Microscopic Theory of Adsorption Kinetics

TL;DR

This paper develops a microscopic theory of adsorption kinetics that derives the Ward-Tordai relation and generalizes it to various conditions, providing exact solutions and new insights into surface science applications.

Contribution

It introduces a self-contained microscopic framework for adsorption kinetics, deriving and generalizing the Ward-Tordai relation for arbitrary conditions.

Findings

Derived the microscopic Ward-Tordai relation.

Generalized the relation to arbitrary dimensions and geometries.

Provided exact analytical solutions to complex adsorption problems.

Abstract

Adsorption is the accumulation of a solute at an interface that is formed between a solution and an additional gas, liquid, or solid phase. The macroscopic theory of adsorption dates back more than a century and is now well-established. Yet, despite recent advancements, a detailed and self-contained theory of single-particle adsorption is still lacking. Here, we bridge this gap by developing a microscopic theory of adsorption kinetics, from which the macroscopic properties follow directly. One of our central achievements is the derivation of the microsopic version of the seminal Ward-Tordai relation which connects the surface and subsurface adsorbate concentrations via a universal equation that holds for arbitrary adsorption dynamics. Furthermore, we present a microscopic interpretation of the Ward-Tordai relation which, in turn, allows us to generalize it to arbitrary dimension, geometry and initial conditions. The power of our approach is showcased on a set of hitherto unsolved adsorption problems to which we present exact analytical solutions. The framework developed herein sheds fresh light on the fundamentals of adsorption kinetics, which opens new research avenues in surface science with applications to artificial and biological sensing and to the design of nano-scale devices.