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A topological method for the classification of entanglements in crystal networks

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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.

Document Type: Research Article

DOI: http://dx.doi.org/10.1107/S0108767312019034

Publication date: July 1, 2012

bsc/aya/2012/00000068/00000004/art00007
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