Non-linear fluctuation effects in dynamics of freely suspended film

TL;DR

This paper investigates how non-linear dynamic fluctuations influence the damping of bending modes in freely suspended films, revealing a coupling mechanism that restores viscous damping absent in harmonic approximation.

Contribution

It introduces a theoretical analysis of non-linear fluctuation effects on bending mode damping, highlighting the coupling to in-plane viscous modes in freely suspended films.

Findings

Bending mode damping is weak in harmonic approximation due to symmetry.

Non-linear effects induce viscous-like damping of bending modes.

Results align with existing experiments and simulations.

Abstract

Long-scale dynamic fluctuation phenomena in freely suspended films is analyzed. We consider isotropic films that, say, can be pulled from bulk smectic A liquid crystals. The key feature of such objects is possibility of bending deformations of the film. The bending (also known as flexular) mode turns out to be anomalously weakly attenuated. In the harmonic approximation there is no viscous-like damping of the bending mode, proportional to q^2 (q is the wave vector of the mode), since it is forbidden by the rotational symmetry. Therefore the bending mode is strongly affected by non-linear dynamic fluctuation effects. We calculate the dominant fluctuation contributions to the damping of the bending mode due to its coupling to the in-plane viscous mode, that restores the viscous-like q^2 damping of the bending mode. Our calculations are performed in the framework of the perturbation theory where the coupling of the modes is assumed to be small, then the bending mode damping is relatively weak. We discuss our results in the context of existing experiments and numeric simulations of the freely suspended films and propose possible experimental observations of our predictions.