Magnetic deformation theory of a vesicle

TL;DR

This paper extends Helfrich's vesicle shape model by incorporating magnetic interactions, providing detailed mathematical derivations to explain reversible and anharmonic deformations observed in artificial vesicles and nanocapsules.

Contribution

It introduces a magnetic deformation theory for vesicles, adding detailed differential geometric formulas to describe magnetic effects on vesicle shape changes.

Findings

Derived formulas for magnetic deformation perturbations.

Explained reversible vesicle shape changes.

Analyzed anharmonic deformations and birefringence.

Abstract

We have extended the Helfrich's spontaneous curvature model [M. Iwamoto and Z. C. Ou-Yang. Chem. Phys. Lett. \textbf{590}(2013)183; Y. X. Deng, et.al., EPL. \textbf{123}(2018)68002] of the equilibrium vesicle shapes by adding the interaction between magnetic field and the constituent molecules to explain the phenomena of the reversibly deformation of artificial stomatocyte[P. G. van Rhee, et.al., Nat. Commun. \textbf{Sep 24;5:5010}(2014)doi: 10.1038/ncomms6010.] and the anharmonic deformation of a self-assembled nanocapsules of bola-amphiphilic molecules and the linear birefringence[O.V. Manyuhina, et.al., Phys. Rev. Lett. \textbf{98}(2007)146101.]. However, the sophistic mathematics in differential geometry is still covered. Here, we present the derivations of formulas in detailed to reveal the perturbation of deformation $\psi$ under two cases.