Fig. 8

Chart of the schematic models of the director fields for Types-A–D. a Type-A, b Type-B, c Type-C, and d Type-D. The upper rows are the numerically depicted nematic directors at certain cross-sectional positions using the trial functions, with Supplementary Equations (1) and (2) for Type-A and Type-B, Supplementary Equations (3) and (4) for Type-C, and Supplementary Equations (5) and (6) for Type-D. The lower rows are the simplified cartoons of the corresponding director field using ellipsoids to show the point-by-point distributions of the directors projected onto the plane. The colour gradation of the ellipsoids from red to blue represents the director tilt from up to down against the plane. For Type-A, only two horizontal cross-sections at the midplane and off-midplane are shown. For each of the other three types, one vertical (xz) and five different horizontal (xyI–xyV) cross-sectional positions are chosen according to the schematic (e). Note that xyIII corresponds to the equatorial plane (=midplane)