Abstract
In manufacturing process, it is necessary to measure change in CSD (Crystal Size Distribution) with time accurately because CSD is one of the most important indices that evaluate quality of products. FBRM (Focused Beam Reflectance Measurement) can measure CLD (Chord Length Distribution) in line, but CLD is different from CSD because of principle of FBRM. However, if CSD is determined beforehand, CLD can be calculated from the CSD with statistical method. First, when crystal shape is defined from the characteristic crystal size, the matrix of each crystal shape which transforms CSD into CLD in a uniform manner is calculated with Monte Carlo analysis. Characteristic crystal size is added to the variables defining chord length in order to avoid complex integrals and apply the change in crystal shape with characteristic crystal size to the transforming matrix. Secondly, CSD and CLD are actually measured in suspension of acetaminophen in ethanol and suspension of L-arginine in water to demonstrate the validity of 2 matrices. Lastly, these matrices are multiplied by some simple CSD models to test the properties of these matrices and demonstrate the utility of this transformation.
Highlights
When crystal shape is defined from the characteristic crystal size, the matrix of each crystal shape which transforms Crystal Size Distribution (CSD) into Chord Length Distribution (CLD) in a uniform manner is calculated with Monte Carlo analysis
Focused Beam Reflectance Measurement (FBRM) can measure CLD in line, but it is well known that CLD is different from CSD because of principle of FBRM [2] [3]
The verification experiments show that the relative error between CLD and CSD after transformation was significantly smaller than that between CLD and CSD before transformation only in the case that the actual crystal shapes corresponded with the definition
Summary
Inmanufacturing process of crystal, powder, or granule products, it is necessary to measure change in CSD (crystal size distribution) or PSD (particle size distribution) with time accurately because CSD is one of the most important indices. FBRM (focused beam reflectance measurement) can measure CLD (chord length distribution) in line, but it is well known that CLD is different from CSD because of principle of FBRM [2] [3]. In FBRM, focused beam from probe enters suspension in vessel, and chord length is measured based on detection time of backscattered light when beam runs cylindrically at high speed. Back scattered light results from beam which hits a crystal, but the chord length can differ from the crystal size because the beam doesn’t necessarily scan the crystal along the characteristic crystal size. If CSD is determined beforehand, CLD can be calculated from the CSD with statistical method [4]
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