Nucleation kinetics estimated by using the modified induction time in cooling crystallization and the applicability to the combined process of antisolvent and cooling crystallization

A previously proposed method for estimating antisolvent crystallization kinetics has been successfully applied to cooling crystallization to yield kinetic parameters for simulating the crystallization process. In particular, the primary nucleation kinetics were analyzed using the modified induction time data, essentially as proposed by Kubota. The number density at the detection point, (N/M)det, is an important value in the kinetic analysis but is difficult to estimate experimentally. Therefore, the numerical optimization was used to estimate the value of (N/M)det in the same manner as for antisolvent crystallization. Primary nucleation was detected for both antisolvent and cooling crystallization with a sensitive detection method, visual detection, to reduce the effects of secondary nucleation. As a result, the (N/M)det values for each method are small and almost identical (approximately 200 #/kg-solvent). The secondary nucleation and growth rate parameters for cooling crystallization were also successfully determined by numerical optimization. All the kinetic parameters determined for cooling crystallization were evaluated with experimental data. Consequently, it is confirmed that these rate parameters can simulate trends in concentration as well as the final number mean diameter of the product crystals with acceptable accuracy. Moreover, the crystallization rate parameters determined for both antisolvent and cooling crystallization were validated with simulations and experimental data from combined crystallization, where antisolvent crystallization is followed by cooling crystallization. The simulation and experimental results for the concentration trend and number mean diameter of the produced crystal were in good agreement. The applicability of our estimation method to both antisolvent and cooling crystallization indicates the broad utility of this method for various crystallization process in the pharmaceutical industry.