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Open AccessArticle

A Linear Regression Model for Determining the Pre-Exponential Factor and Interfacial Energy Based on the Metastable Zone Width Data

1
Department of Chemical and Materials Engineering, Chang Gung University, Taoyuan 333, Taiwan
2
Department of Urology, Chang Gung Memorial Hospital Linkou, Taoyuan 333, Taiwan
Crystals 2020, 10(2), 103; https://doi.org/10.3390/cryst10020103
Received: 8 January 2020 / Revised: 6 February 2020 / Accepted: 7 February 2020 / Published: 11 February 2020
(This article belongs to the Special Issue Crystal Growth from Liquid Phase)
A linear regression model is presented in this study to determine the pre-exponential factor and interfacial energy of the crystallized substance based on classical nucleation theory using the metastable zone width data. The nucleation event is assumed corresponding to a point at which the total number density of the nuclei has reached a fixed (but unknown) value. One equation is derived for any temperature-dependent functional form of the solubility. Another equation is derived for the van’t Hoff solubility expression. The pre-exponential factor and interfacial energy obtained from these two equations are found consistent for the studied systems, including glutamic acid, glycine, and 3-nito-1,2,4-triazol-5-one. The results obtained from these two equations are also compared with those obtained from the integral method and classical 3D nucleation theory approach.
Keywords: crystallization; nucleation; metastable zone width; pre-exponential factor; interfacial energy crystallization; nucleation; metastable zone width; pre-exponential factor; interfacial energy
MDPI and ACS Style

Shiau, L.-D. A Linear Regression Model for Determining the Pre-Exponential Factor and Interfacial Energy Based on the Metastable Zone Width Data. Crystals 2020, 10, 103.

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