Caveats of mean first-passage time methods applied to the crystallization transition: Effects of non-Markovianity

Jungblut, Swetlana; Dellago, Christoph

doi:10.1063/1.4907364

Cited by 11 publications

(20 citation statements)

References 44 publications

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“…This poor choice of reaction coordinate results in the non-Markovian character of the process and distorts the MFPT analysis. The deviations between the MFPT and TIS rates are even larger than in the case of bulk crystallisation at the same conditions, where rates differ by a factor of two 23 . Here, the deviation depends on the type of the seed and varies between a factor of four (for fcc seeds) and a factor of over 13 (for bcc seeds), as specified in Table I.…”

Section: A Crystal Nucleation Ratesmentioning

confidence: 91%

“…However, as found recently 23 , the MFPT analysis is affected by the nonMarkovianity of the time evolution of the largest cluster size used as reaction coordinate resulting in large inaccuracies in the rate estimate. We will discuss this issue in detail in the next section.…”

Section: Simulationsmentioning

confidence: 99%

“…Reaction rates JV , calculated as fn 1 P (ns = 400|no) (TIS) and 1/τ (ns = 400) (MFPT), their ratio for the systems with four types of the seeds. Also included are values computed for bulk crystallisation 23 Note that, for the particular value of ns = 400 used for the rate calculations, the probability P (ns = 400|no) has reached a plateau, as can be inferred from Fig. 1, indicating that the system has crossed the nucleation barrier.…”

Section: A Crystal Nucleation Ratesmentioning

confidence: 99%

“…This result is rather counterintuitive, because in the bulk the bcc structure is only metastable. As in the case of homogeneous crystallisation 23 , the analysis of recurrence times reveals that the size of the largest crystalline nucleus evolves in a non-Markovian way, pointing to the necessity to include additional collective variables such as structure and shape into the description of the nucleation mechanism.…”

Section: Introductionmentioning

confidence: 99%

“…Although recognized to have its faults, this reaction coordinate still performs best in comparison with other suggested collective variables 18,19 . The deficiency of the size of the largest crystalline cluster becomes particularly apparent 23 in the calculation of crystal nucleation rates within the framework of mean first-passage time (MFPT) analysis [24][25][26][27][28] . In this approach, which is practical only for large undercooling, one carries out straightforward molecular dynamics simulations starting in the metastable liquid.…”

Section: Introductionmentioning

confidence: 99%

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On the reaction coordinate for seeded crystallisation

Jungblut

Dellago

2015

Molecular Physics

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Small pre-structured seeds introduced into an undercooled fluid are known to increase the crystal nucleation rate by some orders of magnitude, if the structure of the seeds is commensurate with the bulk crystalline phase. The presence of such seeds also alters the crystallisation mechanism by favouring particular structures at the early stages of the nucleation process. Here, we study with computer simulations the effect of small face-centred cubic and body-centred cubic seeds on the crystallisation of a Lennard-Jones liquid in the strongly undercooled regime. We find that seeds with body-centred cubic structure lead to a larger enhancement of the crystallisation rate than facecentred cubic seeds. An analysis of recurrence times reveals that the size of the largest crystalline cluster used as reaction coordinate is affected by pronounced memory effects, which depend on the particular seed structure and point to the importance of structural information in the definition of a good reaction coordinate for crystallisation.

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Section: A Crystal Nucleation Ratesmentioning

confidence: 91%

Section: Simulationsmentioning

confidence: 99%

Section: A Crystal Nucleation Ratesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the reaction coordinate for seeded crystallisation

Jungblut

Dellago

2015

Molecular Physics

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Diffusion over barriers

Peters¹

2017

Reaction Rate Theory and Rare Events Simulations

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Mechanisms and Nucleation Rate of Methane Hydrate by Dynamical Nonequilibrium Molecular Dynamics

et al. 2017

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We investigate the effects of high solvated-methane concentration on methane-hydrate nucleation at 250 K and 500 atm. We consider solutions at four levels of methane molar fraction in the initial H2O–CH4 solution, χCH4 = 0.038, 0.044, 0.052, and 0.058, which are higher than (metastable) bulk supersaturation. χCH4 is controlled independently of the temperature and pressure thanks to the use of special simulation techniques [Phys. Chem. Chem. Phys. 2011, 13, 13177]. These conditions mimic a possible increase of local methane concentration beyond supersaturation induced, for example, by freeze concentration or thermal fluctuations. The nucleation mechanism and kinetics are investigated using the dynamical approach to nonequilibrium molecular dynamics. We demonstrate a hydrate-forming/-ordering process of solvated methane and water molecules in a manner consistent with both the “blob” hypothesis and “cage adsorption hypothesis”: the system initially forms an amorphous nucleus at high methane concentration, which then gets ordered, forming the clathrate crystallite. We evaluate nucleation rates using both the methods of the mean first-passage time, i.e., the curve of the average time the system takes to reach a crystalline nucleus of given size, and survival probability, i.e., probability that up to a given time the system has not nucleated yet. We found a dependence of the nucleation rate on initial methane concentration of a form consistent with the dependence of classical nucleation theory rate on supersaturation and determined the relevant parameters of this relation. We found a very rapid increase of nucleation rate with solvated-methane concentration, proving that methane molar fraction, even beyond bulk supersaturation, is key at triggering the homogeneous nucleation of clathrate. We derive a kinetic equation that allows for estimation of the nucleation rate over a wide range of concentration conditions.

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Caveats of mean first-passage time methods applied to the crystallization transition: Effects of non-Markovianity

Cited by 11 publications

References 44 publications

On the reaction coordinate for seeded crystallisation

On the reaction coordinate for seeded crystallisation

Diffusion over barriers

Mechanisms and Nucleation Rate of Methane Hydrate by Dynamical Nonequilibrium Molecular Dynamics

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