Appendix 1 - PSL_distribution_analysis.pdf

Polystyrene Latex Histogram and Distributional Analysis

Below is an example of a plotted histogram and the distributional analysis required in the solicitation.

This is only an example and does not need to be rigidly followed as long as the general required information is communicated. The data plotted is from a nominal 200 nm diameter polystyrene latex.

The diameters (heights) of 827 particles were measured using atomic force microscopy. [Transmission or scanning electron microscopy may be used to measure the individual particle diameters instead, or individual particle diameters derived from differential mobility analysis.] The black line is a histogram of the data, plotted as a density distribution. The bin widths of the plotted histogram are approximately

0.01 nm, and a 21-point sliding average smoothing function was applied to the raw data for plotting.

[Other bin widths and smoothing functions—or no smoothing function—may be used.] The pink line is a lognormal functional fit to the data which is used to estimate the location and amplitude of the mode.

[Other functional fits or other methods may be used for estimating the mode and modal amplitude.] The mode and peak modal amplitude of the lognormal fit are 206.0 nm and 0.323 nm-1, respectively.

The green horizontal line is the half maximum level (0.161 nm-1) and the markers on the line are located at +2 % and -2 % of the modal value, roughly 210 nm and 202 nm, respectively. Similarly, the blue horizontal line is the 5 % maximum level (0.0161 nm-1) and the vertical hashes mark +4 % and -4 % of the modal value. The plotted distribution easily falls within the required relative width specifications for this sample. However, it is expected that these specifications will be much more challenging to meet with a 100 nm diameter latex.

Please note that the solicitation does not request a dynamic light scattering (DLS) -derived histogram or distribution plot, nor would such a plot fulfil the solicitation requirement. Histograms or distribution plots derived from DLS data are unreliable and almost always misleading with respect to the actual particle size distribution, as shown in a recent publication Farkas, N., Kramar, J.A., J Nanopart Res 23, 120 (2021).

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195 200 205 210 215 q (n m -1

Height (nm) https://link.springer.com/article/10.1007/s11051-021-05220-6 https://link.springer.com/article/10.1007/s11051-021-05220-6