Efficacy analysis of compartmentalization for ambient CH₄ activation mediated by a Rh^II metalloradical in a nanowire array electrode

Abstract

We integrated theory with experiment to evaluate the catalytic cycle of seemingly incompatible steps enabled by nanowire array for CH4-to-CH3OH conversion, and determined the array’s efficacy in the context of microscopic compartmentalization.

A Generalized Kinetic Model for Compartmentalization of Organometallic Catalysis

“…It is intriguing that the kinetics of deactivation steps are not needed for the design of compartment, as long as it is known that 𝑘 ' < 𝑘 (' and 𝑘 ) < 𝑘 () . As discussed with the examples of nanowire-based CH4 activation, 17,29 Fujiwara-Mirotani reaction, 30,31 and the Negishi coupling reaction, 32,33 a tailored compartment design, including the use of nanomaterials, is needed to suit a specific organometallic catalysis. Such insights will assist in future a priori design of compartmentalized organometallics for enhanced catalytic performance.…”

“…We illustrated the general relationship for specific organometallic catalysis to achieve maximal 𝛾 and 𝑇𝑂𝐹. We additionally employed the developed model to analyze the experimental results in nanowire-based CH4 activation, 17,29 Fujiwara-Mirotani reaction, 30,31 and the Negishi coupling reaction. 32,33 The established kinetic model can be adapted to suit a plethora of catalytic cycles with synthetic compartments, offering a framework to be expanded on for advanced compartmentalization of general chemical catalysis.…”

A generalized kinetic model for compartmentalization of organometallic catalysis

“…As a first-order approximation, a mean-field average diffusion coefficient D is sufficient to describe the permeation of molecules through a compartment at ensemble level as long as the compartment's porosity is isotropic, based on single-molecule studies of molecular diffusion in mesoporous silica and polymer films. 56,57 In the presence of anisotropicity such as highly aligned pores or in our previous work's nanowire arrays, 17,29 a meanfield averaged diffusion coefficient D is still good enough to account for the diffusion phenomena in the specific direction. 58,59 In cases where anisotropic diffusion exists, the values of anisotropic 𝜌 normal to the compartment's boundary should be used when calculating 𝐹 !…”

“…This argument is corroborated by our prior work that utilizes nanowire array electrode to pair CH4 activation from O2-sensitive metalloporphyrin with CH3OH generation with O2 as the terminal oxidant. 17,29 An increase of the nanowire array's length, corresponding to a smaller value of 𝐹 ! (Supplementary Information Section 2), was experimentally observed to yield an increased rate of CH4 activation until the reaction rate plateaued for nanowire arrays of 27 μm length.…”

“…We took advantage of the established theoretical frameworks in biochemistry 16,25,26 and applied such kinetic frameworks to a model compartmentalized cycle with competing deactivation pathways (Figure 1A), 28 and a non-compartmentalized counterpart as a control scenario (Figure 1B). Under assumptions and simplifications applicable to organometallic catalysis, as a proof-of-concept we examined three important metrics of this catalytic cycle in both 17,29 the Fujiwara-Mirotani reaction, 30,31 and the Negishi coupling reaction. 32,33 The established kinetic model can be adapted to suit a plethora of catalytic cycles with synthetic compartments, offering a framework to be expanded on for advanced compartmentalization of general chemical catalysis.…”