Amplification of Chirality of the Majority-Rules Type in Helical Supramolecular Polymers: The Impact of the Presence of Achiral Monomers

Abstract

We present a theoretical treatment describing the conformational state of helical supramolecular polymers that consist of three types of monomer: right-handed and left-handed chiral monomers and achiral ones. We find that chirality amplification of the majority-rules type, that is, a disproportionately large shift in the helix screw sense due to a small enantiomeric excess, can occur in these polymers. The strength of the chirality amplification depends on the free-energy penalty of a helix reversal along the self-assembled chain and on that of a mismatch between the conformation of a bond and the preferred conformation of the preceding monomer. It turns out that the impact of achiral monomers also depends on these two parameters. For high values of these free energies, the net helicity does not change much from the situation where no achiral material is present. However, if the free-energy penalties are not both large, the impact of the achiral monomers on the conformational state of the aggregates can be quite substantial.