Atmospheric Multiphase Chemistry: Fundamentals of Secondary Aerosol Formation [1 ed.] 1119422426, 9781119422426

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Atmospheric Multiphase Chemistry

Atmospheric Multiphase Chemistry Fundamentals of Secondary Aerosol Formation

Hajime Akimoto National Institute for Environmental Studies Tsukuba, Japan

Jun Hirokawa Hokkaido University Sapporo, Japan

This edition first published 2020 © 2020 John Wiley & Sons Ltd All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions. The right of Hajime Akimoto and Jun Hirokawa to be identified as the author(s) of this work has been asserted in accordance with law. Registered Office(s) John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK Editorial Office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com. Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content that appears in standard print versions of this book may not be available in other formats. Limit of Liability/Disclaimer of Warranty While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials, or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Library of Congress Cataloging-in-Publication Data Names: Akimoto, Hajime, author. | Hirokawa, Jun, author. Title: Atmospheric multiphase chemistry : fundamentals of secondary aerosol formation / Hajime Akimoto, Jun Hirokawa. Description: First edition. | Hoboken, NJ : Wiley-Blackwell, 2020. | Includes bibliographical references and index. Identifiers: LCCN 2019051976 (print) | LCCN 2019051977 (ebook) | ISBN 9781119422426 (hardback) | ISBN 9781119422396 (adobe pdf ) | ISBN 9781119422402 (epub) Subjects: LCSH: Atmospheric aerosols. | Chemical reactions. | Multiphase flow. Classification: LCC QC882.42 .A45 2020 (print) | LCC QC882.42 (ebook) | DDC 551.51/13–dc23 LC record available at https://lccn.loc.gov/2019051976 LC ebook record available at https://lccn.loc.gov/2019051977 Cover Design: Wiley Cover Image: © Daniel Haug/Getty Images Set in 10/12pt WarnockPro by SPi Global, Chennai, India Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY 10 9 8 7 6 5 4 3 2 1

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Contents Preface

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1 Historical Background of Atmospheric Secondary Aerosol Research

1

1.1 Introduction 1 1.2 Secondary Inorganic Aerosols 1 1.2.1 Sulfate 2 1.2.2 Nitrate 3 1.3 Secondary Organic Aerosols 4 1.3.1 Photochemical Smog 5 1.3.2 Blue Haze 6 References 7 2 Fundamentals of Multiphase Chemical Reactions 13

2.1 Introduction 13 2.2 Gas–Liquid Phase Equilibrium and Equilibrium in Liquid Phase 13 2.2.1 Fundamentals of Thermodynamics 14 2.2.1.1 Internal Energy and Enthalpy 14 2.2.1.2 Entropy 16 2.2.1.3 Gibbs Energy 18 2.2.1.4 Chemical Potential 19 2.2.2 Chemical Equilibrium and Equilibrium Constant 21 2.2.2.1 Chemical Equilibrium 21 2.2.2.2 Equilibrium Constant of Gas-Phase Reaction 22 2.2.2.3 Equilibrium Constant of Liquid-Phase Reaction 24 2.2.2.4 Temperature Dependence of Equilibrium Constant 26 2.2.3 Gas–Liquid Equilibrium and Henry’s Law Constant 29 2.2.4 Hydration of Carbonyl Compounds and Effective Henry’s Law Constant 31 2.2.5 pH and Equilibrium in the Aqueous Solution 32 2.2.5.1 Dissociation Equilibrium of Pure Water and pH 32 2.2.5.2 Ion Dissociation and Equilibrium in Aqueous Solution 33 2.3 Reactions in the Liquid Phase 35 2.3.1 Thermodynamics and Activity Coefficients of Nonideal Solutions 35

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2.3.1.1 Salting-in, Salting-out 38 2.3.2 Chemical Kinetics of Aqueous-Phase Reaction 39 2.3.2.1 Diffusion Process and Chemical Reaction Kinetics 39 2.3.2.2 Transition State Theory of Solution Reaction and Thermodynamic Expression 42 2.3.3 Cage Effect and Aqueous-Phase Solvent Effect 46 2.3.3.1 Cage Effect 46 2.3.3.2 Solvent Effect in the Aqueous Phase 48 2.4 Uptake Coefficient and Resistance Model 51 2.4.1 Accommodation Coefficient and Uptake Coefficient 52 2.4.2 Resistance Model 54 2.5 Physical Chemistry of Interface Reaction 56 2.5.1 Langmuir-Hinshelwood Mechanism and Eley-Rideal Mechanism 2.5.2 Resistance Model Including Interface Reaction 59 2.5.3 Surface Tension of Air–Water Interface and Thermodynamics of Accommodation Coefficient 65 2.5.3.1 Surface Tension 65 2.5.3.2 Thermodynamics of Accommodation Coefficient at Air–Water Interface 68 2.6 Chemical Compositions and Physical Characters of Particles 71 2.6.1 Elemental and Molecular Composition of Particles 72 2.6.1.1 Inorganic Elements and Compounds 72 2.6.1.2 Organic Compounds 74 2.6.1.3 van Krevelen Diagram 77 2.6.2 Molecular Composition and Vapor Pressure 78 2.6.3 Gas-Particle Partitioning and Volatility Basis Set Model 84 2.6.3.1 Gas-Particle Partitioning and SOA Formation Yield 84 2.6.3.2 Volatility Basis Set Model 88 2.6.3.3 Gas-Aqueous Phase Partitioning of Hydrophilic Compounds 90 2.6.4 Phase State of Particles and Mass Transfer 93 References 95 3 Gas-Phase Reactions Related to Secondary Organic Aerosols 107

3.1 Introduction 107 3.2 Ozone Reactions 107 3.2.1 Properties and Reactions of Criegee Intermediates 108 3.2.1.1 Direct Detection of Criegee Intermediate and Molecular Structure 110 3.2.1.2 Formation of CH2 OO in Ozone-Ethene Reaction 115 3.2.1.3 Formation of syn- and anti-CH3 CHOO in Ozone-Alkene Reactions 118 3.2.2 Alkenes and Dialkenes 130 3.2.2.1 Ethene 130 3.2.2.2 >C3 Alkenes 132 3.2.2.3 1,3-Butadiene 134 3.2.3 Isoprene 135

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3.2.4 Cycloalkenes 139 3.2.4.1 Cyclohexene 139 3.2.4.2 1-Methylcyclohexene 141 3.2.4.3 Methylenecyclohexane 144 3.2.5 Monoterpenes 144 3.2.5.1 α-Pinene 145 3.2.5.2 β-Pinene 148 3.2.5.3 Limonene 150 3.2.6 Sesquiterpenes 155 3.3 OH Radical-Induced Oxidation Reactions 160 3.3.1 Alkanes 160 3.3.1.1 Reactions of Alkyl Peroxy Radicals 165 3.3.1.2 Reactions of Alkoxy Radicals 165 3.3.2 Alkynes 170 3.3.3 Alkenes, Dialkenes, and Cycloalkenes 171 3.3.3.1 Alkenes 171 3.3.3.2 1,3-Butadiene 173 3.3.3.3 Cycloalkenes and Methylene cyclohexane 174 3.3.4 Isoprene 175 3.3.4.1 Fundamental Processes of OH-Induced Oxidation Reaction 175 3.3.4.2 HOx Radicals Regeneration Reaction 178 3.3.4.3 Formation of Isoprene Hydroxy Hydroperoxide (ISOPOOH) and Isoprene Epoxydiol (IEPOX) 179 3.3.4.4 Formation of Hydroxy Isoprene Nitrates 180 3.3.4.5 Reactions of Methyl Vinyl Ketone and Methacrolein 182 3.3.5 Monoterpenes 183 3.3.5.1 α-Pinene 183 3.3.5.2 β-Pinene 185 3.3.5.3 Limonene 187 3.3.6 Monocyclic Aromatic Hydrocarbons 189 3.3.6.1 Benzene 189 3.3.6.2 Toluene 192 3.3.7 Polycyclic Aromatic Hydrocarbons 195 3.3.7.1 Naphthalene 196 3.3.7.2 Other Polycyclic Aromatic Hydrocarbons 198 3.3.8 Carbonyl Compounds: OH Radical Reactions and Photolysis 199 3.3.8.1 Glyoxal 199 3.3.8.2 Methylglyoxal 202 3.3.8.3 Glycolaldehyde 204 3.3.8.4 Hydroxyacetone 207 3.4 NO3 Oxidation Reactions 209 3.4.1 Isoprene 209 3.4.2 Monoterpenes 213 3.4.2.1 α-Pinene 213 3.4.2.2 β-Pinene 214 3.4.2.3 Limonene 215

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3.4.3 Monocyclic and Polycyclic Aromatic Hydrocarbons 217 3.4.3.1 Phenol, and Cresol 217 3.4.3.2 Naphthalene 218 3.4.3.3 Other Polycyclic Aromatic Hydrocarbons 219 References 219 4 Aqueous-Phase Reactions Related to Secondary Organic Aerosols 245

4.1 Introduction 245 4.2 OH Radical Reactions 246 4.2.1 UV Absorption Spectrum of OH Radicals in Aqueous Solution 246 4.2.2 Formation of OH Radicals in Cloud/Fog Droplets and Deliquescent Aerosols 248 4.2.3 Reaction Rate Constants of OH Radicals in the Aqueous Phase 254 4.2.4 Reactions of Formaldehyde and OH Radical Chain Reaction 257 4.2.5 OH Radical Reactions and Photolysis of ≥C2 Carbonyl Compounds 262 4.2.5.1 Glyoxal and Glyoxylic Acid 262 4.2.5.2 Methylglyoxal, Pyruvic Acid, and Acetic Acid 264 4.2.5.3 Glycolaldehyde and Glycolic Acid 267 4.2.5.4 Methacrolein and Methyl Vinyl Ketone 268 4.2.6 Oligomer Formation Reactions from ≥C2 Carbonyl Compounds 270 4.2.6.1 Glyoxal and Methylglyoxal 272 4.2.6.2 Methyl Vinyl Ketone and Methacrolein 273 4.3 Nonradical Reactions 275 4.3.1 Diels-Alder Reaction 276 4.3.2 Hemiacetal and Acetal Formation Reactions 277 4.3.2.1 Glyoxal 279 4.3.2.2 Methylglyoxal 280 4.3.2.3 1,4-Hydroxycarbonyl Compounds 281 4.3.3 Aldol Reaction 281 4.3.3.1 Acetaldehyde 282 4.3.3.2 Methylglyoxal 283 4.3.3.3 Methyl Vinyl Ketone and Methacrolein 284 4.3.4 Esterification Reactions 285 4.4 Formation Reactions of Organic Sulfates 287 4.4.1 C2 and C3 Carbonyl Compounds 287 4.4.2 Monoterpenes 288 4.4.3 Isoprene 291 4.4.4 Monocyclic and Polycyclic Aromatic Hydrocarbons 291 4.5 Formation Reactions of Organic Nitrogen Compounds 292 4.5.1 Organic Nitrates 292 4.5.2 Imidazoles 293 References 295 5 Heterogeneous Oxidation Reactions at Organic Aerosol Surfaces 309

5.1 Introduction 309 5.2 Aging of Organic Aerosols in the Atmosphere 309

Contents

5.3 Reactions of Ozone 313 5.3.1 Oleic Acid and Unsaturated Long-Chain Carboxylic Acids 314 5.3.2 Squalene 316 5.3.3 Polycyclic Aromatic Hydrocarbons 318 5.4 Reactions of OH Radicals 320 5.4.1 Squalane and Long-Chain Alkanes 320 5.4.2 Levoglucosan, Erythritol, and Hopane 325 5.4.3 Saturated Dicarboxylic Acids 326 5.4.4 Squalene and Long-Chain Unsaturated Carboxylic Acids 328 5.4.5 Polycyclic Aromatic Hydrocarbons 330 5.5 Reactions of NO3 Radicals 332 5.5.1 Levoglucosan, Squalane, Long-Chain Alkane, and Alkanoic Acid 332 5.5.2 Squalene and Oleic Acid 334 5.5.3 Polycyclic Aromatic Hydrocarbons 334 References 336 6 Reactions at the Air–Water and Air–Solid Particle Interface 343

6.1 Introduction 343 6.2 Molecular Pictures and Reactions at the Air–Water Interface 344 6.2.1 Thermodynamics of Adsorption 345 6.2.1.1 OH, HO2 , and O3 346 6.2.1.2 Organic and Inorganic Compounds 348 6.2.2 Microscopic Picture of Molecules 349 6.2.2.1 Air–Pure Water Interface 350 6.2.2.2 Hydrophilic Organic Compounds 352 6.2.2.3 Amphiphilic Organic Compounds (Surfactants) 356 6.2.2.4 Hydrophobic Organic Compounds 357 6.2.2.5 NH3 and SO2 358 6.2.3 Reactions of O3 and Organic Compounds 359 6.2.3.1 Oleic Acid 360 6.2.3.2 Sesquiterpene Criegee Intermediates 360 6.2.3.3 Polycyclic Aromatic Hydrocarbons 361 6.2.4 Reactions of OH Radicals and Organic Compounds 362 6.2.4.1 Carboxylic and Dicarboxylic Acids 362 6.2.4.2 Organic Sulfur Compounds 364 6.3 Air–Sea Salt Particle, Seawater, and Sulfate/Nitrate Aerosol Interface 365 6.3.1 Microscopic View of Interface of Air and Alkaline Halide Aqueous Solution 366 6.3.2 Reactions at the Interface of Sea Salt and Alkali Halide Aqueous Solution 368 6.3.2.1 Reaction with O3 369 6.3.2.2 Reaction with OH Radicals 371 6.3.2.3 Uptake of HO2 Radicals 372 6.3.2.4 Reaction with N2 O5 372 6.3.2.5 Reaction with HNO3 373 6.3.3 Reactions of Organic Compounds at the Air–Seawater and Air–Sea Salt Interface 375

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6.3.4 Microscopic View of the Interface of Air and Sulfate/Nitrate Aqueous Solution 377 6.3.4.1 Sulfate Ion (SO4 2− ) 377 6.3.4.2 Nitrate Ion (NO3 − ) 378 6.4 Reactions on Snow/Ice Surface 379 6.4.1 Formation of NOy in the Photochemical Reaction of NO3 − 379 6.4.2 Formation of Inorganic Halogens on the Snow Ice and Sea Ice Surface 382 6.4.2.1 Reaction with O3 382 6.4.2.2 Reaction with OH Radicals 383 6.4.2.3 Reactions with N2 O5 384 6.5 Interface of Water and Mineral Dust, Quartz, and Metal Oxide Surface 385 6.5.1 Microscopic View of Adsorbed Water on Mineral Surface 386 6.5.2 HONO Formation Reaction from NO2 on the Mineral Surface 390 6.5.2.1 Dark Reaction 390 6.5.2.2 Photochemical Reaction 392 6.5.3 Reaction of Organic Monolayer on Mineral Surface 394 References 396 7 Atmospheric New Particle Formation and Cloud Condensation Nuclei 415

7.1 Introduction 415 7.2 Classical Homogeneous Nucleation Theory 415 7.2.1 Homogeneous Nucleation in One-Component Systems 415 7.2.2 Homogeneous Nucleation in Two-Component Systems 419 7.3 Atmospheric New Particle Formation 422 7.3.1 New Particle Formation Rate and Growth Rate 422 7.3.2 Sulfuric Acid in New Particle Formation 425 7.3.3 Basic Substances in New Particle Formation 427 7.3.4 Organic Species in New Particle Formation 430 7.3.5 Other Species in New Particle Formation 433 7.3.5.1 Iodine Oxides 433 7.3.5.2 Atmospheric Ions 434 7.3.6 Field Observation of Nanoclusters 435 7.4 Aerosol Hygroscopicity and Cloud Condensation Nuclei 436 7.4.1 Köhler Theory 436 7.4.2 Nonideality of Solution in a Droplet 441 7.4.3 Hygroscopicity Parameter, 𝜅 442 References 446 453 8.1 Introduction 453 8.2 Global Budget of Aerosols 453 8.3 Analysis Methods of Ambient Aerosol Compositions 458 8.3.1 Positive Matrix Factorization 458 8.3.2 Mass Spectrum Peak Intensity and Elemental Ratio 459 8.3.3 Elemental Composition 460 8.4 Marine Air 461

8 Field Observations of Secondary Organic Aerosols

Contents

8.5 Forest Air 465 8.5.1 Amazon Tropical Forest 465 8.5.2 Finland Boreal Forest 469 8.6 Urban/Rural Air 472 8.6.1 Characterization of Ambient Aerosols 472 8.6.1.1 PMF Analysis 472 8.6.1.2 Mass Signal Intensity Ratio and Elemental Ratio 474 8.6.1.3 Particle Size Distribution 477 8.6.1.4 Elemental Composition 478 8.6.2 Molecular Composition 479 8.6.2.1 Dicarboxylic Acid 480 8.6.2.2 Plant Origin VOC Tracers 481 8.6.2.3 Anthropogenic VOC Tracer 484 8.6.2.4 Organic Sulfate 485 8.6.2.5 Organic Nitrates and Imidazoles 486 8.6.2.6 High-Molecular-Weight Compounds and Oligomers 489 References 493 Index 509

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Preface Reaction kinetics and mechanism are a significant part of the fundamentals of atmospheric chemistry. The chemical reaction system in the atmosphere is composed of homogeneous reactions in the gas and liquid phases and heterogeneous processes involving particle surfaces. Among them, the study of gas-phase homogeneous reaction system in the atmosphere has evolved since the Chapman theory in the 1930s to explain the stratospheric ozone layer, and developed dramatically after 1970s with photochemical air pollution as a trigger. It is now almost established and summarized in many bibliographies, including a book by one of present authors (H.A.) discussed in Chapter 3. In contrast, although the heterogeneous reaction system in the atmosphere has developed substantially with acid rain and stratospheric ozone hole as turning points, the studies have long been confined mainly to inorganic species. The research field of aerosols and heterogeneous kinetics has undergone dramatic changes since the 2000s, when the importance of secondary organic aerosols as cloud condensation nuclei was pointed out. Also, secondary organic aerosols have been recognized as important as inorganic sulfate and nitrate as a constituent of PM2.5 , which is concerned from the point of human health. The formation mechanism of secondary organic aerosols involves condensation of reaction products of homogeneous gas-phase reactions, uptake of the gas-phase products onto the particle surface, complex formation and reaction at the interface, homogeneous aqueous-phase reaction, and evaporation from a particle to the gas phase. We call series of these processes multiphase reaction chemistry. This book intends to serve as a reference book on fundamentals of atmospheric multiphase chemistry. Gas- and aqueous-phase reactions, heterogeneous oxidation processes, and air–water interface and solid particle surface reactions related to secondary organic aerosol formation are first described. After that, new particle formation, cloud condensation nucleus activity, and field observation of organic aerosols are discussed. The book can serve as a comprehensive reference for graduate students and professionals who are interested in homogeneous and heterogeneous atmospheric reactions of organic species related to aerosols.

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Preface

The field of atmospheric multiphase chemistry is still a rapidly developing research area. Many studies described in this book have not become fully established, and future revisions are likely. Finally, we would like to acknowledge Drs. Michihiro Mochida, Satoshi Inomata, Kei Sato, Yasuhiro Sadanaga, and Shinichi Enami, who read the manuscript in their respective parts and gave us valuable comments. October, 2019

Hajime Akimoto Jun Hirokawa

1

1 Historical Background of Atmospheric Secondary Aerosol Research 1.1 Introduction Trace components in the tropospheric atmosphere consist of gaseous molecules and particulate matters. Most of gaseous molecules in the atmosphere do not have absorption bands in the visible region. Some species such as ozone and nitrogen dioxide have the absorption, but they are invisible to the naked eye under the normal atmospheric conditions because their absorbance are small. In contrast, since the particulate matters intercept sunlight and small particles scatter strongly the solar radiation, they are captured easily by the naked eye as haze. Thus, particulate matters in the atmosphere called atmospheric aerosols have been studied from relatively early days in relation to air pollution historically. These atmospheric aerosols are divided broadly into the primary species released directly from emission sources and the secondary compounds formed by chemical reactions in the atmosphere. Further, secondary particulate matter can be classified into secondary inorganic aerosol and secondary organic aerosol (SOA). This book aims at the understanding of chemical reactions forming secondary aerosols in the gas phase, in the liquid phase, and at their interface, particularly focusing on organic aerosols. Therefore, most of the descriptions are focused on organic species, and inorganic species are addressed whenever necessary. As for the formation of secondary inorganic aerosols, detailed discussion has been given by the textbook of Seinfeld and Pandis (2016). In this chapter, historical background of research on atmospheric secondary aerosols, including inorganic aerosols, is described looking back before 1980s, when the atmospheric chemistry was founded as one of the academic fields of the global environmental sciences.

1.2 Secondary Inorganic Aerosols The first capture of atmospheric secondary inorganic aerosol such as nitrate and sulphate was in the form of precipitation component, and their historical reviews are available by Eriksson (1952a, 1952b) and Möller (2008). First discovery of nitrate in precipitation was made by Marggraf (1751), a German chemist, and mineral species (silica and lime), sea salt component (sodium and chloride), ammonium, and organics as brown residue were also detected together with nitrate. It was the earlier half of Atmospheric Multiphase Chemistry: Fundamentals of Secondary Aerosol Formation, First Edition. Hajime Akimoto and Jun Hirokawa. © 2020 John Wiley & Sons Ltd. Published 2020 by John Wiley & Sons Ltd.

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1 Historical Background of Atmospheric Secondary Aerosol Research

nineteenth century when Liebig (1835) advocated a theory that atmospheric nitrogen compounds deposited on ground are essential to plant growth as nutrient salt absorbed by roots, leading to a revolution of agricultural chemistry. Thus, atmospheric nitrate, the main component of the plant nutrient, had been discovered from long ago as a precipitation constituent (Miller 1905; Eriksson 1952a; Möller 2008). On the other hand, the discovery of sulphate was delayed nearly 100 years after that of nitrate. From the view point of air pollution in Manchester, UK, Smith (1852) described based on the analysis of precipitation that three kinds of air can be found: (i) with carbonate of ammonia in the remote field; (ii) with sulphate of ammonia in the suburbs; and (iii) with sulfuric acid in the urban area (Cowling 1982). The described ammonium carbonate ((NH4 )2 CO3 ), ammonium sulfate ((NH4 )2 SO4 ), and sulfuric acid (H2 SO4 ) are formed secondarily by the chemical reactions in the gas phase or in the fog water from atmospheric trace gaseous species, CO2 , NH3 , and SO2 . These aerosols are water-soluble, and recognized as major components of “acid rain” after taken into precipitation. Incidentally, the term of acid rain was used for the first time in the monograph of Smith (1872) as accredited by Cowling (1982). Since then, the measurement of nitrate and ammonium had been made in many places in Europe in the latter half of nineteenth century from the interest of agricultural chemistry, while sulfate had been measured in the eastern part of United States since the 1910s (Cowling 1982). Hydrogen ion concentration (pH) has been measured since the 1950s, started in Europe and United States, over a wide area. Owing to these wide-area observations, spatial distribution and temporal trends of pH and chemical components of precipitation became to be known well in Europe (Emanuelsson et al. 1954; Barrett and Brodin 1955; Odén 1976) and North America (Junge and Werby 1958; Gorham and Gordon 1960; Cogbill 1976). The acid rain causing acidification of lakes and rivers and their impact on fishery was then brought up as a social problem internationally. The quantitative research on the formation of sulfate and nitrate as secondary inorganic aerosol had been developed rapidly as “acid rain” became social concern. 1.2.1

Sulfate

In the earlier studies on acid rain, it was thought that sulfur dioxide (SO2 ), primary air pollutants whose atmospheric concentration had increased rapidly after the Industrial Revolution, was taken up into fog water droplets and converted to sulfate by oxidation in the aqueous phase (Junge and Ryan 1958; Junge 1963): H2 O

O2

NH4 +

SO2 −−−−→ SO3 2− −−−−n+−→ SO4 2− −−−−−→ (NH4 )2 SO4 M

(1.1)

The rate limiting stage of this process is the oxidation step of SO3 2− to SO4 2− , and the oxidation by O2 had been studied for a long time (Fudakowski 1873; Backstrom 1934). However, the oxidation rate of SO3 2− by O2 was found to be very slow (Fuller and Crist 1941; Brimblecombe and Spedding 1974). Therefore, this reaction is not important for O2 alone as the oxidation reaction of SO2 in the atmosphere, but it was found that the reaction is accelerated by the coexistence of trace metal ions such as Fe3+ , Cu2+ , and Mn2+ (Reinders and Vles 1925; Junge and Ryan 1958; Brimblecombe and Spedding 1974; Hegg and Hobbs 1978). The effects of transition metal ions on the SO2 oxidation in the aqueous phase still leaves a lot of unknowns, and the studies are ongoing (Deguillaume et al. 2005; Harris et al. 2013; Herrmann et al. 2015).

1.2 Secondary Inorganic Aerosols

In 1970s, the importance of the reaction of O3 and H2 O2 , formed secondarily in the photochemically polluted atmosphere, was pointed out. The pioneering studies were made by Penkett and Garland (1974), Erickson et al. (1977), and Larson et al. (1978) for O3 , and by Mader (1958), Hoffmann and Edwards (1975), and Penkett et al. (1979) for H2 O2 . Later studies on these aqueous phase reactions revealed that the oxidation by H2 O2 is more important at lower pH than 7, and those of O3 become important in the higher pH region. Details of these aqueous-phase reactions are summarized in the textbooks by Akimoto (2016, pp. 363–372), and Seinfeld and Pandis (2016). Atmospheric oxidation reactions of SO2 to SO4 2− were studied earlier for the aqueous-phase reactions, and the gas-phase reactions was noted later by Cox and Penkett (1972). The years of 1970s are the era that OH radical chain reactions were proposed and demonstrated to cause photochemical air pollution (Akimoto 2016, pp. 288–290). The importance of the reaction of SO2 and OH for the oxidation of SO2 was deduced based on the measured rate constant of the reaction (Eggleton and Cox 1978; Davis et al. 1979). Later, Stockwell and Calvert (1983) showed the oxidation process of SO2 with OH as OH + SO2 + M → HOSO2 + M

(1.2)

HOSO2 + O2 → HO2 + SO3

(1.3)

SO3 + H2 O + M → H2 SO4 + M

(1.4)

HO2 + NO → NO2 + OH

(1.5)

This implies that the HOSO2 forms H2 SO4 without terminating the OH chain reaction. The SO2 oxidation mechanism in the gas-phase has thus been established. Although the relative importance of gas- and aqueous-phase reactions varies widely, depending on meteorological conditions. It is thought in general that both processes are important (Barrie et al. 2001). Most of sulfate in particles exist as ammonium sulfate ((NH4 )2 SO4 ) or ammonium bisulfate (NH4 HSO4 ), and a part of them exists as sulfuric acid (H2 SO4 ) when NH3 is in short stoichiometrically as observed in the sub-micron particles in many urban samples (van den Heuvel and Mason 1963; Ludwig and Robinson 1965; Wagman, Lee, and Axt 1967). 1.2.2

Nitrate

The measurement of nitrate (NO3 − ) in precipitation has been reported in United States early in 1920s from the interest in agricultural chemistry (Wilson 1926). Its atmospheric concentrations increased rapidly, accompanying with the rapid increase of fossil fuel combustion. It has been monitored since the 1950s as an important secondary inorganic aerosol next to SO4 2− (Junge 1954; Lee and Patterson 1969). For example, the equivalent-basis fractions of SO4 2− and NO3 − in precipitation in Eastern United States in early 1960s are reported as ca. 60% and ca. 20%, respectively (Likens and Bormann 1974). Particularly, large amounts of nitrates were reported, together with sulfate and organic aerosols existing in photochemical smog mentioned in the next section (Renzetti and Doyle 1959; Lundgren 1970; Appel et al. 1978). Since the rate constant of the reaction: OH + NO2 + M → HNO3 + M,

(1.6)

3

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1 Historical Background of Atmospheric Secondary Aerosol Research

is one order of magnitude larger than the reaction, OH + SO2 + M, under the atmospheric conditions, and the Henry’s law constant of NO2 is two orders of magnitude smaller than SO2 (Table 2.2), nitric acid (HNO3 ) in the atmosphere is thought to be formed in the gas phase and then taken into the aqueous phase (Orel and Seinfeld 1977). Meanwhile, a formation pathway other than (1.6) is considered to be the hydrolysis of N2 O5 formed via NO3 by the reaction of O3 and NO2 (Orel and Seinfeld 1977): NO2 + O3 → NO3 + O2

(1.7)

NO2 + NO3 + M → N2 O5 + M

(1.8)

N2 O5 + H2 O → 2 HNO3

(1.9)

The rate constant of Reaction (1.9) in the gas phase as a homogeneous reaction is very small, 0 (heat is absorbed by the system from the surroundings) is called endothermic reaction. In general, reaction enthalpy is represented by the values when the reactants and products are in the standard state (also called reference state). In this case, it is called standard reaction enthalpy and represented by Δr H ∘ . Here, the superscript ∘ represents the standard state. The standard state means that the state of the substance is under the pressure of 1 bar = 105 Pa (definition by the recommendation of IUPAC in 1982. Previously, it was defined at 0 ∘ C and 1 atm = 1.013 × 105 Pa). However, for ions in the aqueous solution, standard state is defined as a hypothetical ideal dilute solution with the molality of 1 mol kg−1 (cf. Section 2.2.2). According to the new definition, temperature is not specified, but usually reference temperature 298.15 K (25 ∘ C) is selected and the standard reaction enthalpy is represented by Δr H 298 ∘ . Reaction enthalpy is decided by the difference between the total enthalpy of reactants and products, and does not depend on the intermediate process (Hess’s law). For instance, considering the chemical reaction, 𝜈A A + 𝜈B B → 𝜈C C + 𝜈D D,

(2.13)

15

16

2 Fundamentals of Multiphase Chemical Reactions

where 𝜈 i (i = A, B, C, and D) is the stoichiometric number of reactants and products, the standard reaction enthalpy of this reaction is expressed as Δ H ∘ = [𝜈 H ∘ (C) + 𝜈 H ∘ (D)] − [𝜈 H ∘ (A) + 𝜈 H ∘ (B)], (2.14) r

C

D

A

B

using the enthalpy per mole (molar enthalpy) of the reactants and products in their standard state, H ∘ (i) (i = A, B, C, and D). For more general chemical reactions, it can be written as ∑ ∑ Δ H∘ = 𝜈 H ∘ (i) − 𝜈 H ∘ (i). (2.15) r

i

i

reactants

products

Equations (2.14) and (2.15) are the “definition” of standard reaction enthalpy, which is practically obtained by using standard enthalpy of formation Δf H ∘ of reactants and products. The standard enthalpy of formation is the enthalpy change when 1 mol of a compound is formed from the constituent elements in the most stable state at 1 bar and the specified temperature (usually 298.15 K). Here, the standard enthalpies of formation of the most stable form of the elements are prescribed as zero at all temperatures. For example, Δf H ∘ of gaseous H2 , N2 , O2 , liquid Hg, Br2 , and solid Na, Si, I2 at 1 bar, 298.15 K are all zero. For carbon, Δf H ∘ of the most stable graphite rather than diamond is taken to be zero. For ions in the aqueous solution, Δf H ∘ of hydrogen ion H+ in the standard state mentioned above is prescribed as zero. Standard enthalpy of formation Δf H 0 ∘ and Δf H 298 ∘ of compounds of interest in atmospheric chemistry at 0 and 298.15 K are given in many literatures (e.g. Finlayson-Pitts and Pitts 2000; Burkholder et al. 2015; Akimoto 2016). Table 2.3 lists the standard enthalpy of formation Δf H ∘ 298 (kJ mol−1 ) of compounds related to the formation of inorganic and organic aerosols. Referring to the table, standard reaction enthalpy can be calculated from Δf H ∘ of each reactant and product by ∑ ∑ 𝜈 Δ H ∘ (i) − 𝜈 Δ H ∘ (i). (2.16) Δ H∘ = r

i

f

products

2.2.1.2

i

f

reactants

Entropy

According to the second law of thermodynamics, the spontaneous reaction proceeds to the direction fulfilling the following inequality between the amount of infinitesimal change in thermodynamical entropy dS, incremental heat of exchange with the surroundings δq (δq > 0 when heat is transferred to the system from the surroundings), and the temperature T: δq . (2.17) T The equality holds for reversible change. Thus, expressing the heat quantity going in and out in the reversible change as δqrev , the relationship holds: dS ≥

δqrev (2.18) T This equation also serves as the definition of entropy. Substituting the relationship δqrev = TdS derived from Eq. (2.18) and Eq. (2.4) to Eq. (2.2), the first law of thermodynamics for the reversible change is expressed by dS =

dU = TdS − pdV .

(2.19)

2.2 Gas–Liquid Phase Equilibrium and Equilibrium in Liquid Phase

The entropy of perfect crystals of pure substances is zero at T = 0 K, which is known as the third law of thermodynamics. The molar entropy of compounds and elements at the temperature T is called standard entropy and expressed by S∘ . Table 2.3 cites standard entropy S298 ∘ (J K−1 mol−1 ) at 298.15 K together with the standard enthalpy of formation Δf H 298 ∘ . Using S∘ , the standard reaction entropy Δr S∘ can be defined as ∑ ∑ 𝜈i S∘ (i) − 𝜈i S∘ (i) (2.20) Δr S∘ = products

reactants

similarly to the standard reaction enthalpy given in Eq. (2.15). ∘ ) and standard molar entropy (S∘ ) at 298.15 K and Table 2.3 Standard enthalpy of formation (Δf H298 298 1 bar. Chemical species

∘ 𝚫f H298 (kJ mol−1 )

∘ 𝚫f H298 (kJ mol−1 )

∘ S298 (J K−1 mol−1 )

H

218.0

114.7

H2

0.00

130.7

HCO

44.2

224.3

CH2 O (HCHO)

−109.0

O(3 P)

249.2

161.1

218.8

HC(O)OH

−378.6

248.2

O2

0.00

O3

141.7

205.2

CH2 OO (Criegee Int.)

110

239.0

CH2 O2 (dioxirane)

OH

5.0

37.5

183.7

CH3 OH (g)

−201.0

HO2

11.9

228.1

CH3 OH (l)

−239.1

H2 O (g)

−241.8

188.8

CH3 OOH

−136.8

H2 O (l)

−285.8

70.0

HCN

132

201.8

H2 O2

−135.9

234.5

CH3 CN

74.0

245.1

NH2

186.2

194.9

CH3 ONO

−64.0

284.3 301.9

∘ S298 (J K−1 mol−1 )

Chemical species

NH3

−45.9

192.8

CH3 ONO2

−122.2

NO

91.1

210.8

CH3 OONO2

−62.8

239.9 276.5

NO2

34.0

240.2

C2 H2

227.4

200.9

NO3

74.7

258.4

C2 H4

52.4

219.3

N2 O 3

88.6

314.7

C2 H5

120.9

250.5

N2 O 4

11.1

304.5

C2 H6

−83.9

229.2

N2 O 5

14.4

353.5

CH3 CHO

−166.1

264.0

HNO

109.2

220.9

C2 H5 OH

−234.8

281.6

HNO2 (HONO)

−78.5

254.1

CH3 OCH3

−184.1

267.3 283.4

HNO3 (HONO2 )

−134.3

266.9

CH3 C(O)OH

−253

HO2 NO2

−52.7

297

(CHO)2

−212

CH3

146.7

194.0

CH3 OOCH3

−125.5

CH4

−74.5

186.4

CH3 C(O)OONO2 (PAN)

−240.1

CO

−11.5

197.7

C3 H6

166.1

CO2

−393.5

213.8

n- C3 H7

101.3

308.4 266.6 (Continued)

17

18

2 Fundamentals of Multiphase Chemical Reactions

Table 2.3 (Continued) Chemical species

∘ (kJ mol−1 ) 𝚫f H298

∘ (J K−1 mol−1 ) S298

i-C3 H7

86.6

281

C3 H8

−104.7

270.2

1-C3 H7 OH

−255.1

2-C3 H7 OH

−272.6

C2 H5 CHO

−185.6

CH3 C(O)CH3

−217.1

CH3 C(O)CHO

−271

295.5

CH2 CHCHO

−74.3

Cl

121.3

165.2

Cl2

0.0

223.1

HCl (g)

−92.3

186.9 236.5

HOCl

−74.8

Br

111.9

175.0

Br2 (g)

30.9

245.5

HBr

−36.3

198.7 248.0

HOBr

−80.5

I

106.8

180.8

I2 (g)

62.4

260.7

HI

26.5

206.6 255.0

HOI

−70.7

S

277.2

167.8

H2 S

−20.6

205.8

SO2

−296.8

248.2

SO3

−395.9

256.5

HOSO2

−375.7

294.1

H2 SO4 (g)

−732.7

311.3

Source: NASA-JPL Evaluation Number 18 (Burkholder et al. 2015).

2.2.1.3

Gibbs Energy

Equation (2.17) of the second law can be rewritten as δq ≤ TdS

(2.21)

and coupling it with Eq. (2.8) of the first law, we obtain δq = dU + pdV ≤ TdS

(2.22)

dU + pdV − TdS ≤ 0.

(2.23)

Here, the Gibbs energy is defined as a new state function of the system: G = H − TS = U + pV − TS

(2.24)

2.2 Gas–Liquid Phase Equilibrium and Equilibrium in Liquid Phase

Then dG can be expressed as dG = dU + pdV + V dp − TdS − SdT.

(2.25)

Since the change of G under constant temperature (dT = 0) and constant pressure (dp = 0) is dG = dU + pdV − TdS,

(2.26)

from Eqs. (2.23) and (2.26), then we can obtain dG ≤ 0.

(2.27)

The equality holds for the reversible change, and the above formula implies that the spontaneous change of the reaction proceeds to the direction of the decrease of Gibbs energy when the temperature and pressure are constant. The Gibbs energy change accompanied with chemical reaction is called reaction Gibbs energy Δr G. From the definition of Gibbs energy, Eq. (2.24), and the condition of spontaneous change under constant temperature and pressure, Eq. (2.27), the reaction Gibbs energy fulfills, Δr G = Δr H − TΔr S ≤ 0.

(2.28)

Since in atmospheric chemistry and laboratory experiments, chemical reactions proceed under a constant temperature and pressure in most of the cases, reaction Gibbs energy is often used. If Δr G is negative, the reactants convert spontaneously to the products, and if Δr G is positive, the reaction proceeds to the opposite direction. This means that even for the endothermic reactions with Δr H > 0, if Δr G in Eq. (2.28) is negative with the increase of entropy, the reaction may proceed in the forward direction. Combining the standard reaction enthalpy obtained by Eq. (2.15) and the standard reaction entropy given by Eq. (2.20), the standard reaction Gibbs energy is obtained by the following equation. (2.29) Δ G∘ = Δ H ∘ − TΔ S∘ . r

r

r

Further, similarly to the case of enthalpy, standard Gibbs energy of formation Δf G∘ can be defined using the standard reaction Gibbs energy for the formation of a compound from the most stable elements in the standard state. The standard Gibbs energy of formation for the element in the most stable state is zero as in the case of standard enthalpy of formation. From this, standard reaction Gibbs energy can be calculated by ∑ ∑ 𝜈 Δ G∘ (i) − 𝜈 Δ G∘ (i). (2.30) Δ G∘ = r

i

f

products

i

f

reactants

As mentioned later, standard reaction Gibbs energy is an important quantity closely related to the equilibrium constant. 2.2.1.4

Chemical Potential

The internal energy is a function of the number of moles of chemical species, n1 , n2 , …, nk , involved in the system when the number of moles in the system changes accompanying with the chemical reaction. Thus, for a chemical reaction, a term corresponding to

19

20

2 Fundamentals of Multiphase Chemical Reactions

the change of the chemical species is added to Eq. (2.19), and the internal energy change dU is expressed as ) k ( ∑ 𝜕U dU = TdS − pdV + dn. (2.31) 𝜕ni S,V ,nj(≠i) i i=1 Here, (𝜕U∕𝜕ni )S,V ,nj(≠i) expresses the partial differential of U with respect to ni under the conditions of constant S, V , and nj (j ≠ i). This is defined as chemical potential 𝜇i for a chemical species i. ( ) 𝜕U 𝜇i = . (2.32) 𝜕ni S,V ,nj(≠i) Then, Eq. (2.31) becomes dU = TdS − pdV +

k ∑

𝜇i dni .

