Non-monotonic fluctuation spectra of membranes pinned or tethered discretely to a substrate

TL;DR

This paper calculates the thermal fluctuation spectrum of membranes tethered to substrates, revealing non-monotonic, anisotropic behavior with potential applications in pillar-supported or polymer-tethered membranes.

Contribution

It introduces a detailed calculation of fluctuation spectra for membranes with discrete tethering, highlighting non-monotonic features not previously characterized.

Findings

Spectrum exhibits a maximum at twice the tether distance

Root mean square displacement estimated for membrane displacements

Non-monotonic, anisotropic fluctuation behavior observed

Abstract

The thermal fluctuation spectrum of a fluid membrane coupled harmonically to a solid support by an array of tethers is calculated. For strong tethers, this spectrum exhibits non-monotonic, anisotropic behavior with a relative maximum at a wavelength about twice the tether distance. The root mean square displacement is evaluated to estimate typical membrane displacements. Possible applications cover pillar-supported or polymer-tethered membranes.