title: 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.
authors: Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA.
authors: Vikram
authors: V
authors: Jadhao
authors: Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA.
authors: Zhenwei
authors: Z
authors: Yao
authors: Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA.
authors: Creighton K
authors: CK
authors: Thomas
authors: Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA.|Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA.|Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA.|Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA.
authors: Monica Olvera
authors: MO
authors: de la Cruz
mesh_terms: D008962:Models, Theoretical; D055672:Static Electricity; D013816:Thermodynamics