= Phase registration of screened charged sheets
{title2=$\theta_{\min}=\pi\pmod{2\pi}$}
Two equally modulated charge sheets in identical full-space electrolyte have charging energy per area $\alpha^2[1+e^{-pd}\cos\theta]/(4\varepsilon p)$, where $p=\sqrt{k^2+\kappa_D^2}$. Its phase-dependent interaction favors a half-wavelength offset, with opposite charge patches facing each other. For an electrolyte gap with negligible exterior displacement response, the energy is instead $\alpha^2[\coth(pd)+\cos\theta/\sinh(pd)]/(2\varepsilon p)$, with the same minimizing phase. Absolute energies require specified exterior <electrostatic interface boundary conditions>.
Back to article page
