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Phase transitions of pure and mixed organic and inorganic particles Parsons, Matthew Timothy 2006

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P H A S E T R A N S I T I O N S O F P U R E A N D M I X E D O R G A N I C A N D I N O R G A N I C P A R T I C L E S By MATTHEW TIMOTHY PARSONS B.Sc. Honours (Chemistry) University of British Columbia, 2001 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in T H E FACULTY OF GRADUATE STUDIES (CHEMISTRY) THE UNIVERSITY OF BRITISH COLUMBIA October 2006 © Matthew Timothy Parsons, 2006 11 A B S T R A C T Aerosol particles in the Earth's atmosphere play a significant role in such aspects as health effects, visibility effects, and climate effects. In order to quantify the effects of aerosol particles, it is important to have a thorough understanding of the fundamental behavior of the particles. To address this issue, this thesis investigates the phase transitions of atmospherically relevant particles consisting of organic materials, mixed inorganic-organic materials, and inorganic materials with solid inclusions with a combination of techniques. Techniques used were optical microscopy of particles in a flow cell and optical microscopy of particles in an electrodynamic balance. Phase transitions studied were deliquescence and homogeneous and heterogeneous crystalli2ation as functions of temperature, chemical composition, or particle size. The deliquescence relative humidity (RH) and crystallization R H results were interpreted at a fundamental level in terms of the underlying thermodynamic and kinetic factors that influence phase transitions of small particles. It was found that the deliquescence R H for the organic and mixed inorganic-organic particles could be predicted with reasonable accuracy with solution thermodynamics over the range of conditions studied. Homogeneous and heterogeneous nucleation rates were determined from crystallization R H results and parametrized in terms of classical nucleation theory. The atmospheric implications of the deliquescence RH and crystallization R H results are discussed, with attention to the extrapolation of deliquescence R H and crystallization R H values obtained in laboratory measurements to the expected deliquescence R H and crystallization R H of corresponding particles in atmospheric scenarios. For remote and urban regions of the atmosphere, the results suggest that the deliquescence R H of mixed inorganic-organic particles may be slightly decreased from the deliquescence R H of the pure inorganic material for the compositions studied. In contrast, crystallization R H results suggest that mixed inorganic-organic particles may crystallize at significantly lower R H than the crystallization R H of the pure inorganic materials for remote and urban regions. The heterogeneous crystallization results suggest that solid inclusions used in this study can influence the crystallization R H of inorganic particles in the atmosphere. This work provides extensive characterization of the phase transitions of atmospherically relevant particles, which can be used to improve the general understanding of the effects of aerosol particles in the Earth's atmosphere. iii T A B L E O F C O N T E N T S Abstract ii Table of Contents iii List of Tables vi List of Figures • • viii Acknowledgements xx Dedication xxii Co-Authorship Statement xxiii 1. Background and Motivation: Aerosol Particles and their Effects in the Atmosphere 1 1.1 Aerosols and Aerosol Particles 1 1.1.1 Sources and Sinks of Atmospheric Aerosol Particles 3 1.1.2 Composition of Atmospheric Aerosol Particles 4 1.2 Why Study Aerosol Particle Phase Transitions? 10 1.3 Overview of Thesis 14 1.4 References 15 2. Theory of Deliquescence and Crystallization 21 2.1 Phases and Phase Transitions of Aerosol Particles 21 2.2 Deliquescence 22 2.3 Crystallization 36 2.4 Classical Nucleation Theory 39 2.5 References 43 3. Deliquescence of Malonic, Succinic, Glutaric, and Adipic Acid Particles 44 3.1 Introduction 44 3.2 Experimental 45 3.3 Results and Discussion 51 3.3.1 Deliquescence of Ammonium Sulphate Particles 51 iv 3.3.2 Deliquescence of Dicarboxylic Acid Particles as a Function of Temperature '. 52 3.3.3 Calculations of D R H 58 3.3.4 D R H Values Below the Eutectic Temperature 60 3.4 Summary and Conclusions 61 3.5 References 62 4. Deliquescence and Crystallization of Ammonium Sulfate Particles Internally Mixed with Water-Soluble Organic Compounds 66 4.1 Introduction 66 4.2 Experimental 68 4.3 Results and Discussion 70 4.3.1 D R H * of Mixed Ammonium Sulfate + Organic Particles 73 4.3.2 Thermodynamic Calculations of D R H * as a Function of Composition . 80 4.3.3 Crystallization of Ammonium Sulphate in Aqueous Organic Solutions .... 85 4.3.4 Atmospheric Implications 89 4.4 Conclusions 91 4.5 References 92 5. Crystallization of Aqueous Inorganic-Malonic Acid Particles: Nucleation Rates, Dependence on Size, and Dependence on the Ammonium-to-Sulphate Ratio 96 5.1 Introduction 96 5.2 Experimental 99 5.3 Results and Discussion 102 5.3.1 Crystallization of Aqueous (NH 4) 2S0 4-Mal Particles 102 5.3.2 Crystallization of Aqueous (NH4)3H(S04)2-Mal and NH 4 HS0 4 -Mal Particles 105 5.3.3 Crystallization of Aqueous (NH 4) 2S0 4 and Aqueous (NH 4) 2S0 4-Mal Particles as a Function of Particle Size 107 5.3.4 Nucleation Rates in Aqueous (NH 4) 2S0 4 and Aqueous (NH 4) 2S0 4-Mal Particles 109 5.3.5 Analysis of the Nucleation Rates Using Classical Nucleation Theory 112 5.4 Conclusions and Atmospheric Implications : 116 5.5 References •. 118 6. Crystallization of Aqueous Ammonium Sulphate Particles Internally Mixed with Soot and Kaolinite: Crystallization Relative Humidities and Nucleation Rates 122 6.1 Introduction 122 6.2 Experimental 125 6.3 Results and Discussions 128 6.3.1 Crystallization of Aqueous Ammonium Sulphate Droplets and Droplets Containing Soot or Kaolinite 128 6.3.2 Nucleation Rates from Experimental Data 134 6.3.3 Classical nucleation theory parameters from / h o m 138 6.3.4 Classical Nucleation Theory Parameters from 141 6.4 Atmospheric Implications 142 6.4.1 Atmospheric Implications of the Soot Studies 142 6.4.2 Atmospheric Implications of the Kaolinite Studies 143 6.5 Conclusions and Summary 146 6.6 References 147 7. Concluding Remarks 152 7.1 Conclusions 152 7.2 Considerations for Future Work 154 7.3 References 156 A. Appendix 157 A . l Summary of Previous Studies 157 A.2 Classical Nucleation Theory Details and Considerations 167 A.3 References 172 vi L I S T O F T A B L E S Table 1.1 8 Summary of Organic Compounds Used in this Thesis Table 1.2 9 Summary of Inorganic Compounds and Solid Materials Used in this Thesis Table 2.1 42 Literature Values of Classical Nucleation Theory Parameters at 298.15 K Table 3.1 57 Parameters Describing the Deliquescence Results Table 4.1 68 Structures of Organic Species Used in This Study Table 5.1 116 Classical Nucleation Theory Parameters Table 6.1 126 Properties of Soot and Kaolinite Particles Used in these Experiments Table 6.2 134 Comparison of Measurements of the CRH of Aqueous Ammonium Sulphate Droplets Containing Inorganic Solids Table 6.3 141 Classical Nucleation Theory Parameters for Aqueous Ammonium Sulphate with and without Kaolinite Determined from Experimental Results vii Table A.1 : 158 Summary of Organic and Mixed Organic-Inorganic Phase Transition Studies Table A.2 165 Summary of Mixed Solid-Inorganic Crystallization3 Studies Vlll L I S T O F F I G U R E S Figure 1.1 2 Typical surface area distribution of atmospheric aerosol particles showing the size ranges of aerosol size modes based on studies by Whitby and co-workers.2"6 Figure 1.2 5 Average urban composition of fine atmospheric particles (by mass) on the basis of several field studies.11'13,1648 Figure 1.3 5 Average remote (continental) composition of fine atmospheric particles (by mass) on the basis of several field studies.11'12,1447,19'21,22 Figure 1.4 6 Average remote (marine) composition of fine atmospheric particles (by mass) on the basis of several field studies.1146,20 Figure 1.5 7 (A) Schematic of externally mixed aerosol particles. (B) Schematic of internally mixed aerosol particles. Different shades represent different compounds in the particles. Figure 2.1 23 Relative particle size expressed as a ratio between particle diameter, D, and dry particle diameter, D0, as a function of R H for a particle with a single deliquescent component. Hysteresis is observed between increasing R H (•—) and decreasing R H (--) as discussed within the text. ix Figure 2.2 24 Gibbs free energy for a deliquescent compound as a solid (--) and in an aqueous solution (--"), as a function of R H at constant temperature and pressure. The DRH is observed when the Gibbs free energy of the compound in the solid phase is equal to the Gibbs free energy of the compound in the aqueous solution phase. Figure 2.3 28 Typical phase diagram in the x o r g a n i c domain for organic-inorganic particles where all components behave ideally and both inorganic and organic components are deliquescent. The solid line represents the DRH* for mixed organic-inorganic particles. The minimum of the DRH* curve is the eutonic point. Dotted lines indicate the extrapolations of the DRH* to pure components as discussed in the text. The phases indicated correspond to those predicted by bulk thermodynamics. The dashed line represents the theoretical CRH for mixed organic-inorganic particles based on the discussion in the text. Dot-dashed lines indicate the extrapolations of the theoretical CRH to pure components as discussed in the text. Figure 2.4 30 Typical phase diagram in the x?otsiaic domain for organic-inorganic particles where all components behave ideally and both inorganic and organic components are deliquescent. The solid line shows the DRH* for mixed organic-inorganic particles. The minimum of the DRH* curve is the eutonic point and the dotted line is the DRH* value at the eutonic point. X Figure 2.5 : 32 Relative particle size expressed as a ratio between particle diameter, D, and dry particle diameter, D0, as a function of R H for a particle with two components as described in the text. In this case both components are deliquescent. Hysteresis is observed between increasing R H (—) and decreasing R H (—) as discussed within the text. A two-step crystallization process is possible in this system if the first component crystallizes without inducing crystallization of the second component ("""). Figure 2.6 33 Typical phase diagram in the x?otsmic domain for organic-inorganic particles where all components behave ideally and only the inorganic component is deliquescent. The solid line shows the DRH* for the mixed organic-inorganic particles. The phases indicated correspond to those predicted with bulk thermodynamics. The dashed line shows the theoretical CRH for mixed organic-inorganic particles based on the discussion in the text. Figure 2.7 35 Relative particle size expressed as a ratio between particle diameter, D, and dry particle diameter, D0, as a function of R H for a particle with two components. In this case one component is deliquescent and one component is non-deliquescent. Hysteresis is observed between increasing R H (—) and decreasing R H (--) as discussed within the text. Figure 2.8 41 Change in Gibbs free energy in forming a solute cluster, A G h o m , as a function of solute cluster radius, rclusecr. A G h o m is the sum of volume dependent and surface area dependent terms as shown in Equation 2.6. The height of the kinetic barrier to nucleation, A G h o m c r " , is given by Equation 2.7. A stable nucleus forms from a solute cluster with a radius greater than r c l u s t e r c n t. xi Figure 3.1 46 Diagram of the flow cell and experimental apparatus: (A) side view of the flow cell, and (B) side view of the assembled apparatus. Figure 3.2 49 Images of ammonium sulphate particles recorded during a deliquescence experiment: (A) solid particles prior to deliquescence; (B) solid-liquid particles during deliquescence; and (C) liquid particles just after complete deliquescence. Figure 3.3 52 Deliquescence of ammonium sulphate particles as a function of temperature. Current data (•) were obtained with particles ranging in size from 2 - 4 0 Jim. The uncertainty in the current deliquescence measurements (± 2d) was approximately ±2.1 % RH, based on repeated measurements at a fixed temperature. The results from Braban et al. 1 3 6 (•) and Tang and Munkelwitz137 (O) were also obtained with supermicrometre particles, and the data from both Cziczo and Abbatt138 (A) and Onasch et al. 1 3 9 (V) were obtained using submicrometre particles. The results from Wise et al. 1 2 4 (^) were obtained with bulk solutions. The solid line was calculated using a thermodynamic model by Clegg et al. 1 4 0 Figure 3.4 53 Deliquescence of malonic acid as a function of temperature. Current data (G) were obtained with particles ranging in size from 2 - 4 0 urn. The results from Braban et al. 1 2 2 (O) were obtained using submicrometre and supermicrometre particles, and the data from Brooks et al. 1 2 3 (SI), Wise et al. 1 2 4 (^), and Peng et al.1 2 1 ()$() were obtained using bulk solutions. The thick solid line is the fit to the current data and the thin solid line is the ice saturation line. Details of the calculations are given in the text for: ideal solution calculation (—), UNIFAC calculation 1 ("•••), and UNIFAC calculation 2 (—). xu Figure 3.5 54 Deliquescence of succinic acid as a function of temperature. Current data (•) were obtained with particles ranging in size from 2 - 4 0 um. The results from Peng et al.1 2 1 were obtained using supermicrometre particles (D-bar) and bulk solutions The data from Prenni et al. 1 2 0 (S3-bar) were obtained using submicrometre particles, and the data from Brooks et al. 1 2 3 (^-bar, S3) and Wise et al. 1 2 4 (^) were obtained using bulk methods. The thin solid line is the ice saturation line. Details of the overlapping calculations are given in the text for: ideal solution calculation (—), UNIFAC calculation 1 (•••••), and UNIFAC calculation 2 (—). Figure 3.6 55 Deliquescence of glutaric acid as a function of temperature. Current data (•) were obtained with particles ranging in size from 2 — 40 um. The results from Cruz and Pandis119 (•) were obtained using submicrometre aerosol particles. The results from Peng et al.1 2 1 were obtained using supermicrometre particles (A) and bulk solutions ()2(), and the data from Brooks et al. 1 2 3 (S3) and Wise et al. 1 2 4 were obtained using bulk methods. Figure 3.7 56 Deliquescence of adipic acid as a function of temperature. Current data (•) were obtained with particles ranging in size from 2 - 4 0 (Am. The results from Prenni et al. 1 2 0 (S-bar) were obtained with submicrometre aerosol particles, and the data from Brooks et al. 1 2 3 (^-bar) were obtained using bulk methods. The thin solid line is the ice saturation line. Details of the overlapping calculations are given in the text for: ideal solution calculation (••-), UNIFAC calculation 1 (•••••), and UNIFAC calculation 2 (--). xiii Figure 4.1 72 Images of ammonium sulphate + malonic acid particles (^/Mal = 0.240) during deliquescence at R H equal to (A) 76.3 % RH, (B) 77.2 % RH, (C) 77.7 % RH, (D) 78.2 % RH, and during crystallization at R H equal to (E) 30.4 % RH, (F) 29.3 % RH, (G) 29.2 % RH, (H) 28.1 % RH. Bars indicate a distance of 10 um. Figure 4.2 '. 