(2.33)

𝜇i dni ,

(2.34)

i=1

From Eqs. (2.25) and (2.33), dG = V dp − SdT +

k ∑ i=i

and since under the constant temperature and pressure, dG =

k ∑

𝜇i dni ,

(2.35)

i=1

the chemical potential can be written as, ( ) 𝜕G 𝜇i = . 𝜕ni P,T,nj(j≠i)

(2.36)

Equation (2.36) is another definition of chemical potential. 𝜇i is the Gibbs energy change when the constituent i alone changes in 1 mol with no change of other constituents. In a single component system, Eq. (2.35) can be written as dG = 𝜇 dn, and integrating under the constant temperature and pressure, we obtain (2.37)

G = n𝜇.

Thus, the chemical potential of a single component system equals to the Gibbs energy per 1 mol. Therefore, chemical potential is an intensive quantity, a physical quantity that does not depend on the size of the system (the number of moles of chemical species in this case). For a multicomponent system, G can be shown as the total sum of chemical potential of each component multiplied by the number of moles of chemical species, as follows: k ∑ G= ni 𝜇i (2.38) i=1

Differentiating Eq. (2.38), we obtain dG =

k ∑ i=1

ni d𝜇i +

k ∑ i=1

𝜇i dni ,

(2.39)

2.2 Gas–Liquid Phase Equilibrium and Equilibrium in Liquid Phase

and from this equation and Eq. (2.35), the following relationship is derived at constant temperature and pressure: k ∑

ni d𝜇i = 0

(2.40)

i=1

Equation (2.40) is the special case of the Gibbs-Duhem equation and indicates that chemical potential of a certain component in a mixture cannot be changed independently from other components. 2.2.2

Chemical Equilibrium and Equilibrium Constant

2.2.2.1

Chemical Equilibrium

Assuming that the previous Reaction (2.13) is reversible, −−−−−−−−→ 𝜈A A + 𝜈B B ← −− 𝜈C C + 𝜈D D,

(2.41)

let us consider to which direction the reaction proceeds. As shown in the previous subsection, a spontaneous reaction under the constant temperature and pressure proceeds to the direction to decrease Gibbs energy. The Gibbs energy of the system can be expressed from Eq. (2.38) by using the chemical potential and the amount of substance (the number of moles) as G = nA 𝜇A + nB 𝜇B + nC 𝜇C + nD 𝜇D

(2.42)

Under the conditions of constant temperature and pressure, the incremental change of Gibbs energy accompanying with the reaction is expressed from Eq. (2.35) as dG = 𝜇A dnA + 𝜇B dnB + 𝜇C dnC + 𝜇D dnD .

(2.43)

From the relationship of the stoichiometry of the reaction, we obtain −

d nC d nA dn d nD =− B = = = d𝜉, 𝜈A 𝜈B 𝜈C 𝜈D

(2.44)

where 𝜉 is called the extent of reaction. The 𝜉 increases when the reaction proceeds to the forward direction and decreases when it proceeds to the reverse direction as is apparent from Eq. (2.44), and its value ranges from 0 to 1 mol. Using 𝜉, Eq. (2.43) becomes dG = (−𝜈A 𝜇A − 𝜈B 𝜇B + 𝜈C 𝜇C + 𝜈D 𝜇D ) d𝜉.

(2.45)

Since the spontaneous reaction proceeds to the direction of dG < 0, if 𝜈 A 𝜇A + 𝜈 B 𝜇B > 𝜈 C 𝜇C + 𝜈 D 𝜇D , the reaction proceeds to d𝜉 > 0, i.e. the reactants A and B change to the products C and D, and if 𝜈 A 𝜇A + 𝜈 B 𝜇B < 𝜈 C 𝜇C + 𝜈 D 𝜇D , it proceeds to the reverse direction, i.e. the products C and D change to the reactants A and B. Thus, the quantity in the parenthesis in Eq. (2.45) determines the direction of the reaction, and it corresponds to the reaction Gibbs energy mentioned in the previous subsection, i.e. Δr G = −𝜈A 𝜇A − 𝜈B 𝜇B + 𝜈C 𝜇C + 𝜈D 𝜇D .

(2.46)

When Δr G = 0, i.e. 𝜈C 𝜇C + 𝜈D 𝜇D − 𝜈A 𝜇A − 𝜈B 𝜇B = 0,

(2.47)

21

2 Fundamentals of Multiphase Chemical Reactions

Figure 2.1 Schematic diagram of Gibbs energy change for the reaction A ⇄ B as a function of the extent of reaction, 𝜉.

dG

Gibbs Energy, G


0) when destabilized. The activity coefficient 𝛾 i for the component i of the mixture is linked with excess molar Gibbs energy of the mixture with the relationship, ) ( 1 𝜕Gex ln 𝛾i = . (2.143) RT 𝜕ni T,p,nj(j≠i) According to the AIOMFAC model, total excess Gibbs energy of multi-component ex ex ex mixture is expressed as the sum of the contributions GLR , GMR , and GSR corresponding to the long-range (LR), mid-range (MR), and short-range (SR) interactions, including charged and noncharged chemical species in the solution with different geometrical configurations. ex ex ex Gex = GLR + GMR + GSR

(2.144)

From Eqs. (2.143) and (2.144) ln 𝛾i = ln 𝛾i LR + ln 𝛾i MR + ln 𝛾i SR . ex GLR

(2.145)

The long-range contribution is the interaction by Coulombic electrostatic force between charged ions. Ionic strength, I, of electrolyte solution is generally defined by using the molality mi and the number of charges zi of each ion as 1∑ 2 I= z m. (2.146) 2 i i i

37

38

2 Fundamentals of Multiphase Chemical Reactions

According to the Debye-Hückel theory, the activity coefficient of electrolyte solution at sufficiently low concentration is given by using the ionic strength (Pitzer 1991): √ (2.147) ln 𝛾i LR = −Azi 2 I. Here, A is the Debye-Hückel parameter having the dimension of kg1/2 mol−1/2 . From the above equation, the logarithm of ion activity coefficient is proportional to the 1/2 power to the ionic strength I, i.e. to the half power of the molality of ions. As the ionic strength becomes larger, the above limiting law of Debye-Hückel does not hold, and the activity coefficient of ions is approximated by the extended Debye-Hückel law (Fowler and Guggenheim 1949) as √ −Azi 2 I LR (2.148) ln 𝛾i = √ . 1+B I ex to the excess Gibbs energy is the term due to the The short-range contribution GSR intermolecular interaction between nonelectrolyte molecules in the aqueous solution. It was initially proposed as UNIQUAC (universal quasi-chemical equation) model by Abrams and Prausnitz (1975) and developed as UNIFAC (UNIQUAC Functional Group Activity Coefficients) model by Fredenslund et al. (1975). Since it is not realistic to obtain the activities of enormous number of various mixtures from interaction of each molecule, UNIQUAC model uses the concentration of functional groups instead of molecules as independent variable, which enables the estimation of activity coefficients in the mixed solutions. In the UNIQUAC and UNIFAC models, by generalizing Guggenheim’s quasi-chemical lattice model (Guggenheim 1952), the excess Gibbs energy is expressed as the sum of two contributions, combinatorial part Gex, C arising from geometrical size of molecules and residual part Gex, R arising from interaction between molecules, GSR ex = Gex,C + Gex,R

(2.149)

From this equation, the short-range contribution to activity coefficient of each compound can be expressed as ln 𝛾i SR = ln 𝛾i C + ln 𝛾i R .

(2.150)

ex The term of mid-range contribution GMR

contained in Eq. (2.144) for the excess Gibbs energy of AIOMFAC model is due to the indirect effect arising from the interaction between ions and permanent or induced dipoles. 2.3.1.1

Salting-in, Salting-out

As mentioned above, the uptake of nonelectrolyte gases to the aqueous phase is affected by the types and concentrations of ions in the aqueous solutions; some of electrolytes enhance the uptake of nonelectrolyte gases and some of them suppress the uptake as compared to the pure water. The enhancement effect is called salting-in and the suppression effect is called salting-out. The salting-out effect is well known to organic chemists as a method of adding inorganic salts as solute for the purpose of isolating organic compounds from solvent water. The salting-out effect can be expressed quantitatively by the Setschenow equation, ( 0) KH (2.151) = ks c c, log KH c

2.3 Reactions in the Liquid Phase

where K H 0 and K H c are Henry’s law constants in the pure water and electrolyte solution, respectively, k s c is the Setschenow coefficient (also called salting constant), and c is the molar concentration of ions in the aqueous solution. The Setschenow coefficients of organic compounds for several ions are cited in Perez-Tejeda et al. (1990) and Weisenberger and Schumpe (1996). In general, Henry’s law constants of typical nonpolar organic compounds such as methane, benzene, and halocarbons are smaller for the electrolyte solutions than for pure water (Peng and Wan 1998; Graziano 2008, 2009; Burkholder et al. 2015), thus showing the salting-out effect. Also the salting-out effect of O2 for many electrolyte aqueous solution including ocean water has been measured by Millero et al. (2002). On the other hand, a salting-in effect has been observed for tetra-alkyl ammonium chloride salt, whose solubility increases in electrolyte solution (Perez-Tejeda et al. 1990). Salting-out and salting-in effects correspond to positive and negative Setschenow coefficients, respectively. These changes of solubility for electrolytes are in general explained by the combined effect of nonelectrolytic substances on the electrostatic force and dispersion force of ions (Bockris et al. 1951; Masterton and Lee 1970 and references therein). Further, Setschenow equation, Eq. (2.151), is shown to be a specific case of more general dependence of Henry’s law constants on salt concentration by the derivation of equation based on the Kirkwood-Buff solution theory (Ruckenstein and Shulgin 2002). 2.3.2

Chemical Kinetics of Aqueous-Phase Reaction

Chemical reactions in the solution have characteristics largely different from those in the gas phase due to the presence of solvent. The presence of solvent influences reaction rates and pathways through the effect of diffusion rate of molecules in the solution, formation of complex in the transition state, and solvent effect such as cage effect. In this subsection, chemical kinetics of aqueous-phase reactions that are directly related to atmospheric chemistry are described. 2.3.2.1

Diffusion Process and Chemical Reaction Kinetics

Here we consider the chemical reaction between molecules A and B in the liquid phase: kenc kr −−−−−−−−→ A+B← −− AB −−−→ P kesc

(2.152)

In the reactions in solution, it is necessary for the reactant molecules, A and B, to encounter by diffusion in the solvent to form association complex AB. The complex AB returns back to the reactant system or proceeds to the product system with a certain probability. By representing each reaction rate constant as k enc , k esc , and k r as in Eq. (2.152) and applying the steady state approximation to the complex AB, we obtain d[AB] (2.153) = kenc [A][B] − kesc [AB] − kr [AB] = 0. dt From the equation, the concentration of the complex and formation rate of the product P are given by [AB] =

kenc [A][B] kesc + kr

(2.154)

39

40

2 Fundamentals of Multiphase Chemical Reactions

and kk d[P] = kr [AB] = r enc [A][B], dt kesc + kr

(2.155)

respectively. When we represent the formation rate of P as d[P] = k[A][B], dt the reaction rate constant k is expressed as k=

kr kenc . kesc + kr

(2.156)

(2.157)

When k r is sufficiently larger than k esc , k = k enc and Eq. (2.155) is given by d[P] (2.158) = kenc [A][B]. dt Thus, the reaction rate to form the product P equals the formation rate of the complex AB, and the overall reaction rate is largely affected by the diffusion rate of A and B to encounter in the solvent. Such reaction is called the diffusion-controlled reaction. Fick’s law of diffusion (Fick 1885; Bird et al. 2002) can be applied to the molecular diffusion in solution. The transport flux (number of molecules crossing unit area in unit time), J B , of a molecule B passing at the distance of radius r around a single molecule A is represented by taking the diffusion constant of molecule B as DB , as d [B(r)] , (2.159) dr where [B(r)] is the number density of B at the distance r from a molecule A. Multiplying J B by the surface area 4πr2 of a sphere of radius r, the flow rate of a molecule passing through per unit time, I B , is given by JB = −DB

d [B(r)] . (2.160) dr At r → ∞, [B (∞)] is thought to be equal to the number density of B, [B], in the bulk solution. Integrating Eq. (2.160) under this boundary condition, we obtain IB = −4πr2 DB

[B(r)] =

IB + [B]. 4πrDB

(2.161)

If we assume that the reaction of molecules A and B is sufficiently fast to occur every time when A and B collides, the collision occurs at r = a, the sum of the radius of A and B, leading to [B(a)] = 0, and we obtain IB = −4πaDB [B].

(2.162)

The minus sign of the right-hand side represents that B flows opposite to the direction of r. Neglecting the sign, I B represents the collision frequency of molecule B to the fixed molecule A. Actually, A exists in the solution at the number density [A], and considering that A also participates in the diffusion movement, the collision frequency between molecules A and B per unit volume is expressed as ZAB = 4πa(DA + DB )[A][B].

(2.163)

2.3 Reactions in the Liquid Phase

Here, DA is the diffusion coefficient of A. Assuming that for every collision reaction, the collision frequency given by Eq. (2.163) equals the formation rate of product P. Thus, for the diffusion-controlled reaction, d[P] = 4πa(DA + DB )[A][B], dt and the reaction rate constant k enc in Eq. (2.158) is expressed as kenc = 4πa(DA + DB ).

(2.164)

(2.165)

Taking the typical molecular diffusion coefficients of 2 × 10−9 m2 s−1 in the aqueous solution and molecular radius of 0.2 × 10−9 m for A and B (a = 0.4 × 10−9 m), the rate constant is given by k = 2 × 10−17 m3 molecule−1 s−1 , or 1 × 1010 M−1 s−1 (M = mol L−1 ). In other words, the fastest bimolecular reaction is the diffusion-controlled reaction with the rate constants of (1–3) × 1010 M−1 s−1 . As shown in Table 4.5, the reactions of OH radical with some organic compounds have large rate constants which are few times smaller than those for the diffusion-controlled reactions. In the case of ionic reactions of positive and negative ions in the aqueous solution (A+ + B− → AB), a term of electrostatic attraction potential energy U(r) is added to the term of diffusion flow rate in Eq. (2.160) to give ( ) d [B(r)] [B(r)] dU(r) 2 IB = −4πr DB + (2.166) dr kB T dr where k B is the Boltzmann constant, and U(r) is given by U(r) =

z A z B e2 . 4π𝜀r 𝜀0 r

(2.167)

Here, zA and zB are the electric charge of ions A and B, respectively, 𝜀0 is the dielectric constant in vacuum, and 𝜀r is the relative dielectric constant. From the integration of Eq. (2.166), the collision frequency of molecules A and B per unit volume is obtained as r0 [A][B], (2.168) ZAB = 4π(DA + DB ) ( ) r exp a0 − 1 and the rate constant of the bimolecular reaction of ions A+ and B− is given by r0 ( )

kenc = 4π(DA + DB ) exp

r0 a

(2.169) −1

instead of Eq. (2.165). Here, r0 is the distance where the Coulomb potential equals the thermal energy. For instance, considering the reaction of H+ and OH− in water, the diffusioncontrolled reaction rate constant, k enc = 4.9 × 1010 M−1 s−1 is obtained using the diffusion coefficients, 9.2 × 10−9 and 5.1 × 10−9 m2 s−1 for H+ and OH− , respectively, r0 = 7.1 × 10−10 m, and a = 7.5 × 10−10 m. Thus, the rate constants of ion reactions are even greater than the diffusion-controlled rate constants of the reactions between nonelectrolytes in water.

41

2 Fundamentals of Multiphase Chemical Reactions

2.3.2.2

Transition State Theory of Solution Reaction and Thermodynamic Expression

Chemical reactions in the gas and liquid phase can be modeled in general as ‡ −−−−−−−−→ A + B← −− AB → P.

(2.170)

‡

Here, AB is an association complex called activated complex formed in the course of the transformation of the reactants A and B to the product P, which corresponds to the energy maximum along the reaction coordinate. As shown in Figure 2.2, the reaction is thought to proceed over the energy barrier through the activated complex (cf. e.g. Akimoto 2016, pp. 23–31). The activated complex is also called the transition state of the reaction. The transition state theory assumes the chemical equilibrium between the reactants and the transition state, and the rate constant is treated thermodynamically. The rate equation of Reaction (2.170) can be written as d[P] = k[A][B]. (2.171) dt When Reaction (2.170) is the gas-phase reaction or solution-phase reaction between solutes fulfilling the condition of ideal dilute solution, the standard equilibrium constant K c ‡ on the molar concentration basis between the reactants and the activated complex is given by [AB]‡ ∕c∘ [AB‡ ]c∘ Kc ‡ = = . (2.172) ∘ ∘ ([A]∕c )([B]∕c ) [A][B] If we think the reaction rate is the product of the concentration of the activated complex [AB‡ ] and the frequency, 𝜈, of the activated complex passing through the energy barrier, the reaction rate formula is expressed as K ‡ [A][B] d[P] = 𝜈[AB‡ ] = 𝜈 c ∘ . dt c From this equation, the rate constant k of Eq. (2.171) becomes

(2.173)

𝜈Kc ‡ . (2.174) c∘ Meanwhile, using the molecular partition functions, qA , qB , and qAB ‡ , for A, B, and AB‡ , the equilibrium constant can be written as ( ) ΔE q ‡ Kc ‡ = AB exp − 0 , (2.175) qA qB kB T k=

Figure 2.2 Schematic diagram of chemical reaction pathway passing through the activation barrier for transition state (AB‡ ).

ABǂ

Energy

42

Ea A+B P

Reaction Coordinate

2.3 Reactions in the Liquid Phase

where ΔE0 is ΔE0 = E0 (AB‡ ) − E0 (A) − E0 (B).

(2.176)

The reaction from AB‡ to P is thought to proceed through the transition state by one vibrational mode along the reaction coordinate of the activated complex AB‡ . Since the frequency of molecular vibration along the reaction coordinate is very small so that h𝜈/k B T ≪ 1, the partition function qC of this vibration is written as qC =

kB T 1 . ( )≈ h𝜈 h𝜈 1 − exp − kB T

(2.177)

Putting the partition function of all other vibrational modes of the activated complex as qAB‡ , we obtain kB T q ‡. h𝜈 AB From Eqs. (2.175) and (2.178), we obtain ( ) ΔE0 kB T qAB‡ ‡ exp − . Kc = h𝜈 qA qB kB T qAB‡ =

From this equation and Eq. (2.174), ( ) ΔE k T q ‡ k = B ∘ AB exp − 0 hc qA qB kB T is obtained. Here, putting ( ) ‡ ΔE0 qAB‡ Kc = exp − , qA qB kB T k is obtained as k T ‡ k = B ∘ Kc , hc

(2.178)

(2.179)

(2.180)

(2.181)

(2.182)

‡

where K c is the equilibrium constant of the reactants and activated complex excluding the freedom of vibration related to the reaction coordinate. Defining the standard activation Gibbs energy Δ‡ G∘ as the change of Gibbs energy for the reacting process from the reactants to the transition state, the relationship between ‡ Δ‡ G∘ and K becomes c

‡ Δ G∘ = −RT ln K c ‡

(2.183)

and the thermodynamic expression formula of transition state theory is obtained: ( ) kB T Δ‡ G∘ k = ∘ exp − (2.184) hc RT The temperature dependence of reaction rate constant is expressed by the well-known Arrhenius equation, ( ) E k(T) = A exp − a . (2.185) RT

43

44

2 Fundamentals of Multiphase Chemical Reactions

In the Arrhenius equation, the preexponential factor A is called frequency factor and Ea is called activation energy. Taking logarithm of Eq. (2.185) and differentiating with respect to temperature, ln k = ln A −

Ea RT

(2.186)

E d ln k (2.187) = a2 dT RT are obtained. The relation of Arrhenius equation and the above expression derived from the transition state theory is as follows. Taking the logarithm of both sides of Eq. (2.182), ‡ kB + ln T + ln K c ∘ hc is obtained, and differentiating this with respect to temperature, we obtain

ln k = ln

(2.188)

‡

d ln k 1 d ln K c = + . (2.189) dT T dT In the case of the gas-phase reactions, as treated in Section 2.2.2, Eq. (2.90) holds for standard equilibrium constant on the molar concentration basis, and by putting the standard internal energy change accompanying the activation Δ‡ U ∘ , the second term of Eq. (2.189) can be expressed as ‡

d ln K c Δ‡ U ∘ . (2.190) = dT RT 2 The Δ‡ U ∘ can be obtained by using the enthalpy change Δ‡ H ∘ (standard activation enthalpy) and volume change Δ‡ V associated with the activation as Δ‡ U ∘ = Δ‡ (H ∘ − p∘ V ) = Δ‡ H ∘ − p∘ Δ‡ V . (2.191) ∘ ‡ ‡ ‡ For the gas-phase reaction, p Δ V = (Δ n)RT from the ideal gas law. Here, Δ n is the change of the amount of substance accompanying the activation. As shown in Reaction (2.170), Δ‡ n = −1 when the AB‡ is formed from A and B. Thus, if Reaction (2.170) is the gas-phase reaction, the following relationship can be obtained: Δ‡ U ∘ = Δ‡ H ∘ + RT (2.192) From these, Eq. (2.189) can be transformed to Δ‡ H ∘ + 2RT d ln k 1 Δ‡ H ∘ + RT = . (2.193) = + dT T RT 2 RT 2 Comparing Eqs. (2.187) and (2.193), the activation energy Ea is found to be related with the standard activation enthalpy by E = Δ‡ H ∘ + 2 RT. (2.194) a

Meanwhile, Eq. (2.184) shows the relationship between k and standard activation Gibbs energy Δ‡ G∘ . Δ‡ G∘ can be related to Δ‡ H ∘ and standard activation entropy Δ‡ S∘ as Δ‡ G∘ = Δ‡ H ∘ − TΔ‡ S∘ . (2.195)

2.3 Reactions in the Liquid Phase

Substituting this into Eq. (2.184), we get: ( ‡ ∘) ( ) kB T ΔS Δ‡ H ∘ exp exp − k= h R RT Substituting this into Eq. (2.194) results in the following: ( ‡ ∘) ( ) Ea − 2RT kB T ΔS k= exp exp − h R RT ( ‡ ∘) ( ) Ea kB T ΔS = exp(2) exp exp − h R RT

(2.196)

(2.197)

In the liquid-phase reaction, van’t Hoff’s equation holds approximately for the standard equilibrium constant as shown in Eq. (2.96), and the following equations are derived: ‡

d ln K c Δ‡ H ∘ = dT RT 2 Δ‡ H ∘ + RT d ln k 1 Δ‡ H ∘ = = + 2 dT T RT RT 2 E = Δ‡ H ∘ + RT a

Substituting Δ‡ H ∘ from Eq. (2.200) into Eq. (2.196), we get the following: ( ‡ ∘) ( ) Ea kB T ΔS exp exp − k = exp(1) h R RT

(2.198) (2.199) (2.200)

(2.201)

By interpreting the transition state theory thermodynamically in this way, a frequency factor of Arrhenius equation is found to be related to the entropy change Δ‡ S∘ accompanying the formation of the activated complex from reactants. Further, the diffusion-controlled reaction corresponding to every collision reaction is found to correspond to the reaction with the minimal activation energy (Ea ≈ 0) in the transition state theory. In the case of a reaction of solutes that do not fulfill the condition of ideal dilute solution, the equilibrium constant between the reactants and activated complex is expressed in terms of activities instead of molar concentrations: aAB‡ (c) 𝛾 ‡ (c) [AB‡ ]c∘ = AB (2.202) Kc ‡ = (c) (c) aA aB 𝛾A (c) 𝛾B (c) [A][B] Here, ai (c) is the molar-concentration-basis activity of chemical species i, and 𝛾 i (c) is its activity coefficient. From Eq. (2.202), we obtain [AB‡ ] =

Kc ‡ 𝛾A (c) 𝛾B (c) [A][B]. c∘ 𝛾AB‡ (c)

(2.203)

According to the transition state theory, using the rate constant k 0 for the reaction in the ideal gas or in the ideal dilute solution as expressed by Eq. (2.174), the rate constant k in the real solution is given by k = k0

𝛾A (c) 𝛾B (c) , 𝛾AB‡ (c)

(2.204)

45

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2 Fundamentals of Multiphase Chemical Reactions

which shows that k deviates from k 0 by the factor of activity coefficient ratio of the reactants and the activated complex. 2.3.3

Cage Effect and Aqueous-Phase Solvent Effect

We note here the effects of the presence of a solvent on chemical reactions in the aqueous phase, which brings different reactivity from that in the gas phase, as solvent effects in a broad sense. There are two effects: (i) the cage effect over which the diffusion is suppressed by the solvent and active species such as radicals are confined in the solvent cage to retard the reaction with other reactants; and (ii) the solvent effect in a narrow sense, in which the transition state of the reaction is affected by the solvation, and the reactivity and reaction rate are greatly changed. Since the liquid-phase reaction that is important in atmospheric chemistry is the aqueous-phase reaction, we discuss the solvent effect here only for water solvency. In some cases of the aqueous-phase reactions, a water molecule hydrates a reactant molecule to give different reaction rates and pathways. This case is thought to be a reaction of a different molecule, so that it is not included in the solvent effect here. A typical example of this case is the reaction of OH radicals with the hydrated carbonyl compounds (diols, cf. Section 2.2.4) in the aqueous phase, which will be mentioned in Sections 4.2.4–4.2.6. The absorption spectra of molecules in the aqueous phase are naturally quite different from those in the gas phase when the hydrated molecules are formed. For example, the characteristic bands in the 250–350 nm region ascribed to the carbonyl group observed in the gas phase (cf. Akimoto 2016, pp. 94–102) disappear for diols in the aqueous phase. Since diols do not have the absorption bands in the longer wavelength region than 290 nm, they are not photolyzed in the troposphere (cf. Section 4.2.5). When such hydration reaction does not occur, the absorption spectrum in the aqueous phase does not change drastically from that in the gas phase, but a shift of absorption bands and change in absorption cross sections are seen in general, which affect the photolysis rates in aerosols. Particularly in the case that fine rotational-vibrational bands due to predissociation of the excited molecules are seen in the gas-phase spectrum (cf.Akimoto 2016, pp. 13–17), they disappear in general to give continuum absorption in the aqueous phase. Such changes in the absorption bands in the aqueous phase are due to the effect of electric field of surrounding water molecules (Stark effect) and to the effect of shortening of the lifetime of the excited state to give broader absorption bandwidth (Franck and Rabinowitsch 1934). 2.3.3.1

Cage Effect

In order for the active species such as atoms and radicals formed in either photolysis or thermal decomposition: AB + hν → [A ∙ + ∙ B]cage → A ∙ + ∙ B

(2.205)

AB → [A ∙ + ∙ B]cage → A ∙ + ∙ B,

(2.206)

to react with other solute molecules, they have to escape from the solvent cage and encounter the solute molecules. A phenomenon of the decrease of effective photolysis yield due to the recombination between the product species formed in the photolysis has early been found (Franck and Rabinowitsch 1934), and became called cage effect

2.3 Reactions in the Liquid Phase

later (Herk et al. 1961). The cage effect is greatly affected by the size of the radicals and the viscosity of solvents; the cage effect becomes larger as the size of active species and viscosity of solvents increase. As a typical example of the cage effect in organic solvents, photolysis of diazomethane (CH3 )2 N2 at 5 × 10−3 M in 1,4-cyclohexadiene (cyclo-C6 H8 ) has been reported (Herk et al. 1961). Photolysis of diazomethane at ∼360 nm gives only methane (CH4 ), ethane (C2 H6 ), and nitrogen (N2 ) in the 1,4-cyclohexadiene solvent as well as in the gas-phase, and the reaction mechanism has been thought as follows: (CH3 )2 N2 + hν → 2 [CH3 ⋅ CH3 ]cage + N2 [CH3 ⋅ CH3 ]cage → C2 H6 → 2 CH3 CH3 + cyclo-C6 H8 → CH4 + cyclo-C6 H7 ⋅ CH3 + CH3 + M → C2 H6 + M.

(2.207) (2.208a) (2.208b) (2.209) (2.210)

The relative quantum yields of CH4 /N2 , 2C2 H6 /N2 , and (CH4 + 2C2 H6 )/N2 are 1.81, 0.03, and 1.85 in the gas phase while they are 0.59, 1.29, and 1.88 in the liquid phase. In the liquid phase, production of C2 H6 due to the cage reaction (2.208a) predominates while in the gas phase the formation of C2 H6 due to the mutual reaction of CH3 is almost negligible, and CH4 formation by the reaction of CH3 to abstract hydrogen atom from the CH2 groups of 1,4-cyclohexadiene (Reaction (2.209)) predominates. As for the kinetic analysis of the reactions in solution including the cage effect, a general model has been proposed by Khudyakov et al. (2010), and the comparison with the real-time tracing experiment in organic solvent using pulsed-laser photolysis has been made (Levin et al. 1989). As an example of the cage effect directly relevant to atmospheric chemical reactions, the quantum yield of the photolysis of nitrate ion NO3 − decreases in water. Photolysis of NO3 − in water is thought to proceed as NO3 − + hν → [NO2 − + O]cage → NO2 − + O

(2.211)

NO3 + hν + H → [NO2 + OH]cage → NO2 + OH,

(2.212)

−

+

and an O atom and OH radical are formed together with NO2 − and NO2 , respectively. The quantum yields of the formation of O and OH in these reactions have been obtained as Φ(O) = ∼1 × 10−3 and Φ(OH) = ∼0.01 from the yield of ethene and acetone using cyclopentene and 2-propanol as the scavenger, respectively (Warneck and Wurzinger 1988; Nissenson et al. 2010). The reason of small formation yields of O and OH is presumed that the most of them recombine with the other products, NO2 and NO2 − , returning to the reactant, NO3 − , in the solvent cage (Nissenson et al. 2010). As an empirical proof, a sufficient amount of Br− has been added to the system. The Br− captures OH in the cage to form Br2 − : 2Br− + OH → Br2 − + OH− , −

(2.213)

and the formed Br2 is easy to escape from the solvent cage to the bulk water. When DMS that is reactive to Br2 − is added, the degradation of DMS has been shown to accelerate (Bouillon and Miller 2005; Das et al. 2009). A similar cage effect has been reported to the photolysis of FeOH2+ in the aqueous phase (Nissenson et al. 2010).

47

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2 Fundamentals of Multiphase Chemical Reactions

The above-mentioned photolysis of NO3 − in the aqueous phase has been paid attention in atmospheric chemistry from the point of NO2 formation in the photolysis of snow ice in the Arctic and Antarctic (cf. Section 6.4.1). When NO3 − is present at the air-ice interface, the number of surrounding water molecules is smaller than in the bulk water, the cage effect is expected to decrease, and the experimental and theoretical studies from the point of molecular chemistry have recently been conducted (Wingen et al. 2008; Miller et al. 2009). 2.3.3.2

Solvent Effect in the Aqueous Phase

In atmospheric chemistry, reactions in the aqueous phase in cloud/fog and hydrous aerosols are particularly concerned. In solution solvent molecules are attracted around a solute molecule by the short-range interaction as described in Section 2.3.1 to form a layer of solvent molecules, which is called solvation. The change of thermodynamic quantities by the solvation of reactant molecules and activated complex (transition state) can cause the change of reaction pathways and reaction rate in the liquid phase. The solvent effect well-known in general organic chemistry is composed of nonspecific solvent polarity represented by the relative dielectric constants and specific solute-solvent interaction such as hydrogen bonding capacity and electron donor acceptor interaction. The empirical parameters based on these interactions have been proposed and used (Gutmann and Wychera 1966; Kamlet and Taft 1976; Laurence et al. 1994). If a solvent parameter can be defined for which a linear relationship holds for the free energy difference between the solvated reactant system and activated complex, it would be useful for the estimates of reaction rates and equilibrium constants. The solvent parameters based on such consideration have been proposed and used (Grunwald and Winstein 1948; Winstein et al. 1951). Solvent effects in organic chemistry have been summarized in books (Reichardt and Welton 2010; Buncel and Stairs 2015). The solvents used widely in organic chemistry can be divided into two classes, protic solvents such as water, alcohols, and carboxylic acids, which have hydrogen atoms combined with a hetero atom and are easy to solvate by hydrogen bonding, and aprotic solvents which do not have such hydrogen atoms. Further, aprotic solvents are divided into polar solvents (e.g. acetone, acetaldehyde, nitromethane, etc.), low-polar solvents (ethers, haloalkanes, acetic acid esters, etc.), and nonpolar solvents (alkanes, cycloalkanes, benzene, toluene, carbon tetrachloride, etc.) according to the relative dielectric constants. Water has a very large dielectric constant (𝜀 = 80.1) and has a strong hydrogen bonding ability, so that it is one extreme of solvents, and the reactions in the aqueous phase attract much interest from the point of the difference from those in the gas-phase and in organic solvents. Comparing the reactions in the gas and those in the liquid phase, the gas phase reaction proceeds on the potential energy surface for the isolated molecules, while in the solution it proceeds on the potential surface which deviates by an amount of solvation enthalpy Δsolv H for the whole reaction pathway. As a typical example in which the solvent effect is theoretically calculated, the following bimolecular nucleophilic reaction (so called SN 2 reaction) of CH3 Br with OH− can be considered. In the aqueous phase, this reaction is considered as the reaction between a water-solvated OH− , OH− ⋅(H2 O)n , and CH3 Br to produce CH3 OH and a water-solvated Br− , OH− ⋅ (H2 O)n + CH3 Br → [OH ⋅ ⋅ ⋅ CH3 ⋅ ⋅ ⋅ Br]− ⋅ (H2 O)n → CH3 OH + Br− ⋅ (H2 O)n .

(2.214)

2.3 Reactions in the Liquid Phase

On the other hand, Henchman et al. (1983) found that the reaction of CH3 Br with OH− ⋅H2 O in the gas phase produces Br− rather than Br− ⋅(H2 O) as the major product as follows: OH− ⋅ H2 O + CH3 Br → [OH ⋅ ⋅ ⋅ CH3 ⋅ ⋅ ⋅ Br]− ⋅ (H2 O) → CH3 OH + Br− + H2 O. (2.215) Bohme and Mackay (1981) experimentally determined the rate constant of the gas-phase reaction between CH3 Br and OH− ⋅(H2 O)n for the different level of hydration (n = 0–3) and proposed the semiquantitative potential energy change for the reactions in agreement with their measured rate constants. Figure 2.3 shows the schematic potential energy change along the reaction coordinate for the reaction between OH− and CH3 Br at various degree of hydration. As shown in Figure 2.3, nonhydrated OH− and CH3 Br form an energetically stable associated complex, and the transition state energy is lower than the reactant system (Δ‡ H < 0). Therefore, the reaction proceeds spontaneously with a negative activation energy. A very large reaction rate constant of the gas-phase reaction, 1.0 × 10−9 cm3 molecule−1 s−1 , has been reported for n = 0 (Bohme and Mackay 1981). As the number of H2 O molecules solvating OH− increases to n = 1 and 2, the stabilization energy of the associated complex of OH− and CH3 Br decreases, yielding the transition energy higher than the reactant system, so that the reaction rate constant is one-half for n = 1 and one-tenth for n = 2 as compared to n = 0. In contrast, in the aqueous-phase reaction, the experimental value of activation energy is Ea = 96 kJ mol−1 (23 kcal mol−1 ) and the reaction rate constant is reported to be 12 – OH •CH 3Br

OH –•CH3Br

–

Potential energy/(kcal mole –1 )

0

OH +CH3Br

CH3H•Br – HO C Br

CH3OH+Br–

–20 OH –•H2O –

–40

OH •(H2O)2 –

OH •(H2O)3

Br –+CH3OH

–60

Br –•H2O Br –•(H2O)2

–80

Br –•(H2O)3 –100 –

OH •(H2O)n

23

–120 Br –•(H2O)n –140

Reaction Coordinate

Figure 2.3 Schematic potential energy change along the reaction coordinate for the nucleophilic displacement reaction between OH− and CH3 Br at various degree of hydration. Source: Adapted with permission from Bohme and Mackay (1981). Copyright 1981 American Chemical Society.

49

50

2 Fundamentals of Multiphase Chemical Reactions

orders of magnitude smaller than in the gas phase (Bathgate and Moelwyn-Hughes 1959; Bohme and Mackay 1981). Although the above reaction for n ≥ 2 in the gas phase may proceed as below (Henchman et al. 1983), OH− ⋅ (H2 O)n + CH3 Br → CH3 OH + Br− + n H2 O,

(2.216)

which does not correspond to the product system shown in Figure 2.3, the qualitative feature of the change of the potential energy curve for different number of solvated H2 O is thought to be represented in the figure. Similar hydration effect for the SN 2 reactions in the gas phase, X− ⋅ (H2 O)n + CH3 X → XCH3 + X− ⋅ (H2 O)n

(2.217)

has been studied for the symmetric halogen substitution reaction with X = Cl and I theoretically (Morokuma 1982) and experimentally (Doi et al. 2013). Since the potential energy decrease of the associated complexes and transition states is smaller than that of the reactant system when one or two H2 O molecules hydrate X− , similar inhibition of the SN 2 reaction by the hydration has been obtained. In order to discuss the effect of water solvent from the viewpoint of solvent effect on organic chemistry, it would be most appropriate to take up the Diels-Alder reaction. The Diels-Alder reaction is the cyclic addition of an alkene to a conjugated diene to form a six-membered cyclic compound (cf. Section 4.3.1). Rideout and Breslow (1980) found that the rates of the Diels-Alder reactions of acrolein (ACR) and methyl vinyl ketone (MVK) with cyclopentadiene in water, which are shown as,

+

O

O

(2.218)

+

O

O

(2.219)

are 30 and 740 times larger than those in the hydrocarbon solvents. This discovery is the kickoff of organic chemistry reactions in the aqueous phase to attract high attention. From this reason, Diels-Alder reaction is the best-studied cyclic addition reactions theoretically (e.g. Chiappe et al. 2010) and their reaction rates, positional selectivity, and stereo-selectivity are the benchmark of solvent effect studies. As for the reason of the increase of reaction rate by changing the solvent to water, many discussions have been made (Otto and Engberts 2000; Chandrasekhar et al. 2002). One of them is the decrease of activation energy due to the enforced hydrophobic effect (Rideout and Breslow 1980; Blokzijl et al. 1991). The enforced hydrophobic effect means the effect that hydrophobic organic molecules become easier to associate and bind with each other by being surrounded by polar molecules. On the other hand, recent theoretical calculations suggest that the cause of the increase of rate constant in the aqueous

2.4 Uptake Coefficient and Resistance Model

phase is mainly due to the decrease of activation energy by the hydrogen bonding to the transition state for the molecules that are easy to form hydrogen bonding such as ACR and MVK. For instance, theoretical calculation for the reaction of cyclopentadiene and ACR showed that among the reduction of activation energy (ΔEa,298 ) from the gas to the aqueous phase, the contribution of the hydrogen bonding and the enforced hydrophobic effect are estimated to be ca. 50% and 30%, respectively (Kong and Evanseck 2000). According to the calculation by Chandrasekhar et al. (2002), the decrease of activation free energy when the solvent is changed from organic to water solvent is 6.3 and 11.7 kJ mol−1 for ACR and MVK, which agree well with the experimental values of 8.8 and 15.9 kJ mol−1 (Rideout and Breslow 1980), respectively. Thus, it is presumed that the hydrogen bonding to the transition state is the main contributor and the enforced hydrophobic effect contributes less to the decrease of activation free energy. As a new example of solvent effect related to the water solvent, the reaction rate of Claisen rearrangement is found to be much larger when the water and organic reactant molecules become an emulsion state as compared to homogeneous water solvent (Narayan et al. 2005). The similar effect has also been found for aldol reaction (Mase et al. 2006) and 1,3-dipolar-cycloaddition reaction (González-Cruz et al. 2006). These reactions are called “on water” reaction instead of in water, and the theoretical analysis has been made by Jung and Marcus (2007). As for the interface of water and hydrophobic molecules, it has been shown by sum-frequency generation (SFG) spectroscopy (cf. Section 6.2.2) that about 25% of surface H2 O molecules have one dangling bond (Shen and Ostroverkhov 2006). Such a dangling OH bond combines with the transition state by hydrogen bonding to decrease the activation energy, and the “on water” reaction rate is a factor of 105 larger than the rate in the neat organic solvent and 600 times larger than that in the homogeneous aqueous phase (Jung and Marcus 2007).

