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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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Abstract

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.

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

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Publication details

The article was received on 20 Feb 2018, accepted on 21 Mar 2018 and first published on 27 Mar 2018


Article type: Edge Article
DOI: 10.1039/C8SC00830B
Citation: Chem. Sci., 2018, Advance Article
  • Open access: Creative Commons BY-NC license
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    Elements of fractal geometry in the 1H NMR spectrum of a copolymer intercalation-complex: identification of the underlying Cantor set

    J. S. Shaw, R. Vaiyapuri, M. P. Parker, C. A. Murray, K. J. C. Lim, C. Pan, M. Knappert, C. J. Cardin, B. W. Greenland, R. Grau-Crespo and H. M. Colquhoun, Chem. Sci., 2018, Advance Article , DOI: 10.1039/C8SC00830B

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