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

Co-polycondensation of the diimide-based diols N,N'-bis(2-hydroxyethyl)hexafluoro-isopropylidene-diphthalimide, (HFDI), and N,N'-bis(2-hydroxy-ethyl)naphthalene-1,4,5,8-tetracarboxylic-diimide, (NDI), with aliphatic diacyl chlorides ClOC(CH2)xCOCl (x = 5 to 8) affords linear copoly(ester-imide)s. Such copolymers interact with pyrene via supramolecular binding of the polycyclic aromatic molecule at NDI residues. This results in upfield complexation shifts and sequence-related splittings of the NDI 1H NMR resonances, but gives a very different resonance-pattern from the corresponding copolymer where x = 2. Computational modelling of the polymer with x = 5 suggests that, in this system, each pyrene molecule binds to just a single NDI residue rather than to an adjacent pair of NDI's in a tight chain-fold ("dual-site" binding) as found for x = 2. The new single-site binding model enables the pattern of 1H NMR resonances for copolymers with longer spacers (x = 5 to 8) to be reproduced and assigned by simulation from sequence-specific shielding factors based on the fractal known as the fourth-quarter Cantor set. As this set also enables an understanding of dual-site binding systems, it evidently provides a general numerical framework for supramolecular sequence-analysis in binary copolymers.