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