Next Article in Journal
Enhanced Mechanical Properties of Surface Treated AZ31 Reinforced Polymer Composites
Previous Article in Journal
Unexpected Sandwiched-Layer Structure of the Cocrystal Formed by Hexamethylbenzene with 1,3-Diiodotetrafluorobenzene: A Combined Theoretical and Crystallographic Study
Previous Article in Special Issue
Effects of Various Inhibitors on the Nucleation of Calcium Oxalate in Synthetic Urine
Open AccessArticle

Parameter Estimation of the Stochastic Primary Nucleation Kinetics by Stochastic Integrals Using Focused-Beam Reflectance Measurements

Department of Applied Chemistry, Waseda University, Okubo 3-4-1, Shinjuku, Tokyo 169-8555, Japan
*
Author to whom correspondence should be addressed.
Crystals 2020, 10(5), 380; https://doi.org/10.3390/cryst10050380
Received: 27 April 2020 / Revised: 1 May 2020 / Accepted: 4 May 2020 / Published: 7 May 2020
(This article belongs to the Special Issue Kinetic Processes of Crystal Growth)
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. View Full-Text
Keywords: focused-beam reflectance measurement; primary nucleation; stochastic process focused-beam reflectance measurement; primary nucleation; stochastic process
Show Figures

Graphical abstract

MDPI and ACS Style

Unno, J.; Hirasawa, I. Parameter Estimation of the Stochastic Primary Nucleation Kinetics by Stochastic Integrals Using Focused-Beam Reflectance Measurements. Crystals 2020, 10, 380.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop