Scale-dependent rigidity of polymer-ornamented membranes

TL;DR

This paper investigates how grafted polymers affect the fluctuation spectrum of fluid membranes, revealing a scale-dependent elastic modulus that alters membrane behavior beyond simple rigidity renormalization.

Contribution

It introduces the concept of a scale-dependent elastic modulus for polymer-ornamented membranes, challenging traditional models that only consider rigidity renormalization.

Findings

Membranes exhibit a scale-dependent elastic modulus due to grafted polymers.

Polymer ornamentation modifies the Caille parameter in lamellar stacks.

The fluctuation spectrum cannot be fully described by a simple renormalization of bending rigidity.

Abstract

We study the fluctuation spectrum of fluid membranes carrying grafted polymers. Contrary to usual descriptions, we find that the modifications induced by the polymers cannot be reduced to the renormalization of the membrane bending rigidity. Instead we show that the ornamented membrane exhibits a scale-dependent elastic modulus that we evaluate. In ornamented lamellar stacks, we further show that this leads to a modification of the Caille parameter characterizing the power-law singularities of the Bragg peaks.