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
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag
