Abstract
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.
Highlights
The nucleation behavior in a supersaturated solution is closely related to the induction time or metastable zone width (MSZW) measurements [1,2,3]
Shiau and Lu [31,32,33] developed an integral model to determine the pre-exponential factor and interfacial energy based on classical nucleation theory (CNT) using the MSZW data
A linear regression method is proposed in this work to determine the pre-exponential factor and interfacial energy based on CNT using the MSZW data
Summary
The nucleation behavior in a supersaturated solution is closely related to the induction time or metastable zone width (MSZW) measurements [1,2,3]. The MSZW data should be more reliable than the induction time data in determination of the nucleation rate for a system. In classical nucleation theory (CNT) [1,2,3], the nucleation rate of a crystallization system depends on both the pre-exponential factor and interfacial energy, which are usually determined using induction time data by assuming J ∝ ti −1 , where J is the nucleation rate and ti is the induction time [4,5,6,7,8,9,10]. Due to the complicated data interpretation method, determination of the pre-exponential factor and interfacial energy using MSZW data has long been a challenging task. Based on the Nyvlt’s approach [11,12], Sangwal [13,14,15,16] proposed a self-consistent
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