We study the strong-coupling (SC) interaction between two like-charged membranes of finite thickness embedded in a medium of higher dielectric constant. A generalized SC theory is applied along with extensive Monte-Carlo simulations to study the imag
e charge effects induced by multiple dielectric discontinuities in this system. These effects lead to strong counterion crowding in the central region of the inter-surface space upon increasing the solvent/membrane dielectric mismatch and change the membrane interactions from attractive to repulsive at small separations. These features agree quantitatively with the SC theory at elevated couplings or dielectric mismatch where the correlation hole around counterions is larger than the thickness of the central counterion layer.
We present general arguments for the importance, or lack thereof, of the structure in the charge distribution of counterions for counterion-mediated interactions between bounding symmetrically charged surfaces. We show that on the mean field or weak
coupling level, the charge quadrupole contributes the lowest order modification to the contact value theorem and thus to the intersurface electrostatic interactions. The image effects are non-existent on the mean-field level even with multipoles. On the strong coupling level the quadrupoles and higher order multipoles contribute additional terms to the interaction free energy only in the presence of dielectric inhomogeneities. Without them, the monopole is the only multipole that contributes to the strong coupling electrostatics. We explore the consequences of these statements in all their generality.
