Coulomb energy of uniformly-charged spheroidal shell systems
Abstract
We provide exact expressions for the electrostatic energy of uniformly-charged prolate and oblate spheroidal shells. We find that uniformly-charged prolate spheroids of eccentricity greater than 0.9 have lower Coulomb energy than a sphere of the same area. For the volume-constrained case, we find that a sphere has the highest Coulomb energy among all spheroidal shells. Further, we derive the change in the Coulomb energy of a uniformly-charged shell due to small, area-conserving perturbations on the spherical shape. Our perturbation calculations show that buckling-type deformations on a sphere can lower the Coulomb energy. Finally, we consider the possibility of counterion condensation on the spheroidal shell surface. We employ a Manning-Oosawa two-state model approximation to evaluate the renormalized charge and analyze the behavior of the equilibrium free energy as a function of the shell's aspect ratio for both area-constrained and volume-constrained cases. Counterion condensation is seen to favor the formation of spheroidal structures over a sphere of equal area for high values of shell volume fractions.
Keywords
Cite
@article{arxiv.1501.03582,
title = {Coulomb energy of uniformly-charged spheroidal shell systems},
author = {Vikram Jadhao and Zhenwei Yao and Creighton K. Thomas and Monica Olvera de la Cruz},
journal= {arXiv preprint arXiv:1501.03582},
year = {2015}
}
Comments
15 pages, 7 figures, Accepted in Physical Review E