The effect of $^{22}$Ne diffusion in the evolution and pulsational
  properties of white dwarfs with solar metallicity progenitors
  Because of the large neutron excess of $^{22}$Ne, this isotope rapidly
sediments in the interior of the white dwarfs. This process releases an
additional amount of energy, thus delaying the cooling times of the white
dwarf. This influences the ages of different stellar populations derived using
white dwarf cosmochronology. Furthermore, the overabundance of $^{22}$Ne in the
inner regions of the star, modifies the Brunt-V\"ais\"al\"a frequency, thus
altering the pulsational properties of these stars. In this work, we discuss
the impact of $^{22}$Ne sedimentation in white dwarfs resulting from Solar
metallicity progenitors ($Z=0.02$). We performed evolutionary calculations of
white dwarfs of masses $0.528$, $0.576$, $0.657$ and $0.833$ M$_{\sun}$,
derived from full evolutionary computations of their progenitor stars, starting
at the Zero Age Main Sequence all the way through central hydrogen and helium
burning, thermally-pulsing AGB and post-AGB phases. Our computations show that
at low luminosities ($\log(L/L_{\sun})\la -4.25$), $^{22}$Ne sedimentation
delays the cooling of white dwarfs with Solar metallicity progenitors by about
1~Gyr. Additionally, we studied the consequences of $^{22}$Ne sedimentation on
the pulsational properties of ZZ~Ceti white dwarfs. We find that $^{22}$Ne
sedimentation induces differences in the periods of these stars larger than the
present observational uncertainties, particularly in more massive white dwarfs.