74 Measured and predicted DRH* for the (NH 4) 2S0 4 + Mai system as a function of dry Mai mole fraction, x?Mal = moles Mai / (moles Mai + moles (NH4)2S04). (•) This study; (V) Brooks et al.;171 (A) Choi and Chan;176 (•) Prenni et al.;183 (O) Wise et al.;1 8 4 (--) Calculations 1; (•••••) Calculation 2; (—) Calculation 3. Calculations are described within the text. Figure 4.3 76 Measured and predicted DRH* for the (NH 4) 2S0 4 + Gly system as a function of dry Gly mole fraction, z?Gi = moles Gly / (moles Gly + moles (NH 4) 2S0 4). (•) This study; (A) Choi and Chan;176 (—) Calculation 1; (•••••) Calculation 2; (—) Calculation 3. Calculations are described within the text. Figure 4.4 77 Measured and predicted DRH* for the (NH 4) 2S0 4 + Lev system as a function of dry Lev mole fraction, x/^ = moles Lev / (moles Lev + moles (NH 4) 2S0 4). (•) This study; (--) Calculation 1; (•••••) Calculation 2. Calculations are described within the text. xiv Figure 4.5 78 Measured and predicted DRH* for the (NH 4) 2S0 4 + Ful system as a function of dry Ful mass fraction, » / F d = mass Ful / (mass Ful + mass (NH 4) 2S0 4). (•) This study; (V) Brooks et al.;1 7 3 (A) Chan and Chan;174 (—) Calculation 1; and (•••••) Calculation 2. Calculations are described within the text. The secondary scale of dry Ful mole fraction, y F u l = moles Ful / (moles Ful + moles (NH 4) 2S0 4), is approximate and based on an estimated molecular weight of 645 g mol"1 for this particular fulvic acid sample.197 Figure 4.6 80 Summary of the DRH* (filled symbols) and CRH50 (open symbols) results for (NH 4) 2S0 4 + organic systems from the current study and from previous work.182 (•, • ) pure (NH 4) 2S0 4; ( • , O) (NH 4) 2S0 4 + Mai; (A, A ) (NH 4) 2S0 4 + Gly; ( • , V ) (NH 4) 2S0 4 + Lev; (•) (NH 4) 2S0 4 + Ful; and (• , O) (NH 4) 2S0 4 + Glut. Data is plotted in terms of water-soluble organic material (WSOM) mole fraction, ^ W S O M = moles WSOM / (moles WSOM + moles inorganic). The two overlapping hatched regions correspond to WSOM mole fraction in remote (marine) and urban aerosol particles as discussed within the text. Shaded regions show variation of data between each system. Figure 4.7 84 Comparison of thermodynamic calculations with previously measured values of DRH* for (NH 4) 2S0 4 + Glut as a function of dry Glut mole fraction, V G l u t = moles Glut / (moles Glut + moles (NH 4) 2S0 4). (--) Calculation 1; (•••••) Calculation 2; (—) Calculation 3; (•) Pant et al.;1 8 2 (V) Brooks et al.;171 (A) Choi and Chan;176 (O) Wise et al. 1 8 4 Calculations are described within the text. XV Figure 4.8 86 Crystallization of (A) (NH 4) 2S0 4 + Mai, (B) (NH 4) 2S0 4 + Gly, and (C) (NH 4) 2S0 4 + Lev from the current study and (D) (NH 4) 2S0 4 + Glut from previous work182 as a function of dry organic mole fraction, o^rganic = moles organic / (moles organic + moles (NH4)2S04). Data points represent CRH50 and vertical bars indicate the range over which crystallization was observed. (O) this study; (•) Pant et al.;1 8 2 ( • ) Braban;194 (•) Braban and Abbatt;170 (A) Choi and Chan.176 Dashed lines represent a ARH offset of 45.2 % RH from the measured DRH* data sets as discussed in the text. Values of 0 % RH signify some or all particles were not observed to crystallize under dry conditions. Figure 5.1 100 Panel A: Electrodynamic balance (EDB) and optical system for determining the phase of levitated particles. Panel B: Image of the elastically scattered light from a completely liquid aqueous (NH 4) 2S0 4-Mal particle recorded prior to crystallization at 35.7 % RH. Panel C: Image of the elastically scattered light from the same particle recorded after crystallization at 29.6 % RH. Figure 5.2 103 CRH50 of (NH 4) 2S0 4-Mal particles as a function of >/Mal = (moles Mai) / (moles Mai + moles (NH 4) 2S0 4). Key: (*) Braban and Abbatt;223 (A) Choi and Chan;237 (•) Parsons et al. 2 4 3 (Chapter 4), (O) Current data. The vertical bars indicate the range of R H over which crystallization was observed for the current data. Values of 0 % RH indicate that less than 50 % of the particles crystallized, even under dry conditions. xvi Figure 5.3 105 CRH50 of inorganic-Mai particles as a function of >/Mil, = (moles Mai) / (moles Mai + moles (NH 4) 2S0 4). Key: (•) (NH 4) 2S0 4-Mal; (O) (NH4)3H(S04)2-Mal; (A) NH 4 HS0 4 -Mal. The vertical bars indicate the range of R H over which crystallization was observed for the current data. Values of 0 % RH indicate that less than 50 % of the particles crystallized, even under dry conditions. CRH of single particles as a function of particle volume, V, for (NH 4) 2S0 4 and (NH 4) 2S0 4-Mal particles. Key: (O) (NH 4) 2S0 4; (•) (NH 4) 2S0 4-Mal (V M r i = 0.36). The top abscissa indicates the diameter, D, of each particle. The uncertainty in R H at which the particles crystallize is approximately ± 1 % RH and the uncertainty associated with determining the particle diameter is ± 1 [xm. Each data point represents one observed crystallization event. Panel A: number of particles remaining completely liquid, N, as a function of R H for (NH 4) 2S0 4. Panel B: number of particles remaining completely liquid, N, as a function of R H for (NH4)2S04-Mal (x/Mal = 0.36). Figure 5.4 108 Figure 5.5 110 Figure 5.6 112 Homogeneous nucleation rate, / h o m , as a function of R H for the (NH 4) 2S0 4 and (NH 4) 2SGyMal systems. Key: (O) (NH 4) 2S0 4; (•) (NH 4) 2S0 4-Mal (*V, = 0.36); lines are to guide the eye and have no physical meaning. xvii Figure 5.7 115 Natural logarithm of the homogeneous nucleation rate, / h o m , as a function of T*3(ln S)'2 (where S is the supersaturation as defined in Equation 5.4 and T is temperature) for (NH 4) 2S0 4 particles. The solid line in Panel A is a linear fit to the complete data set. The solid line in Panel B is a linear fit to the data, excluding the data from the first 10 % of particles to crystallize (i.e., excluding the data with T3(ln S)'2 > 3.25 x 10'9 K"3). Dashed lines in Panel B indicate the 95 % prediction band associated with the linear fit. Change in the intensity of the light reflected by a single aqueous ammonium sulphate droplet containing kaolinite as a function of R H during a crystallization experiment. At 46.3 % RH, the change in intensity deviates significandy from zero, indicating that the droplet crystallized. Examples of results from typical R H cycles (i.e., experimental runs). The fraction of particles remaining liquid during the experimental run is given by N/N0, where N is the number of particles remaining liquid and N0 is the total number of particles. Each data set corresponds to a single R H cycle, and each data point corresponds to a single crystallization event. During the experiments the relative humidity was decreased at a rate of 0.5 % RH minute"1. Key: (•) aqueous ammonium sulphate; and aqueous ammonium sulphate internally mixed with: (O) n-hexane soot (diffusion flame); (O) n-hexane soot (Air : Fuel = 0.53); (A) n-hexane soot (Air : Fuel = 2.4); (•) kaolinite. The solid inclusion to ammonium sulphate mass ratio was 0.01 in these experiments. Figure 6.1 128 Figure 6.2 129 XV111 Figure 6.3 131 (A) CRH50 as a function of aqueous droplet diameter, D, for the current data and (B) comparison of current CRH50 data for aqueous ammonium sulphate droplets free of solid material with CRH data from previous studies. Key: aqueous ammonium sulphate: (•) current data; (•) Han and Martin;301 (•) Badger et al.;330 (•) Brooks et al.;331 (A) Cziczo et al.;3 3 2 ( • ) Onasch et al.;333 (^) Orr et al.;334 (*) Parsons et al. 3 3 5 (Chapter 5); aqueous ammonium sulphate internally mixed with: (O) n-hexane soot current data (diffusion flame); (O)-n-hexane soot current data (Air : Fuel = 0.53); (A) n-hexane soot current data (Air : Fuel = 2.4); (•) kaolinite current data. The vertical bars indicate the 20th and 80th percentiles of the CRH data in each particle size bin. Figure 6.4 136 Side view of an aqueous ammonium sulphate solution droplet on a PTFE substrate. The contact angle of the droplet on the PTFE substrate was about 120 ° for all systems studied. Figure 6.5 137 Nucleation rates as a function of relative humidity. The open squares correspond to the nucleation rates (/hom) of solid ammonium sulphate in aqueous ammonium sulphate droplets determined in this study (corresponding to the left ordinate). The solid circles correspond to nucleation rates (/heekao1) of solid ammonium sulphate in aqueous ammonium sulphate droplets containing kaolinite (corresponding to the right ordinate). xix Figure 6.6 : 140 Nucleation results as a function of supersaturation. The open squares correspond to the nucleation rates (In / h o m) of solid ammonium sulphate in aqueous ammonium sulphate droplets (corresponding to the left ordinate). The solid circles correspond to nucleadon rates (In / h e t k a o 1) of solid ammonium sulphate in aqueous ammonium sulphate droplets containing solid kaolinite (corresponding to the right ordinate). The lines are linear fits to the data (neglecting the first 13 % of crystallization events of aqueous ammonium sulphate droplets without solid material). Figure 6.7 145 The calculated size of a kaolinite inclusion needed to crystallize 50 % (i.e., the CRH50) of the aqueous ammonium sulphate droplets in the atmosphere (solid line). The calculation assumes that every aqueous ammonium sulphate droplet contains a single, spherical kaolinite inclusion with diameter, Dkao], and surface area, Ak!loi, and that the relevant time in the atmosphere for crystallization is approximately 8 hours, which is a simplification to the diurnal cycle of R H (see text). Calculations were carried out using Equation 6.12 and the parameters listed in Table 6.3. The dashed lines indicate the uncertainty of the calculation based on the uncertainty of the parameters given in Table 6.3. XX A C K N O W L E D G E M E N T S I thank the members of the Department of Chemistry at the University of British Columbia with whom I have had the pleasure of working. Dr. Yoshikata Koga kindly took me under his wing and showed me the joys of scientific research and the power of thermodynamics so many years ago. Dr. Allan K. Bertram believed in me and gave me an opportunity to venture into the exciting field of atmospheric chemistry. Allan, you have been an extraordinary mentor. I thank you for your patience in letting me figure things out myself, sometimes the hard way, and for letting me use my imagination and creativity in every project we undertook. The many people I have worked alongside throughout my Ph.D. research have all been excellent colleagues and friends: Mike Eastwood, Sarah Lipetz, Limin Sun, Chee Chan, Abel Fok, Pavel Glaze, Lori Anthony (and Moka), Sarah Hanna, Emily Simpson, and Simone Gross. In particular, Jackson Mak and Magda Dymarska have shared plenty of laughs to keep me from getting too overwhelmed with research. I also thank Jenna Riffell for helping me with my work and being patient as my apprentice. Allen Haddrell and George Agnes from Simon Fraser University were invaluable resources by lending equipment and offering advice for the electrodynamic balance experiments. Of course, there are also the post-docs: Atul Pant, Ben Murray, Daniel Knopf, and Pedro Campuzano-Jost, all of whom have told many good stories while also keeping me thinking rigorously and critically throughout my research. I am greatly indebted to my family: Shannon, Christopher, Mom and Dad. You have all encouraged me in all that I have done. Many thanks go to my grandparents, Ray and Gracebaby, who have forever shown a keen interest in all of my accomplishments. I especially want to thank my parents. Mom, you have helped me immensely throughout my life and I thank you for your countless hours of editing my work in everything from my elementary school projects to this thesis. You have given me a sense of creativity and love for life that is impossible to learn from school. Dad, you sparked my imagination and introduced me to science and math. You have taught me all I know about how to figure things out and make things work—an invaluable skill for building functional equipment in research. Finally, I thank Mary Schmidt. Mary, you have been my support xxi from the beginning of this adventure. You have challenged me beyond science and helped shape me to who I am now. I hope you are always as happy as I am especially now that "one day" has finally come. "In this house we obey the laws of thermodynamics!" - Homer Simpson D E D I C A T I O N To Mom and Dad XX111 C O - A U T H O R S H I P S T A T E M E N T Chapters 3 through 6 are co-authored