A Holistic Approach to Model the Kinetics of Photocatalytic Reactions

Abstract

Understanding and modeling kinetics is an essential part of the optimization and implementation of chemical reactions. In the case of photocatalytic reactions this is mostly done one-dimensionally, i.e., only considering the effect of one parameter at the same time. However, as discussed in this study, many of the relevant reaction parameters have mutual interdependencies that call for a holistic multi-dimensional approach to accurately model and understand their influence. Such an approach is described herein, and all the relevant equations given so that researchers can readily implement it to analyze and model their reactions.

Reaction Rate Study of the Photocatalytic Degradation of Dichloroacetic Acid in a Black Body Reactor

“…The kinetics of light-induced reactions of organic compounds in photocatalyst suspensions are usually analyzed by Langmuir−Hinshelwood-type rate laws [53][54][55][56][57][58][59][60][61][62][63], which can all be written as…”

“…Depending on the underlying mechanistic assumptions, the physical meaning of the kinetic parameters k 1 , k 2 , and k 3 are different in the different Langmuir−Hinshelwood-type rate laws [53][54][55][56][57][58][59][60][61][62][63]. It is well known, that the macroscopic reaction rate dC/dt depends not only on the substrate concentration C but also on the concentration of the photocatalyst γ and the photon flux density I 0 .…”

“…A macroscopic rate law for a photocatalytic reaction must however result from the integration of the local volumetric reaction rates over the entire suspension volume (Equation (10)). This approach was very recently used by Bloh and co-authors, resulting in a rate law which describes the impact of the concentration of the reactant C, the mass concentration of the heterogeneous photocatalyst γ, and the photon flux density I 0 on the observable macroscopic reaction rate dC/dt [62,63]. As this rate law was used to analyze the kinetic data presented in the Figure 1B, Figure 2B, and Figure 4B, the essential steps of the derivation are presented here to elucidate the restricting assumptions and simplifications.…”

“…Essential in his approach is the ascertainment that only a limited number of sites on the photocatalyst surface are capable of forming these reactive surface sites. For the concentration of the reactive surface sites C rs in a small volume within the suspension, he assumed a steady-state of formation, decay (recombination), and reaction with the reactant [63] dC…”

“…For the derivation of the local rate of photon absorption, Bloh neglected scattering effects by the photocatalyst particles and assumed that the photon absorption is correctly described by the Lambert-Beer law [63]. This approach results in…”