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

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.

SUBMITTER: Shaw JS

PROVIDER: S-EPMC5939609 | biostudies-literature | 2018 May

REPOSITORIES: biostudies-literature

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

Shaw John S JS Vaiyapuri Rajendran R Parker Matthew P MP Murray Claire A CA Lim Kate J C KJC Pan Cong C Knappert Marcus M Cardin Christine J CJ Greenland Barnaby W BW Grau-Crespo Ricardo R Colquhoun Howard M HM

Chemical science 20180327 17

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 <sup>1</sup>H 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 ...[more]

PMID: 29780534

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Project description:Alkali ion intercalation is fundamental to battery technologies for a wide spectrum of potential applications that permeate our modern lifestyle, including portable electronics, electric vehicles, and the electric grid. In spite of its importance, the Nernstian nature of the charge transfer process describing lithiation of carbon has not been described previously. Here we use the ultrathin few-layer graphene (FLG) with micron-sized grains as a powerful platform for exploring intercalation and co-intercalation mechanisms of alkali ions with high versatility. Using voltammetric and chronoamperometric methods and bolstered by density functional theory (DFT) calculations, we show the kinetically facile co-intercalation of Li+ and K+ within an ultrathin FLG electrode. While changes in the solution concentration of Li+ lead to a displacement of the staging voltammetric signature with characteristic slopes ca. 54-58 mV per decade, modification of the K+/Li+ ratio in the electrolyte leads to distinct shifts in the voltammetric peaks for (de)intercalation, with a changing slope as low as ca. 30 mV per decade. Bulk ion diffusion coefficients in the carbon host, as measured using the potentiometric intermittent titration technique (PITT) were similarly sensitive to solution composition. DFT results showed that co-intercalation of Li+ and K+ within the same layer in FLG can form thermodynamically favorable systems. Calculated binding energies for co-intercalation systems increased with respect to the area of Li+-only domains and decreased with respect to the concentration of -K-Li- phases. While previous studies of co-intercalation on a graphitic anode typically focus on co-intercalation of solvents and one particular alkali ion, this is to the best of our knowledge the first study elucidating the intercalation behavior of two monovalent alkali ions. This study establishes ultrathin graphitic electrodes as an enabling electroanalytical platform to uncover thermodynamic and kinetic processes of ion intercalation with high versatility.

Dataset Information

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

Publications

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

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