Eur. Phys. J. E

**5**, 189-205

## Static van der Waals interactions in electrolytes

**R.R. Netz**

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

(Received 17 February 2000)

** Abstract **

Using a field-theoretic formalism, we calculate the static
contribution to the van der Waals interaction between two dielectric
semi-infinite half-spaces in the presence of mobile salt ions. The
ions can be located in the slab, in one, or in both half-spaces. We
include an excess polarizability of the salt ions, *i.e.*, each
(spherical) ion has a dielectric constant which in general is
different from the surrounding medium. This leads to a modification of
the effective dielectric constant of the medium hosting the ions.
This shift can be large for high salt concentrations and therefore
influences the Hamaker constant decisively. Salt ions in the slab
screen the static van der Waals interaction, as was shown by Davies
and Ninham. The salt-modified van der Waals interaction also contains
salt-confinement and salt-correlation effects. This is clearly
demonstrated by the fact that the interaction is non-zero even in the
case when the dielectric constant is homogeneous throughout the
system, in which case salt correlations are solely responsible for the
interaction. If the salt ions are in one or both of the two half-spaces
(and no ions in the slab), the van der Waals interaction is not
screened but the effective Hamaker constant approaches a universal
value for large slab thickness which is different from the value in
the absence of salt ions and which is independent of the salt
concentration and of the effective electrolyte dielectric constant.
If both half-spaces contain salt, the asymptotic value of the Hamaker
constant for large separation between the half-spaces is the one
obtained for the interaction between two metallic half-spaces through
an arbitrary dielectric medium, which is given by
.
As is explicitly demonstrated, ion enrichment or depletion at the
interfaces due to image-charge effects is already included on the
one-loop level and therefore does not lead to a change of the screened
van der Waals interaction as given by Davies and Ninham. For positive
and negative ions with different valencies or different excess
polarizabilities, we obtain different adsorbed surface excesses of
positive and negative ions, leading to a non-vanishing surface
potential, which is computed explicitly. All of these results are
obtained on the linear one-loop level. For a special case we extend
the calculation of the dispersion interaction to the two-loop
level. We find the corrections to the one-loop results to be quite
large for high salt concentrations or multivalent ions.

**PACS**

82.70.-y - Disperse systems; complex fluids.

61.20.Qg - Structure of associated liquids: electrolytes, molten salts, etc..

82.45.+z - Electrochemistry and electrophoresis.

**©**

*EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001*