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Characterization of Optimal Carbon Nanotubes Under Stretching and Validation of the Cauchy–Born Rule

Abstract

Carbon nanotubes are modeled as point configurations and investigated by minimizing configurational energies including two- and three-body interactions. Optimal configurations are identified with local minima and their fine geometry is fully characterized in terms of lower-dimensional problems. Under moderate tension, we prove the existence of periodic local minimizers, which indeed validates the so-called Cauchy–Born rule in this setting.

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Acknowledgements

Open access funding provided by Austrian Science Fund (FWF). M.F. acknowledges support from the Alexander von Humboldt Stiftung. E.M. acknowledges support from the Austrian Science Fund (FWF) project M 1733-N20. P. P. acknowledges support from the Austrian Science Fund (FWF) project P 29681, and from the Vienna Science and Technology Fund (WWTF), the City of Vienna, and the Berndorf Private Foundation through Project MA16-005. U.S. acknowledges support from the Austrian Science Fund (FWF) projects P 27052, I 2375, and F 65 and from the Vienna Science and Technology Fund (WWTF) through project MA14-009. The authors would like to acknowledge the kind hospitality of the Erwin Schrödinger International Institute for Mathematics and Physics, where part of this research was developed under the frame of the thematic program Nonlinear Flows.

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Friedrich, M., Mainini, E., Piovano, P. et al. Characterization of Optimal Carbon Nanotubes Under Stretching and Validation of the Cauchy–Born Rule. Arch Rational Mech Anal 231, 465–517 (2019). https://doi.org/10.1007/s00205-018-1284-7

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