Robertson Bryan, Schofield Jeremy, Gaspard Pierre, Kapral Raymond
Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (U.L.B.), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium.
J Chem Phys. 2020 Sep 28;153(12):124104. doi: 10.1063/5.0020553.
Active colloidal particles that are propelled by a self-diffusiophoretic mechanism are often described by Langevin equations that are either postulated on physical grounds or derived using the methods of fluctuating hydrodynamics. While these descriptions are appropriate for colloids of micrometric and larger size, they will break down for very small active particles. A fully microscopic derivation of Langevin equations for self-diffusiophoretic particles powered by chemical reactions catalyzed asymmetrically by the colloid is given in this paper. The derivation provides microscopic expressions for the translational and rotational friction tensors, as well as reaction rate coefficients appearing in the Langevin equations. The diffusiophoretic force and torque are expressed in terms of nonequilibrium averages of fluid fields that satisfy generalized transport equations. The results provide a description of active motion on small scales where descriptions in terms of coarse grained continuum fluid equations combined with boundary conditions that account for the presence of the colloid may not be appropriate.
由自扩散泳机制驱动的活性胶体粒子通常由朗之万方程描述，这些方程要么基于物理原理假设，要么使用波动流体动力学方法推导得出。虽然这些描述适用于微米级及更大尺寸的胶体，但对于非常小的活性粒子来说，它们将不再适用。本文给出了由胶体不对称催化的化学反应驱动的自扩散泳粒子的朗之万方程的完全微观推导。该推导给出了平移和旋转摩擦张量的微观表达式，以及出现在朗之万方程中的反应速率系数。扩散泳力和扭矩用满足广义输运方程的流场非平衡平均值表示。结果提供了小尺度下活性运动的描述，在这种情况下，用粗粒化连续流体方程结合考虑胶体存在的边界条件进行描述可能并不合适。
