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

Abstract

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.

Dynamic light scattering distributions by any means

“…It is generally accepted that the NNLS distributions are broad due to the data weighting and smoothing necessary for dealing with the inherent noise in the ACF during the inversion process (Xu et al 2018), but the fact that the broadness of the distribution is regularizer-dependent is largely ignored. With simple modification of the regularizer value (or other inversion parameters, such as the size range and the number of bins), very different size distributions may be produced from the same ACF data.…”

Particle Size Measurement Using Dynamic Light Scattering at Ultra-Low Concentration Accounting for Particle Number Fluctuations

“…Furthermore, at long delay times, the noise is more apparent in the intensity ACF. This region is essentially the ACF baseline at normal particle concentrations and it is usually dealt with using truncation or weighting methods [32,33]. However, this segment is located in the number fluctuation region of the ACFs at ultra-low concentration.…”

“…The signal is weaker and the background noise is relatively larger due to the low tions. Furthermore, at long delay times, the noise is more apparent in the This region is essentially the ACF baseline at normal particle concentration ally dealt with using truncation or weighting methods [32,33]. However, t located in the number fluctuation region of the ACFs at ultra-low concen data is noisy, it will be difficult for any model to recover the number flu successfully.…”

Statistical numerical investigation of translational-rotational ultrafast image-based dynamic light scattering to measure a bimodal Gaussian sample of cylindrical nanoparticles

“…The particles are illuminated by a focused Gaussian beam and scatter the light toward a photodetector. The autocorrelation of the intensity scattered by the particles permits retrieval of the size distribution of the particles in the sample using a constrained regularized method [5], a genetic algorithm [6], or Tikhonov regularization [7]. If the particles are nonspherical, the size distribution measured is the distribution of the Stokes translational radius.…”

“…However, the electric field ACFs described in the present paper are based on the DLS theory described in [14] which is involved with the light interferences scattered by the particles. Rather than fitting the bivariate scatter plot 𝐺 versus 𝐺 shown in figures 2 and figure 3, using TR-UIDLS simulations, we suggest an alternative approach based on the linear fit of the scatter plot 𝐺 versus 𝐺 .The first step is to measure the average Stokes radii corresponding to both Gaussian modes, using for instance conventional DLS and derived methods such as a constrained regularization method [5]. Another way currently under study is to fit the histogram of cross-correlation coefficients measured in VV geometry using TR-UIDLS numerical simulations where spherical particles are illuminated.…”