(616c) Relationship between Particle Size Distribution and Chord Length Distribution

Focused Beam Reflectance Measurement (FBRM) has become increasingly popular in pharmaceutical production and research as an in situ particle sizing tool. The interpretation of FBRM data, however, is far from certain and consistent. The objective of this study is to investigate the dependence of chord length counts on the number of particles and particle size, and to elucidate the relationship between particle size distribution (PSD) and chord length distribution (CLD). A series of particle samples with known sizes were prepared. They were added to a crystallizer equipped with a FBRM probe in such a sequence and proportion that from the perspective of FBRM, crystallization events such as nucleation and crystal growth were taking place separately or simultaneously. FBRM data, i.e. counts of chord length and chord length distribution, could be scrutinized in light of the true particle size distribution and the number of particles since they were known at each moment. Perfect spheres as well as real particles commonly used in crystallization research were employed. Three scenarios in crystallization were simulated by blending particle samples in a stirred vessel, that is, pure nucleation, pure crystal growth, simultaneous nucleation and crystal growth. With mono-sized particles, there was a linear relationship between the counts of chord lengths and the number of particles. At the same time, the counts of chord lengths were affected by particle size apart from particle counts. The statistics of CLD such as weighted or un-weighted mean chord length and mode could not be linearly correlated with the statistics of PSD when both particle counts and PSD were changing. The CLD of a mono-sized population deviated significantly from theoretical values as obtained in first principles methods to restore PSD from CLD. FBRM could be used to follow crystallization processes, but it was extremely difficult to extract two critical process variables, i.e., the number of particles and PSD, either by empirical or first principles methods without supplementary information from other process analytical technologies.