Surface anchoring and temperature variations of the pitch in thin cholesteric layers

Abstract

The temperature variations of the cholesteric pitch in thin planar layers of cholesterics and their dependence on the surface anchoring force are investigated theoretically. It is shown that the temperature variations of the pitch in a layer are of a universal character. This is manifested in the fact that they depend not separately on the parameters of the sample but only on one dimensionless parameter S d =K22/dW, where K22 is the torsional modulus in the Frank elastic energy, W is the height of the surface-anchoring potential, and d is the thickness of the layer. The investigation is performed the parameter S d in a range where the change per unit number of cholesteric half-turns within the thickness of the layer accompanying a change in the temperature is due to the slipping of the director on the surface of the layer through the potential barrier for surface anchoring. The critical values of the parameter S d (which are most easily attained experimentally by varying the thickness of the layer), determining the region of applicability of the approach employed, are presented. The temperature variations of the free energy of the layer and the pitch of the cholesteric helix in the layer as well as the temperature hysteresis in the variations of the pitch with increasing and decreasing temperature are investigated for the corresponding values of S d . Numerical calculations of the quantities mentioned above are performed using the Rapini anchoring potential.