ConspectusRecent 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 n equations can be formed with the n free monomer
concentrations as the only unknowns. This set of mass-balance equations
can then be solved numerically, yielding the free monomer concentrations,
from which the complete system can be reconstituted.By a step-by-step
extension of the model for the aggregation of
a single monomer type to include the formation of multiple aggregate
types and the coassembly of multiple monomer types, we can capture
increasingly complex supramolecular (co)polymerizations. In each step
we illustrate how the extended model explains in detail another of
the experimentally observed nonlinear effects, with the common denominator
that small differences in association energies are intricately amplified
at the supramolecular level. We finally arrive at our latest and most
general approach to modeling (cooperative) supramolecular (co)polymerization,
which encompasses all of our earlier models and shows great promise
to help rationalize also future systems featuring ever-increasing
complexity.