Non-self-averaging nucleation rate due to quenched disorder

Sear, Richard P.

doi:10.1088/0953-8984/24/5/052205

Cited by 12 publications

(22 citation statements)

References 24 publications

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“…So, even for macroscopic systems the nucleation rate may not have reached the thermodynamic limit. 7 For crystallising droplets although properties such as their heat capacity may be in the thermodynamic limit, the nucleation rate is not. Thus whereas the heat capacity will scale linearly with the volume, the nucleation rate may have a different scaling.…”

Section: Resultsmentioning

confidence: 99%

“…To test the model, I use previously published simulation data 7 for nucleation rates at randomly varying nucleation sites. These sites are clusters produced via a diffusion-limited-aggregation like process.…”

Section: Testmentioning

confidence: 99%

“…These sites are clusters produced via a diffusion-limited-aggregation like process. See Sear 7 for details. I use a large set of 270,000 of these sites (clusters), and for the nucleation rates I use the fit to nucleation rates obtained at a supersaturation given by the lattice model parameter h/kT = 0.03.…”

Section: Testmentioning

confidence: 99%

“…If the rate is the same for all members of a set of samples, then the fraction where nucleation has not occurred must decrease exponentially with time, this is not the case. [1][2][3][4][5][6][7] When I say that the nucleation rate does not exist, I mean that the rate is far from the thermodynamic limit. 11 Properties of a crystallising droplet, such as the heat capacity, viscosity, etc, are in the thermodynamic limit.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of the Scaling of the Nucleation Time with Volume When the Nucleation Rate Does Not Exist

Sear

2013

Crystal Growth & Design

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Recent experimental [Diao et al., J. Am. Chem. Soc. 2011 133, 3756.] and simulation results [Sear, J. Phys. Cond. Matt. 2012 24, 052205.] are not consistent with a nucleation rate that is in the thermodynamic limit. This has consequences, if the rate is not in the thermodynamic limit, the time for nucleation will not necessarily scale as one over system size.Here, I show how to analyse data for nucleation times to test for the existence of a well defined nucleation rate. I also show how to estimate the scaling of the nucleation time with the number of nucleation sites. The prediction is that the farther the system is from the thermodynamic limit, the more rapidly the nucleation time varies with system size. To make this prediction, I use extreme-value statistics. I also show how nucleation data can be analysed to extract information on the heterogeneity in the surfaces nucleation is occurring on.

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Section: Resultsmentioning

confidence: 99%

Section: Testmentioning

confidence: 99%

Section: Testmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimation of the Scaling of the Nucleation Time with Volume When the Nucleation Rate Does Not Exist

Sear

2013

Crystal Growth & Design

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“…Lattice models remain a useful tool in nucleation theory, yielding insights into nonclassical phenomena, [15][16][17] multistep pathways, 18,19 heterogeneous nucleation, 20,21 and limitations of calculation methodology. 22,23 In the following contribution, we present a lattice model of nucleation from solution, where the solute may form disordered, ordered, or semi-ordered solids.…”

Section: Introductionmentioning

confidence: 99%

Nucleation barrier reconstruction via the seeding method in a lattice model with competing nucleation pathways

Lifanov

Vorselaars

Quigley

2016

The Journal of Chemical Physics

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We study a three-species analogue of the Potts lattice gas model of nucleation from solution in a regime where partially disordered solute is a viable thermodynamic phase. Using a multicanonical sampling protocol, we compute phase diagrams for the system, from which we determine a parameter regime where the partially disordered phase is metastable almost everywhere in the temperature-fugacity plane. The resulting model shows non-trivial nucleation and growth behaviour, which we examine via multidimensional free energy calculations. We consider the applicability of the model in capturing the multi-stage nucleation mechanisms of polymorphic biominerals (e.g., CaCO 3 ). We then quantitatively explore the kinetics of nucleation in our model using the increasingly popular "seeding" method. We compare the resulting free energy barrier heights to those obtained via explicit free energy calculations over a wide range of temperatures and fugacities, carefully considering the propagation of statistical error. We find that the ability of the "seeding" method to reproduce accurate free energy barriers is dependent on the degree of supersaturation, and severely limited by the use of a nucleation driving force ∆µ computed for bulk phases. We discuss possible reasons for this in terms of underlying kinetic assumptions, and those of classical nucleation theory. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

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Nucleation and Growth Kinetics from LaMer Burst Data

2017

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In LaMer burst nucleation, the individual nucleation events happen en masse, quasi-simultaneously, and at nearly identical homogeneous conditions. These properties make LaMer burst nucleation important for applications that require monodispersed particles and also for theoretical analyses. Sugimoto and co-workers predicted that the number of nuclei generated during a LaMer burst depends only on the solute supply rate and the growth rate, independent of the nucleation kinetics. Some experiments confirm that solute supply kinetics control the number of nuclei, but flaws in the original theoretical analysis raise questions about the predicted roles of growth and nucleation kinetics. We provide a rigorous analysis of the coupled equations that govern concentrations of nuclei and solutes. Our analysis confirms that the number of nuclei is largely determined by the solute supply and growth rates, but our predicted relationship differs from that of Sugimoto et al. Moreover, we find that additional nucleus size dependent corrections should emerge in systems with slow growth kinetics. Finally, we show how the nucleation kinetics determine the particle size distribution. We suggest that measured particle size distributions might therefore provide ways to test theoretical models of homogeneous nucleation kinetics.

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Non-self-averaging nucleation rate due to quenched disorder

Cited by 12 publications

References 24 publications

Estimation of the Scaling of the Nucleation Time with Volume When the Nucleation Rate Does Not Exist

Estimation of the Scaling of the Nucleation Time with Volume When the Nucleation Rate Does Not Exist

Nucleation barrier reconstruction via the seeding method in a lattice model with competing nucleation pathways

Nucleation and Growth Kinetics from LaMer Burst Data

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