Equilibrium Model for Supramolecular Copolymerizations

The coassembly of
different building blocks into supramolecular
copolymers provides a promising avenue to control their properties
and to thereby expand the potential of supramolecular polymers in
applications. However, contrary to covalent copolymerization which
nowadays can be well controlled, the control over sequence, polymer
length, and morphology in supramolecular copolymers is to date less
developed, and their structures are more determined by the delicate
balance in binding free energies between the distinct building blocks
than by kinetics. Consequently, to rationalize the structures of supramolecular
copolymers, a thorough understanding of their thermodynamic behavior
is needed. Though this is well established for single-component assemblies
and over the past years several models have been proposed for specific
copolymerization cases, a generally applicable model for supramolecular
cooperative copolymers is still lacking. Here, we provide a generalization
of our earlier mass-balance models for supramolecular copolymerizations
that encompasses all our earlier models. In this model, the binding
free energies of each pair of monomer types in each aggregate type
can be set independently. We provide scripts to solve the model numerically
for any (co)­polymerization of one or two types of monomer into an
arbitrary number of distinct aggregate types. We illustrate the applicability
of the model on data from literature as well as on new experimental
data of triarylamine triamide-based copolymers in three distinct solvents.
We show that apart from common properties such as the degree of polymerization
and length distributions, our approach also allows us to investigate
properties such as the copolymer microstructure, that is, the internal
ordering of monomers within the copolymers. Moreover, we show that
in some cases, also intriguing analytical approximations can be derived
from the mass balances.