On the influence of the Frank elasticity on the magnetic reorientation of nematic polymers

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Abstract
We study the influence of the anisotropy of the Frank elastic constants on the magnetic reorientation of the nematic phase of polymer liquid crystals. In the magnetic reorientation following a 90° director rotation with respect to an aligning magnetic field, a pattern of inversion walls develops which depends on the relative magnitude of the elastic constants and the magnetic coherence length. We show how this dependence can be experimentally studied by proton NMR. The transition from a homogeneous director reorientation to a distorted director reorientation is theoretically studied as a function of the rotation angle α. A critical angle of rotation αc shows up, and we study its dependence on the anisotropies K 3/K 1 and K 3/K 2. Depending on these ratios and on the wavelength of the distortion, critical angles 45° < αc < 90° are predicted for materials with positive anisotropy of the magnetic susceptibility χa and 0° < αc < 45° (mod π/2) for materials with χa < 0. Within the frame of a phase transition analogy, a Landau-like theory predicts the transition to be second order.