Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS - Ecole Polytechnique, IP Paris, 91128 Palaiseau, France.
J Chem Phys. 2019 Sep 14;151(10):104108. doi: 10.1063/1.5115030.
We propose a general theoretical description of chemical reactions occurring on a catalytic surface with heterogeneous reactivity. The propagator of a diffusion-reaction process with eventual absorption on the heterogeneous partially reactive surface is expressed in terms of a much simpler propagator toward a homogeneous perfectly reactive surface. In other words, the original problem with the general Robin boundary condition that includes, in particular, the mixed Robin-Neumann condition, is reduced to that with the Dirichlet boundary condition. Chemical kinetics on the surface is incorporated as a matrix representation of the surface reactivity in the eigenbasis of the Dirichlet-to-Neumann operator. New spectral representations of important characteristics of diffusion-controlled reactions, such as the survival probability, the distribution of reaction times, and the reaction rate, are deduced. Theoretical and numerical advantages of this spectral approach are illustrated by solving interior and exterior problems for a spherical surface that may describe either an escape from a ball or hitting its surface from outside. The effect of continuously varying or piecewise constant surface reactivity (describing, e.g., many reactive patches) is analyzed.
我们提出了一个在具有非均相反应性的催化表面上发生化学反应的一般理论描述。扩散-反应过程的传播子，最终在非均相部分反应表面上发生吸收，用向均匀完全反应表面的传播子来表示。换句话说，具有一般 Robin 边界条件的原始问题，包括特别是混合 Robin-Neumann 条件，被简化为具有 Dirichlet 边界条件的问题。表面上的化学动力学被纳入到表面反应性的矩阵表示中，作为 Dirichlet-to-Neumann 算子的本征基的一部分。扩散控制反应的重要特征的新的谱表示，如生存概率、反应时间分布和反应速率，被推导出来。这种谱方法的理论和数值优势通过求解内部和外部问题来说明，这些问题可以描述从球体内的逃逸或从外部撞击球体表面。分析了连续变化或分段常数表面反应性（描述例如许多反应性斑块）的影响。
