Isotensional and isometric force-extension response of chains with bistable units and Ising interactions

Editors suggestion –  Phys. Rev. E 98, 052146 – Published 29 November 2018

Authors : Manon Benedito and Stefano Giordano


The combination of bistability and cooperativity plays a crucial role in several biological and artificial micro- and nanosystems. In particular, the exhaustive understanding of the mechanical response of such systems under the effect of thermal fluctuations is essential to elucidate a rich variety of phenomena. Here a linear chain composed of elastic units, which are bistable (folded or unfolded) and coupled through an Ising-like interaction, is selected as a case study. We assess the macroscopic thermoelastic response of this chain in terms of its microscopic description. For small systems, far from the thermodynamic limit, this response depends on the applied isometric or isotensional boundary conditions, which correspond to the Helmholtz or Gibbs ensembles of the statistical mechanics, respectively. The theoretical analysis is conducted through the spin variables approach, based on a set of discrete quantities able to identify the folded or unfolded state of the chain units. Eventually, this technique yields closed-form expressions for the force-extension curves and the average number of unfolded units, as function of the applied fields. In addition, it allows to unveil a critical behavior of such systems, characterizing the operating regions with negative differential stiffness (spinoidal phase).

©2018 American Physical Society