A rigorous method is proposed to describe and classify the topology of entanglements between periodic networks if the links are of the Hopf type. The catenation pattern is unambiguously identified by a net of barycentres of catenating rings with edges corresponding to the Hopf links; this net is called the Hopf ring net. The Hopf ring net approach is compared with other methods of characterizing entanglements; a number of applications of this approach to various kinds of entanglement (interpenetration, polycatenation and self-catenation) both in modelled network arrays and in coordination networks are considered.
A topological method for the classification of entanglements in crystal networks / E.V. Alexandrov, V.A. Blatov, D.M. Proserpio. - In: ACTA CRYSTALLOGRAPHICA. SECTION A, FOUNDATIONS OF CRYSTALLOGRAPHY. - ISSN 0108-7673. - 68:4(2012), pp. 484-493. [10.1107/S0108767312019034]
A topological method for the classification of entanglements in crystal networks
D.M. ProserpioUltimo
2012
Abstract
A rigorous method is proposed to describe and classify the topology of entanglements between periodic networks if the links are of the Hopf type. The catenation pattern is unambiguously identified by a net of barycentres of catenating rings with edges corresponding to the Hopf links; this net is called the Hopf ring net. The Hopf ring net approach is compared with other methods of characterizing entanglements; a number of applications of this approach to various kinds of entanglement (interpenetration, polycatenation and self-catenation) both in modelled network arrays and in coordination networks are considered.File | Dimensione | Formato | |
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