Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, IP Paris, 91128 Palaiseau, France.
Phys Rev Lett. 2020 Aug 14;125(7):078102. doi: 10.1103/PhysRevLett.125.078102.
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation, and filtration processes. Their current description via diffusion equations with mixed boundary conditions is limited to simple surface reactions with infinite or constant reactivity. In this Letter, we propose a probabilistic approach based on the concept of boundary local time to investigate the intricate dynamics of diffusing particles near a reactive surface. Reformulating surface-particle interactions in terms of stopping conditions, we obtain in a unified way major diffusion-reaction characteristics such as the propagator, the survival probability, the first-passage time distribution, and the reaction rate. This general formalism allows us to describe new surface reaction mechanisms such as for instance surface reactivity depending on the number of encounters with the diffusing particle that can model the effects of catalyst fooling or membrane degradation. The disentanglement of the geometric structure of the medium from surface reactivity opens far-reaching perspectives for modeling, optimization, and control of diffusion-mediated surface phenomena.
扩散介导的表面现象对人类生活和工业至关重要，其例子包括肺肺泡表面的氧气捕获到多相催化、基因调控、膜渗透和过滤过程。目前通过带有混合边界条件的扩散方程来描述这些现象仅限于具有无限或恒定反应性的简单表面反应。在这封信中，我们提出了一种基于边界局部时间概念的概率方法来研究扩散粒子在反应性表面附近的复杂动力学。通过停止条件重新表述表面-粒子相互作用，我们以统一的方式得到了扩散-反应的主要特征，如传播子、存活概率、首次通过时间分布和反应速率。这种通用形式允许我们描述新的表面反应机制，例如表面反应取决于与扩散粒子的相遇次数，可以模拟催化剂愚弄或膜降解的影响。将介质的几何结构与表面反应分离，为扩散介导的表面现象的建模、优化和控制开辟了广阔的前景。
