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Blow KE, Tribello GA, Sosso GC, Quigley D. Interplay of multiple clusters and initial interface positioning for forward flux sampling simulations of crystal nucleation. J Chem Phys 2023; 158:2895225. [PMID: 37290068 DOI: 10.1063/5.0152343] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Accepted: 05/19/2023] [Indexed: 06/10/2023] Open
Abstract
Forward flux sampling (FFS) is a path sampling technique widely used in computer simulations of crystal nucleation from the melt. In such studies, the order parameter underpinning the progress of the FFS algorithm is often the size of the largest crystalline nucleus. In this work, we investigate the effects of two computational aspects of FFS simulations, using the prototypical Lennard-Jones liquid as our computational test bed. First, we quantify the impact of the positioning of the liquid basin and first interface in the space of the order parameter. In particular, we demonstrate that these choices are key to ensuring the consistency of the FFS results. Second, we focus on the frequently encountered scenario where the population of crystalline nuclei is such that there are multiple clusters of size comparable to the largest one. We demonstrate the contribution of clusters other than the largest cluster to the initial flux; however, we also show that they can be safely ignored for the purposes of converging a full FFS calculation. We also investigate the impact of different clusters merging, a process that appears to be facilitated by substantial spatial correlations-at least at the supercooling considered here. Importantly, all of our results have been obtained as a function of system size, thus contributing to the ongoing discussion on the impact of finite size effects on simulations of crystal nucleation. Overall, this work either provides or justifies several practical guidelines for performing FFS simulations that can also be applied to more complex and/or computationally expensive models.
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Affiliation(s)
- Katarina E Blow
- Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Gareth A Tribello
- Centre for Quantum Materials and Technologies, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Gabriele C Sosso
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - David Quigley
- Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
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Galimzyanov BN, Yarullin DT, Mokshin AV. Kinetics of inherent processes counteracting crystallization in supercooled monatomic liquid. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:454002. [PMID: 36067789 DOI: 10.1088/1361-648x/ac8fd1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2022] [Accepted: 09/06/2022] [Indexed: 06/15/2023]
Abstract
Crystallization of supercooled liquids is mainly determined by two competing processes associated with the transition of particles (atoms) from liquid phase to crystalline one and, vice versa, with the return of particles from crystalline phase to liquid one. The quantitative characteristics of these processes are the so-called attachment rateg+and the detachment rateg-, which determine how particles change their belonging from one phase to another. In the present study, acorrespondence rulebetween the ratesg+andg-as functions of the sizeNof growing crystalline nuclei is defined for the first time. In contrast to the well-known detailed balance condition, which relatesg+(N)andg-(N)atN=nc(wherencis the critical nucleus size) and is satisfied only at the beginning of the nucleation regime, the foundcorrespondence ruleis fulfilled at all the main stages of crystallization kinetics (crystal nucleation, growth and coalescence). On the example of crystallizing supercooled Lennard-Jones liquid, the rateg-was calculated for the first time at different supercooling levels and for the wide range of nucleus sizesN∈[nc;40nc]. It was found that for the whole range of nucleus sizes, the detachment rateg-is only≈2% less than the attachment rateg+. This is direct evidence that the role of the processes that counteract crystallization remains significant at all the stages of crystallization. Based on the obtained results, a kinetic equation was formulated for the time-dependent distribution function of the nucleus sizes, that is an alternative to the well-known kinetic Becker-Döring-Zeldovich-Frenkel equation.