2.4 Uptake Coefficient and Resistance Model Various processes are related to the multiphase reactions of gaseous molecules cooperating with liquid/solid particles. The first step of the multiphase reaction is the collision of a molecule in the gas phase to the surface of a particle. A part of colliding molecules are adsorbed on the particle surface. If the particle is solid, the adsorbed molecule can react with another adsorbed molecule or participate in surface reaction with a constituent molecule of the particle. When the particle is liquid, the adsorbed molecule participates in surface reaction, as in the case of solid particle, or it is absorbed into the inside of the liquid and can react with a molecule in the liquid. In order to distinguish the interior of the liquid from the surface, it is called as bulk liquid. In Figure 2.4, various processes related to the multiphase reaction such as collision to the surface, adsorption to and desorption from the surface, and absorption into the bulk are represented by the fluxes, J coll , J ads , J des , and J abs , respectively (Kolb et al. 2010). Also, production and loss of molecules at the surface are shown by Ps and Ls , and those in the bulk are shown by Pb and Lb , respectively. On the basis of these surface and bulk processes, the net flux J net of molecules transferred from the gas phase to a particle are shown by J net = J ads − J des . The kinetics of the reaction between a molecule in the gas phase and a liquid/solid particle has been treated by a so-called resistance model, in which the uptake rate of a gaseous molecule onto the particle surface as well as the rates of mass transfer and

51

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2 Fundamentals of Multiphase Chemical Reactions

Jcoll = 1 ux[X(g)] 4 Jads = 𝛼surf Jcoll

gas phase

Jabs = 𝛼bulk Jcoll Ps, Ls

Jdes= kdes {X(surf)} Jnet = 𝛾 Jcoll = Jads–Jdes

surface/interface Pb, Lb particle bulk phase

Figure 2.4 Schematic diagram of resistant model for gas–liquid multiphase reactions. Source: Adapted from Kolb et al. (2010). Copyright 2010 Author(s). Creative Commons Attribution 3.0 License.

reaction within the particle have been formulated. In this section, heterogeneous reactions, in which the molecular-level processes at the air-particle interface are not taken into consideration, are mentioned, and the resistance model including the microscopic processes at the interface will be described later in Section 2.5.2. As for the treatment of the uptake of a gaseous species into the aerosol particles and surface chemical reactions using the resistance models, reviews are available in Ammann et al. (2003), Davidovits et al. (2006), and Pöschl et al. (2007). 2.4.1

Accommodation Coefficient and Uptake Coefficient

As described above, the multiphase reaction between a gas-phase molecule and a condensed-phase particle is initiated by the adsorption of the colliding molecule to the particle surface. When a gaseous molecule collides to a particle, fundamental parameter of molecular theory determining the transfer rate of the molecule to the liquid/solid particle is called mass accommodation coefficient, which is defined by 𝛼=

Number of molecules taken up by the liquid∕solid surface . Number of molecules colliding with the liquid∕solid surface

(2.220)

Until the middle of 1990s, reactions between a gaseous molecule and a liquid particle had been interpreted as an absorption of a gaseous molecule to the bulk liquid followed by a bulk liquid-phase reaction, and the accommodation process was considered as one of elementary processes. In recent years, however, the importance of reaction processes at the liquid particle surface has been recognized, and the mass accommodation is treated in general as two separate processes. The first step is the adsorption of a gaseous molecule to the surface of a particle. The adsorbed molecule is combined to the surface with a weak interaction such as van der Waals force or hydrogen bonding. The second step is the uptake of the adsorbed molecule into the bulk liquid by means of complex formation or solvation. The first step is now called the surface mass accommodation process, and the overall process, including both of the first and second processes, is proposed to be called bulk mass accommodation (Kolb et al. 2010; Crowley et al. 2010). According to this distinction, the parameter for each accommodation process is designated as 𝛼 surf and 𝛼 bulk , respectively, which will be used in the subsequent sections to treat the surface processes separately from those in the bulk liquid.

2.4 Uptake Coefficient and Resistance Model

The bulk mass accommodation coefficient is in general possible to be determined by the molecular science calculation but is difficult to be obtained experimentally. This is because the several processes following the bulk accommodation process affect the uptake rate of a gaseous molecule to the condensed phase. As a result, a quantity obtained in experiments is the uptake coefficient 𝛾, defined by the following equation as the number of molecules lost from the gas phase after the uptake to the surface versus the number of colliding molecules. 𝛾=

Number of molecules lost to the liquid∕solid surface Number of molecules colliding with the liquid∕solid surface

(2.221)

The net uptake coefficient as defined here is the resultant of the above bulk accommodation process and the subsequent processes such as diffusion and reaction in the liquid phase. Thus, it changes with the coverage of the surface by molecules and is dependent on concentrations of reactants and reaction time. The initial uptake coefficient obtained experimentally is often expressed by 𝛾 0 . It should be cautioned that the experimentally obtained 𝛾 0 depends on the time scale of the experimental method. The uptake coefficient controlled by surface or bulk reaction is sometimes expressed by 𝛾 r . The molecular flux J coll (molecules cm−2 s−1 ) colliding to the liquid/solid surface per unit time and unit surface area is 1 Jcoll = uX [X(g)]. (2.222) 4 Here, uX (cm s−1 ) and [X(g)] (molecules cm−3 ) are the mean thermal velocity and the number density, respectively, of species X in the gas phase. uX is given from the Boltzmann distribution in the gas kinetic theory as ( )1∕2 8RT . (2.223) uX = πMX Here, T is absolute temperature, MX is the molar mass of X, and R is the gas constant. Therefore, using the uptake coefficient 𝛾, a molecular flux J net (molecules cm−2 s−1 ), the net number of molecules taken to the particle per unit time and unit surface area is 1 (2.224) 𝛾u [X(g)]. 4 X Multiplying the surface area density Ap (cm2 cm−3 ) of particles contained in the gas phase to J net , the loss rate (molecules cm−3 s−1 ) of molecules from the gas phase is obtained. Thus, representing the loss rate of gas-phase molecules by the equation for the pseudo-first-order process, Jnet =

d[X(g)] (2.225) = −khet [X(g)], dt the pseudo-first order rate constant k het (s−1 ) of the heterogeneous process can be expressed as 1 (2.226) 𝛾u A . 4 X p Accordingly, the value of 𝛾 can be obtained experimentally from Eq. (2.226) by using experimental value of k het and the values of uX and Ap . When the uptake on the surface is very large and the concentration gradient of X in the gas phase arises near the surface, khet =

53

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2 Fundamentals of Multiphase Chemical Reactions

a correction is necessary to the above treatment. In the resistance model mentioned in the following subsection, a correction is incorporated as resistance due to the gas-phase diffusion, 1/Γdiff . Surface area density Ap can be obtained for spherical particles such as liquid by ∞

Ap =

∫0

4πrp 2 Np (rp ) d rp ,

(2.227)

where N p (rp ) is the number density distribution function of particles with a range of radius rp ∼ rp + drp . However, most of atmospheric solid particles are nonspherical and if the surface is porous, actual surface area is much larger than the geometrical area. In such a case, it is a big problem that the experimental 𝛾 values differ largely depending on the used value of Ap . 2.4.2

Resistance Model

Considering that the fluxes corresponding to each process for uptake of gaseous molecules to liquid/solid surface followed by the liquid-phase reactions are independent, a model expressing the coupling of these processes by analogy with the coupling circuit of electric resistance is called resistance model (Finlayson-Pitts and Pitts 2000; Pöschl et al. 2007, and references therein). A prototype of the resistance model is a treatment of Danckwerts (1951) in 1950s, and he proposed for the first time an analytical formula for the uptake rate of gaseous species into the liquid phase based on the heat transfer equation, taking into consideration the bulk mass accommodation, Henry’s law solubility, and liquid-phase reactions of dissolved molecules. Figure 2.5 shows a schematic diagram of the resistance model considering the multi-phase reaction processes for a liquid droplet. As shown in the figure, the multi-phase reaction between a gaseous molecule and a liquid droplet involves: (i) transport and diffusion of a gaseous molecule to the droplet surface; (ii) bulk accommodation at the droplet surface; (iii) physical dissolution and diffusion into the bulk liquid; and (iv) chemical reaction process in the bulk liquid phase. In addition, the reaction at the gas–liquid interface could be involved, which will be treated in the next subsection. 1 Γsol

Gas-phase diffusion

1 Γdiff

Bulk mass accommodation

1 αbulk

Dissolution/ Liquid-phase diffusion

Chemical reaction

1 Γrxn

Figure 2.5 Schematic diagram of resistance model for gas-liquid multiphase reactions.

2.4 Uptake Coefficient and Resistance Model

The resistance model is a technique to treat a series of these processes kinetically. In this model, the ratio of the flux of each process to the collisional flux of gaseous molecules to the interface is expressed by the “conductance (Γ).” The uptake coefficient 𝛾 of a gaseous molecule is expressed by a serial- and parallel-coupling of the “resistance,” the reciprocal of the conductance. 1 1 1 1 + + = 𝛾 Γdiff 𝛼bulk Γsol + Γrxn

(2.228)

Here, 𝛼 bulk is the bulk mass accommodation coefficient described in the preceding subsection, and Γdiff , Γsol , and Γrxn are the conductance corresponding to the diffusion of gas-phase molecules to the interface, the physical dissolution and diffusion of the captured molecules from the interface to the bulk liquid phase, and the reaction in the bulk liquid, respectively. In the case that the processes after the bulk mass accommodation process are very fast and the uptake is limited only by gaseous diffusion, the diffusion rate of gaseous molecules to the surface of a spherical particle with a radius rp is given by 4πrp Dg [X(g)] (molecules s−1 ) using the diffusion coefficient, Dg (cm2 s−1 ). Thus, the number of gaseous molecules transported to the interface by the gas-phase diffusion per unit time and unit area, namely, the gaseous diffusion flux, J diff (molecules cm−2 s−1 ), is given by Jdiff =

4πrp Dg 4πrp

2

[X(g)] =

Dg rp

[X(g)].

(2.229)

The diffusion conductance near the interface Γdiff is given by normalizing J diff by the collisional flux to the surface J coll , ( ) 4Dg 4Dg πMX 1∕2 Jdiff Γdiff = = = . (2.230) Jcol rp uX rp 8RT In this equation, ux is expressed as Eq. (2.223) based on the Boltzmann distribution function. For a rapid uptake process, however, the velocity distribution is distorted from the Boltzmann distribution. Considering this distortion, Eq. (2.230) would be rewritten as ( ) rp uX 1 −1 Γdiff = − . (2.231) 4Dg 2 Further, Γsol and Γrxn are represented by the following equations (Danckwerts 1951; Davidovits et al. 2006). √ 4KH RT Dliq Γsol = (2.232) uX πt √ 4KH RT Γrxn = kbulk I Dliq (2.233) uX Here, K H (M atm−1 ) is the Henry’s law constant, Dliq (cm2 s−1 ) is the liquid-phase diffusion constant, and R is the gas constant (atm M−1 K−1 ). t in the formula of Γsol is the gas-liquid interaction time and k bulk I in Γrxn is the liquid phase pseudo-first order reaction rate constant (s−1 ), which is given by k bulk I = k bulk II [Y], where k bulk II (M−1 s−1 ) is

55

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2 Fundamentals of Multiphase Chemical Reactions

the second-order rate constant, and [Y] (M) is the concentration of reactant Y in the liquid phase. Γsol is the solubility-limited conductance depending on the solubility of a molecule to the solution as well as on the concentration of the molecules in the solution, so that it is a time-dependent parameter as seen in Eq. (2.232). Therefore, in the case that only physical absorption occurs as a bulk process, Γsol approaches zero as the bulk liquid approaches the saturation condition with time t. Meanwhile, although Γrxn also depends on the gas-liquid interaction time, it approaches a limiting value when k bulk I t ≫ 1, and becomes independent of time as shown in Eq. (2.233). If Γsol ≪ Γrxn , the net uptake coefficient 𝛾 in Eq. (2.228) becomes 1 1 1 1 + + , (2.234) = 𝛾 Γdiff 𝛼 Γrxn and 𝛾 does not depend on time.

2.5 Physical Chemistry of Interface Reaction For the multiphase reactions in the atmosphere, it is important to consider the microscopic processes at the air–water interface. In this section, after describing the general Langmuir-Hinshelwood mechanism and Eley-Rideal mechanism, interface reaction within the framework of the resistance model described in Section 2.4.2 and thermodynamics of the surface tension and accommodation coefficient will be explained. Since the water vapor pressure in equilibrium with an aqueous droplet changes with the surface tension, the surface tension is known to be an important parameter relevant to new particle formation, particle growth, and CCN activity, which will be mentioned in Chapter 7. Detailed descriptions on the structure and thermodynamical treatment of liquid surface are available in the books by Adamson and Gast (1997) and Butt et al. (2013). 2.5.1

Langmuir-Hinshelwood Mechanism and Eley-Rideal Mechanism

The first step of the heterogeneous interface reaction involving the adsorption of gaseous molecule X at the surface is expressed as kads −−−−−−−−→ X (g) ← −− X (surf), kdes

(2.235)

where X (g) and X (surf ) are the molecules in the gas-phase and at the surface, and k ads (cm3 molecule−1 s−1 ) and k des (s−1 ) are the adsorption and desorption rate constant, respectively. The change of surface concentration of X(surf ) can be expressed by the difference of adsorption flux J ads (molecules cm−2 s−1 ) and desorption flux J des (molecules cm−2 s−1 ). Here we assume that the gas-phase diffusion is not rate-limiting. Then, J ads is proportional to [X(g)] and the fraction of unoccupied adsorption sites. When the gas-phase diffusion affects the mass transfer, concentration gradient arises near the surface, and [X(g)] should be replaced by [X(gs)], the concentration of X near the surface. The concentration of the unoccupied adsorption sites at the surface can be represented by the difference between the overall surface concentration of adsorbed free surface sites {SS} (molecules cm−2 ) and {X(surf )}, the surface concentration of adsorbed X. Here, the

2.5 Physical Chemistry of Interface Reaction

surface concentration (number of molecules per unit area) is expressed by { } distinguishing from the number density of molecules per unit volume. ) ( {X(surf)} (2.236) {SS} = (1 − 𝜃X ){SS} {SS} − {X(surf)} = 1 − {SS} where 𝜃 X is the surface coverage defined by 𝜃X =

the number of sites occupied by X on the surface {X(surf)} = . {SS} the total number of adsorption sites on the surface (2.237)

From these, J ads can be expressed by using the adsorption rate constant k ads as Jads = kads (1 − 𝜃X ) {SS} [X(g)].

(2.238)

In the literature on heterogeneous reactions of atmospheric chemistry, k ads (1 − 𝜃 X ){SS} is often represented by k a 0 (1 − 𝜃 X ) or k a with a unit cm s−1 . In this case, Eq. (2.238) is expressed as Jads = ka 0 (1 − 𝜃X )[X(g)] (2.239)

= ka [X(g)].

Here, k a = k ads (1 − 𝜃 X ){SS}, and k a 0 = k ads {SS} corresponds to k a when 𝜃 X = 0. As shown in this equation, it should be noted that k a changes depending on the surface coverage 𝜃 X . Desorption flux J des is proportional to the surface concentration {X(surf )}, and since {X(surf )} = 𝜃 X {SS}, J des is represented by Jdes = kdes 𝜃X {SS},

(2.240)

where k des is the desorption rate constant. Based on the above discussion, the following equation is available for the time variation of {X(surf )}. d{X(surf)} = Jads − Jdes dt = ka 0 (1 − 𝜃X )[X(g)] − kdes 𝜃X {SS} (2.241) When the adsorption flux and desorption flux are equal, i.e. when the adsorptiondesorption equilibrium is established, the Langmuir adsorption isotherm is obtained by taking d{X(surf )}/dt = 0. 𝜃X =

[ka 0 ∕(kdes {SS})][X(g)] 0

1 + [ka ∕(kdes {SS})[X(g)]

=

KL [X(g)] 1 + KL [X(g)]

(2.242)

Here, K L (cm3 molecule−1 ) is called the Langmuir adsorption constant and is expressed by the following equation: KL =

kads ka 0 = kdes kdes {SS}

(2.243)

In the Langmuir-Hinshelwood mechanism (LH-mechanism) for the surface reaction, an atom or a molecule, Y, in the gas phase is thought to be adsorbed on the surface before reaction with a surface-adsorbed molecule, X(surf ). Thus, the reaction is written as X (surf) + Y (surf) → P (surf).

(2.244)

57

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2 Fundamentals of Multiphase Chemical Reactions

If the adsorption-desorption rates of X and Y are very fast, and the adsorption of both of X and Y follows the Langmuir isotherm, their surface coverage, 𝜃 X and 𝜃 Y , respectively, is represented by 𝜃X = 𝜃Y =

KL,X [X(g)] 1 + KL,X [X(g)] + KL,Y [Y(g)] KL,Y [Y(g)] 1 + KL,X [X(g)] + KL,Y [Y(g)]

(2.245) .

(2.246)

Here, [X(g)] and [Y(g)] are the concentration of X and Y in the gas phase, and K L,X and K L,Y are Langmuir adsorption equilibrium constant of X and Y, respectively. The net loss flux of X due to the surface reaction, J surf (molecules cm−2 s−1 ), is equal to the time variation of the surface concentration of X, {X(surf )}, and expressed by the following equation: d{X(surf)} = kLH II {X(surf)}{Y(surf)} = kLH II (𝜃X {SS})(𝜃Y {SS}) dt kLH II KL,X KL,Y [X(g)][Y(g)]{SS}2

Jsurf = − =

(1 + KL,X [X(g)] + KL,Y [Y(g)])2

(2.247)

Here, k LH II is the bimolecular rate constant (unit, cm2 molecule−1 s−1 ) of the Reaction (2.244). In the Eley-Rideal mechanism (ER-mechanism), on the other hand, a reactant X in the gas phase is thought to react with adsorbed molecule Y without being adsorbed on the surface. X (g) + Y (surf) → P (surf)

(2.248)

In this case, J surf is thought to be proportional to the gas-phase concentration of X, [X(g)], and the surface concentration of Y, {Y(surf )}, and J surf can be represented as follows when the adsorption of Y follows the Langmuir isotherm. Jsurf = kER II [X(g)]{Y(surf)} = kER II [X(g)] (𝜃Y {SS}) =

kER II KL,Y [X(g)][Y(g)]{SS} 1 + KL,Y [Y(g)]

(2.249)

Here, k ER II is the bimolecular rate constant (unit, cm3 molecule−1 s−1 ) of Reaction (2.248). In the atmospheric multiphase reaction relevant to aerosols, the desorption (evaporation) of one of the reactants of bimolecular interface reaction is often neglected. For instance, if the desorption of Y is neglected in the surface reaction following the LH-mechanism, J surf expressed by Eq. (2.247) can be simplified to Jsurf =

kLH II KL,X [X(g)]{SS}{Y(surf)} 1 + KL,X [X(g)] I

=

kLH KL,X [X(g)]{SS} 1 + KL,X [X(g)]

(2.250)

where k LH I = k LH II {Y(surf )} is the pseudo-first-order rate constant for the loss of X(surf ) by this reaction. In the literature of atmospheric chemistry, the reciprocal of {SS}, which

2.5 Physical Chemistry of Interface Reaction

represents the effective surface area occupied by one adsorbed molecule of X, 𝜍 X , is sometimes used instead of {SS} itself (although the effective surface area is usually represented by 𝜎, 𝜍 is used here since 𝜎 is used for surface tension in this book). In this case, K L,X and J surf take a form, KL,X = Jsurf =

𝜍X ka 0 kdes

(2.251)

kLH I KL,X [X(g)] 𝜍X (1 + KL,X [X(g)])

,

(2.252)

respectively. In the derivation of equations so far, it has been assumed that the adsorption and desorption of X on the surface is much faster than the surface reaction, and the equilibrium is hold between the adsorption and desorption. However, when the surface reaction is fast, it should also be taken into account in the mass balance equation. d{X(surf)} = Jads − Jdes − Jsurf dt = ka [X(g)] − kdes {X} − kLH I {X} = ka 0 (1 − 𝜃X ) [X(g)] − (kdes + kLH I )𝜃X ∕𝜍X

(2.253)

Assuming the steady state for X(surf ), 𝜃X =

𝜍X ka 0 ∕(kdes + kLH I )[X(g)] 1 + [𝜍X ka 0 ∕(kdes + kLH I )][X(g)]

=

′ [X(g)] KL,X ′ 1 + KL,X [X(g)]

.

(2.254)

where K′ L,X is called effective Langmuir adsorption equilibrium constant represented by ′ = KL,X

𝜍X ka 0 kdes + kLH I

.

(2.255)

In this case, J surf is represented by Jsurf = kLH I {X} = kLH I 𝜃X ∕𝜍X =

′ [X(g)] kLH I KL,X ′ 𝜍X (1 + KL,X [X(g)])

.

(2.256)

Thus, J sur is represented by replacing K L,X in Eq. (2.252) by K′ L,X . The atmospheric reactions of a gaseous molecule such as O3 with adsorbed organic molecules at the air–water interface are considered to proceed mostly by the LH-mechanism, as will be seen in Section 6.2. 2.5.2

Resistance Model Including Interface Reaction

The resistance model for multiphase reactions described in Section 2.4.2 is a model in which the gas–liquid equilibrium is established at the interface, followed by the diffusion of molecules into the bulk liquid and the subsequent bulk liquid-phase

59

60

2 Fundamentals of Multiphase Chemical Reactions 1 Γs→b

Gas-phase diffusion

Surface mass accommodation

1 Γdiff

1

1 Γrxn

Surface-to-bulk transport

Bulk-phase reaction

Surface reaction

αsurf 1 Γsurf

Figure 2.6 Schematic diagram of resistance model for gas–liquid multiphase reactions including surface reactions.

reactions. However, trace species including O3 and OH radicals adsorbed on the surface of cloud/fog droplets, aerosol particles, and sea salt particles are known to react with solute molecules in a different manner from those in the bulk liquid. Since the reactions of a molecule adsorbed on the water surface with solute molecules mostly follow the Langmuir-Hinshelwood mechanism, as will be mentioned in Chapter 6, here a resistance model in which this mechanism is taken into account explicitly, as shown in Figure 2.6, is described (Hanson 1997; Ammann et al. 2003; Pöschl et al. 2007). In this section, the equations are derived under the assumption that the gas-phase diffusion is not rate-limiting and the concentration of species is uniform in the gas phase. When the diffusion in the gas phase would affect the uptake rate, it would be necessary to take into account the resistance corresponding to the gas-phase diffusion and to use gas-phase concentration nearby the surface, [X(gs)], instead of the bulk gas-phase concentration, [X(g)], in the description of the Langmuir isotherm. At first, let us assume that only the surface reaction is related to the uptake of X(g), and the dissolution and reactions in the bulk liquid can be neglected. ka −−−−−−−−→ X (g) ← −− kdes

ksurf X(surf) −−−−→

products

(2.257)

The mass balance equation for the surface-adsorbed species can be written as d{X(surf)} = Jads − Jdes − Jsurf dt = ka [X(g)] − kdes {X(surf)} − ksurf {X(surf)}. (2.258) Here, J surf is assumed to be the first order to {X(surf )} with the first-order rate constant of k surf . From the steady-state approximation for X(surf ), {X(surf)} =

ka [X(g)]. kdes + ksurf

(2.259)

In this case, since the net loss flux J net of X(g) is equal to the loss flux J surf of X(surf ) due to the surface reaction, we obtain ka ksurf [X(g)]. (2.260) Jnet = Jads − Jdes = Jsurf = kdes + ksurf

2.5 Physical Chemistry of Interface Reaction

From Eq. (2.222) and (2.224), the uptake coefficient 𝛾 can be expressed by ( ) ( ) ka ksurf Jnet 1 = [X(g)] ∕ uX [X(g)] 𝛾= Jcoll kdes + ksurf 4 4ka ksurf = uX kdes + ksurf ksurf = 𝛼surf . kdes + ksurf

(2.261)

Here, 𝛼 surf is the surface mass accommodation coefficient introduced in Section 2.4.1 and defined by 𝛼surf =

4ka . uX

(2.262)

Thus, 𝛼 surf equals the adsorption flux J ads of gaseous molecules given by Eq. (2.239) divided by the collision flux J coll . Taking the reciprocal of Eq. (2.261), kdes 1 1 + = 𝛾 𝛼surf 𝛼surf ksurf 1 1 = + 𝛼surf Γsurf

(2.263)

is obtained, where 𝛼surf ksurf kdes

Γsurf =

(2.264)

is the conductance accompanying the surface reaction. From the treatment in the previous section, J surf can be expressed by Eq. (2.256) when the surface reaction rate is comparable to the adsorption-desorption rate. Then, 𝛼surf = 𝛼surf 0 (1 − 𝜃X ) = =

𝛼surf 0 ′ 1 + KL,X [X(g)]

𝛼surf 0 (kdes + kLH I ) 𝜍X ka 0 [X(g)] + kdes + kLH I

,

(2.265)

where 𝛼 surf 0 is the surface accommodation coefficient for the clean surface (𝜃 X = 0), and k surf has been substituted by k LH I . Substituting this to Eq. (2.263), ( ) uX 𝜍X 1 + KL,X [X(g)] 1 1 + (2.266) = 𝛾 𝛼surf 0 4kLH I KL,X is finally derived. Putting, Γsurf 0 =

KL,X 4kLH I , uX 𝜍X 1 + KL,X [X(g)]

(2.267)

Eq. (2.266) can be expressed as 1 1 1 + . = 0 𝛾 𝛼surf Γsurf 0

(2.268)

61

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2 Fundamentals of Multiphase Chemical Reactions

Next, a multiphase chemical reaction system including both of the interface reaction and bulk solution reaction, ka X (g)

kdes

ks→b X (surf) ksurf

kb→s

kliqI X (liq)

Dliq

Products,

(2.269)

Products

is considered. In this case, mass balance equation for the surface adsorbed X(surf ) can be expressed as d{X(surf)} (2.270) = Jads − Jdes − Jsurf − Js→b + Jb→s dt by adding terms for the mass transport flux J s → b from the surface to the bulk liquid and the reverse mass transport flux J s → b from the bulk liquid to the surface. Here, expressing the net flux J s → b,net from the surface to the bulk liquid phase with the first-order rate constant, k s → b,net , as Js→b,net = Js→b − Jb→s = ks→b,net {X(surf)},

(2.271)

Equation (2.270) is given by d{X(surf)} = ka [X(g)] − kdes {X(surf)} − ksurf {X(surf)} − ks→b,net {X(surf)}, dt (2.272) and using the steady state approximation for {X(surf )}, {X(surf)} =

ka [X(g)] kdes + ksurf + ks→b,net

(2.273)

is obtained. In this case, J net can be expressed as Jnet = Jads − Jdes = Jsurf + Js→b,net = (ksurf + ks→b,net ) {X(surf)} ka (ksurf + ks→b,net ) = [X(g)]. kdes + ksurf + ks→b,net

(2.274)

Therefore, 𝛾 is expressed as Jnet Jcoll ksurf + ks→b,net 4k = a uX kdes + ksurf + ks→b,net ksurf + ks→b,net = 𝛼surf kdes + ksurf + ks→b,net

𝛾=

(2.275)

and taking the reciprocal, 1 1 1 + . = 𝛾 𝛼surf 𝛼surf ksurf 𝛼surf ks→b,net + kdes kdes

(2.276)

2.5 Physical Chemistry of Interface Reaction

The first term in the denominator of the second term of the right-hand side can be replaced by Γsurf introduced in Eq. (2.264). Putting the second term in the denominator of the second term of the right-hand side as Γs→b,net =

𝛼surf ks→b,net kdes

,

(2.277)

the expression of Γs → b,net can be derived as follows. Firstly, the transport flux J s → b from the surface to the bulk liquid phase depends on {X(surf )} in the first order and can be written by Js→b = ks→b {X(surf)},

(2.278)

where k s → b (s−1 ) is the first-order rate constant of this transport process. The transport flux of the reverse direction, J b → s , is thought to depend on the concentration of X in the bulk liquid phase adjacent to the surface, [X(liq)]0 , and putting the first-order rate constant of the transport process as k b → s (s−1 ), J b → s can be expressed as Jb→s = kb→s [X(liq)]0 .

(2.279)

The net flux J s → b,net , the difference of J s → b and J b → s , depends on the gradient of the concentration of X in the liquid phase, [X(liq)]. Using the diffusion coefficient Dliq in the liquid phase, J s → b,net can be expressed by the Fick’s diffusion law as Js→b,net = −Dliq

d[X(liq)] || dz ||z=0

(2.280)

where z is the depth of the liquid from the surface. In the case of the semi-infinite planar liquid, [X(liq)] is expressed by the exponential form regarding to z, ( ) z [X(liq)] = [X(liq)]0 exp − (2.281) lrd Here, lrd is the reacto-diffusive length defined by √ Dliq lrd = . kbulk I

(2.282)

Substituting Eq. (2.281) to Eq. (2.280), Js→b,net =

Dliq

[X(liq)]0 lrd √ = kbulk I Dliq [X(liq)]0

(2.283)

is obtained. Substituting Eqs. (2.278), (2.279), and (2.283) to Eq. (2.271), we obtain √ kbulk I Dliq [X(liq)]0 = ks→b {X(surf)} − kb→s [X(liq)]0 . (2.284) From Eq. (2.284), [X(liq)]0 =

ks→b {X(surf)}, √ kb→s + kbulk I Dliq

(2.285)

63

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2 Fundamentals of Multiphase Chemical Reactions

and J s → b,net is expressed as √ ks→b kbulk I Dliq {X(surf)}. Js→b,net = √ kb→s + kbulk I Dliq Thus, from Eq. (2.271), k s → b,net is written as √ ks→b kbulk I Dliq . ks→b,net = √ kb→s + kbulk I Dliq Substituting this to Eq. (2.277), √ I 𝛼surf ks→b kbulk Dliq Γs→b,net = √ kdes kb→s + kbulk I Dliq

(2.286)

(2.287)

(2.288)

and taking the reciprocal, 1 Γs→b,net

√ k + kbulk I Dliq kdes b→s = √ 𝛼surf ks→b kbulk I Dliq =

kdes k k 1 + des b→s √ . 𝛼surf ks→b 𝛼surf ks→b kbulk I Dliq

(2.289)

The second term on the second line of the right-hand side can be further transformed as follows. When the uptake of molecules from the gas phase to the liquid phase is saturated, i.e. the dissolution equilibrium following the Henry’s law is established, the concentrations of X in the gas phase, [X(g)], and in the bulk liquid phase, [X(liq)], can be related through the Henry’s law constant K H , [X(liq)] = KH RT [X(g)].

(2.290)

In the saturation conditions, since adsorption-desorption at the surface and mass transport between the surface and the bulk liquid phase are also in equilibrium, ka [X(g)] = kdes {X(surf)}

(2.291)

ks→b {X(surf)} = kb→s [X(liq)]

(2.292)

and hold. From Eqs. (2.290)–(2.292), the relationships, k k [X(g)] 1 = = des b→s [X(liq)] KH RT ka ks→b ka uX 𝛼surf kdes kb→s = = ks→b KH RT 4KH RT are obtained, and substituting Eq. (2.293) to Eq. (2.289), kdes uX 1 1 = + . √ Γs→b,net 𝛼surf ks→b 4KH RT kbulk I Dliq

(2.293)

(2.294)

2.5 Physical Chemistry of Interface Reaction

The second term of the right-hand side is found to be the reciprocal of the conductance Γrxn for the bulk liquid-phase reaction given in Eq. (2.233). Expressing the reciprocal of the first term of the right-hand side of Eq. (2.294) by Γs→b =

𝛼surf ks→b , kdes

(2.295)

it is found that the net uptake resistance(1/Γs → b,net ) from the surface to the bulk liquid phase is the series sum of the mass transfer resistance (1/Γs → b ) and bulk liquid-phase reaction resistance (1/Γrxn ). Finally, the uptake coefficient 𝛾 in the case that both of surface reaction and bulk liquid-phase reaction contribute can be expressed from Eq. (2.276) as 1 1 1 + . (2.296) = 1 𝛾 𝛼surf Γsurf + 1 1 + Γs→b Γrxn Considering that the parameters in the equation is the reciprocal of the resistances, this equation is found to show that the uptake coefficient is expressed by the combination of resistances shown in Figure 2.6 (Hanson 1997; Ammann et al. 2003; Pöschl et al. 2007). In the resistance scheme shown in Figure 2.6, in the absence of the reaction term Γsurf , the resistance for the bulk mass accommodation process (1/𝛼 bulk ) is found to be the series sum of the resistance for the surface mass accommodation process (1/𝛼 surf ) and the resistance for the mass transport process from the surface to the bulk liquid (1/Γs → b ). Therefore, using Eq. (2.295), ( ) kdes kdes 1 1 1 = + = 1+ , (2.297) 𝛼bulk 𝛼surf 𝛼surf ks→b 𝛼surf ks→b and 𝛼bulk =

𝛼surf ks→b kdes + ks→b

(2.298)

can be derived. 2.5.3 Surface Tension of Air–Water Interface and Thermodynamics of Accommodation Coefficient In the thermodynamics related to liquid, discussions are made usually for bulk solution, and the surface and air–water interface which are important in atmospheric chemistry are seldom addressed. In this subsection, thermodynamical treatment of interface is explained, particularly on surface tension and surface adsorption energy. Since the surface tension affects the vapor pressure in equilibrium with an aqueous droplet, it is an important parameter that is related to the fundamental processes of new particle formation, particle growth, and CCN activity (McNeill et al. 2014) (cf. Chapter 7). 2.5.3.1

Surface Tension

In a liquid, the maximum number of molecules tends to reside in the bulk in order to be stabilized by maximizing the molecular interactions with the surrounding molecules. This gives the reason that there is a tendency for a liquid droplet to take a spherical shape by minimizing the surface/volume ratio.

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Since the work, δw, necessary for changing the surface area A of a liquid by the amount dA is proportional to dA, the relationship can be expressed as δw = 𝜎 dA,

(2.299)

where the proportional constant 𝜎 is called surface tension. From the above equation, the dimension of the surface tension is energy/area and the unit is J m−2 ; since 1 J = 1 N m, it is usually described as N m−1 . Since work under constant temperature and pressure is equal to the change of Gibbs energy, G, we obtain dG = 𝜎 dA,

(2.300)

and the decrease of surface area (dA < 0) brings the decrease of Gibbs energy (dG < 0). In other words, surface area tends to shrink spontaneously. If the Gibbs energy change per unit area accompanying the change in surface area is expressed by surface Gibbs energy, GS , from the above equation, we obtain ( ) 𝜕G GS = = 𝜎, (2.301) 𝜕A T,p and the surface Gibbs energy is found to be equal to the surface tension. Similarly, the surface entropy SS , the entropy change per changing unit surface area, can be defined by ( ) 𝜕S SS = . (2.302) 𝜕A T,p From Eq. (2.18), we obtain a relationship between the amount of reversible heat change δqrev and entropy change dS as δqrev = TdS = TSS dA,

(2.303)

showing that the heat accompanying the reversible change gives the surface entropy. Under the constant pressure, (𝜕G/𝜕T)p = − S, and ( S) 𝜕G = −SS (2.304) 𝜕T p is obtained. From the above and Eq. (2.301), d𝜎 (2.305) dT is available. Thus, excess entropy that the surface possesses can be obtained from the temperature dependence of surface tension. Further, if we write surface enthalpy as H S , from Eq. (2.24), we obtain SS = −

H S = GS + TSS .

(2.306)

In many cases where the changes of pressure and volume are small, internal energy U is nearly equal to enthalpy H, and if we write surface energy as U S , using Eqs. (2.301) and (2.305), we obtain: d𝜎 (2.307) dT Thus, if the experimental data of temperature dependence of surface tension is available, surface energy can be obtained. Figure 2.7 shows the temperature change of U S ≅ GS + TSS = 𝜎 − T

2.5 Physical Chemistry of Interface Reaction

80 Surface Tension / mN m–1

Figure 2.7 Variation of surface tension of water with temperature. Source: Based on the data by Vargaftik et al. (1983).

70 60 50 40 30 20 10 0 0

50

100 150 200 250 300 350 400 Temperature / °C

surface tension of water (Vargaftik et al. 1983). As seen in the figure, surface tension generally decreases with temperature and becomes zero at the gas-liquid critical temperature T c . The reason that the surface tension plays an important role in atmospheric chemistry is because the equilibrium vapor pressure of a small liquid droplet depends largely on the curvature of the spherical surface of the droplet. Let us think the case that gaseous molecules of X condense by the amount of dnX mol on a spherical liquid droplet with radius rp composed of only a species X. In this case, the volume change dV of the liquid droplet accompanying the condensation of a gaseous species X is given by dV = V liq dnX ,

(2.308)

where V liq is the molar volume of liquid species X. Since dV can be expressed by using the infinitesimal changes of the droplet radius, drp , as 4 4 π(r + drp )3 − πrp 3 ≈ 4πrp 2 drp , 3 p 3 from these two equations, we get this relationship: dV =

drp =

V liq dn 4πrp 2 x

(2.309)

(2.310)

Expressing the chemical potential of X in the gas phase as 𝜇X g and that of pure liquid as 𝜇X liq , the Gibbs energy change dGtrs accompanying the phase transformation from gas to liquid is dGtrs = (𝜇X liq − 𝜇X g ) dnX .

