Local biaxiality in cholesteric liquid crystals from the surface interaction model

The feature of local biaxiality of the orientational order in twisted nematics and cholesteric liquid-crystalline phases is faced by modeling the mean field orientational potential on the basis of the surface interaction model [A. Ferrarini, G. J. Moro, P. L. Nordio, and G. R. Luckhurst, Mol. Phys. 77, 1 (1992)]. Here we present a tool for the complete parameterization of the potential for general molecular structures and recover the long-pitch approximation usually invoked to model the molecular order in these phases. The method is applied to archetype molecular geometries (an ellipsoidal object, a conical object, a lath-shaped molecule, and the shape's enantiomers of a propellerlike molecule) in order to evaluate the dependence of the second-rank orientational order parameters on the pitch of the phase. Special emphasis is given to the so-called biaxiality parameter B [Z. Yaniv, N. A. P. Vaz, G. Chidichimo, and J. W. Doane, Phys. Rev. Lett. 47, 46 (1981)], which can be experimentally determined by the analysis of time-averaged (2)H-NMR spectra of deuterated probes dissolved in the twisted phase. The model calculations show how probes with different geometries are sensitive to the local biaxiality.