四极场中多分散棒的连续渗流：理论与模拟
Continuum Percolation of Polydisperse Rods in Quadrupole Fields: Theory and Simulations
摘要：
我们研究渗流在纳米棒的混合物中存在的外部领域，对齐或不对齐的粒子与场轴。这种条件在纳米复合材料的配制和加工中发现，其中场可以是电的、磁的或由于拉伸流动。我们的重点是长度多分散性的影响，这-在没有一个字段-是已知的，以产生一个逾渗阈值，尺度与粒子长度的倒数重量平均。使用模型的非相互作用spherocylinders与连通渗流理论，我们表明，一个四极场总是增加渗流阈值和通用的缩放与反加权平均不再成立，如果该字段耦合到粒子长度。相反，逾渗阈值成为长度分布的高阶矩的函数，其中相关矩的阶次关键地取决于所施加的场的强度和类型。理论预测与我们的蒙特卡罗模拟，消除有限尺寸的影响，利用的事实，即通用的缩放的包装概率函数，即使在各向异性系统的结果进行比较。理论和模拟表明，多分散混合物的逾渗阈值可以低于单个组分的逾渗阈值，证实了最近的工作的基础上映射到Bethe晶格以及早期的计算机模拟涉及偶极场。我们的工作表明，纳米复合材料的配方可用于补偿在实际制造条件下不可避免的对准场的不利影响。
英文摘要：
We investigate percolation in mixtures of nanorods in the presence of external fields that align or disalign the particles with the field axis. Such conditions are found in the formulation and processing of nanocomposites, where the field may be electric, magnetic, or due to elongational flow. Our focus is on the effect of length polydispersity, which -- in the absence of a field -- is known to produce a percolation threshold that scales with the inverse weight average of the particle length. Using a model of non-interacting spherocylinders in conjunction with connectedness percolation theory, we show that a quadrupolar field always increases the percolation threshold and that the universal scaling with the inverse weight average no longer holds if the field couples to the particle length. Instead, the percolation threshold becomes a function of higher moments of the length distribution, where the order of the relevant moments crucially depends on the strength and type of field applied. The theoretical predictions compare well with the results of our Monte Carlo simulations, which eliminate finite size effects by exploiting the fact that the universal scaling of the wrapping probability function holds even in anisotropic systems. Theory and simulation demonstrate that the percolation threshold of a polydisperse mixture can be lower than that of the individual components, confirming recent work based on a mapping onto a Bethe lattice as well as earlier computer simulations involving dipole fields. Our work shows how the formulation of nanocomposites may be used to compensate for the adverse effects of aligning fields that are inevitable under practical manufacturing conditions.
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