  The ion distribution around charged colloids in solution has been
investigated intensely during the last decade. However, few theoretical
approaches have included the influence of variation in the dielectric
permittivity within the system, let alone in the surrounding solvent. In this
article, we introduce two relatively new methods that can solve the Poisson
equation for systems with varying permittivity. The harmonic interpolation
method (HIM) approximately solves the Green's function in terms of a spherical
harmonics series, and thus provides analytical ion-ion potentials for the
Hamiltonian of charged systems. The Maxwell Equations Molecular Dynamics (MEMD)
algorithm features a local approach to electrostatics, allowing for arbitrary
local changes of the dielectric constant. We show that the results of both
methods are in very good agreement. We also found that the renormalized charge
of the colloid, and with it the effective far field interaction, significantly
changes if the dielectric properties within the vicinity of the colloid are
changed.