(2.311)

Meanwhile, since the surface Gibbs energy change dGsurf accompanying the change of radius drp of the liquid droplet can be expressed as dGsurf = 𝜎X dA = 𝜎X [4π(rp + drp )2 − 4πrp 2 ] ≈ 8π𝜎X rp drp ,

(2.312)

the total Gibbs energy change dG is given by dG = dGtrs + dGsurf = (𝜇X liq − 𝜇X g ) dnX + 8π𝜎X rp drp .

(2.313)

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2 Fundamentals of Multiphase Chemical Reactions

Using Eq. (2.310) for the relationship between dnX and drp , dG = (𝜇X liq − 𝜇X g ) dnX +

8π𝜎X rp V liq

4πrp 2 [ ] 2𝜎 V liq = 𝜇X liq − 𝜇X g + X d nX rp

d nX (2.314)

is obtained. As described in Section 2.2, the chemical potential of a gaseous species is given by Eq. (2.57) using the partial pressure of X, pX , while the chemical potential of pure liquid can be expressed by Eq. (2.63) using the saturation vapor pressure pL,X ∘ over planer surface of pure liquid X. Therefore, ( ) ( ) pL,X ∘ pX ∘ ∘ liq g 𝜇X − 𝜇X = 𝜇X + RT ln ∘ − 𝜇X + RT ln ∘ p p pX = −RT ln (2.315) pL,X ∘ Substituting this to Eq. (2.314), ) ( 2𝜎X V liq pX + d nX dG = −RT ln pL,X ∘ rp

(2.316)

is obtained. Since dG = 0 in the equilibrium, putting 0 in the parenthesis of the righthand side of Eq. (2.316), the relationship, ln

2𝜎X V liq pX eq = pL,X ∘ RTrp

(2.317)

is obtained where pX eq is the partial pressure of surrounding gas X in equilibrium with the liquid particle. This equation is called Kelvin equation, which is a formula to obtain the change of vapor pressure by the change in radius of a liquid droplet. Since the molar volume V liq can be expressed as V liq = MX /𝜌X liq by using the molar mass, MX , and the density of liquid, 𝜌X liq , the Kelvin equation can be expressed also by ln

2𝜎X MX pX eq = . ∘ pL,X RT𝜌X liq rp

(2.318)

From Eq. (2.318), for example, pH2 O eq ∕pL,H2 O ∘ for the water droplet with rp = 1, 0.1, and 0.01 μm are 1.001, 1.011, and 1.114, respectively (Adamson and Gast 1997). From the Kelvin equation, Köhler theory (Köhler 1936), which is important for determining the equilibrium size of aerosols under specific relative humidity and discussing the growth of an aqueous droplet in the atmosphere, is developed. These topics are described in detail in Section 7.4. 2.5.3.2

Thermodynamics of Accommodation Coefficient at Air–Water Interface

Dissolution process from the gas to liquid phase involving adsorption process at the water surface is expressed by ka ks→b * −−−−−−−−→ −−−−−−−−→ X(g) ← −− X (surf) ⇄ X (surf) ← −− X(liq) kdes kb→s

(2.319)

2.5 Physical Chemistry of Interface Reaction

kdes

ks→b X*(surf)

Vapor

X(g)

∆Gobs ∆G* ∆Gg,surf

X(surf) ∆G*surf

∆Gg ∆Gsurf

X(liq) Liquid N=1 Distance

N = N* N = very large Cluster size

Figure 2.8 Postulated free energy diagram for the liquid vapor interface (see text). Source: Adapted with permission from Nathanson at al. (1996). Copyright 1996. American Chemical Society.

where X(g), X(surf ), and X(liq) are molecules in the gas phase, at the surface, and in the liquid phase, respectively. Here, it is assumed that a gas phase molecule X(g) is adsorbed at the air–water interface as X(surf ), which is then coordinated by several H2 O molecules to form a cluster-like transition state X*(surf ) before it is solvated in the bulk liquid. Such a model is called critical cluster model, and the concept of Gibbs energy change at the air–water interface in this model is depicted in Figure 2.8 (Nathanson et al. 1996; Davidovits et al. 2006). Chemical adsorption of atmospheric trace species at the air–water interface has been studied by vibrational SFG and other methods for inorganic molecules, such as SO2 (Donaldson et al. 1995) and NH3 (Donaldson 1999), and organic molecules, such as alcohols, carboxylic acids, acetone (Donaldson and Anderson 1999), amines (Mmereki et al. 2000), and methanesulfonic acid (MSA) (Allen et al. 2001). Also, as will be described in Section 6.2, it has been revealed by the quantum chemical calculation that the reactive species such as OH, HO2 , and O3 are captured temporarily at the air–water interface near at ca. 1 nm in depth from the interface, at which the Gibbs energy has the minimum value, 3–5 kJ mol−1 (Vácha et al. 2004). In Figure 2.8, ΔGobs is the free energy that determines the uptake coefficients measured experimentally, and corresponds to the difference between the Gibbs energies of ΔGg and ΔG*surf for X(g) and X*(surf ), respectively, which can be obtained by quantum chemical calculations. Meanwhile, the bulk accommodation coefficient, 𝛼 bulk , of X(g) to the water surface is expressed from Eq. (2.298) by assuming 𝛼 surf = 1 as 𝛼bulk =

ks→b , kdes + ks→b

(2.320)

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which can be transformed to ( ) k ΔGobs 𝛼bulk = s→b = exp − . 1 − 𝛼bulk kdes RT

(2.321)

By using ΔGobs = ΔH obs − TΔSobs , ln

𝛼bulk ΔHobs ΔSobs =− + 1 − 𝛼bulk RT R

(2.322)

is obtained. From this equation, by plotting ln [𝛼 bulk /(1 − 𝛼 bulk )] vs. 1/T using the experimentally determined 𝛼 bulk , the values of ΔH obs and ΔSobs are obtained from the slope and intercept, respectively. As mentioned above, the theoretical value corresponding to ΔGobs is obtained from the theoretical analysis of uptake process, and thus ΔGobs is a point connecting theory and experiment. Table 2.7 gives the values of 𝛼 bulk , ΔH obs , ΔSobs , and ΔGobs (273 K) measured at the water surface for typical atmospheric molecules and compiled by Davidovits et al. Table 2.7 Measured 𝛼 bulk , ΔHobs , ΔSobs , and ΔGobs (273 K) on water surface.

Gas phase species

𝜶 bulk (273 K)

𝚫Hobs (kcal mol−1 )

𝚫Sobs (cal mol−1 K−1 )

𝚫Gobs (kcal mol−1 )

C10 H8 (naphthalene)

0.00022 (296 K)

−29.4

−115.2

4.7

(CH3 O)2 C(O)

0.009

−26

−99

1.0

C6 H5 OH

0.0037 (278 K)

−14.8

−59.3

1.6

CH3 C(O)CH3

0.026

−12.7

−53.7

2.0

(CH3 )3 COH

0.052

−8.2

−35.8

1.6

CH3 CH(OH)CH3

0.033

−9.9

−43.0

1.8 2.0

CH3 CH2 CH2 OH

0.026

−9.2

−40.9

CH3 CH2 OH

0.049

−11.0

−46.2

1.6

CH3 OH

0.10

−8.0

−34.9

1.5

CH3 C(O)OH

0.067

−8.1

−34.9

1.4

HC(O)OH

0.047

−7.9

−34.4

1.5

CH3 OOH

0.012

−6.5

−32.5

2.4

HOCH2 CH2 OH

0.072

−5.3

−24.5

1.4 1.2

HI

0.091

−10.6

−43.4

HBr

0.079

−10.0

−41.5

1.3

HCl

0.18

−7.2

−29.4

0.83

CH3 SO3 H (MSA)

0.11

−2.7

−14.0

1.1

(CH3 )2 SO2 (DNSO2 )

0.098

−10.7

−43.0

1.0

(CH3 )2 SO (DMSO)

0.20

−5.1

−23.1

1.2

NH3

0.20

−9.3

−36.8

0.75

SO2

0.35

−7.6

−29.2

0.37

HNO3

0.15

−6.6

−27.6

0.93

H2 O2

0.22

−5.5

−22.5

0.64

H2 O

0.06

−4.8

−20.3

0.74

Source: Davidovits et al. (2006).

2.6 Chemical Compositions and Physical Characters of Particles

71

0 H2O ET(OH)2 N* = 1 Methanol –10

N* = 1.5

Acetone

N*= 2 H2O2

∆Hobs(kcal mol–1)

N* = 2.5 N* = 2.8

–20

N* = 3 Diethyl carbonate

–30

N* = 5

–40 –140

–120

–100

–80 –60 ∆Sobs(cal mol–1 K–1)

–40

–20

Figure 2.9 Correlation of the experimental (•) and calculated (⊞) values of ΔHobs vs. ΔSobs on water surfaces. Source: Reprinted with permission from Davidovits at al. (2006). Copyright 2006 American Chemical Society.

(2006). As shown in Table 2.7, ΔH obs and ΔSobs are both negative values, and the positive ΔGobs values are due to the effect of the decrease of entropy by coordination of several H2 O molecules at the transition state X(surf )* . Figure 2.9 depicts the correlation between experimentally obtained ΔH obs and ΔSobs (Davidovits et al. 2006). As seen in Figure 2.9, almost all of the experimentally obtained values of ΔH obs and ΔSobs are located on the straight line. In the figure, the calculated values of ΔH obs and ΔSobs corresponding to the number of H2 O molecules, N*, are also shown. Thus, it can be seen that X*(surf ) is surrounded by several H2 O molecules (N* = 1–5) for species shown in Figure 2.9.

2.6 Chemical Compositions and Physical Characters of Particles Atmospheric aerosols consist of numerous inorganic and organic compounds chemically, and of liquid, semi-solid, and solid particles physically. As for the aerosol concentrations in the atmosphere, the gas-particle partitioning of these chemical species is very important. In this section, after describing the chemical compositions of atmospheric aerosols, the relationship between the molecular structures and

0

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2 Fundamentals of Multiphase Chemical Reactions

vapor pressures of organic compounds, and volatility basis set (VBS) model will be described. Hydrophilic and hydrophobic properties of aerosols, which are related to the hygroscopic growth and CCN activity, and glassy (semisolid) phase state and mass transfer of aerosols, which are related to the surface adhesion and multiphase reaction rate, are also mentioned. The properties of inorganic compounds in aerosols have been described in detail in Seinfeld and Pandis (2016), so that discussion is mainly focused on organic compounds here. Relationship between the new particle formation and chemical composition of particles, which is interesting regarding the indirect effect of aerosols on climate, will be described in Chapter 7. 2.6.1

Elemental and Molecular Composition of Particles

Atmospheric aerosols consist of primary particles emitted directly from terrestrial and marine sources and secondary particles formed by chemical reactions in the atmosphere. Chemical compositions of particles are different depending on aerosol size. Fine particles with diameter less than 2.5 μm (usually called PM2.5 ) contain primary particles, from combustion of fossil fuels and biofuels, and secondary particles formed in the atmospheric reactions, while course particles with diameter 2.5–10 μm (PM10-2.5 ) contain mineral dust from Earth crustal rocks and soil, sea salt from ocean, and fly ash from coal combustion. Chemical composition of atmospheric aerosols is broadly classified into inorganic and organic compounds. The inorganic components include mineral dust, elemental carbon such as soot, sea salt, and water-soluble ions formed from gaseous molecules, SO2 , NOx , and NH3 . The organic compounds include primary species emitted by biomass and fossil fuel combustion and secondary components formed by chemical reaction of volatile organic compounds (VOCs) from natural and anthropogenic origin. 2.6.1.1

Inorganic Elements and Compounds

As for the inorganic elements in atmospheric aerosols, O, Si, Al, Fe, Mg, Ca, Na, K, and Ti of Earth crust origin, Pb, V, and Ni of petroleum combustion origin, As, Se, etc. of coal combustion origin, and Cl, Na, Mg, S, K, Ca, Br, and C of sea salt origin are included (Finlayson-Pitts and Pitts 2000 and references therein). Figure 2.10 shows the inorganic elemental composition of PM10-2.5 sampled over the Yellow Sea and East China Sea influenced by terrestrial origin particles (Zhao et al. 2015). As shown in Figure 2.10, the composition of the inorganic elements in the coarse aerosols over these oceans includes Al, Ca, Fe, Mg, Na, K, Ti, Cr, Zn, P, Zr, Ba, and Pb in the order of weight, and these 13 elements occupy 96% of the inorganic metal components. Although the crustal source elements, O and Si, are not analyzed here, the elemental composition of Al, Ca, Fe, Mg, Na, K, Ti, and P is close to the crustal elemental composition (Mason and Moore 1982). Other than these, elemental carbon (EC), also called black carbon (BC) originated from combustion, has positive radiative forcing and has attracted interest from the view of climate change (Bond et al. 2013). As for the water-soluble inorganic ions in the atmospheric aerosols, anions, SO4 2− , NO3 − , Cl− and HCO3 − , and cations, Na+ , Ca2+ , Mg2+ , and NH4 + are the major components, of which Na+ , Mg2+ , Ca2+ , SO4 2− , and Cl− are the primary species from sea salt and soil, and SO4 2− , NO3 − , HCO3 − , and NH4 + are the secondary species from SO2 , NOx , CO2 , and NH3 of anthropogenic and natural origins. Table 2.8 shows the

2.6 Chemical Compositions and Physical Characters of Particles

Yellow Sea East China Sea

1000

PM1.0–2.5

100

10

1

0.1 AI

Ba Ca

Fe Mg

Zr

Sr

Ti

Na

P

K

V

Cr Mn

Ni

Cu Zn

As

Y

Mo Sn Pb

Figure 2.10 Element composition of atmospheric PM10-2.5 in the Yellow Sea and East China Sea (ng m−3 ). Source: Adapted from Zhao et al. (2015). Copyright 2015 Author(s). Creative Commons Attribution 3.0 License. Table 2.8 Typical composition of seawater. Elemental species

Dissolved species

Elemental concentration (g kg−1 )

Molar concentration (mol L−1 )

Cl

Cl−

19.35

0.559

Na

Na+

10.78

0.481

Mg

Mg2+

1.28

0.0541

S

SO4 2−

0.904

0.0289

Ca

Ca2+

0.412

0.0105

K

K+

0.399

0.0105

Br

Br−

0.0673

8.6 × 10−4

0.0244

2.1 × 10−3

−

C

HCO3

Sr

2+

Sr

0.0078

8.9 × 10−5

B

B(OH)3

0.0045

4.2 × 10−4

Si

SiO3 2−

F I

0.0025

1.0 × 10−6

−

0.0013

7.0 × 10−5

−

0.00058

3.5 × 10−7

F I

Density = 1.0247 kg L−1 at 293 K. Source: Pilson (1998), Li (2000), Nozaki (2001).

elemental composition of seawater. As seen in the table, other than Na+ and Cl− , the concentrations of Mg2+ , SO4 2− , Ca2+ , and K+ are relatively high, and these constitute the major components of sea salt. Among the water-soluble inorganic ions, SO4 2− is the most commonly observed as a major ion in the tropospheric aerosols. Even in the Antarctica, where there is almost no anthropogenic influence (Maenhaut and Zoller 1977), remote site at Mauna Loa, Hawaii (Johnson and Kumar 1991), and the upper troposphere, it has been reported that SO4 2− is the major constituent of aerosols. SO4 2− in the Antarctic aerosols is not from sea salt but is thought to be produced via SO2 and dimethyl sulfoxide (CH3 S(O)CH3 ) formed

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from atmospheric oxidation of dimethyl sulfide (CH3 SCH3 ) by OH (Davis et al. 1998; Bao et al. 2000). Since these inorganic ions are formed in either the gas-phase reactions or in the aqueous phase reactions after taken into water droplet, most of them exist in the sub-micron particles. However, NO3 − is taken into sea salt as NaNO3 by the substitution reaction with Cl− in a sea salt. Thus formed NO3 − exists in coarse particles (c.f. Section 6.3). Similarly, a part of SO4 2− is also included in the coarse particles as Na2 SO4 by the reaction with sea salt (e.g. Zhuang et al. 1999). 2.6.1.2

Organic Compounds

Thousands of organic species have been analyzed by mass spectrometry in biomass burning, urban, and marine aerosols (e.g. Willoughby et al. 2016). Among these enormous numbers of particulate organic compounds, the identified fraction is estimated as only ca. 20% (Williams et al. 2007). Although a considerable fraction of organic aerosols is composed of compounds having the elemental composition of carbon, hydrogen, and oxygen (CHO), compounds having nitrogen, sulfur, and phosphor atoms (CHON, CHOS, CHONS, and CHOP(N, S)) are also found in significant fractions (e.g. Willoughby et al. 2016). For instance, it is the characteristic of marine aerosols that the ratios of CHOS, CHONS, and CHOP(N, S) are much higher than those in other aerosols due to the influence of phospholipids of marine biology origin (Wozniak et al. 2014; Willoughby et al. 2016). On the other hand, the abundance ratios of CHON and CHO are high and those of CHOS and CHOP(N, S) are low in the biomass burning aerosols. The elemental composition of urban aerosols will be described in Section 8.6. Atmospheric organic aerosols are composed of primary organic aerosols (POAs) released directly from emission sources and SOAs produced secondarily by chemical reactions in the atmosphere. As typical POAs, C25 -C35 n-alkanes from epicuticular waxes of plants and C15 -C30 n-alkanes from fossil fuel combustion are known (Simoneit et al. 1988; Sicre et al. 1990; Hildemann et al. 1996). The characteristics of these hydrocarbons are that the concentrations of n-alkanes with the odd-numbered carbon atoms are a few times higher than those with the even-numbered carbon atoms in the plant origin species, whereas there is no such singularity of odd- and even-number of carbon atoms in the fossil fuel origin species (Schneider and Gagosian 1985; Simoneit et al. 1988). Other than n-alkane, n-alkanoic acid (C22 -C34 ), n-alkanol (C22 -C34 ), ketones, aldehydes, ethers, etc. have been identified in POAs (Simoneit et al. 1988; Rogge et al. 1993b; Chen and Simoneit 1994). In n-alkanoic acid and n-alkanol, the species with the even number of carbon atoms characteristically have a few times higher concentration than those with the odd number of carbon atoms contrary to n-alkanes (Simoneit et al. 1988). As for the POAs of the marine origin, aliphatic hydrocarbons (n-alkane) and aliphatic esters have been reported as markers of lipids (Eichmann et al. 1980; Gagosian et al. 1982; Marty and Saliot 1982). Other than these, molecular species from fossil fuel combustion, forest fires, agricultural waste burning, and cooking are important as POAs. The POAs from auto exhaust have been reported to contain more 100 organic compounds including n-alkanes, n-alkanoic acids, benzoic acid, benzaldehyde, polycyclic aromatic hydrocarbons (PAHs), oxidized PAHs, hopanes, steranes, and dicarboxylic acids (Kawamura and

2.6 Chemical Compositions and Physical Characters of Particles

Chart 2.1 Chemical structures of typical primary organic aerosols (POA) components from terrestrial plants, marine biology, biomass burning, and fossil fuel combustion observed in the fields.

Kaplan 1987; Rogge et al. 1993a; Schauer et al. 1999, 2002). It has long been known that many kinds of PAHs and their derivatives are emitted from coal combustion (Gohda et al. 1993; Finlayson-Pitts and Pitts 2000; Liu et al. 2001). Chart 2.1 shows chemical formulas of typical primary organic compounds. A few tens of semi- and low-volatile particulate organic compounds have been identified in biomass burning including characteristic species such as levoglucosan (monosaccharide derivative from cellulose), catechol (thermal decomposition product of lignin) (shown in Chart 2.1), and palmitic acid (vaporized fatty acid from vegetable), which are used as tracers of biomass burning (Simoneit et al. 1999; Alfarra et al. 2007). Also, from meat cooking, characteristic compounds such as palmitic and stearic acid (n-alkanoic acids) and oleic acid (n-alkenoic acid) (cf. Chart 5.1) are emitted and used as tracers (Rogge et al. 1991). In addition, more than 75 kinds of organic compounds including n-alkanes, n-alkanoic acids, dicarboxylic acids, n-alkanals, n-alkenals, n-alkanones, n-alkanols, furan, and lactones have been identified (Rogge et al. 1991). On the other hand, chemical species of SOAs are in general multi-functional oxygen containing compounds, and species such as ketocarboxylic acids, ketodicarboxylic acids, dicarboxylic acids (Suzuki et al. 2001; Sempéré & Kawamura 2003), C5 -C9 alkanals, alkanedials, C8 -C13 alkanones, cyclo-alkanones, C3 -C20 carboxylic acids, alkanediones, benzaldehyde, phenol, hydroxy-benzaldehyde (Hamilton et al. 2004), and hydroxy-carboxylic acids (Yu et al. 2005) have been detected in the atmosphere. Particularly, photochemical oxidation products of isoprene, including 2-methylglyceric acid, 2-methylthreitol, and 2-methylerythritol (Kleindienst et al. 2007), and those of

75

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2 Fundamentals of Multiphase Chemical Reactions

Chart 2.2 Chemical structure of typical secondary organic aerosols (SOAs) observed in the fields.

monoterpenes, including pinonic acid, nor-pinonic acid, pinic acid, pinonaldehyde, and nopinone, have been observed in the atmosphere above forests (Kavouras et al. 1999; Kleindienst et al. 2007), and used as tracers of SOAs from plant-origin hydrocarbons. Chart 2.2 depicts the chemical formulas of typical SOA components mentioned above. The gas-phase photooxidation products of toluene, 2,3-dihydroxy-4-oxopentanoic acid has been detected in the atmosphere (Kleindienst et al. 2007). Typical organosulfates, including 2-methyltetrol sulfate, 3-methyglyceric acid sulfate, 2,3-epoxy-2methyl-1,4-butanediol sulfate (IEPOX sulfate), glycolic acid sulfate, and hydroxy acetone sulfate, have been observed in ambient aerosols (Olson et al. 2011; Budisulistiorini et al. 2013; Hettiyadura et al. 2015; Liao et al. 2015). As for organic nitrates, other than imidazoles (Teich et al. 2016), many chemical species containing elemental composition of CHON have been detected by high-resolution mass spectrometry (Laskin et al. 2009). Among them, species with chemical composition of C5 H4-9 NO4-9 and C10 H15, 17, 19 NO4-11 are included, which are presumed to be hydroxynitrates from isoprene and α-pinene, but molecular identification has not been made. Other than these compounds, high molecular weight compounds (HMWCs) with molecular weight of 100–1000 including oligomers are contained in SOAs (Denkenberger et al. 2007; Krivácsy et al. 2008) (c.f. Section 8.5.2). Oligomers are molecules composed of fewer repeating units than polymers and are known to be formed in the

2.6 Chemical Compositions and Physical Characters of Particles

77

77 97 100

115

62

171 187

60

165

%

201 215

131

233 265

0 50

100

77

150

200

250

300

350

400

450

500

m/z 600

550

187

100 201

215 171 229 231

%

267 94

271 301

143

371 385

0 200

400

600

800

m/z 1000

Figure 2.11 Mass spectra of the oligomers of Budapest (upper trace) and Mace Head (lower trace) aerosol. Source: Reprinted with permission from Krivácsy et al. (2008). Copyright 2007 Elsevier B.V.

gas and aqueous phase (c.f. Sections 3.2, 4.2, and 4.3). Figure 2.11 shows mass spectra of HMWC observed at Budapest and Mace Head (Krivácsy et al. 2008). 2.6.1.3

van Krevelen Diagram

In order to perceive a whole picture of elemental composition of oraganic aerosols containing enormous number of unidentified chemical species, visualization by the

2 Fundamentals of Multiphase Chemical Reactions

2.5 + water (hydration) (slope = +2)

2

+ alcohol/ peroxide (slope = 0)

1.5

+ carboxylic acid (slope = –1)

H :C

78

ox state=1

1.0

+ ketone/aldehyde (slope = –2)

0.5 ox state=0

0 0

0.2

0.4

0.6 O :C

0.8

1

1.2

Figure 2.12 Schematic plots of van Krevelen diagram for alcohols, carboxylic acids, and ketone/aldehydes. Source: Adapted with permission from Heald et al. (2010). Copyright 2010 American Geophysical Union.

use of van Krevelen diagram has been attempted. The van Krevelen diagram (van Krevelen 1950) (also called van Krevelen plot) was proposed to illustrate the change of elemental composition of coal formation under the ground by the correlation plot of hydrogen-carbon ratio (H : C) and oxygen-carbon ratio(O : C). It is widely utilized for the interpretation of elemental ratios of huge number of organic compounds in the atmospheric aerosols measured by high-resolution mass spectrometers (Kim et al. 2003; Heald et al. 2010; Chen et al. 2015). Figure 2.12 depicts a schematic picture of van Krevelen diagram. For example, when a methylene group (-CH2 -) of alkane is substituted by a carbonyl group (-C(=O)-), two H atoms are lost and one O atom is added. Therefore, if such a reaction occurs for a large number of compounds with different carbon numbers, the slope of the van Krevelen diagram becomes −2. For the transformation in which an H atom of a CH2 group is substituted by a OH group to form alcohol, the slope of the diagram is 0 to give a horizontal plot. A plot with an intermediate slope of −1 is expected for the chemical reaction to form carboxylic acid (-C(=O)OH) or hydroxycarbonyl compound with one carbonyl group and one OH group accompanying a loss of two H atoms of a CH2 group. Based on the van Krevelen diagram plotting the average of H : C and O : C ratios for many ambient observations, Figure 2.13 illustrates a plot with a slope of −0.6 (Chen et al. 2015). The van Krevelen plots for more than a few hundreds of molecular species obtained by high-resolution mass spectrometers will be described in Section 8.6.1. 2.6.2

Molecular Composition and Vapor Pressure

Vapor pressure is an important property that controls gas-particle partitioning, and that of pure compound is an important parameter in the SOA formation model.

2.6 Chemical Compositions and Physical Characters of Particles

2.6 2.4

–1.0

0.0 OSc

1.0

2.2 2.0

H:C

1.8 1.6 1.4 HR-AMS Urban Downwind Remote/Rural MILAGRO(5 × 10−12 cm3 molecule−1 s−1 , corresponding to the atmospheric reaction lifetime of the order of one day. The peroxy radicals formed in the initiating reaction by OH react with O2 in the atmosphere to form alkyl peroxy radicals, RO2 . As for the atmospheric reactions of RO2 radicals, reactions with NO, NO2 , HO2 , and CH3 O2 (Reactions (3.85a, 3.85b)–(3.88)) are presumed. Reaction (3.86) with NO2 is the equilibrium reaction, and since RO2 NO2 is thermally unstable at room temperature, its effect on aerosol formation would be minimal near the ground. 3.3.1.1

Reactions of Alkyl Peroxy Radicals

The reaction rate constants of methyl peroxy radical (CH3 O2 ), a prototype of alkyl peroxide radical, has been obtained as 7.6 × 10−12 , 1.8 × 10−11 , 5.1 × 10−12 , and 3.5 × 10−13 cm3 molecule−1 s−1 at 298 K for NO, NO2 , HO2 , and CH3 O2 , respectively (Calvert et al. 2008). Although the rate constant with NO2 is the largest among these reactions, the atmospheric lifetime of the product, CH3 O2 NO2 is less than 1 s at room temperature, and the reaction is not important in the boundary layer in general. However, CH3 O2 NO2 is important as a reservoir of NO2 in the upper troposphere where the temperature is low, and it is actually observed by Nault et al. (2015). The rate constant of the self-reaction of CH3 O2 is more than one order of magnitude smaller than that of the reaction with HO2 ; the reaction is not so important as compared to CH3 O2 + HO2 . As reactions of alkyl peroxy radicals in the polluted atmosphere, the reactions with NO and HO2 are the most important. The rate constants of the reaction of NO with alkyl peroxides with higher carbon numbers are 9.2 × 10−12 , 7.9 × 10−12 , and 1.1 × 10−11 cm3 molecule−1 s−1 for ethyl peroxy (C2 H5 O2 ), t-butyl peroxy ((CH3 )3 CO2 ), and cyclopentyl peroxy (cyclo-C5 H9 O2 ) radicals, respectively, so that their rate constants are about the same as CH3 O2 (Calvert et al. 2008). Meanwhile, the rate constants of ethyl peroxy (C2 H5 O2 ), 2,2-dimethyl-1-propyl peroxy ((CH3 )3 CCH2 O2 ), cyclo-C5 H9 O2 , and decyl peroxy (n-C10 H21 O2 ) radicals with HO2 are 7.8 × 10−12 , 1.5 × 10−11 , 1.7 × 10−11 , and 2.0 × 10−11 cm3 molecule−1 s−1 , respectively, thus showing the higher reaction rate constants for higher carbon number radicals (Calvert et al. 2008). Therefore, ROOH formed from Reaction (3.91) could be a source of low-volatile compounds contributing to the formation of SOA. 3.3.1.2

Reactions of Alkoxy Radicals

Among the reaction pathways of RO2 radical with NO, Reaction (3.85a) forms an RO radical accompanying the oxidation of NO to NO2 , and since OH is regenerated from RO, this reaction is an important step for constituting chain reaction system producing O3 in the troposphere (Akimoto 2016, p. 291). Meanwhile, Reaction (3.85b) acts as a chain termination by forming stable compound, alkyl nitrate RONO2 , and the branching ratio of these reactions k 3.85b /k 3.85a is an important parameter for photochemical ozone formation rate in the polluted atmosphere. Further, since the RONO2 produced from hydrocarbons with large carbon numbers are low volatile, they are important from the point of SOA formation. Table 3.8 compiles the formation ratio of RONO2 in the reaction of each peroxy radical with NO, including those forming from alkene-OH reactions (Calvert et al. 2008). The formation ratio of RONO2 generally increases with the

165

166

3 Gas-Phase Reactions Related to Secondary Organic Aerosols

Table 3.8 Yields of alkyl nitrate and hydroxyalkyl nitrate in the reaction of OH-induced reaction of alkanes and alkenes at room temperature and at 1atm. Reactants

Products

Nitrate Yield

Ethane

Ethyl nitrate

≤0.014

Propane

1-Propyl nitrate

Alkanes, Cycloalkanesa)

2-Propyl nitrate

0.020 0.05 ≤0.04

n-Butane

1-Butyl nitrate

i-Butane

2-Methyl-1-propyl nitrate

0.075

t-Butyl nitrate

0.18

1-Pentyl nitrate

0.06

2-Pentyl nitrate

0.13

2-Butyl nitrate

n-Pentane

n-Hexane

n-Heptane

0.083

3-Pentyl nitrate

0.12

1-Hexyl nitrate

0.12

2-Hexyl nitrate

0.22

3-Hexyl nitrate

0.22

1-Heptyl nitrate

0.20

2-Heptyl nitrate

0.32

3-Heptyl nitrate

0.31

4-Heptyl nitrate

0.29

1-Octyl nitrate

0.36

2-Octyl nitrate

0.35

3-Octyl nitrate

0.34

4-Octyl nitrate

0.32

Cyclopentane

Cyclopentyl nitrate

0.05

Cyclohexane

Cyclohexyl nitrate

0.09

Cycloheptane

Cycloheptyl nitrate

0.05

Ethene

Nitrooxy ethanol

0.0086

Propene

1-Nitrooxy-2-propanol

0.0062

2-Nitrooxy-1-propanol

0.0092

n-Octane

Alkenes,

Cycloalkenesb)

1-Butene

1-Nitrooxy-2-butanol

0.011

2-Nitrooxy-1-butanol

0.014

Z-2-Butene

2-Nitrooxy-3-butanol

0.034

1-Hexene

1-Nitrooxy-2-hexanol

0.023

2-Nitrooxy-1-hexanol

0.032

a) Lightfoot et al. (1992) and references therein. b) O’Brien et al. (1998).

3.3 OH Radical-Induced Oxidation Reactions

decrease of temperature and increase of pressure, but varies significantly with molecular structure. As shown in Table 3.8, the formation ratios of RONO2 under atmospheric conditions are 108 s−1 , which is two orders of magnitude larger than the experimental value noted above due to the much lower estimated activation energy (4–5 kJ mol−1 ) (Méreau et al. 2003). From these discussions, the preferential pathways among the intermolecular H-atom abstraction by O2 , unimolecular decomposition, and unimolecular isomerization via intramolecular H-atom abstraction need to be evaluated for each alkoxy radical relevant to the atmosphere.

Table 3.9 Unimolecular decomposition rate of alkoxy radicals. Alkoxy radicals

Unimolecular decomposition reactions

1-Butoxy 2-Butoxy

Decomposition rates (s−1 )

Ea (kJ mol−1 )

Ref.

CH3 CH2 CH2 CH2 O → C3 H7 ⋅ + HCHO

1

4.0 × 10 1.4 × 102

62 68

Somnitz and Zellner (2000b)a) Méreau et al. (2000)a)

CH3 CH2 CH(O⋅)CH3 → C2 H5 ⋅ + CH3 CHO

2.7 × 104 3.5 × 104 1.6 × 104

50 53

Somnitz and Zellner (2000b)a) Méreau et al. (2000)a) Hein et al. (1998)

CH3 CH2 CH(O⋅)CH3 → CH3 ⋅ + C2 H5 CHO

4.6 × 101 3.1 × 101

61 72

Somnitz and Zellner (2000b)a) Méreau et al. (2000)a)

∙

Isobutoxy

(CH3 )2 CHCH2 O⋅ → (CH3 )2 CH⋅ + HCHO

5.7 × 104

52

Méreau et al. (2000)a)

tert-Butoxy

(CH3 )3 CO⋅ → CH3 ⋅ + CH3 COCH3

3.0 × 103 1.7 × 103

62 53

Méreau et al. (2000)a) Blitz et al. (1999)

1-Pentoxy

CH3 CH2 CH2 CH2 CH2 O⋅ → C4 H9 + HCHO

2.6 × 100

60

Somnitz and Zellner (2000b)a)

2-Pentoxy

CH3 CH2 CH2 CH(O⋅)CH3 → C3 H7 ⋅ + CH3 CHO

1.0 × 104 2.2 × 104 1.2 × 104

51 55 57

Somnitz and Zellner (2000b)a) Méreau et al. (2000)a) Dóbé et al. (1986)

CH3 CH2 CH2 CH(O⋅)CH3 → CH3 ⋅ + C3 H7 CHO

5.1 × 101 4.7 × 101

60 71

Somnitz and Zellner (2000b)a) Méreau et al. (2000)a)

CH3 CH2 CH(O⋅)CH2 CH3 → C2 H5 ⋅ + C2 H5 CHO

3.3 × 104 3.4 × 104

52 56

Somnitz and Zellner (2000b)a) Méreau et al. (2000)a) Méreau et al. (2000)a)

3-Pentoxy

(CH3 )2 C(O⋅)CH2 CH3 → C2 H5 ⋅ + CH3 COCH3

9.4 × 105

44

(CH3 )2 C(O⋅)CH2 CH3 → CH3 ⋅ + C2 H5 COCH3

1.1 × 104

58

Méreau et al. (2000)a)

Neopentoxy

(CH3 )3 CCH2 O⋅ → t-C4 H9 ⋅ + HCHO

3.6 × 106 ∼ 1 × 106

40 43

Méreau et al. (2000)a) Lightfoot et al. (1990)

Cyclopentoxy

Cyclo-C5 H10 O⋅→ ⋅CH2 CH2 CH2 CH2 CHO

> 1 × 107

< 42

Orlando et al. (2000)

Cyclohexoxy

Cyclo-C6 H12 O⋅→ ⋅CH2 CH2 CH2 CH2 CH2 CHO

5 × 104

48

Orlando et al. (2000)

2-Methyl-2-butoxy

a)

Theoretical studies.

170

3 Gas-Phase Reactions Related to Secondary Organic Aerosols

Reaction Scheme 3.12 Reaction mechanism of the isomerization pathway of 2-hydroxy radical via 1,5-hydrogen atom shift.

3.3.2

Alkynes

The oxidation reaction of acetylene (C2 H2 ) with OH radicals in the presence of NO has long been studied, and the main product is known to be glyoxal (HC(O)CHO) (Hatakeyama et al. 1986b; Akimoto 2016, p. 305). The reaction was later studied in the flow system by the use of chemical ionization mass spectrometer (CIMS), and glyoxal was confirmed to be the primary product (Yeung et al. 2005). Other than glyoxal, formic acid has been found as a product of OH-induced oxidation of acetylene (Hatakeyama et al. 1986b; Yeung et al. 2005). Similarly, methylglyoxal (CH3 C(O)CHO) and biacetyl (CH3 COCH3 CO) are the products from propyne (C3 H4 ) and 2-butyne (C4 H6 ), respectively (Hatakeyama et al. 1986b; Yeung et al. 2005), although the mixing ratios of these compounds are much lower than acetylene in the polluted atmosphere. Glyoxal and methylglyoxal are water-soluble and form dicarboxylic acids and oligomers by the aqueous phase reactions in cloud/fog droplets and aerosol water particles, as will be mentioned in Chapter 4. The pathways to form glyoxal and formic acid in the OH-induced reaction of acetylene have been proposed as follows (Hatakeyama et al. 1986b; Galano et al. 2008). CH ≡ CH + OH (+M) → HOCH = CH (+M)

(3.91)

HOCH=CH + O2 (+M) → HOCH=CHO2 (+M)

(3.92)

HOCH=CHO2 + NO → HOCH=CHO + NO2

(3.93)

HOCH=CHO + O2 → HC(O) − CHO + HO2

(3.94)

HOCH=CHO2 → HOCH(O) − CHO → HCOOH + HCO

(3.95)

3.3 OH Radical-Induced Oxidation Reactions

3.3.3 3.3.3.1

Alkenes, Dialkenes, and Cycloalkenes Alkenes

As for the photooxidation reactions of alkenes by OH radicals related to secondary aerosol, the formation of two category of products, water-soluble C2 carbonyl compounds such as glycolaldehyde (HOCH2 CHO) from ethene (ethylene) serving as precursors of SOA formation by the aqueous phase reactions, and semi-volatile molecules such as hydroxynitrates and dihydroxynitrates from ≥C6 alkenes is concerned. The OH-induced photooxidation of ethene (C2 H4 ) in the presence of NO forms glycolaldehyde and formaldehyde with the yield of 0.22 and 0.78, respectively (Niki et al. 1981). The reaction pathways to form these compounds have been thought as follows (Calvert et al. 2000). CH2 =CH2 + OH (+M) → HOCH2 CH2 (+M)

(3.96)

HOCH2 CH2 + O2 (+M) → HOCH2 CH2 O2 (+M)

(3.97)

HOCH2 CH2 O2 + NO → HOCH2 CH2 O + NO2

(3.98a)

HOCH2 CH2 O + O2 → HOCH2 CHO + HO2

(3.99)

HOCH2 CH2 O (+M) → HOCH2 + HCHO (+M)

(3.100)

HOCH2 + O2 → HCHO + HO2 .

(3.101)

Other than these carbonyl compounds, 2-hydroxyethyl nitrate (HOCH2 CH2 ONO2 ) is known to form with the yield of 0.09 in the OH-induced reaction of ethene under the presence of NO competing with Reaction (3.98a) (O’Brien et al. 1998). HOCH2 CH2 O2 + NO → HOCH2 CH2 ONO2 .

