(303h) The Influence of Ion Size and Effective Polarizability of the Capacitance of the Electric Double Layer

Theories for the dynamics of charged colloids in electrolyte solutions
under applied electric fields are, for the most part, still based on
using the Poisson-Boltzmann theory to describe the electric double
layer.  This theory is known to neglect several import, including the
neglect of ion size, ion polarizability, and charge correlations.
These shortcomings can lead to qualitatively incorrect predictions in
the electrokinetic motion of charged particles.

In this work, we employ a simple model that includes both ion size and
polarizability to examine their effect on the structure and response
of the electric double layer.  Including either finite ion size or a
negative excess ion polarizability leads to a decrease in differential
capacitance above a threshold potential.  For the case of excluded
volume interactions, this is due to the well studied ion crowding
effect.  In the case of ion polarizability, the decrease can be
interpreted in terms of thickening of the double layer due to
ion-induced polarizability holes in water.  We identify a new length scale
which controls the role of excess ion polarizability in the double
layer, and show that when this is comparable to the size of the
effective Debye screening length, ion polarizability can significantly
influence the properties of the double layer [1].

We obtain analytical results for the surface charge and differential
capacitance of the double layer as a function of the applied potential
on a planar surface.  The model is found to be able to quantitatively
describe experimental data for the differential capacitance of various
systems.

Finally, we discuss how ion correlations can be incorporated into the
theory, based on a recently developed variational field theory to
account for fluctuations in the electric potential [2].

[1] MM Hatlo, R van Roij, and L Lue, "The electric double layer at
    high surface potentials: The influence of excess ion
    polarizability," EPL 97, 28010 (2012).

[2] MM Hatlo and L Lue, "Electrostatic interactions of charged bodies
    from the weak- to the strong-coupling regime," EPL 89, 25002
    (2010).