Stewart I W
Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, United Kingdom.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Aug;60(2 Pt B):1888-96. doi: 10.1103/physreve.60.1888.
This paper derives theoretical results for the onset of Helfrich-Hurault-type transitions in samples of smectic-A liquid crystals arranged in concentric cylindrical layers [J. Chem. Phys. 55, 839 (1971); 59, 2068 (1973)]. A magnetic field is applied in the azimuthal direction, parallel to the layers. The governing equilibrium equation is solved in order to derive the critical magnitude H(c) of the magnetic field above which the onset of periodic smectic layer distortions is expected. The distortion solution is shown to be energetically favorable for H>H(c). Some examples of critical thresholds are given, by means of figures, for relevant physical parameters. The qualitative features of the solution at H(c) are displayed via the plot of a typical variable solution to the equilibrium equation in a particular case. The consequences of the results, especially the relationship between H(c) and the radial depth, are explored, and comparisons are drawn with known results for infinite planar aligned smectic-A samples. The results are also interpreted for the case of an electric field which follows the plane of the layers in the usual wedge geometry. Critical applied voltage magnitudes U(c) are derived for various radial sample depths and wedge angles.
本文推导了排列成同心圆柱层的近晶 - A 型液晶样品中出现赫尔弗里希 - 胡拉尔特型转变的理论结果[《化学物理杂志》55, 839 (1971); 59, 2068 (1973)]。在方位角方向上施加平行于层的磁场。求解控制平衡方程，以得出磁场的临界大小H(c)，高于此值预计会出现周期性近晶层畸变。对于H > H(c)，畸变解在能量上是有利的。通过图表给出了一些相关物理参数的临界阈值示例。在特定情况下，通过绘制平衡方程的典型变量解来展示H(c)处解的定性特征。探讨了结果的影响，特别是H(c)与径向深度之间的关系，并与无限平面排列的近晶 - A 型样品的已知结果进行了比较。对于在通常楔形几何结构中沿层平面的电场情况，也对结果进行了解释。推导了各种径向样品深度和楔角的临界施加电压大小U(c)。
