Particle Size Distribution Recovery Research Articles

Particle size distribution recovery from non-Gaussian intensity autocorrelation functions obtained from dynamic light scattering at ultra-low particle concentrations

Dynamic light scattering (DLS) from ultra-low concentration suspensions (the average number of particles in the scattering volume is less than ~100) gives rise to autocorrelation functions (ACFs) containing a non-Gaussian term due to particle number fluctuations. This term is difficult to characterize and account for and makes recovery of particle size distribution (PSD) information unreliable. We show that an initial analysis of the intensity ACF to determine parameters describing the amplitude and relaxation rate of the non-Gaussian term and then using these parameters to create a better theoretical non-Gaussian ACF model allows a more accurate recovery of the PSD. The modified model is consistent with the measured ACF data, and a reconstructed kernel matrix matching the measured data is obtained. When compared with the usual kernel function reconstruction (KFR) method, the proposed method gives significantly improved PSD recovery accuracy with experimental data. Furthermore, the PSDs obtained have no obvious differences to those obtained from measurements at normal particle concentrations. • Fitting the measured ACF data with a non-Gaussian ACF model of lower concentration. • Reducing focused beam waist value to obtain non-Gaussian model at lower concentration. • Providing a solution for nanoparticle size measurement at ultra-low concentration.

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

Dynamic light scattering (DLS) is a popular method of particle size measurement, but at ultra-low particle concentrations, the occurrence of number concentration fluctuations limits the use of the technique. Number fluctuations add a non-Gaussian term to the scattered light intensity autocorrelation function (ACF). This leads to an inaccurate particle size distribution (PSD) being recovered if the normal DLS analysis model is used. We propose two methods for inverting the DLS data and recovering the PSDs when number fluctuations are apparent. One is to directly establish the relationship between the non-Gaussian ACF and the PSD by the kernel function reconstruction (KFR) method while including the non-Gaussian term to recover the PSD. The other is to remove the effect of the non-Gaussian term in the ACF by the baseline reset (BR) method. By including the number fluctuation term, the ideal recovered PSD can be obtained from the simulated data, but this will not happen in the experimental measurement data. This is because the measured intensity ACF contains more noise than the simulated ACF at ultra-low concentration. In particular, the baseline noise at the tail of long delay time of ACF overwhelms the number fluctuation term, making it difficult to recover reliable PSD data. Resetting the baseline can effectively remove the digital fluctuation term in ACF, which is also a feasible method to improve PSD recovery under ultra-low concentration. However, increasing noise at ultra-low concentrations can lead to errors in determining an effective baseline. This greatly reduces the accuracy of inversion results. Results from simulated and measured ACF data show that, for both methods, noise on the ACF limits reliable PSD recovery.

Methanol-based extraction protocol for insoluble and moderately water-soluble nanoparticles in plants to enable characterization by single particle ICP-MS.

The detection and characterization of soluble metal nanoparticles in plant tissues are an analytical challenge, though a scientific necessity for regulating nano-enabled agrichemicals. The efficacy of two extraction methods to prepare plant samples for analysis by single particle ICP-MS, an analytical method enabling both size determination and quantification of nanoparticles (NP), was assessed. A standard enzyme-based extraction was compared to a newly developed methanol-based approach. Au, CuO, and ZnO NPs were extracted from three different plant leaf materials (lettuce, corn, and kale) selected for their agricultural relevance and differing characteristics. The enzyme-based approach was found to be unsuitable because of changes in the recovered NP size distribution of CuO NP. The MeOH-based extraction allowed reproducible extraction of the particle size distribution (PSD) without major alteration caused by the extraction. The type of leaf tissue did not significantly affect the recovered PSD. Total metal losses during the extraction process were largely due to the filtration step prior to analysis by spICP-MS, though this did not significantly affect PSD recovery. The methanol extraction worked with the three different NPs and plants tested and is suitable for studying the fate of labile metal-based nano-enabled agrichemicals.

Multi-angle dynamic light scattering analysis based on successive updating of the angular weighting

The angular weighting coefficient is key to accurate particle size distribution (PSD) measurement using multiangle dynamic light scattering (MDLS). However, determining the weighting coefficient is affected by the noise in the measured MDLS data. In this paper, a novel successive updating of the angular weighting (AWSU) method is proposed. By using information character weighting, the angular weighting coefficient and the character weighting matrix are updated once with each additional angle. The effect of autocorrelation function (ACF) denoising and information extraction is improved by using information character weighting step-by-step. The results for broad unimodal and closely-spaced bimodal PSDs demonstrate the effectiveness of this method. Compared with another routinely used inversion method, it is found that the increase in PSD information retrieved from MDLS depends not only on increasing the number of angles, but also on the calculation of the angular weightings. An accurate weighting algorithm can reduce the number of scattering angles required. Using the AWSU method for PSD recovery with 4 scattering angles can give better results than the usual method with 6 scattering angles. It is also found that the AWSU method not only improves the accuracy of the weightings, but it also contributes directly to the PSD recovery by reconstructing the ACF with the PSD obtained by the weighted inversion. The combination of these two contributions not only reduces the number of scattering angles needed, but also keeps the PSD recovery results from getting worse because of excessive scattering angles.

