Apparent Activation Energies in Complex Reaction Mechanisms: A Simple Relationship via Degrees of Rate Control

Reproducible graphene synthesis by oxygen-free chemical vapour deposition

Chemical vapour deposition (CVD) synthesis of graphene on copper has been broadly adopted since the first demonstration of this process1. However, widespread use of CVD-grown graphene for basic science and applications has been hindered by challenges with reproducibility2 and quality3. Here we identify trace oxygen as a key factor determining the growth trajectory and quality for graphene grown by low-pressure CVD. Oxygen-free chemical vapour deposition (OF-CVD) synthesis is fast and highly reproducible, with kinetics that can be described by a compact model, whereas adding trace oxygen leads to suppressed nucleation and slower/incomplete growth. Oxygen affects graphene quality as assessed by surface contamination, emergence of the Raman D peak and decrease in electrical conductivity. Epitaxial graphene grown in oxygen-free conditions is contamination-free and shows no detectable D peak. After dry transfer and boron nitride encapsulation, it shows room-temperature electrical-transport behaviour close to that of exfoliated graphene. A graphite-gated device shows well-developed integer and fractional quantum Hall effects. By highlighting the importance of eliminating trace oxygen, this work provides guidance for future CVD system design and operation. The increased reproducibility and quality afforded by OF-CVD synthesis will broadly influence basic research and applications of graphene.

Operando Characterization and Molecular Simulations Reveal the Growth Kinetics of Graphene on Liquid Copper During Chemical Vapor Deposition

In recent years, liquid metal catalysts have emerged as a compelling choice for the controllable, large-scale, and high-quality synthesis of two-dimensional materials. At present, there is little mechanistic understanding of the intricate catalytic process, though, of its governing factors or what renders it superior to growth at the corresponding solid catalysts. Here, we report on a combined experimental and computational study of the kinetics of graphene growth during chemical vapor deposition on a liquid copper catalyst. By monitoring the growing graphene flakes in real time using in situ radiation-mode optical microscopy, we explore the growth morphology and kinetics over a wide range of CH4-to-H2 pressure ratios and deposition temperatures. Constant growth rates of the flakes' radius indicate a growth mode limited by precursor attachment, whereas methane-flux-dependent flake shapes point to limited precursor availability. Large-scale free energy simulations enabled by an efficient machine-learning moment tensor potential trained to density functional theory data provide quantitative barriers for key atomic-scale growth processes. The wealth of experimental and theoretical data can be consistently combined into a microkinetic model that reveals mixed growth kinetics that, in contrast to the situation at solid Cu, is partly controlled by precursor attachment alongside precursor availability. Key mechanistic aspects that directly point toward the improved graphene quality are a largely suppressed carbon dimer attachment due to the facile incorporation of this precursor species into the liquid surface and a low-barrier ring-opening process that self-heals 5-membered rings resulting from remaining dimer attachments.

Early Steps in the O2 Scavenger Process in the Aqueous Phase: Hydrazine vs DEHA

We investigate the first direct proton abstraction reactions from reducing agents (RAHs) hydrazine and diethyl hydroxylamine (DEHA), toward dioxygen (O2) in the aqueous phase, spanning ambient to high-temperature conditions. Quantum chemistry methods and molecular dynamics simulations are employed in this study. Quantum chemistry methods are used to analyze the quasi-equilibrium between a reactive conformation and a transition state in the [RAH,O2] cluster. On the other hand, molecular dynamics simulations estimate the probability of observing a reactive conformation of the [RAH,O2] cluster in the solution. In this study, we assume that the energy barrier of the quasi-equilibrium is sufficiently high for the RAH/O2 association process to be at equilibrium. Our findings indicate that the first proton abstraction process from a reactive conformation cluster by DEHA is energetically favored compared to hydrazine. Conversely, the association process of hydrazine and O2 in solution is more favorable than that of DEHA. Consequently, the rate constant for the first proton abstraction process is similar for both hydrazine and DEHA, particularly at high temperatures, with activation energies of approximately 21.5 ± 1.5 kcal mol-1 for both compounds. These results align with recent experiments investigating the complete O2 scavenger process in liquid water with hydrazine and DEHA. Therefore, our findings support the assumption that first proton abstraction reactions are the rate-determining steps in O2 scavenger processes in the aqueous phase.

