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arXiv · 1501.03582

Coulomb energy of uniformly-charged spheroidal shell systems

Vikram Jadhao·Zhenwei Yao·Creighton K. Thomas·Monica Olvera de la Cruz
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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.

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Vikram Jadhao, Zhenwei Yao, Creighton K. Thomas, Monica Olvera de la Cruz. 2015-01-15. Coulomb energy of uniformly-charged spheroidal shell systems. https://doi.org/10.1103/physreve.91.032305

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