Amplification of Asymmetry for Dynamic Helical Polymers through 1:1 Host–Guest Interactions: Theoretical Models for Majority Rule and Sergeants and Soldiers Effects

Amplification of asymmetry (chiral amplification) is one of the distinctive phenomena of dynamic helical polymers whose helical sense excess is significantly enhanced with a small amount of chiral units through the strong cooperative interactions among the monomer units. The Ising model for the amplification of asymmetry in the dynamic helical copolymers bearing the chiral side chains has been well-established. However, the theoretical models have not yet been developed for the amplification of asymmetry in the dynamic helical polymers induced by noncovalent intermolecular (host-guest) interactions of the achiral side chains with the chiral/chiral (majority rule effect) and chiral/achiral (sergeants and soldiers effect) guest molecules. In this work, we propose the theoretical models for two types of 1:1 host-guest interactions: the majority rule effect type 1:1 host-guest interaction (MRHG) and sergeants and soldiers effect type 1:1 host-guest interaction (SSHG) models, in which each twisting unit of the dynamic helical polymers is assumed to interact with one guest molecule. The excess energy of the helical reversal state (Δ<i>G</i>_r), per unit energy favoring one helical state over the other (2Δ<i>G</i>_h), and enantioselectivity (α) can be effectively determined using the MRHG model. Moreover, it was revealed that the chiral solvation model reported by Green, Morawetz, and co-workers is a particular solution of the SSHG model.