1
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Engsvang M, Wu H, Elm J. Iodine Clusters in the Atmosphere I: Computational Benchmark and Dimer Formation of Oxyacids and Oxides. ACS OMEGA 2024; 9:31521-31532. [PMID: 39072118 PMCID: PMC11270685 DOI: 10.1021/acsomega.4c01235] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/07/2024] [Revised: 06/19/2024] [Accepted: 06/21/2024] [Indexed: 07/30/2024]
Abstract
The contribution of iodine-containing compounds to atmospheric new particle formation is still not fully understood, but iodic acid and iodous acid are thought to be significant contributors. While several quantum chemical studies have been carried out on clusters containing iodine, there is no comprehensive benchmark study quantifying the accuracy of the applied methods. Here, we present the first study in a series that investigate the role of iodine species in atmospheric cluster formation. In this work, we have studied the iodic acid, iodous acid, iodine tetroxide, and iodine pentoxide monomers and their dimers formed with common atmospheric precursors. We have tested the accuracy of commonly applied methods for calculating the geometry of the monomers, thermal corrections of monomers and dimers, the contribution of spin-orbit coupling to monomers and dimers, and finally, the accuracy of the electronic energy correction calculated at different levels of theory. We find that optimizing the structures either at the ωB97X-D3BJ/aug-cc-pVTZ-PP or the M06-2X/aug-cc-pVTZ-PP level achieves the best thermal contribution to the binding free energy. The electronic energy correction can then be calculated at the ZORA-DLPNO-CCSD(T0) level with the SARC-ZORA-TZVPP basis for iodine and ma-ZORA-def2-TZVPP for non-iodine atoms. We applied this methodology to calculate the binding free energies of iodine-containing dimer clusters, where we confirm the qualitative trends observed in previous studies. However, we identify that previous studies overestimate the stability of the clusters by several kcal/mol due to the neglect of relativistic effects. This means that their contributions to the currently studied nucleation pathways of new particle formation are likely overestimated.
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Affiliation(s)
- Morten Engsvang
- Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
| | - Haide Wu
- Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
| | - Jonas Elm
- Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
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2
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Watanabe S, Wada Y, Kawano M, Higashibayashi S, Sugai T, Hanaya K. Selective modification of tryptophan in polypeptides via C-N coupling with azoles using in situ-generated iodine-based oxidants in aqueous media. Chem Commun (Camb) 2023; 59:13026-13029. [PMID: 37842839 DOI: 10.1039/d3cc03731b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2023]
Abstract
This study demonstrates the C-N coupling of tryptophan with azoles, promoted by an in situ-generated iodine-based oxidant. The protocol was successfully applied to the selective modification of tryptophan in nonprotected polypeptide bearing oxidatively sensitive residues in acidic aqueous media. The present method allows the attachment of reactive handles to polypeptides and the peptide stapling.
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Affiliation(s)
- Shunsuke Watanabe
- Faculty of Pharmacy, Keio University, 1-5-30 Shibakoen, Minato-ku, Tokyo 105-8512, Japan.
| | - Yuki Wada
- Department of Chemistry, School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
| | - Masaki Kawano
- Department of Chemistry, School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
| | - Shuhei Higashibayashi
- Faculty of Pharmacy, Keio University, 1-5-30 Shibakoen, Minato-ku, Tokyo 105-8512, Japan.
| | - Takeshi Sugai
- Faculty of Pharmacy, Keio University, 1-5-30 Shibakoen, Minato-ku, Tokyo 105-8512, Japan.
| | - Kengo Hanaya
- Faculty of Pharmacy, Keio University, 1-5-30 Shibakoen, Minato-ku, Tokyo 105-8512, Japan.
