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Razdan NK, Lin TC, Bhan A. Concepts Relevant for the Kinetic Analysis of Reversible Reaction Systems. Chem Rev 2023; 123:2950-3006. [PMID: 36802557 DOI: 10.1021/acs.chemrev.2c00510] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/23/2023]
Abstract
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.
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Affiliation(s)
- Neil K Razdan
- Department of Chemical Engineering and Materials Science, University of Minnesota─Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States
| | - Ting C Lin
- Department of Chemical Engineering and Materials Science, University of Minnesota─Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States
| | - Aditya Bhan
- Department of Chemical Engineering and Materials Science, University of Minnesota─Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States
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2
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Chen Z, Liu Z, Xu X. Accurate descriptions of molecule-surface interactions in electrocatalytic CO 2 reduction on the copper surfaces. Nat Commun 2023; 14:936. [PMID: 36807556 PMCID: PMC9941474 DOI: 10.1038/s41467-023-36695-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2022] [Accepted: 02/14/2023] [Indexed: 02/22/2023] Open
Abstract
Copper-based catalysts play a pivotal role in many industrial processes and hold a great promise for electrocatalytic CO2 reduction reaction into valuable chemicals and fuels. Towards the rational design of catalysts, the growing demand on theoretical study is seriously at odds with the low accuracy of the most widely used functionals of generalized gradient approximation. Here, we present results using a hybrid scheme that combines the doubly hybrid XYG3 functional and the periodic generalized gradient approximation, whose accuracy is validated against an experimental set on copper surfaces. A near chemical accuracy is established for this set, which, in turn, leads to a substantial improvement for the calculated equilibrium and onset potentials as against the experimental values for CO2 reduction to CO on Cu(111) and Cu(100) electrodes. We anticipate that the easy use of the hybrid scheme will boost the predictive power for accurate descriptions of molecule-surface interactions in heterogeneous catalysis.
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Affiliation(s)
- Zheng Chen
- grid.8547.e0000 0001 0125 2443Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, 200433 Shanghai, People’s Republic of China
| | - Zhangyun Liu
- grid.8547.e0000 0001 0125 2443Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, 200433 Shanghai, People’s Republic of China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, 200433, Shanghai, People's Republic of China. .,Hefei National Laboratory, 230088, Hefei, P. R. China.
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3
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Paredes-Salazar EA, Calderón-Cárdenas A, Varela H. Sensitivity Analysis in the Microkinetic Description of Electrocatalytic Reactions. J Phys Chem A 2022; 126:2746-2749. [PMID: 35452581 DOI: 10.1021/acs.jpca.2c00624] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A methodology to determine how the variation in a kinetic parameter affects the global kinetic response of an electrochemical reaction is proposed. The so-called sensitivity analysis is applied to quantify the contribution of single reaction steps of an electrocatalytic system under an oscillatory regime using microkinetic analysis.
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Affiliation(s)
- Enrique A Paredes-Salazar
- . São Carlos Institute of Chemistry, University of São Paulo, P.O. Box 780, São Carlos, São Paulo CEP 13560-970, Brazil
| | - Alfredo Calderón-Cárdenas
- . São Carlos Institute of Chemistry, University of São Paulo, P.O. Box 780, São Carlos, São Paulo CEP 13560-970, Brazil.,GIFBA, Universidad de Nariño, San Juan de Pasto 520002, Nariño, Colombia
| | - Hamilton Varela
- . São Carlos Institute of Chemistry, University of São Paulo, P.O. Box 780, São Carlos, São Paulo CEP 13560-970, Brazil.,. Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Str., Dresden 38 01187, Germany
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4
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Yang Y, Achar SK, Kitchin JR. Evaluation of the Degree of Rate Control via Automatic Differentiation. AIChE J 2022. [DOI: 10.1002/aic.17653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Yilin Yang
- Chemical Engineering Carnegie Mellon University Pittsburgh Pennsylvania USA
| | - Siddarth K. Achar
- Chemical Engineering Carnegie Mellon University Pittsburgh Pennsylvania USA
| | - John R. Kitchin
- Chemical Engineering Carnegie Mellon University Pittsburgh Pennsylvania USA
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5
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Calderón-Cárdenas A, Paredes-Salazar EA, Varela H. Micro-kinetic Description of Electrocatalytic Reactions: The Role of Self-organized Phenomena. NEW J CHEM 2022. [DOI: 10.1039/d2nj00758d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this perspective we proposed a workflow for the construction of micro-kinetic models that consists of at least four stages, starting with information gathering that allows proposing possible reaction mechanisms....
