Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces

Abstract

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 general Robin boundary condition that includes in particular mixed Robin-Neumann condition, is reduced to that with 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.

References in corpus (15)

• First-passage times in complex scale-invariant media
• Diffusion-limited reactions in dynamic heterogeneous media
• Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
• Mortality, Redundancy, and Diversity in Stochastic Search
• Diffusive escape through a narrow opening: new insights into a classic problem
• Towards a full quantitative description of single-molecule reaction kinetics in biological cells
• First passage statistics for diffusing diffusivity
• Exit time distribution in spherically symmetric two-dimensional domains
• Duality Between Relaxation and First Passage in Reversible Markov Dynamics: Rugged Energy Landscapes Disentangled
• Partially Reflected Brownian Motion: A Stochastic Approach to Transport Phenomena
• Narrow escape of interacting diffusing particles
• Kinetics of active surface-mediated diffusion in spherically symmetric domains
• Semi-analytical computation of Laplacian Green functions in three-dimensional domains with disconnected spherical boundaries
• Exact mean exit time for surface-mediated diffusion
• Narrow Escape, Part III: Riemann surfaces and non-smooth domains

Cited by in corpus (37)

• Paradigm shift in diffusion-mediated surface phenomena
• Full distribution of first exit times in the narrow escape problem
• From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of $N$ random walkers
• Probability distribution of the boundary local time of reflected Brownian motion in Euclidean domains
• Diffusion-mediated surface reactions and stochastic resetting
• Surface Hopping Propagator: An Alternative Approach to Diffusion-Influenced Reactions
• Diffusion toward non-overlapping partially reactive spherical traps: fresh insights onto classic problems
• Microscopic Theory of Adsorption Kinetics
• Statistics of boundary encounters by a particle diffusing outside a compact planar domain
• Joint distribution of multiple boundary local times and related first-passage time problems with multiple targets
• The narrow capture problem: an encounter-based approach to partially reactive targets
• Spectral theory of diffusion in partially absorbing media
• Encounter-based model of a run-and-tumble particle II: absorption at sticky boundaries
• First-encounter time of two diffusing particles in confinement
• Statistics of diffusive encounters with a small target: Three complementary approaches
• First-passage times to anisotropic partially reactive targets
• First-passage times of multiple diffusing particles with reversible target-binding kinetics
• Encounter-based model of a run-and-tumble particle
• Distribution of first-reaction times with target regions on boundaries of shell-like domains
• Reversible Target-Binding Kinetics of Multiple Impatient Particles
• Diffusion-influenced reactions on non-spherical partially absorbing axisymmetric surfaces
• An encounter-based approach to the escape problem
• Reversible reactions controlled by surface diffusion on a sphere
• Close encounters of the sticky kind: Brownian motion at absorbing boundaries
• Boundary conditions at a thin membrane for normal diffusion equation which generate subdiffusion
• First-encounter time of two diffusing particles in two- and three-dimensional confinement
• A numerical study of the Dirichlet-to-Neumann operator in planar domains
• Diffusion in a partially absorbing medium with position and occupation time resetting
• Spectral properties of the Dirichlet-to-Neumann operator for spheroids
• Accumulation times for diffusion-mediated surface reactions
• Stochastically switching diffusion with partially reactive surfaces
• The Steklov problem for exterior domains: asymptotic behavior and applications
• Adsorption and permeation events in molecular diffusion
• Subdiffusion in a system with a partially permeable partially absorbing wall
• An encounter-based approach for restricted diffusion with a gradient drift
• Encounter-based approach to target search problems: a review
• Enhancing search efficiency through diffusive echo