(3.98b)

As for the semi-volatile products related directly to the SOA formation in the OH reaction of ≥ C6 alkenes, β-hydroxy carbonyls (β- stands for the bonding of -OH to the carbon atom next to the carbonyl group), dihydroxy carbonyls, β-hydroxy nitrates, and dihydroxy nitrates are formed together with formaldehyde (Atkinson 1997; Calvert et al. 2000; Atkinson and Arey 2003). Among the ≥C6 alkenes, photooxidation of 1-octene (1-C8 H16 , CH2 =CHCH2 CH2 CH2 CH2 CH2 CH3 ) has been studied well and β-hydroxy nitrates and dihydroxy nitrates are identified in the aerosol phase, and heptanal and 4-hydroxy hexanal in the gas phase (Forstner et al. 1997; Aschmann et al. 2010). One of the characteristics of the photooxidation of ≥C6 alkenes is the formation of dihydroxyalkyl radicals by intramolecular 1,5-hydrogen shift in the OH-added oxyradicals competing with the unimolecular decomposition. O• R1

R2

OH OH-added oxyradical

H

(a) O• (b) R2 (a) 1,5-hydrogen

R1 OH

(b)

shift

OH R1

R2

de

(3.102a)

• co

mp o

OH dihydroxyalkyl radical

sit

ion

R1 O + R2CHOH

(3.102b)

171

172

3 Gas-Phase Reactions Related to Secondary Organic Aerosols

Dihydroxy nitrates and dihydroxy carbonyl compounds are produced from the dihydroxyalkyl radical formed in Reaction (3.102a) by the similar reaction of hydroxyalkyl radical, Reaction (3.98b) and (3.98a) followed by (3.99) , respectively. Based on these considerations, reaction mechanism of OH-induced oxidation of straight-chain 1-alkenes in the presence of NO is shown in Reaction Scheme 3.13 (Matsunaga and Ziemann 2009). The pathway of alkyl nitrate formation competing with the oxidation of NO seen in Reaction (3.98a, 3.98b) and Reaction Scheme 3.13, RO2 + NO → RO + NO2

(3.85a)

→ RONO2

(3.85b)

is well known, and is important as a chain termination reaction (Finlayson-Pitts and Pitts Jr. 2000; Akimoto 2016, p. 199). The yields of hydroxy nitrates Φ(RONO2 ) = k 98b /(k 98a + k 98b ) formed in type of Reaction (3.98b) have been obtained experimentally for C2 -C8 alkenes (O’Brien et al. 1998; Teng et al. 2015), C8 -C17 1-alkenes, and C14 -C17 internal alkenes (Matsunaga and Ziemann 2009). In general C2 -C6 β-hydroxy nitrates are reaction products in the gas phase, and C8 -C17 β-hydroxy nitrates are partitioned between the gas phase and particle phase (Matsunaga and Ziemann 2009). Production yields of alkyl nitrate generally increase with carbon number, but the yields of hydroxy nitrates from alkenes are less than 50% of the yields of alkyl nitrates from alkanes with α1 R1

R2

OH

αc=c

R2 P2 ONO2 O

R1 P6

α2

R1

R2

OO • R1

R2

R1

NO

same pathways

P4 O O2NO OH R1 R2 R1

HO2 R2

O2 O P5

HO2 decomposition

OH R1

R2

O

R1 P6

OH

P10 O

R2 P3 OH

isomerization

R2

R1

O2

R2

P5 OH OH

ONO2 R2

R1

P1 OH O

OH

O

P8 OH

+ NO α3

O• R2

R2

OH α5 NO2

R1

OH

OH R1

+ O2

OH OH

H-abstraction 1 - αc=c products

R2

R1

+ O2 OH R1 NO

R2 O•

OO • NO2

OH R1

R2

OH

R2 OH

OH R1

OH OH

isomerization R 1

+ NO

OH

O2 HO2

R2 ONO2 OH P7 O

R1

R2 OH OH P9

Reaction Scheme 3.13 Reaction Scheme of OH-induced oxidation of straight chain 1-alkenes. Source: Adapted with permission from Matsunaga and Ziemann (2009). Copyright 2009 American Chemical Society.)

3.3 OH Radical-Induced Oxidation Reactions

the same carbon number (Arey et al. 2001). According to the ab initio calculation of O’Brien et al. (1998), the O—O bond energy, D0 (O—O), in the peroxynitrite (ROONO) formed from the β-hydroxy alkylperoxy radical and NO as a reaction intermediate is lowered due to intramolecular hydrogen bond, and the yield is suggested to decrease compared to alkyl nitrate from alkanes. Matsunaga and Ziemann (2009) reported that the yield of C14 -C17 hydroxyalkyl nitrates reaches a constant value of 0.140 ± 0.009. 3.3.3.2

1,3-Butadiene

1,3-Butadiene (CH2 =CHCH=CH2 ) is important as a fundamental prototype compound of isoprene as well as an anthropogenic volatile organic compound (VOC), which exists widely in polluted atmosphere. The OH-induced atmospheric oxidation reaction of 1,3-butadiene is known to form SOA like the O3 reaction mentioned in Section 3.2.2. The reaction of OH and 1,3-butadiene in the presence of NOx forms acrolein (CH2 =CHCHO) (yield, 0.59), 4-hydroxy-2-butenal (HOCH2 CH=CHCHO) (0.23), and formaldehyde (HCHO) (0.64) as main products, and furan (1-oxa-2,4-cyclopentadiene) (0.05) and organic nitrates (0.11) as side products (Tuazon et al. 1999; Sprengnether et al. 2002; Berndt and Böge 2007). Formation mechanism of main products of the OH-induced oxidation of 1,3-butadiene is shown in Reaction Scheme 3.14 (Liu et al. 1999a; Berndt and Böge 2007).

Reaction Scheme 3.14 Formation mechanism of formaldehyde, acrolein, and 4-hydroxy-2-butenal in the OH-induced oxidation reaction of 1,3-butadiene in the presence of NOx . Source: Based on Liu et al. (1999a); Berndt and Böge (2007).

The addition of OH radicals to the double bond of 1,3-butadiene is known to occur in the terminal carbon in the ratio of 0.87 ± 0.08 (Ghosh et al. 2010). As seen in Reaction Scheme 3.14, 1,2-adduct forms acrolein and formaldehyde, and 1,4-adduct forms E-4-hydroxy-2-butenal. Although the reaction mechanism of the formation of furan has not been established, Reaction Scheme 3.15 has been proposed to form furan from cis-1,4-adduct (Berndt and Böge 2007). In Reaction Scheme 3.15, it is assumed that the intramolecular H-shift of 𝛿-hydroxyalkoxy radical is faster than bimolecular H-abstraction by O2 based on the quantum chemical calculation by Dibble (2002). Organic nitrates in the photooxidation of 1,3-butadiene are thought to form by the type of Reaction (3.98b) mentioned in the previous subsection (Sprengnether et al. 2002). The main products, acrolein and 4-hydroxy-2-butenal, further react with OH with large rate constants to form glyoxal, glycolaldehyde, and hydroxy malondialdehyde as secondary products, which are precursors of SOA formation in the aqueous phase. Reaction Scheme 3.16 shows the formation scheme of these compounds in the OH-induced reaction of acrolein and 4-hydroxy-2-butenal (Liu et al. 1999b; Berndt and Böge 2007).

173

174

3 Gas-Phase Reactions Related to Secondary Organic Aerosols

Reaction Scheme 3.15 Formation mechanism of furan in the OH-induced oxidation reaction of 1,3-butadiene to form 1,4-cis-adduct in the presence of NOx . Source: Based on Berndt and Böge (2007).

Reaction Scheme 3.16 Secondary formation mechanism of glyoxal, glycolaldehyde, and hydroxy malondialdehyde in the OH-induced oxidation reaction of acrolein and 4-hydroxy-2-butanal. Source: Based on Liu et al. (1999b); Berndt and Böge (2007).

As will be mentioned in the next subsection, the reaction product, epoxides (isoprene epoxydiol, IEPOX), is an important precursor of SOA in the OH-induced oxidation reaction of isoprene. In the case of 1,3-butadiene, butadiene epoxydiol (BEPOX) corresponding to IEPOX has been presumed to be an SOA-precursor product, but this has not been confirmed experimentally (Jaoui et al. 2014). 3.3.3.3

Cycloalkenes and Methylene cyclohexane

Cyclohexene, 1-methylcyclohexene, and methylenecyclohexane are interesting as prototype compounds of α-pinene and β-pinene. The OH-induced oxidation reaction of cyclohexene does not form SOA being different from the O3 reaction discussed in Section 3.2.4. Although the reaction products of the OH-induced reaction of cycloalkenes and methylenecyclohexane have scarcely been identified, Aschmann et al. (2012) reported 1,6-hexanedial (yield 0.76) and 1,2-dihydroxy-cyclohexyl nitrate (0.05–0.07) for the cyclohexene-OH reaction, and 6-oxo-heptanal (0.82) and 1-methyl-1-hydroxycyclohexyl nitrate (0.07–0.09) for the 1-methylcyclohexene reaction in the presence of NO. Reaction Scheme 3.17 shows reaction pathways of OH-induced oxidation reaction of 1-methylcyclohexene in the presence of NO (Aschmann et al. 2012). A reaction

3.3 OH Radical-Induced Oxidation Reactions

Reaction Scheme 3.17 Mechanism of the OH-induced oxidation reaction of 1-methylcyclohexene in the presence of NO. Source: Based on Aschmann et al. (2012).

product from the isomerization reaction via the intramolecular hydrogen abstraction of 1,2-hydroxyalkoxy radical has not been identified. In the case of cyclohexene, since there is no ring strain, relatively high energy barrier of 48 ± 9 kJ mol−1 has been estimated for the rupture of the ring of cyclohexoxy radical, but the energy barrier for cyclopentoxy radical is lower, 42 kJ mol−1 , so that the ring cleavage is thought to be easier (Orlando et al. 2000). 3.3.4

Isoprene

A lot of studies have been conducted on the OH-induced photooxidation of isoprene since isoprene has the highest emission among the biogenic hydrocarbons globally, and is a very important species in atmospheric chemistry. The OH-induced oxidation reaction of isoprene does not produce aerosols directly since the primary products have relatively high volatility. However, it has been well known that OH-induced oxidation reaction of isoprene is actually an important source of SOA from many chamber experiments and field observations, and various studies on its reaction mechanism have been made (Claeys et al. 2004; Surratt et al. 2006 and references therein). Among the gaseous products of the OH reaction of isoprene, two categories of compounds are important as precursors of SOA formation; one is carbonyl compounds such as glyoxal (GLY), methylglyoxal (MGLY), glycolaldehyde (GLCA), hydroxyacetone (HACT), etc., which are formed in the secondary OH reaction of main products of the isoprene reaction, i.e. methyl vinyl ketone (MVK) and methacrolein (MACR), and the other is isoprene epoxydiol (IEPOX), formed in the secondary OH reaction of hydroxy isoprene nitrate (ISOPN) and isoprene hydroxy hydroperoxide (ISOPOOH) (Paulot et al. 2009b; Surratt et al. 2010; Lin et al. 2013; Jacobs et al. 2014). The formation of MVK and MACR and C2 and C3 carbonyl compounds from them, and the production of ISOPN, ISOPOOH, and IEPOX are discussed here, and the SOA formation from the C2 and C3 carbonyl compounds and IEPOX will be mentioned in Chapter 4 since they proceed in the aqueous phase in the atmosphere. 3.3.4.1

Fundamental Processes of OH-Induced Oxidation Reaction

The main products of the oxidation reaction of isoprene initiated by OH radicals are MVK (CH2 =CHC(O)CH3 ) (yield, 0.21–0.28), MACR (CH2 =C(CH3 )CHO) (0.30–0.44),

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and formaldehyde (HCHO) (0.6–0.7) (Tuazon and Atkinson 1990b; Miyoshi et al. 1994; Sprengnether et al. 2002; Fan and Zhang 2004; Karl et al. 2006; Paulot et al. 2009a; Galloway et al. 2011). Other products reported are organic nitrate esters such as hydroxy isoprene nitrate (Sprengnether et al. 2002; Paulot et al. 2009b; Lockwood et al. 2010), and hydroxy hydroperoxides (Paulot et al. 2009b). Among them organic nitrate esters and hydroperoxides are formed in the competitive reactions of alkylperoxy-type radicals (RO2 ) with NO and HO2 , respectively, RO2 + NO → RONO2

(3.85b)

RO2 + HO2 → ROOH + O2

(3.87)

so that their yields depend largely on experimental conditions such as the mixing ratio of NOx . In addition to these compounds, glyoxal (GLY, HC(O)CHO), methylglyoxal (MGLY, CH3 C(O)CHO), glycolaldehyde (GLCA, HOCH2 CHO), and hydroxyacetone (HACT, CH3 C(O)CH2 OH) are reported to be formed as minor primary products with yields of less than a few % (Paulot et al. 2009a; Galloway et al. 2011). These compounds are the main products of the OH reactions of MVK and MACR. The 95% of isoprene-OH reaction is the addition to C=C double bonds, and the H-abstraction is estimated to be 5% (Campuzano-Jost et al. 2000). The main pathways of the formation of MACR, MVK, and other carbonyl compounds in the OH-induced oxidation of isoprene are shown in Reaction Scheme 3.18 (Sprengnether et al. 2002; Dibble 2002; Fan and Zhang 2004; Paulot et al. 2009a; Peeters and Nguyen 2012). Since isoprene has two nonequivalent, nonsymmetrically substituted C=C double bonds, there are four different carbon atoms to which an OH radical attaches. Among them, the main route is the attachment to either of terminal carbon-atoms to form more stable allyl-type radicals such as follows. (A)

∙

CH2 = C(CH3 ) − CH = CH2 + OH → HOCH2 − C(CH3 ) − CH = CH2 ↕ ∙ HOCH2 − C(CH3 ) = CH − CH2 (B)

(3.103)

∙

CH2 = C(CH3 ) − CH = CH2 + OH → CH2 = C(CH3 ) − CH − CH2 OH ↕ ∙ CH2 − C(CH3 ) = CH − CH2 OH

(3.104)

The ratio of Reaction (3.103) and (3.104) has been estimated to be 0.56 : 0.37 (Fan and Zhang 2004). In the atmosphere, O2 would add to either of unpaired electron of these two allyl-type hydroxy isoprenyl radicals to give peroxy radicals (Fan and Zhang 2004; Paulot et al. 2009a). As shown in Reaction Scheme 3.18, when O2 adds to the carbon atom adjacent to the OH-added carbon atom, 1-hydroxy-2-isoprenylperoxy and 4-hydroxy-3-isoprenylperoxy radicals ((1,2)-OO and (4,3)-OO, respectively) are formed, from which the main products, MVK and MACR, are produced. On the other hand, when O2 adds to the carbon atom far from the OH-added carbon atom, (1,4)and (4,1)-type hydroxy-isoprenyl peroxy radicals are formed. For these radicals, two different stereo conformations are possible in regard to the OH- and OO- groups.

3.3 OH Radical-Induced Oxidation Reactions

When the OH- and OO- are on the same or opposite side of the C=C double bond, the conformer is called Z or E respectively. Thus formed Z1,4 , E1,4 , and Z4,1 , E4,1 -type peroxy radicals react with NO to form corresponding oxy radicals. In Reaction Scheme 3.18, only the reaction pathways through the Z1,4 -OO and Z4,1 -OO peroxy radicals are shown for simplicity. The ratios of reaction pathways (a) and (b) in the scheme are 0.41 and 0.15 (total 0.56), and those of (c) and (d) are 0.23 and 0.14 (total 0.37), while the formation ratio of Z1,4 - and E1,4 -radicals and that of Z4,1 and E4,1 -radicals are both estimated to be 0.85 : 0.15 (Paulot et al. 2009a). Peculiar type of reactions of hydroxy-isoprenyloxy radicals (Z1,4 -O and Z4,1 -O) to form allyl-type dihydroxy isoprenyl radicals via the fast intramolecular 1,5-H shift reaction has been suggested by the quantum chemical calculation (Dibble 2002). Corresponding peroxy radicals are thought to form from dihydroxy isoprenyl radicals in the atmosphere, as shown in Reaction Scheme 3.18. It has been estimated that the energy barriers of intramolecular 1,6-hydrogen shift in the (Z1,4 -OH)-OO and (Z4,1 -OH)-OO radicals are very low to form hydroxy-hydroperoxy-ketoisoprenyl radicals based on the theoretical calculation (Peeters and Nguyen 2012). These 1,6-H shift reactions are thought to proceed faster than bimolecular reactions with NO to form oxy radicals even under high NOx conditions. The hydroxy-hydroperoxy-ketoisoprenyl radical from (Z1,4 -OH)-OO reacts with O2 /NO to form oxy radicals, and their decomposition would produce MGLY and GLCA as shown in the scheme. Similarly, GLY and HACT would be formed from (Z4,1 -OH)-OO.

Reaction Scheme 3.18 Reaction mechanism of primary production of MACR, MVK, and other carbonyl compounds in the OH-induced oxidation of isoprene in the presence of NOx . Source: Based on Sprengnether et al. (2002); Dibble (2002), Fan and Zhang (2004), Paulot et al. (2009a), and Peeters and Nguyen (2012).

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3.3.4.2

HOx Radicals Regeneration Reaction

In the ambient air of pristine forest where isoprene concentration is high like in Amazonia, much higher concentrations of OH radicals than predicted by conventional models have been observed (Tan et al. 2001; Carslaw et al. 2001; Kuhn et al. 2007; Lelieveld et al. 2008) (cf. Section 8.5), and the OH regeneration pathways in the reaction of isoprene with OH has been considered theoretically and experimentally. Based on the quantum chemical calculations, it has been proposed that OH radicals are regenerated in the intra-molecular hydrogen abstraction reactions to form OH + HCHO + MVK and OH + HCHO + MACR via the 1,5-H-shft of peroxy radicals, (1,2-OO) and (4,3-OO), formed in the OH addition to the 1- and 4-position carbon atoms of isoprene as shown in Reaction Scheme 3.18 (Peeters et al. 2009; Silva et al. 2010). Peeters et al. (2009) also proposed that HO2 and hydroperoxy methylbutenal are formed via 1,6-H-shift from peroxy radicals, (Z1,4 -OO) and (Z4,1 -OO), from the OH addition to the 1- and 4-position carbon atoms of isoprene. Reaction Scheme 3.19 shows the regeneration mechanism of OH and HO2 radicals in the OH-isoprene reaction based on the proposal of Peeters et al. (2009).

Reaction Scheme 3.19 Mechanism for OH and HO2 radical formation in the OH addition reaction to isoprene under the low NO conditions. Source: Based on Peeters et al. (2009).

Hydroperoxy methylbutenal in the above scheme is also called C5 -hydroperoxyenals (C5 -HPALD), and is suggested to produce additional OH radicals by the photolysis (Peeters et al. 2009), which is confirmed experimentally (Wolfe et al. 2012). In the chamber experiment under low concentration of NO (100 pptv), the ratio of measured OH concentration increased by a factor of 2 compared to the calculated values of the master chemical mechanism (MCM) model (Saunders et al. 2003), which supported the theoretical presumption of OH regeneration by the 1,5-and 1,6-shifts in the isoprene peroxy radicals (Fuchs et al. 2013). From this experimental result, it is suggested that more than 50% of OH radicals consumed by isoprene in the isoprene-rich forest regions are recycled by the reactions mentioned above.

3.3 OH Radical-Induced Oxidation Reactions

3.3.4.3 Formation of Isoprene Hydroxy Hydroperoxide (ISOPOOH) and Isoprene Epoxydiol (IEPOX)

In Reaction Scheme 3.18, although only the main reaction pathways of hydroxyisoprenyl peroxy radicals to form oxy radicals RO2 + NO → RO + NO2

(3.85a)

are shown, other pathways to form organic nitrates and hydroperoxides are also important as have been mentioned regarding to 1,3-butadiene. RO2 + NO → RONO2

(3.85b)

RO2 + HO2 → ROOH + O2

(3.87)

The isoprene hydroxy hydroperoxides (ISOPOOH, also called hydroxy-isoprenyl hydroperoxide) are formed from the reactions of the hydroxy peroxy radicals, 4,3-OO and Z4,1 -OO, in the MACR forming pathway with HO2 as follows (Paulot et al. 2009b; Surratt et al. 2010; St. Clair et al. 2016). •O

HO O

O

HO2 –O2 OH

OH

(4,3)-OO

O

(4,3)-ISOPOOH

O•

O OH

Z4,1-OO

(3.105)

OH

HO2

OH

–O2 Z4,1-ISOPOOH

(3.106)

Similarly, ISOPOOH is formed from 1,2-OO and Z1,4 -OO radicals in the MVK forming pathway. The rate constant of the reaction of the primary product, ISOPOOH, with OH is very large, ∼1 × 10−10 cm3 molecule−1 s−1 , as seen in Table 3.7. The pathway of the OH-ISOPOOH reaction is thought to be both addition to C=C double bond and H-atom abstraction. The main pathway is the addition reaction and the ratio of the hydrogen abstraction has been estimated as 15% and 7% for (1,2)- and (4,3)-ISOPOOH, respectively (St. Clair et al. 2016). From the addition reaction, isoprene epoxydiol (IEPOX) that is deeply related to the SOA formation is formed as a main product (Paulot et al. 2009b; Surratt et al. 2010; St. Clair et al. 2016). The formation pathways of IEPOX from the OH addition reaction of ISOPOOH formed by Reactions (3.105) and (3.106) are as follows.

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HO

HO O

O

HO

+ OH

O

HO

•

+ OH

OH

OH

OH β-IEPOX

(4,3)-ISOPOOH

(3.107)

O

OH

OH

O OH

O

OH

+ OH •

OH + OH OH

OH

δ4-IEPOX

Z4,1-ISOPOOH

(3.108) Thus, 2-methyl-2,3-epoxy-1,4-butandiol (β-IEPOX) and 3-methyl-3,4-epoxy1,2-butandiol (δ4 -IEPOX) are formed, and similarly β-IEPOX and 2-methyl-3,4-epoxy1,2-butanediol (δ1 -IEPOX) are formed from (1,2)- and Z1,4 -ISOPOOH (Paulot et al. 2009b). Paulot et al. (2009b) confirmed the reaction mechanism by the experiment using the 18 OH and also showed ISOPOOH correlates energetically favorably with IEPOX by the quantum chemical calculation. The yield of IEPOX formation in the OH-ISOPOOH reaction has been estimated as 80% and the remaining products are thought to be GLCA and HACT e.g. in the case of (4,3)-ISOPOOH (St. Clair et al. 2016). HO

O O2

O

HO •

OH

NO NO2

OOH

HO O•

OH

O +

OH HACT

+ OH OH GLCA

(3.109) Similarly, other isomers of ISOPOOH also form HACT and GLCA. Although IEPOX is an important intermediate to give SOA components (e.g. organic sulfate) in the aqueous phase in the atmosphere, it should be noted that the reaction rate constant with OH in the gas-phase is also as large as ∼1 × 10−11 cm3 molecule −1 s−1 . In comparison with un-substituted epoxide (e.g. ethylene oxide, propylene oxide, and butene oxide), whose OH rate constants are given in Table 3.7, large rate constant of IEPOX is thought to be due to the substituent such as adjacent OH groups. The products and pathways of OH-IEPOX reaction in the gas phase are given by Jacobs et al. (2013) and Bates et al. (2014). The reactions of IEPOX in the atmospheric aqueous phase will be discussed in Chapter 4. 3.3.4.4

Formation of Hydroxy Isoprene Nitrates

In the presence of NO above a certain level, hydroxy isoprene nitrates (ISOPN) are formed as primary products (Paulot et al. 2009b; Surratt et al. 2010; Jacobs et al. 2014; Bates et al. 2014). For example, (4,3)- and Z4,1 -ISOPN are formed from the reactions

3.3 OH Radical-Induced Oxidation Reactions

of (4,3)- and Z4,1 -hydroxy isoprenylperoxy radicals (ISOPOO) with NO in the MACR formation pathway. •O O

ONO2

NO

OH

OH (4,3)-OO

O

(4,3)-ISOPN

O• NO OH

Z4,1 -OO

(3.110)

ONO2 OH Z4,1 -ISOPN

(3.111)

Since similar nitrates are formed from ISOPOO in the MVK forming pathway and ISOPOO formed from OH addition to the internal carbon atoms of C=C double bond, altogether 8 kinds of ISOPN can exist (Lockwood et al. 2010; Lee et al. 2014; Jacobs et al. 2014). A large value for the rate constant of ISOPOO and NO reaction has been reported to be 1.1 × 10−11 cm3 molecule −1 s−1 (Chuong and Stevens 2002), and overall formation ratio of RONO2 as 0.07–0.15 under typical atmospheric conditions (Sprengnether et al. 2002; Chuong and Stevens 2002; Lockwood et al. 2010). Since the reaction rate constants of ISOPN with OH are very large, ∼10−11 –10−10 cm3 molecule−1 s−1 , as seen in Table 3.7, they participate in the secondary photooxidation reactions in the atmosphere (Paulot et al. 2009a; Lee et al. 2014). For example, (4,3)-ISOPN gives hydroxy methyl ketone nitrate (HMKN) (yield 0.70), HACT (0.17), IEPOX (0.13), GLCA, and formaldehyde as products (Jacobs et al. 2014). Their formation mechanism is shown in Reaction Scheme 3.20 (Jacobs et al. 2014; Lee et al. 2014). While the rate constants of the reaction of ISOPN and O3 are very large, ∼10−17 cm3 molecule−1 s−1 for the E1,4 and Z1,4 - isomers with an internal double bond (see Table 3.2), and their reactions have to be considered together with the OH reaction, those for the

Reaction Scheme 3.20 The mechanism of the OH-induced oxidation reaction of (4,3)-ISOPN. Source: Based on Jacobs et al. (2014); Lee et al. (2014).

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4,3-isomers with the terminal double bond are two orders of magnitude smaller, and the reactions with O3 are not important. The reaction mechanisms of O3 with E1,4 - and Z1,4 -ISOPN have been discussed by Lee et al. (2014). 3.3.4.5

Reactions of Methyl Vinyl Ketone and Methacrolein

Methyl vinyl ketone (MVK) and methacrolein (MACR), which are the main products both of OH-induced reaction and O3 reaction (Section 3.2.3) of isoprene, further react with OH radicals in the atmosphere to form GLCA and MGLY from MVK and HACT and MGLY from MACR according to Reaction Scheme 3.21 (Tuazon and Atkinson 1990a; Orlando et al. 1999b; Paulot et al. 2009a).

Reaction Scheme 3.21 Formation mechanism of metylglyoxal (MGLY), glycolaldehyde (GLCA) and hydroxyacetone (HACT) in the reactions of methyl vinyl ketone (MVK) and methacrolein (MACR) in the presence of NO.

The reaction of OH with MVK is initiated by the addition to either of terminal or internal carbon atom of C=C double bond. The main reaction pathway is the addition to the terminal carbon atom with the ratio of ca. 72% (Calvert et al. 2011). The formation yields of GLCA and MGLY from MVK are reported to be 0.63–0.67 and 0.24–0.27, respectively (Tuazon and Atkinson 1989; Galloway et al. 2011). In the case of MACR, 55% of the total reaction is the addition to the double bond, and 45% is the aldehydic H-atom abstraction (Calvert et al. 2011). The main products are HACT (0.40–0.47) and MGLY(0.08-0.12) as shown in Reaction Scheme 3.21. The byproducts are reported as methacrolein hydroxy nitrate from addition reaction (Crounse et al. 2012) and methacryloylperoxy nitrate (MPAN) (also called peroxy methacryloyl nitrate) from the H-atom abstraction reaction (Tuazon and Atkinson 1990a, Orlando et al. 1999b; Galloway et al. 2011; Kjaergaard et al. 2012). Further, from the results of the chamber experiments (Kjaergaard et al. 2012; Lin et al. 2013), it has been reported that methacrylic peroxy acid (MAPA) is formed together with MPAN, and subsequent formation of hydroxymethyl-methyl-α-lactone (HMML) and

3.3 OH Radical-Induced Oxidation Reactions

methacrylic acid epoxide (MAEPOX) is also reported. These species are suggested to be intermediates contributing to the SOA formation from isoprene (Surratt et al. 2010; Chan et al. 2010; Lin et al. 2013). Proposed reaction mechanism to form HMML and MAEPOX is shown in Reaction Scheme 3.22 (Kjaergaard et al. 2012).

Reaction Scheme 3.22 Reaction mechanism of the formation of MPAN, MAPA, MAEPOX, and HMML from the OH-induced reaction of MACR. Source: Based on Kjaergaard et al. (2012).

The peculiar three membered ring compounds, HMML and MAEPOX, are thought to be related directly to SOA formation (Kjaergaard et al. 2012). MPAN formed in this reaction pathway is a kind of peroxy acyl nitrates (PANs) well known in photochemical air pollution. The precursor species, peroxy acyl radical gives MPAN and MAPA in the higher and lower concentration of NO, respectively. Quantum chemical calculation has been made for this reaction system, and the high yield formation of HMML from MPAN, and the formation of MAEPOX from MAPA have been shown theoretically (Kjaergaard et al. 2012; Lin et al. 2013). 3.3.5 3.3.5.1

Monoterpenes 𝛂-Pinene

α-pinene is thought to react with OH and O3 almost equally in the atmosphere (each rate constants are given in Tables 3.6 and 3.1, respectively). There have been many studies on the oxidation reaction of α-pinene by OH by the chamber experiments under the condition in which O3 is not formed. Early studies revealed that pinonaldehyde (C10 H16 O2 ), acetone, formaldehyde, formic acid, CO, CO2 , and nitrates are produced as primary products as well as aerosols (Hatakeyama et al. 1991; Nozière et al. 1999; Larsen et al. 2001). Recent experiments using a proton transfer reaction mass spectrometry (PTR-MS) have identified many hydroxy hydroperoxides (yield ∼0.23) and pinonaldehyde (∼0.20) mostly in the gas phase and partially in the particulate phase under the low NOx conditions where RO2 + HO2 reaction prioritizes RO2 + NO reaction (Lee et al.

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2006b; Eddingsaas et al. 2012). The secondary OH reactions of hydroxy hydroperoxides also produce pinonaldehyde, and its overall yield under the low NOx conditions is estimated to be ∼0.20 (Eddingsaas et al. 2012). On the other hand, under the high NOx conditions, the yield of pinonaldehyde increases by a factor of 1.5 as compared to the low NOx conditions, and many organic nitrates are formed from the primary reactions of α-pinene and secondary reactions of pinonaldehyde (Eddingsaas et al. 2012). The reaction of α-pinene and OH is initiated mainly by the addition to the cyclic double bond but hydrogen abstraction is also suggested to occur in the ratio of ∼ 12% (Peeters et al. 2001; Capouet et al. 2004). Reaction Scheme 3.23 shows the mechanism of formation of hydroxy hydroperoxides, pinonaldehyde, typical hydroxy nitrates, acetone, formaldehyde, etc. produced in the oxidation of α-pinene initiated by the OH addition reaction (Nozière et al. 1999; Eddingsaas et al. 2012).

Reaction Scheme 3.23 Reaction mechanism of the OH-initiated oxidation of α-pinene initiated by the addition of OH to the ring double bond. Source: Based on Nozière et al. (1999); Eddingsaas et al. (2012).

Quantum chemical calculations have been conducted for the reaction of α-pinene with OH, and the obtained rate constants agree well with the experimental values (Fan et al. 2005; Vereecken et al. 2007). As for the position of the OH addition, the branching ratio of reaction (a) and (b) in Reaction Scheme 3.23 is 0.66 : 0.34, and the addition to the carbon atom of the C=C double bond that does not have a methyl group to form tertiary radical is predominant according to the calculation (Fan et al. 2005). The calculation also shows that the energy barrier of C—C bond rupture of β-hydroxyalkoxy radical in the

3.3 OH Radical-Induced Oxidation Reactions

pathway to form pinonaldehyde shown in the scheme by reaction step (d) and (e) is as low as ca. 13 kJ mol−1 supporting the experimental evidence (Dibble 2001). Pinonaldehyde is a volatile compound that is produced primarily in a high yield not only by the OH reaction but also by the O3 reaction of α-pinene (cf. Section 3.2.5). Pinonaldehyde is a C10 -ketoaldehyde with dimethyl cyclobutane structure as seen in the above scheme and reacts with OH with a large rate constant, 3.5 × 10−11 cm3 molecule−1 s−1 (Table 3.7) to form SOA in the atmosphere (Davis et al. 2007), but does not react with O3 . As for the products of OH reaction of pinonaldehyde, pinonaldehyde PAN, pinonaldehyde nitrate, and norpinonaldehyde are known to form under the high NOx condition, and hydroperoxides under the low NOx condition (Eddingsaas et al. 2012). A part of these compounds are condensed to particles to form SOA (Chacon-Madrid et al. 2013). Reaction Scheme 3.24 shows the oxidation mechanism of pinonaldehyde by OH in the gas phase. The H-atom abstraction predominates in the reaction of pinonaldehyde with OH, and the ratio of abstraction from aldehydic hydrogen (CHO), exocyclic secondary hydrogen (CH2 ), and endocyclic tertiary hydrogen (CH) has been obtained as 0.59 : 0.23 : 0.14 from the theoretical calculation by Vereecken and Peeters (2002). In the above Reaction Scheme 3.24, the reaction pathways initiated by the H atom abstraction of aldehydic and tertiary hydrogen are shown. The reaction of tertiary hydrogen abstraction gives acetone that is observed experimentally and also explained theoretically (Fantechi et al. 2002).

Reaction Scheme 3.24 Oxidation reaction mechanism of pinonaldehyde initiated by the H-atom abstraction by OH radical. Source: Based on Nozière et al. (1999); Eddingsaas et al. (2012).

3.3.5.2

𝛃-Pinene

β-Pinene has larger and smaller rate constants than α-pinene for the OH and O3 reaction, respectively, so that in general it reacts predominantly with OH in the

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atmosphere (cf. Tables 3.6 and 3.1 for each rate constant). In the presence of NOx , nopinone (6,6-dimethyl-bicyclo[3.1.1]heptan-2-one), acetone, formaldehyde, formic acid, CO, and CO2 are known to be the main primary products (Arey et al. 1990; Hatakeyama et al. 1991; Larsen et al. 2001), and dihydroxy carbonyls, hydroxy nitrates, and dihydroxy nitrates are formed as minor products (Aschmann et al. 1998; Larsen et al. 2001; Jaoui and Kamens 2003; Auld and Hastie 2011). The yields of the nopinone and acetone are reported to be 0.25–0.27 and 0.09–0.11, respectively (Arey et al. 1990; Larsen et al. 2001). Other than these gaseous products, particulate matters are formed and their yields are reported to increase under low NOx conditions in early studies (Pandis et al. 1991; Hatakeyama et al. 1991; Palen and Allen 1992). Pinic acid, pinonic acid, hydroxy-nopinone, hydroxy-pinonic acid, hydroxy-pinic acid, and norpinic acid are reported as constituents of the particulate matter (Larsen et al. 2001; Jaoui and Kamens 2003). They are partly formed as primary products, but mostly as secondary products of the OH reaction with nopinone, etc. The reaction of OH with β-pinene is mainly initiated by the addition of OH to the C=C double bond, but the H atom abstraction from the ring can also be seen with the ratio of ca. 15%. Reaction Scheme 3.25 depicts the mechanism of the reaction initiate by the OH addition to the C=C double bond (Larsen et al. 2001; Jaoui and Kamens 2003). The OH addition to the C=C double bond predominates to occur at the terminal carbon atom as in the case of chain alkenes, and the ratio of the addition to the terminal and internal carbon atom has been estimated to be 9 : 1 (Peeters et al. 1994). From the hydroxyperoxy radical formed by the OH addition to β-pinene, hydroxy hydroperoxide and hydroxy oxyradicals are formed as shown in Reaction Scheme 3.25.

Reaction Scheme 3.25 Reaction mechanism of oxidation of β-pinene initiated by the addition of OH. Source: Based on Larsen et al. (2001); Jaoui and Kamens (2003).

3.3 OH Radical-Induced Oxidation Reactions

Additionally, hydroxy nitrates would be formed by the reaction of the peroxy radicals with NO under high NOx conditions. Nopinone, pinonic acid, and acetone are formed by the C—C bond rupture of the hydroxy oxyradicals shown in the scheme as pathways (c), (d), and (e), respectively. The theoretical calculation also suggested that such C—C bond rupture would occur easily (Dibble 2001). The theoretical calculation has also been carried out for the mechanism of the reaction of β-pinene and OH radical (Vereecken and Peeters 2012), and the calculated rate constant agreed well with the value given in Table 3.6 (Fan et al. 2005; Dash and Rajakumar 2013). The main product, nopinone, is a volatile compound formed not only by the reaction of β-pinene with OH but also with O3 as a primary product. The reaction rate constant of nopinone with OH is substantially large, k 298 = 1.7 × 10−11 cm3 molecule−1 s−1 , as seen in Table 3.7 (Calogirou et al. 1999), but it scarcely reacts with O3 and NO3 . Therefore, nopinone reacts mainly with OH in the atmosphere to give 3-oxonopinone, 3-hydroxynopinone, and 3,7-dihydroxynopinone in the gas phase, and pinic acid, norpinic acid, and terpenylic acid in the particulate phase as SOA components (Calogirou et al. 1999; Larsen et al. 2001; Jaoui and Kamens 2003; Sato et al. 2016). The initial reaction of OH with nopinone could be H-atom abstraction from any of the C—H bond within the molecule. Based on the quantum chemical calculation, Lewis et al. (2005) presumed that the energy barrier is the smallest for the H-atom abstraction from the endocyclic CH2 (labeled C3 carbon) adjacent to the carbonyl group followed by from the endocyclic CH (C1 carbon) of the cyclobutane ring adjacent to the carbonyl group since these H-atom abstractions lead to more stabilized radicals due to the resonant stabilization. The fraction of the H-atom abstraction from the C3 carbon has been estimated to be 44% according to the theoretical calculation (Lewis et al. 2005). Reaction Scheme 3.26 gives the mechanism of the OH-induced oxidation reaction of nopinone initiated by the H-atom abstraction of the C3 -carbon in the presence of NOx . 3.3.5.3

Limonene

Limonene has an endocyclic and exocyclic double bond (see Chart 3.4) and the reaction rate constants for OH and O3 are larger than for α- and β- pinene (cf. Tables 3.6 and 3.1). Particularly, the rate constant for OH is very large, 1.7 × 10−10 cm3 molecule−1 s−1 , and the OH reaction would predominate in the atmosphere. In the presence of NOx , the OH-induced photooxidation reaction of limonene gives limononaldehyde (3-isopropenyl-6-oxoheptanal), limonaketone (4-acetyl-1-methylcyclohexene), formaldehyde, formic acid, CO, and CO2 as primary products in the gas phase (Arey et al. 1990; Hakola et al. 1994; Larsen et al. 2001), and limononic acid, hydroxy limononic acid, keto-limononic acid, etc. in the particulate phase (Larsen et al. 2001; Jaoui et al. 2006). These particulate compounds are thought to be secondary products either by the reactions with OH or photochemically formed O3 . From the product analysis and quantum chemical calculations (Ramírez-Ramírez and Nebot-Gil 2005; Dash and Rajakumar 2015), the reaction of limonene with OH is known to be initiated by both the addition to the endocyclic and exocyclic C=C double bonds and H-atom abstraction. Under the atmospheric conditions, the ratio of the H-atom abstraction has been estimated as 0.34 ± 0.08 based on the experimental kinetic analysis of peroxy radicals (Rio et al. 2010). The ratio of the abstraction based on the measurements of HOD in the experiment of limonene with OD by Braure et al. (2014) agreed well with the above value, and showed the negative temperature dependence. This would

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Reaction Scheme 3.26 Oxidation reaction mechanism of nopinone initiated by the H-atom abstraction from C3 -carbon by OH in the presence of NOx . Source: Based on Larsen et al. (2001); Jaoui and Kamens (2003); Sato et al. (2016).

suggest that the O-atom abstraction by OH from limonene is not a direct abstraction reaction but proceed via addition and elimination steps, which has been confirmed by the theoretical calculation by Dash and Rajakumar (2015). Thus, although the addition to the C=C double bond is the predominant pathway, it is characteristic for the reaction of limonene with OH that the H-atom abstraction is much more important pathway as compared to the case of α- and β- pinene. Reaction Scheme 3.27 shows the pathways of reactions initiated by the OH addition to limonene in the presence of NOx (Grosjean et al. 1992).

