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Elements of fractal geometry in the 1H NMR spectrum of a copolymer intercalation-complex: Identification of the underlying Cantor set

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Version 2 2023-06-12, 08:51
Version 1 2023-06-09, 12:40
journal contribution
posted on 2023-06-12, 08:51 authored by John S Shaw, Rajendran Vaiyapuri, Matthew P Parker, Claire A Murray, Kate J C Lim, Cong Pan, Marcus Knappert, Christine J Cardin, Barnaby GreenlandBarnaby Greenland, Ricardo Grau-Crespo, Howard M Colquhoun
Sequence-selective intercalation of pyrene into the chain-folds of a random, binary copolyimide under fast-exchange conditions results in the development of self-similar structure in the diimide region of the 1H NMR spectrum. The resulting spectrum can be described by the mathematics of fractals, an approach that is rationalised in terms of a dynamic summation of ring-current shielding effects produced by pyrene molecules intercalating into the chain at progressively greater distances from each "observed" diimide residue. The underlying set of all such summations is found to be a defined mathematical fractal namely the fourth-quarter Cantor set, within which the observed spectrum is embedded. The pattern of resonances predicted by a geometric construction of the fourth-quarter Cantor set agrees well with the observed spectrum.

History

Publication status

  • Published

File Version

  • Published version

Journal

Chemical Science

ISSN

2041-6539

Publisher

Royal Society of Chemistry

Issue

17

Volume

9

Page range

4052-4061

Department affiliated with

  • Chemistry Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-03-28

First Open Access (FOA) Date

2018-03-28

First Compliant Deposit (FCD) Date

2018-03-28

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