Landau-de Gennes Theory For A Degenerate Hybrid-aligned Nematic Cell

Within Landau–de Gennes theory,we have investigated structural characteristic and structural transition in a cylindrically confined degenerate hybrid-aligned nematic?DHAN?LC cell with a-1 boojum,and the change situation of a boojum under different boundary conditions in a DHAN cell are investigated using a finite-difference iterative method.In the first part,by studying a cylindrically confined DHAN LC cell with a-1 boojum imposed strong anchoring at the upper and lower substrates,respectively,the LC molecules are homeotropic alignment at the upper plate,and planar alignment at the lower plate,we find that there is no axial symmetry for the director distribution of-1 boojum,whereas the biaxial distribution of the frustrated structure presents axial symmetry.Below the critical thickness h_c=10?,the eigenvalue exchange occurs from one side to the other,and the director distribution has rotational symmetry of order 4.In the second part,for a DHAN LC cell with a+1 boojum imposed strong tangential and homeotropic anchoring strengths at the upper and lower substrates respectively,when an arbitrary section which can be denoted as z?z_c1=26?is selected as the upper boundary,the fine structure of the boojum in a thick cell is the same as that induced in the original structure,meanwhile,the biaxial transition of the system is basically consistent with the original structure as the cell thickness decreases.However,when a section which can be denoted as z?z_c1 is selected as the upper boundary,the fine structure of the boojum in a thick cell is different from that induced in the original structure,meanwhile,with the cell thickness decreasing,the system structure changes greatly,and the boojum structure disappears gradually,existing only one defect ring.In the third part,for a DHAN LC cell with a-1 boojum,with cell thickness h=30?,when choosing an arbitrary cross section as the lower boundary in two ranges z?z_c2=3?and z?z_c2,both the fine structure of the boojum in a thick cell and the biaxial transformation process are similar to that of the second part.By intercepting different cross sections of the DHAN cell containing the+1 boojum and-1 boojum structures as boundaries,it was found that the boojum structure gradually vanished during the transition of the polar angle?far away from the symmetry axis from?/2 to zero at that boundary.