  We construct phase diagrams for charged rodlike colloids within the
second-virial approximation as a function of rod concentration, salt
concentration, and colloidal charge. Besides the expected isotropic-nematic
transition, we also find parameter regimes with a coexistence between a nematic
and a second, more highly aligned nematic phase including an
isotropic-nematic-nematic triple point and a nematic-nematic critical point,
which can all be explained in terms of the twisting effect. We compute the
Frank elastic constants to see if the twist elastic constant can become
negative, which would indicate the possibility of a cholesteric phase
spontaneously forming. Although the twisting effect reduces the twist elastic
constant, we find that it always remains positive. In addition, we find that
for finite aspect-ratio rods the twist elastic constant is also always
positive, such that there is no evidence of chiral symmetry breaking due to a
uniaxial charge distribution.
