Co-polycondensation
of the diimide-based diols<i> N</i>,<i>N</i>'-bis(2-hydroxyethyl)hexafluoro-isopropylidene-diphthalimide,
(HFDI), and <i>N</i>,<i>N</i>'-bis(2-hydroxy-ethyl)naphthalene-1,4,5,8-tetracarboxylic-diimide,
(NDI), with aliphatic diacyl chlorides ClOC(CH<sub>2</sub>)<i><sub>x</sub></i>COCl (<i>x</i> = 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 <sup>1</sup>H NMR resonances, but gives a very different resonance-pattern
from the corresponding copolymer where <i>x</i>
= 2. Computational modelling of the polymer with <i>x</i> = 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 <i>x</i> = 2. The new single-site binding model enables the pattern of <sup>1</sup>H
NMR resonances for copolymers with longer spacers (<i>x</i> = 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.