Power-law forces between particles in a nematic
Power-law forces between particles in a nematic
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DOI：
10.1080/10587259608034594
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发表时间：
1996-01-01
影响因子：
--
通讯作者：
Prost, J
中科院分区：
文献类型：
--
作者：
Ramaswamy, S;Nityananda, R;Prost, J
尺寸为a的宏观粒子浸入液晶溶剂中（例如溶致液晶中的聚苯乙烯球）将通过扭曲它们周围的有序参数场而相互施加长程力。作为第一步，对这类新的悬浮液的完整理论，我们展示了如何计算作为分离r的函数的相互作用的能量，r远大于一个粒子之间的各种形状和取向的液晶。我们的方法可以被理解为（i）作为一个连续描述的浓度场的粒子，浓度梯度和导演场之间的耦合或（ii）在静电类比由于Brochard和de Gennes，其中指向矢畸变的远场横向分量被处理为两个-库仑场的分量，其中各种形状和取向的粒子是基本多极源。与Raghunathan等人的实验最有可能相关的结果是球体：它们的行为类似于四极杆，相互作用与Ka（6）/r（5）成比例，并且对于在帽上方与α轴（n）成50度的范围内定向的r是吸引的，尽管对于帽上方垂直或平行于（n）的r是排斥的。在最近的计算中的错误，在文献中，声称总是排斥，r（-3）的相互作用，指出。
Macroscopic particles of size a immersed in liquid crystalline solvents (e.g. polystyrene spheres in a lyotropic nematic) will exert long-range forces on each other by distorting the order-parameter field around them. As a first step towards a full theory of this novel class of suspensions, we show how to calculate the energy of interaction as a function of the separation r for r much greater than a between particles of various shapes and orientations in a nematic liquid crystal. Our approach can be understood (i) as a continuum description of the concentration field of the particles, with symmetry-allowed couplings between concentration gradients and director fields or (ii) in terms of an electrostatic analogy due to Brochard and de Gennes, in which the far-field transverse components of the director distortion are treated as a two-component Coulomb field of which particles of various shapes and orientations are elementary multipolar sources. The results with the greatest potential relevance to the experiments of Raghunathan et al. are for spheres: these act like quadrupoles, and the interaction is proportional to Ka(6)/r(5), and attractive for r oriented in a range around 50 degrees to the nematic axis (n) over cap, although it is repulsive for r normal or parallel to (n) over cap. The error in a recent calculation in the literature, claiming an always repulsive, r(-3) interaction, is pointed out.