Context :

Aims : Gravitational settling of ^ { 22 } Ne in cooling white dwarfs can affect the outcome of thermonuclear supernovae .
We investigate how the supernova energetics and nucleosynthesis are in turn influenced by this process .
We use realistic chemical profiles derived from state-of-the-art white dwarf cooling sequences .
The cooling sequences provide a link between the white dwarf chemical structure and the age of the supernova progenitor system .

Methods : The cooling sequence of a 1 M _ { \sun } white dwarf was computed until freezing using an up-to-date stellar evolutionary code .
We computed explosions of both Chandrasekhar mass and sub-Chandrasekhar mass white dwarfs , assuming spherical symmetry and neglecting convective mixing during the pre-supernova carbon simmering phase to maximize the effects of chemical separation .

Results : Neither gravitational settling of ^ { 22 } Ne nor chemical differentiation of ^ { 12 } C and ^ { 16 } O have an appreciable impact on the properties of Type Ia supernovae , unless there is a direct dependence of the flame properties ( density of transition from deflagration to detonation ) on the chemical composition .
At a fixed transition density , the maximum variation in the supernova magnitude obtained from progenitors of different ages is \sim 0.06 magnitudes , and even assuming an unrealistically large diffusion coefficient of ^ { 22 } Ne it would be less than \sim 0.09 mag .
However , if the transition density depends on the chemical composition ( all other things being equal ) the oldest SNIa can be as much as 0.4 magnitudes brighter than the youngest ones ( in our models the age difference is 7.4 Gyr ) .
In addition , our results show that ^ { 22 } Ne sedimentation can not be invoked to account for the formation of a central core of stable neutron-rich Fe-group nuclei in the ejecta of sub-Chandrasekhar models , as required by observations of Type Ia supernovae .

Conclusions :