Physical Effects And Experimental Measurement Of The K₁₃ Surfacelike Elastic Term In Nematic Liquid Crystal Cell

The surfacelike elastic term is a focal subject in surface physics of liquid crystal at present, which originates from(δn)² term in the expression of free energy. There are two theories: one isPergamenshchik's. and the other is Faetti's. Their discrepancy embodies in the different boundary conditions. Stallinga [Phys. Rev. E 53, 1701 (1996)] have made careful theoretical calculation and experiment on ECB cells to test these two theories. The discrimination between two theories is whether K₁₃ equals to zero or not. For their experimental inaccuracy of parameters and without taking other effects of the same order into account such as the flexoelectric effect, they cannot determine the K\i term existing or not. The weak anchoring nematic liquid crystal cell with an external magnetic field is studied in detail based on the expression of surface elastic energy according to Pergamenshchik [Phys. Rev. E 48, 1265 (1993)]. and the precise mathematical process is adopted. We pose: (1) k=K^/K\\ can bedetermined by two threshold fields (one corresponds to the external magnetic field perpendicular to substrates, and the other corresponds to the external magnetic field parallel to substrates) if both the Freedericksz transitions are second order. (2) The existence of the KU term may change the property of the Freedericksz transition, i.e., from first order to second order, or vice versus. The condition for first order transition is also given. (3) The various curves of relative optical retardation versus reduced magnetic field h for different k are intersected at same point, and the slopes at the common point are sensitive to k. These results can help us to design the experiments to check the existence of the K\$ term. We conclude that the property of the transition can be used to explicitly test the K\3 term. So an experimental method is proposed and the value of k can be calculated from some relative parameters of three transitions (one is second order and others are first order) at threshold point in a liquid crystal cell with two unparallel substrates.