Theory of Chiral Order in Random Copolymers

TL;DR

This paper explains the chiral majority rule in random copolymers by mapping them onto the random-field Ising model, providing a theoretical framework that matches experimental observations and allows control over the sharpness of chiral ordering.

Contribution

It introduces a novel theoretical model linking copolymer chirality to the random-field Ising model, explaining experimental majority rule behavior.

Findings

The model accurately predicts chiral order based on enantiomer concentration.

The sharpness of the majority-rule transition can be tuned.

Quantitative agreement with experimental data is achieved.

Abstract

Recent experiments have found that polyisocyanates composed of a mixture of opposite enantiomers follow a chiral ``majority rule:'' the chiral order of the copolymer, measured by optical activity, is dominated by whichever enantiomer is in the majority. We explain this majority rule theoretically by mapping the random copolymer onto the random-field Ising model. Using this model, we predict the chiral order as a function of enantiomer concentration, in quantitative agreement with the experiments, and show how the sharpness of the majority-rule curve can be controlled.