When bubbles matter: hydrogen transport governs apparent kinetics in 4-nitrophenol hydrogenation reaction

TL;DR

The paper addresses the misinterpretation of 4-nitrophenol hydrogenation kinetics as pseudo-first-order, showing that hydrogen transport, via hydrolysis-produced $H_2$ and subsequent diffusion or bubbling, strongly shapes apparent rates. It introduces a minimal kinetic model that couples two hydrogenation pathways, $k_A$ for $H_2$-mediated steps and $k_{AB}$ for transfer hydrogenation, along with a hydrolysis rate $k_B$ and a time-dependent transport term $\alpha$ in the equations for $C_{\text{4-NiP}}$, $C_{\text{NaBH}_4}$, and $C_{H_2}$: $\frac{dC_{\text{4-NiP}}}{dt} = - k_A C_{H_2} - 4 k_{AB} C_{\text{4-NiP}} C_{\text{NaBH}_4}$, $\frac{dC_{\text{NaBH}_4}}{dt} = - k_B C_{\text{NaBH}_4} - 3 k_{AB} C_{\text{4-NiP}} C_{\text{NaBH}_4}$, $\frac{dC_{H_2}}{dt} = 4 k_B C_{\text{NaBH}_4} - 3 k_A C_{H_2} - \alpha C_{\text{H}_2}$, with $\alpha(t) = \alpha_s$ for $t < t_{\text{bub}}$ and $\alpha_l$ for $t \ge t_{\text{bub}}$. Analysis of Pt-SiO$_2$ supraparticles with different pore architectures shows that bubbling accelerates $H_2$ loss and yields distinct kinetic regimes; Type A and Type B data can be reconciled with a single parameter set, highlighting the role of hydrogen-transport rather than intrinsic catalyst differences, and Type C reveals a late-stage activity surge when bubbling stops. The findings imply that benchmarking catalytic performance for transfer hydrogenation reactions must account for hydrogen transport and the evolving transport regime, with broader relevance to other hydrogen-donor systems and flow reactors.

Abstract

The reduction of 4-nitrophenol (4-NiP) with sodium borohydride is widely used to benchmark heterogeneous catalysts, yet its kinetics are commonly oversimplified as pseudo-first-order. In reality, borohydride hydrolysis and hydrogenation by dissolved hydrogen proceed concurrently, making hydrogen transport a decisive factor in shaping apparent activity. Re-examining data on Pt-SiO2 supraparticles with different pore structures, we attribute contrasting kinetic behavior to distinct regimes of hydrogen transport: diffusive transport sustains pseudo-first-order kinetics, while bubble-mediated escape causes hydrogen loss and incomplete conversion. We propose a kinetic model that captures this transition and enables consistent interpretation of experimental data. More broadly, our analysis shows that apparent differences in activity during 4-NiP benchmarking can arise from hydrogen transport rather than intrinsic properties of the catalyst, underscoring the need to account for transport effects when comparing catalyst performance.

Figures (4)

• Figure 1: (a) Reaction scheme of 4-NiP hydrogenation, depicting different mechanisms: (I) transfer hydrogenation by borohydride and (II) hydrolysis of borohydride and hydrogenation by dissolved hydrogen. (b) Sketch of hydrogen transport mechanisms: bubbling vs. degassing from the liquid/gas interface.
• Figure 2: Time evolution of normalized 4-NiP concentration and reaction rate for Types A (a,b), B (c,d), and C (e,f). Dotted curves with symbols: experiments; solid curves: model fits to Eqs. (\ref{['eq:frank_nip']}--\ref{['eq:frank_h2']}). Shaded areas: time range within which bubbling stops.
• Figure 3: Semi-logarithmic plot of normalized 4-NiP concentration for Type A and Type B supraparticles with the same initial activity.
• Figure 4: Influence of the hydrogen transport coefficient on apparent kinetics: time evolution of 4-NiP (a), borohydride (b, dashed), and hydrogen (d, solid) for systems with identical $k_{AB}$, $k_B$, $k_A$ and varying $\alpha$.