Algorithm to Calculate Particle Size Distributions of Different Particle Shapes from Chord Length Distributions

Tufts University
posted on 01/07/2009

Tufts University Categories:
instrumentation:analytical

Additional Keywords:
(none specified)

Invention Summary

This invention is a computer algorithm, referred hereafter as the Forward Particle Size Distribution Method (FPSDM). It has been developed to convert Chord Length Distribution (CLD) obtained from the Focus Beam Reflectance Measurement (FBRM) instrument, or other similar analytical equipments, into a Particle Size Distribution (PSD). The PSD is a critical piece of information needed to control the quality of commercial products either off-line or on-line and in real time in different polymerization, crystallization, or other similar chemical, pharmaceutical, or food processes. The FPSDM estimates the PSD from the measured CLD very accurately and with very small computational time. It is different form the existing methods such as regularization and projection over convex sets (POCS) , which try to invert a rank deficient matrix relating PSD to CLD based on a single given crystal shape. The advantage of the FPSDM is that it does not need to invert the ill-conditioned conversion matrix. As a result, the FPSDM provides a PSD estimate that does not have an oscillatory behavior when one is not warranted. It also avoids altogether the calculation of erroneous negative number of particles for a given size range. Furthermore, the computation time of the algorithm is less than one minute while the data acquisition time is less than ten seconds. The algorithm can be easily applied as an add-on calculation to the on-line FBRM measurement. Instead of following a rigid operating procedure in a given process, such as constant cooling rate of constant supersaturation, the invention enables the use of a vast variety of other operational procedures focused on the characteristics of the particle size distribution. This could significantly improve the performance of many Pharmaceutical, Chemical, Food, or other related processes.