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Energetically favoured defects in dense packings of particles on spherical surfaces

Paquay, S.; Kusumaatmaja, H.; Wales, D.J.; Zandi, R.; van der Schoot, P.

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Authors

S. Paquay

D.J. Wales

R. Zandi

P. van der Schoot



Abstract

The dense packing of interacting particles on spheres has proved to be a useful model for virus capsids and colloidosomes. Indeed, icosahedral symmetry observed in virus capsids corresponds to potential energy minima that occur for magic numbers of, e.g., 12, 32 and 72 identical Lennard-Jones particles, for which the packing has exactly the minimum number of twelve five-fold defects. It is unclear, however, how stable these structures are against thermal agitation. We investigate this property by means of basin-hopping global optimisation and Langevin dynamics for particle numbers between ten and one hundred. An important measure is the number and type of point defects, that is, particles that do not have six nearest neighbours. We find that small icosahedral structures are the most robust against thermal fluctuations, exhibiting fewer excess defects and rearrangements for a wide temperature range. Furthermore, we provide evidence that excess defects appearing at low non-zero temperatures lower the potential energy at the expense of entropy. At higher temperatures defects are, as expected, thermally excited and thus entropically stabilised. If we replace the Lennard-Jones potential by a very short-ranged (Morse) potential, which is arguably more appropriate for colloids and virus capsid proteins, we find that the same particle numbers give a minimum in the potential energy, although for larger particle numbers these minima correspond to different packings. Furthermore, defects are more difficult to excite thermally for the short-ranged potential, suggesting that the short-ranged interaction further stabilises equilibrium structures.

Citation

Paquay, S., Kusumaatmaja, H., Wales, D., Zandi, R., & van der Schoot, P. (2016). Energetically favoured defects in dense packings of particles on spherical surfaces. Soft Matter, 12(26), 5708-5717. https://doi.org/10.1039/c6sm00489j

Journal Article Type Article
Acceptance Date May 23, 2016
Online Publication Date May 25, 2016
Publication Date May 25, 2016
Deposit Date Jun 28, 2016
Publicly Available Date Mar 28, 2024
Journal Soft Matter
Print ISSN 1744-683X
Electronic ISSN 1744-6848
Publisher Royal Society of Chemistry
Peer Reviewed Peer Reviewed
Volume 12
Issue 26
Pages 5708-5717
DOI https://doi.org/10.1039/c6sm00489j
Related Public URLs http://arxiv.org/abs/1602.07945

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