van Bijnen R M W, Otten R H J, van der Schoot P
Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 1):051703. doi: 10.1103/PhysRevE.86.051703. Epub 2012 Nov 12.
We present a generalized approach to compute the shape and internal structure of two-dimensional nematic domains. By using conformal mappings, we are able to compute the director field for a given domain shape that we choose from a rich class, which includes drops with large and small aspect ratios and sharp domain tips as well as smooth ones. Results are assembled in a phase diagram that for given domain size, surface tension, anchoring strength, and elastic constant shows the transitions from a homogeneous to a bipolar director field, from circular to elongated droplets, and from sharp to smooth domain tips. We find a previously unaccounted for regime, where the drop is nearly circular, the director field bipolar, and the tip rounded. We also find that bicircular director fields, with foci that lie outside the domain, provide a remarkably accurate description of the optimal director field for a large range of values of the various shape parameters.
我们提出了一种通用方法来计算二维向列相畴的形状和内部结构。通过使用共形映射，我们能够为从丰富的类别中选择的给定畴形状计算指向矢场，该类别包括具有大纵横比和小纵横比的液滴、尖锐的畴尖端以及平滑的畴尖端。结果汇总在一个相图中，对于给定的畴尺寸、表面张力、锚定强度和弹性常数，该相图显示了从均匀指向矢场到双极指向矢场的转变、从圆形液滴到细长液滴的转变以及从尖锐畴尖端到平滑畴尖端的转变。我们发现了一个以前未被考虑的区域，其中液滴近似圆形，指向矢场为双极，尖端呈圆形。我们还发现，焦点位于畴外的双圆指向矢场，对于各种形状参数的大范围值，能提供对最优指向矢场的非常准确的描述。
