optics 40, 4087) has pointed out that, despite greater computational complexity, a non-linear, iterative, analysis of the data has advantages over the linear least-squares analysis used originally. In order to explore further the potential and limitations of cumulant methods we analyse, by both linear and non-linear methods, computer-generated data with realistic `noise', where the parameters of the distribution can be set explicitly. We find that, with modern computers, non-linear analysis is straightforward and robust. The mean and variance of the distribution of diffusion constants can be obtained quite accurately for distributions of width (standard deviation/mean) up to about 0.6, but there appears to be little prospect of obtaining meaningful higher moments.