Energy Barrier Scalings in Driven Systems

TL;DR

This paper investigates how energy barrier heights in driven molecular systems scale with residual load, revealing a surprising robustness of the $ ext{delta}^{3/2}$ scaling law beyond the theoretically predicted regime, impacting rate theory corrections.

Contribution

It demonstrates that the $ ext{delta}^{3/2}$ energy barrier scaling persists at finite residual loads, extending catastrophe theory predictions to practical, finite-temperature conditions.

Findings

Barrier heights scale as $ ext{delta}^{3/2}$ under load.

Scaling law remains valid beyond the vanishing load regime.

Results suggest new corrections to rate theories at finite temperature.

Abstract

Energy landscape mappings are performed for two different molecular systems under mechanical loads. Barrier heights are observed to scale as $\Delta U\sim\delta^{3/2}$, where $\delta$ is a residual load. Catastrophe theory predicts that this scaling should arise for vanishing $\delta$, however, this region is irrelevant in physical processes at finite temperature because thermal fluctuations cause the system to cross over the barrier before reaching the small $\delta$ regime. Surprisingly, we find that the $\Delta U\sim\delta^{3/2}$ scaling is valid far beyond the vanishing $\delta$ regime described by catastrophe theory. This scaling will therefore be relevant at finite temperatures, and can be the basis for corrections to standard rate theoretic approaches.