Finite-temperature buckling of an extensible rod

TL;DR

This paper investigates how thermal fluctuations influence the buckling behavior of extensible rods at finite temperatures, revealing that fluctuations delay buckling and significantly affect the transition near criticality, supported by theoretical analysis and simulations.

Contribution

It provides a theoretical framework for understanding finite-temperature buckling of extensible rods, including fluctuation effects and phase diagram predictions verified by simulations.

Findings

Thermal fluctuations delay buckling transition.

Near the transition, fluctuations contribute an order √T force.

Monte Carlo simulations confirm the theoretical phase diagram.

Abstract

Thermal fluctuations can play an important role in the buckling of elastic objects at small scales, such as polymers or nanotubes. In this paper, we study the finite-temperature buckling transition of an extensible rod by analyzing fluctuation corrections to the elasticity of the rod. We find that, in both two and three dimensions, thermal fluctuations delay the buckling transition, and near the transition, there is a critical regime in which fluctuations are prominent and make a contribution to the effective force that is of order $\sqrt{T}$. We verify our theoretical prediction of the phase diagram with Monte Carlo simulations.