Buckled nano rod - a two state system and its dynamics

TL;DR

This paper analyzes the buckling and transition dynamics of a nano elastic rod under compression, highlighting the effects of potential energy regimes, saddle point variations, and quantum corrections on transition rates.

Contribution

It introduces a detailed transition state theory analysis of buckled nano rods, including methods to correct rate divergences and the impact of zero point energy contributions.

Findings

Transition rates depend on strain and saddle point shape.

Classical and quantum corrections are necessary near divergence points.

Zero point energy can significantly alter transition rate calculations.

Abstract

We consider a suspended elastic rod under longitudinal compression. The compression can be used to adjust potential energy for transverse displacements from harmonic to double well regime. The two minima in potential energy curve describe two possible buckled states at a particular strain. Using transition state theory (TST) we have calculated the rate of conversion from one state to other. If the strain $\epsilon$ is between $\epsilon_c$ and $4 \epsilon_c$, the saddle point is the straight rod. But for $\epsilon_c < 4 \epsilon_c$, the saddle is S-shaped. At $\epsilon_c = 4 \epsilon_c$ the simple TST rate diverges. We suggest methods to correct this divergence, both for classical and quantum calculations. We also find that zero point energy contributions can be quite large (as large as $10^9$) so that single mode calculations can lead to large errors in the rate.