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Modeling Aggregation Processes of Lennard-Jones particles Via Stochastic Networks

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Abstract

We model an isothermal aggregation process of particles/atoms interacting according to the Lennard-Jones pair potential by mapping the energy landscapes of each cluster size N onto stochastic networks, computing transition probabilities from the network for an N-particle cluster to the one for \(N+1\), and connecting these networks into a single joint network. The attachment rate is a control parameter. The resulting network representing the aggregation of up to 14 particles contains 6427 vertices. It is not only time-irreversible but also reducible. To analyze its transient dynamics, we introduce the sequence of the expected initial and pre-attachment distributions and compute them for a wide range of attachment rates and three values of temperature. As a result, we find the configurations most likely to be observed in the process of aggregation for each cluster size. We examine the attachment process and conduct a structural analysis of the sets of local energy minima for every cluster size. We show that both processes taking place in the network, attachment and relaxation, lead to the dominance of icosahedral packing in small (up to 14 atom) clusters.

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Notes

  1. The dataset for LJ\(_{13}\) found in [43] containing 28970 Morse-index one saddles significantly oversamples the set of transition states in comparison with our networks LJ\(_N\), \(N\ge 8\). Therefore, we computed the set of transition states for LJ\(_{13}\) using our technique, so that it is sampled consistently with our networks LJ\(_{N}\), \(6\le N\le 12\) and \(N=14\).

  2. S. Sousa Castellanos (East Carolina University) was M. Cameron’s MAPS-REU student in Summer 2016.

  3. Courtesy of David Wales.

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Acknowledgements

This work was partially supported by the NSF Grant DMS1554907 and the NSF REU Grant DMS1359307 at the University of Maryland, College Park.

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Authors and Affiliations

  1. Yeshiva University, 500 W 185th St, New York, NY, 10033, USA

    Yakir Forman

  2. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Maria Cameron

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  1. Yakir Forman
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Correspondence to Maria Cameron.

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Forman, Y., Cameron, M. Modeling Aggregation Processes of Lennard-Jones particles Via Stochastic Networks. J Stat Phys 168, 408–433 (2017). https://doi.org/10.1007/s10955-017-1794-y

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