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3
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Liu L, Li S, Zu H, Zhang X. Unexpectedly significant stabilizing mechanism of iodous acid on iodic acid nucleation under different atmospheric conditions. THE SCIENCE OF THE TOTAL ENVIRONMENT 2023; 859:159832. [PMID: 36404466 DOI: 10.1016/j.scitotenv.2022.159832] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2022] [Revised: 10/15/2022] [Accepted: 10/26/2022] [Indexed: 06/16/2023]
Abstract
Iodous acid (HIO2) has been shown to play a stabilizing role in the nucleation of iodic acid (HIO3) (He et al., 2021). However, the stabilization effect and specific stabilizing mechanism of HIO2 on HIO3 nucleation under different atmospheric conditions remain unclear. Therefore, we studied these two issues under different temperatures and nucleation precursor concentrations using density functional theory combined with the Atmospheric Cluster Dynamics Code. We found that HIO2 can form clusters with HIO3 via strong hydrogen bonds, halogen bonds, and proton-transfer, substantially enhancing the stability of HIO3 clusters and decreasing the energy barrier of HIO3-based cluster formation at different temperatures and nucleation precursor concentrations. The particle formation rate and cluster concentrations of HIO3-HIO2 nucleation were negatively correlated with temperature and positively correlated with HIO2 concentration. The enhancements by HIO2 on the particle formation rate and cluster concentration of HIO3 nucleation were positively correlated with temperature and HIO2 concentration. Interestingly, even at a low HIO2 concentration (1.0 × 105 molecules cm-3), the enhancement on the particle formation rate and cluster concentration of HIO3 nucleation by HIO2 were both unexpectedly up to 4.1 × 104-fold at 283 K. Therefore, HIO3-HIO2 nucleation can be extremely rapid in cold regions, and the enhancement by HIO2 can be significant, especially in warm regions even at relatively high HIO2 concentrations.
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Affiliation(s)
- Ling Liu
- Key Laboratory of Cluster Science, Ministry of Education of China, School of Chemistry and Chemical Engineering, Beijing Institute of Technology, Beijing 100081, China
| | - Shuning Li
- Key Laboratory of Cluster Science, Ministry of Education of China, School of Chemistry and Chemical Engineering, Beijing Institute of Technology, Beijing 100081, China; National Supercomputer Center in Tianjin, Tianjin 300451, China
| | - Haotian Zu
- Key Laboratory of Cluster Science, Ministry of Education of China, School of Chemistry and Chemical Engineering, Beijing Institute of Technology, Beijing 100081, China
| | - Xiuhui Zhang
- Key Laboratory of Cluster Science, Ministry of Education of China, School of Chemistry and Chemical Engineering, Beijing Institute of Technology, Beijing 100081, China.
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4
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Zhang R, Xie HB, Ma F, Chen J, Iyer S, Simon M, Heinritzi M, Shen J, Tham YJ, Kurtén T, Worsnop DR, Kirkby J, Curtius J, Sipilä M, Kulmala M, He XC. Critical Role of Iodous Acid in Neutral Iodine Oxoacid Nucleation. ENVIRONMENTAL SCIENCE & TECHNOLOGY 2022; 56:14166-14177. [PMID: 36126141 PMCID: PMC9536010 DOI: 10.1021/acs.est.2c04328] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Nucleation of neutral iodine particles has recently been found to involve both iodic acid (HIO3) and iodous acid (HIO2). However, the precise role of HIO2 in iodine oxoacid nucleation remains unclear. Herein, we probe such a role by investigating the cluster formation mechanisms and kinetics of (HIO3)m(HIO2)n (m = 0-4, n = 0-4) clusters with quantum chemical calculations and atmospheric cluster dynamics modeling. When compared with HIO3, we find that HIO2 binds more strongly with HIO3 and also more strongly with HIO2. After accounting for ambient vapor concentrations, the fastest nucleation rate is predicted for mixed HIO3-HIO2 clusters rather than for pure HIO3 or HIO2 ones. Our calculations reveal that the strong binding results from HIO2 exhibiting a base behavior (accepting a proton from HIO3) and forming stronger halogen bonds. Moreover, the binding energies of (HIO3)m(HIO2)n clusters show a far more tolerant choice of growth paths when compared with the strict stoichiometry required for sulfuric acid-base nucleation. Our predicted cluster formation rates and dimer concentrations are acceptably consistent with those measured by the Cosmic Leaving Outdoor Droplets (CLOUD) experiment. This study suggests that HIO2 could facilitate the nucleation of other acids beyond HIO3 in regions where base vapors such as ammonia or amines are scarce.
