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