Particle size distribution recovery in dynamic light scattering by optimized multi-parameter regularization based on the singular value distribution

Multi-parameter regularization can improve the over-regularization or under-regularization in the regularized inversion of dynamic light scattering (DLS) data. However, the regularization parameter selected by a fixed adjustment factor is not independent of the other parameters, which results in all the selected parameters being affected by the singular value of the truncation point. This leads to oscillations and false peaks in the recovered particle size distribution (PSD) as the noise in the data increases. In this paper, the singular value distribution characteristics are investigated, and this leads to the proposal of a novel multi-parameter selection method. Using the proportional relationship between two adjacent singular values, a regular parameter function is constructed for the parameter selection. Parameter optimization is performed using fixed point iteration to obtain the regularization parameter sequence corresponding to the singular value distribution. Thus, the effects of small singular values on noise are suppressed. Simulated DLS data for monomodal, closely-spaced bimodal, widely-spaced bimodal and trimodal PSDs were inverted under a range of different noise levels. The results show that, the proposed method greatly reduces the oscillations and false peaks and significantly improves the resolution of the peak position in the recovered PSDs as the noise in the data increases. The performance of the method was also verified using experimental DLS data.

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.

A hybrid artificial bee colony algorithm and pattern search method for inversion of particle size distribution from spectral extinction data

In this paper, a hybrid artificial bee colony (ABC) algorithm and pattern search (PS) method is proposed and applied for recovery of particle size distribution (PSD) from spectral extinction data. To be more useful and practical, size distribution function is modelled as the general Johnson’s function that can overcome the difficulty of not knowing the exact type beforehand encountered in many real circumstances. The proposed hybrid algorithm is evaluated through simulated examples involving unimodal, bimodal and trimodal PSDs with different widths and mean particle diameters. For comparison, all examples are additionally validated by the single ABC algorithm. In addition, the performance of the proposed algorithm is further tested by actual extinction measurements with real standard polystyrene samples immersed in water. Simulation and experimental results illustrate that the hybrid algorithm can be used as an effective technique to retrieve the PSDs with high reliability and accuracy. Compared with the single ABC algorithm, our proposed algorithm can produce more accurate and robust inversion results while taking almost comparative CPU time over ABC algorithm alone. The superiority of ABC and PS hybridization strategy in terms of reaching a better balance of estimation accuracy and computation effort increases its potentials as an excellent inversion technique for reliable and efficient actual measurement of PSD.

Analysis of noisy dynamic light scattering data using constrained regularization techniques

Dynamic light scattering (DLS) from colloidal particles often contains noise, which makes inversion of the correlation function to obtain the particle size distribution (PSD) unreliable. In this work, poor-quality correlation function data with baseline error were analyzed using constrained regularization techniques. The effect of baseline error was investigated, and two strategies were proposed to compensate for baseline error. One strategy is based on edge proportion detection of spurious peaks at large size in the PSD, and the other is based on the solution norm. Results from simulated and experimental data demonstrate the effectiveness of our proposed strategies. The L-curve rules for standard Tikhonov and for constrained regularization, the generalized cross-validation (GCV) rule, and the robust GCV rule were investigated for determination of the regularization parameter. A comparison of these rules was done using both simulated and experimental data. It is shown that correction of baseline error with baseline compensation as well as a reasonable regularization parameter choice improves the accuracy of PSD recovery in poor-quality DLS data analysis.

Particle Size Distribution by Combined Elastic Light Scattering and Turbidity Measurements. A Novel Method to Estimate the Required Normalization Factor

AbstractTurbidity (T) and Elastic Light Scattering (ELS) measurements can be combined to estimate the particle size distribution (PSD) of a polymer latex. To this effect a “normalization factor” must be employed to adequately scale both measurements. In a real application, such factor is a priori unknown, and it must be estimated for determining the PSD. In a previous publication, a method was proposed to simultaneously estimate the normalization factor and the PSD by solving an inverse nonlinear problem. In this work, a simpler technique is presented which estimates the normalization factor and the PSD by sequentially solving two inverse linear problems. To evaluate the proposed technique, a synthetic example based on a polystyrene latex sample with a bimodal PSD was solved. It is shown that, for slight noise measurements, the errors in the estimation of the normalization factor are quite small and have a low effect on the PSD recovery.