A Local Order Parameter-Based Method for Simulation of Free Energy Barriers in Crystal Nucleation

Eslami, Hossein; Khanjari, Neda; Müller‐Plathe, Florian

doi:10.1021/acs.jctc.6b01034

Cited by 34 publications

(38 citation statements)

References 67 publications

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“…The solid‐liquid free energy profiles in Figure consist of two equally deep basins, showing the equilibrium between coexisting liquid and solid phases. The minimum depth in liquid and solid basins correspond to q̃ 6 ≈ 0.2 and 0.8, respectively . The calculated barrier heights for this system, obtained from ANBMTD, from MTD, and from WTMTD are (10.9 ± 0.6) ɛ , (11.2 ± 1.1) ɛ , and (10.8 ± 0.6) ɛ , respectively, which are in close agreement with our recently reported value (≈11 ɛ ).…”

Section: Resultssupporting

confidence: 90%

“…The estimate of the melting point in the literature for a repulsive soft‐sphere system at p* = 24.21 is

T_{m}^{*}

= 1. However, because of the finite‐size effects the coexistence temperature for this small system shifts to a higher temperature,

T_{m}^{*}

= 1.14.…”

Section: Resultsmentioning

confidence: 95%

“…The same two systems have been used by Singh et al to validate their flux‐tempered MTD method. The third system is used as a test system about which much is known from former simulations by van Duijneveldt and Frenkel, by Chopra et al, and from our recent MTD simulations …”

Section: Methodsmentioning

confidence: 99%

“…For studying solid–liquid equilibrium in the repulsive soft sphere system, the collective variable is the same order parameter as recently used in our MTD simulation of crystallization and nucleation, that is,

{\overset{q}{true}}_{6} = \frac{1}{N} {false\sum}_{i = 1}^{N} \frac{1}{N_{b} (|, i)} \underset{j \in N_{b} (i)}{false\sum} {boldq}_{6} (|, i) \cdot {boldq}_{6} (|, j)

where N b ( i ) is the number of neighbors of particle i within a cutoff distance (1.3 σ ). The dot product of normalized 13‐dimensional vectors of neighboring particles i and j , q 6 ( i ) .q 6 ( j ), is defined as

{boldq}_{6} true(i true) . {boldq}_{6} true(j true) = {true \sum}_{m = - 6}^{6} \frac{q_{6 m} true(i true)}{{true(\sum_{m = - 6}^{6} {true| q_{6 m} true(i true) true|}^{2} true)}^{1 / 2}} \cdot \frac{q_{6 m} true(j true)}{{true(\sum_{m = - 6}^{6} {true| q_{6 m} true(j true) true|}^{2} true)}^{1 / 2}}

…”

Section: Methodsmentioning

confidence: 99%

“…The third system is used as a test system about which much is known from former simulations by van Duijneveldt and Frenkel, [33] by Chopra et al, [34] and from our recent MTD simulations. [35] For the first two systems, simulations were carried out for a constant number of particles, N, at constant temperature, T, and constant volume, V, and the same set of parameters reported by Singh et al [32] were used. The third system, however, has been simulated at constant T and constant pressure, p. All simulations were performed with our simulation package, YASP.…”

Section: Simulation Setupmentioning

confidence: 99%

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Adaptive‐numerical‐bias metadynamics

2017

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A metadynamics scheme is presented in which the free energy surface is filled with progressively adding adaptive biasing potentials, obtained from the accumulated probability distribution of the collective variables. Instead of adding Gaussians with assigned height and width in conventional metadynamics method, here we add a more realistic adaptive biasing potential to the Hamiltonian of the system. The shape of the adaptive biasing potential is adjusted on the fly by sampling over the visited states. As the top of the barrier is approached, the biasing potentials become wider. This decreases the problem of trapping the system in the niches, introduced by the addition of Gaussians of fixed height in metadynamics. Our results for the free energy profiles of three test systems show that this method is more accurate and converges more quickly than the conventional metadynamics, and is quite comparable (in accuracy and convergence rate) with the well-tempered metadynamics method. © 2017 Wiley Periodicals, Inc.

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Section: Resultssupporting

confidence: 90%

“…The estimate of the melting point in the literature for a repulsive soft‐sphere system at p* = 24.21 is

T_{m}^{*}

= 1. However, because of the finite‐size effects the coexistence temperature for this small system shifts to a higher temperature,

T_{m}^{*}

= 1.14.…”

Section: Resultsmentioning

confidence: 95%

Section: Methodsmentioning

confidence: 99%

{\overset{q}{true}}_{6} = \frac{1}{N} {false\sum}_{i = 1}^{N} \frac{1}{N_{b} (|, i)} \underset{j \in N_{b} (i)}{false\sum} {boldq}_{6} (|, i) \cdot {boldq}_{6} (|, j)

{boldq}_{6} true(i true) . {boldq}_{6} true(j true) = {true \sum}_{m = - 6}^{6} \frac{q_{6 m} true(i true)}{{true(\sum_{m = - 6}^{6} {true| q_{6 m} true(i true) true|}^{2} true)}^{1 / 2}} \cdot \frac{q_{6 m} true(j true)}{{true(\sum_{m = - 6}^{6} {true| q_{6 m} true(j true) true|}^{2} true)}^{1 / 2}}

…”

Section: Methodsmentioning

confidence: 99%

Section: Simulation Setupmentioning

confidence: 99%

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Adaptive‐numerical‐bias metadynamics

2017

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Self‐Assembly Pathways of Triblock Janus Particles into 3D Open Lattices

Eslami,

Müller‐Plathe

2023

Small

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The self‐assembly of triblock Janus particles is simulated from a fluid to 3D open lattices: pyrochlore, perovskite, and diamond. The coarse‐grained model explicitly takes into account the chemical details of the Janus particles (attractive patches at the poles and repulsion around the equator) and it contains explicit solvent particles. Hydrodynamic interactions are accounted for by dissipative particle dynamics. The relative stability of the crystals depends on the patch width. Narrow, intermediate, and wide patches stabilize the pyrochlore‐, the perovskite‐, and the diamond‐lattice, respectively. The nucleation of all three lattices follows a two‐step mechanism: the particles first agglomerate into a compact and disordered liquid cluster, which does not crystallize until it has grown to a threshold size. Second, the particles reorient inside this cluster to form crystalline nuclei. The free‐energy barriers for the nucleation of pyrochlore and perovskite are ≈10 kBT, which are close to the nucleation barriers of previously studied 2D kagome lattices. The barrier height for the nucleation of diamond, however, is much larger (>20 kBT), as the symmetry of the triblock Janus particles is not perfect for a diamond structure. The large barrier is associated with the reorientation of particles, i.e., the second step of the nucleation mechanism.

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Conformational Disorder Within the Crystalline Region of Silica-Filled Polydimethylsiloxane: A Solid-State NMR Study

Xiong,

Li,

et al. 2024

Chin J Polym Sci

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A Local Order Parameter-Based Method for Simulation of Free Energy Barriers in Crystal Nucleation

Cited by 34 publications

References 67 publications

Adaptive‐numerical‐bias metadynamics

Adaptive‐numerical‐bias metadynamics

Self‐Assembly Pathways of Triblock Janus Particles into 3D Open Lattices

Conformational Disorder Within the Crystalline Region of Silica-Filled Polydimethylsiloxane: A Solid-State NMR Study

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