Electrostatic stretching of a charged vesicle

We present a closed-form solution of electrostatic potential self-induced by a uniformly charged micro/nanovesicle and the corresponding elastic deformation of the vesicle membrane due to Maxwell stress. At equilibrium, the electrostatic force induced on both sides of the membrane is balanced by the elastic force of the stretched membrane. We develop differential and integral solutions of the coupled Poisson-Boltzmann system for a spherical vesicle and demonstrate that the integral solution is relatively flexible in formulating asymmetric configurations. Analytical results are formulated in terms of vesicle size, Debye length, and the surface charge density. The membrane stretching is characterized by the dimensionless group that defines the relative strength of the net electric force with respect to the membrane stiffness. We found that the self-induced electrostatic interaction will lead to a pre-stressed membrane although the small displacement is often negligible compared with the vesicle size. Quantitative analysis also reveals that the electric force can assist the vesicle in recovering its opening pore.