# Thermal stiffening of clamped elastic ribbons

## TL;DR

This study uses molecular dynamics to investigate how thermal fluctuations influence the vibrational properties and effective bending rigidity of clamped elastic membranes, revealing thermal renormalization effects.

## Contribution

It provides a detailed analysis of the thermal renormalization of bending rigidity in elastic membranes using molecular dynamics simulations, highlighting the role of thermal contraction and tension.

## Key findings

- Effective bending rigidity approaches a constant as microscopic rigidity vanishes.
- Thermal fluctuations significantly renormalize the membrane's bending rigidity.
- Results are relevant for atomically thin materials and biological membranes.

## Abstract

We use molecular dynamics to study the vibrations of a thermally fluctuating two-dimensional elastic membrane clamped at both ends. We directly extract the eigenmodes from resonant peaks in the frequency domain of the time-dependent height and measure the dependence of the corresponding eigenfrequencies on the microscopic bending rigidity of the membrane, taking care also of the subtle role of thermal contraction in generating a tension when the projected area is fixed. At finite temperatures we show that the effective (macroscopic) bending rigidity tends to a constant as the bare bending rigidity vanishes, consistent with theoretical arguments that the large-scale bending rigidity of the membrane arises from a strong thermal renormalization of the microscopic bending rigidity. Experimental realizations include covalently-bonded two-dimensional atomically thin membranes such as graphene and molybdenum disulfide or soft matter systems such as the spectrin skeleton of red blood cells or diblock copolymers.