Uncertainty estimation of nanoparticle size distribution from a finite number of data obtained by microscopic analysis

Abstract

Various techniques are used to measure the mean particle size (PS) and the particle size distribution (PSD) and relevant uncertainties of the measured mean PS and PSD can be obtained by using statistical treatments. Among those techniques, microscopic analysis methods provide the possibility to observe individual particles, allowing detailed information about the PS. However, there is no existing method to estimate the uncertainty of the PSD from a finite number of data obtained by microscopic measurement. We found that it is possible to adopt the method of deducing the standard deviation of the sample standard deviation to estimate the PSD uncertainty from the result of a microscopic analysis when the sample data follow a normal or log-normal distribution. The recommended minimum number of data for the application of developed statistical methods was deduced by simulation with population data sets of pseudorandom numbers. It was found that the PS of gold nanoparticles (NPs) synthesized by the conventional reduction method in aqueous solution followed a log-normal distribution, indicating that this method is applicable to estimate the PSD uncertainty of synthetic Au NPs from the measured PS data obtained by microscopic methods.

The effect of the system polydispersity on voltammograms of nanoparticles electrooxidation

“…Considering that the properties of nanoparticles of varying sizes differ (in fact, the smaller the size, the more significant the difference), it is important to take into account not only the average size of nanoparticles but also the distribution of particles according to size. For example, two sols with the same average size but different degrees of dispersion will exhibit different toxicity in biological structures due to the presence of small particles in polydisperse sol that are able to penetrate cell membranes quite easily [7]. Therefore, in general, degree of dispersity should be taken into account interpreting the processes involving polydisperse system participation.…”

Comparison of nanoparticle diameter measurements by Atomic Force Microscopy and Scanning Electron Microscopy

“…Indeed, the edge of the nanoparticles merges often with the noise. The threshold must be carefully fixed because it straight 06007-p. 4 impacts the calculation of the NP lateral diameter in the case of SEM measurements.…”

“…Finally the final size distribution histogram is shown to the user, with the mean value and the standard deviation. The user has the choice to fit the histogram with a normal or a lognormal distribution [4].…”

CARMEN : une plateforme de caractérisation métrologique dédiée aux nanomatériaux

“…Grâce à cette technique, il est aisé d'atteindre les 100 nanoparticules nécessaires afin que la distribution en taille déterminée soit représentative de l'ensemble de la population [25] de la solution colloïdale de départ. Ce traitement sera par la suite adapté aux images SEM afin de mieux étudier la complémentarité AFM/SEM.…”