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Feng Y, Wang C. Surface Confinement of Finite-Size Water Droplets for SO 3 Hydrolysis Reaction Revealed by Molecular Dynamics Simulations Based on a Machine Learning Force Field. J Am Chem Soc 2023; 145:10631-10640. [PMID: 37130210 DOI: 10.1021/jacs.3c00698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
As an important source for sulfuric acid in the atmosphere, hydrolysis of sulfur trioxide (SO3) takes place with water clusters of sizes from several molecules to several nanometers, resulting in various final products, including neutral (H2SO4)-(H2O) clusters and ionic (HSO4)--(H3O)+ clusters. The diverse products may be due to the ability of proton transfer and the formation of hydrated ions for water cluster of finite sizes, especially the sub-micrometer ones. However, the detailed molecular-level mechanism is still unclear due to the lack of available characterization and simulations tools. Here, we developed a quantum chemistry-level machine learning (ML) model to simulate the hydrolysis of SO3 with water clusters of sizes up to nanometers. The simulation results demonstrate diverse reaction paths taking place between SO3 and water clusters of different sizes. Generally, neutral (H2SO4)-(H2O) clusters are preferred by water clusters of ultra-small size, and a loop structure-mediated mechanism with SO3(H2O)n≤4 structures and a non-loop structure-mediated mechanism with structure relaxation are observed. As the water cluster size increases to (H2O)8, a (HSO4)--(H3O)+ ion-pair product emerges; and the Eigen-Zundel ion conversion-like proton transfer mechanism takes place and stabilizes the ion pairs. As the water cluster sizes further increase beyond several nanometers ((H2O)n≥32), the (SO4)2-[(H3O)+]2 ion-pair product appears. The reason could be that the surface of these water clusters is large enough to screen Coulomb repulsion between two tri-coordinated ion-pair complexes. These findings would provide new perspectives for understanding SO3 hydrolysis in the real atmosphere and sulfuric acid chemistry in atmospheric aerosols.
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Affiliation(s)
- Yajuan Feng
- School of Information Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Chao Wang
- National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui 230026, China
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2
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Burkholder JB, Cox RA, Ravishankara AR. Atmospheric degradation of ozone depleting substances, their substitutes, and related species. Chem Rev 2015; 115:3704-59. [PMID: 25893463 DOI: 10.1021/cr5006759] [Citation(s) in RCA: 87] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- James B Burkholder
- †Chemical Sciences Division, Earth System Laboratory, National Oceanic and Atmospheric Administration, 325 Broadway, Boulder, Colorado 80305, United States
| | - R A Cox
- ‡Centre for Atmospheric Science, Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EP, United Kingdom
| | - A R Ravishankara
- §Departments of Chemistry and Atmospheric Science, Colorado State University, 1872 Campus Delivery, Fort Collins, Colorado 80523, United States
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Sakaguchi S, Morita A. Molecular Dynamics Study of Water Transfer at Supercooled Sulfuric Acid Solution Surface Covered with Butanol. J Phys Chem A 2013; 117:4602-10. [DOI: 10.1021/jp310305a] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Affiliation(s)
- Suguru Sakaguchi
- Department of Chemistry, Graduate
School of Science, Tohoku University, Sendai
980-8578, Japan
| | - Akihiro Morita
- Department of Chemistry, Graduate
School of Science, Tohoku University, Sendai
980-8578, Japan
- Elements Strategy Initiative
for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8520, Japan
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4
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Abbatt JPD, Lee AKY, Thornton JA. Quantifying trace gas uptake to tropospheric aerosol: recent advances and remaining challenges. Chem Soc Rev 2012; 41:6555-81. [DOI: 10.1039/c2cs35052a] [Citation(s) in RCA: 161] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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5
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Davidovits P, Kolb CE, Williams LR, Jayne JT, Worsnop DR. Update 1 of: Mass Accommodation and Chemical Reactions at Gas−Liquid Interfaces. Chem Rev 2011; 111:PR76-109. [DOI: 10.1021/cr100360b] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Paul Davidovits
- Chemistry Department, 2609 Beacon Street, Boston College, Chestnut Hill, Massachusetts 02467, United States
| | - Charles E. Kolb
- Center for Aerosol and Cloud Chemistry, Aerodyne Research, Inc., 45 Manning Road, Billerica, Massachusetts 01821, United States
- This is a Chemical Reviews Perennial Review. The root paper of this title was published in Chem. Rev.2006, 106 (4), 1323−1354, DOI: 10.1021.cr040366k; Published (Web) March 16, 2006. Updates to the text appear in red type
| | - Leah R. Williams
