Amplification of chirality in helical supramolecular polymers beyond the long-chain limit

The optical activity of helical homopolymers devoid of chiral centers increases drastically when a small amount of homochiral monomers is incorporated into them. We study this so-called sergeants-and-soldiers effect of chirality amplification in solutions of helical supramolecular polymers with a theoretical model that bears a strong resemblance to a one-dimensional, two-component Ising model. In the limit of very long self-assembled helical polymers, the strength of the sergeants-and-soldiers effect depends strongly on the free energy of a helix reversal and less so on the concentration of aggregating material. Outside the long-chain limit, we find the reverse--that is, a strong concentration dependence and a weak dependence on the helix-reversal energy. Our treatment gives an excellent agreement with recently published circular-dichroism measurements on mixed aggregates of discotic molecules in the solvents water and n-butanol, at two different overall concentrations.