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We perform model calculations of the macroscopic diffusion coefficient for a solute moving in a chiral nematic (cholesteric) liquid crystal (LC) phase applying the methodology developed by Frezzato et al. [J. Chem. Phys. 122, 164904 (2005)]. Three types of solutes with different features are studied: ellipsoid [roto-translational coupling (RTC) absent], bent rod (RTC present), and two-blade propeller (with RTC and chiral shape). For each prototype molecule we estimate the effect of cholesteric helix pitch and local order on the diffusion along the helix axis. For the ellipsoidal particle we find that translational diffusion is slowed down by rotation around the short axis. For the chiral solute we show that the enantiomer with shape chirality opposite to that of the LC phase is slowed down more than the other. This provides a proof of principle of the possibility of separating the two enantiomers via transport in a suitable chiral medium. [ABSTRACT FROM AUTHOR]

The possibility of using cholesteric phases for discriminating enantiomers of a chiral solute on the basis of their different transport properties, motivates the investigation of the translational diffusion by taking fully into account the roto-translational coupling. In this article a detailed theoretical analysis is presented for the transport properties evaluated according to the asymptotic limit of the mean-squared displacement. A general relation is derived for the transport coefficients, having as main ingredients the mean-field potential due to the mesophase, and the diffusion tensor with its purely translational and rotational components, and with the blocks describing the roto-translational coupling. The application of the theory to nematic phases shows that the roto-translational coupling generates a dynamical contribution reducing the transport coefficients evaluated by taking into account only the translational diffusion components in the center of diffusion. The theory is also specialized to a cholesteric phase with a given helical pitch for the director arrangement, in a form which is suitable for calculations of model systems of chiral solutes to be presented in a forthcoming paper. [ABSTRACT FROM AUTHOR]