Reaction rate of a composite core-shell nanoreactor with multiple, spatially distributed embedded nano-catalysts

TL;DR

This paper develops a comprehensive theoretical model for the reaction rate of a composite core-shell nanoreactor with embedded nano-catalysts, considering geometry, diffusion, and chemical factors to optimize design.

Contribution

It introduces a detailed theory and an approximate analytical formula for the reaction rate, accounting for geometry, diffusion, and chemical interactions in nanoreactors.

Findings

Derived simple rules for estimating nanocatalyst numbers for optimal performance.

Analyzed how core size influences diffusion-controlled reaction rates.

Provided a flexible tool for designing high-performance nanoreactors.

Abstract

We present a detailed theory for the total reaction rate constant of a composite core-shell nanoreactor, consisting of a central solid core surrounded by a hydrogel layer of variable thickness, where a given number of small catalytic nanoparticles are embedded at prescribed positions and are endowed with a prescribed surface reaction rate constant. Besides the precise geometry of the assembly, our theory accounts explicitly for the diffusion coefficients of the reactants in the hydrogel and in the bulk as well as for their transfer free energy jump upon entering the hydrogel shell. Moreover, we work out an approximate analytical formula for the overall rate constant, which is valid in the physically relevant range of geometrical and chemical parameters. We discuss in depth how the diffusion-controlled part of the rate depends on the essential variables, including the size of the central core. In particular, we derive some simple rules for estimating the number of nanocatalysts per nanoreactor for an efficient catalytic performance in the case of small to intermediate core sizes. Our theoretical treatment promises to provide a very useful and flexible tool for the design of superior performing nanoreactor geometries and with optimized nanoparticle load.