  The Casimir force between graphene sheets is investigated with emphasis on
the effect from spatial dispersion using a combination of factors, such as a
nonzero chemical potential and an induced energy gap. We distinguish between
two regimes for the interaction - T=0 $K$ and $T\neq 0$ $K$. It is found that
the quantum mechanical interaction (T=0 $K$) retains its distance dependence
regardless of the inclusion of dispersion. The spatial dispersion from the
finite temperature Casimir force is found to contribute for the most part from
$n=0$ Matsubara term. These effects become important as graphene is tailored to
become a poor conductor by inducing a band gap.
