Diffusion of microstructured anisotropic particles in an external field

TL;DR

This paper presents a systematic analysis of how microstructured anisotropic particles diffuse under external fields, deriving a general framework that accounts for shape, heterogeneity, and external alignment effects, with applications to spheroidal particles.

Contribution

It develops a coarse-grained Fokker-Planck model for anisotropic particles in external fields, extending diffusion analysis to arbitrary shapes and heterogeneities, and explores specific cases like spheroids and bonded pairs.

Findings

Derived explicit generalized Stokes-Einstein relations for heterogeneous spheroids.

Analyzed superimposed relaxation processes of particle pairs from non-equilibrium states.

Identified anomalous MSD scaling relevant to complex biological media.

Abstract

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.