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

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Shaw, J. S., Vaiyapuri, R., Parker, M. P., Murray, C. A., Lim, K. J. C., Pan, C., Knappert, M., Cardin, C. J. ORCID: https://orcid.org/0000-0002-2556-9995, Greenland, B. W., Grau-Crespo, R. ORCID: https://orcid.org/0000-0001-8845-1719 and Colquhoun, H. M. (2018) Elements of fractal geometry in the 1H NMR spectrum of a copolymer intercalation-complex: identification of the underlying Cantor set. Chemical Science, 9 (17). pp. 4052-4061. ISSN 1478-6524 doi: 10.1039/C8SC00830B

Abstract/Summary

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.

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Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/76182
Item Type	Article
Refereed	Yes
Divisions	Life Sciences > School of Chemistry, Food and Pharmacy > Department of Chemistry Interdisciplinary centres and themes > Chemical Analysis Facility (CAF) > Mass Spectrometry (CAF) Interdisciplinary centres and themes > Chemical Analysis Facility (CAF) > NMR (CAF) Interdisciplinary centres and themes > Chemical Analysis Facility (CAF) > Optical Spectroscopy (CAF) Interdisciplinary centres and themes > Chemical Analysis Facility (CAF) > Xray (CAF) University of Reading Malaysia
Publisher	Royal Society of Chemistry
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Funders:	Engineering and Physical Sciences Research Council	The sponsoring bodies who contributed funding for the creation of this item. Example: NERC Example: The Royal Society of Chemistry A pick list of funders may appear as you type in the funder's name in full or as an acronym. Select a correct match to complete the field or type in a new entry in full. For new entries, the full name is preferred.
Projects:	Nanostructured Polymeric Materials Funded by: Engineering and Physical Sciences Research Council (EP/G026203/1 - £1,082,660) Project Lead: Howard Matthew Colquhoun 1 January 2009 - 31 December 2013 RECOGNITION OF DIGITAL INFORMATION IN SYNTHETIC MACROMOLECULES Funded by: Engineering and Physical Sciences Research Council (EP/E00413X/1 - £365,549) Project Lead: Howard Matthew Colquhoun 1 October 2006 - 31 May 2010	Click Add to select your project (received at Reading) from an autocomplete list.

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Date Deposited:	04 Apr 2018 10:21	Date item deposited into CentAUR
Last Modified:	30 Jun 2024 01:11	Date item last modified

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