Jadhao Vikram, Yao Zhenwei, Thomas Creighton K, de la Cruz Monica Olvera
Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA.
Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Mar;91(3):032305. doi: 10.1103/PhysRevE.91.032305. Epub 2015 Mar 5.
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.
我们给出了均匀带电的长椭球壳和扁椭球壳静电能的精确表达式。我们发现，偏心率大于0.9的均匀带电长椭球体的库仑能低于具有相同面积的球体。对于体积受限的情况，我们发现球体在所有椭球壳中具有最高的库仑能。此外，我们推导了由于球形形状上小的、面积守恒的微扰而导致的均匀带电壳库仑能的变化。我们的微扰计算表明，球体上的屈曲型变形可以降低库仑能。最后，我们考虑了椭球壳表面反离子凝聚的可能性。我们采用曼宁-大泽二态模型近似来评估重整化电荷，并分析了在面积受限和体积受限情况下，平衡自由能随壳的纵横比的变化行为。对于高壳体积分数，反离子凝聚有利于形成比具有相同面积的球体更优的椭球结构。