published journal articles. The details of my contribution to each chapter are as follows: Chapter 3: (first author status on published article) • Identified and designed research program with help from my supervisor. • Built experimental apparatus with help from my supervisor and fellow authors. • Performed over half of the preliminary test and calibration work. • Obtained the majority of the data presented in the publication. • Performed all of the data analysis. • Prepared all of the figures for the manuscript. • Shared manuscript text preparation with my supervisor. Chapter 4 (first author status on published article): • Identified and designed research program with help from my supervisor. • Built experimental apparatus. • Performed all of the preliminary test and calibration work. • Obtained all of the data presented in the publication. • Performed all of the data analysis. • Prepared all of the figures for the manuscript. • Shared manuscript text preparation with my supervisor. Chapter 5 (first author status on published article): • Identified and designed research program with help from my supervisor. • Built experimental apparatus. • Performed the majority of the preliminary test and calibration work. • Obtained all of the data presented in the publication. • Performed all of the data analysis. • Prepared all of the figures for the manuscript. • Shared manuscript text preparation with my supervisor. xxiv Chapter 6 (second author status on published article): • Helped build experimental apparatus with first author. • Obtained half of the data presented in the publication. • Shared the data analysis with first author. • Prepared all of the figures for the manuscript. • Shared manuscript text preparation with my supervisor. Chapter 1 1 1. B A C K G R O U N D A N D M O T I V A T I O N : A E R O S O L P A R T I C L E S A N D T H E I R E F F E C T S I N T H E A T M O S P H E R E 1.1 Aerosols and Aerosol Particles in the Atmosphere Aerosols, suspensions of solid, liquid, or mixed solid-liquid particles in a gas, are ubiquitous in Earth's atmosphere with particle concentrations of up to 108 cm"3.1 Atmospheric particles with diameters in the range of 0.002 — 10 fj.m play the most significant role in terms of atmospheric chemistry and physics.1 Figure 1.1 shows the typical surface area distribution of aerosol particles found in the atmosphere based on studies by Whitby and co-workers.2"6. Atmospheric aerosol particles can be described as fine particles (less than 2.5 [im in diameter) or coarse particles (greater than 2.5 [im in diameter). The distinction between fine and coarse particles is made to account for the different sources, sinks, compositions, respiratory properties, and optical properties of fine and coarse particles. Chapter 1 2 Figure 1.1: Typical surface area distribution of atmospheric aerosol particles showing the size ranges of aerosol size modes based on studies by Whitby and co-workers.2"6 Fine particles are further divided into three modes based on observed distributions as shown in Figure 1.1: ultra fine mode (less than 0.01 fim in diameter), transient or Aitken nuclei mode (0.01 — 0.08 \im in diameter), and accumulation mode (0.08 - 2.5 [xm in diameter).1"6 Production and removal mechanisms for each mode are discussed in more detail below. Chapter 1 3 /. /. / Sources and Sinks of Atmospheric Aerosol Particles Aerosol particles can be released direcdy into the atmosphere from a source or can form in the atmosphere from condensation of low volatility vapours or from chemical processing of precursor gases.1,7 Examples of direct emission of aerosol particles into the atmosphere include dust particles or sea spray droplets entrained by wind.7 An example of condensation of low volatility vapours includes the formation of "tar ball" particles after cooling smoke from biomass burning.8 Examples of condensation following chemical processing include oxidation of gaseous S0 2 to form H 2 S0 4 droplets, and subsequent neutralization by N H 3 to form (NH4)2SG"4 particles.7 An additional production pathway exists for accumulation mode particles in the atmosphere, which are often formed from coagulation of ultra fine and Aitken mode aerosol particles.1 In general, coarse particles are from sources that emit aerosol particles directly into the atmosphere, whereas fine particles are from condensation of gases or coagulation of smaller particles in the atmosphere. Atmospheric aerosol particle and precursor gas sources can be divided into either anthropogenic or natural sources. Anthropogenic sources emit aerosol particles and precursor gases to the atmosphere as a result of human activity, and include industrial processes, agricultural processes, and fossil fuel burning.7 Natural sources emit aerosol particles and precursor gases in the atmosphere as a result of natural processes, and include volcanic emissions, biogenic processes (microbial particles and metabolic gases, for example), and lightning.7 Removal mechanisms for atmospheric aerosol particles depend on the size of the particles. As noted above, particles in the ultra fine and Aitken modes are generally transformed into larger accumulation mode particles via coagulation. Accumulation mode particles are generally removed from the atmosphere via wet deposition.1 This process involves condensation of atmospheric water vapour onto the aerosol particles, thereby increasing the size and the settling velocity of the particles. Wet deposition can also occur by collision of aerosol particles with falling precipitation in the atmosphere. Coarse particles are generally removed from the atmosphere via dry deposition.1 This process involves sedimentation of aerosol particles in the atmosphere from gravity. Chapter 1 4 /. 1.2 Composition of Atmospheric Aerosol Particles The composition of aerosol particles can vary widely depending on the source of the particles, and consequently, specific compounds in aerosol particles are not often found in all size ranges of particles.1 Instead, compounds associated with a given source are most prevalent in the particle size range produced by that source.1 Ultra fine particles (see Figure 1.1) often contain homogeneous nucleation products such as sulphates and secondary organic compounds whereas accumulation and Aitken nuclei particles often contain combustion, condensation, and coagulation products such as carbon, nitrates, and polar organic compounds.1 Coarse particles often contain mechanically produced compounds such as dust and soil components and sea salt.1 Because the composition of aerosol particles is linked to their sources, composition of aerosol particles also varies with location. For example, sea salt particles are prominent in marine aerosol particles, and dust particles are prominent in continental aerosol particles.1 Both inorganic and organic compounds exist in aerosol particles. The majority of inorganic species involve ammonium, sodium, chloride, sulphate, and nitrate ions.7,9 In contrast, hundreds of different organic compounds with a range of chemical and physical properties have been identified in atmospheric aerosol particles (see, for example, the review by Saxena and Hildemann10). Also, a variety of mineral dust and soot components have been observed in the atmosphere.7 As noted above, aerosol particle composition can depend on location. Studies have shown the ratio of inorganic to organic material can also depend on location.11"17 Figure 1.2, Figure 1.3, and Figure 1.4 show the average composition of fine particles, based on measurements at several sites and illustrate the dependence of aerosol particle composition on location.11"22 For example, organic compounds are more prevalent in aerosol particles from urban locations than in aerosol particles from remote marine locations.11 Other field measurements suggest that, overall, the organic material typically accounts for 10-50 % of the fine particle mass.23 Furthermore, it is estimated that 29 - 66 % (by mass) of organic carbon in urban aerosol particles is water soluble,17,18'24 and 41 - 80 % (by mass) of organic carbon in remote (continental and marine) aerosol particles is water soluble.12,17,19,25"27 Chapter 1 5 Figure 1.2: Average urban composition of fine atmospheric particles (by mass) on 11 t% 1£ 1 fl the basis of several field studies. ' ' Other Figure 1.3: Average remote (continental) composition of fine atmospheric particles (by mass) on the basis of several field studies.11'12,14"17'19,21,22 Chapter 1 6 Figure 1.4: Average remote (marine) composition of fine atmospheric particles (by mass) on the basis of several field studies.11"16,20 A further distinction can be made regarding the mixing state of aerosol particles: externally mixed and internally mixed. Figure 1.5 illustrates the difference between externally mixed aerosol particles and internally mixed aerosol particles. Externally mixed systems have various components in different particles whereas internally mixed systems have various components in a single particle. Composition measurements of single particles have shown that organic material is often internally mixed with inorganic species in the troposphere (the region of the atmosphere extending from sea level to an altitude of about 15 km).28'29 Chapter 1 7 Externally Mixed Aerosol Particles ( A ) oo # # oo oo oo Internally Mixed Aerosol Particles (B) € o € 0 € O 3^ Figure 1.5: (A) Schematic of externally mixed aerosol particles. (B) Schematic of internally mixed aerosol particles. Different shades represent different compounds in the particles. Due to the overwhelming variety of organic species observed in the atmosphere, Fuzzi et al.30 have suggested that the water-soluble organic material in aerosol particles can be represented with mixtures of the following classes of organic species: alkanedioic acids, aromatic acids, dialkyl ketones, hydroxyalkanoic acids, polycarboxylic acids, polyphenols, and polyols. The organic compounds used in this thesis were selected from these general categories. Table 1.1 and Table 1.2 list the organic, inorganic, and solid compounds used in this thesis and their sources in the atmosphere. Chapter 1 8 Table 1.1: Summary of Organic Compounds Used in this Thesis Compound Compound Class Dicarboxylic Malonic acid acids Succinic acid Chemical Formula/ Structure3 O O A A OH HO OH Examples of Atmospheric Sources Fossil fuel burning,31 meat cooking,32 photochemical oxidation,33 tobacco smoke34 Glutaric acid HO' OH Adipic acid OH O Alcohols Glycerol Levoglucosan HO-HO-OH Biomass burning, industrial processes, tobacco smoke35 Biomass burning36,37 OH Chapter 1 9 Table 1.1 (continued) Compound Class Compound Chemical Formula/Structure" Examples of Atmospheric Sources Polycarboxylic acid Suwannee River fulvic acid (Not observed in the atmosphere, but representative of polycarboxylic acids in the atmosphere)30 Aerosol phase polymerization of organic degradation products from soil.38 a Suwannee River Fulvic acid does not have a unique structure. The structure given is a proposed average structural model.39 Table 1.2: Summary of Inorganic Compounds and Solid Materials Used in this Thesis Compound Class Compound Chemical Formula/Structure Examples of Atmospheric Sources Inorganic Salts Ammonium sulphate Letovicite Ammonium bisulphate (NH 4) 2S0 4 (NH 4) 3H(S0 4) 2 N H 4 H S 0 4 Complete or partial neutralization of sulphuric acid particles by gas phase ammonia7 Solid Materials Kaolinite (Representative of dust particles in the atmosphere) Al 4Si 4O 1 0(OH) 8 Wind entrainment, soil disturbance, industrial processes7 n-Hexane soot (Representative of soot particles in the atmosphere) Various Biomass burning, fossil fuel combustion7 The phase of an aerosol particle can be liquid, solid, or mixed solid-liquid, depending on the composition of the particle and on the atmospheric conditions surrounding the Chapter 1 10 particle. Transitions between liquid, solid, or mixed solid-liquid pases include melting, freezing, deliquescence, and crystallization. Freezing and melting behaviour of aerosol particles, although important in the atmosphere, is only briefly discussed in this thesis. The major focus of this thesis is to investigate the deliquescence and crystallization phase transitions of particles. Very briefly, deliquescence occurs when a solid compound absorbs surrounding water vapour and dissolves into a saturated solution at high relative humidity (RH). The R H at which deliquescence occurs is called the deliquescence R H (DRH). Crystallization occurs when a supersaturated solution precipitates to form a solid compound at low relative humidity (RH). The R H at which crystallization occurs is called the crystallization R H (CRH). See Chapter 2 for a more detailed discussion of deliquescence and crystallization. 