Quantifying Chirality in Helical Polymers via a Geometric Extension of the Kremer-Grest Model

Abstract

Chirality in polymeric systems enables a wide range of emergent optical, mechanical, and transport phenomena, yet a unified framework that quantitatively connects molecular-scale geometry to chiral behavior remains lacking. Existing theoretical descriptions typically emphasize either continuum models, such as the helical wormlike chain (HWLC), which neglect intermolecular interactions, or mesophase-level theories, which obscure the role of molecular geometry. In this work, we introduce a comprehensive framework for quantifying chirality in helical polymers by extending the Kremer-Grest bead-spring model to explicitly map intrinsic curvature and torsion onto bond angle and dihedral potentials. We establish direct theoretical relationships between helical parameters such as pitch and radius, and connect them to a normalized, dimensionless chirality characteristic, $\chi$ that captures local geometric correlations absent from conventional HWLC descriptions. Furthermore, using molecular dynamics simulations, we systematically quantify the influence of excluded volume interactions and thermal fluctuations on helical geometry and chirality, dispelling the common assumption that monotonic increases in chirality are associated only with decreasing pitch. Finally, we present a coarse-graining procedure that facilitates a direct comparison between experimental helical polymers and the Kremer-Grest helical chain, demonstrating quantitative agreement across a diverse set of polymer classes. This unified geometric and particle-based description provides a predictive roadmap for selecting and engineering chiral Kremer-Grest models and offers a general platform for designing polymeric materials with controlled and tunable chirality.