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Yao L, Jack RL. Heterogeneous nucleation in the random field Ising model. J Chem Phys 2023; 159:244110. [PMID: 38149735 DOI: 10.1063/5.0181596] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2023] [Accepted: 11/30/2023] [Indexed: 12/28/2023] Open
Abstract
We investigate the nucleation dynamics of the three-dimensional random field Ising model under an external field. We use umbrella sampling to compute the free-energy cost of a critical nucleus and use forward flux sampling for the direct estimation of nucleation rates. For moderate to strong disorder, our results indicate that the size of the nucleating cluster is not a good reaction coordinate, contrary to the pure Ising model. We rectify this problem by introducing a coordinate that also accounts for the location of the nucleus. Using the free energy barrier to predict the nucleation rate, we find reasonable agreement, although deviations become stronger as disorder increases. We attribute this effect to cluster shape fluctuations. We also discuss finite-size effects on the nucleation rate.
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Affiliation(s)
- Liheng Yao
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert L Jack
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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2
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Yang X, Lu ZY. Nanoparticle cluster formation mechanisms elucidated via Markov state modeling: Attraction range effects, aggregation pathways, and counterintuitive transition rates. J Chem Phys 2022; 156:214902. [DOI: 10.1063/5.0086110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Nanoparticle clusters are promising candidates for developing functional materials. However, it is still a challenging task to fabricate them in a predictable and controllable way, which requires investigation of the possible mechanisms underlying cluster formation at the nanoscale. By constructing Markov state models (MSMs) at the microstate level, we find that for highly dispersed particles to form a highly aggregated cluster, there are multiple coexisting pathways, which correspond to direct aggregation, or pathways that need to pass through partially aggregated, intermediate states. Varying the range of attraction between nanoparticles is found to significantly affect pathways. As the attraction range becomes narrower, compared to direct aggregation, some pathways that need to pass through partially aggregated intermediate states become more competitive. In addition, from MSMs constructed at the macrostate level, the aggregation rate is found to be counterintuitively lower with a lower free-energy barrier, which is also discussed.
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Affiliation(s)
- Xi Yang
- Institute of Theoretical Chemistry, State Key Laboratory of Supramolecular Structure and Materials, Jilin University, Changchun 130021, China
| | - Zhong-Yuan Lu
- Institute of Theoretical Chemistry, State Key Laboratory of Supramolecular Structure and Materials, Jilin University, Changchun 130021, China
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Moritz C, Geissler PL, Dellago C. The microscopic mechanism of bulk melting of ice. J Chem Phys 2021; 155:124501. [PMID: 34598556 DOI: 10.1063/5.0064380] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
We study the initial stages of homogeneous melting of a hexagonal ice crystal at coexistence and at moderate superheating. Our trajectory-based computer simulation approach provides a comprehensive picture of the events that lead to melting, from the initial accumulation of 5+7 defects, via the formation of L-D and interstitial-vacancy pairs, to the formation of a liquid nucleus. Of the different types of defects that we observe to be involved in melting, a particular kind of 5+7 type defect (type 5) plays a prominent role as it often forms prior to the formation of the initial liquid nucleus and close to the site where the nucleus forms. Hence, like other solids, ice homogeneously melts via the prior accumulation of defects.
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Affiliation(s)
- Clemens Moritz
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Phillip L Geissler
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Christoph Dellago
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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Moritz C, Sega M, Innerbichler M, Geissler PL, Dellago C. Weak scaling of the contact distance between two fluctuating interfaces with system size. Phys Rev E 2020; 102:062801. [PMID: 33465946 DOI: 10.1103/physreve.102.062801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2020] [Accepted: 10/30/2020] [Indexed: 06/12/2023]
Abstract
A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers-of-mass remain separated by a nonzero distance ℓ. An example of such a situation is the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Here we present a general approach to calculate the probability distribution of the contact distance ℓ and determine how its most likely value ℓ^{*} depends on the surfaces' lateral size L. Using the Edward-Wilkinson equation as a model for interfaces, we demonstrate that ℓ^{*} scales weakly with system size, i.e., the dependence of ℓ^{*} on L for both (1+1)- and (2+1)-dimensional interfaces is such that lim_{L→∞}(ℓ^{*}/L)=0. In particular, for (2+1)-dimensional interfaces ℓ^{*} is an algebraic function of logL, a result that is confirmed by computer simulations of slab-shaped domains formed under periodic boundary conditions. This weak scaling implies that such domains remain topologically intact until ℓ becomes very small compared to the lateral size of the interface, contradicting expectations from equilibrium thermodynamics.