1.2 Why Study Aerosol Particle Phase Transitions? There are a number of effects of aerosol particles in the atmosphere. These effects are related to aspects such as human health, atmospheric chemistry, visibility, and climate and all depend on the phase of aerosol particles in the atmosphere. Aerosol particles in the atmosphere may play a role in human health effects. First, particles may be toxic due to specific chemical or physical properties, including the presence of adsorbed or absorbed toxic species.40 Second, particles may influence mechanisms that clear the respiratory tract.40 Increased exposure to particulate matter in the atmosphere has been associated with an increase in death and illness due to respiratory and cardiac diseases.41 Deposition of atmospheric particles in the respiratory tract depends on the size of the particles. Generally, particles greater than 2.5 am in diameter are removed from the respiratory system by inertial impaction onto the mucus of the upper airway.41 In contrast, particles less than 2.5 am in diameter (especially in the 0.01 - 0.5 urn diameter range) can penetrate deeper into the respiratory system and be deposited on the air exchange regions of the lungs.1 Health effects of aerosol particles in the atmosphere can be influenced by the phase of aerosol particles. For example, the size of aerosol particles in the atmosphere depends on the phase of the particles: aqueous particles are generally larger than crystalline particles. Also, potentially toxic gases (e.g. formaldehyde, hydrogen peroxide, and sulphur dioxide), which are normally deposited to the mucus in the upper airway, can be dissolved Chapter 1 11 into aqueous particles (but not crystalline particles) and transported to the air exchange regions of the lungs.42 Thus, it is useful to have knowledge of the phase of aerosol particles in the atmosphere to understand the health effects associated with these particles. Effects of aerosol particles on chemical reactions in the atmosphere have also been noted. A number of reactions of gas phase species are too slow to be atmospherically important without the presence of a surface on which to react.1,43 An example of this chemistry is the conversion of gas phase unreactive chlorine on polar stratospheric cloud particles to form molecular chlorine that photodissociates to form active chlorine, which in turn destroys stratospheric ozone.44"47 Also, aerosol particles can be transformed by reactions with gas phase species. An example of this chemistry is the formation of HCl^, and NaN0 3 ( s ) from reactions of sea salt particles (containing NaCl (s)) and H N 0 3 ( ^ in the atmosphere.1 Some atmospheric chemistry reactions that occur on the surface of aerosol particles are influenced by the presence of water on the aerosol particles. An example of this chemistry is the hydrolysis of N 2 0 5 ( g ) on malonic acid particles.48 Thornton et al.48 observed a significant increase in reactivity of N 2 0 5 ( ^ on aqueous malonic acid particles relative to solid malonic acid particles. Thus, it is useful to have knowledge of the phase of aerosol particles in the atmosphere to predict reaction pathways of atmospheric species. Reduced visibility is one of the most obvious effects of aerosol particles in the atmosphere. The limit of visibility in unpolluted air is about 260 km, due to Rayleigh scattering by air molecules.1,41 In contrast, the limit of visibility in air with 1 [xm diameter particles at a concentration of 100 particles cm"3 is reduced to about 16 km, due to radiation scattering by the particles.41 Particles with diameters of 0.1 — 1 \im are the most efficient at scattering radiation and therefore are the most important in terms of reduced visibility.1 Radiation absorption in the visible spectrum by aerosol particles can also occur in the atmosphere and is often attributed to soot or black carbon.1,41 In general, scattering of light by particles can be described with Rayleigh scattering (when the particle diameter is much less than the wavelength of scattered light), Mie scattering (when the particle diameter is about the same as the wavelength of scattered light), and geometrical scattering (when the particle diameter is much greater than the wavelength of scattered light).1 Since aqueous particles are larger than corresponding dry particles, the phase of aerosol particles in the atmosphere can be used to predict the type of scattering that is important for the particles. Additionally, it has been shown that light scattering efficiency of particles depends on Chapter 1 12 composition and water content.49 Thus, it is useful to have knowledge of the phase of aerosol particles in the atmosphere to consider the effects of these particles on visibility. Climate effects of aerosol particles in the atmosphere are also related to radiation scattering and absorption and are classified as either direct or indirect effects on the radiation forcing of the Earth.1'7,9'43 The Earth's radiation forcing determines if there is a net warming or net cooling effect on the climate. Aerosol particles can influence the Earth's radiation forcing directly by scattering or absorbing radiation as discussed above.1,7'9'43 Aerosol particles can also influence the Earth's radiation forcing indirectly by acting as cloud condensation nuclei, or ice nuclei, thereby forming clouds.1,7'9,43 Clouds can subsequently influence the Earth's radiation forcing by increasing the Earth's albedo, or reflectivity.1'7'9'43 Overall, the direct and indirect aerosol effects likely introduce a net cooling effect of the atmosphere, but due to the shorter lifetimes of aerosol particles (relative to atmospheric gases) and variable size and composition distributions, it is difficult to assess the long term offset to warming effects by greenhouse gases.7 The phase of aerosol particles in the atmosphere can also influence the Earth's radiation forcing. Martin et al.50 have shown that radiation forcing due to the direct aerosol effect varies by about 24 % depending on the phase of inorganic aerosol particles. Information about the phase of aerosol particles is also necessary to predict the ability of the particles to act as ice nuclei, thereby influencing the indirect effect.9,43'51,52 Particles in the atmosphere containing solid material, for example, can nucleate ice heterogeneously whereas completely liquid particles only act as ice nuclei by homogeneous freezing. Thus, knowledge of the phase of aerosol particles in the atmosphere can be used to estimate the size and also the composition of these particles, thereby improving the current understanding of the direct and indirect aerosol effects. According to the Intergovernmental Panel on Climate Change (IPCC) report on Climate Change 2001, aerosol particles in the atmosphere may influence the global mean radiative forcing.53 However, this report also suggests that the scientific level of understanding is very low in terms of the effect of aerosol particles in the atmosphere on the global mean radiative forcing.53 Among the knowledge required to reduce the uncertainty in estimating the effects of aerosols on the global mean radiative forcing is information on the chemical and physical properties of aerosol particles in the atmosphere,7 such as the phase transition behaviour of these particles. Chapter 1 13 Phase transitions of pure and mixed inorganic compounds in the atmosphere have been studied extensively (see for example, the review by Martin9). However, in addition to inorganic compounds, a significant mass fraction of aerosol particles in the atmosphere is attributed to organic compounds (see Section 1.1.2 above). Despite the abundance of organic material present in aerosol particles, information about phase transitions of organic and mixed organic-inorganic particles is not at a level comparable to inorganic particles.54 Measurements of atmospheric aerosol particles have shown that many aerosol particles contain complex mixtures of both water soluble and water insoluble inorganic and organic compounds (see Section 1.1.2 above). There is a need to study systems that chemically and physically resemble atmospheric aerosols to have a better understanding of the effects of aerosol particles in the atmosphere. Laboratory based investigations into the phase transitions of atmospheric aerosol particles have only recendy become focused on organic and mixed organic-inorganic systems. Initial studies have typically measured phase transition behaviour of single component systems. These studies involved deliquescence and/or crystallization of single components: alcohols,55 dicarboxylic acids,55"61 polycarboxylic acids,62,63 multi-functional acids,57 proteins,64 and organic salts.63,65 More recendy, studies have measured the phase transition behaviour of two or more component systems. These studies involved the deliquescence and/or crystallization of internal mixtures of inorganic compounds with: alkanes,66 alcohols,67,68 monocarboxylic acids,66'69 dicarboxylic acids,57,67,70"78 polycarboxylic acids,62,67,79,80 keto-carboxylic acids,72 multi-functional acids,57'78 and proteins.64 For a more detailed summary of these studies, see Table A . l in the Appendix. Another study focused on deliquescence in bulk multi-component systems with mixed organic compounds (malonic, glutaric, methylsuccinic, maleic, and malic acids).81 Deliquescence and crystallization of multi-component systems with mixed organic-inorganic compounds (malonic, glutaric, methylsuccinic, maleic, and malic acids, glycerol, 1,4-butanediol, and 1,2-hexanediol with ammonium sulphate, ammonium nitrate, or sodium chloride) have also been investigated.68,81 Many of the studies listed here are discussed further throughout the work presented in this thesis. Several recent studies have also investigated the crystallization of inorganic compounds in the presence of a solid. These studies involved the crystallization of internal mixtures of inorganic compounds with: solid dicarboxylic acid,75 mineral dust components,82" Chapter 1 14 8 4 solid salts,85"87 and black carbon or soot.88,89 For a more detailed summary of these studies, see Table A.2 in the Appendix. Another study focused on the crystallization of internally mixed ammonium nitrate-ammonium sulphate-soot.89 Many of the studies listed here are discussed further in Chapter 6. Although significant progress in the field of phase transitions of particles has been made in the past several years, there is still a lack of information regarding the fundamental understanding of these phase transitions. As useful as it is to know the R H of phase transitions for various systems, the work in this thesis will show that it is also beneficial to have a more thorough understanding of the phase transitions of particles in terms of the underlying thermodynamics and kinetics. It is the aim of the work in this thesis to not only report the R H at which phase transitions occur in particles and add to the knowledge from the studies noted above, but to also investigate the underlying thermodynamics and kinetics of the phase transitions. In this manner, the knowledge of phase transitions becomes robust and applicable to aerosol particles in the atmosphere. This is accomplished with the use of equipment specifically designed and built to learn about the deliquescence and crystallization phase transitions of particles. It is with this intention that this thesis focuses on the following major goals: i. Deliquescence and thermodynamic modelling of deliquescence for pure dicarboxylic acid particles. ii. Deliquescence and thermodynamic modelling of deliquescence for internally mixed organic-inorganic particles. iii. Crystallization and kinetic analysis of homogeneous nucleation for internally mixed organic-inorganic particles. iv. Crystallization and kinetic analysis of heterogeneous nucleation for internally mixed inorganic-solid particles. 1.3 Overview of Thesis This thesis consists of four projects that have been published as stand-alone journal articles. The projects described in this thesis follow the natural progression towards understanding the phase transitions of particles resembling those found in atmospheric Chapter 1 15 aerosols starting from deliquescence and crystallization of single component systems, to deliquescence and crystallization of multi-component systems. In particular, Chapter 2 focuses on the fundamental theory of deliquescence and crystallization in general. Chapter 3 focuses on the thermodynamics of deliquescence of single component particles (dicarboxylic acids and ammonium sulphate) as a function of temperature. Chapter 4 focuses on the thermodynamics of deliquescence and kinetics of crystallization of internally mixed two component particles (organic + inorganic) as a function of particle composition. Chapter 5 focuses on the kinetics of crystallization of internally mixed two component particles (malonic acid + inorganic) as a function of particle composition and as a function of particle size. Chapter 6 focuses on the kinetics of crystallization of internally mixed two component particles (ammonium sulphate + insoluble solid). The thesis concludes with Chapter 7, relating the findings of each previous chapter and discussing future directions that are now possible with the knowledge that has been gained in this thesis. Additional information is also given in the Appendix. 1.4 References (1) Finlayson-Pitts, B. J.; Pitts, J. N . Chemistry of the Upper and LowerAtmosphere: Theory, Experiments and Applications; Academic Press: San Diego, CA, 2000. (2) Husar, R. B.; Liu, B. Y. H.; Whitby, K. T. /. Colloid Interface Sci. 1972, 39, 211. (3) Whitby, K. T.; Barsic, N . J.; Husar, R. B.; Liu, B. Y. H. /. Colloid Interface Sci. 1972, 39, 136. (4) Whitby, K. T.; Liu, B. Y. H.; Husar, R. B. /. Colloid Interface Sci. 1972, 39, 177. (5) Whitby, K. T.; Cantrell, B. "Atmospheric Aerosols - Characteristics and Measurement"; in International Conference on Environmental Sensing and Assessment, Las Vegas, NV, September 14 - 19,1975, Institute of Electrical & Electronics Engineers: New York, 1976. (6) Whitby, K. T.; Sverdrup, G. M. Adv. Environ. Sci. Technol. 1980, 9, All. (7) Penner, J. E.; Andreae, M.; Annegarn, H.; Barrie, L.; Feichter, J.; Hegg, D.; Jayaraman, A.; Leaitch, R.; Murphy, D.; Nganga, J.; Pitari, G. Aerosols, Their Direct and Indirect Effects. In Climate Change 2001: The Scientific Basis. Contributions of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change; Houghton, J. T., Ding, Y., Griggs, D. J., Noguer, M., van der Linden, P. J., Dai, X., Maskell, K., Johnson, C. A., Eds.; Cambridge University Press: Cambridge, New York, 2001; pp 289-348. Chapter 1 16 (8) Posfai, M.; Gelencser, A.; Simonies, R.; Arato, K.; Li , J.; Hobbs, P. V.; Buseck, P. R. /. Geophys. Res. 2004, 109, art. no. 