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Affiliation(s)
- Rongjie Zhang
- Key
Laboratory of Industrial Ecology and Environmental Engineering (Ministry
of Education), School of Environmental Science and Technology, Dalian University of Technology, Dalian 116024, China
| | - Hong-Bin Xie
- Key
Laboratory of Industrial Ecology and Environmental Engineering (Ministry
of Education), School of Environmental Science and Technology, Dalian University of Technology, Dalian 116024, China
- . Phone: +86-411-84707251
| | - Fangfang Ma
- Key
Laboratory of Industrial Ecology and Environmental Engineering (Ministry
of Education), School of Environmental Science and Technology, Dalian University of Technology, Dalian 116024, China
| | - Jingwen Chen
- Key
Laboratory of Industrial Ecology and Environmental Engineering (Ministry
of Education), School of Environmental Science and Technology, Dalian University of Technology, Dalian 116024, China
| | - Siddharth Iyer
- Aerosol
Physics Laboratory, Faculty of Engineering and Natural Sciences, Tampere University, Tampere 33014, Finland
| | - Mario Simon
- Institute
for Atmospheric and Environmental Sciences, Goethe University Frankfurt, Frankfurt am Main 60438, Germany
| | - Martin Heinritzi
- Institute
for Atmospheric and Environmental Sciences, Goethe University Frankfurt, Frankfurt am Main 60438, Germany
| | - Jiali Shen
- Institute
for Atmospheric and Earth System Research/Physics, Faculty of Science, University of Helsinki, Helsinki 00014, Finland
| | - Yee Jun Tham
- School
of Marine Sciences, Sun Yat-sen University, Zhuhai 519082, China
| | - Theo Kurtén
- Department
of Chemistry, University of Helsinki, Helsinki 00014, Finland
| | - Douglas R. Worsnop
- Institute
for Atmospheric and Earth System Research/Physics, Faculty of Science, University of Helsinki, Helsinki 00014, Finland
- Aerodyne
Research, Inc., Billerica, Massachusetts 01821, United States
| | - Jasper Kirkby
- Institute
for Atmospheric and Environmental Sciences, Goethe University Frankfurt, Frankfurt am Main 60438, Germany
- CERN,
the European Organization for Nuclear Research, CH-1211 Geneva 23, Switzerland
| | - Joachim Curtius
- Institute
for Atmospheric and Environmental Sciences, Goethe University Frankfurt, Frankfurt am Main 60438, Germany
| | - Mikko Sipilä
- Institute
for Atmospheric and Earth System Research/Physics, Faculty of Science, University of Helsinki, Helsinki 00014, Finland
| | - Markku Kulmala
- Institute
for Atmospheric and Earth System Research/Physics, Faculty of Science, University of Helsinki, Helsinki 00014, Finland
- Joint
International Research Laboratory of Atmospheric and Earth System
Sciences, School of Atmospheric Sciences, Nanjing University, Nanjing 210023, China
- Aerosol
and Haze Laboratory, Beijing Advanced Innovation Center for Soft Matter
Science and Engineering, Beijing University
of Chemical Technology, Beijing 100029, China
| | - Xu-Cheng He
- Institute
for Atmospheric and Earth System Research/Physics, Faculty of Science, University of Helsinki, Helsinki 00014, Finland
- Center
for Atmospheric Particle Studies, Carnegie
Mellon University, Pittsburgh, Pennsylvania 15213, United States
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5
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Kinetics and mechanism of I(+ 3) reactions and consequences for other iodine reactions. REACTION KINETICS MECHANISMS AND CATALYSIS 2022. [DOI: 10.1007/s11144-022-02155-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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6
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Manzano Martı́nez AN, Haase AS, Assirelli M, van der Schaaf J. Alternative Kinetic Model of the Iodide–Iodate Reaction for Its Use in Micromixing Investigations. Ind Eng Chem Res 2020. [DOI: 10.1021/acs.iecr.0c04901] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Arturo N. Manzano Martı́nez
- Laboratory of Chemical Reactor Engineering, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - A. Sander Haase
- Nouryon, Zutphenseweg 10, P.O. Box 10, 7400 AA Deventer, The Netherlands
| | - Melissa Assirelli
- Nouryon, Zutphenseweg 10, P.O. Box 10, 7400 AA Deventer, The Netherlands
| | - John van der Schaaf
- Laboratory of Chemical Reactor Engineering, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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7
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Stanbury DM, Hoffman D. Systematic Application of the Principle of Detailed Balancing to Complex Homogeneous Chemical Reaction Mechanisms. J Phys Chem A 2019; 123:5436-5445. [PMID: 31240925 DOI: 10.1021/acs.jpca.9b03771] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
It is not uncommon for proposed complex reaction mechanisms to violate the principle of detailed balancing. Here, we draw attention to three ways in which such violations can occur: reversible reaction loops where the rate constants do not attain closure, illegal loops, and reversible steps having rate equations in the forward and reverse directions that are inconsistent with the equilibrium expressions. We present two simple methods to test whether a proposed mechanism is consistent with the first two aspects of the principle of detailed balancing. Both methods are restricted to closed homogeneous isothermal reactions having mechanisms that consist of stoichiometrically balanced reaction steps. The first method is restricted to mechanisms in which all reaction steps are reversible; values of Δf G° are assigned to all reaction species, equilibrium constants are then computed for all steps, and all rate constants for elementary steps are constrained by the relationship Keq = kf/ kr. The second method is applicable to mechanisms that can consist of a series of reversible and/or irreversible reaction steps. One first examines the subset of reversible steps to determine whether any of these steps are stoichiometrically equivalent to a combination of any of the other steps. If so, the forward and reverse rate expressions must yield equilibrium constants that are in agreement with the stoichiometric relationships. Next, the complete set of steps is examined to look for "illegal reaction loops". Both of these procedures are performed by constructing matrices that represent the stoichiometries of the various reaction steps and then performing row reductions to identify basis sets of loops. A method based on linear programming is described that determines whether a mechanism contains any illegal loops. These methods are applied in the analysis of several published reaction mechanisms.
