Morphological stability analysis of vesicles with mechanical-electrical coupling effects

Using a recently established liquid crystal model for vesicles, we present a theoretical method to analyze the morphological stability of liquid crystal vesicles in an electric field. The coupled mechanical-electrical effects associated with elastic bending, osmotic pressure, surface tension, Maxwell pressure, as well as flexoelectric and dielectric properties of the membrane are taken into account. The first and second variations of the free energy are derived in a compact form by virtue of the surface variational principle. The former leads to the shape equation of a vesicle embedded in an electric field, and the latter allows us to examine the stability of a given vesicle morphology. As an illustrative example, we analyze the stability of a spherical vesicle under a uniform electric field. This study is helpful for understanding and revealing the morphological evolution mechanisms of vesicles in electric fields and some associated phenomena of cells.