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T H E O R Y O F D E L I Q U E S C E N C E A N D C R Y S T A L L I Z A T I O N 2.1 Phases and Phase Transitions of Aerosol Particles As noted in Chapter 1, the phase of an aerosol particle can be liquid, solid, or mixed solid-liquid, depending on the composition of the particle and on the atmospheric conditions surrounding the particle. Here deliquescence and crystallization are discussed in greater detail with an emphasis on the theory behind each phase transition. The majority of this discussion is based on the assumption of ideal behaviour of the systems considered, and is used to give a general description of the phase transitions of binary and ternary systems. This chapter provides information to understand the phase transition measurements throughout this thesis. In truth, however, the experimentally observed systems are not ideal and measurements such as those presented in this thesis are needed to assess the deviation from ideal behaviour as well as to predict deliquescence and crystallization under atmospheric conditions. Briefly, deliquescence is defined as "the absorption of atmospheric water vapour by a crystalline solid until the crystal eventually dissolves into a saturated solution."90 In contrast, crystallization is the precipitation of solute material from a supersaturated solution, often as a result of solvent loss (water loss in the case of aqueous solutions). Subsequently, deliquescence and crystallization of atmospheric particles involve the absorption and desorption of water vapour, respectively. Water vapour over the particles is in equilibrium with water vapour in the surrounding gas such that an increase (or decrease) in water vapour in the surrounding gas causes the particle to absorb (or desorb) water vapour. The amount of water vapour in a gas can be described in a number of ways. However, in this thesis the water vapour content of a gas is described by the relative humidity (RH) of the gas with respect to water. R H as used in this thesis is defined as: 2.1 R H ( T ) = f j . • 100 % RH K(T) where pw is the partial pressure of water vapour in the gas, and p*^ (T) is the partial pressure of saturated water vapour over a flat surface of bulk water at temperature, T. Note that the Chapter 2 22 term —t J . is equivalent to the water activity in an aqueous solution, aw(T), at temperature, A, CO T. In the simplest terms, to deliquesce a particle, one must increase the R H over the particle, and to crystallize a particle, one must decrease the R H over the particle. 2.2 Deliquescence Consider a dry particle consisting of a single component in equilibrium with water vapour. The relative size of the particle as a function of RHis represented by D/D0, where D is the particle diameter and D0 is the dry particle diameter. D/D0 is commonly measured in studies of hygroscopic properties of particles. Figure 2.1 shows a typical example of the behaviour of relative particle diameter with increasing R H (see, for example, Tang and Munkelwitz91). An example of a type of particle that would have this behaviour includes ammonium sulphate. The particle is dry at low R H and remains dry as the R H of the surrounding water vapour increases. At a specific RH, the deliquescence R H (DRH), the particle absorbs water from the surrounding water vapour. Upon deliquescence, the particle completely dissolves to form a saturated solution with a subsequent increase in particle size as shown in Figure 2.1. With an increase in RH, the solution is further diluted by absorption of water from the surrounding water vapour causing the particle to grow as illustrated in Figure 2.1. This growth, referred to as hygroscopic growth, is a result of maintaining equilibrium between the water activity in the aqueous solution and the water activity (RH) of the surrounding water vapour.92 Compounds that undergo deliquescence are referred to as deliquescent compounds. Compounds that do not undergo deliquescence are referred to as non-deliquescent compounds. (Note that non-deliquescent compounds also do not show crystallization behaviour.) Chapter 2 23 1 RH [% RH] t CRH DRH Figure 2.1: Relative particle size expressed as a ratio between particle diameter, D, and dry particle diameter, D0, as a function of RH for a particle with a single deliquescent component. Hysteresis is observed between increasing RH (—) and decreasing RH(—) as discussed within the text. To understand why a compound undergoes deliquescence, consider the Gibbs free energy of this deliquescent compound as a solid and in aqueous solution as a function of RH. By definition, the Gibbs free energy of the compound in the solid phase is constant. In contrast, the Gibbs free energy of the solute in aqueous solution depends on the activity of the solute in solution, which decreases as the solute becomes more dilute in solution.92 Figure 2.2 shows the Gibbs free energy of the compound for these two phases as a function of RH. According to thermodynamics, the compound prefers to exist in the phase with the lowest Gibbs free energy. As shown in Figure 2.2, for R H < DRH, the compound has a lower Gibbs free energy in the solid phase than in the aqueous solution phase and therefore Chapter 2 24 the system exists as a solid. Likewise, for R H > DRH, the compound has a lower Gibbs free energy in the aqueous solution phase than in the solid phase and therefore the system exists as an aqueous solution. When RH — DRH, the Gibbs free energy of the compound in the solid phase is equal to the Gibbs free energy of the compound in the aqueous solution phase and therefore the solid and aqueous solution phases coexist in an equilibrium state.92 Figure 2.2: Gibbs free energy for a deliquescent compound as a solid (--) and in an aqueous solution (—), as a function of RH at constant temperature and pressure. The DRH is observed when the Gibbs free energy of the compound in the solid phase is equal to the Gibbs free energy of the compound in the aqueous solution phase. Chapter 2 25 The DRH of a deliquescent compound is the R H at which the solid and aqueous solution phases coexist. Therefore, the value of DRH of a deliquescent compound can be related to the solubility of the deliquescent compound. Assuming ideal behaviour of the deliquescent compound in solution, manipulation of the Gibbs-Duhem equation for this system can be used to give:92 2.2 * w =exp(-M w/* s o l u t e) where aw is the water activity in the aqueous solution, M w is the molecular weight of water, and msoiuK is the molality of the solute in solution. Thus, if the saturation molality of the deliquescent compound is applied to Equation 2.2, the D R H of the deliquescent compound can be estimated with the assumption of ideal behaviour, recalling that R H = rfw • 100 % RH. It should be noted again that the experimentally observed systems are not ideal and measurements such as those presented in this thesis are needed to assess the deviation from ideal behaviour. The fact that a single deliquescent compound can only coexist with its aqueous solution at a single R H (the DRH) at a given temperature can also be seen with the Gibbs phase rule:93 2.3 f = c-p + 2 where/is the number of degrees of freedom in the system, c is the number of components in the system, p is the number of phases coexisting in the system, and the term 2 accounts for the temperature and pressure variables.93 Consider a system similar to one that will be used in the projects described in this thesis: a particle in equilibrium with surrounding water vapour. For a system with a single deliquescent component and water discussed above, the variables that are required to completely describe the system are temperature, pressure, and the mole fractions of the deliquescent component and water in the particle, xx and xw, respectively. Note that in this system pressure is directly related to R H (i.e., water vapour is the only source of pressure), and mole fractions are related through x, + x w = 1. As noted above, deliquescence occurs when the deliquescent compound is in equilibrium with its aqueous solution, therefore p — 3 (solid deliquescent compound + aqueous solution + water vapour) and c — 2 (deliquescent compound + water). Thus, Equation 2.3 gives / = 1, and by fixing one independent variable, the values of the remaining independent and dependent variables can be Chapter 2 26 determined for this system. Practically, experiments are conducted at a fixed temperature, and this fixes the remaining variables (RH, xu and xw) at which deliquescence occurs, and these remaining variables cannot be changed without reducing the number of phases in the 93 system. Now consider a similar situation for another system that will be used in the projects described in this thesis: a particle with two deliquescent compounds in equilibrium with water vapour (i.e., deliquescent compound 1 + deliquescent compound 2 + water; c — 3). The variables required to completely describe the system are temperature, pressure, and the mole fractions of deliquescent component 1, deliquescent component 2, and water in the particle, xu x2, and xw, respectively. Again, pressure is directly related to R H for this system (i.e., water vapour is the only source of pressure), and mole fractions are related through x^ + x2 + xv = 1. When this system has deliquescent component 1 coexisting in solid and aqueous solution phases, p = 3 (solid deliquescent compound 1 + aqueous solution of deliquescent compound 1 and deliquescent compound 2 + water vapour). Thus, Equation 2.3 gives/= 2, and after fixing temperature the system requires one additional independent variable to be fixed to determine the values of the remaining independent and dependent variables. This means the value of one independent variable may be changed without reducing the number of phases in the system. In other words, there is a range of R H over which a solid deliquescent compound coexists with an aqueous solution for such a ternary system. The conditions at which / = 1 (after fixing temperature) can be represented on a ternary phase diagram. A typical ternary phase diagram for an ideal system with two deliquescent compounds + water is shown in Figure 2.3 (see, for example, Mullin94). Again, the system is treated as ideal here for the purposes of illustration. Recall that experimentally observed systems are not ideal and measurements such as those presented in this thesis are needed to assess the deviation from ideal behaviour. For the current example, the system is composed of a deliquescent organic compound, a deliquescent inorganic compound, and water. The mole fraction of the organic compound, inorganic compound and water in the particle, •^norganio ^ o r g a n i c a n d ^ respectively, is plotted on each axis of the phase diagram such that the sum of x i n o r g a n j c , x o r g a n i c , and xv equals 1. Note that with the assumption of ideal behaviour, x w is equivalent to aw and proportional to RH. This way, at fixed temperature, all the remaining variables are related with the ternary phase diagram shown in Figure 2.3. Furthermore, Chapter 2 27 Equation 2.2 can be derived for a multi-component system, assuming ideality of all solutes, giving the result:95 2.4 * w = expf V where /», is the molality of solute i in solution. The solid lines in Figure 2.3 represent the phase transitions where a solid component (either organic or inorganic) is in equilibrium with an organic + inorganic aqueous solution such that f—\ after fixing temperature. For mixture conditions above the solid lines in Figure 2.3, the system exists only as an aqueous solution as indicated. For mixture compositions below the solid lines in Figure 2.3, the system may contain solid organic and/or inorganic material as indicated. Thus, the solid lines in Figure 2.3 represent the complete deliquescence R H (DRH*) of the system. The DRH* describes when all solid material in the system completely dissolves. The DRH* lines are obtained assuming ideal behaviour of all components in the system with Equation 2.4. Practically, the following method can be used to construct the ternary phase diagram shown in Figure 2.3. Starting from the saturation composition of the pure inorganic component (^organic = 0, x w = 0.8 in this case), a straight line is drawn extending to xot&nic = 1, representing the ideal addition of the organic component to the system (dotted line in Figure 2.3). Similarly, a straight line is also drawn from the saturation composition of the pure organic component (x i n o r g a n i c = 0, xw = 0.7 in this case) extending to x i n o r g a n i c = 1, representing the ideal addition of the inorganic component to the system (dotted line in Figure 2.3). The point at which the dotted lines meet indicates the eutonic point, the conditions at which an aqueous solution of the inorganic and organic components is saturated with respect to both inorganic and organic components. Chapter 2 28 Figure 2.3: Typical phase diagram in the xocgimic domain for organic-inorganic particles where all components behave ideally and both inorganic and organic components are deliquescent. The solid line represents the DRH* for mixed organic-inorganic particles. The minimum of the DRH* curve is the eutonic point. Dotted lines indicate the extrapolations of the DRH* to pure components as discussed in the text. The phases indicated correspond to those predicted by bulk thermodynamics. The dashed line represents the theoretical CRH for mixed organic-inorganic particles based on the discussion in the text. Dot-dashed lines indicate the extrapolations of the theoretical CRH to pure components as discussed in the text. Note that at the eutonic point, p = 4 (solid organic + solid inorganic + aqueous solution + water vapour), and c = 3 (organic compound + inorganic compound + water), and Equation 2.3 gives f = 1. Practically, experiments are conducted at a fixed temperature, and this fixes the remaining variables (RH, x o r g a n i c , x i n o r g a n i c , and xw) at the eutonic point, and these remaining variables cannot be changed without reducing the number of phases in the 93 system. Chapter 2 29 Figure 2.3 is plotted in terms of the mole fractions of all components in the system. It is more practical to plot this type of phase diagram in terms of RH and the dry mole fraction of component /, x\. For this case, consider the phase diagram with R H as a function of x' ^ where: 2.5 x' - n°^c organic n + ft organic inorganic and where « o t g a n i c is the moles of organic compound and » i n o r g a n i c is the moles of inorganic compound. Figure 2.4 shows the phase diagram plotted in Figure 2.3 in the x' nic domain. The solid lines in Figure 2.4 represent the DRH* for the mixed organic-inorganic system as a function of composition. Correspondingly, the eutonic point for this system is the lowest DRH* value. Note that, in general and assuming ideal behaviour, the DRH* of a solid component in a mixed system is less than the D R H of that component in a pure system.92 Chapter 2 30 80-• i i i i 1 1 1 1 Solution -• Solution + ^ ^ ^ ^ ^ 60-Solid Inorganic RH] Solid Organic + Solid Inorganic / RH [% 40-Solution + Solid Organic -20-«••. I 1 I 1 I i • i • 0.0 0.2 0.4 0.6 0.8 1.0 Pure Pure Inorganic organic Organic Figure 2.4: Typical phase diagram in the A , o r g a n i c domain for organic-inorganic particles where all components behave ideally and both inorganic and organic components are deliquescent. The solid line shows the DRH* for mixed organic-inorganic particles. The minimum of the DRH* curve is the eutonic point and the dotted line is the DRH* value at the eutonic point. The phases indicated correspond to those predicted with bulk thermodynamics. The dashed line shows the theoretical CRHfot mixed organic-inorganic particles based on the discussion in the text. The relative particle size as a function of R H for this system with an organic compound, inorganic compound, and water is shown in Figure 2.5 (also see, for example, Tang and Munkelwitz96). Figure 2.5 is based on Figure 2.4 with x' ^ = 0.2. Starting at low RH, the system remains solid until reaching the eutonic R H (60 % RH in this case), at which point the system absorbs water and the organic component dissolves to form an aqueous solution saturated with respect to the organic component.92 As R H increases, the Chapter 2 31 organic component absorbs water hygroscopically and the inorganic component also begins to dissolve, resulting in a coexisting solid + aqueous solution and a larger particle size. The composition of the particle can be found with the use of tie lines in Figure 2.4. Using tie lines in the region between the eutonic R H and the DRH*, it can be shown that the aqueous solution has a composition of x'oIgink > 0.2, which decreases with increasing RH. When R H = DRH*, the aqueous solution has a composition of x' ^ = 0.2, saturated with respect to the inorganic compound, and coexists with the solid inorganic compound. For R H > DRH*, the aqueous solution has a composition of x' ^ — 0.2, no solid remains in the particle, and the particle continues to undergo hygroscopic growth. Chapter 2 32 1 1 - ' ' 20 30 40 50 60 70 80 90 100 t RH [% RH] I CRH DRH* Figure 2.5: Relative particle size expressed as a ratio between particle diameter, D, and dry particle diameter, D0, as a function of RH for a particle with two components as described in the text. In this case both components are deliquescent. Hysteresis is observed between increasing RH (—) and decreasing RH(") as discussed within the text. A two-step crystallization process is possible in this system if the first component crystallizes without inducing crystallization of the second component ("•"). Another possibility for a ternary system is one with a deliquescent compound + a non-deliquescent compound + water. For the purposes of this example, consider a deliquescent inorganic compound + a non-deliquescent organic compound + water. In this case, the non-deliquescent organic compound does not show any deliquescent behaviour. Instead, the non-deliquescent organic compound displays continuous water uptake or release with increasing or decreasing RH, respectively. Such a system has a phase diagram Chapter 2 33 very similar to that shown in Figure 2.4, with the exception that there is no region where solid organic may exist, and the DRH* line for the pure inorganic compound extends to x ' n i c = 1 and R H = 0 % RH. This type of phase diagram is shown in Figure 2.6. Figure 2.6: Typical phase diagram in the A f o r ^ c domain for organic-inorganic particles where all components behave ideally and only the inorganic component is deliquescent. The solid line shows the DRH* for the mixed organic-inorganic particles. The phases indicated correspond to those predicted with bulk thermodynamics. The dashed line shows the theoretical CRH for mixed organic-inorganic particles based on the discussion in the text. The relative particle size as a function of R H for this system with a deliquescent inorganic compound, non-deliquescent organic compound, and water is shown in Figure 2.7. Figure 2.7 is based on Figure 2.6 with x„ ^ = 0.2. As R H increases from low RH, Chapter 2 34 the organic component absorbs water hygroscopically and the inorganic component also begins to dissolve, resulting in a coexisting solid + aqueous solution and a larger particle size. The composition of the particle can be found with the use of tie lines in Figure 2.6. Using tie lines in the region under the DRH* line, it can be shown that the aqueous solution has a composition of x^ i r g a n j c > 0.2, which decreases with increasing RH. When R H = DRH*, the aqueous solution has a composition of x'orgLnic = 0.2, saturated with respect to the inorganic compound, and coexists with solid inorganic compound. For R H > DRH*, the aqueous solution has a composition of x' ^ = 0.2, no solid remains in the particle, and the particle continues to undergo hygroscopic growth. Chapter 2 35 1-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20 30 40 50 60 70 80 90 100 t RH [% RH] t CRH DRH* Figure 2.7: Relative particle size expressed as a ratio between particle diameter, D, and dry particle diameter, DM as a function of RH for a particle with two components. In this case one component is deliquescent and one component is non-deliquescent. Hysteresis is observed between increasing RH (—) and decreasing RH (~~) as discussed within the text. As noted above, deliquescence can be estimated with bulk thermodynamics, namely, knowledge of the solubility of the components in the particle (Equations 2.2 and 2.4). Thus, it is possible to measure DRH and DRH* in bulk systems and in particles. In the projects described in this thesis, D R H and DRH* was measured for particles. The D R H of particles with one deliquescent component, the DRH* of particles with two deliquescent components, and the DRH* of particles with one deliquescent component and one non-deliquescent component were measured. Due to limitations of the experimental methods used, it was not possible to determine when particles started to uptake water, instead, only Chapter 2 36 D R H (for particles with one compound) or DRH* (for particles with more than one compound) could be observed when all solid material dissolved in the particles. 2.3 Crystallization Consider an aqueous particle consisting of a single deliquescent component in equilibrium with water vapour. The relative size of the particle as a function of R H is represented by D/D0, where D is the particle diameter and D0 is the dry particle diameter. Figure 2.1 shows a typical examplep( the behaviour of relative particle diameter for this type of particle with decreasing RH. The particle is aqueous at high R H (RH > DRH) and remains aqueous as the R H of the surrounding water vapour decreases, reversibly following the hygroscopic growth curve shown in Figure 2.1. When R H = DRH, the particle is saturated with respect to the solute and any decrease in R H will result in supersaturation of the solute in solution. Therefore, at R H < DRH, thermodynamics predicts that the particle will crystallize to form a solid (see Figure 2.2). However, due to a kinetic barrier to forming a solid in the solution, as will be discussed below, the particle continues to lose water reversibly and shrink as R H continues to decrease. When the R H has reached a critical value (the crystallization RH, CRH) and the particle is sufficiently supersaturated, the particle suddenly crystallizes and a subsequent decrease in particle size is observed as shown in Figure 2.1. This type of hysteresis behaviour shown in Figure 2.1 is commonly observed for deliquescent particles (i.e., when a particle can contain solid material or only aqueous solution at a given value of RH, depending on the R H history of the particle). For single components in aqueous solution, the crystallization process is also often referred to as efflorescence. However, the more general term crystallization (i.e., formation of a solid) is used throughout this thesis since efflorescence implies the complete loss of solvent, which may not be the case for systems with more than one solute as discussed below. If crystallization of an aqueous particle requires a critical supersaturation of the solute in solution, this same critical supersaturation can theoretically be used as a first approximation to estimate the CRH of a more complicated aqueous solution. Consider, for example, an aqueous solution with two deliquescent components (deliquescent organic compound + deliquescent inorganic compound + water), which was represented on a ternary phase diagram shown in Figure 2.3. The dashed lines in Figure 2.3 represent Chapter 2 37 constant supersaturation of the organic or inorganic component. Starting from the supersaturation required for crystallization of the pure inorganic + water system (x o r g a n i c = 0, x w = 0.35), a straight line is drawn extending to x o r g a n i c = 1, representing the ideal addition of the organic component to the system (dot-dashed line in Figure 2.3). Similarly, a straight line is also drawn from the supersaturation required for crystallization of the pure organic + water system ( X j n o i g a n i c = 0, x w = 0.2) extending to x{noTgmic - 1, representing the ideal addition of the inorganic component to the system (dot-dashed line in Figure 2.3). Thus, the dashed lines in Figure 2.3 represent a theoretical CRH for this ideal system. In fact, crystallization is a stochastic process as will be discussed below; nevertheless, these arguments are useful to understand the trends in CRH over a range of particle composition. Figure 2.4 shows the same theoretical CRH lines as in Figure 2.3, but Figure 2.4 is plotted in the x' nic domain. The dashed lines in Figure 2.4 represent the theoretical CRH for the mixed organic-inorganic system as a function of composition. Note that, in general and assuming ideal behaviour, the CRH of a solid component in a mixed system is expected to be less than the CRH of that component in a pure system. The relative particle size as a function of R H for this system with a deliquescent organic compound, deliquescent inorganic compound, and water is shown as the dashed line in Figure 2.5. Figure 2.5 is based on Figure 2.4 with x^ j r g a n i c = 0.2. Starting at high RH, the system remains aqueous with decreasing RH, losing water reversibly and shrinking. When the RH has reached the CRH, the inorganic component crystallizes and a subsequent decrease in particle size is observed as shown in Figure 2.5. The presence of the solid inorganic component may immediately induce the crystallization of the organic component, in which case the particle loses all water at the CRH (dashed line in Figure 2.5). In contrast, it is also possible that the presence of the inorganic solid component does not induce the crystallization of the organic component, in which case the particle does not lose all water at the CRH, but continues to lose water reversibly until the organic component crystallizes at a lower R H (dotted line in Figure 2.5). For a system with a deliquescent compound, a non-deliquescent compound, and water, the non-deliquescent compound will not crystallize even at very low RH. The phase diagram for this system (deliquescent inorganic + non-deliquescent organic + water) is shown in Figure 2.6 and is similar to that of Figure 2.4, with the exception that there is no Chapter 2 38 region where solid organic may exist, and the theoretical CRH line from the pure inorganic compound extends to x' nic = 1 and R H = 0 % RH. The relative particle size as a function of R H for this system with a deliquescent inorganic compound, non-deliquescent organic compound, and water is shown in Figure 2.7. Figure 2.7 is based on Figure 2.6 with x'OT&nic = 0.2. As R H decreases from high RH, the particle remains aqueous while reversibly losing water. When the R H has reached the CRH, the inorganic component crystallizes and a subsequent decrease in particle size is observed as shown in Figure 2.7 (dashed line). The non-deliquescent organic component in this system remains in solution over the entire range of RH. Therefore, as R H is decreased further, the particle continues to reversibly lose water and shrink as shown in Figure 2.7. As noted in Chapter 1, atmospheric particles may contain complex mixtures of organic compounds. Marcolli et al.9 5'9 7 have shown that complex mixtures of deliquescent and non-deliquescent organic compounds behave as a non-deliquescent compound, reversibly absorbing and releasing water with changing RH. Thus, it is expected that the phase diagram for particles in the atmosphere with numerous organic compounds internally mixed with a deliquescent inorganic compound will resemble that in Figure 2.6. Unlike deliquescence, the CRH in bulk systems is not equivalent to the CRH in particles. In contrast to a bulk system that crystallizes when predicted by thermodynamics, particles typically require significant supersaturation of the solution before crystallization occurs. This is due to the fact that crystallization requires nucleation of the solute, which is a kinetically controlled process as there is a kinetic barrier to nucleation (see below). In bulk systems, this kinetic barrier to nucleation can be reduced by the presence of container walls or foreign objects within the solution (such as dust particles). Also, there