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8
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Dutt AK. Chloride Ion Inhibition, Stirring, and Temperature Effects in an Ethylacetoacetate Briggs-Rauscher Oscillator in Phosphoric and Hydrochloric Acids in a Batch Reactor. J Phys Chem B 2019; 123:3525-3534. [PMID: 30894000 DOI: 10.1021/acs.jpcb.9b01590] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Briggs-Rauscher oscillating reaction has been investigated in hydrochloric acid media and in the presence of added chloride ions in phosphoric acid media in a batch reactor using ethylacetoacetate as the organic substrate. The changes in key oscillation parameters, namely, induction period, oscillation period, amplitude, and so forth, have been explained in terms of the steps of the skeleton mechanism proposed by Furrow and Noyes and by de Kepper and Epstein. In spite of several shortcomings as outlined in section 2 in the text, the same mechanistic steps are good enough to explain qualitatively most of the changes in oscillation parameters under different stirring rates and temperatures in phosphoric acid and hydrochloric acid media, particularly stirring effects explained well by the theory of imperfect mixing. Potential data indicate that 0.018 M HCl medium has the ability to exhibit near-zero/zero amplitudes before cessation of oscillations. Inhibition reactions from a low Cl- concentration in the 0.018 M HCl media appear to be responsible for this interesting dynamical transformation, as toward the end of oscillations, the difference between [I-] and [I-]crit [see eq J in the text] becomes very small because of depleted component chemicals due to chemical reactions.
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Affiliation(s)
- Arun K Dutt
- Faculty of Applied Science , University of the West of England (Frenchay Campus) , Bristol BS16 1QY , U.K.,Chemical Physics Research Unit , 16 Ghanarajpur Jalapara , Dhaniakhali , Hooghly WB712302 , India
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9
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Bifurcation analysis: a tool for determining model parameters of the considered process. REACTION KINETICS MECHANISMS AND CATALYSIS 2017. [DOI: 10.1007/s11144-017-1324-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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10
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Domination of thermodynamically demanding oxidative processes in reaction of iodine with hydrogen peroxide. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.06.061] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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11
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Tolmachev YV, Piatkivskyi A, Ryzhov VV, Konev DV, Vorotyntsev MA. Energy cycle based on a high specific energy aqueous flow battery and its potential use for fully electric vehicles and for direct solar-to-chemical energy conversion. J Solid State Electrochem 2015. [DOI: 10.1007/s10008-015-2805-z] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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12
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Szabo E, Ševčík P. Reexamination of gas production in the Bray-Liebhafsky reaction: what happened to O2 pulses? J Phys Chem A 2013; 117:10604-14. [PMID: 24087917 DOI: 10.1021/jp407540s] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Results of high-precision measurements of gas production in the BL reaction are presented, and an efficient kinetic model for their analysis is proposed. Based on this model, the data have been examined pulse by pulse, and for the first time, the entire records of gas production could be successfully reduced to series of just a few key parameters. It has been confirmed that the kinetics of O2(g) production is of the first order with respect to its precursor. Overall, only two steps have been found necessary to fit the observed pulses in gas production. The first step produces the precursor of the recorded O2(g), and its rate has two components. One component provides the peaks, and its approximation in the form of Gaussian functions has been found as satisfactory. The other component provides the constant baseline of gas production between the pulses. Finally, the precursor gives rise to O2(g) in the second step, and the simple first-order kinetics suggests that the precursor is otherwise relatively unreactive, making O2(aq) a logical candidate. However, the rate constant of this process showed almost perfect linearity with the actual concentrations of H2O2, and it was affected only little by variations in the rate of stirring. It thus seems possible that this final step in gas production, responsible for the majority of O2 produced in pulses, might not be the interphase transport O2(aq) → O2(g), as expected. Instead, it might be a truly chemical process, giving rise to O2(g) in a reaction of H2O2 with another precursor, which is not involved significantly in any other process, but it is not O2(aq). If this is true, the second-order rate constant of this process in the system with initial composition of 0.360 M KIO3, 0.345 M H2O2, and 0.055 M HClO4 at 60 °C would be 0.25-0.30 M(-1)·s(-1), depending on the rate of stirring.
