On the influence of an orienting field on the static twist-splay periodic distortions of nematic liquid crystals

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Abstract
A homogeneously aligned nematic liquid crystal layer with positive dielectric anisotropy is considered to be acted upon by an electric field normal to and a magnetic field parallel to its initial orientation direction. The ratio of the twist to splay elastic constants of the nematic is supposed sufficiently small so that static twist-splay periodic distortion is exhibited by it as a threshold effect. The dependence of the threshold values of the electric field and the spatial wavenumber of the distortion on the orienting magnetic field is described. Also the existence of a limiting value of the orienting field, beyond which no periodic distortion has to be expected, is predicted. The dependence of this limiting field on the twist to splay elastic constants ratio is given in the two cases of the boundary conditions considered