Mass-Balance Models for Scrutinizing Supramolecular (Co)polymerizations in Thermodynamic Equilibrium.

Recent years have witnessed increasing attention on supramolecular polymerization, i.e., the formation of one-dimensional aggregates in which the monomeric units bind together via reversible and usually highly directional non-covalent interactions. Because of the presence of these reversible interactions, such as hydrogen bonding, π-π interactions, or metal coordination, supramolecular polymers exhibit numerous desirable properties ranging from high thermoresponsiveness to self-healing and great capacity for processability and recycling. These properties relate to intriguing experimentally observed nonlinear effects such as the monomer-dependent presence of a critical temperature for aggregation and a solvent- and temperature-tunable aggregate morphology. For coassemblies this is complemented with monomer-ratio- and monomer-compatibility-dependent internal order as well as majority-rules-type chiral amplification. However, the dynamic nature of the (co)polymers and the intricate interplay of many interactions make these effects difficult to rationalize without theoretical models. This Account presents recent advances in the development and use of equilibrium models for supramolecular copolymerization based on mass balances, mainly developed by our group. The basic idea of these models is that we describe a supramolecular (co)polymerization by a set of independent equilibrium reactions, like monomer associations and dissociations, and that in thermodynamic equilibrium the concentrations of the reactants and products in each reaction are coupled via the equilibrium constant of that reaction. Recursion then allows the concentration of each possible aggregate to be written as a function of the free monomer concentrations. Because a monomer should be present either as a free monomer or in one of the aggregates, a set of