Substantial impact of surface charges on electrochemical reaction kinetics on S vacancies of MoS2 using grand-canonical iteration method

The surface charges of catalysts have intricate influences on the thermodynamics and kinetics of electrochemical reactions. Herein, we develop a grand-canonical iteration method based on density functional theory calculations to explore the effect of surface charges on reaction kinetics beyond the traditional Butler-Volmer picture. Using the hydrogen evolution reaction on S vacancies of MoS2 as an example, we show how to track the change of surface charge in a reaction and to analyze its influence on the kinetics. Protons adsorb on S vacancies in a tough and charge-insensitive water splitting manner, which explains the observed large Tafel slope. Grand-canonical calculations report an unanticipated surface charge-induced change of the desorption pathway from the Heyrovsky route to a Volmer-Tafel route. During an electrochemical reaction, a net electron inflow into the catalyst may bring two effects, i.e., stabilization of the canonical energy and destabilization of the charge-dependent grand-canonical part. On the contrary, a net outflow of electrons from the catalyst can reverse the two effects. This surface charge effect has substantial impacts on the overpotential and the Tafel slope. We suggest that the surface charge effect is universal for all electrochemical reactions and significant for those involving interfacial proton transfers.

Kinetic Barrier Diagrams to Visualize and Engineer Molecular Nonequilibrium Systems

Molecular nonequilibrium systems hold great promises for the nanotechnology of the future. Yet, their development is slowed by the absence of an informative representation. Indeed, while potential energy surfaces comprise in principle all the information, they hide the dynamic interplay of multiple reaction pathways underlying nonequilibrium systems, i.e., the degree of kinetic asymmetry. To offer an insightful visual representation of kinetic asymmetry, we extended an approach pertaining to catalytic networks, the energy span model, by focusing on system dynamics - rather than thermodynamics. Our approach encompasses both chemically and photochemically driven systems, ranging from unimolecular motors to simple self-assembly schemes. The obtained diagrams give immediate access to information needed to guide experiments, such as states' population, rate of machine operation, maximum work output, and effects of design changes. The proposed kinetic barrier diagrams offer a unifying graphical tool for disparate nonequilibrium phenomena.

Concepts Relevant for the Kinetic Analysis of Reversible Reaction Systems

The net rate of a reversible chemical reaction is the difference between unidirectional rates of traversal along forward and reverse reaction paths. In a multistep reaction sequence, the forward and reverse trajectories, in general, are not the microscopic reverse of one another; rather, each unidirectional route is comprised of distinct rate-controlling steps, intermediates, and transition states. Consequently, traditional descriptors of rate (e.g., reaction orders) do not reflect intrinsic kinetic information but instead conflate unidirectional contributions determined by (i) the microscopic occurrence of forward/reverse reactions (i.e., unidirectional kinetics) and (ii) the reversibility of reaction (i.e., nonequilibrium thermodynamics). This review aims to provide a comprehensive resource of analytical and conceptual tools which deconvolute the contributions of reaction kinetics and thermodynamics to disambiguate unidirectional reaction trajectories and precisely identify rate- and reversibility-controlling molecular species and steps in reversible reaction systems. The extrication of mechanistic and kinetic information from bidirectional reactions is accomplished through equation-based formalisms (e.g., De Donder relations) grounded in principles of thermodynamics and interpreted in the context of theories of chemical kinetics developed in the past 25 years. The aggregate of mathematical formalisms detailed herein is general to thermochemical and electrochemical reactions and encapsulates a diverse body of scientific literature encompassing chemical physics, thermodynamics, chemical kinetics, catalysis, and kinetic modeling.

CO2 Methanation over Nickel Catalysts: Support Effects Investigated through Specific Activity and Operando IR Spectroscopy Measurements

Renewed interest in CO2 methanation is due to its role within the framework of the Power-to-Methane processes. While the use of nickel-based catalysts for CO2 methanation is well stablished, the support is being subjected to thorough research due to its complex effects. The objective of this work was the study of the influence of the support with a series of catalysts supported on alumina, ceria, ceria–zirconia, and titania. Catalysts’ performance has been kinetically and spectroscopically evaluated over a wide range of temperatures (150–500 °C). The main results have shown remarkable differences among the catalysts as concerns Ni dispersion, metallic precursor reducibility, basic properties, and catalytic activity. Operando infrared spectroscopy measurements have evidenced the presence of almost the same type of adsorbed species during the course of the reaction, but with different relative intensities. The results indicate that using as support of Ni a reducible metal oxide that is capable of developing the basicity associated with medium-strength basic sites and a suitable balance between metallic sites and centers linked to the support leads to high CO2 methanation activity. In addition, the results obtained by operando FTIR spectroscopy suggest that CO2 methanation follows the formate pathway over the catalysts under consideration.

