Spin variable approach for the statistical mechanics of folding and unfolding chains

Abstract

The force–extension response of chains composed of bistable (or multistable) units strongly depends on the applied boundary conditions. As a matter of fact, isotensional conditions (soft devices) lead to a plateau-like response, whereas isometric conditions (hard devices) lead to a sawtooth-like pattern. We develop an equilibrium statistical mechanics methodology, based on the introduction of a set of discrete or spin variables, which is able to describe the thermal and mechanical properties of a folding and unfolding chain under arbitrary external conditions. In particular, we will work within the Gibbs and Helmholtz ensembles, which correspond to soft and hard devices, respectively. We introduce a one-dimensional system composed of multistable units and a bistable freely jointed chain. For both systems we obtain explicit expressions for the force–extension relation and we study the spinoidal behavior induced by the isometric conditions.