Polymer Conjugation as a Strategy for Long-Range Order in Supramolecular Polymers

Supramolecular polymers are polymers in which the individual subunits self-assemble via noncovalent and reversible bonds. An important axis of control for systems of mixed subunit composition is the order in which the subunit types assemble. Existing ordering techniques, which rely on pairwise interactions through the inclusion of highly specific chemistry, have the downside that patterns of length n require n specific chemistries, making long-range order complicated to attain. Here we present a simple alternative method: we attach varying numbers of polymers to self-assembling subunits, in our case ring shaped macrocycles, and the polymers' aversion to confinement imposes system order. We evaluate the feasibility of the strategy using coarse-grained molecular dynamics simulations of polymer-conjugated rings designed to model cyclic peptide nanotubes. We discuss the effects of polymer conjugation on the energetics of association and predict the equilibrium orderings for various ratios of ring types. The emergent patterns are associated with a certain stochastic disorder, which we quantify by deriving and employing a formula for the expected statistical weight of any pattern within the ensemble of all possible orderings.