Reaction Scheme 3.27 Oxidation reaction mechanism of limonene initiated by the addition reaction of OH. Source: Based on Grosjean et al. (1992).

3.3 OH Radical-Induced Oxidation Reactions

The product yields of limononaldehyde and limonaketone have been reported as 0.29 and 0.20, respectively, by Hakola et al. (1994). This means that the addition to the endocyclic C=C double bond has the higher ratio than to the exocyclic double bond, which agrees well with the theoretical prediction (Dash and Rajakumar 2015). The abstraction of H-atom by OH from the endocyclic secondary CH2 group has the lower transition state energy than the abstraction from the side chain since the formed radicals are more stabilized by conjugated resonance, and therefore can compete with the OH addition to the C=C double bond (Dash and Rajakumar 2015). An example of the reaction pathway initiated by the secondary H-atom abstraction from limonene is shown in Reaction Scheme 3.28. Limononaldehyde production can be expected in the abstraction reaction from either of CH2 group adjacent to the double bond. No specific product expected from the abstraction of tertiary H-atom has been identified.

Reaction Scheme 3.28 Example of oxidation reaction mechanism of limonene initiated by the H-atom abstraction.

Since the limononaldehyde and limonaketone produced in the OH-initiated reaction of limonene still have a C=C double bond within the molecules, they have large reaction rate constants with OH as seen in Table 3.7, and are subject to aging in the atmosphere to form SOA consisting of ketocarboxylic acids, etc. (Jaoui et al. 2006). Possible mechanisms of the oxidation reactions of limononaldehyde and limonaketone in the atmosphere are shown in Reaction Scheme 3.29. 3.3.6

Monocyclic Aromatic Hydrocarbons

The aromatic hydrocarbons that have one benzene ring are of mostly anthropogenic origin, and react almost exclusively with OH radicals since the rate constants of the reaction with O3 are very small. The OH-induced oxidation reactions of aromatic hydrocarbons are known to produce various kinds of low volatile species and are interesting from the point of SOA formation. However, pathways of the OH-induced oxidation reaction of aromatic hydrocarbons have not been fully elucidated yet, and many studies are still going on. 3.3.6.1

Benzene

Since the rate constant of the reaction of benzene with OH is not very large, 1.4 × 10−12 cm3 molecule−1 s−1 , as shown in Table 3.6, benzene is not very important for photochemical ozone formation in the boundary layer, but is interesting as a

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Reaction Scheme 3.29 Reaction mechanism of the OH-initiated oxidation reaction of limononaldehyde and limonaketone in the gas phase. Source: Based on Grosjean et al. (1992).

prototype of aromatic hydrocarbons which produce SOA by secondary reactions (e.g. Sato et al. 2012). The OH-induced oxidation reaction of benzene in the gas phase in the presence of NOx is known to give phenol and a ring-opened product, glyoxal, as main products from early studies (Hoshino et al. 1978; Bandow and Akimoto 1985; Tuazon et al. 1986; Atkinson et al. 1989a). The yield of phenol has been reported as 0.53 ± 0.07 (Volkamer et al. 2002), while there is a large difference, 0.21–0.42, in the reported yield of glyoxal (Tuazon et al. 1986; Volkamer et al. 2001; Berndt and Böge 2006; Gómez Alvarez et al. 2007). Later studies have identified ring-opened products other than glyoxal such as Z- and E-2-butene-1,4-dial with the Z- and E- total yield of 0.10–0.17 (Berndt and Böge 2006; Gómez Alvarez et al. 2007), and 2,4hexadiene-1,6-dial (muconaldehyde) (Klotz et al. 2002) experimentally, and they are also explained by theoretical calculations (Lay et al. 1996; Ghigo and Tonachini 1999; Motta et al. 2002; Glowacki et al. 2009; Wang et al. 2013). Meanwhile, production of 2,3-epoxy-butanedial, corresponding to an epoxide produced from OH-induced oxidation reaction of toluene, has been suggested by quantum chemical calculations (Motta et al. 2002; Wang et al. 2013), but has not been identified experimentally. The rate constant of benzene-OH reaction under the atmospheric conditions is in nearly high-pressure limit, and the initial reaction step is the addition of OH to the aromatic ring to form a hydroxycyclohexadienyl radical as confirmed directly by UV absorption spectroscopy (Bjergbakke et al. 1996; Johnson et al. 2002; Grebenkin and Krasnoperov 2004). The ratio of H-atom abstraction reaction from the benzene ring is less than a few % at room temperature (Knispel et al. 1990). Figure 3.17 depicts the UV absorption spectrum of the hydroxycyclohexadienyl radical measured by Johnson et al. (2002). From the direct measurement by the UV absorption of this radical, the rate

3.3 OH Radical-Induced Oxidation Reactions

12

σ/10–18 cm2 molecule–1

Figure 3.17 UV absorption spectrum of hydroxycyclohexadienyl radical. Reproduced from Source: Johnson et al. (2002) with permission from the PCCP Owner Societies.

10 8 6 4 2 0 250

270

290 310 λ / nm

330

350

constant of the reaction of hydroxycyclohexadienyl radical with O2 , HO − C6 H6 + O2 ⇄ HO − C6 H6 − O2

(3.112)

has been reported as k(T) = 1.4 × 10−12 exp(−2240/T) cm3 molecule−1 s−1 , and at 298 K, as k 298 = 7.6 × 10−16 (Grebenkin and Krasnoperov 2004), 2 × 10−15 (Bohn and Zetzsch 1999), and 6 × 10−16 cm3 molecule−1 s−1 (Johnson et al. 2002). From these values it is thought that the hydroxycyclohexadienyl radical reacts almost exclusively with O2 in the atmosphere (Koch et al. 2007). The reaction enthalpy of Reaction (3.112) is estimated as ca. 46 kJ mol−1 (Lay et al. 1996; Johnson et al. 2002), and the equilibrium constants of 2.7 × 10−19 and 1.2 × 10−19 cm3 molecule−1 have been reported (Bohn and Zetzsch 1999; Johnson et al. 2002). The reaction of hydroxycyclohexadienyl radical with O2 is the addition of O2 to the benzene ring, and it has been shown theoretically that the hydroxycyclohexadienyl peroxy radical in which O2 is added to the carbon atom adjacent to OH (ortho position) is the most stable energetically (Johnson et al. 2002). Reaction Scheme 3.30 shows the reaction mechanism of the OH-induced oxidation of benzene via o-hydroxy hydroxycyclohexadienyl radical (Lay et al. 1996; Calvert et al. 2002; Motta et al. 2002). According to the quantum chemical calculation by Lay et al. (1996), the addition reaction of OH to benzene is exothermic by 80 kJ mol−1 , and the addition of O2 to the stabilized hydroxycyclohexadienyl radical is also exothermic by 48 kJ mol−1 . One of the main products, phenol in the atmospheric reaction of benzene with OH is thought to form either via the H-atom abstraction from hydroxycyclohexadienyl radical by O2 or intramolecular hydrogen shift reaction of hydroxycyclohexadienyl peroxy radical followed by HO2 elimination as shown in Reaction Scheme 3.30. Energy diagrams for the major feature of benzene ring rupture in the OH reaction of aromatic compounds have been given by Lay et al. (1996). From hydroxycyclohexadienyl peroxy radical, an annular adduct radical, in which the OO of the peroxy group adds annularly to a carbon atom of benzene ring, is formed. As for the position of carbon atom to which OO adds annularly, although there are four possibilities except the OH- and OO-added carbon atoms, it is shown that the addition to the ortho- and para-position with regard to OH is energetically favorable. In Reaction Scheme 3.30, pathways via ortho-adduct radicals are shown. As shown in the scheme, formation

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Reaction Scheme 3.30 Mechanism of OH-induced oxidation reaction of benzene in the presence of NOx . Source: Based on Lay et al. (1996); Ghigo and Tonachini (1999).

of 2-butene-1,4-dial and glyoxal can be presumed theoretically by the unimolecular decomposition of oxy radical formed by the reaction of NO with the peroxy radical from O2 addition to the annularly OO-added radical. Figure 3.18 depicts energy diagram for this series of reactions based on the data of Lay et al. (1996). From the photooxidation of butenedial formed in the benzene oxidation, formaldehyde, acrolein, glycolaldehyde, glyoxal, malondialdehyde, etc. are known to form secondarily (Liu et al. 1999b). Thus, glyoxal is also formed secondarily in addition to the primary product (Volkamer et al. 2001), which could be one of the reasons of large discrepancy for the yield of glyoxal depending on experimental conditions. Further, formation of 2-butenedial, glyoxal, etc. in the OH-induced photooxidation of E,E-2,4-hexadiene-1,6-dial shown in Reaction Scheme 3.30 has been reported (Klotz et al. 1995, 1999). Photooxidation of benzene by OH radicals is known to form SOA in the high yield in the presence of NOx (Sato et al. 2010, 2012; Nakao et al. 2011; Borrás and TortajadaGenarob 2012). These SOA consist of carboxylic acids, oxocarboxylic acids, dicarboxylic acids, etc. and they are thought to form in the secondary oxidation of phenol, hexadienedial, butenedial, etc. mentioned above in the gas- and particulate-phases. 3.3.6.2

Toluene

Since the reaction rate constants of toluene with OH radical is larger than benzene by a factor of 5 (cf. Table 3.6) and its concentration is usually the highest among aromatic hydrocarbons in the atmosphere, toluene is an important causative species of photochemical air pollution and it has been studied rather extensively. Recently, SOA formation in the secondary reactions has been reported and many studies have been conducted also from this viewpoint (e.g. Hurley et al. 2001; Sato et al. 2007, 2010; Cao and Jang 2010). The OH-induced photooxidation of toluene in the presence of NOx is known to form benzaldehyde, o, m, p-cresol, benzyl nitrate, and o, m, p-nitrotoluene

3.3 OH Radical-Induced Oxidation Reactions

kcal mol–1 0 –20

0.0

(1.2) –19.1

+OH

(3.8)

H OH

–40 –60

(18.8) –30.5 H

–42.5 (0.0)

OH H OO

(8.2)

H O

O

OH

–61.4

O H

–80

H O

O

OH

–100 –120

–117.1 CHO CHO + CHO CHOH

Figure 3.18 Energy diagram for the ring opening pathways of the reaction of benzene with OH. Source: Based on the data of Lay et al. (1996).

as benzene-ring retaining products, and methylglyoxal, glyoxal, etc. as ring ruptured products in early studies (Hoshino et al. 1978; Atkinson et al. 1980; Atkinson et al. 1989a,b; Shepson et al. 1984; Bandow and Akimoto 1985; Leone et al. 1985; Tuazon et al. 1986; Klotz et al. 1998; Smith et al. 1998; Calvert et al. 2002). Under the low NOx conditions, their yields have been reported as 0.06 ± 0.01 for benzaldehyde, 0.12 ± 0.01, 0.026 ± 0.005, and 0.031 ± 0.005 for o-, m-, and p-cresol, respectively, and the production of benzyl nitrate and nitrotoluene is thought to be negligible under the atmospheric conditions (Calvert et al. 2002). The reported yields of methylglyoxal and glyoxal have a large range, 0.04–0.15 and 0.04–0.24, respectively, and the cause is thought to be due to the difference in contribution of secondary formation in different experimental conditions (Calvert et al. 2002). Recent experiments by Baltaretu et al. (2009) using a flow system have quantified ring-opened compounds such as methyl hexadienedial (0.24 ± 0.09) and epoxide (0.07 ± 0.03) as main products in addition to benzaldehyde (0.05 ± 0.02) and cresols (0.28 ± 0.06 for total isomers). On the other hand, glyoxal ( Cl− , which rewrote the classical picture of ion aqueous solutions and resulted in a breakthrough for the solution interface chemistry. Meanwhile, organic compounds are known to be concentrated at the air–sea water interface of oceans as compared to bulk seawater. Further, ammonium sulfate and ammonium nitrate particles in the urban aerosols are aqueous particles with different

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thickness of surface water layer depending on humidity. Although the interface reactions for these particles have not been fully investigated, their microscopic views are being revealed by the experimental studies by SFG spectroscopy and X-ray photoelectron spectroscopy (XPS), and theoretical analysis by MD calculation. As for these interface characteristics, reviews by Shultz et al. (2000), Jungwirth and Tobias (2006), Chang and Dang (2006), Gopalakrishnan et al. (2006), Petersen and Saykally (2006), and Netz and Horinek (2012) are available, and the reactions of O3 and OH at the sea salt interface have been reviewed by Finlayson-Pitts et al. (2003), and Reid and Sayer (2003). Background tropospheric halogen chemistry has also been reviewed by Simpson et al. (2007) and Saiz-Lopez and von Glasow (2012). 6.3.1 Microscopic View of Interface of Air and Alkaline Halide Aqueous Solution The interface of air and alkali halide aqueous solution has been studied by the SFG spectroscopy and comparison with the pure water interface has been made (Liu et al. 2004; Raymond and Richmond 2004). Figure 6.15 depicts the SFG spectra of the interface of air and aqueous solutions of NaF (0.9 M), NaCl, NaBr, and NaI (1.7 M) in the OH stretching vibrational frequency region comparing with the pure water interface. As shown in the figure, the frequency and strength of peaks due to the dangling bond (cf. Section 6.2.2) of pure water at 3700 cm−1 do not change in the presence of alkali halide. On the other hand, the peak intensities of the broad spectrum near 3400 cm−1 due to the hydrogen-bonded OH decrease for the air–NaF solution interface while they increase slightly for NaCl and increase greatly for NaBr and NaI. This would imply that the number of O-H bonds contributing to the SFG spectrum increases due to the reorientation of surface H2 O molecule in the presence of halide ions with larger polarizability, and the interface becomes thicker (Raymond and Richmond 2004). In order to understand the characteristics of sea salt aerosol (SSA) at the air–aqueous solution interface, MD calculation for the water cluster with a small number of molecules is suggestive. Jungwirth and Tobias (2002) demonstrated by the MD calculation of NaCl water cluster (4Na+ + 4Cl− + 32H2 O and 32Na+ + 32Cl− + 288H2 O), that highly polarizable Cl− is exposed to the cluster surface, and nonpolarizable Na+ is buried into the water molecule assembly and do not exist at the surface. Such an effect does not appear without considering polarizability, and it has been revealed that the surface characteristics of halide ion are mainly determined by polarizability. As a model of air and sea salt aqueous solution interface, MD calculation for the dilute (1.2 M) and saturated solution (6.1 M) showed that the ratio of Cl− at the interface increases with the concentration, and the ratio of paired Na+ and Cl− is relatively low, 54%, at the interface of the saturated solution as compared to 75% in the bulk solution. The ratio of unpaired Cl− is relatively high accordingly at the interface, and the isolated Cl− has higher reactivity with gaseous molecules to cause atmospheric reactions as will be mentioned below. For the saturated aqueous solution of NaCl, average number of H2 O molecules coordinated around Cl− is 4.5, which is smaller than 6.0 for the infinitely diluted aqueous solution. This is thought to be due to the increase of Cl− ion paired with Na+ as the concentration increases (Jungwirth and Tobias 2002). The NaCl

6.3 Air–Sea Salt Particle, Seawater, and Sulfate/Nitrate Aerosol Interface

0.16

0.016 mfNaF SF Intensity (a.u.)

SF Intensity (a.u.)

0.16 0.12 0.08 0.04 0.00

0.12 0.08 0.04 0.00

3000 3200 3400 3600 3800

3000 3200 3400 3600 3800 Wavenumber (cm–1)

Wavenumber (cm–1) 0.16

0.03 mfNaBr SF Intensity (a.u.)

SF Intensity (a.u.)

0.16

0.03 mfNaCl

0.12 0.08 0.04 0.00

0.03 mfNal

0.12 0.08 0.04 0.00

3000 3200 3400 3600 3800 Wavenumber (cm–1)

3000 3200 3400 3600 3800 Wavenumber (cm–1)

Figure 6.15 Vibrational sum frequency (SFG) spectra of NaF, NaCl, NaBr, and NaI aqueous solutions (black). An air–neat water spectrum is shown with each salt solution spectrum for comparison (gray). Source: Reprinted with permission from Raymond and Richmond. (2004). Copyright 2004 American Chemical Society.

aqueous solution interface is very similar to the 32 Na+ + 32 Cl− + 288 H2 O molecular clusters mentioned above. From the MD calculation for the interfaces of air and NaF, NaCl, NaBr, and NaI aqueous solution (1.2 M), snapshot views and normalized number densities of each negative ion (F− , Cl− , Br− , and I− ), positive ion (Na+ ), and H2 O are shown in Figure 6.16 (Jungwirth and Tobias 2001). The z(Å) shown in the figure is the distance from the center of the calculated box. As seen in the figure, both of F− and Na+ exist only inside of water surface, and do not exist at the surface. On the other hand, Cl− exists near the interface separated from Na+ , and Br− and I− reside more at the interface outside of the water molecules. The polarizability of Br− is larger than Cl− by 30% (Markovich et al. 1996), and the pictures shown in Figure 6.16 are thought to be attributable to the polarizability of ions (Jungwirth and Tobias 2001; Gladich et al. 2011). Although halide ions are surrounded by H2 O molecules in the bulk water and the net dipole is zero, ions are surrounded asymmetrically and net dipole is caused at the interface. Ions with larger polarizability are thought to be attracted to the interface by polarization overcoming the lost of solvation energy (Dang 2002; Jungwirth and Tobias 2001, 2002). Surface propensity of Br− and I− having larger polarizability has been proved by the direct observation of ions by SHG (Petersen et al. 2004), XPS (Zangmeister et al. 2001; Ghosal et al. 2000, 2005, 2008), and ESI-MS (Cheng et al. 2006). Hess et al. (2007)

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ρ(z)/ρb 0.0

0.5

1.0

(a)

2.0

1.5 O

2.5

3.0

(e) F–

16 12

Na+

z (Å)

8 NaF

4 0

(b)

O

(f)

Cl– Na+

16 12

z (Å)

8 NaCl

4 0

(c)

O

Br –

(g)

16 12

Na+

z (Å)

8 4

NaBr

0 (d)

O

I–

(h)

16 12

Na+ Nal

z (Å)

8 4 0

Figure 6.16 Snapshots and number desities of Na+ , F− , Cl− , Br− , I− ions and water from MD simulation of 1.2 M sodium halide solutions. In (a)–(d), small gray dots: O atom of H2 O; white open circles: Na+ ion; larger gray circles: F− , Cl− , Br− , and I− . In (e)–(h), number densities of ions are plotted vs distance from the center of slabs in the direction normal to the interface, z. Source: Adapted with permission from Jungwirth and Tobias (2001). Copyright 2001 American Chemical Society.

suggested that the Br/Cl ratio on the surface of natural sea salts increased to 0.2 from the experiment of Rutherford backward scattering spectroscopy. 6.3.2 Reactions at the Interface of Sea Salt and Alkali Halide Aqueous Solution Since water plays a major role in the dynamical behavior of halide ions in the sea salt, it is also presumed that water layer at the particle surface would have a large effect on the reactions of gaseous species at the air–sea salt interface (Knipping et al. 2000). The adsorptive coverage of H2 O on NaCl is ∼0.5 layer at RH 35%, increases to ∼1.0 and ∼2.5 layers for RH 40 and 45%, respectively, and is over 3.0 layers at RH higher than 50%

6.3 Air–Sea Salt Particle, Seawater, and Sulfate/Nitrate Aerosol Interface

(Finlayson-Pitts et al. 2003). The infrared absorption spectroscopy measurements show that the peak wavenumber assigned to O-H stretching vibration is around 3500 cm−1 for 0.1 monolayer, and shifts to the lower wavenumber, 3420 cm−1 for 2 monolayers, which is undistinguishable from the bulk water (Peters and Ewing 1997; Foster and Ewing 1999). NaCl disolves into water completely at the deliquescent point of RH 75% to form saturated aqueous solution (Finlayson-Pitts et al. 2003). Since Barrie et al. (1988) found the significant decrease of boundary layer ozone due to Br in Arctic spring, release of Br2 , BrCl, and Cl2 by O3 and OH at the sea salt surface has attracted interest as an emission process of photochemically active halogen species (Finlayson-Pitts and Hemminger 2000; Rossi 2003; Finlayson-Pitts 2009). Meanwhile, as for the reactions of nitrogen oxides on sea salt, the release of HCl by the uptake of gaseous HNO3 and substitution of Cl− with NO3 − has been well known. Further, the formation of photochemically active ClNO2 by the interface reaction of N2 O5 and sea salt has been found and brought the discussion on the importance of halogen chemistry in the troposphere (Finlayson-Pitts and Hemminger 2000, Rossi 2003, Finlayson-Pitts 2009). 6.3.2.1

Reaction with O3

In the reaction of O3 at the interface of air and sea salt particles, preferential release of bromine rather than chlorine is seen, and Br2 , BrCl, and BrO have been detected in the wide range of marine boundary layer including the polar region (Akimoto 2016, pp. 348–356 and references therein). In the experiments using NaBr as an proxy species of sea salt, the uptake coefficient of O3 on the solid surface of dry NaBr is small to such an extent that the O3 loss cannot be detected (𝛾 ≈ 10−6 ). It increases to 𝛾 ∼1 × 10−3 for the deliquescent NaBr or synthetic sea salt (Mochida et al. 2000), and the release of Br2 in dark has been reported (Hirokawa et al. 1998; Oum et al. 1998a; Mochida et al. 2000). The formation of Br2 in the reaction of NaBr and O3 in the bulk acidic aqueous solution has long been known as follows (Taube 1942; Finlayson-Pitts et al. 2003; Hunt et al. 2004). O3 + Br− → BrO− + O2

(6.12)

BrO− + H+ ⇄ HOBr

(6.13)

HOBr + Br− + H+ → Br2 + H2 O

(6.14)

Recent experimental and theoretical studies have given the new aspects for the reaction. According to the MD calculation by Roeselová et al. (2003), the residence time of O3 and OH for the NaCl surface complexes is 16 and 43 ps, respectively, which is not much different from the water surface complexes. Hunt et al. (2004) found that the formation rate of Br2 for the deliquescent NaBr-O3 reaction in the chamber experiment is one order of magnitude larger than that expected from the bulk liquid phase reaction, and the MD calculation suggested the formation of [O3 · · ·Br− ] complex at the air interface. From these results, the formation and release of Br2 to the gas phase in the reaction of O3 and NaBr is suggested to occur at the interface via [O3 · · ·Br− ] rather than in the bulk aqueous solution (Hunt et al. 2004; Thomas et al. 2006). Further, Clifford and Donaldson (2007) showed the pH increases by the formation of OH at the interface in the reaction of gaseous O3 and interface Br− . Considering these evidences, the following

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formation pathways of Br2 and BrCl have been proposed (Hunt et al. 2004; Clifford and Donaldson 2007): O3(g) + Br− (int) → (O3 · · · Br− )(int)

(6.15)

(O3 · · · Br− )(int) → O3 − (aq) + 1∕2 Br2(g)

(6.16)

O3(aq) → O2(g) + O− (aq)

(6.17)

O− (aq) + H2 O → OH− (aq) + OH(aq) ,

(6.18)

but the detailed reaction mechanism has not been elucidated yet (cf. Section 6.3.3). The reason of preferential release of Br2 in the reaction with O3 is thought to be due to the fact that the relative concentration of Br− near the interface is high as described in the previous subsection, which allows the easier formation of the O3 complex. Similarly, it has been reported that I2 and IO are released with the ratio of [I2(g) ] > 100[IO(g) ] via IOOO in the reaction of O3 at the interface of air and NaI aqueous solution (Sakamoto et al. 2009; Reeser and Donaldson 2011). From the evidence that HOI is formed being independent of pH and the yield of I2 is accelerated with the decrease of pH, the following reaction pathways have been proposed: O3(g) + I− (int) → (IOOO− )(int)

(6.19)

(IOOO− )(int) → IO− (aq) + O2(aq)

(6.20)

IO− (aq) + H+ (aq) ⇄ HOI(aq)

(6.21)

HOI(aq) + I− (aq) + H+ → I2(aq) + H2 O

(6.22)

Meanwhile, since the reaction of I2 formation in the bulk aqueous solution of O3 and I− is very fast, not only the interface reaction but also the bulk solution reaction is thought to contribute to the release of inorganic iodine into the atmosphere from the ocean (Carpenter et al. 2013; Carpenter and Nightingale 2015). In contrast, the release of Cl2 in the reaction of O3 and NaCl is known to be much less efficient than that of Br2 formation in the reaction of NaBr and O3 in general. Sadanaga et al. (2001) reported that the uptake coefficient of O3 to NaCl increased significantly from 30 M. The ratio of the formed ClNO2 to the decreased amount of N2 O5 , Δ [ClNO2 ]/Δ [N2 O5 ], increases with the increase of Cl− concentration at the NaCl surface and reaches nearly unity at [Cl− ] > 1 M. The uptake coefficients of 𝛾 for the natural sea salt (Stewart et al. 2004) and synthetic sea salt (Thornton and Abbatt 2005) are reported to be (2.8–3.1) × 10−2 (RH 30–80%) and (2.2–3.0) × 10−2 (RH 50–70%), respectively. The uptake coefficient for the sea salt is one order of magnitude larger than for the pure NaCl particles and the yield of ClNO2 for the synthetic sea salt is nearly unity, as reported by Hoffman et al. (2003). From these results, the mechanism of the reaction of N2 O5 with the NaCl particle surface coated by water has been proposed (Bertram and Thornton 2009; Roberts et al. 2009; IUPAC 2017) as follows: N2 O5(aq) + H2 O(l) → H2 ONO2 + (aq) + NO3 − (aq)

(6.33)

H2 ONO2 + (aq) + H2 O(l) → HNO3(aq) + H3 O+ (aq)

(6.34)

H2 ONO2 + (aq) + Cl− (aq) → ClNO2(aq) + H2 O(l) .

(6.35)

N2 O5 dissolves to the surface water on the salt and dissociates into NO2 + and NO3 − , and NO2 + and its hydrated ion, H2 ONO2 + , are thought to react with H2 O and Cl− competitively to form HNO3 and ClNO2 , respectively. Roberts et al. (2008) reported the formation of Cl2 in the reaction of N2 O5 with Cl− in the acidic particles (pH < 2), and suggested that it would be the source of Cl2 in the marine boundary layer affected by urban pollution and coastal urban atmosphere. 6.3.2.5

Reaction with HNO3

It has long been known that the Cl− /Na+ ratio of sea salt sampled in the marine boundary layer affected by urban pollution is smaller than that of sea water, which has been called chlorine deficit (Finlayson-Pitts et al. 2003; Rossi 2003, and references therein). The cause has been proposed since 1970s to be due to the reaction of HNO3 at the surface of sea salt particles (Martens et al. 1973), which can be presented overall as ∘ HNO3(g) + NaCl(s) → NaNO3(s) + HCl(g) ΔH298 = −14 kJ mol−1 . (6.36) This reaction converts gaseous nitric acid (HNO3 ) to particulate sodium nitrate (NaNO3 ) so that it changes atmospheric lifetime and the deposition area of nitrate (NO3 − ). Many studies have been made due to the importance of the reaction in tropospheric chemistry (Finlayson-Pitts et al. 2003; Rossi 2003 and references therein). The reactive uptake coefficients of HNO3 for this reaction on sea salt and NaCl as its proxy species have been reviewed and compiled (Rossi 2003; Burkholder et al. 2015). As will be mentioned below, it has been generally known that Reaction (6.36) is accelerated by the surface-adsorbed water (SAW). Thus, although the uptake coefficient is small 𝛾 = ∼4 × 10−4 at the dry NaCl (Laux et al. 1994), it is more than one order of magnitude larger as 𝛾 = (1–3) × 10−2 for the normal NaCl powder (Fenter et al. 1994; Leu et al. 1995; Beichert and Finlayson-Pitts 1996), and still larger value, 𝛾 ≥ 0.2, has been reported for the deliquescent NaCl (Abbatt and Waschewsky 1998; Liu et al. 2007; Stemmler et al.

373

6 Reactions at the Air–Water and Air–Solid Particle Interface

2008). From these experiments, it has been reported that HCl is a sole gaseous reaction product of the surface reaction of HNO3 and NaCl, and the formation yield of HCl is unity for the uptake of HNO3 (Leu et al. 1995; Davies and Cox 1998). Also, the formation of NaNO3 at the NaCl crystal surface has been confirmed experimentally by XPS (Laux et al. 1994). Under the coexistence of MgCl2 , the uptake coefficient is very large as 𝛾 > 0.1 even at the low humidity of RH 10% (Saul et al. 2006), and 𝛾 > 0.5 for deliquescent natural and synthetic sea salt is even higher than the NaCl doped with MgCl2 (Guimbaud et al. 2002), which implies the possibility that the existence of ions other than Mg2+ would enhance the uptake coefficient even further. Thus, the replacement of Cl− by NO3 − on the sea salt completes within a few hours, much shorter timescale than the atmospheric lifetime of sea salt, causing the chlorine deficit (Saul et al. 2006). As for the surface reaction of HNO3 on NaCl particles, detailed analyses have been made for the relevance of SAW by chemical dynamic experiments. Figure 6.17 depicts the change of the uptake coefficient 𝛾 of HNO3 on the NaCl crystal as a function of reaction time using a Knudsen cell by Hoffman et al. (2003). As typically seen in the figure, the uptake coefficient of this reaction decreases with reaction time from the initial value 𝛾 0 to stationary state value 𝛾 ss by a factor of two to three. As an interpretation, it has been proposed that SAW plays a crucial role for the uptake of HNO3 to the NaCl surface, and there are two kinds of adsorbed water at the surface. One is a weakly bound water molecule that can be removed by evacuation, and the other is a strongly adsorbed water molecule that cannot be removed even by the evacuation at 100 ∘ C (De Haan and Finlayson-Pitts 1997; Hoffman et al. 2003; Ghosal and Hemminger 2004). The weakly bound water is thought to be the adsorption to the flat (100) plane of NaCl, and the strongly adsorbed water is adsorbed to the lattice defect sites and crystal steps (Ghosal and Hemminger 1999; Hoffman et al. 2003). The uptake coefficient of HNO3 corresponds to the dissolution process to SAW, and both the weakly bound and 40 35 30 γcorr (10–4)

374

25 20 15 10 5 0 0

100

200

300

400

500

Time (s)

Figure 6.17 Decay in uptake coefficient (𝛾) with reaction time for the surface reaction of HNO3 on NaCl single crystal. Source: Reprinted with permission from Hoffman et al. (2003). Copyright 2003 American Chemical Society.

6.3 Air–Sea Salt Particle, Seawater, and Sulfate/Nitrate Aerosol Interface

strongly adsorbed SAW brought 𝛾 0 , while 𝛾 ss is induced only by the latter (Beichert and Finlayson-Pitts 1996). The presence of strongly adsorbed H2 O has been confirmed by the experimental evidence that HCl instead of DCl is released in the reaction of NaCl and HNO3 exposed to D2 O after heated evacuation (De Haan and Finlayson-Pitts 1997). The HNO3 molecules taken to the strongly adsorbed SAW forms NO3 − by dissociation, and are kept at the lattice defect and step sites. HCl is released into the gas phase from NaCl aqueous solution by the acidification of SAW, and NO3 − crystallizes as NaNO3 . For the single crystal of NaCl, it is more free from lattice defects compared to powder, and the fraction of the strongly adsorbed surface water is small so that the uptake coefficient decreases from ∼10−2 to ∼10−3 by one order of magnitude (Beichert and Finlayson-Pitts 1996; Ghosal and Hemminger 2004). From the experiment using the XPS, it has been presumed that the crystallized NaNO3 subsides in SAW and the interface is always refreshed by Cl− , so that the uptake rate reaches a steady state, and the Cl− deficit reaction proceeds (Laux et al. 1996). From these results, the reaction between HNO3 and NaCl in SAW has been proposed as follows (Davies and Cox 1998; Rossi 2003): HNO3(ad) + H2 O ⇄ H3 O+ + NO3 −

(6.37)

H3 O+ + Cl− ⇄ HCl(ad) + H2 O

(6.38)

HCl(ad) → HCl(g)

(6.39)

Na+ + NO3 − ⇄ NaNO3(s)

(6.40)

where (ad) stands for chemical species adsorbed on the surface. 6.3.3 Reactions of Organic Compounds at the Air–Seawater and Air–Sea Salt Interface Seawater has an inorganic elemental composition shown in Table 2.8. The concentrations of halogen anions in the near surface water are [Cl− ] = 0.567 M, [Br− ] = 8.6 × 10−4 M, and [I− ] = (3.5) × 10−7 M at the mid-latitude, and the concentrations of ions at the tropics are higher. Other than these inorganic ions, many organic compounds of biogenic origin are contained in the seawater. Dissolved organic matter (DOM) consists of proteins (25–50%), lipids (5–25%), carbohydrates (1000 Da) (35–40%), including humic substances (HS, 0.7–2.4%), and low molecular weight compounds (LMW-DOM, 100, and ClNO2 is the main product for the natural sea salt being independent of temperature between 225 and 250 K.

6.5 Interface of Water and Mineral Dust, Quartz, and Metal Oxide Surface Mineral dusts are mainly emitted from arid areas such as the Sahara and Gobi deserts, and farmland attributable to anthropogenic activity. Their global total emissions are estimated as 1500∼2000 Tg yr.−1 (cf. Table 8.1). Although their emissions are next to the sea salt, since their average particle size is smaller and the atmospheric residence time (a few days) is longer than the sea salt, their atmospheric loadings are estimated as ∼20 Tg, about two times of that of the sea salt (Textor et al. 2006). As for the natural mineral dust,

385

386

6 Reactions at the Air–Water and Air–Solid Particle Interface

Table 6.2 Typical minerals in dust, chemical formulas, emission fluxes and atmospheric loadings.a) Mineral

Formulab)

Flux (Tg yr−1 )

Loadings (Tg)

Quartz

SiO2

569

4.1

Illite

(K,H3 O)(Al,Mg,Fe)2 (Si,Al)O10 [OH]2 ,H2 O

370

4.2

Montmorillonite

(Na, Ca)0.33 (Al,Mg)2 Si4 O10 (OH)2 ∙nH2 O

246

2.8

Feldspar

(Na,K,Ca,Ba)(Si,Al)4 O8

205

1.4

Kaolinite

Al4 Si4 O10 (OH)8

192

2.2

Calcite

CaCO3

145

1.3

Hematite

α-Fe2 O3

24

0.2

Gypsum

CaSO4 ∙2H2 O

15

0.1

a) Tang et al. (2016). b) Usher et al. (2003).

Saharan dust and Asian dust are well known, but their chemical composition, hygroscopicity, and CCN characteristics have large variability, depending on the sampling sites. For this reason, Arizona test dust (ATD) whose composition is relatively constant has been used in many experiments as a representative of authentic natural dust (Tang et al. 2016). From recent satellite observation, it has been estimated that the natural dust is 75%, and anthropogenic one by cultivation soil and desertification due to overgrazing is 25% among the global emissions of mineral dust (Ginoux et al. 2012). As shown in Table 6.2, mineral dusts are composed of quartz, illite, kaolinite, montmorillonite, calcite, feldspar, gypsum, etc. and these minerals have composition represented by metal oxides, such as SiO2 , α-Al2 O3 , α-Fe2 O3 , CaCO3 , and TiO2 (Usher et al. 2003) so that the characteristics of water adsorption and heterogeneous chemical reactions on mineral dusts have often been studied using these oxides as representative species. As for the particle size distribution of mineral dust, coarse mode particles with diameter larger than 2.5 μm is the most abundant regarding volume and mass, followed by the fine particles with diameter 0.1–2.5 μm. The fine mode particles are dominant regarding the surface area (Gomes et al. 1990). The atmospheric lifetime of the fine mode particles is from a few days to a week, and those particles participate in the heterogeneous reactions in the atmosphere among mineral dust. The heterogeneous reactions on mineral dust surface change the surface chemical composition and hygroscopicity, and affect their optical property, CCN activity, ice nucleation activity, and wet deposition velocity, so that many studies have been made from these interests in atmospheric chemistry (Usher et al. 2003; Cwiertny et al. 2008; Finlayson-Pitts 2009, and references therein). 6.5.1

Microscopic View of Adsorbed Water on Mineral Surface

Surface adsorbed water (SAW) plays a central role in the heterogeneous reactions between the mineral dust and atmospheric trace gases, and many studies have been conducted focusing on this aspect (Fenter and Sturchio 2004; Schrödle and Richmond 2008; Tang et al. 2016, and references therein). About 60% of mineral dust is composed of silica, and since α-quartz is the most general allotrope among them (Usher et al. 2003), many molecular-level studies on the water-adsorption on mineral dust surface

6.5 Interface of Water and Mineral Dust, Quartz, and Metal Oxide Surface

have been made using α-quartz as a representative substance. It has long been known that water molecules are adsorbed dissociatively to form a silanol group (-SiOH) on the silica-water interface, either for crystal such as α-quartz or amorphous silicon like fused silica, and this process has been confirmed to be advantageous thermodynamically by theoretical calculations (de Leeuw et al. 1999; Walsh et al. 2000). The silanol group has high polarity and is easily dissociated to silanolate ion (SiO− ) and hydronium ion (H3 O+ ). Ka

− + −−−−−−− → —SiOH + H2 O ← − —SiO + H3 O

(6.63)

Here, K a is the acid dissociation constant. The silanol group exists as neutral, SiOH, at pH 2, the fraction of silanolate ion, SiO− , increases with the increase of pH, and it exists almost solely as silanolate ion at pH 10 (Iler 1979). Ong et al. (1992) found that there are two different sites of silanol at the air interface from the pH dependence of -SiOH/SiO− ratio, on the fused silica by the use of SHG spectroscopy. Further, it has been shown that most silanol is in the form of geminal diol (gem-diol, cf. Section 4.2.4) from the measurement of XPS (Duval et al. 2002). Since silanol group has high polarity, it tends to adsorb more H2 O and other molecules at the surface, which gives large effects on reaction activity of the silica surface. Many experimental and theoretical studies have shown that the thickness of adsorbed water layer increases with humidity in air (Gerber et al. 2015; Tang et al. 2016 and references therein). For example, the change in absorption spectrum by attenuated total reflection (ATR)-FTIR and the number of H2 O monolayers by quartz crystal microbalance (QCN) are depicted in Figure 6.24a and b, respectively (Schuttlefield et al. 2007). As shown in Figure 6.24a, a strong absorption band of O-H stretching vibration with a peak at ∼3400 cm−1 and a shoulder around 3240 cm−1 , and that of H-O-H bending vibration peaking around 1650 cm−1 can be seen, and their intensities get stronger with the increase of RH. Meanwhile, the number of H2 O monolayer on the SiO2 is one at RH ∼20%(298 K), two at ∼50%, and three at ∼70%, as shown in Figure 6.24b. The increase of the thickness of the H2 O layer on the surface corresponds to the increase of the absorbance of the infrared bands. The SFG spectroscopy that is useful for the measurement of the form and orientation of hydrogen bonds at the air–liquid interface is also applicable to the air–solid interface (Du et al. 1994), and molecular level information of air–water-SiO2 interface has been obtained by this method (Hopkins et al. 2005; Shen and Ostroverkhov 2006 and references therein). The SFG spectrum of the H2 O on α-quartz at the air interface is shown in Figure 6.25 (Ostroverkhov et al. 2004). This spectrum is qualitatively the same as the SFG spectrum of air–water interface shown in Figure 6.7, except it lacks the peak at 3700 cm−1 due to the OH dangling bond. Further, the broad absorption of the O-H stretching vibration as seen in the spectrum of Figure 6.24a is clearly separated into two peaks at ∼3200 cm−1 and ∼3400 cm−1 in Figure 6.25. The former peak is thought to be ascribed to the O-H of strongly organized hydrogen-bonded H2 O molecule with a tetrahedral structure similar to ice, and the latter to the O-H of not well organized H2 O like liquid water. The intensity of these signals increases with the increase of pH as seen in the figure, which is thought to be due to the increase of the dissociation of SiOH to SiO− + H+ . The surface electric field due to the SiO− anion orientates more strongly the hydrogen bonding network of the H2 O molecules at the interface (Ostroverkhov et al. 2004).

