Instability and Periodic Deformation in Bilayer Membranes Induced by Freezing

TL;DR

This paper investigates how bilayer membranes become unstable and develop periodic shapes during freezing, identifying a threshold condition and describing specific deformation patterns consistent with experimental results.

Contribution

It introduces a theoretical model linking membrane energy differences to deformation patterns, revealing a threshold for instability and characterizing the shape of resulting textures.

Findings

Existence of a stability threshold for membrane deformation.

Identification of periodic curved square textures as solutions.

Optimal period-to-amplitude ratio approximately equal to (2)^{1/2}pi.

Abstract

The instability and periodic deformation of bilayer membranes during freezing processes are studied as a function of the difference of the shape energy between the high and the low temperature membrane states. It is shown that there exists a threshold stability condition, bellow which a planar configuration will be deformed. Among the deformed shapes, the periodic curved square textures are shown being one kind of the solutions of the associated shape equation. In consistency with recent expe rimental observations, the optimal ratio of period and amplitude for such a texture is found to be approximately equal to (2)^{1/2}\pi.