Exact results for the reactivity of a single-file system

TL;DR

This paper provides exact analytical expressions for the reactivity of a single-file system, revealing how reaction speed and system size influence conversion efficiency and particle distribution.

Contribution

It derives exact formulas for reactivity in single-file systems, highlighting the effects of reaction speed and system size on conversion and particle distribution.

Findings

Fast reactions lead to near 100% conversion regardless of size.

Reactivity scales with system size when reactions are slow.

Nonconverted particles decrease exponentially with distance in large systems.

Abstract

We derive analytical expressions for the reactivity of a Single-File System with fast diffusion and adsorption and desorption at one end. If the conversion reaction is fast, then the reactivity depends only very weakly on the system size, and the conversion is about 100%. If the reaction is slow, then the reactivity becomes proportional to the system size, the loading, and the reaction rate constant. If the system size increases the reactivity goes to the geometric mean of the reaction rate constant and the rate of adsorption and desorption. For large systems the number of nonconverted particles decreases exponentially with distance from the adsorption/desorption end.