The electrostatic interactions between two corrugated charged planes

The surfaces of association colloids often undergo undulating motion due to thermal fluctuations. The electrostatic interactions between two charged planes of arbitrary corrugation are investigated on the basis of the Poisson- Boltzmann equation under the Debye-Huckle approximation. The surfaces are parallel and subject to the spatial periodicity of the amplitude A and wavelength q^-1. When the amplitude is small compared to the wavelength, i.e., (qA)² << 1, the electric field can be calculated by using the perturbation method. The interaction free energy is then obtained for surfaces associated with the condition of either constant surface potential or constant surface charge density during interactions. The effects of the amplitude and phase angle on the interaction energy are discussed and asymptotic expressions are obtained when the mean separation is large compared to the amplitude. At the same mean separation, the interaction energy for the corrugated surfaces is always higher than that for the planar surfaces. In other words, undulation enhances the electrostatic repulsion. The repulsive energy is minimum when the two surfaces are in-phase and maximum for the out-of-phase mode.