Can Dynamic Helical Polymers be Reduced to Linear Chains of Spins? Non-Local Effects from Polymer Self-Avoidance

Abstract

Cooperative chiral order in dynamic helical polymers (DHPs) is commonly understood through their reduction to one-dimensional (1D) Ising-spin chains. In this framework, each spin, adopting the values σ = −1 and σ = 1, represents a left- and right-handed helical twist. Spins interact ferromagnetically, capturing the energetic cost of boundaries between domains of opposite chirality. All current spin models of DHPs assume that nearest-neighbor (NN) spin–spin interactions suffice to describe the system. We challenge this assumption using a minimal molecular model to investigate whether the self-avoidance of DHP chains, due to excluded volume, induces an effective, non-local coupling of spins. Our approach combines a 1D description of helicity, based on NN spin–spin interactions, with an explicit representation of DHPs as freely-jointed chains with flexible hinges. We generate both ideal and self-avoiding chain conformations through a Monte Carlo scheme. For ideal chains, the spin behavior agrees with the predictions of a NN 1D Ising model with coupling strength J. However, we find that chain self-avoidance does create effective long-range interactions, as demonstrated by spin–spin correlation functions and free-energy calculations. These interactions renormalize J and lead to finite-size effects that are inconsistent with the NN 1D Ising behavior.