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Affiliation(s)
- B N Galimzyanov
- Kazan Federal University, 420008 Kazan, Russia
- Udmurt Federal Research Center of the Ural Branch of the RAS, 426067 Izhevsk, Russia
| | | | - A V Mokshin
- Kazan Federal University, 420008 Kazan, Russia
- Udmurt Federal Research Center of the Ural Branch of the RAS, 426067 Izhevsk, Russia
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Koperwas K, Kaśkosz F, Affouard F, Grzybowski A, Paluch M. The role of the diffusion in the predictions of the classical nucleation theory for quasi-real systems differ in dipole moment value. Sci Rep 2022; 12:9552. [PMID: 35688874 PMCID: PMC9187745 DOI: 10.1038/s41598-022-13715-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Accepted: 04/20/2022] [Indexed: 12/03/2022] Open
Abstract
In this paper, we examine the crystallization tendency for two quasi-real systems, which differ exclusively in the dipole moment's value. The main advantage of the studied system is the fact that despite that their structures are entirely identical, they exhibit different physical properties. Hence, the results obtained for one of the proposed model systems cannot be scaled to reproduce the results for another corresponding system, as it can be done for simple model systems, where structural differences are modeled by the different parameters of the intermolecular interactions. Our results show that both examined systems exhibit similar stability behavior below the melting temperature. This finding is contrary to the predictions of the classical nucleation theory, which suggests a significantly higher crystallization tendency for a more polar system. Our studies indicate that the noted discrepancies are caused by the kinetic aspect of the classical nucleation theory, which overestimates the role of diffusion in the nucleation process.
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Affiliation(s)
- Kajetan Koperwas
- Institute of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1, 41-500, Chorzów, Poland.
| | - Filip Kaśkosz
- Institute of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1, 41-500, Chorzów, Poland.
| | - Frederic Affouard
- Université de Lille, CNRS, INRAE, Centrale Lille, UMR 8207-UMET-Unité Matériaux et Transformations, 59000, Lille, France
| | - Andrzej Grzybowski
- Institute of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1, 41-500, Chorzów, Poland
| | - Marian Paluch
- Institute of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1, 41-500, Chorzów, Poland
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Koperwas K, Tu W, Affouard F, Adrjanowicz K, Kaskosz F, Paluch M. Pressure Dependence of the Crystallization Rate for the S-Enantiomer and a Racemic Mixture of Ibuprofen. CRYSTAL GROWTH & DESIGN 2021; 21:7075-7086. [PMID: 34880715 PMCID: PMC8641391 DOI: 10.1021/acs.cgd.1c00980] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Revised: 10/15/2021] [Indexed: 06/13/2023]
Abstract
This paper examines the pressure effect on the crystallization rate of the pharmaceutically active enantiomerically pure S-enantiomer and the racemic mixture of the well-known drug ibuprofen. Performed experimental studies revealed that at ambient pressure S-ibuprofen crystallizes faster than the racemic mixture. When the pressure increases, the crystallization rate slows down for both systems, but interestingly it is more apparent in the case of the S-enantiomer. It is found that this experimentally observed trend can be understood based on the predictions of the classical nucleation theory. We suggest that the solid-liquid interfacial free energy is the main reason for the observed variations in S- and RS-ibuprofen's stability behaviors. Employing a special method of computational studies, i.e., the capillary fluctuation method, we show that the increase in pressure affects the solid-liquid interfacial free energy for S- and RS-ibuprofen in an entirely different way. Importantly, the detected differences correspond to the experimentally observed variations in the overall crystallization rates.
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Affiliation(s)
- Kajetan Koperwas
- Institute
of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland
- Silesian
Center for Education and Interdisciplinary Research SMCEBI, 75 Pułku Piechoty 1a, 41-500 Chorzów, Poland
| | - Wenkang Tu
- Institute
of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland
- Silesian
Center for Education and Interdisciplinary Research SMCEBI, 75 Pułku Piechoty 1a, 41-500 Chorzów, Poland
| | - Frédéric Affouard
- Université
de Lille, CNRS, INRAE, Centrale Lille, UMR 8207 - UMET - Unité
Matériaux et Transformations, F-59000 Lille, France
| | - Karolina Adrjanowicz
- Institute
of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland
- Silesian
Center for Education and Interdisciplinary Research SMCEBI, 75 Pułku Piechoty 1a, 41-500 Chorzów, Poland
| | - Filip Kaskosz
- Institute
of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland
- Silesian
Center for Education and Interdisciplinary Research SMCEBI, 75 Pułku Piechoty 1a, 41-500 Chorzów, Poland
| | - Marian Paluch
- Institute
of Physics, University of Silesia in Katowice, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland
- Silesian
Center for Education and Interdisciplinary Research SMCEBI, 75 Pułku Piechoty 1a, 41-500 Chorzów, Poland
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