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Designability of Graphitic Cones

Published online by Cambridge University Press:  21 March 2011

M. M. J. Treacy and
J. Kilian
M. M. J. Treacy
Affiliation:
NEC Research Institute, Inc. 4 Independence Way, Princeton, NJ 08540–6685, USA
J. Kilian
Affiliation:
NEC Research Institute, Inc. 4 Independence Way, Princeton, NJ 08540–6685, USA
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Abstract

We show that, with topologically flexible seeds which are allowed to explore different growth modes, graphitic cones are inherently more “designable” than flat graphitic disks. The designability of a structure is the number of seed topologies encoding that structure.

We illustrate designability with a simple model, where graphite grows onto Cn (5≤n≤30) ring seeds. For a wide range of ring sizes, cones are the most likely topological outcome. Results from the model agree well with data from special cone-rich carbon black samples.

The concept of designability allows entropy to be incorporated into the “pentagon road” model of the formation of curved graphitic structures.

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