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Affiliation(s)
- Erik Szabo
- Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University in Bratislava , Mlynská dolina, 842 15 Bratislava, Slovakia
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13
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Affiliation(s)
- Guy Schmitz
- Faculty of Applied Sciences; Université Libre de Bruxelles; CP165/63 1050 Brussels Belgium
| | - Stanley D. Furrow
- Penn State Berks College; Pennsylvania State University; Reading PA 19610
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14
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Stanisavljev DR, Milenković MC, Popović-Bijelić AD, Mojović MD. Radicals in the Bray–Liebhafsky Oscillatory Reaction. J Phys Chem A 2013; 117:3292-5. [DOI: 10.1021/jp402381b] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Dragomir R. Stanisavljev
- Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12-16, P.O.
Box 47, 11158 Belgrade, Serbia
| | - Maja C. Milenković
- Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12-16, P.O.
Box 47, 11158 Belgrade, Serbia
| | - Ana D. Popović-Bijelić
- Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12-16, P.O.
Box 47, 11158 Belgrade, Serbia
| | - Miloš D. Mojović
- Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12-16, P.O.
Box 47, 11158 Belgrade, Serbia
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15
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Schmitz G, Furrow S. Kinetics of the iodate reduction by hydrogen peroxide and relation with the Briggs–Rauscher and Bray–Liebhafsky oscillating reactions. Phys Chem Chem Phys 2012; 14:5711-7. [DOI: 10.1039/c2cp23805e] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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16
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Thermodynamic Redox Calculations for One and Two Electron Transfer Steps: Implications for Halide Oxidation and Halogen Environmental Cycling. ACTA ACUST UNITED AC 2011. [DOI: 10.1021/bk-2011-1071.ch002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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17
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Schmitz G. Iodine oxidation by hydrogen peroxide and Bray–Liebhafsky oscillating reaction: effect of the temperature. Phys Chem Chem Phys 2011; 13:7102-11. [DOI: 10.1039/c1cp00006c] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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18
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Schmitz G. Iodine oxidation by hydrogen peroxide in acidic solutions, Bray-Liebhafsky reaction and other related reactions. Phys Chem Chem Phys 2010; 12:6605-15. [DOI: 10.1039/b927432d] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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19
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Schmitz G, Kolar-Anić LZ, Anić SR, Čupić ŽD. Stoichiometric Network Analysis and Associated Dimensionless Kinetic Equations. Application to a Model of the Bray−Liebhafsky Reaction. J Phys Chem A 2008; 112:13452-7. [DOI: 10.1021/jp8056674] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Guy Schmitz
- Faculté des Sciences Appliquées, Universté Libre de Bruxelles, CP165/63, Av. F. Roosevelt 50, 1050 Bruxelles, Belgium, Faculty of Physical Chemistry, University of Belgrade, P.O.Box 47, 11000 Belgrade, Serbia, and Department of Catalysis and Chemical Engineering, IChTM, University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia
| | - Ljiljana Z. Kolar-Anić
- Faculté des Sciences Appliquées, Universté Libre de Bruxelles, CP165/63, Av. F. Roosevelt 50, 1050 Bruxelles, Belgium, Faculty of Physical Chemistry, University of Belgrade, P.O.Box 47, 11000 Belgrade, Serbia, and Department of Catalysis and Chemical Engineering, IChTM, University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia
| | - Slobodan R. Anić
- Faculté des Sciences Appliquées, Universté Libre de Bruxelles, CP165/63, Av. F. Roosevelt 50, 1050 Bruxelles, Belgium, Faculty of Physical Chemistry, University of Belgrade, P.O.Box 47, 11000 Belgrade, Serbia, and Department of Catalysis and Chemical Engineering, IChTM, University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia
| | - Željko D. Čupić
- Faculté des Sciences Appliquées, Universté Libre de Bruxelles, CP165/63, Av. F. Roosevelt 50, 1050 Bruxelles, Belgium, Faculty of Physical Chemistry, University of Belgrade, P.O.Box 47, 11000 Belgrade, Serbia, and Department of Catalysis and Chemical Engineering, IChTM, University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia
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