Process analytical technology (PAT) tools play a crucial role in various industries, enabling monitoring of critical parameters and thus facilitating the understanding of entire processes . Among the various available instrument types, those that allow insight into the particle size distribution (PSD) of crystals are of particular importance, due to its strong impact on downstream processes and overall product quality. While several commercial devices exist, based on different physical principles, among the most widely used particle sizing techniques are the Coulter Counter (CC), Laser Diffraction (LD) , Focused Beam Reflectance Measurement (FBRM)  and imaging methods based on single projection (SP) of crystals. In addition to the particle size, crystal shape is an important characteristic that, together with the size, determines the product’s filterability, flowability and possibly bioavailability.
The goal of this work  is to investigate commonly used particle sizing techniques and to explore whether failing to accurately account for particle shape may have negative and unforeseen consequences in the interpretation of experimental data. As PSD data, typically of one dimension, is utilized more frequently for the assessment of processes and the development of process models, the study of the validity and applicability of different particle sizing techniques for quantitative purposes is of primary importance both for academia and industry.
To this end, we have performed a detailed in silico study, specifically through highly idealized simulations of different particle sizing devices. This approach allows to effectively decouple the impact of shape from other issues present in real applications. In particular, the relationship between the “true” PSSD of an ensemble of growing needle-like crystals (described as convex polytopes) and the PSD measured using various particle sizing techniques, namely LD, CC, FBRM, Single Projection (SP) and Dual Projection (DP)  imaging devices, is investigated.
An analysis is presented for flat vanillin needle-like crystals as grown in water. The “true” (not shown) PSSD was rigidly shifted without a variance increase along any dimension. Simulated measurements of initial and final PSDs and their standard deviations plotted with respect to average sizes are shown in Figs.1 and 2 . The measured PSDs have variances which increased, providing insights into how various measurement techniques may significantly affect experimental data.
Figure. 1 Single Projection (blue) and Dual Projection (red) measurements of growing vanillin needles. Left: initial PSD shown by dashed lines and final PSD shown by solid lines. Right: Variance along the length and width as a function of average crystal length and width, respectively.
Figure. 2 Coulter Counter (CC), Laser Diffraction (LD), and Focused Beam Reflectance Measurement (FBRM) in silico measurements of growing vanillin needles. Left: initial PSD shown by dashed lines and final PSD shown by solid lines. Right: Variance as a function of average diameter ( average chord length in the FBRM case).
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