Singlet oxygen production by photosystem II is caused by misses of the oxygen evolving complex

Singlet oxygen (¹ O₂ ) is a harmful species that functions also as a signaling molecule. In chloroplasts, ¹ O₂ is produced via charge recombination reactions in photosystem II, but which recombination pathway(s) produce triplet Chl and ¹ O₂ remains open. Furthermore, the role of ¹ O₂ in photoinhibition is not clear. We compared temperature dependences of ¹ O₂ production, photoinhibition, and recombination pathways. ¹ O₂ production by pumpkin thylakoids increased from -2 to +35°C, ruling out recombination of the primary charge pair as a main contributor. S₂ Q_A ^- or S₂ Q_B ^- recombination pathways, in turn, had too steep temperature dependences. Instead, the temperature dependence of ¹ O₂ production matched that of misses (failures of the oxygen (O₂ ) evolving complex to advance an S-state). Photoinhibition in vitro and in vivo (also in Synechocystis), and in the presence or absence of O₂ , had the same temperature dependence, but ultraviolet (UV)-radiation-caused photoinhibition showed a weaker temperature response. We suggest that the miss-associated recombination of P₆₈₀ ⁺ Q_A ^- is the main producer of ¹ O₂ . Our results indicate three parallel photoinhibition mechanisms. The manganese mechanism dominates in UV radiation but also functions in white light. Mechanisms that depend on light absorption by Chls, having ¹ O₂ or long-lived P₆₈₀ ⁺ as damaging agents, dominate in red light.

Effect of single and multilayered Ti3C2TX MXene as a catalyst and adsorbent on enhanced sonodegradation of diclofenac and verapamil

Single and multilayered Ti₃C₂T_X MXene (referred to as SLM and MLM in this study, respectively) was applied as catalysts in the ultrasonic (US) process to treat selected pharmaceutical compounds including diclofenac and verapamil (VRP). Due to solid surface, elemental composition, and functional groups of Ti₃C₂T_X MXene, the free OH• production was increased by 48.8% for the US treatment with SLM and 59.8% for the US treatment with MLM compared with the US-only treatment. Additionally, adsorption affected the performance during the US treatment in the presence of the catalyst. Thus, the US treatment in the presence of Ti₃C₂T_X MXene had an enhanced performance not only because of increased oxidation but also because of adsorption, particularly between positively charged VRP and negatively charged Ti₃C₂T_X MXene. Moreover, although the degradation of the performance was higher for SLM (85.1%) than for MLM (81.8%), by improving the dispersion and reducing the size via sonication, the US treatment in the presence of MLM showed the highest synergy effect. In other words, the US treatment in the presence of MLM showed higher performance than the simple sum of oxidation and adsorption. These findings confirm that the US treatment in the presence of MLM may be a promising technology to treat various pharmaceuticals as a more degradable, strongly reusable, and less toxic process.

Decoding reactive structures in dilute alloy catalysts

Rational catalyst design is crucial toward achieving more energy-efficient and sustainable catalytic processes. Understanding and modeling catalytic reaction pathways and kinetics require atomic level knowledge of the active sites. These structures often change dynamically during reactions and are difficult to decipher. A prototypical example is the hydrogen-deuterium exchange reaction catalyzed by dilute Pd-in-Au alloy nanoparticles. From a combination of catalytic activity measurements, machine learning-enabled spectroscopic analysis, and first-principles based kinetic modeling, we demonstrate that the active species are surface Pd ensembles containing only a few (from 1 to 3) Pd atoms. These species simultaneously explain the observed X-ray spectra and equate the experimental and theoretical values of the apparent activation energy. Remarkably, we find that the catalytic activity can be tuned on demand by controlling the size of the Pd ensembles through catalyst pretreatment. Our data-driven multimodal approach enables decoding of reactive structures in complex and dynamic alloy catalysts.