387

388

6 Reactions at the Air–Water and Air–Solid Particle Interface

0.01

3404

3235

A b s o r b a n c e

1645

% RH

3500

4000

3000 2500 Wavenumbers (cm–1)

2000

1500

(a) 6

5 M o 4 n o l 3 a y e 2 r s 1

1 ML

0 0

10

20

30

40

50

60

70

80

90

100

% RH (b)

Figure 6.24 (a) ATR-FTIR spectra following the water uptake on SiO2 at different RH (5%, 8%, 13%, 20%, 27%, 37%, 47%, 66%, 74%, and 78%); (b) the number of adsorbed water layer at different RH. The curve represents a Brunauer-Emmett-Teller (BET) surface area determined by Goodman et al. 2001. Source: Reprinted with permission from Schuttlefield et al. (2007). Copyright 2007 Society for Applied Spectroscopy.

6.5 Interface of Water and Mineral Dust, Quartz, and Metal Oxide Surface

Figure 6.25 Vibrational SFG spectra of water/α-quartz interface at various bulk pH values. Consecutive curves are vertically displaced by 2 units. The ice/fused silica spectrum is shown for comparison. Source: Reprinted with permission from Ostroverkhov et al. (2004). Copyright 2003 Elsevier B.V.

22 20 ice/silica 18 16 11.0 ∣χ01∣2 ×10–42 m4 V–2

14 9.5 12 8.0 10 5.7 8 4.5 6 3.0 4 2.0 2 pH = 1.5 0 2800

3000

3200 3400 3600 Wavenumber, cm–1

3800

The molecular-level understanding of silica–water interface has been developed also by the quantum chemical calculations (Rimola et al. 2013, and references therein). It was revealed by the theoretical calculation that the two kinds of hydrogen-bonded water molecule correspond to the two types of silanol group (Si-OH) at the quartz surface (Sulpizi et al. 2012; Pfeiffer-Laplaud et al. 2015). Figure 6.26 depicts a diagram of –SiOH group at the quartz surface and the hydrogen bonded H2 O molecules obtained by Sulpizi et al. (2012). As shown in the figure, one –SiOH is the out-of-plane silanol orientated to nearly perpendicular to the air–quartz surface, and the other is in-plane silanol, in which OH of –SiOH lies nearly in parallel to the interface. The latter has pK a = 8.5 and forms weak hydrogen bonds with H2 O. These correspond to the ice-like and liquid-like water molecule obtained experimentally from the SFG spectrum. As seen in Figure 6.24b, H2 O forms multiple monolayers with the increase of RH, and the hydrogen bonding structure of the monolayers after the second layer approaches those of bulk liquid water (Yang and Wang 2006; Chen et al. 2011; Sulpizi et al. 2012). Similar spectroscopic studies have been conducted for the interface between water and hydrophilic metal oxides such as α-Al2 O3 , γ-Fe2 O3 , TiO2, and CaO, and pictures corresponding to the case of SiO2 have been obtained (Goodman et al. 2001; Al-Abadleh and Grassian 2003; Ma et al. 2010). Further, studies on natural dust have also been available for Saharan dust (Seisel et al. 2005) and Asian dust (Ma et al. 2012), in addition to ATD (Gustafsson et al. 2005). The measurement of SFG vibrational spectroscopy for the

389

390

6 Reactions at the Air–Water and Air–Solid Particle Interface

O H

H O 1.64

H

‶ice″-like H

H

‶liquid″-like 1.82

O

1.73

Si

H

Figure 6.26 Schematic illustrations of the orientations of water molecules in the interface region of quartz with respect to the z-axis normal to the surface. Source: Adapted with permission from Sulpizi et al. (2012). Copyright 2012 American Chemical Society.

O

Si

interface of water and α-Al2 O3 gave a conceptually similar picture as for SiO2 (Ma et al. 2004; Zhang et al. 2008; Boulesbaa and Borguet 2014). 6.5.2

HONO Formation Reaction from NO2 on the Mineral Surface

Formation of nitrous acid by the heterogeneous dark reaction of NO2 and H2 O on solid surface and its photo-enhancement with the irradiation with light of wavelength longer than 330 nm were first discovered relating to the “unknown radical source” in smog chambers (Sakamaki et al. 1983; Pitts et al. 1984; Akimoto et al. 1987). Later, much higher concentrations of HONO that cannot be explained by the gas-phase reaction of OH + NO + M → HONO + M

(6.64)

have widely been observed in the urban atmosphere at various places, and the heterogeneous formation of HONO on the ground soil surface and aerosol surface has attracted much attention (e.g. Reisinger 2000; Kleffmann et al. 2003; Wang et al. 2003; Su et al. 2008; Yu et al. 2009). Atmospheric HONO is easily photolyzed by the sunlight, HONO + h𝜈 → OH + NO,

(6.65)

to form OH radicals and gives large impact on the photochemical production of O3 . Meanwhile, since atmospheric HONO is dissipated by this photolysis, its concentration is expected to be very low in daytime according to the reaction models. However, unexpectedly high concentrations of HONO have been observed even during daytime, and the heterogeneous reaction of HONO formation on soil and aerosol surface and its enhancement by solar radiation in the ambient atmosphere have been suggested (Zhou et al. 2002a; Kleffmann 2007; Su et al. 2008; Zhou et al. 2011). 6.5.2.1

Dark Reaction

Although the dark heterogeneous reaction of NO2 on solid surface has long been known and described stoichiometrically: 2NO2 + H2 O → HONO + HNO3 ,

(6.66)

it is also known that this equation does not represent the proper reaction mechanism, and the reaction is negligible as a homogeneous gas-phase process (Finlayson-Pitts et al. 2003; Finlayson-Pitts 2009). The formation of HONO from NO2 in the dark and photochemical heterogeneous reactions has been found on various solid surfaces, i.e. natural dust (Kebede et al. 2016), metal oxide (Stemmler et al. 2007), soot (Ammann et al. 1998), silica (Goodman et al. 1999), silicate glass (Syomin and Finlayson-Pitts 2003), Teflon

6.5 Interface of Water and Mineral Dust, Quartz, and Metal Oxide Surface

(Sakamaki et al. 1983; Pitts et al. 1984), etc., but the reaction mechanism itself is still under investigation. From laboratory experiments, it has been reported that HONO and NO are formed in the gas phase as the main products with the initial yield of 1, the contribution of the first term on the right-hand side of Eq. (7.11) is negative, and ΔG may decrease. Equation (7.11) shows that the relative contribution of the first and second terms depends on rp . Figure 7.1 depicts dependence of ΔG on the cluster radius, rp , at constant SX higher than unity. ΔG increases with rp at small rp because the contribution of the second term dominates. As rp increases, the negative contribution of the first term increases more rapidly than the positive contribution of the second term. Consequently, ΔG reaches a maximum, ΔG*, at rp = rp∗ and then turns to decrease. Thermodynamically, this means that the liquid cluster equilibrates with the surrounding vapor at r = rp∗ Figure 7.1 Gibbs energy change for nucleation, ΔG, as a function of the cluster radius, rp . There is a nucleation barrier of height, ΔG*, at the critical cluster radius, rp∗ .

ΔG

ΔG*

0

rp*

rp

417

418

7 Atmospheric New Particle Formation and Cloud Condensation Nuclei

and can grow spontaneously at rp > rp∗ . Therefore, the cluster needs to surmount ΔG* to grow to larger particles. rp∗ is called the critical radius, and the cluster at rp∗ is called the critical cluster. The critical radius, rp∗ , can be obtained by setting the partial derivative of ΔG with respect to rp equal to zero. k T 𝜕ΔG || = −4 πrp∗ 2 B ln SX + 8 πrp∗ σX = 0 | 𝜕rp ||r=r∗ vX

(7.12)

p

rp∗ =

2𝜎X vX kB T ln SX

(7.13)

This equation can be rearranged, leading to a molecular-based expression of the Kelvin equation for a single-component system, which is derived based on molar quantities in Chapter 2. ln SX = ln

2𝜎 v pX = X X∗ pL,X ∘ kB Trp

(7.14)

By substituting Eq. (7.13) into Eqs. (7.10) and (7.11), we can obtain the following equations: 3 2 32π 𝜎X vX 3 (kB T ln SX )3 3 2 16π 𝜎X vX ΔG* = 3 (kB T ln SX )2

NX∗ =

(7.15) (7.16)

where NX∗ is the number of molecules composing the critical cluster. From Eq. (7.16), it is found that the derivative of (ΔG*/k B T) with respect to ln SX gives the following relation: 3 2 d(ΔG∗ ∕kB T) 32π 𝜎X vX =− = −NX∗ . d ln SX 3 (kB T ln SX )3

(7.17)

Thus, a plot of ΔG*/k B T versus ln SX would give the value of NX∗ from its slope. Practically, however, it is difficult to obtain ΔG*. What is experimentally measured is the nucleation rate, J*, which can be defined as the number of clusters that surmount the energy barrier, ΔG*, to grow per unit volume and unit time. Thus, it is expressed as ( ) ΔG∗ J ∗ = A exp − , (7.18) kB T where A is a kinetic prefactor. Taking the logarithm gives ln J ∗ = ln A −

ΔG∗ . kB T

(7.19)

By differentiating with respect to ln SX and using Eq. (7.17), we obtain d(ΔG∗ ∕kB T) d ln J ∗ d ln A d ln A = − = + NX∗ , d ln SX d ln SX d ln SX d ln SX

(7.20)

and therefore, NX∗ =

d ln J ∗ d ln A − . d ln SX d ln SX

(7.21)

7.2 Classical Homogeneous Nucleation Theory

Although it requires an effort to obtain an expression of A, Seinfeld and Pandis (2016) present a detailed derivation of A in a kinetic approach for the classical nucleation theory. According to their derivation, A is given as follows (Seinfeld and Pandis 2016): )1 ( 2𝜎X 2 vX [X]2 (7.22) A= πmX SX where mX is the molecular mass of X and [X] is the number density of X. From the ideal gas low, [X] is expressed as SX pL,X ∘ p [X] = X = . (7.23) kB T kB T From Eqs. (7.22) and (7.23), A depends on SX linearly, and thus d ln A = 1. d ln SX

(7.24)

Consequently, Eq. (7.21) can be rewritten as NX∗ =

d ln J ∗ − 1. d ln SX

(7.25)

This relation holds regardless of the specific nucleation theory and is referred to as the nucleation theorem (Kashchiev 1982). 7.2.2

Homogeneous Nucleation in Two-Component Systems

The discussion for a one-component system in the previous subsection can be expanded to two- or more-component systems (Oxtoby and Kashchiev 1994). Here, we focus our attention on the homogeneous nucleation theory for a two-component system (homogeneous binary nucleation). We can start from an expression of the Gibbs energy change associated with phase transfer from gas molecules to a liquid cluster composed of two species, X and Y: ΔG = NX (𝜇X sol − 𝜇X g ) + NY (𝜇Y sol − 𝜇Y g ) + 4 πrp2 𝜎sol ,

(7.26)

where N i denotes the number of molecules of species i (i = X, Y) contained in a cluster, and 𝜇i g stands for the chemical potential, or Gibbs energy per molecule, of gas-phase i. 𝜇i sol and 𝜎 sol represent the chemical potential for i and the surface tension, respectively, of the binary solution of the same composition as that of the cluster. Using the equilibrium vapor pressure, pi sol , of i over a flat surface of the binary solution, 𝜇i sol is expressed as follows: p sol (7.27) 𝜇i sol = 𝜇i ∘ + kB T ln i ∘ , p where 𝜇 ∘ stands for the chemical potential of i at p∘ . Since 𝜇 g is expressed in a similar i

manner to Eq. (7.5), Eq. (7.26) is rewritten as follows: p p ΔG = −NX kB T ln Xsol − NY kB T ln Ysol + 4 πrp2 𝜎sol . pX pY

i

(7.28)

This equation, which corresponds to Eq. (7.7) for nucleation in the one-component systems, shows that ΔG can decrease with size and thus the cluster can grow spontaneously at pX > pX sol and pY > pY sol . What is important is that the equilibrium vapor

419

420

7 Atmospheric New Particle Formation and Cloud Condensation Nuclei

pressure over the solution, pi sol , is generally lower than that over pure liquid, pL,i ∘ , and therefore the binary nucleation may occur at lower vapor pressure than that for the one-component nucleation. Since ΔG depends on both N X and N Y , the location of the critical cluster has to be determined on a ΔG surface in the N X − N Y space. Mathematically, the following two equations are satisfied at the critical radius, rp∗ : ( ) 𝜕ΔG =0 (7.29) 𝜕N ( X )T,p,NY 𝜕ΔG =0 (7.30) 𝜕NY T,p,NX From Eqs. (7.26) and (7.29), we obtain the following equation (Renninger et al. 1981; Zeng and Oxtoby 1991): ( ) 𝜕rp || 𝜕ΔG = 𝜇X sol − 𝜇X g + 8πrp∗ 𝜎sol = 0. (7.31) | 𝜕NX T,p,NY 𝜕NX ||r =r∗ p

p

The radius of a cluster can be related to N X and N Y by 4 NX vX + NY vY = πrp3 , (7.32) 3 where vX and vY stand for partial molecular volume of X and Y, respectively. Differentiation of both sides of Eq. (7.32) with respect to N X gives the following relation: 𝜕rp vX = 4πrp2 . (7.33) 𝜕NX Therefore, Eq. (7.31) is rewritten as 2𝜎 v (7.34) 𝜇X sol − 𝜇X g + sol∗ X = 0. rp When Δ𝜇X is defined as 𝜇X sol − 𝜇X g , then the following equation is obtained: 2𝜎 v Δ𝜇X + sol∗ X = 0. rp Similarly, from Eqs. (7.26), (7.30), and (7.32), we obtain 2𝜎 v Δ𝜇Y + sol∗ Y = 0, rp

(7.35)

(7.36)

where Δ𝜇Y is defined as 𝜇Y sol − 𝜇Y g . Eqs. (7.35) and (7.36) correspond to the Kelvin equations for binary systems. If the mole fractions of X and Y in the critical cluster are denoted by x∗X and x∗Y , respectively, and x∗X × (7.35) + x∗Y × (7.36) is calculated, rp∗ is expressed as follows: rp∗ = −

2𝜎sol (x∗X vX + x∗Y vY ) x∗X Δ𝜇X + x∗Y Δ𝜇Y

=−

2𝜎sol v∗m 2𝜎sol v∗m = − , x∗X Δ𝜇X + x∗Y Δ𝜇Y x∗X Δ𝜇X + (1 − x∗X )Δ𝜇Y (7.37)

where

v∗m v∗m

is defined as = x∗X vX + x∗Y vY

(7.38)

7.2 Classical Homogeneous Nucleation Theory

and corresponds to the average molecular volume of the critical cluster if the cluster is composed of an incompressible liquid. In the last transformation in Eq. (7.37), the relation x∗X + x∗Y = 1 is used. Using Eqs. (7.32), (7.35), and (7.36), ΔG* is given by ΔG∗ = NX∗ Δ𝜇X + NY∗ Δ𝜇Y + 4 πrp∗ 2 𝜎sol 2𝜎 4 = − ∗sol (NX∗ vX + NY∗ vY ) + 4 π rp∗ 2 𝜎sol = πrp∗ 2 𝜎sol , rp 3

(7.39)

where NX∗ and NY∗ denote the number of X and Y molecules contained in the critical cluster. Information on the critical cluster composition in the binary nucleation systems can be obtained in a similar manner to the one-component systems. From Eq. (7.26), ΔG* is expressed as ΔG∗ = NX∗ (𝜇X sol − 𝜇X g ) + NY∗ (𝜇Y sol − 𝜇Y g ) + 4 πrp∗ 2 𝜎sol .

(7.40)

While 𝜇i sol is expressed as Eq. (7.27), it can be also represented in reference to the pure liquid state. Taking into account nonideality of the solution, it is expressed as follows: 𝜇i sol = 𝜇i liq + kB T ln

pi sol = 𝜇i liq + kB T ln ai , pL,i ∘

(7.41)

where 𝜇i liq stands for the chemical potential of pure liquid i, pL,i ∘ is the saturation vapor pressure of i over a flat surface of the pure liquid, and ai is the activity of i in the solution. Using the mole fraction, xi , and the activity coefficient, 𝛾 i , of i in the solution, Eq. (7.41) is rewritten as 𝜇i sol = 𝜇i liq + kB T ln(𝛾i xi ).

(7.42)

Here, the activity coefficient is defined according to Raoult’s law on the mole-fraction scale, that is ai → xi and 𝛾 i → 1 as xi → 1 (while the mole-fraction-scale activity coefficient is denoted by 𝛾 i (x) in Chapter 2, the superscript (x) is omitted in this chapter because molality- or molarity-scale-activity coefficients are not used). Although 𝜇i g is commonly expressed in a similar manner to Eq. (7.5), it is expressed in reference to 𝜇i liq here. Then, the following relation is obtained: pL,i ∘ p p (7.43) 𝜇i g = 𝜇i ∘ + kB T ln ∘ + kB T ln i ∘ = 𝜇i liq + kB T ln i ∘ . p pL,i pL,i Here we introduce gas-phase activity, bi , which is defined as follows: bi =

pi . pL,i ∘

(7.44)

Then, Eq. (7.43) is rewritten as 𝜇i g = 𝜇i liq + kB T ln bi .

(7.45)

By substituting Eqs. (7.42) and (7.45) into Eq. (7.40), we obtain the following equation: ΔG∗ = −NX∗ kB T ln bX + NX∗ kB T ln(𝛾X xX ) − NY∗ kB T ln bY + NY∗ kB T ln(𝛾Y xY ) + 4πrp∗ 2 𝜎sol .

(7.46)

421

422

7 Atmospheric New Particle Formation and Cloud Condensation Nuclei

Then, partial derivative of (ΔG*/k B T) with respect to bX at constant T, p, and bY finally gives the following simple equation (Strey and Viisanen 1993): ] [ 𝜕(ΔG∗ ∕kB T) = −NX∗ . (7.47) 𝜕 ln bX T,p,bY From Eqs. (7.18) and (7.47), the following relation is obtained: ( ( [ ( ) ) ] ) 𝜕(ΔG∗ ∕kB T) 𝜕 ln J ∗ 𝜕 ln A 𝜕 ln A = − = + NX∗ . 𝜕 ln bX T,p,bY 𝜕 ln bX T,p,bY 𝜕 ln bX 𝜕 ln bX T,p,bY T,p,bY (7.48) Although the expression of A in the binary system is more complicated than that in the one-component system (Seinfeld and Pandis 2016), its dependence on the gas-phase activity is weak and the first term on the right-hand side in Eq. (7.48) typically ranges only from 0 to 1 (Oxtoby and Kashchiev 1994). Therefore, ignoring this contribution would give ( ) 𝜕 ln J ∗ ∗ . (7.49) NX ≈ 𝜕 ln bX T,p,bY From Eq. (7.49) and considering that pL,X ∘ is constant at constant temperature, the derivative with respect to ln bX can be replaced by that with respect to ln pX or ln [X]. Thus, ( ) 𝜕 ln J ∗ NX∗ ≈ . (7.50) 𝜕 ln[X] T,p,[Y] Similarly, NY∗ is expressed as ( ) 𝜕 ln J ∗ ∗ NY ≈ . 𝜕 ln[Y] T,p,[X]

(7.51)

Therefore, when measured nucleation rates would be plotted against the concentration of the species involved in the nucleation on a full logarithmic scale, the number of molecules contained in the critical cluster could be estimated from its slope. In such a manner, the information on the critical cluster composition can be obtained from nucleation rates that are measured in laboratory experiments or field observations.

7.3 Atmospheric New Particle Formation 7.3.1

New Particle Formation Rate and Growth Rate

In the 1990s, studies on new particle formation processes in the atmosphere were made possible by measurements of the size distribution of particles as small as about 3 nm. Field measurements in the continental boundary layer have frequently observed the formation of new particles at a few nm, which grow to about 50–100 nm within the subsequent one to two days (Kulmala et al. 2004). Such phenomena can be observed at various locations and appear to occur ubiquitously (Kulmala et al. 2004). Figure 7.2 shows an example of a new particle formation event observed at a fixed observatory in

7.3 Atmospheric New Particle Formation

Diameter (m)

Fitted Dp,g GR fit

10–7 GR = 4.8 nm/h

10–8 00:00

03:00

06:00

10

Concentration (cm–3)

2 1.5

09:00 100

× 104

12:00

dN/dlogDp (cm–3)

15:00

18:00

21:00

1000

00:00 10000

J3 = dN/dt + Coagulation Scavenging = 1.90 cm–3s–1 + 0.25 cm–3s–1 = 2.15 cm–3s–1

Total number < 25 nm number dN/dt fit

1 Slope = dN/dt

0.5 0 00:00

03:00

06:00

09:00

12:00

15:00

18:00

21:00

00:00

Time

Figure 7.2 Typical new particle formation event observed in Hyytiälä, Finland. The upper panel depicts particle size distribution ranging from 3 to 500 nm as a function of time. The open squares show geometric mean diameters of the nucleation mode particles and the dashed line shows the growth curve obtained from the fitting. The lower panel depicts the total number concentration and the number concentration of the nucleation mode particles as a function of time. Source: Reprinted with permission from Kulmala and Kerminen (2008). Copyright 2008 Elsevier B.V.

Hyytiälä, a rural continental site surrounded by homogeneous coniferous boreal forests in Finland (Dal Maso et al. 2005; Kulmala and Kerminen 2008). The upper panel shows evolution of the particle size distribution ranging from 3 to 500 nm while the lower panel shows the total number concentration of particles integrated over the measured size range and the number concentration of the nucleation mode particles (100%). At a given supersaturation, particles that can be activated over the critical size are called cloud condensation nuclei (CCN). The activation of CCN is affected by the curvature effect of a particle (droplet), as described in Section 7.2, as well as by the ability of a particle to take up water vapor, or hygroscopicity. The hygroscopicity of a particle is related to the lowering of the equilibrium water vapor pressure due to the presence of solutes in an aqueous droplet, and therefore highly affected by aerosol chemical composition (McFiggans et al. 2006; Farmer et al. 2015). The effect of chemical composition on the CCN activation is examined on the basis of the Köhler equation (Köhler 1936), which describes the relationship between diameter of an aqueous droplet and its equilibrium water vapor pressure. Here, we derive the Köhler equation from the Kelvin equation for the binary system outlined in Section 7.2.2. While two components involved in nucleation are denoted by X and Y in Section 7.2.2, water and a solute in an aqueous droplet are denoted by W and X, respectively, in this section. Also note that we use molar quantities rather than molecular quantities to describe the equations. Keeping these modifications in mind, we can rewrite Eq. (7.34) in order to describe relation between chemical potentials of water and the droplet radius, rp , at equilibrium as 𝜇W sol − 𝜇W g +

2𝜎sol vW = 0, rp

(7.67)

where 𝜇W sol and 𝜇W g denote the chemical potential of water in solution and in the gas phase, respectively, and vW is the partial molar volume of water in the solution. By replacing rp by the droplet diameter, dp , and rearranging the equation, we obtain 𝜇W g − 𝜇W sol =

4𝜎sol vW . dp

(7.68)

Here, 𝜇W g and 𝜇W sol are written from Eqs. (7.41) and (7.43), respectively, as 𝜇W sol = 𝜇W liq + RT ln aW

(7.69)

and 𝜇W g = 𝜇W liq + RT ln

pW , pL,W ∘

(7.70)

where 𝜇W liq is the chemical potential of pure liquid water, pW is the partial pressure of water vapor adjacent to a droplet surface, and pL,W ∘ is the water vapor pressure over a flat surface of pure liquid water. Equation (7.69) takes into account the nonideality of solution by introducing the mole-fraction-scale activity, aW , defined according to Raoult’s law. Substituting Eqs. (7.69) and (7.70) into Eq. (7.68) gives pW 4𝜎 v RT ln = sol W , (7.71) ∘ pL,W aW dp or equivalently, p 4𝜎 v ln W ∘ = sol W + ln aW pL,W RTdp or ( ) 4𝜎sol vW pW = a exp . W pL,W ∘ RTdp

(7.72)

(7.73)

437

438

7 Atmospheric New Particle Formation and Cloud Condensation Nuclei

Now we consider that a dry particle composed of solute species X absorbs water to grow to a droplet. The volume of the dry particle, V X , is expressed as 1 VX = πddry 3 = nX vX , (7.74) 6 where ddry is the diameter of the particle, nX is the number of moles of X, and vX is the molar volume of X. If we assume that the volume of the droplet is equal to the sum of that of the dry particle and that of the absorbed water, then the volume of the droplet, V p , is expressed as 1 (7.75) πd 3 = nW vW + nX vX , 6 p where nW is the number of moles of water. From these equations, nW is represented by Vp =

π(dp 3 − ddry 3 )

. (7.76) 6vW For dilute solutions, aW is approximately equal to the mole fraction of water in the solution, xW . Thus, in the case of nonelectrolyte solutions, the following relation is obtained: n 1 1 ≈ =1+ X. (7.77) aW xW nW This equation is another expression of Raoult’s law for the ideal solution presented in Chapter 2. From Eqs. (7.74), (7.76), and (7.77), we obtain nW =

vW ddry 3 1 . =1+ aW vX (dp 3 − ddry 3 )

(7.78)

The partial molar volume, vW , can be approximately expressed in terms of the molar mass, MW , and the density, 𝜌W , of water as MW . (7.79) 𝜌W Similarly, vX is expressed as M vX = X , (7.80) 𝜌X where MX and 𝜌X represent the molar mass and density of the solute X, respectively. Substituting these equations into Eq. (7.78), we obtain vW =

MW 𝜌X ddry 1 . =1+ aW MX 𝜌W (dp 3 − ddry 3 ) 3

(7.81)

This relation is further substituted into Eq. (7.72), and then ] [ MW 𝜌X ddry 3 pW 4MW 𝜎sol ln = − ln 1 + p ∘ RT𝜌 d M 𝜌 (d 3 − d 3 ) L,W

W p

X W

p

(7.82)

dry

is obtained. Using ln (1 + x) ≈ x for x ≪ 1, this equation is simplified to MW 𝜌X ddry p 4MW 𝜎sol ln W ∘ = . − pL,W RT𝜌W dp MX 𝜌W (dp 3 − ddry 3 ) 3

(7.83)

7.4 Aerosol Hygroscopicity and Cloud Condensation Nuclei

This is an expression of the Köhler equation showing the relation between droplet diameter, dp , and equilibrium water vapor pressure, pW . When the solute X is electrolyte, the number of ions generated on dissolution should be taken into account instead of the number of the solute itself in Eq. (7.77). If the solute completely dissociates, Eq. (7.77) is replaced by 𝜔 n 1 = 1 + X X, (7.84) aW nW where 𝜔X is the number of ions generated from one solute molecule in the solution; for example, 𝜔X = 2 for sodium chloride and 𝜔X = 3 for ammonium sulfate. When we start from Eq. (7.84), we finally obtain the following relation instead of Eq. (7.83): ln

𝜔X MW 𝜌X ddry 3 pW 4MW 𝜎sol . = − pL,W ∘ RT𝜌W dp MX 𝜌W (dp 3 − ddry 3 )

This form of the Köhler equation is applicable to cases of electrolyte solutions. Since the saturation ratio of water, SW , is expressed as p SW = W ∘ , pL,W

(7.85)

(7.86)

Eq. (7.85) is rewritten as 𝜔X MW 𝜌X ddry 4MW 𝜎sol . − RT𝜌W dp MX 𝜌W (dp 3 − ddry 3 ) 3

ln SW =

(7.87)

For ddry ≪ dp , Eq. (7.87) is simplified to ln SW

3 4MW 𝜎sol 𝜔X MW 𝜌X ddry = − . RT𝜌W dp MX 𝜌W dp 3

(7.88)

Equation (7.88) is often expressed as ln SW =

A B − , dp dp 3

(7.89)

where A=

4MW 𝜎sol RT𝜌W

(7.90)

and B=

𝜔X MW 𝜌X ddry 3 MX 𝜌 W

.

(7.91)

Also, the saturation ratio, SW , is sometimes replaced by supersaturation, SSW , which is defined by the difference from saturation (SW = 1) as SSW = SW − 1.

(7.92)

Keeping in mind that ln (1 + SSW ) ≈ SSW for small SSW , we can rewrite Eq. (7.89) as SSW ≈

A B − . dp dp 3

(7.93)

439

7 Atmospheric New Particle Formation and Cloud Condensation Nuclei

1.006

0.6 Kelvin term

1.004

0.4 Köhler curve

0.2

0

1.002

1 Raoult term

–0.2

–0.4 0.1

Saturation Ratio, SW

Supersaturation, SSW (%)

440

Figure 7.6 An example of a Köhler curve representing the relation between supersaturation, SSW , (or saturation ratio, SW ) and droplet wet diameter, dp . Individual contributions of the Kelvin and Raoult (solute) terms are also shown in this figure.

0.998

1

10

0.996 100

dp/μm

The first term on the right-hand side of Eqs. (7.88), (7.89), and (7.93) is derived from the Kelvin equation describing the curvature effect on the equilibrium vapor pressure and thus called the Kelvin term, while the second term is derived from the effect of solutes on the basis of Raoult’s law and is thus called the solute term or Raoult term. Because the Kelvin term and solute term depend on dp in different ways, the dependence of SW or SSW on dp is nonmonotonic. The solid line in Figure 7.6 shows SSW (%) based on Eq. (7.93) as a function of dp for a NaCl particle with ddry = 0.05 μm. The resultant curve is called the Köhler curve. Figure 7.6 shows also the individual contributions of the Kelvin and Raoult terms to the Köhler curve. While the contribution of the Raoult term dominates at small dp , that of the Kelvin term increases with dp and dominates at large dp . As a result, the supersaturation increases, reaches a maximum at a certain size, and then decreases asymptotically to SSW = 0 as dp increases. The droplet diameter at which the supersaturation reaches the maximum is the critical droplet diameter, dp,crit . The position of dp,crit can be found by the derivative of SSW with respect to dp . Using A and B represented by Eqs. (7.90) and (7.91), dp,crit is given by ( )1∕2 3B . (7.94) dp,crit = A The critical supersaturation, SSW,crit , and the critical saturation ratio, SW,crit , are obtained as follows: ( 3 )1∕2 4A ln SW,crit = ln(SSW,crit + 1) = . (7.95) 27B On a Köhler curve, liquid water in a droplet equilibrates with the water vapor in the surrounding air. However, the stability of the equilibrium is entirely different at dp < dp,crit and dp > dp,crit . At dp < dp,crit , the supersaturation at equilibrium increases with dp . Thus, if a droplet at equilibrium with the surroundings absorbs a few water molecules to grow at a fixed water vapor pressure, the supersaturation of the surrounding air becomes lower than the supersaturation to be in equilibrium with the droplet, and thus the droplet diameter decreases down to the original size by evaporating water molecules. Conversely, if a droplet at equilibrium with the surrounding air loses a few

7.4 Aerosol Hygroscopicity and Cloud Condensation Nuclei

water molecules, the supersaturation of the surrounding air becomes higher than the equilibrium supersaturation, and the droplet diameter increases up to the original size by absorbing water molecules. Therefore, on a Köhler curve at dp < dp,crit , a droplet is in a stable equilibrium with the surroundings. At dp > dp,crit , on the other hand, the supersaturation at equilibrium decreases with dp . If a droplet grows by absorbing a few water molecules, the supersaturation of the surrounding air becomes higher than the equilibrium supersaturation, and the droplet can absorb additional water molecules to grow further. Conversely, evaporation of a few molecules from a droplet in equilibrium with the surroundings leads to further shrinkage of the droplet because the supersaturation of the surroundings is lower than that to be in equilibrium with the droplet. Therefore, a droplet is in an unstable equilibrium at dp > dp,crit . When SSw,crit of a particle is lower than the supersaturation of the surrounding air, the particle cannot reach any equilibrium. In this case, the supersaturation of the surroundings is always higher than the supersaturation to be equilibrium with droplets of any size, and the droplets may continue to grow to become cloud droplets of ∼10 μm in diameter. In this way, at ambient supersaturation higher than SSw,crit , particles are activated to grow to cloud droplets. 7.4.2

Nonideality of Solution in a Droplet

In the derivation of the above equations, ideal solution is assumed in Eqs. (7.77) and (7.84) as solution in a droplet is dilute. More precisely, however, nonideality of the solution should be taken into account. While the deviations from the ideal solutions or ideal dilute solutions are usually taken into account by introducing activity coefficients as mentioned in Chapter 2, another way is to use a molal osmotic coefficient, 𝜙m , or van’t Hoff factor, ivH , in expression of the activity. In the case of using 𝜙m , the activity of water in solution, aW , is represented by ln aW = −𝜔X MW mX 𝜙m ,

(7.96) −1

where MW is the molar mass of water (kg mol ) and mX is the molal concentration (molality) of the solute X (mol kg−1 ). Note that when MW would be represented conventionally by molecular weight, the right-hand side of Eq. (7.96) should be divided by 1000 for the conversion of g to kg. Using the number of moles, nW and nX , in the solution, Eq. (7.96) is rewritten as follows: ln aW = −

𝜔X 𝜙m nX . nW

Then, transformation of this equation into ( ) 𝜔X 𝜙m nX 1 = exp , aW nW and a series expansion of the exponent on the right-hand side give )2 ( 𝜔 𝜙 n 1 𝜔X 𝜙m nX 1 =1+ X m X + + …. aW nW 2 nW

(7.97)

(7.98)

(7.99)

441

442

7 Atmospheric New Particle Formation and Cloud Condensation Nuclei

Neglecting the higher order terms than the first order, we finally obtain 𝜔 𝜙 n 1 ≈ 1 + X m X. aW nW

(7.100)

The Köhler equation could be derived from Eq. (7.100) as the starting point when the nonideality of solution is considered. As seen from the above equations, the discussion of particle hygroscopicity based on the Köhler equation requires physical parameters including molar mass and density of solutes as well as the information on water activity of the solution. While few data are available on inorganic and organic mixed solutions, activities of these solutions can be calculated using models such as Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) model (Zuend et al. 2008) mentioned in Section 2.3.1. 7.4.3

Hygroscopicity Parameter, 𝜿

As already described, the Köhler equation includes physicochemical parameters specific to solutes and water activity, which are highly uncertain for species composing ambient aerosols. In particular, for a variety of organic species in ambient aerosols, even molar masses and densities are often unknown. Therefore, it is difficult to estimate hygroscopicity of aerosols quantitatively from the physicochemical parameters of individual constituents of aerosols to predict CCN concentrations. An alternative approach is to combine molar masses, densities, and nonideality of the solution into an adjustable parameter and to describe the aerosols’ hygroscopicity in terms of this parameter. Petters and Kreidenweis (2007) proposed the 𝜅-Köhler theory as one of these approaches. This theory introduces the hygroscopicity parameter, 𝜅, defined as V 1 =1+𝜅 X, aW VW

(7.101)

where V X and V W stand for the volume of the solute and water, respectively. Because V X is expressed in terms of the dry particle diameter, ddry , by Eq. (7.74), V W is expressed as 1 π(d 3 − ddry 3 ). 6 p Substituting Eqs. (7.74) and (7.102) into Eq. (7.101) gives VW =

(7.102)

𝜅ddry 3 dp 3 − (1 − 𝜅)ddry 3 1 =1+ 3 = . aW dp − ddry 3 dp 3 − ddry 3

(7.103)

From Eqs. (7.73), (7.79), (7.86), and (7.103), the following equation is obtained: ( ) dp 3 − ddry 3 4MW 𝜎sol SW = 3 exp . (7.104) RT𝜌W dp dp − (1 − 𝜅)ddry 3 This equation shows that a larger 𝜅 value gives a smaller saturation ratio of water to be equilibrated with a solution droplet, or a higher hygroscopicity. For 𝜅 = 0, Eq. (7.103) gives aW = 1, and Eq. (7.104) reduces to the Kelvin equation for a pure water droplet,

7.4 Aerosol Hygroscopicity and Cloud Condensation Nuclei

corresponding to wetting of a water-insoluble particle by pure water. For 𝜅 > 0.2, ln SW,crit is approximated by the following equation (Petters and Kreidenweis 2007): ( 3 )1∕2 4A ddry −3∕2 𝜅 −1∕2 . (7.105) ln SW,crit = ln(SSW,crit + 1) = 27 The 𝜅 values can be obtained experimentally from hygroscopicity data for particles. One approach is to measure the critical supersaturation for a particle to be activated as a function of the dry particle diameter and fit the data to Eq. (7.105) to determine 𝜅. Petters and Kreidenweis (2007) reported that the 𝜅 values thus determined range from 0.6 to 1.3 for inorganic salts with high hygroscopicity. Another approach to obtain 𝜅 values is to measure hygroscopic growth of particles. This approach utilizes a Hygroscopicity Tandem Differential Mobility Analyzer (HTDMA), in which particles at a dry diameter, ddry , selected under dry conditions by the first differential mobility analyzer, is allowed to grow at a fixed saturation ratio, SW < 1, and the resultant size distribution (dp ) is measured by the second differential mobility analyzer. Through the measurement, the hygroscopic growth factor, GF, defined below is obtained: dp . (7.106) GF = ddry By using GF, Eq. (7.104) is rewritten as ) ( GF 3 − 1 A SW = . exp ddry GF GF 3 − (1 − 𝜅)

(7.107)

From the fitting using this equation, the 𝜅 values are obtained from the measured GF. A 𝜅 value for a particle containing multiple solutes can be given from those of individual components by the simple mixing rule (Petters and Kreidenweis 2007), ∑ 𝜀i 𝜅i , (7.108) 𝜅= i

where 𝜅 i and 𝜀i denote the hygroscopicity parameter and the volume fraction of the individual component, respectively. In a similar way to a single-component particle, the 𝜅 value for a multi-component particle can be estimated from measured hygroscopicity data. Petters and Kreidenweis (2007) found that 𝜅 values for mixtures containing appreciable amounts of inorganic species are close to unity, whereas moderately hygroscopic organic species have 𝜅 values of 0.01 – 0.5. The 𝜅-Köhler theory is now widely used to describe hygroscopicity of particles in laboratory and field studies. For example, Jimenez et al. (2009) and Duplissy et al. (2011) investigated the relationship between 𝜅 values and photochemical aging for SOAs generated from VOC oxidation in a chamber by the HTDMA measurements of the particle hygroscopicity coupled with the aerosol composition analysis using AMS. In these studies, the fraction of the total organic signal at m/z 44, f 44 , which is mainly attributed to CO2 + , is used to estimate the atomic O : C ratio of organics (Aiken et al. 2008). Figure 7.7 shows the correlation between 𝜅 values and atomic O : C ratios for SOAs generated from the photooxidation of α-pinene, isoprene, and TMB

443

444

7 Atmospheric New Particle Formation and Cloud Condensation Nuclei

Figure 7.7 Relationship between the O : C ratio and hygroscopicity, 𝜅 org (or equivalently the particle growth factor, GF, at 95% relative humidity) of OA for several field data sets (a high-altitude site at Jungfraujoch, Switzerland; above Mexico City, a polluted megacity; and at the forested site of Hyytiälä, Finland) and for laboratory smog chamber SOA. Source: Reprinted with permission from Jimenez et al. (2009). Copyright 2009 American Association for the Advancement of Science.

in chamber experiments as well as for ambient aerosols at several field sites (Jimenez et al. 2009). The 𝜅 value for organics, 𝜅 org , in the ambient aerosols was deduced by using Eq. (7.108) from those for inorganic species and volume fractions of individual components obtained by AMS. As shown in this figure, the 𝜅 org value increases with the increase in the atomic O : C ratio, suggesting that the aerosol hygroscopicity correlates with the aerosol aging. While the 𝜅 org values for anthropogenic secondary organic aerosols (ASOAs) from TMB appear to be higher than those for biogenic secondary organic aerosols (BSOAs) from α-pinene and isoprene at the same O : C ratio in Figure 7.7, laboratory studies using a flow reactor found no significant difference between 𝜅 org values for ASOAs and those for BSOAs (Lambe et al. 2011), suggesting that the 𝜅 org values may be affected by experimental conditions. Another study with a flow reactor reported that 𝜅 org obtained from the CCN activation measurements under supersaturation conditions depend nonlinearly on O : C ratio (Massoli et al. 2010). The relationship between the hygroscopicity of aerosols represented by 𝜅 org and the oxidation level of organic aerosols measured by AMS is extensively investigated in the subsequent field studies. Mei et al. (2013) characterize size-resolved CCN spectra and aerosol composition at urban supersite in Pasadena, California, during the CalNex campaign. They obtained hygroscopicity of CCN-active particles, 𝜅 CCN , using Eq. (7.105) from the estimated critical supersaturation, SSW,crit , and then they determined the hygroscopicity of organics, 𝜅 org , under the assumption that the observed aerosols are composed only of ammonium nitrate, ammonium sulfate, black carbon (BC), and organics. Thus, 𝜅 org can be determined from 𝜅 i and 𝜀i of the individual components, i, by 𝜅org =

1 (𝜅 − 𝜀NH4 NO3 𝜅NH4 NO3 − 𝜀(NH4 )2 SO4 𝜅(NH4 )2 SO4 ), 𝜀org CCN

(7.109)

7.4 Aerosol Hygroscopicity and Cloud Condensation Nuclei

Figure 7.8 Organic hygroscopicity, 𝜅 org , plotted as a function of O : C atomic ratio for ambient organic aerosols. The solid line shows the result of least squares fitting. Source: Adapted with permission from Mei et al. (2013). Copyright 2013 American Geophysical Union.

where BC is treated as nonhygroscopic (𝜅 BC = 0). Figure 7.8 shows the correlation between 𝜅 org thus determined and the atomic O : C ratio estimated from f 44 measured with AMS. From the least squares fit, 𝜅 org = (0.83 ± 0.06) × (O : C) + (−0.19 ± 0.02) is obtained. This relationship is consistent with that obtained for SOAs generated from photooxidation of TMB in chamber studies (Duplissy et al. 2011), which can be explained by the fact that SOA formed from anthropogenic precursors contributed substantially to the total organic aerosol concentration at the CalNex-LA site, which was principally a receptor site for pollution from downtown LA. However, the 𝜅 org values derived by Mei et al. (2013) exhibit stronger increase with O : C ratio than those of SOAs obtained from CCN measurements under supersaturated conditions in flow reactors (Massoli et al. 2010; Lambe et al. 2011). Mei et al. (2013) explain this discrepancy by the difference in chemical compositions between ambient organic aerosols and SOAs generated in the flow reactors. While the relationship between the 𝜅 org values and the O : C ratio has been parameterized for organic aerosols in field observations as shown above, recent laboratory studies have pointed out that the relation between aerosol hygroscopicity and the degree of oxidation is more complicated. Frosch et al. (2011) investigated the relation between 𝜅 org values and the degree of oxidation for organic aerosols produced from α-pinene ozonolysis under different experimental conditions in a smog chamber and found that the 𝜅 org value is largely independent of O : C ratio in the range of 0.3 < O : C < 0.6. Zhao et al. (2016) also conducted chamber studies to investigate CCN activity of SOAs produced from monoterpenes and aromatics. They reported that although CCN activity increases with the degree of oxidation for individual reaction systems, the 𝜅 org value does not correlate with O : C when all different types of oxidation are considered together. Rickards et al. (2013) found that 𝜅 org values have a large variation among compounds of even the same O : C ratio from their measurements of subsaturated hygroscopic growth of aerosols composed of single organic components using aerosol optical tweezers and an electrodynamic balance technique. While they found the positive correlation between 𝜅 org values and O : C ratios through comparison of their results to literature data, they observed significant variations among 𝜅 org vs. O : C parameterization with different aerosol types, reflecting different chemical functionality, composition, and oxidation history. These results suggest that further studies are needed for better understanding of hygroscopicity of ambient organic aerosols.

