Mesoscopic modeling of dynamically helical polymers: Cooperative phenomena & topological properties*

Synthetic helical polymers are interesting for applications including catalysis, chirality recognition, and templating assembly of functional molecules. Some of these polymers, exhibit dynamic helicity: their conformations can randomly switch between left- and right-handed helical senses because of moderate inversion barriers. The helicity of dynamical polymers can be controlled [1] by "doping" their chain with small chiral groups. The influence of biasing groups on helicity has been investigated by mapping helical polymers onto generic 1D Ising models, which have explained [1] co-operative effects such as majority rules and sergeants-soldiers behavior. However 1D Ising models cannot describe the conformational properties of a polymer in three dimensional (3D) space. Therefore we develop a mesoscopic molecular model for dynamical helical polymers, combining the worm-like chain representation with special chiral potentials [2]. We sample polymer conformations with Monte Carlo simulations and compare our model with the predictions from 1D Ising chains regarding sizes and distributions of chiral domains. We further investigate 3D conformational properties of dynamical helical polymers, focusing on their knotting behaviour.

[1] Green et al, Angew. Chem. Int. Ed. 1999, 38, 3138

[2] Zhao et al, ACS Macro 2023, 12, 234