- Center for Aerosol and Cloud Chemistry, Aerodyne Research, Inc., 45 Manning Road, Billerica, Massachusetts 01821, United States
- This is a Chemical Reviews Perennial Review. The root paper of this title was published in Chem. Rev.2006, 106 (4), 1323−1354, DOI: 10.1021.cr040366k; Published (Web) March 16, 2006. Updates to the text appear in red type
| | - John T. Jayne
- Center for Aerosol and Cloud Chemistry, Aerodyne Research, Inc., 45 Manning Road, Billerica, Massachusetts 01821, United States
- This is a Chemical Reviews Perennial Review. The root paper of this title was published in Chem. Rev.2006, 106 (4), 1323−1354, DOI: 10.1021.cr040366k; Published (Web) March 16, 2006. Updates to the text appear in red type
| | - Douglas R. Worsnop
- Center for Aerosol and Cloud Chemistry, Aerodyne Research, Inc., 45 Manning Road, Billerica, Massachusetts 01821, United States
- This is a Chemical Reviews Perennial Review. The root paper of this title was published in Chem. Rev.2006, 106 (4), 1323−1354, DOI: 10.1021.cr040366k; Published (Web) March 16, 2006. Updates to the text appear in red type
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Park SC, Burden DK, Nathanson GM. Surfactant control of gas transport and reactions at the surface of sulfuric acid. Acc Chem Res 2009; 42:379-87. [PMID: 19119820 DOI: 10.1021/ar800172m] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Aerosol particles in the atmosphere are tiny chemical reactors that catalyze numerous reactions, including the conversion of benign gases into ozone-destroying ones. In the lower stratosphere, these particles are often supercooled mixtures of water and sulfuric acid. The different species present at the surface of these droplets (H(2)O, H(3)O(+), HSO(4)(-), H(2)SO(4), and SO(4)(2-)) stand at the "gas-liquid frontier"; as the first to be struck by impinging molecules, these species provide the initial environment for solvation and reaction. Furthermore, aerosol particles may contain a wide range of organic molecules, some of which migrate to the surface and coat the droplet. How do ambient gases dissolve in the droplet if it is coated with an organic layer? At one extreme, monolayer films of insoluble, long-chain alcohols can dramatically reduce gas transport, packing so tightly at the surface of water that they impede water evaporation by factors of 10,000 or more. Shorter chain surfactants are expected to pack less tightly, but we wondered whether these incomplete monolayers also block gas transport and whether this system could serve as a model for understanding the surfaces of atmospheric aerosol particles. To address these questions, our research focuses on small, soluble surfactants such as butanol and hexanol dissolved in supercooled sulfuric acid. These amphiphilic molecules spontaneously segregate to the surface and coat the acid but only to a degree. Gas-liquid scattering experiments reveal that these porous films behave in surprisingly diverse ways: they can impose a barrier (to N(2)O(5) hydrolysis), be "invisible" (to water evaporation), or even enhance gas uptake (of HCl). The transition from obstacle to catalyst can be traced to specific interactions between the surfactant and each gas. For example, the hydrolysis of N(2)O(5) may be impeded because of its large size and because alcohol molecules that straddle the interface limit contact between N(2)O(5) and its H(3)O(+) and H(2)O reaction partners. However, these same alcohol molecules assist HCl dissociation because the alcohol OH groups provide extra interfacial protonation sites. Interestingly, butanol does not impede water evaporation, in part because the butyl chains pack much more loosely than insoluble, long-chain surfactants. Through these investigations, we hope to gain insight into the mechanisms by which surfactants on sulfuric acid and other aqueous solutions affect transport and reactivity at the gas-liquid interface.
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Affiliation(s)
- Seong-Chan Park
- Department of Chemistry, University of Wisconsin—Madison, 1101 University Avenue, Madison, Wisconsin 53706
| | - Daniel K. Burden
- Department of Chemistry, University of Wisconsin—Madison, 1101 University Avenue, Madison, Wisconsin 53706
| | - Gilbert M. Nathanson
- Department of Chemistry, University of Wisconsin—Madison, 1101 University Avenue, Madison, Wisconsin 53706
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7
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Theoretical Studies of the Dissociation of Sulfuric Acid and Nitric Acid at Model Aqueous Surfaces. ADVANCES IN QUANTUM CHEMISTRY 2008. [DOI: 10.1016/s0065-3276(07)00218-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/07/2023]
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Davidovits P, Kolb CE, Williams LR, Jayne JT, Worsnop DR. Mass accommodation and chemical reactions at gas-liquid interfaces. Chem Rev 2007; 106:1323-54. [PMID: 16608183 DOI: 10.1021/cr040366k] [Citation(s) in RCA: 210] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Paul Davidovits
- Chemistry Department, 2609 Beacon Street, Boston College, Chestnut Hill, Massachusetts 02467, USA.