exists a greater probability of forming a nucleus homogeneously within a bulk solution to initiate crystallization in a bulk system due to the greater volume of the system (see below). In the projects described in this thesis, CRH was measured for particles. The C R H of particles with two deliquescent components, and the CRH of particles with one deliquescent component and one non-deliquescent component were measured. Due to limitations of the experimental methods used, it was not possible to determine if the particles still contained solution or if the particles were completely solid after a solid was formed in the particles. Chapter 2 39 Also, it was not possible to observe any secondary crystallization as illustrated in Figure 2.5, instead, only the CRH could be observed (i.e., when a solid first forms in the particles). Also, as noted above, crystallization is a stochastic process, implying that identical particles may have a range of observed values of CRH. In order to account for the stochastic nature of CRH measurements, the CRH values for a statistically large population size of particles are observed in this thesis. To ensure accurate representation and communication of the crystallization results in this thesis, the convention of this thesis will be to report both the median CRH value for given conditions and the range of the observed CRH values for given conditions. The median CRH value, or the R H at which 50 % of the particles have crystallized, is referred to as the CRH50 throughout this thesis. The range of CRH values is either reported as the entire range in CRH values, or in terms of the 20th and 80th percentiles of the CRH data. 2.4 Classical Nucleation Theory Crystallization of particles is a stochastic process. Classical nucleation theory can be used to understand the thermodynamics and kinetics of crystallization. The following discussion regarding classical nucleation theory provides a foundation for calculations presented in later chapters of this thesis. Note that the homogeneous and heterogeneous nucleation rates obtained in the studies described in this thesis were obtained experimentally without the use of the assumptions inherent to classical nucleation theory. Rather, classical nucleation theory was used throughout this thesis as a convenient method to parametrize the homogeneous and heterogeneous nucleation rates obtained experimentally to gain insight into the nucleation process. Further considerations of classical nucleation theory are briefly discussed in the Appendix. Due to random fluctuations and collisions of solute molecules in a homogeneous solution (i.e., no solid surfaces that initiate nucleation are present), solute-rich or crystalline regions can form solute clusters. If the solution is supersaturated with respect to the solute, the solute molecules will be thermodynamically more stable in the solid phase than in the solution phase. At the same time, the formation of a solid solute cluster introduces a new surface, which costs energy (interfacial tension). According to classical nucleation theory Chapter 2 40 and assuming the formation of a spherical solute cluster, the overall change in Gibbs free energy in homogeneously forming the solute cluster, A G h o m , is thus given by:94 ,98 2-6 A G h o m = | c^Leer AG V + 4nrlSKj where AG V and y is the cluster volume based change in Gibbs free energy and the cluster surface area based interfacial tension associated with forming a solute cluster of radius, r d u s t c r, respectively. If the solution is supersaturated with respect to the solute, AG V will be negative because the solute cluster is thermodynamically more stable than keeping the solute in solution as noted above. Likewise, the energy cost of forming a new surface forces y to be positive. The competition between the volume and surface dependent terms in Equation 2.6 can be seen with the plot of A G h o m in Figure 2.8 and is the source of the kinetic barrier to nucleation. The height of this kinetic barrier is given by A G ^ , at a critical solute cluster radius, 4 n s ' t e r. Chapter 2 41 Figure 2.8: Change in Gibbs free energy in forming a solute cluster, AGhom, as a function of solute cluster radius, r c l u s t„. AGhom is the sum of volume dependent and surface area dependent terms as shown in Equation 2.6. The height of the kinetic barrier to nucleation, AGj," ,^ is given by Equation 2.7. A stable nucleus forms from a solute cluster with a radius greater than rj^tet. Classical nucleation theory provides a method to determine AG£"m (see the Appendix for the derivation) to give:94,98 3k2T'2 (in Sf where vis the molecular volume of the solid, k is Boltzmann's constant, Tis temperature, and S is the supersaturation, as given by: Chapter 2 42 2.8 S = sat s^olute Literature values of y, v, S, and A G ^ , for two common atmospheric species are listed in Table 2.1 as an example. Table 2.1: Literature Values of Classical Nucleation Theory Parameters at 298.15 K Ammonium Sulphate" Sodium Chlorideb 0.052 0.064 vfA 3] 0 124 45 S 29.9 4.64 Cluster [Al 9.2 9.1 A C h c i 0] 1.9 x 10"19 2.2 x 10"19 a Values from Onasch et al. b Values from Richardson and Snyder.100 c Values of V based on molecular weight and density of bulk material. If a solute cluster forms with rclusKr < rc™s'ter, a decrease in A G h o m can only result from a decrease in r c l u s t e r (see Figure 2.8). Therefore, a solute cluster with r c l u s t e r < rc™s'ter will be unstable: the solute cluster will dissolve back into solution. If a solute cluster forms with Cluster > rdustcr > a decrease in A G h o m can only result from an increase in r c l u s t e r. Therefore, a solute cluster with rc luster > r^"lm will be a stable nucleus. In the absence of heterogeneous surfaces such as dust and other foreign objects, the formation of stable nuclei is referred to as homogeneous nucleation. Larger crystals can grow from the stable nuclei, thus stable nuclei are required for crystallization. The rate of formation of these stable nuclei is given by the homogeneous nucleation rate, Jhom, (often referred to as the homogeneous nucleation rate coefficient in the atmospheric literature) and is defined as the number of nucleation events of solid per unit volume of solution per unit time. In the presence of heterogeneous surfaces such as dust and other foreign objects, the formation of stable nuclei is referred to as heterogeneous nucleation. The rate of formation of stable nuclei in the presence of heterogeneous surfaces is given by the heterogeneous nucleation rate, / h e t , (often referred to Chapter 2 43 as the heterogeneous nucleation rate coefficient in the atmospheric literature) and is defined as the number of nucleation events of solid per unit surface area of foreign objects per unit time. Details of the classical nucleation theory interpretation of / h o m and / h e t are discussed in Chapters 4 — 6 and in the Appendix. Crystallization also depends on the rate at which solute molecules move towards the surface of the nuclei to grow the crystal (referred to as the crystal growth rate). Under the experimental conditions used throughout this thesis, it is reasonable to assume that the crystal growth rate was much faster than the homogeneous nucleation rate such that the formation of only one stable nucleus was required for crystallization. Also note that the classical nucleation theory parameters presented in this thesis were obtained at room temperature and the temperature dependence of these parameters discussed here and later in this thesis is not clear. 2.5 References (90) Parker, S. P., Ed-.; Dictionary of Chemistry; McGraw-Hill: New York, 1997, pp x, 454. (91) Tang, I. N . ; Munkelwitz, H. R. /. Colloid Interface Sci. 1984, 98, 430. (92) Seinfeld, J. H.; Pandis, S. N . Atmospheric Chemistry and Physics: From Air Pollution to Climate Change; Wiley: New York, 1998. (93) Laidler, K. J.; Meiser, J. H. Physical Chemistry, 2nd ed.; Houghton Mifflin: Boston, 1995. (94) Mullin, J. W. Crystallisation, 4th ed.; Butterworth-Heinemann: Oxford, U.K. and Boston, MA, 2001. (95) Marcolli, C ; Luo, B. P.; Peter, T. /. Phys. Chem. A 2004, 108, 2216. (96) Tang, I. N . ; Munkelwitz, H. R. Atmos. Environ. 1993, 27, 467. (97) Marcolli, C ; Krieger, U. K. /. Phys. Chem. A 2006, /10,1881. (98) Walton, A. G. Nucleation in Liquids and Solids. In Nucleation; Zetdemoyer, A. C , Ed.; M. Dekker: New York, 1969; pp 225-327. (99) Onasch, T. B.; McGraw, R.; Imre, D. /. Phys. Chem. A 2000, 104,10797. (100) Richardson, C. B.; Snyder, T. D. Langmuirl994, 10, 2462. Chapter 3 44 3. D E L I Q U E S C E N C E O F M A L O N I C , S U C C I N I C , G L U T A R I C , A N D A D I P I C A C I D P A R T I C L E S 3.1 Introduction Condensed phase organic material is abundant in the atmosphere. In urban areas of the U.S., for example, organic material typically accounts for 10 — 40 % of the fine particle mass, and in rural and remote areas of the U.S., organic material typically accounts for 30 — 50 % of the fine particulate mass.101 Furthermore, in certain areas, such as the Amazon basin, the organic fraction can approach 90 % of the total aerosol mass.102,103 The total amount of condensed phase organic material produced from these sources is estimated to be nSTgyr- 1 . 1 0 4- 1 0 5 Despite the abundance of condensed-phase organic material in the atmosphere, relatively litde is known about the possible phase transitions of organic particles. In order to understand and predict the role of organic particles in the atmosphere, these phase transitions must be understood. For example, recent laboratory studies have shown that the hydrolysis of N 2 O s to form H N 0 3 will vary dramatically depending on whether or not particles are solid or aqueous solution droplets.106,107 Radiative forcing by atmospheric particles and the mechanism of ice nucleation on or in these particles will also depend strongly on the phase and water content.108'111 We have carried out a series of experiments to determine the deliquescence properties of pure dicarboxylic acid particles. Deliquescence is an atmospherically relevant phase transition that involves the uptake of water by solid particles to form solution droplets. These studies should lead to a better understanding of the more complex organic particles found in the atmosphere. Specifically, we focused on malonic, succinic, glutaric, and adipic acid particles. These organic compounds were chosen since field measurements have shown that these acids are a significant component of fine particulate matter in the A version of this chapter has been published. Parsons, M. T.; Mak, J.; Lipetz, S. R.; Bertram, A. K. Deliquescence of Malonic, Succinic, Glutaric, and Adipic Acid Particles J . Geophys. Res., 2004, 109, art. no. D06212, doi: 10.1029/2003JD004075. Reproduced with permission from The Journal of Geophysical Research - Atmospheres, 2004, 109, art. no. D06212, doi: 10.1029/2003JD004075. Copyright 2004 American Geophysical Union. Chapter 3 45 troposphere.112"117 Sources of these dicarboxylic acids include biomass burning, fossil fuel combustion, and photochemical oxidation of gas-phase hydrocarbons.112"114'118 The deliquescence of dicarboxylic acid particles have previously been studied using a tandem differential mobility analyzer,119,120 an electrodynamic balance,121 an aerosol flow tube-FTIR (Fourier transform infrared) system,122 a static mode chamber-FTIR system,122 and bulk methods.121"124 In contrast, we used an optical microscope to study particles with sizes ranging from 2 - 4 0 um. We investigated deliquescence at temperatures ranging from 293 to 243 K, which extends the temperature range covered in most previous studies. These studies include measurements below the eutectic temperatures. At such temperatures the vapour is supersaturated with respect to ice prior to deliquescence, and hence, ice could nucleate. Currently there is a dearth of experimental data on deliquescence at temperatures below the eutectic. In the following we present the deliquescence measurements and compare these measurements with previous studies and calculations. 