Two-step crystal nucleation kinetics: solution of the master equation

2021 ◽  
pp. 126469
Author(s):  
Stefan Auer ◽  
Dimo Kashchiev
IUCrJ ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 468-479
Author(s):  
Danning Li ◽  
Yongli Wang ◽  
Shuyi Zong ◽  
Na Wang ◽  
Xin Li ◽  
...  

As the first step in the crystallization process, nucleation has been studied by many researchers. In this work, phenacetin (PHEN) was selected as a model compound to investigate the relationship between the solvent and nucleation kinetics. Induction times at different supersaturation in six solvents were measured. FTIR and NMR spectroscopy were employed to explore the solvent–solute interactions and the self-association properties in solution. Density functional theory (DFT) was adopted to evaluate the strength of solute–solvent interactions and the molecular conformations in different solvents. Based on these spectroscopy data, molecular simulation and nucleation kinetic results, a comprehensive understanding of the relationship between molecular structure, crystal structure, solution chemistry and nucleation dynamics is discussed. Both the solute–solvent interaction strength and the supramolecular structure formed by the self-association of solute molecules affect the nucleation rate. The findings reported here shed new light on the molecular mechanism of nucleation in solution.


1985 ◽  
Vol 57 ◽  
Author(s):  
D. R. Uhlmann ◽  
M. C. Weinberg

AbstractThe role of nucleation kinetics in affecting glass formation behavior is discussed. Also considered are measurements of homogeneous crystal nucleation in a variety of liquids. For a number of oxide glass-forming liquids, available data indicate pre-exponential factors which are larger than those predicted from classical nucleation theory by factors of 1017 to 1049. Possible sources of this discrepancy are discussed.


Author(s):  
Dmitri V. Alexandrov ◽  
Alexander A. Ivanov ◽  
Irina V. Alexandrova

The processes of particle nucleation and their evolution in a moving metastable layer of phase transition (supercooled liquid or supersaturated solution) are studied analytically. The transient integro-differential model for the density distribution function and metastability level is solved for the kinetic and diffusionally controlled regimes of crystal growth. The Weber–Volmer–Frenkel–Zel’dovich and Meirs mechanisms for nucleation kinetics are used. We demonstrate that the phase transition boundary lying between the mushy and pure liquid layers evolves with time according to the following power dynamic law: , where Z 1 ( t )= βt 7/2 and Z 1 ( t )= βt 2 in cases of kinetic and diffusionally controlled scenarios. The growth rate parameters α , β and ε are determined analytically. We show that the phase transition interface in the presence of crystal nucleation and evolution propagates slower than in the absence of their nucleation. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.


2016 ◽  
Vol 145 (21) ◽  
pp. 211920 ◽  
Author(s):  
Prabhat K. Gupta ◽  
Daniel R. Cassar ◽  
Edgar D. Zanotto

2002 ◽  
Vol 2 (5) ◽  
pp. 395-400 ◽  
Author(s):  
Venkateswarlu Bhamidi ◽  
Sasidhar Varanasi ◽  
Constance A. Schall

2015 ◽  
Vol 41 (4) ◽  
pp. 327-338 ◽  
Author(s):  
Ivaylo L. Dimitrov ◽  
Feyzim V. Hodzhaoglu ◽  
Dobryana P. Koleva

2017 ◽  
Vol 18 (1) ◽  
pp. 540-551 ◽  
Author(s):  
Yan Xiao ◽  
Jingkang Wang ◽  
Xin Huang ◽  
Huanhuan Shi ◽  
Yanan Zhou ◽  
...  

2015 ◽  
Vol 179 ◽  
pp. 41-58 ◽  
Author(s):  
Andrea Sauter ◽  
Felix Roosen-Runge ◽  
Fajun Zhang ◽  
Gudrun Lotze ◽  
Artem Feoktystov ◽  
...  

We report a real-time study on protein crystallization in the presence of multivalent salts using small angle X-ray scattering (SAXS) and optical microscopy, focusing particularly on the nucleation mechanism as well as on the role of the metastable intermediate phase (MIP). Using bovine beta-lactoglobulin as a model system in the presence of the divalent salt CdCl2, we have monitored the early stage of crystallization kinetics which demonstrates a two-step nucleation mechanism: protein aggregates form a MIP, which is followed by the nucleation of crystals within the MIP. Here we focus on characterizing and tuning the structure of the MIP using salt and the related effects on the two-step nucleation kinetics. The results suggest that increasing the salt concentration near the transition zonepseudo-c** enhances the energy barrier for both MIPs and crystal nucleation, leading to slow growth. The structural evolution of the MIP and its effect on subsequent nucleation is discussed based on the growth kinetics. The observed kinetics can be well described, using a rate-equation model based on a clear physical two-step picture. This real-time study not only provides evidence for a two-step nucleation process for protein crystallization, but also elucidates the role and the structural signature of the MIPs in the nonclassical process of protein crystallization.


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