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Fabrication of elliptic cylindrical confinement. (a) A schematic diagram of how to fabricate the elliptic cylindrical hole in a PDMS slab. The arrows in the lower left corner represent the x, y, and z axes of Cartesian coordinates. (b) Bright-field microscopy images of empty cylindrical holes. The top row shows xz-plane images of channels. The right column shows channels that are stretched along the direction of the diameter. The bottom row shows xy-plane images of the above channels. Note that xy-plane images are taken at the end of the channel.
Optical microscopy images of LCs confined in a cylinder according to LC phase and strain of the PDMS slab. (a) Nematic phase. (b) Smectic-A phase. The first column shows bright-field images. The second and third columns are POM images. The white arrows in the upper right corners represent the directions of the crossed polarizer. (c) A magnified bright-field image of smectic-A LCs confined in an elliptic cylinder. Note that, to observe the defect region clearly, we enhance the contrast of this image.
The defect region as a function of the aspect ratio of a channel. (a) An image sequence of smectic-A LCs confined in an elliptic cylinder in the order of the aspect ratio. Note that each image is taken in the middle of the channel and is contrast-enhanced. (b) The normalized width of the defect-free region as a function of the aspect ratio of the channel. Each symbol represents the data from 6 channels of different sizes. The legend represents the diameters of their undeformed circular cross sections. Solid lines are fitting results obtained using Eq. (4). The inset plots the absolute width of the defect-free region as a function of the aspect ratio. (c) The minimum aspect ratio where FCDs start to appear. The x-axis of (c) is a diameter of a circular channel. The error bars represent the measured maximum aspect ratio without FCDs. (d) The width of the defect-free region at as a function of a channel size.
A schematic diagram of smectic layers in the elliptic cross section. The ellipse of a solid line represents the boundary of the confinement. The dotted lines are equidistant curves of the ellipse, and are parallel to the smectic layers. The dotted lines in the inset, which magnifies the region around , represent the smectic layers of thickness . d is the thickness in the dilated region.
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