Rational catalyst design is crucial toward achieving more energy-efficient and sustainable catalytic processes. Here the authors report a data-driven approach for understanding catalytic reactions mechanisms in dilute bimetallic catalysts by combining X-ray absorption spectroscopy with activity studies and kinetic modeling.

Visible-Light-Driven Site-selective Alkylation of Benzo Core of Coumarins

An unprecedented, straightforward photochemical platform for efficient site-selective C-H alkylation of C7 position of benzocore via the cross coupling between coumarins and NHPI ester, employing Ru(II) as photocatalyst in visible...

Dynamic Microkinetic Modeling for Heterogeneously Catalyzed Hydrogenation Reactions: a Coverage-Oriented View

In most studies, the microkinetics for multistep reactions are numerically solved due to their complexity; the obtained numerical results are only valid under given reaction conditions at a static point. In this work, the microkinetics of heterogeneously catalyzed hydrogenation reactions are analytically solved as a function of three coupled physical parameters, which are energy, reaction rate, and coverage. The results correlate the surface reactions and the gaseous-phased reactant/product by energy and thus provide a dynamic view over the whole reaction process rather than at a static point. The analytical expressions are given for a simple hydrogenation reaction and three more complicated hypothetical hydrogenation reactions with side products, side reaction paths, or even multiple active sites. Compared with the numerical solution, the analytical solution is valid under all reaction conditions in practice and can provide more guidance to optimize the overall outcome or catalyst development.

Microkinetic Modeling: A Tool for Rational Catalyst Design

The design of heterogeneous catalysts relies on understanding the fundamental surface kinetics that controls catalyst performance, and microkinetic modeling is a tool that can help the researcher in streamlining the process of catalyst design. Microkinetic modeling is used to identify critical reaction intermediates and rate-determining elementary reactions, thereby providing vital information for designing an improved catalyst. In this review, we summarize general procedures for developing microkinetic models using reaction kinetics parameters obtained from experimental data, theoretical correlations, and quantum chemical calculations. We examine the methods required to ensure the thermodynamic consistency of the microkinetic model. We describe procedures required for parameter adjustments to account for the heterogeneity of the catalyst and the inherent errors in parameter estimation. We discuss the analysis of microkinetic models to determine the rate-determining reactions using the degree of rate control and reversibility of each elementary reaction. We introduce incorporation of Brønsted-Evans-Polanyi relations and scaling relations in microkinetic models and the effects of these relations on catalytic performance and formation of volcano curves are discussed. We review the analysis of reaction schemes in terms of the maximum rate of elementary reactions, and we outline a procedure to identify kinetically significant transition states and adsorbed intermediates. We explore the application of generalized rate expressions for the prediction of optimal binding energies of important surface intermediates and to estimate the extent of potential rate improvement. We also explore the application of microkinetic modeling in homogeneous catalysis, electro-catalysis, and transient reaction kinetics. We conclude by highlighting the challenges and opportunities in the application of microkinetic modeling for catalyst design.

Top-Down Syntheses of Nickel-Based Structured Catalysts for Hydrogen Production from Ammonia

We report the fabrication and catalytic performance evaluation of highly active and stable nickel (Ni)-based structured catalysts for ammonia dehydrogenation with nearly complete conversion using nonprecious metal catalysts. Low-temperature chemical alloying (LTCA) followed by selective aluminum (Al) dealloying was utilized to synthesize foam-type structured catalysts ready for implementation in commercial-scale catalytic reactors. The crystalline phases of Ni-Al alloy (NiAl₃, Ni₂Al₃, or both) in the near-surface layer were controlled by tuning the alloying time. The best-performing catalyst was obtained from a Ni foam substrate with a NiAl₃/Ni₂Al₃ overlayer synthesized by LTCA at 400 °C for 20 h. The developed Ni catalyst exhibited an activity enhancement of 10-fold over the nontreated Ni foam and showed outstanding activities of 15 800 mol_H2mol_Ni^-1h^-1 (TOF: 4.39 s^-1) and 19 978 mol_H2mol_Ni^-1h^-1 (TOF: 5.55 s^-1) at 550 and 600 °C, respectively. This performance is unprecedented compared with previously reported Ni-based ammonia cracking catalysts with higher-end performance (TOFs of 0.08-1.45 s^-1 at 550 °C). Moreover, this catalyst showed excellent stability for 100 h at 600 °C while discharging an extremely low NH₃ concentration of 1034 ppm. The NH₃ concentration in the exhaust gas was further reduced to 690 and 271 ppm at 700 and 800 °C, respectively, while no deactivation was observed at these elevated temperatures. Through material characterizations, we clarified that controlling the degree of Al alloying in the outermost layer of Ni is a crucial factor in determining the activity and stability because residual Al possibly modifies the electronic structure of Ni for enhanced activity as well as transforming to acidic alumina for increased intrinsic activity and stability.

