Luis A. Clementi

Information-weighted constrained regularization for particle size distribution recovery in multiangle dynamic light scattering

In particle size measurement with dynamic light scattering (DLS), it is difficult to get an accurate recovery of a bimodal particle size distribution (PSD) with a peak position ratio less than ~2:1, especially when large particles (>350nm) are present. This is due to the inherent noise in the autocorrelation function (ACF) data and the scarce utilization of PSD information during the inversion process. In this paper, the PSD information distribution in the ACF data is investigated. It was found that the initial decay section of the ACF contains more information, especially for a bimodal PSD. Based on this, an information-weighted constrained regularization (IWCR) method is proposed in this paper and applied in multiangle DLS analysis for bimodal PSD recovery. By using larger (or smaller) coefficients for weighting the ACF data, more (or less) weight can then be given to the initial part of the ACF. In this way, the IWCR method can enhance utilization of the PSD information in the ACF data, and effectively weaken the effect of noise at large delay time on PSD recovery. Using this method, bimodal PSDs (with nominal diameters of 400:608 nm, 448:608 nm, 500:600 nm) were recovered successfully from simulated data and it appears that the IWCR method can improve the recovery resolution for closely spaced bimodal particles. Results of the PSD recovery from experimental DLS data confirm the performance of this method.

Size distribution of nanoparticles by dynamic light scattering. Comparison of Bayesian and Tikhonov inversion methods

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 performances of both methods were tested on the basis of: (i) two 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.