Observation of One-dimensional Spinodal Decomposition in a Liquid Crystal

实验研究了外场作用下液晶中展曲壁的锯齿形不稳定性粗化，作为对守恒序参量系统中调幅分解的一维模拟研究。当外加电场作用于液晶时，首先出现正弦调制，然后液晶壁的形状变为锯齿形。在粗化后期，锯齿形顶点的平均宽度随时间呈对数增长，与理论预测一致; 2.分析了Ising畴的结构函数、相关函数以及锯齿形顶点的密度相关性.在粗化后期，动力学标度律仍然成立。3.对一维相序的扭结-反扭结动力学进行了数值研究。畴宽的对数增长也得到了证实。畴大小的分布和相关函数满足比例关系。两次自相关函数服从幂律，其指数依赖于计算的开始时间。4.实验分析了粗化初期正弦调制的时间演化。结果发现，正弦调制指数发展到一个平衡值，正如所预期的Spinodal分解理论。在对展曲壁运动方程线性稳定性分析的基础上，讨论了正弦调制的增长率。在锯齿形失稳区附近，实验结果与线性稳定性分析的预测一致。

The zigzag instability coarsening of a splay-bend wall formed in a nematic liquid crystal under external fields is investigated experimentally as a study of a one-dimensional analog of the spinodal decomposition in a conserved order parameter system. When an electric field is applied on the liquid crystal, a sinusoidal modulation first appears, then the shape of wall changes to zigzag. In the late stage, the coarsening of zigzag vertexes proceeds due to the coalescence of zigzag vertexes.1.In the late stage of coarsening, a characteristic length, i.e.the mean width of the zigzag period, shows logarithmic increase in time, which agrees with the theoretical prediction.2.The structure function and the correlation function for the Ising domain and the density correlation of zinzag vertexes are analyzed. Then it is clarified that the dynamical scaling law holds in the late stage of coarsening.3.The kink-antikink kinetics of one-dimensional phase ordering is studied numerically. The logarithmic growth of the mean width of domains is also confirmed. The distribution of domain size and the correlation function are shown to satisfy a scaling relation. The two-time autocorrelation function follows a power law whose exponent depends on the start time of the calculation.4.The time evolution of the sinusoidal modulation in the early stage of coarsening is analyzed experimentally. It is found that the sinusoidal modulation develops exponentially up to an equilibrium value as expected in the theory of spinodal decomposition. Basing our study on the linear stability analysis of the splay-bend wall equation of motion, the growth rate of the sinusoidal modulation is discussed. In the vicinity of the zigzag instability, the experimental result agrees with the prediction form the linear stability analysis.