2019 Impact factor 1.812
Soft Matter and Biological Physics

Eur. Phys. J. E 3, 131-141

Debye-Hückel theory for slab geometries

R.R. Netz

Max-Planck-Institut für Kolloid- und Grenzflächenforschung, Am Mühlenberg, 14424 Potsdam, Germany
netz@mpikg-golm.mpg.de

Received 25 January 2000

Abstract
The electrostatic interaction of charged particles through or at a low-dielectric slab, such as a lipid bilayer immersed in water or a self-assembled monolayer (SAM) on a metal substrate, is considered theoretically in the presence 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 charge with the slab via the formation of polarization surface charges. For SAMs on metal substrates, there is an intricate crossover from image-charge attraction to the metal substrate (for large distances) to image-charge repulsion 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 water, the interaction of a single charge is always repulsive. ii) The surface potential of a SAM is calculated for the case when the hydrophobic layer contains dipole moments, which might explain the recently observed long-ranged repulsion of hydrophobic scanning tips from PEG-terminated SAMs on gold. 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 between self-repulsion from the slab and interparticle attraction and is located at a separation from the membrane surface which equals 15 times the membrane thickness. iv) Surface charges on the two surfaces of a bilayer attract each other through the bilayer unless the surface charge densities are the same, even if the signs are the same. v) All these effects are strongly influenced by the presence of salt.

PACS
82.70.-y Disperse systems - 77.55.+f Dielectric thin films

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