Parameter Estimation of the Stochastic Primary Nucleation Kinetics by Stochastic Integrals Using Focused-Beam Reflectance Measurements
The kinetic parameters of stochastic primary nucleation were estimated for the batch-cooling crystallization of L-arginine. It is difficult for process analytical tools to detect the first nucleus. In this study, the latent period for the total number of crystals to be increased to a predetermined t...
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MDPI AG
2020-05-01
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| Series: | Crystals |
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| Online Access: | https://www.mdpi.com/2073-4352/10/5/380 |
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| author | Joi Unno Izumi Hirasawa |
| author_facet | Joi Unno Izumi Hirasawa |
| author_sort | Joi Unno |
| collection | DOAJ |
| description | The kinetic parameters of stochastic primary nucleation were estimated for the batch-cooling crystallization of L-arginine. It is difficult for process analytical tools to detect the first nucleus. In this study, the latent period for the total number of crystals to be increased to a predetermined threshold was repeatedly measured with focused-beam reflectance measurements. Consequently, the latent periods were different in each measurement due to the stochastic behavior of both primary and secondary nucleation. Therefore, at first, the distribution of the latent periods was estimated by a Monte Carlo simulation for some combinations of the kinetic parameters of primary nucleation. In the simulation, stochastic integrals of the population and mass balance equations were solved. Then, the parameters of the distribution of latent periods were estimated and correlated with the kinetic parameters of primary nucleation. The resulting correlation was represented by a mapping. Finally, the parameters of the actual distribution were input into the inverse mapping, and the kinetic parameters were estimated as the outputs. The estimated kinetic parameters were validated using statistical techniques, which implied that the observed distribution function of the latent periods for the thresholds used in the estimation coincided reasonably with the simulated one based on the estimated parameters. |
| first_indexed | 2024-03-10T19:59:50Z |
| format | Article |
| id | doaj.art-e0bb9f508d7b49e288b0a56325648842 |
| institution | Directory Open Access Journal |
| issn | 2073-4352 |
| language | English |
| last_indexed | 2024-03-10T19:59:50Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Crystals |
| spelling | doaj.art-e0bb9f508d7b49e288b0a563256488422023-11-19T23:43:01ZengMDPI AGCrystals2073-43522020-05-0110538010.3390/cryst10050380Parameter Estimation of the Stochastic Primary Nucleation Kinetics by Stochastic Integrals Using Focused-Beam Reflectance MeasurementsJoi Unno0Izumi Hirasawa1Department of Applied Chemistry, Waseda University, Okubo 3-4-1, Shinjuku, Tokyo 169-8555, JapanDepartment of Applied Chemistry, Waseda University, Okubo 3-4-1, Shinjuku, Tokyo 169-8555, JapanThe kinetic parameters of stochastic primary nucleation were estimated for the batch-cooling crystallization of L-arginine. It is difficult for process analytical tools to detect the first nucleus. In this study, the latent period for the total number of crystals to be increased to a predetermined threshold was repeatedly measured with focused-beam reflectance measurements. Consequently, the latent periods were different in each measurement due to the stochastic behavior of both primary and secondary nucleation. Therefore, at first, the distribution of the latent periods was estimated by a Monte Carlo simulation for some combinations of the kinetic parameters of primary nucleation. In the simulation, stochastic integrals of the population and mass balance equations were solved. Then, the parameters of the distribution of latent periods were estimated and correlated with the kinetic parameters of primary nucleation. The resulting correlation was represented by a mapping. Finally, the parameters of the actual distribution were input into the inverse mapping, and the kinetic parameters were estimated as the outputs. The estimated kinetic parameters were validated using statistical techniques, which implied that the observed distribution function of the latent periods for the thresholds used in the estimation coincided reasonably with the simulated one based on the estimated parameters.https://www.mdpi.com/2073-4352/10/5/380focused-beam reflectance measurementprimary nucleationstochastic process |
| spellingShingle | Joi Unno Izumi Hirasawa Parameter Estimation of the Stochastic Primary Nucleation Kinetics by Stochastic Integrals Using Focused-Beam Reflectance Measurements Crystals focused-beam reflectance measurement primary nucleation stochastic process |
| title | Parameter Estimation of the Stochastic Primary Nucleation Kinetics by Stochastic Integrals Using Focused-Beam Reflectance Measurements |
| title_full | Parameter Estimation of the Stochastic Primary Nucleation Kinetics by Stochastic Integrals Using Focused-Beam Reflectance Measurements |
| title_fullStr | Parameter Estimation of the Stochastic Primary Nucleation Kinetics by Stochastic Integrals Using Focused-Beam Reflectance Measurements |
| title_full_unstemmed | Parameter Estimation of the Stochastic Primary Nucleation Kinetics by Stochastic Integrals Using Focused-Beam Reflectance Measurements |
| title_short | Parameter Estimation of the Stochastic Primary Nucleation Kinetics by Stochastic Integrals Using Focused-Beam Reflectance Measurements |
| title_sort | parameter estimation of the stochastic primary nucleation kinetics by stochastic integrals using focused beam reflectance measurements |
| topic | focused-beam reflectance measurement primary nucleation stochastic process |
| url | https://www.mdpi.com/2073-4352/10/5/380 |
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