Measurement uncertainties of size, shape, and surface measurements using transmission electron microscopy of near-monodisperse, near-spherical nanoparticles

Abstract

Transmission electron microscopy (TEM) in combination with a systematic selection procedure for unbiased random image collection, semi-automatic image analysis, and data processing has been validated for size, shape, and surface topology measurements of silica nanoparticles. The validation study, assessing the precision and accuracy of the TEM method, consists of series of measurements on two colloidal silica-certified reference materials, with number-based modal area-equivalent circular diameters (ECD) of 19.4 nm (ERM-FD100) and 27.8 nm (ERM-FD304). The measurement uncertainties are estimated for the modal and median particle size, shape, and surface topology parameters of single primary particles. The single primary particles are distinguished from agglomerates using a linear discriminant analysis approach. After optimization of the binning process, the mode associated with the number-based particle size distribution is obtained by lognormal fitting. The methodology described in this paper relies on a high level of automation of calibration, image acquisition, image analysis, and data analysis and gives robust results for the modal ECD. The expanded uncertainty of the modal ECD is estimated to be about 3 %. The largest contribution to the expanded uncertainty stems from the uncertainty associated with the trueness of the TEM method.

Appendices

Appendix 1

See Fig. 6.

Fig. 6

Schematic overview of the experimental setup

Appendix 2

See Table 6.

Table 6 Overview of the pixel size and the size of the field of view, together with the corresponding lower and upper primary particle size quantification limits at magnifications of 18,500 and 68,000 times

Appendix 3

See Table 7.

Table 7 Correlation of the 23 measurands with the ECD size measurand, measured in a subdataset containing only single primary particles of ERM-FD100 and ERM-FD304 at magnifications of 18,500 and 68,000 times

Appendix 4

See Table 8.

Table 8 Type I and Type II separation errors related to the uniparametric linear discriminant analysis of single primary particles and agglomerates in ERM-FD100 and ERM-FD304

Appendix 5

See Fig. 7.

Fig. 7

Comparison of sphericity-based separation of single primary particles and agglomerated primary particles of samples ERM-FD100 and ERM-FD304 at magnifications of 18,500 and 68,000 times. The number-based sphericity distributions of ERM-FD100 and ERM-FD304 at magnifications of 18,500 times (filled circle) and 68,000 times (unfilled circle) are given in (a) and (c), respectively. The separation threshold, which separates the primary particles and agglomerates, is set to 0.4 for ERM-FD100 and to 0.5 for ERM-FD304. This threshold is indicated by a black arrow in (a) and (c). Micrographs (b) and (d) are recorded at a magnification of 68,000 times and illustrate the separation method. Particles in green are primary particles with a sphericity higher than 0.4 for ERM-FD100 (c) and higher than 0.5 for ERM-FD304 (d). Particles with a sphericity lower than these respective thresholds are colored red. Blue circles indicate the misclassified particles. Scale bar corresponds to 200 nm. (Color figure online)

Appendix 6

See Fig. 8.

Fig. 8

Number-based size distributions of ERM-FD100 (a) and ERM-FD304 (b) at magnification of 68,000 times. The reported fittings are based on the mean values of the mode and FWHM in Appendix 7

Appendix 7

See Table 9.

Table 9 Primary particle mean mode and full width at half maximum (FWHM) of the number-based size distributions and the corresponding intra-laboratory uncertainty u(lab) for ERM-FD100 and ERM-FD304 at magnification of 68,000 times

Appendix 8

See Table 10.

Table 10 Mean median values of 23 quantitative measurands, their corresponding standard deviations, s, and intra-laboratory uncertainty, u(lab), for ERM-FD100 at magnifications of 18,500 and 68,000 times

Appendix 9

See Table 11.

Table 11 Mean median values of 23 quantitative measurands, their corresponding standard deviations, s, and intra-laboratory uncertainty, u(lab), for ERM-FD304 at magnifications of 18,500 times and 68,000 times

Appendix 10

See Fig. 9.

Fig. 9

Relative uncertainties (%) for ERM-FD100 at magnification of 18,500 (a) and 68,000 times (b) and for ERM-FD304 magnification of 18,500 (c) and 68,000 times (d). For 23 median measured measurands, the repeatability uncertainty is indicated in blue; the intermediate precision uncertainty is indicated in red and intra-laboratory uncertainty is indicated in green. (Color figure online)