Dynamics of strained nanoribbons at finite temperature

The mechanics and the equilibrium critical behavior (including scale-dependent elastic constants) of thermally fluctuating two-dimensional crystalline membranes, such as graphene, have been studied extensively over the last two decades through field theoretic approaches, numerical simulations and experiments. However, investigations of dynamics, such as the characteristic oscillation times and damping times, remain limited. Here, we use molecular dynamics simulations to study the time trajectory of the midpoint (the height center-of-mass) of doubly clamped nanoribbons under various strain conditions. By treating the nanoribbon midpoint as a Brownian particle confined to a double-well potential, we formulate an effective theory describing the ribbon's tunneling rate across the two wells and its oscillation inside the wells. We find that, for nanoribbons compressed above the Euler buckling point and thermalized above the temperature at which the non-linear effects become significant, the energy barrier increases linearly with temperature. The cancelation between the energy barrier and the thermal energy results in escape time that depends only on the geometry, which is quite different from the usual Arrhenius behavior. Similarly, the natural oscillation time of nanoribbons under tension also becomes temperature dependent due to bending stiffening. Our findings suggest a simple connection between the dynamical critical exponent describing the collective motion characterizing by the midpoint time history, and the static critical exponent near the buckling transition.