Smith A A T, Brown C V, Mottram N J
School of Biomedical and Natural Sciences, Nottingham Trent University, Erasmus Darwin Building, Clifton Lane, Clifton, Nottingham, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Apr;75(4 Pt 1):041704. doi: 10.1103/PhysRevE.75.041704. Epub 2007 Apr 18.
We have derived an approximate analytical expression for the static director distortion of a planar nematic layer subject to a magnetic field H immediately above the critical Fréedericksz transition H=H{c} . The layer contains a voltage-independent density of positively and negatively singly charged ionic species that interact with the flexoelectric and dielectric polarizations which appear when the director is distorted. The analytical solution is shown to correspond closely to a full numerical calculation when H/H{c}=1.01. The analytical approach allows a quantitative insight into how the mobile charge shields the polarization for different values of the elastic constants, the ionic density, the flexoelectric coefficients, and the layer thickness.
我们推导了一个近似解析表达式，用于描述平面向列层在刚好高于临界弗雷德里克斯转变磁场(H = H_{c})时，受到磁场(H)作用下的静态指向矢畸变。该层包含电压无关的正、负单电荷离子种类密度，它们与指向矢畸变时出现的挠曲电和介电极化相互作用。当(H/H_{c} = 1.01)时，解析解与全数值计算结果非常吻合。该解析方法能够定量洞察移动电荷如何针对不同的弹性常数、离子密度、挠曲电系数和层厚度值屏蔽极化。