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7
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Campbell CT, Mao Z. Analysis and prediction of reaction kinetics using the degree of rate control. J Catal 2021. [DOI: 10.1016/j.jcat.2021.10.002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
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8
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Razdan N, Bhan A. Catalytic site ensembles: A context to reexamine the Langmuir-Hinshelwood kinetic description. J Catal 2021. [DOI: 10.1016/j.jcat.2021.09.016] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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10
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Schwartz TJ, Bond JQ. Leveraging De Donder relations for a thermodynamically rigorous analysis of reaction kinetics in liquid media. J Catal 2021. [DOI: 10.1016/j.jcat.2021.09.026] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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11
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Liu R. Dynamic Microkinetic Modeling for Heterogeneously Catalyzed Hydrogenation Reactions: a Coverage-Oriented View. ACS OMEGA 2021; 6:29432-29448. [PMID: 34778616 PMCID: PMC8581974 DOI: 10.1021/acsomega.1c03292] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/23/2021] [Accepted: 10/12/2021] [Indexed: 06/13/2023]
Abstract
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.
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12
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Chen Z, Liu Z, Xu X. Coverage-Dependent Microkinetics in Heterogeneous Catalysis Powered by the Maximum Rate Analysis. ACS Catal 2021. [DOI: 10.1021/acscatal.1c01997] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Zheng Chen
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
| | - Zhangyun Liu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
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Legnani L, Darù A, Jones AX, Blackmond DG. Mechanistic Insight into the Origin of Stereoselectivity in the Ribose-Mediated Strecker Synthesis of Alanine. J Am Chem Soc 2021; 143:7852-7858. [PMID: 33979125 DOI: 10.1021/jacs.1c03552] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Enantioenriched amino acids are produced in a hydrolytic kinetic resolution of racemic aminonitriles mediated by chiral pentose sugars. Experimental kinetic and spectroscopic results combined with DFT computational studies and microkinetic modeling help to identify the nature of the intermediate species and provide insight into the stereoselectivity of their hydrolysis in the prebiotically relevant ribose-alanine system. These studies support a synergistic role for sugars and amino acids in the emergence of homochirality in biological molecules.
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Affiliation(s)
- Luca Legnani
- Department of Chemistry, Scripps Research, La Jolla, California 92037, United States
| | - Andrea Darù
- Department of Chemistry, Scripps Research, La Jolla, California 92037, United States
| | - Alexander X Jones
- Department of Chemistry, Scripps Research, La Jolla, California 92037, United States
| | - Donna G Blackmond
- Department of Chemistry, Scripps Research, La Jolla, California 92037, United States
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14
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Lund CRF, Tatarchuk B, Cardona-Martínez N, Hill JM, Sanchez-Castillo MA, Huber GW, Román-Leshkov Y, Simonetti D, Pagan-Torres Y, Schwartz TJ, Motagamwala AH. A Career in Catalysis: James A. Dumesic. ACS Catal 2021. [DOI: 10.1021/acscatal.0c05325] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Carl R. F. Lund
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States
| | - Bruce Tatarchuk
- Center for Microfibrous Materials, Department of Chemical Engineering, Auburn University, Auburn, Alabama 36849 United States
| | - Nelson Cardona-Martínez
- Department of Chemical Engineering, University of Puerto Rico - Mayagüez, Mayagüez 00681-9000, Puerto Rico
| | - Josephine M. Hill
- Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta T2N 1N4, Canada
| | - Marco A. Sanchez-Castillo
- Facultad de Ciencias Químicas, Universidad Autónoma de San Luis Potosí, Manuel Nava 6, 78210 San Luis Potosí, Mexico
| | - George W. Huber
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States
| | - Yuriy Román-Leshkov
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 United States
| | - Dante Simonetti
- Department of Chemical and Biomolecular Engineering, University of California-Los Angeles, Los Angeles, California 90095 United States
| | - Yomaira Pagan-Torres
- Department of Chemical Engineering, University of Puerto Rico - Mayagüez, Mayagüez 00681-9000, Puerto Rico
| | - Thomas J. Schwartz
- Department of Chemical and Biomedical Engineering, University of Maine, Orono, Maine 04469, United States
| | - Ali Hussain Motagamwala
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States
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Abstract
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.
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Affiliation(s)
- Ali Hussain Motagamwala
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, Wisconsin 53706, United States
| | - James A Dumesic
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, Wisconsin 53706, United States
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16
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Affiliation(s)
- Huijie Tian
- Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States
| | - Srinivas Rangarajan
- Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States
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Abstract
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.