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References Aiken, A.C., Decarlo, P.F., Kroll, J.H. et al. (2008). O/C and OM/OC ratios of primary, secondary, and ambient organic aerosols with high-resolution time-of-flight aerosol mass spectrometry. Environ. Sci. Technol. 42: 4478–4485. Almeida, J., Schobesberger, S., Kürten, A. et al. (2013). Molecular understanding of sulphuric acid−amine particle nucleation in the atmosphere. Nature 502: 359–363. Ball, S.M., Hanson, D.R., Eisele, F.L., and McMurry, P.H. (1999). Laboratory studies of particle nucleation: initial results for H2 SO4 , H2 O, and NH3 vapors. J. Geophys. Res. 104: 23709–23718. Benson, D.R., Young, L.-H., Kameel, F.R., and Lee, S.-H. (2008). Laboratory-measured nucleation rates of sulfuric acid and water binary homogeneous nucleation from the SO2 + OH reaction. Geophys. Res. Lett. 35: L11801, doi:10.1029/2008GL033387. Benson, D.R., Yu, J.H., Markovich, A., and Lee, S.-H. (2011). Ternary homogeneous nucleation of H2 SO4 , NH3 , and H2 O under conditions relevant to the lower troposphere. Atmos. Chem. Phys. 11: 4755–4766. Berndt, T., Böge, O., Stratmann, F. et al. (2005). Rapid formation of sulfuric acid particles at near-atmospheric conditions. Science 307: 698–700. Berndt, T., Böge, O., and Stratmann, F. (2006). Formation of atmospheric H2 SO4 /H2 O particles in the absence of organics: a laboratory study. Geophys. Res. Lett. 33: L15817, doi:10.1029/2006GL026660. Berndt, T., Stratmann, F., Sipilä, M. et al. (2010). Laboratory study on new particle formation from the reaction OH + SO2 : influence of experimental conditions, H2 O vapour, NH3 and the amine tert-butylamine on the overall process. Atmos. Chem. Phys. 10: 7101–7116. Berndt, T., Sipilä, M., Stratmann, F. et al. (2014). Enhancement of atmospheric H2 SO4 /H2 O nucleation: organic oxidation products versus amines. Atmos. Chem. Phys. 14: 751–764. Brus, D., Hyvärinen, A.-P., Viisanen, Y. et al. (2010). Homogeneous nucleation of sulfuric acid and water mixture: experimental setup and first results. Atmos. Chem. Phys. 10: 2631–2641. Curtis, J. (2006). Nucleation of atmospheric aerosol particles. C.R. Phys. 7: 1027–1045. Dal Maso, M., Kulmala, M., Riipinen, I. et al. (2005). Formation and growth of fresh atmospheric aerosols: eight years of aerosol size distribution data from SMEAR II, Hyytiälä, Finland. Boreal Environ. Res. 10: 323–336. Donahue, N.M., Kroll, J.H., Pandis, S.N., and Robinson, A.L. (2012). A two-dimensional volatility basis set − Part 2: diagnostics of organic-aerosol evolution. Atmos. Chem. Phys. 12: 615–634. Donahue, N.M., Ortega, I.K., Chuang, W. et al. (2013). How do organic vapors contribute to new-particle formation? Faraday Discuss. 165: 91–104. Duplissy, J., DeCarlo, P.F., Dommen, J. et al. (2011). Relating hygroscopicity and composition of organic aerosol particulate matter. Atmos. Chem. Phys. 11: 1155–1165. Ehn, M., Junninen, H., Petäjä, T. et al. (2010). Composition and temporal behavior of ambient ions in the boreal forest. Atmos. Chem. Phys. 10: 8513–8530. Ehn, M., Kleist, E., Junninen, H. et al. (2012). Gas phase formation of extremely oxidized pinene reaction products in chamber and ambient air. Atmos. Chem. Phys. 12: 5113–5127.

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Köhler, H. (1936). The nucleus in and the growth of hygroscopic droplets. Trans. Faraday Soc. 32: 1152–1161. Kroll, J.H., Donahue, N.M., Jimenez, J.L. et al. (2011). Carbon oxidation state as a metric for describing the chemisty of atmospheric organic aerosol. Nat. Chem. 3: 133–139. Kuang, C., McMurry, P.H., McCormick, A.V., and Eisele, F.L. (2008). Dependence of nucleation rates on sulfuric acid vapor concentration in diverse atmospheric locations. J. Geophys. Res. 113: D10209, doi:10.1029/2007JD009253. Kulmala, M. and Kerminen, V.-M. (2008). On the formation and growth of atmospheric nanoparticles. Atmos. Res. 90: 132–150. Kulmala, M., Vehkamäki, H., Petäjä, T. et al. (2004). Formation and growth rates of ultrafine atmospheric particles: a review of observations. J. Aerosol Sci. 35: 143–176. Kulmala, M., Lehtinen, K.E., and Laaksonen, A. (2006). Cluster activation theory as an explanation of the linear dependence between formation rate of 3 nm particles and sulfuric acid concentration. Atmos. Chem. Phys. 6: 787–793. Kulmala, M., Kontkanen, J., Junninen, H. et al. (2013). Direct observations of atmospheric aerosol nucleation. Science: 339, 943–946. Kulmala, M., Petäjä, T., Ehn, M. et al. (2014). Chemistry of atmospheric nucleation: on the recent advances on precursor characterization and atmospheric cluster composition in connection with atmospheric new particle formation. Annu. Rev. Phys. Chem. 65: 21–37. Kürten, A., Jokinen, T., Simon, M. et al. (2014). Neutral molecular cluster formation of sulfuric acid-dimethylamine observed in real time under atmospheric conditions. Proc. Natl. Acad. Sci. 111: 15019–15024. Laaksonen, A., Talanquer, V., and Oxtoby, D.W. (1995). Nucleation: measurements, theory, and atmospheric applications. Annu. Rev. Phys. Chem. 46: 489–524. Lambe, A.T., Onasch, T.B., Massoli, P. et al. (2011). Laboratory studies of the chemical composition and cloud condensation nuclei (CCN) activity of secondary organic aerosol (SOA) and oxidized primary organic aerosol (OPOA). Atmos. Chem. Phys. 11: 8913–8928. Mäkelä, J.M., Hoffmann, T., Holzke, C. et al. (2002). Biogenic iodine emissions and identification of end-products in coastal ultrafine particles during nucleation bursts. J. Geophys. Res. 107: 8110, doi:10.1029/2001JD000580. Manninen, H.E., Nieminen, T., Asmi, E. et al. (2010). EUCAARI ion spectrometer measurements at 12 European sites – analysis of new particle formation events. Atmos. Chem. Phys. 10: 7909–7927. Massoli, P., Lambe, A.T., Ahern, A.T. et al. (2010). Relationship between aerosol oxidation level and hygroscopic properties of laboratory generated secondary organic aerosol (SOA) particles. Geophys. Res. Lett. 37: L24801, doi:10.1029/2010GL045258. McFiggans, G., Coe, H., Burgess, R. et al. (2004). Direct evidence for coastal iodine particles from Laminaria macroalgae – linkage to emissions of molecular iodine. Atmos. Chem. Phys. 4: 701–713. McFiggans, G., Artaxo, P., Baltensperger, U. et al. (2006). The effect of physical and chemical aerosol properties on warm cloud droplet activation. Atmos. Chem. Phys. 6: 2593–2649. McMurry, P.H. (1983). New particle formation in the presence of an aerosol: rates, time scales, and sub-0.01 μm size distributions. J. Colloid Interface Sci. 95: 72–80. McMurry, P.H. and Friedlander, S.K. (1979). New particle formation in the presence of an aerosol. Atmos. Environ. 13: 1635–1651.

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Mei, F., Hayes, P.L., Ortega, A. et al. (2013). Droplet activation properties of organic aerosols observed at an urban site during CalNex-LA. J. Geophys. Res. 118: 2903–2917. Merikanto, J., Spracklen, D.V., Mann, G.W. et al. (2009). Impact of nucleation on global CCN. Atmos. Chem. Phys. 9: 8601–8616. Metzger, A., Verheggen, B., Dommen, J. et al. (2010). Evidence for the role of organics in aerosol particle formation under atmospheric conditions. Proc. Natl. Acad. Sci. 107: 6646–6651. O’Dowd, C.D., Hämeri, K., Mäkelä, J.M. et al. (2002a). A dedicated study of new particle formation and fate in the coastal environment (PARFORCE): overview of objectives and achievements. J. Geophys. Res. 107: 8108, doi:10.1029/2001JD000555. O’Dowd, C.D., Jimenez, J.L., Bahreini, R. et al. (2002b). Marine aerosol formation from biogenic iodine emissions. Nature 417: 632–636. Oxtoby, D.W. and Kashchiev, D. (1994). A general relation between the nucleation work and the size of the nucleus in multicomponent nucleation. J. Chem. Phys. 100: 7665–7671. Paasonen, P., Nieminen, T., Asmi, E. et al. (2010). On the roles of sulfuric acid and low-volatility organic vapours in the initial steps of atmospheric new particle formation. Atmos. Chem. Phys. 10: 11223–11242. Petters, M.D. and Kreidenweis, S.M. (2007). A single parameter representation of hygroscopic growth and cloud condensation nucleus activity. Atmos. Chem. Phys. 7: 1961–1971. Renninger, R., Hiller, F.C., and Bone, R.C. (1981). Comment on “self-nucleation in the sulfuric acid-water system”. J. Chem. Phys. 75: 1584–1586. Riccobono, F., Schobesberger, S., Scott, C.E. et al. (2014). Oxidation products of biogenic emissions contribute to nucleation of atmospheric particles. Science 344: 717–721. Rickards, A.M.J., Miles, R.E.H., Davies, J.F. et al. (2013). Measurements of the sensitivity of aerosol hygroscopicity and the 𝜅 parameter to the O/C ratio. J. Phys. Chem. A 117: 14120–14131. Riipinen, I., Sihto, S.-L., Kulmala, M. et al. (2007). Connections between atmospheric sulfuric acid and new particle formation during QUEST III−IV campaigns in Heidelberg and Hyytiälä. Atmos. Chem. Phys. 7: 1899–1914. Riipinen, I., Yli-Juuti, T., Pierce, J.R. et al. (2012). The contribution of organics to atmospheric nanoparticle growth. Nat. Geosci. 5: 453–458. Schobesberger, S., Junninen, H., Bianchi, F. et al. (2013). Molecular understanding of atmospheric particle formation from sulfuric acid and large oxidized organic molecules. Proc. Natl. Acad. Sci. 110: 17223–17228. Seinfeld, J.H. and Pandis, S.N. (2016). Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, 3e. Hoboken, NJ: Wiley. Sihto, S.-L., Kulmala, M., Kerminen, V.-M. et al. (2006). Atmospheric sulfuric acid and aerosol formation: implications from atmospheric measurements for nucleation and early growth mechanisms. Atmos. Chem. Phys. 6: 4079–4091. Sipilä, M., Berndt, T., Petäjä, T. et al. (2010). The role of sulfuric acid in atmospheric nucleation. Science 327: 1243–1246. Smith, J.N., Dunn, M.J., VanReken, T.M. et al. (2008). Chemical composition of atmospheric nanoparticles formed from nucleation in Tecamac, Mexico: evidence for an important role for organic species in nanoparticle growth. Geophys. Res. Lett. 35: L04808, doi:10.1029/2007GL032523.

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Smith, J.N., Barsanti, K.C., Friedli, H.R. et al. (2010). Observations of aminium salts in atmospheric nanoparticles and possible climate implications. Proc. Natl. Acad. Sci. 107: 6634–6639. Strey, R. and Viisanen, Y. (1993). Measurement on the molecular content of binary nuclei. Use of the nucleation rate surface for ethanol-hexanol. J. Chem. Phys. 99: 4693–4704. Svensmark, H., Pedersen, J.O.P., Marsh, N.D. et al. (2007). Experimental evidence for the role of ions in particle nucleation under atmospheric conditions. Proc. R. Soc. A 463: 385–396. Tröstl, J., Chuang, W.K., Gordon, H. et al. (2016). The role of low-volatility organic compounds in initial particle growth in the atmosphere. Nature 533: 527–531. Viisanen, Y., Kulmala, M., and Laaksonen, A. (1997). Experiments on gas-liquid nucleation of sulfuric acid and water. J. Chem. Phys. 107: 920–926. Weber, R.J., Marti, J.J., McMurry, P.H. et al. (1996). Measured atmospheric new particle formation rates: implications for nucleation mechanisms. Chem. Eng. Commun. 151: 53–64. Weber, R.J., Marti, J.J., McMurry, P.H. et al. (1997). Measurements of new particle formation and ultrafine particle growth rates at a clean continental site. J. Geophys. Res. 102: 4375–4385. Weber, R.J., McMurry, P.H., Mauldin, R.L. III, et al. (1999). New particle formation in the remote troposphere: a comparison of observations at various sites. Geophys. Res. Lett. 26: 307–310. Went, F.W. (1960). Blue hazes in the atmosphere. Nature 187: 641–643. Wyslouzil, B.E. and Wölk, J. (2016). Overview: homogeneous nucleation from the vapor phase – the experimental science. J. Chem. Phys. 145: 211702, doi: 10.1063/1.4962283. Wyslouzil, B.E., Seinfeld, J.H., and Flagan, R.C. (1991). Binary nucleation in acid-water systems. II. Sulfuric acid-water and a comparison with methanesulfonic acid-water. J. Chem. Phys. 94: 6842–6850. Young, L.H., Benson, D.R., Kameel, F.R. et al. (2008). Laboratory studies of H2 SO4 /H2 O binary homogeneous nucleation from the SO2 +OH reaction: evaluation of the experimental setup and preliminary results. Atmos. Chem. Phys. 8: 4997–5016. Yu, F. and Luo, G. (2009). Simulation of particle size distribution with a global aerosol model: contribution of nucleation to aerosol and CCN number concentrations. Atmos. Chem. Phys. 9: 7691–7710. Zeng, X.C. and Oxtoby, D.W. (1991). Binary homogeneous nucleation theory for the gas-liquid transitions: a nonclassical approach. J. Chem. Phys. 95: 5940–5947. Zhang, R., Suh, I., Zhao, J. et al. (2004). Atmospheric new particle formation enhanced by organic acids. Science 304: 1487–1490. Zhang, R., Wang, L., Khalizov, A.F. et al. (2009). Formation of nanoparticles of blue haze enhanced by anthropogenic pollution. Proc. Natl. Acad. Sci. 106: 17650–17654. Zhang, R., Khalizov, A., Wang, L. et al. (2012). Nucleation and growth of nanoparticles in the atmosphere. Chem. Rev. 112: 1957–2011. Zhao, J., Khalizov, A., Zhang, R., and McGraw, R. (2009). Hydrogen-bonding interaction in molecular complexes and clusters of aerosol nucleation precursors. J. Phys. Chem. A 113: 680–689. Zhao, J., Ortega, J., Chen, M. et al. (2013). Dependence of particle nucleation and growth on high-molecular-weight gas-phase products during ozonolysis of α-pinene. Atmos. Chem. Phys. 13: 7631–7644.

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8 Field Observations of Secondary Organic Aerosols 8.1 Introduction Particulate matters are atmospheric constituents existing universally in the troposphere together with gaseous species, and can give impacts on human health as air pollutants and on climate as radiative forcers. Chemical composition of atmospheric aerosols can be divided broadly into inorganic and organic components, and their sources are classified to natural and anthropogenic origin, and also to primary emitted directly and secondary formed by chemical reactions in the atmosphere. The main components of primary inorganic aerosols consist of Na+ , Mg2+ , Cl− , and SO4 2− in sea salt, Al, Ca, and Si in soil dust, K+ and elemental carbon (EC) in biomass burning, Zn, NO3 − , and EC in diesel exhaust, and Fe and Cr in fly ash from coal burning and other sources, while SO4 2− , NO3 − , and NH4 + formed from gaseous SO2 , NOx , and NH3 are the main components of secondary inorganic aerosols. As for the primary organic aerosols (POA), levoglucosan and palmitic acid from biomass burning, oleic acid, palmitic acid, and stearic acid from cooking, n-alkane, n-alkanoic acid, benzoic acid, benzaldehyde, polycyclic aromatic hydrocarbons (PAHs), and hopane in automobile exhaust, and various kinds of PAHs from coal burning are well known (cf. Section 2.6.1, Figure 2.11). In secondary organic aerosol (SOA), various kinds of oxygenated compounds are contained as described in Section 2.6.1 and detected in ambient air. In this chapter, after summarizing our knowledge on global budget of atmospheric aerosols and methodology of characterizing chemical species measured in ambient aerosols, recent information on the observed constituents of organic aerosols (OAs) in the marine, forest, and urban/rural air are overviewed.

8.2 Global Budget of Aerosols Global sources of particulate matters can be divided into natural and anthropogenic origin, and primary emission and secondary formation as noted above. Table 8.1 cites the global emissions and productions of inorganic particulate matters, and Table 8.2 summarizes the data for organic and carbonaceous particulate substances. As for the anthropogenic emission sources, most of the estimates in the tables targeted the year 1990–2000. Since about 70% of the Earth’s surface is ocean, the amount of emission of marine aerosols (sea spray) is the largest among the global primary particles from natural Atmospheric Multiphase Chemistry: Fundamentals of Secondary Aerosol Formation, First Edition. Hajime Akimoto and Jun Hirokawa. © 2020 John Wiley & Sons Ltd. Published 2020 by John Wiley & Sons Ltd.

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Table 8.1 Estimates of global annual emissions of inorganic particulate matters. Estimated flux (Tg yr−1 )

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(3 nm, and chemical analysis has been made for only submicron particles larger than the nucleation mode (3–10 nm). For this reason, although the molecular species relevant to nucleation itself has not been established experimentally, O’Dowd et al. (2002) found for the first time that the chemical components of nucleation mode particles of 3–6 nm in the boreal forest in Finland include pinonic acid and pinic acid, demonstrating the possibility that the condensable secondary organic vapor from BVOC is related to the new particle formation in the boreal forest air. The new particle formation in the boreal forest in southern Finland is thus thought to be caused by H2 SO4 or condensable secondary organic vapor. For the particle growth to form CCN over 70 nm which follows the new particle formation, the oxidative organics, particularly pinic acid and pinonic acid, are mainly responsible and H2 SO4 contributes only 10% (Boy et al. 2005; Cavalli et al. 2006; Laaksonen et al. 2008; Spracklen et al. 2008). The Aitken and accumulation mode particles have been revealed to consist of SOA originated from α-pinene, and it has been substantiated that they are responsible to the particle growth (Allan et al. 2006; Laaksonen et al. 2008). Later, extremely

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low-volatility organic compounds (ELVOCs) (cf. Section 7.3.4) formed from BVOC have been observed in the boreal forest air in Finland, and found to play an important role for the particle growth (Kulmala et al. 2013; Ehn et al. 2014).

8.6 Urban/Rural Air As compared to the air over the ocean and forest, urban and rural air contains primary particles and VOCs from much more variability of sources so that the composition of SOA are also much more complex. This section introduces studies clarifying the characteristics of aerosols in urban air using the analytical methods described in Section 8.3. As typical molecular constituents of OC, which have been identified in the urban/rural air dicarboxylic acids, organic sulfates (OS), organic nitrogen compounds, several characteristic water-soluble organic carbons (WSOCs), and high-molecular-weight compound (HMWC) are summarized. Quantification of the contribution of aerosols from primary and secondary sources to urban and rural air quality and investigation of their biogenic and anthropogenic origins is particularly important regarding the mitigation of PM2.5 . Efforts have been made to get useful information for this purpose by use of the PMF analysis and identification of characteristic tracers from different sources. 8.6.1 8.6.1.1

Characterization of Ambient Aerosols PMF Analysis

Here, application of the PMF analysis for three-factors is first introduced as a fundamental OA mass spectral analysis of the urban/rural air. Figure 8.11 shows the factor mass spectra of OOA-1 and OOA-2, and HOA, obtained by the three-factor analysis of the urban air in Pittsburgh, Pennsylvania, by Ulbrich et al. (2009). It has been found that HOA correlates well with NO, CO, and EC, OOA-2 with nitrate (NH4 NO3 ), and OOA-1 with sulfate (SO4 2− ). Thus, HOA, OOA-2, and OOA-1 can be ascribed to POA, fresh SOA, and aged SOA, respectively, in the same way as for the PMF analysis for the 0.12 0.08

OOA-1

0.04 0.00 60 40 20 0 0.10

OOA-2

×10–3

Fraction of Signal

472

HOA

0.05 0.00 20

40

60

80

100

m/z

Figure 8.11 Mass spectra of OOA-1, OOA-2, and HOA from the three component PMF analysis of the Pittsburgh aerosol data. Source: Adapted from Ulbrich et al. (2009). Copyright 2009 Author(s). Creative Commons Attribution 3.0 License.

8.6 Urban/Rural Air

aerosols of Amazonian forest air (cf. Figure 8.9) described in the previous section. As for the nomenclature of OOA-1 and OOA-2, LV-OOA (low-volatile OOA) and SV-OOA (semi-volatile OOA) are also proposed (Jimenez et al. 2009) and used in the literature. Since the factors such as LV-OOA, SV-OOA, and HOA in the PFM analysis are consistent with the kinetic behavior of POA and SOA, they are extremely useful for the source apportionment of atmospheric aerosols. As an example, Figure 8.12 depicts the averaged diurnal variation of LV-OOA, SV-OOA, NOA (nitrogen-enriched OA), COA (cooking-related OA), and HOA obtained in the five-factor PFM analysis of the urban air in New York City in July–August (Sun et al. 2011). As shown in Figure 8.12, HOA peaks in early morning when the traffic is heavy, with high correlation with EC implying the correspondence to the mobile sources. The SV-OOA has a maximum at night Figure 8.12 Diurnal patterns of five OA factors determined by PMF analysis of the AMS dataset obtained in summer 2009 in New York City. NOA and COA are nitrogen-enriched OA and cooking-related OS, respectively. Source: Adapted with permission from Zhang et al. (2011). Copyright 2011 Author(s).

5

LV-OOA

4 3 2 1 0 6

SV-OOA

4 2 0 2.0

NOA

1.5 1.0 0.5 0.0 4

COA

3 2 1 0 3.0

HOA

2.0 1.0 0.0 0 2 4 6 8 10 12 14 16 18 20 22 24 Hour of Day

473

474

8 Field Observations of Secondary Organic Aerosols

with a good correlation with NH4 + . This is thought to be that the SV-OOA contains relatively high vapor pressure OOA, which is condensed when the temperature is low. The LV-OOA has a good correlation with SO4 2− here again, and has a maximum in the afternoon to the evening agreeing with the production in the photochemical processes. NOA correlates with the peak of alkyl amines, suggesting marine or industrial origin. The COA has peaks at lunch and dinner time and is thought to be POA emitted from cooking (Sun et al. 2011; Zhang et al. 2011). The ratios of LV-OOA, SV-OOA, and NOA in OA have been estimated to be 30%, 34%, and 5.8%, respectively. In the PFM analysis of the field campaign (MILAGRO) in Mexico City, four factors of HOA, OOA, BBOA, and LOA (local nitrogen containing OA) were obtained, and BBOA is extracted as POA originated from biomass burning (Aiken et al. 2009). In the PMF analysis in Riverside, California, seven factors were extracted; in addition to HOA, amine containing POA, LOA-AC (local aerosol containing amine), MV-OOA (medium-volatility OOA) in between LV-OOA and SV-OOA (Docherty et al. 2011). From these results, the ratios of LV-OOA, MV-OOA and SV-OOA were obtained as 31%, 30%, and 14%, respectively, showing that the LV-OOA and MV-OOA have the highest ratios (Lanz et al. 2007). The mass spectrum of SV-OOA is similar to those in Pittsburgh (Ulbrich et al. 2009) supporting that this methodology can give a consistent results. From the analysis of the data in Riverside, if we assume POA is the sum of HOA and LOA, the amount of SOA is four times of POA. If the MV-OOA is thought to be aged POA, SOA is estimated to be the double of POA (Docherty et al. 2011). The PMF/MCA analysis based on AMS data for urban air has been obtained in many areas of the world, e.g. in southwestern Ontario in Canada (Slowik et al. 2011), Paris (Paciga et al. 2016), Mexico City (DeCarlo et al. 2010), Fukuoka, Japan (Takami et al. 2016), Beijing (Sun et al. 2010, 2016; Zhang et al. 2017), Pearl River Delta in China (Wang et al. 2017), and Hong Kong (Hu et al. 2010). Zhang et al. (2007) assembled the PMF/MCA analysis of AMS measurements at 11, 5, and 11 places in the urban, downwind of urban, and rural/remote areas, respectively, in the Northern Hemisphere, and showed the averaged components of submicron aerosols as OA(HOA + OOA) (18–70%, av. 45%), SO4 2− (10–67%, av. 32%), NO3 − (1.2–28%, av. 10%), and NH4 + (6.9–19%, av. 13%). Although overall average of each component varies widely region by region, they expanded their results to the averaged constituents of submicron aerosols at 43 sites in urban, downwind of urban, and rural/remote sites and depict as Figure 8.13 (Zhang et al. 2011). As seen in the figure, although the percentages of OA are about the same as 45–50%, the ratio of SO4 2− increases from 23% in urban area to 39% in rural/remote area. The ratio of NO3 − is about 18% close to SO4 2− in urban area, decreases with distance from urban area and only 5% in remote/rural sites. The ratio of NH4 + does not change much in these three areas and at 11–14%. The ratio of total SOA and total POA in OA is 58% and 42% in urban area, 82% and 12% at downwind of urban, and 90% and 10% at rural/remote area. Thus, it is clearly shown that the ratio of POA is the maximum in urban area, and the ratio of SOA increases with the distance from the urban area. 8.6.1.2

Mass Signal Intensity Ratio and Elemental Ratio

Figure 8.14a (Ng et al. 2010) shows the assembled plot of f 44 against f 43 of OOA obtained from several data including those in Mexico City (Aiken et al. 2009; Jimenez et al. 2009). As shown in Figure 8.14a, the plot of f 44 vs. f 43 scatters for fresh aerosols, it merges to f 44 ≈ 0.30 and f 43 ≈ 0.02 as the aging proceeds with increasing f 44 and decreasing

8.6 Urban/Rural Air

Urban

Rural/Remote

Downwind

Cl– NH4+

OOA

NO3–

POA

SO42–

Figure 8.13 Average ratios of total mass composition deduced from PMF analysis in PM1 at various urban, downwind and rural/remote sites in the northern hemisphere. Source: Data from Zhang et al. (2011). Copyright 2011 The American Geophysical Union. 0.30

1.2

0.25

0.25

1.0

0.20

0.20

f44 0.15

f44 0.15

0.10

0.10

0.05

0.05

0.00

0.00

0.8 0.6

O:C atomic ratio

0.30

0.4 0.2

0.00

0.06

0.10 f43 (a)

0.16

0.20

0

2

4

6

8

44/43 (b)

Figure 8.14 (a) f 44 vs. f 43 for the OOA components from different sites. (b) f 44 and O : C vs. 44/43 for the OOA components from different sites. Source: Adapted from Ng et al. (2010). Copyright 2010 Author(s). Creative Commons Attribution 3.0 License.

f 43 . This implies that even if the original source of SOA is different, they approaches to nearly the same end point of oxidative state as the photochemical oxidation proceeds by aging. Figure 8.14b is the replot of f 44 against the intensity ratio of 44/43 using the data of Figure 8.14a (Ng et al. 2010). The relationship of increase of f 44 toward 0.30 as 44/43 increases by aging is clearly shown in Figure 8.14b. The O/C ratio is also scaled in the vertical axis. Typical example of average diurnal variation of O/C, H/C, N/C, and OM/OC for the ground observation data in Mexico City in April is shown in Figure 8.15 (Aiken et al. 2008). Here, OM/OC is the ratio of the mass of organic matter (OM) to organic carbon (OC). As seen in the figure, H/C is the highest in the morning reflecting the influence of the emission of POA and the lowest in the afternoon when the SOA is more important. Similar diurnal variation can be seen for the N/C ratio showing that most of nitrogen in OA is contained in POA. Meanwhile, O/C and OM/OC ratios have a maximum in late afternoon, agreeing with the result in Mexico City where SOA formation is expected in

475

0.55

0.024

1.70

O/C

0.50

0.020 1.65

0.45 0.40

1.60

0.35

1.55

0.016

N/C

0.012

22:00 – 23:00

18:00 – 19:00

20:00 – 21:00

16:00 – 17:00

14:00 – 15:00

12:00 – 13:00

8:00 – 9:00

10:00 – 11:00

6:00 – 7:00

4:00 – 5:00

Legend: O/C OM/OC H/C N/C

2:00 – 3:00

0.008 0:00 – 1:00

1.85 1.80 1.75 1.70 1.65 1.60

H/C

OM/OC

8 Field Observations of Secondary Organic Aerosols

Figure 8.15 Diurnal averages of atomic O/C, H/C, N/C, and OM/OC for the samples at the ground site in Mexco City. Source: Reprinted with permission from Aiken et al. (2008). Copyright 2008 American Chemical Society. Ambient Averages

Atomic O/C

1

Total

PMF Factors (from Ambient) HOA

BBOA OOA-II OOA-I

Laboratory-Produced Sources POA P-BBOA

C-SOA

0.8 0.6 0.4 0.2

ex M Gro ex u G nd M ro AM ex un d M ex Pla PM ne M Pla C ex n i Pl e O ty an ut flo e R w M eg ex io n G al M rou ex nd M Pla ex n G e M rou ex nd M Pla ex n G e M rou ex nd M Pla ex n G e M rou ex n D Pl d ie a G Lo as sel ne Tr dg ol Sa ep ine uck ge ole Ve al /Ra Pin hicl ph bb e e al e-P itbr (FS ph in us L ) e- en h Pi e/ (F ne NO SL ) Is ne x To opr /O3 (PS en lu I ( ) G ene e/N UC as /O O -R ol ) x H in e/ ,NO (PS O H (U I) ,N C O -R (U ) C -R )

0

M

476

Figure 8.16 O/C for ambient aerosol sampled at the ground site and by air plain in and over Mexco City (left and middle), and laboratory and chamber sources of OA. Average ground OA, AM and PM are from local 4–9 a.m. and 1–6 p.m., respectively. Source: Adapted with permission from Aiken et al. (2008). Copyright 2008 American Chemical Society.

the afternoon by photochemistry. The average values of O/C, H/C, N/C, and OM/OC obtained here are 0.41, 1.62, 0.02, and 1.71, respectively. Figure 8.16 depicts the correspondence between the O/C ratio and the factor mass spectra of HOA, BBOA, OOA-II, and OOA-I obtained by applying PMF to the ground and aircraft observation of OA in Mexico City (Aiken et al. 2008). In the right-most figure, POA is the primary aerosol in the auto-exhaust of diesel and gasoline cars, and P-BBOA is the POA obtained in the laboratory experiment of biomass burning, and C-SOA is the SOA obtained in the chamber experiments. As shown in the figure, it is clearly seen that there is a distinct correspondence between the O/C ratio and HOA, BBOA, OOA-II, OOA-I for the OAs. Thus, the ratio of O/C in HOA is the smallest, 0.06–0.10, which is closer to those in automobile exhaust, 0.03–0.04. The O/C ratio of

8.6 Urban/Rural Air 2.5

O/C Atomic Ratio

1.0

OM/OC

2.0

1.5

0.0

0.2

0.4

0.6

0.6 0.4

f(x) = (0.0382 ± 0.0005)(x) + (0.0794 ± 0.0070) R2 = 0.84 (95% Cl)

0.2

f(x) = (1.260 ± 0.02)x + (1.180 ± .001) R2 = 0.997 (95% Cl)

1.0

0.8

0.0 0

O/C

10 15 m/z 44 / OA (%)

(a)

(b)

0.8

1.0

5

20

25

Figure 8.17 (a) Scatter plot of OM/OC vs. O/C for all ambient and chamber OA. (b) Scatter plot of m/z 44/OA vs. O/C from AMS data. Source: Reprinted with permission from Aiken et al. (2008). Copyright 2008 American Chemical Society.

BBOA is 0.31 on the ground and 0.42 in the airplane samples showing that the aging proceeds more in the upper air. The O/C ratio of fresh oxygenated aerosol, OOA-II, is 0.31 and 0.42 on the ground and upper air, respectively, showing that it is more aged in the upper sky. The OOA-I corresponding to the regionally aged OA has the highest O/C ratio, which is 0.83 on the ground, and 1.02 in the upper air showing the same tendency of aging. The O/C ratios for the experimentally obtained POA and BBOA shown in the right-most graph in Figure 8.16 agree well with those obtained from the PMF analysis for the ambient ground-based samples. The ratio values of C-SOA obtained in the chamber experiments for α-pinene, isoprene, toluene, and gasoline are 0.27–0.43, close to the value of BBOA on the ground, and less oxidized than the OOA-II observed in the ambient air. The time variation of OM/OC ratio is known to have very good parallel relationship with O/C ratio, and the plot of OM/OC ratio against O/C ratio for the previous Mexico City observation is shown in Figure 8.17a (Aiken et al. 2008). As shown in Figure 8.17a, O/C and OM/OC range widely in 0.02–1.0 and 1.2–2.5, respectively, but the good linear relationship can be seen between them with a slope, 1.26, and intercept, 1.18. Figure 8.17b is the plot of O/C ratio against f 44 (%) (Aiken et al. 2008). As shown in the figure, good linear relationship can also be seen between O/C ratio and f 44 . 8.6.1.3

Particle Size Distribution

Size distribution of the number density of submicron particles in urban air has been obtained in Helsinki by Hussein et al. (2004), which showed the tri-modal distribution similar to the forest air (Figure 8.9). They reported the annual averaged number density of 5500–7000, 4000–6500, and 900–950 cm−3 for the nucleation mode (