  We present a molecular dynamics study of reentrant nematic phases using the
Gay-Berne-Kihara model of a liquid crystal in nanoconfinement. At densities
above those characteristic of smectic A phases, reentrant nematic phases form
that are characterized by a large value of the nematic order parameter
$S\simeq1$. Along the nematic director these "supernematic" phases exhibit a
remarkably high self-diffusivity which exceeds that for ordinary, lower-density
nematic phases by an order of magnitude. Enhancement of self-diffusivity is
attributed to a decrease of rotational configurational entropy in confinement.
Recent developments in the pulsed field gradient NMR technique are shown to
provide favorable conditions for an experimental confirmation of our
simulations.