Rotaxane-Branched Dendrimers with Enhanced Photosensitization

During the past few decades, fabrication of functional rotaxane-branched dendrimers has become one of the most attractive yet challenging topics within supramolecular chemistry and materials science. Herein, we present the successful fabrication of a family of new rotaxane-branched dendrimers containing up to 21 platinum atoms and 42 photosensitizer moieties through an efficient and controllable divergent approach. Notably, the photosensitization efficiencies of these rotaxane-branched dendrimers gradually increased with the increase of dendrimer generation. For example, third-generation rotaxane-branched dendrimer PG3 revealed 13.3-fold higher ¹O₂ generation efficiency than its corresponding monomer AN. The enhanced ¹O₂ generation efficiency was attributed to the enhancement of intersystem crossing (ISC) through the simple and efficient incorporation of multiple heavy atoms and photosensitizer moieties on the axles and wheels of the rotaxane units, respectively, which has been validated by UV-visible and fluorescence techniques, time-dependent density functional theory calculations, photolysis model reactions, and apparent activation energy calculations. Therefore, we develop a new promising platform of rotaxane-branched dendrimers for the preparation of effective photosensitizers.

Requiem for the Rate-Determining Step in Complex Heterogeneous Catalytic Reactions?

The concept of the rate determining step, i.e., the step having the strongest influence on the reaction rate or even being the only one present in the rate equation, is often used in heterogeneous catalytic reactions. The utilization of this concept mainly stems from a need to reduce complexity in deriving explicit rate equations or searching for a better catalyst based on the theoretical insight. When the aim is to derive a rate equation with eventual kinetic modelling for single-route mechanisms with linear sequences, the analytical rate expressions can be obtained based on the theory of complex reactions. For such mechanisms, a single rate limiting step might not be present at all and the common practice of introducing such steps is due mainly to the convenience of using simpler expressions. For mechanisms with a combination of linear and nonlinear steps or those just comprising non-linear steps, the reaction rates are influenced by several steps depending on reaction conditions, thus a reduction in complexity to a single rate limiting step can lead to misinterpretations. More widespread utilization of a microkinetic approach when the reaction rate constants can be computed with reasonable accuracy based on the theoretical insight, and availability of software for kinetic modelling, when a system of differential equations for reactants and products will be solved together with differential equations for catalytic species and the algebraic conservation equation for the latter, will eventually make the concept of the rate limiting step obsolete.

Reactivity triggered by an organic microcrystal interface: a case study involving an environmentally benign, aromatic boric acid reaction

At a self-assembled {002} crystal-solution interface, inactive 9-anthracene boric acid was transformed into a highly active state, for catalyst-free aromatic substitution and oxidation.

Influence of Structure Sensitivity on Apparent Activation Energy of Parallel Heterogeneous Catalytic Reactions

Abstract

Analysis of apparent activation energy is presented for different heterogeneous catalytic reactions with parallel reaction routes. In the case of kinetic coupling between catalytic cycles the activation energy in a particular route depends not only on the activation energies of the elementary steps comprising this route, but also on the frequency of the steps in a parallel route. Expressions were derived for coupling between routes through irreversible adsorption of the substrate, quasi-equilibrated binding as well as different substrate adsorption modes. Theoretical analysis of the apparent activation energy was extended for the reaction network with two routes possessing mechanistically different rate determining steps (i.e. monomolecular vs bimolecular). For structure sensitive reactions an expression for the apparent activation energy for parallel reactions was developed for cases with a continuous distribution of active centers and a cubo-octahedral representation of the metal clusters. A comparison between the theoretical analysis and experimental data on transformations of furfural to furfuryl alcohol and furan on ruthenium clusters shows applicability of the developed theoretical framework.

Graphic Abstract