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Affiliation(s)
- Clemens Moritz
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Marcello Sega
- Forschungszentrum Jülich GmbH, Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Fürther Straße 248, 90429 Nürnberg, Germany
| | - Max Innerbichler
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Phillip L Geissler
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Christoph Dellago
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
- Erwin Schrödinger Institute for Mathematics and Physics, Boltzmanngasse 9, 1090, Vienna, Austria
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Sigg D, Voelz VA, Carnevale V. Microcanonical coarse-graining of the kinetic Ising model. J Chem Phys 2020; 152:084104. [PMID: 32113343 PMCID: PMC7042020 DOI: 10.1063/1.5139228] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2019] [Accepted: 02/06/2020] [Indexed: 11/15/2022] Open
Abstract
We propose a scheme for coarse-graining the dynamics of the 2-D kinetic Ising model onto the microcanonical ensemble. At subcritical temperatures, 2-D and higher-dimensional Ising lattices possess two basins of attraction separated by a free energy barrier. Projecting onto the microcanonical ensemble has the advantage that the dependence of the crossing rate constant on environmental conditions can be obtained from a single Monte Carlo trajectory. Using various numerical methods, we computed the forward rate constants of coarse-grained representations of the Ising model and compared them with the true value obtained from brute force simulation. While coarse-graining preserves detailed balance, the computed rate constants for barrier heights between 5 kT and 9 kT were consistently 50% larger than the true value. Markovianity testing revealed loss of dynamical memory, which we propose accounts for coarse-graining error. Committor analysis did not support the alternative hypothesis that microcanonical projection is incompatible with an optimal reaction coordinate. The correct crossing rate constant was obtained by spectrally decomposing the diffusion coefficient near the free energy barrier and selecting the slowest (reactive) component. The spectral method also yielded the correct rate constant in the 3-D Ising lattice, where coarse-graining error was 6% and memory effects were diminished. We conclude that microcanonical coarse-graining supplemented by spectral analysis of short-term barrier fluctuations provides a comprehensive kinetic description of barrier crossing in a non-inertial continuous-time jump process.
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Affiliation(s)
| | - Vincent A. Voelz
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Vincenzo Carnevale
- Institute for Computational Molecular Science, College of Science and Technology, Temple University, Philadelphia, Pennsylvania 19122, USA
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Richard D, Speck T. Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension. J Chem Phys 2018; 148:224102. [DOI: 10.1063/1.5025394] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- David Richard
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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Tröster A, Schmitz F, Virnau P, Binder K. Equilibrium between a Droplet and Surrounding Vapor: A Discussion of Finite Size Effects. J Phys Chem B 2017; 122:3407-3417. [DOI: 10.1021/acs.jpcb.7b10392] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Andreas Tröster
- Institute of Materials Chemistry, Vienna University of Technology, Getreidemarkt 9, A-1060 Wien, Austria
| | - Fabian Schmitz
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany
| | - Peter Virnau
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany
| | - Kurt Binder
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, D-55099 Mainz, Germany
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Tiwary P. Molecular Determinants and Bottlenecks in the Dissociation Dynamics of Biotin–Streptavidin. J Phys Chem B 2017; 121:10841-10849. [DOI: 10.1021/acs.jpcb.7b09510] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Pratyush Tiwary
- Department of Chemistry and
Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park 20742, United States
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