论文标题
显微结构各向异性颗粒在外场的扩散
Diffusion of microstructured anisotropic particles in an external field
论文作者
论文摘要
微结构颗粒被广泛用于行业和最先进的研发。颗粒的扩散，尤其是通过远程应用的场的受控扩散，启发了新的应用，从靶向药物传递，量化纳米颗粒物理特性的新型程序和环境流体，到具有增强特性的复合材料的制造。在这项工作中，我们报告了有关微结构颗粒的现场控制扩散的系统分析。由于形状各向异性和粒子的结构异质性，我们研究了粒子在$ \ mathbb {r}^3 \ times $ so（3）中耦合粒子的耦合。从运动的显微镜随机微分方程开始，我们实现了在粒子的位置和方向上控制概率分布函数的演变的粗粒fokker-Planck方程。在某些轻度条件下，我们确定了外场中微结构颗粒的长时间扩散率。该公式适用于任意形状和异质性的微结构颗粒。作为应用的示例，我们分析了异质球颗粒的扩散和一对由弹性韧带键合的球体颗粒。对于异质球颗粒，我们获得了显式的广义Stokes-Einstein的关系，以扩散性，这说明了形状各向异性，异质性和外部排列场的影响。对于成对的球体颗粒，我们考虑了从初始非平衡状态到最终平衡状态的叠加弛豫过程。相对于此类过程的时间，均方根位移（MSD）的异常缩放可能为理解复杂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提供了重要的见解。
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.
