Amplification of chirality in helical supramolecular polymers: The majority-rules principle

Amplification of chirality, being a strongly nonlinear response of the optical activity of helical polymers to a small (net) amount of optically active material, has recently been discovered in supramolecular copolymers. Apart from the sergeants-and-soldiers type we discussed in earlier work, chirality amplification can also occur in copolymers consisting of the two enantiomeric forms of the monomeric building blocks. We outline the first theoretical treatment of this "majority-rules" type of chirality amplification in self-assembled aggregates. Our treatment, which is based on the one-dimensional, two-component Ising model, is analytical and exact in the infinite-chain limit. We find a strong dependence of the strength of the chirality amplification on the free-energy penalty of a helix reversal as well as on that of a mismatch between the preferred helical handedness of a monomer and the actual screw sense of the bond that follows it. The strength of the chirality amplification shows a monotonic increase with increasing helix reversal penalty but a strongly nonlinear and nonmonotonic dependence on the mismatch penalty.