Strain dependent twist-stretch elasticity in chiral filaments

Abstract

Coupling between axial and torsional degrees of freedom often modifies the conformation and expression of natural and synthetic filamentous aggregates. Recent studies on chiral single-walled carbon nanotubes and B-DNA reveal a reversal in the sign of the twist-stretch coupling at large strains. The similarity in the response in these two distinct supramolecular assemblies and at high strains suggests a fundamental, chirality dependent non-linear elastic behaviour. Here, we seek the link between the microscopic origin of the non-linearities and the effective twist-stretch coupling using energy based theoretical frameworks and model simulations. Our analysis reveals a sensitive interplay between the deformation energetics and the sign of the coupling, highlighting robust design principles that determine both the sign and extent of these couplings. These design principles have been already exploited by Nature to dynamically engineer such couplings, and have broad implications in mechanically coupled actuation, propulsion and transport in biology and technology.