Magnetic Deformation Theory of a Vesicle

Abstract

We have extended the Helfrich's spontaneous curvature model [M. Iwamoto and Z. C. Ou-Yang. Chem. Phys. Lett. 590(2013)183; Y. X. Deng, et al., EPL. 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. 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. 98(2007)146101]. However, the sophisticated mathematics in differential geometry is still covered. Here, we present the derivations of formulas in detail to reveal the perturbation of deformation $ψ$ under two cases. New features such as the influence of temperature on the bend modulus of vesicle membrane have been revealed.