Supramolecular complexation between chain-folding poly(ester-imide)s and polycyclic aromatics: a fractal-based pattern of NMR ring-current shielding

Abstract

Supramolecular complexation of pyrene with a chain-folding, NDI-based co-poly(ester-imide) generates a 1H NMR pattern showing fractal-type character.

Single-site binding of pyrene to poly(ester-imide)s incorporating long spacer-units: prediction of NMR resonance-patterns from a fractal model

“…[12][13][14][15] Using the latter technique, we recently showed that highly sequence-dependent 1 H NMR complexation shis are produced in the spectra of copolyimides based on 1,4,5,8-naphthalene tetracarboxylic diimide (NDI) on complexation of an aromatic "probe" molecule such as pyrene or perylene. 15,16 This phenomenon results from cumulative ring-current shielding 17,18 of the central residue in an NDI-centred sequence by probemolecules binding through complementary p-p-stacking. [19][20][21] Such shielding results not only from the probe-molecule binding directly at the central "observed" NDI residue but, additionally, from complexation to NDI residues at neighbouring (and next-neighbouring, and next-next-neighbouring etc.)…”

“…the spectra consist of multiple copies of themselves over a range of different length-scales. 15,16 These resonance-patterns have been shown to reect an underlying fractal distribution [34][35][36][37] of ring-current shieldings generated by pyrene molecules binding to all the different sequences within which a "central" NDI residue is embedded. 15,16 The mathematical fractal underpinning the pattern of complexation shis in such systems was identied 15 as a "last fraction" Cantor set.…”

“…1). 15,16 This "factor of four" in turn dened the set of all predicted complexation shis, mathematically, as the fourth-quarter Cantor set. A complete mathematical description of this set is given in Section 3.3 and in the ESI † but, as with all onedimensional Cantor sets, it can be visualised graphically by the iteration of an operation on a line.…”

“…Studies of homopoly(ester-imide)s containing p-electronpoor NDI residues linked by aliphatic diester units (polymers 1 to 8 in Chart 1) have shown that the strength of supramolecular binding is highly dependent on the length of the diester spacer, with a sharp maximum in binding energy for homopolymer 2, where x ¼ 2. 16 Computational modelling suggested that the short, "x ¼ 2" diester spacer-unit forms a tight chain- Fig. 1 Schematic of pyrene binding to a chain-folding copoly(esterimide) sequence.…”

“…1 Schematic of pyrene binding to a chain-folding copoly(esterimide) sequence. 16 Key: purple ¼ pyrene; blue ¼ "observed" protons of the central NDI residue (red); black ¼ other NDI residues; gold ¼ nonbinding (HFDI) residues. The aromatic diimide residues are linked by aliphatic diester units, [-CH 2 CH 2 OCO(CH 2 ) 2 COOCH 2 CH 2 -], represented as thin black lines.…”