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9
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Glass SV, Park SC, Nathanson GM. Evaporation of Water and Uptake of HCl and HBr through Hexanol Films at the Surface of Supercooled Sulfuric Acid. J Phys Chem A 2006; 110:7593-601. [PMID: 16774202 DOI: 10.1021/jp057260t] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Vacuum evaporation and molecular beam scattering experiments have been used to monitor the loss of water and dissolution of HCl and HBr in deuterated sulfuric acid at 213 K containing 0 to 100 mM hexanol. The addition of 1-hexanol to the acid creates a surface film of hexyl species. This film becomes more compact with decreasing acidity, ranging from approximately 62% to approximately 68% of maximum packing on 68 to 56 wt % D(2)SO(4), respectively. D(2)O evaporation from 68 wt % acid remains unaltered by the hexyl film, where it is most porous, but is impeded by approximately 20% from 56 and 60 wt % acid. H --> D exchange experiments further indicate that the hexyl film on 68 wt % acid enhances conversion of HCl and HBr into DCl and DBr, which is interpreted as an increase in HCl and HBr entry into the bulk acid. For this permeable hexyl film, the hydroxyl groups of surface hexanol molecules may assist uptake by providing extra sites for HCl and HBr hydrogen bonding and dissociation. In contrast, HCl --> DCl exchange in 60 wt % D(2)SO(4) at first rises with hexyl surface coverage but then drops back to the bare acid value as the hexyl species pack more tightly. HCl entry is actually diminished by the hexyl film on 56 wt % acid, where the film is most compact. These experiments reveal a transition from a porous hexanol film on 68 wt % sulfuric acid that enhances HCl and HBr uptake to one on 56 wt % acid that slightly impedes HCl and D(2)O transport.
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Affiliation(s)
- Samuel V Glass
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Ave, 53706, USA
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Zeng T, Wang Y, Chance K, Blake N, Blake D, Ridley B. Halogen-driven low-altitude O3and hydrocarbon losses in spring at northern high latitudes. ACTA ACUST UNITED AC 2006. [DOI: 10.1029/2005jd006706] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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11
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Bianco R, Wang S, Hynes JT. Theoretical Study of the First Acid Dissociation of H2SO4 at a Model Aqueous Surface. J Phys Chem B 2005; 109:21313-21. [PMID: 16853764 DOI: 10.1021/jp055107t] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
Electronic structure calculations on the H2SO4.(H2O)(4,6) model system embedded at the surface of an aqueous layer have been performed to examine the feasibility of the first acid dissociation of H2SO4 to an H2SO4-.H3O+ contact ion pair over a wide temperature range, with a special focus on the 190-250 K range relevant for atmospheric sulfate aerosols. The results indicate that the acid dissociation can be either thermodynamically favored or disfavored depending on the degree of solvation of the acid and the produced ions, as well as on the temperature.
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Affiliation(s)
- Roberto Bianco
- Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, USA.
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12
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Santschi C, Rossi MJ. The heterogeneous interaction of HOCl with solid KBr substrates: The catalytic role of adsorbed halogens. Phys Chem Chem Phys 2005; 7:2599-609. [PMID: 16189570 DOI: 10.1039/b503071d] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The heterogeneous reactivity of HOCl on solid KBr at ambient temperature has been studied using a Knudsen flow reactor. On solid KBr steady-state uptake experiments reveal the formation of Br- and Cl-containing reaction products formed in secondary reactions such as Br(2), BrCl, HOBr, BrOCl, Cl(2) and Cl(2)O with the latter two predominating in the late stages of the reaction. The uptake coefficient gamma spanning a range between 0.15 and 1 x 10(-3) and product yields of HOCl strongly depend on the nature of the solid sample, whether grain, ground grain or thin sprayed film, as well as on sample processing such as pumping and/or heating. Furthermore, the presence of adsorbed halogen species such as Br(2)(a) are crucial for the kinetics of the reaction of HOCl with solid KBr substrates. The presence of surface-adsorbed water (SAW) leads to deactivation of KBr whereas mechanical stress such as grinding leads to the formation of surface defects that become reaction centers. Desorption of SAW at T > 620 K induces high reactivity of the KBr sample at ambient temperature. A reaction mechanism encompassing all significant observations including unusual autocatalytic activity is given as there is no direct reaction of HOCl with solid KBr. It stresses the importance of adsorbed Br-containing species such as Br(2)(a) and HBr(a) that initiate the heterogeneous chemistry of HOCl on solid KBr in the presence of SAW. The role of surface acidity and SAW for the extent of reaction is emphasized.
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Affiliation(s)
- Ch Santschi
- Laboratoire de Pollution Atmosphérique et Sol (LPAS), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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13
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Abstract
Molecular beam scattering experiments provide a way to disentangle the elementary steps involved in energy transfer and chemical reactions between gases and liquids. After surveying the history and recent progress in this field, we review studies of the kinematics of gas-liquid collisions and proton exchange of HCl, DCl, and HBr with supercooled sulfuric acid and liquid glycerol. These experiments help to clarify the role of the surface region in controlling trapping and interfacial- and bulk-phase reactions.
