Thermal control of nucleation and propagation transition stresses in discrete lattices with non-local interactions and non-convex energy

Abstract

Non-local and non-convex energies represent fundamental interacting effects regulating the complex behavior of many systems in biophysics and materials science. We study one dimensional, prototypical schemes able to represent the behavior of several biomacromolecules and the phase transformation phenomena in solid mechanics. To elucidate the effects of thermal fluctuations on the non-convex non-local behavior of such systems, we consider three models of different complexity relying on thermodynamics and statistical mechanics: (i) an Ising-type scheme with an arbitrary temperature dependent number of interfaces between different domains, (ii) a zipper model with a single interface between two evolving domains, and (iii) an approximation based on the stationary phase method. In all three cases, we study the system under both isometric condition (prescribed extension, matching with the Helmholtz ensemble of the statistical mechanics) and isotensional condition (applied force, matching with the Gibbs ensemble). Interestingly, in the Helmholtz ensemble the analysis shows the possibility of interpreting the experimentally observed thermal effects with the theoretical force-extension relation characterized by a temperature dependent force plateau (Maxwell stress) and a force peak (nucleation stress). We obtain explicit relations for the configurational properties of the system as well (expected values of the phase fractions and number of interfaces). Moreover, we are able to prove the equivalence of the two thermodynamic ensembles in the thermodynamic limit. We finally discuss the comparison with data from the literature showing the efficiency of the proposed model in describing known experimental effects.

References in corpus (6)

• Snapping Mechanical Metamaterials under Tension
• Thermal denaturation of fluctuating finite DNA chains: the role of bending rigidity in bubble nucleation
• Graphene Ripples as a Realization of a Two-Dimensional Ising Model: A Scanning Tunneling Microscope Study
• Rigidity-Controlled Crossover: From Spinodal to Critical Failure
• Bifurcation analysis and phase diagram of a spin-string model with buckled states
• STM driven transition from rippled to buckled graphene in a spin-membrane model

Cited by in corpus (2)

• Thermal effects on fracture and brittle-to-ductile transition
• Buckling in a rotationally invariant spin-elastic model