微结构各向异性颗粒在外场中的扩散
Diffusion of microstructured anisotropic particles in an external field
摘要：
微结构颗粒广泛应用于工业和最先进的研究和开发中。颗粒的扩散，特别是通过远程施加场的受控扩散，已经激发了新的应用，从靶向药物递送、用于量化纳米颗粒和环境流体的物理性质的新程序到具有增强性质的复合材料的制造。在这项工作中，我们报告了一个系统的分析场控制扩散的微结构粒子。考虑到粒子的形状各向异性和结构不均匀性，我们研究了$\mathbb{R}^3\times$ SO（3）中粒子的耦合布朗运动。从微观随机运动微分方程出发，我们得到了粗粒度的Fokker-Planck方程，它控制着概率分布函数关于粒子位置和方向的演化。在一些温和的条件下，我们确定了在外场微结构颗粒的长时间扩散系数。该配方适用于微结构颗粒的任意形状和异质性。作为应用的例子，我们分析了一个非均匀的球形粒子和一对球形粒子的弹性韧带结合的扩散。对于非均匀的球形颗粒，我们得到明确的广义斯托克斯-爱因斯坦的扩散率的关系，占形状各向异性，异质性，和外部对齐字段的影响。对于球形粒子对，我们考虑从初始非平衡态到最终平衡态的叠加弛豫过程。相对于这样的过程的时间的均方位移（MSD）的异常标度可以提供重要的洞察力，了解在复杂的粘弹性介质中的大分子和细胞的迁移中观察到的异常扩散。
英文摘要：
Microstructured particles are widely used in industries and state-of-the-art research and development. Diffusion of particles, particularly, controlled diffusion by a remotely applied field, has inspired novel applications ranging from targeted drug deliveries, novel procedures for quantifying physical properties of nanoparticles and ambient fluids, to fabrication of composites with enhanced properties. In this work, we report a systematic analysis on field-controlled diffusion of microstructured particles. In account of shape anisotropy and structural heterogeneity of a particle, we study coupled Brownian motions of the particle in $\mathbb{R}^3\times$SO(3). Starting from the microscopic stochastic differential equations of motions, we achieve the coarse-grained Fokker-Planck equation that governs the evolution of the probability distribution function with respect to the position and orientation of the particle. Under some mild conditions, we identify the long-time diffusivity for microstructured particles in an external field. The formulation is applicable to microstructured particles of arbitrary shapes and heterogeneities. As examples of applications, we analyze the diffusion of a heterogeneous spheroidal particle and a pair of spheroidal particles bonded by an elastic ligament. For heterogeneous spheroidal particles, we obtain explicit generalized Stokes-Einstein's relations for diffusivity that accounts for the effects of shape anisotropy, heterogeneity, and an external alignment field. For pairs of spheroidal particles, we consider the superimposed relaxation process from an initial non-equilibrium state to the final equilibrium state. The anomalous scaling of Mean Square Displacement (MSD) with respect to the time of such processes may provide important insight for understanding anomalous diffusions observed in migration of macromolecules and cells in complex viscoelastic media.
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