Intrinsic curvature determines the crinkled edges of "crenellated disks"

TL;DR

This paper presents a new method to measure the Gaussian curvature modulus of fluid membranes by analyzing the intrinsic curvature effects on crenellated disk structures, enabling better understanding of their stability and topology.

Contribution

It introduces a concise relation linking Gaussian curvature modulus to edge parameters in crenellated disks, facilitating measurement of intrinsic membrane properties.

Findings

Derived a relation between curvature moduli and edge parameters.

Provided a method to measure Gaussian curvature modulus in complex membranes.

Analyzed the structure and stability of crenellated disks.

Abstract

Elastic curvature constants determine many structural and functional properties of fluid membranes. Methods to measure the mean curvature modulus have proved to be robust. In contrast, Gaussian curvature is an intrinsic property of a surface. Thus, measuring the relevant modulus $\bar{k}$ in fluid membranes remains a challenging task. Inspired from colloidal "crenellated disks" observed in a model system composed of hard rods, we propose a concise relation between the two curvature moduli and the parameters associated with the free, crinkled edges. Our approach offers a straightforward way to determine $\bar{k}$ of these reconfigurable membranes, where various complex topologies can be nanosculpted. Further, we reveal the structure and stability of the "crenellated disks."