Debye-Huckel theory for slab geometries

The electrostatic interaction of charged particles through or at a low-diel ectric slab, such as a lipid bilayer immersed in water or a self-assembled monolayer (SAM) on a metal substrate, is considered theoretically in the pr esence of salt within the Gaussian approximation using a generalized Green' s formalism. A number of separate situations are discussed: i) The presence of a low-dielectric slab leads to pronounced interactions of a single char ge with the slab via the formation of polarization surface charges. For SAM s on metal substrates, there is an intricate crossover from image-charge at traction to the metal substrate (for large distances) to image-charge repul sion from the SAM (for small distances) with a stable minimum at a distance of roughly 20 times the thickness of the hydrophobic film. For bilayers in mater, the interaction of a single charge is always repulsive. ii) The sur face potential of a SAM is calculated for the case when the hydrophobic lay er contains dipole moments, which might explain the recently observed long- ranged repulsion of hydrophobic scanning tips from PEG-terminated SAMs on g old. iii) The interaction between charged particles through the bilayer is weakened. Oppositely charged particles still attract each other through the membrane. The free-energy minimum occurs as a result of the competition be tween self-repulsion from the slab and interparticle attraction and is loca ted at a separation from the membrane surface which equals 15 times the mem brane thickness, iv) Surface charges on the two surfaces of a bilayer attra ct each other through the bilayer unless the surface charge densities are t he same, even if the signs are the same. v) All these effects are strongly influenced by the presence of salt.