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18
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Degree of rate control and De Donder relations – An interpretation based on transition state theory. J Catal 2020. [DOI: 10.1016/j.jcat.2020.02.008] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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19
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The degree of rate control of catalyst-bound intermediates in catalytic reaction mechanisms: Relationship to site coverage. J Catal 2020. [DOI: 10.1016/j.jcat.2019.09.044] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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20
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Mao Z, Campbell CT. Apparent Activation Energies in Complex Reaction Mechanisms: A Simple Relationship via Degrees of Rate Control. ACS Catal 2019. [DOI: 10.1021/acscatal.9b02761] [Citation(s) in RCA: 43] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Zhongtian Mao
- Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, United States
| | - Charles T. Campbell
- Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, United States
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21
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Cervantes C, Mora JR, Rincón L, Rodríguez V. Theoretical study of the mechanism of 2,5-diketopiperazine formation during pyrolysis of proline. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1594422] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Cristian Cervantes
- Instituto de Simulación Computacional (ISM), Universidad San Francisco de Quito (USFQ), Quito, Ecuador
- Departamento de Ingeniería Química – Grupo de Química Computacional y Teórica (QCT), Universidad San Francisco de Quito (USFQ), Quito, Ecuador
| | - José R. Mora
- Instituto de Simulación Computacional (ISM), Universidad San Francisco de Quito (USFQ), Quito, Ecuador
- Departamento de Ingeniería Química – Grupo de Química Computacional y Teórica (QCT), Universidad San Francisco de Quito (USFQ), Quito, Ecuador
| | - Luis Rincón
- Instituto de Simulación Computacional (ISM), Universidad San Francisco de Quito (USFQ), Quito, Ecuador
- Departamento de Ingeniería Química – Grupo de Química Computacional y Teórica (QCT), Universidad San Francisco de Quito (USFQ), Quito, Ecuador
| | - Vladimir Rodríguez
- Departamento de Matemáticas, Universidad San Francisco de Quito (USFQ), Quito, Ecuador
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Motagamwala AH, Ball MR, Dumesic JA. Microkinetic Analysis and Scaling Relations for Catalyst Design. Annu Rev Chem Biomol Eng 2018; 9:413-450. [DOI: 10.1146/annurev-chembioeng-060817-084103] [Citation(s) in RCA: 56] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Microkinetic analysis plays an important role in catalyst design because it provides insight into the fundamental surface chemistry that controls catalyst performance. In this review, we summarize the development of microkinetic models and the inclusion of scaling relationships in these models. We discuss the importance of achieving stoichiometric and thermodynamic consistency in developing microkinetic models. We also outline how analysis of the maximum rates of elementary steps can be used to determine which transition states and adsorbed intermediates are kinetically significant, allowing the derivation of general reaction kinetics rate expressions in terms of changes in binding energies of the relevant transition states and intermediates. Through these analyses, we present how to predict optimal surface coverages and binding energies of adsorbed species, as well as the extent of potential rate improvement for a catalytic system. For systems in which the extent of potential rate improvement is small because of limitations imposed by scaling relations, different approaches, including the addition of promoters and formation of catalysts containing multiple functionalities, can be used to break the scaling relations and obtain further rate enhancement.
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Affiliation(s)
- Ali Hussain Motagamwala
- Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706, USA;, ,
| | - Madelyn R. Ball
- Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706, USA;, ,
| | - James A. Dumesic
- Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706, USA;, ,
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23
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Vandichel M, Moscu A, Grönbeck H. Catalysis at the Rim: A Mechanism for Low Temperature CO Oxidation over Pt3Sn. ACS Catal 2017. [DOI: 10.1021/acscatal.7b02094] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Matthias Vandichel
- Department of Physics and Competence
Centre for Catalysis, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - Alina Moscu
- Department of Physics and Competence
Centre for Catalysis, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - Henrik Grönbeck
- Department of Physics and Competence
Centre for Catalysis, Chalmers University of Technology, 412 96 Göteborg, Sweden
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Praserthdam S, Balbuena PB. Performance evaluation of catalysts in the dry reforming reaction of methane via the ratings concept. REACTION KINETICS MECHANISMS AND CATALYSIS 2017. [DOI: 10.1007/s11144-017-1241-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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25
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Murzin DY. Interpretation of rate optima vs reaction parameters in steady state catalytic kinetics: Molecular aspects beyond concentration dependences. MOLECULAR CATALYSIS 2017. [DOI: 10.1016/j.mcat.2016.12.008] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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26
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Affiliation(s)
- Charles T. Campbell
- Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, United States
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27
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Bond JQ, Jungong CS, Chatzidimitriou A. Microkinetic analysis of ring opening and decarboxylation of γ-valerolactone over silica alumina. J Catal 2016. [DOI: 10.1016/j.jcat.2016.10.021] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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