In this thesis, the transient planar phase in cholesteric liquid crystal is investigated. The homeotropic - planar transition as currently understood proceeds as follows.
homeotropic → transient planar → focal comic - like → planar
First, we investigate the physical reasons why the system makes the transition from the homeotropic state to the meta-stable transient planar state instead of directly relaxing to the equilibrium planar state. To understand this phenomena, we numerically simulate the time evolution and spatial distribution of directors during the homeotropic to the transient planar transition. The simulation results show that in the region where the homeotropic to the transient planar transition is in process, the elastic energy due to the twist deformation becomes minimum when the value of the pitch is $P_{0}$, the equilibrium planar pitch, whereas, the elastic energy due to the bend deformation has lower value as the pitch becomes longer. Thus the pitch of transient planar state is determined by the balance between the twist and bend deformation and the elastic energy for bend deformation compels the pitch of transient planar state to have longer value than the equilibrium planar pitch $P_{0}$. And also from the analytic solution of the dynamic equation the maximum growth rate for the $n_{x}$ and $n_{y}$ is obtained when $P=(K_{33}/K_{22})P_{0}$. Therefore the system relaxes to the transient planar state whose pitch is $(K_{33}/K_{22})P_{0}$, instead of the equilibrium planar state.
Second, the relation between the pitch and the elastic constants of the transient planar state is determined from the experimental measurements. Approximate solution of the dynamic equation for cholesteric liquid crystals obtained by Yang et. al. shows that the pitch of the transient planar state is given by $P_{transient} = (K_{33}/K_{22})P_{0}$. To verify this relation experimentally, we measure the equilibrium pitch $P_{0}$ and $P_{transient}$ by optical reflection technique. The twist and bend elastic constants are obtained from the measured values of the threshold fields of the focal conic → homeotropic and homeotropic → focal conic transitions for the samples of different thicknesses. By comparing these values, we experimentally confirm the theoretically suggested relation for the pitch of the transient planar state, $P_{transient} = (K_{33}/K_{22})P_{0}$.
Third, the growth and propagation of the transient planar state in the tansition from the homeotropic to the planar state is investigated by both experiments and numerical simulations for planar boundary conditions. We could observe interference fringes in the measured reflection spectra during the homeotropic to the transient planar transition and we are the first to measure such fringes. These interference fringes are assumed to be caused by a Fabry-Perot interferometric structure formed in the cell. The change in the fringe intervals with time obtained from the experimental and simulated reflection spectra also show that the length of the nematic layer reduces linearly with time as the material relaxes to the transient planar texture. These interference fringes observed in the reflection spectra and the reduction of the nematic layer with time are the experimental evidences that the transient planar state in a cholesteric material grows from the surfaces and propagates to the bulk in the homeotropic to transient planar transition for planar boundary conditions.
