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

DOI: 10.1039/C8SC00830B DOI Help

Authors: John S. Shaw (University of Reading) , Rajendran Vaiyapuri (University of Reading) , Matthew Parker (University of Reading) , Claire A. Murray (University of Reading) , Kate J. C. Lim (University of Reading) , Cong Pan (University of Reading) , Marcus Knappert (University of Reading) , Christine J. Cardin (University of Reading) , Barnaby W. Greenland (University of Reading) , Ricardo Grau-crespo (University of Reading) , Howard M. Colquhoun (University of Reading)
Co-authored by industrial partner: No

Type: Journal Paper
Journal: Chemical Science , VOL 12

State: Published (Approved)
Published: March 2018

Open Access Open Access

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.

Subject Areas: Chemistry, Mathematics

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