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Affiliation(s)
- Gilbert M Nathanson
- Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706-1322, USA.
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14
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Voegele AF, Tautermann CS, Loerting T, Liedl KR. Reactions of HOBr + HCl + nH2O and HOBr + HBr + nH2O. Chem Phys Lett 2003. [DOI: 10.1016/s0009-2614(03)00447-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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15
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Hanson DR. Reactivity of BrONO2and HOBr on sulfuric acid solutions at low temperatures. ACTA ACUST UNITED AC 2003. [DOI: 10.1029/2002jd002519] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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16
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Evans MJ. Coupled evolution of BrOx-ClOx-HOx-NOxchemistry during bromine-catalyzed ozone depletion events in the arctic boundary layer. ACTA ACUST UNITED AC 2003. [DOI: 10.1029/2002jd002732] [Citation(s) in RCA: 71] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
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17
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Drdla K, Schoeberl MR. Microphysical modeling of the 1999-2000 Arctic winter 2. Chlorine activation and ozone depletion. ACTA ACUST UNITED AC 2002. [DOI: 10.1029/2001jd001159] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- K. Drdla
- NASA Ames Research Center; Moffett Field California USA
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Affiliation(s)
- Ayman Al-Halabi
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, Einsteinweg 55, P.O. Box 9502 2300 RA, Leiden, The Netherlands, Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, and Departement de Chimie, CNRS UMR 8640 PASTEUR, Ecole Normale Supérieure, 24 rue Lhomond, Paris 75231, France
| | - Roberto Bianco
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, Einsteinweg 55, P.O. Box 9502 2300 RA, Leiden, The Netherlands, Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, and Departement de Chimie, CNRS UMR 8640 PASTEUR, Ecole Normale Supérieure, 24 rue Lhomond, Paris 75231, France
| | - James T. Hynes
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, Einsteinweg 55, P.O. Box 9502 2300 RA, Leiden, The Netherlands, Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, and Departement de Chimie, CNRS UMR 8640 PASTEUR, Ecole Normale Supérieure, 24 rue Lhomond, Paris 75231, France
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19
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Huff AK, Abbatt JPD. Kinetics and Product Yields in the Heterogeneous Reactions of HOBr with Ice Surfaces Containing NaBr and NaCl. J Phys Chem A 2002. [DOI: 10.1021/jp014296m] [Citation(s) in RCA: 57] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
- Amy K. Huff
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6
| | - Jonathan P. D. Abbatt
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6
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20
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Shi Q, Jayne JT, Kolb CE, Worsnop DR, Davidovits P. Kinetic model for reaction of ClONO2with H2O and HCl and HOCl with HCl in sulfuric acid solutions. ACTA ACUST UNITED AC 2001. [DOI: 10.1029/2000jd000181] [Citation(s) in RCA: 74] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Wagner T, Leue C, Pfeilsticker K, Platt U. Monitoring of the stratospheric chlorine activation by Global Ozone Monitoring Experiment (GOME) OClO measurements in the austral and boreal winters 1995 through 1999. ACTA ACUST UNITED AC 2001. [DOI: 10.1029/2000jd900458] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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22
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Morita A, Hynes JT. A theoretical analysis of the sum frequency generation spectrum of the water surface. Chem Phys 2000. [DOI: 10.1016/s0301-0104(00)00127-0] [Citation(s) in RCA: 263] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Morris JR, Behr P, Antman MD, Ringeisen BR, Splan J, Nathanson GM. Molecular Beam Scattering from Supercooled Sulfuric Acid: Collisions of HCl, HBr, and HNO3 with 70 wt D2SO4. J Phys Chem A 2000. [DOI: 10.1021/jp000105o] [Citation(s) in RCA: 62] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Affiliation(s)
- John R. Morris
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706
| | - Peter Behr
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706
| | - Melissa D. Antman
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706
| | - Bradley R. Ringeisen
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706
| | - Jennifer Splan
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706
| | - Gilbert M. Nathanson
- Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706
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Cziczo DJ, Abbatt JPD. Infrared Observations of the Response of NaCl, MgCl2, NH4HSO4, and NH4NO3 Aerosols to Changes in Relative Humidity from 298 to 238 K. J Phys Chem A 2000. [DOI: 10.1021/jp9931408] [Citation(s) in RCA: 142] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- D. J. Cziczo
- Department of the Geophysical Sciences, The University of Chicago, Chicago, Illinois 60637
| | - J. P. D. Abbatt
- Department of the Geophysical Sciences, The University of Chicago, Chicago, Illinois 60637
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