3.2 Experimental The apparatus used in these studies is illustrated in Figure 3.1, Panels A and B. The particles of interest are deposited on the bottom surface of the flow cell, the relative humidity in the cell is controlled by the continuous flow of a mixture of dry and humidified N 2 , and the phase of the particles is monitored with an optical microscope. This approach is similar to the approach recently used to study the microphysics of NaCl-H 2 0 and H N 0 3 -H 2 0 particles.125"127 This methodology enables long observation times, temperature cycling, control of the relative humidity, and statistically significant results (typically 30 - 80 particles are monitored in a single experiment). Chapter 3 46 (A) Inlet 7~ Cell Body .Jop Window Outlet Bottom Surface (B) Particles Objective Cooling Stage Thermocouple Figure 3.1: Diagram of the flow cell and experimental apparatus: (A) side view of the flow cell, and (B) side view of the assembled apparatus. The cell body and the inlet and oudet were constructed of stainless steel. The top window was sealed to the cell body with high vacuum grease (Dupont, Krytox LVP, vapour pressure less than 10"13 Torr) and the bottom surface was sealed with a Viton o-ring. Two different bottom surfaces were used in these experiments: the first surface consisted of a thin glass cover slide treated with an organosilane to form a monomolecular hydrophobic layer, and the second surface consisted of a 0.03 mm polytetrafluoroethylene (PTFE) film annealed to a plain glass cover slide. The annealing process significantiy reduced the number of defects on the surface of the PTFE film and provided adhesion between the glass substrate and the film. These hydrophobic surfaces were chosen to prevent ice nucleation directly on the bottom surface at sub-eutectic temperatures. We have also performed measurements at room temperature on several different substrates, ranging from Chapter 3 47 hydrophobic (PTFE) to hydrophilic (bare glass). In all cases, we observed the same result, indicating that the surface did not influence deliquescence. The relative humidity (RH) over the particles was controlled by continuously flowing a mixture of dry and humidified N 2 through the cell (total flow rate of 100 to 300 cm3 min - 1 at standard temperature and pressure). Ultra high purity nitrogen (Praxair, 99.999 %) was first passed through a hydrocarbon filter (Supelco, Supelcarb HC 24449) and then subsequendy split into two flows. One flow was passed through a water bubbler situated inside a refrigerating circulator (Thermo Neslab, RTE-140) to generate humidified N 2 , and the second flow served as the dry N 2 line. The relative humidity in the cell was varied by adjusting the relative flows of the dry and humidified N 2 or adjusting the temperature of the refrigerating circulator, while maintaining a constant total flow. A dew point hygrometer (General Eastern, Hygro M4) was used to determine the R H of the combined flows. This instrument measured the dew point or ice frost point of the gas, from which the relative humidity was calculated with the Goff and Gratch equations128 and knowledge of the substrate temperature. The sample cell was mounted on a cooling stage for temperature control. The temperature of the cooling stage and hence the sample cell was regulated with a refrigerating circulator ^Thermo Neslab RTE-740). A type T thermocouple located in the cooling stage just below the flow cell was used to determine the temperature of the bottom surface of the flow cell. This thermocouple was calibrated against the dew point or ice frost point, as done previously in the literature.129 Briefly, calibration involved the following steps: first, a constant relative humidity was established in the flow cell. Next, the temperature of the flow cell was decreased until liquid water or ice particles condensed on the bottom surface of the cell due to heterogeneous nucleation on the PTFE substrate. The temperature of the flow cell was then slowly increased while visually monitoring the size of the particles with a reflected-light microscope (see below). From these observations we determined the temperature at which water particles neither grew nor shrunk in size. Under these conditions the particles were in equilibrium with the gas phase water vapour, and the temperature of the bottom surface of the cell was equal to the dew point or ice frost point, which was determined with the hygrometer. The difference between the temperature measured with the thermocouple and the dew point or ice frost point was used to construct Chapter 3 48 a calibration curve for the thermocouple. At 273 K the correction was 0.1 K, and at 243 K the correcdon was 0.7 K. Deliquescence of the particles was monitored with a reflected-light microscope (Zeiss, Axiotech 100) equipped with a 20 x objective (numerical aperture = 0.4, resolution « 0.6 urn) and a 50 x objective (numerical aperture = 0.5, resolution « 0.5 urn). Images of the particles were recorded with a CCD camera attached to a monitor and video recorder, and the temperature and dew point/ice frost point were recorded simultaneously. From the images we determined the size and morphology of the particles and the deliquescence relative humidities. In most of the experiments we used polarized light to enhance the contrast between solid and liquid particles; however, phase transitions were also discernable with unpolarized light as demonstrated previously.125'130'131 Shown in Figure 3.2, Panels A, B, and C, are images recorded during a typical experiment. Figure 3.2, Panel A, shows images of ammonium sulfate particles prior to deliquescence; Figure 3.2, Panel B, shows images during deliquescence; and Figure 3.2, Panel C, shows images after deliquescence. Note that in our experiments we cannot determine if the solid particles are crystalline or amorphous. Previous studies have shown that solid particles of the compounds used in this study are crystalline before deliquescence.132'133 Chapter 3 49 m • © * • 0 o . CD • 0 ( A ) o • * 9 • ' 60 urn 0 ° o * o • O 0 © ft) i © ( B ) o O ° IP O O ° :• • o o • -* e o if* ® ( C ) # o .:: * • K I f W 50 um Figure 3.2: Images of ammonium sulphate particles recorded during a deliquescence experiment: (A) solid particles prior to deliquescence; (B) solid-liquid particles during deliquescence; and (C) liquid particles just after complete deliquescence. Chapter 3 50 Particles ranging in size from 2 to 40 fim were produced by two methods. The first method consisted of grinding crystals and placing the resulting particles directiy on the bottom surface prior to assembling the flow cell. The second method involved directing a stream of submicrometre particles from an atomizer (TSI 7660), at the PTFE substrate for 1 - 5 s. During this time the submicrometre particles impacted on the surface and coagulated resulting in supermicrometre particles. Solutions used in the atomizer were made with either deionized ultra-filtered water (Fisher), or HPLC-grade water (Fisher), both of which have been passed through a submicrometre filter. The results were independent of the grade of water used. Ammonium sulphate (Fisher, 99.8 %), malonic acid (Aldrich, 99 %), succinic acid (Fisher, 99.8 %), glutaric acid (Aldrich, 99 %), and adipic acid (Fisher, 99.9 % minimum) were all used as supplied without further purification. Ammonium sulphate was used to validate the experimental setup as discussed below. Atmospheric particles most relevant to atmospheric chemistry and physics range in size from approximately 0.002 to 10 |xm.134 As mentioned, the size of the particles used in the current experiments ranged from 2 — 40 fxm. Hence the smallest particles studies in the current experiments fall within the size range that is important for atmospheric chemistry and physics. Furthermore, the current deliquescence results were independent of particle size, suggesting that these results could be applicable to smaller particles sizes. During a deliquescence experiment the relative humidity was first held close to 0 % RH to ensure all the particles were solid. Then the relative humidity was increased by either adjusting the dry and humidified N 2 flows or adjusting the temperature of the humidifying bubbler as discussed above. Close to the deliquescence the relative humidity was increased at a rate of approximately 0.05 % RH per minute. The uncertainty in the current deliquescence measurements (± d) was approximately ± 2.1 % RH, based on repeated measurements at a fixed temperature. For measurements below the eutectic temperatures we modified the experimental apparatus slighdy. In these experiments a 2 mm thick PTFE spacer was inserted between the stainless steel cell body and the bottom surface. The PTFE spacer maintained a large temperature differential (at least 10 K) between the cell body and the bottom substrate. This ensured that ice did not nucleate directly on the cell body and ice supersaturation was maintained above the organic particles. Chapter 3 51 3.3 Results and Discussion 3.3.1 Deliquescence of Ammonium Sulphate Particles In order to evaluate the performance of the experimental apparatus and approach, we first studied ammonium sulphate particles. The deliquescence of these particles has been studied extensively and is well understood.135 The deliquescence results are shown in Figure 3.3. Also shown are experimental results from other groups and predictions based on thermodynamic considerations. The results from Braban et al. 1 3 6 and Tang and Munkelwitz137 were obtained with supermicrometre particles; the data from both Cziczo and Abbatt138 and Onasch et al. 1 3 9 were obtained using submicrometre aerosol particles; and the data from Wise et al. 1 2 4 were obtained using bulk solutions. The solid line was calculated using a thermodynamic model by Clegg et al.1 4 0 The current results are in excellent agreement with the previous experimental measurements and the theoretical predictions. Chapter 3 52 Figure 3.3: Deliquescence of ammonium sulphate particles as a function of temperature. Current data (•) were obtained with particles ranging in size from 2 - 40 urn. The uncertainty in the current deliquescence measurements (± 2d) was approximately ± 2.1 % RH, based on repeated measurements at a fixed temperature. The results from Braban et al.136 (•) and Tang and Munkelwitz137 (O) were also obtained with supermicrometre particles, and the data from both Cziczo and Abbatt138 (A) and Onasch et al.139 (V) were obtained using submicrometre particles. The results from Wise et al.124 were obtained with bulk solutions. The solid line was calculated using a thermodynamic model by Clegg et al.140 3.3.2 Deliquescence of Dicarboxylic Acid Particles as a Function of Temperature . The deliquescence relative humidity (DRH) as a function of temperature for the four organic acids studied are shown in Figure 3.4 - Figure 3.7. Succinic acid and adipic acid deliquesce close to 100 % RH; whereas malonic acid and glutaric acid deliquesce at lower relative humidities, consistent with the solubilities of these organics. The high DRH values Chapter 3 53 for both adipic acid and succinic acid suggest that these organics may crystallize in atmospheric particles if these organics are a significant component of the aerosol mass. For comparison, the solubilities for malonic, succinic, and adipic acid at 298.15 K are 0.2176, 0.01337, and 0.00307 mole fraction acid, respectively;141 and the solubility for glutaric acid at 297.05 K is 0.1506 mole fraction acid.142 Figure 3.4: Deliquescence of malonic acid as a function of temperature. Current data (•) were obtained with particles ranging in size from 2-40 um. The results from Braban et al.122 (O) were obtained using submicrometre and supermicrometre particles, and the data from Brooks et al.123 (&), Wise et al.124 (^), and Peng et al.121 ()2() were obtained using bulk solutions. The thick solid line is the fit to the current data and the thin solid line is the ice saturation line. Details of the calculations are given in the text for: ideal solution calculation (••"), UNIFAC calculation 1 (•••••), and UNIFAC calculation 2 (—). Chapter 3 54 Figure 3.5: Deliquescence of succinic acid as a function of temperature. Current data (#) were obtained with particles ranging in size from 2 — 40 urn. The results from Peng et al . m were obtained using supermicrometre particles (d-bar) and bulk solutions The data from Prenni et al.120 (^-bar) were obtained using submicrometre particles, and the data from Brooks et al.123 (^-bar, $3) and Wise et al.124 (^) were obtained using bulk methods. The thin solid line is the ice saturation line. Details of the overlapping calculations are given in the text for: ideal solution calculation (••-), UNIFAC calculation 1 ("•")» and UNIFAC calculation 2 (~). Chapter 3 55 105 -i 1 1 1 1 1 1 1 1 • r 70 -| 1 1 1 1 1 1 1 1 1 1 • 1 240 250 260 270 280 290 300 T[K] Figure 3.6: Deliquescence of glutaric acid as a function of temperature. Current data (•) were obtained with particles ranging in size from 2 — 40 um. The results from Cruz and Pandis119 (•) were obtained using submicrometre aerosol particles. The results from Peng et al.121 were obtained using supermicrometre particles (A) and bulk solutions and the data from Brooks et al.123 (&) and Wise et al.124 ($t) were obtained using bulk methods. The thick solid line is the fit to the current data and the thin solid line is the ice saturation line. Details of the calculations are given in the text for: ideal solution calculation (•••), UNIFAC calculation 1 (•••••), and UNIFAC calculation 2 (—). Chapter 3 56 Figure 3.7: Deliquescence of adipic acid as a function of temperature. Current data (#) were obtained with particles ranging in size from 2-40 um. The results from Prenni et al.120 (E3-bar) were obtained with submicrometre aerosol particles, and the data from Brooks et al.123 (E3-bar) were obtained using bulk methods. The thin solid line is the ice saturation line. Details of the overlapping calculations are given in the text for: ideal solution calculation ("'"), UNIFAC calculation 1 ('"")> and UNIFAC calculation 2 (--). As done previously in the literature for inorganic salts,110'139 we fit the temperature-dependent DRH data for malonic and glutaric acid to the following empirical equation: 3.1 ^ ( D R H ^ + A + A + A where D R H is the deliquescence relative humidity (in units of % RH) and T is the temperature (in units of K). The solid thick lines shown in Figure 3.4 and Figure 3.6 are the results from this least-squares analysis, and the parameters (A0,AUA2, andA3) that describe these curves are given in Table 3.1. We did not perform a similar analysis for succinic and Chapter 3 57 adipic acid since within experimental uncertainty the DRH for these particles was 100 % RH and independent of temperature. Table 3.1: Parameters Describing the Deliquescence Results Acid A A A2 A Malonic Acid 2.5930 463.17 7.1176 x 104 -1.7740 x 107 Glutaric Acid 3.1912 384.68 4.6458 x 104 -1.3706 x 107 Also shown in Figure 3.4 - Figure 3.7 are results from other groups. Cruz and Pandis119 as well as Prenni et al. 1 2 0 investigated the deliquescence of submicrometre particles using a tandem differential mobility analyzer system. Peng et al.1 2 1 investigated the deliquescence using an electrodynamic balance and bulk methods, and Brooks et al. 1 2 3 and Wise et al. 1 2 4 determined the deliquescence relative humidity of these acids from bulk measurements. Braban et al. 1 2 2 measured the deliquescence properties of submicrometre and supermicrometre particles using an aerosol flow tube-FTIR system and a static mode chamber-FTIR system. In several of the measurements mentioned above only lower limits to deliquescence were determined. These limits are represented by the thick bars in the Figure 3.5 and Figure 3.7. In general the current results are in good agreement with the results from previous studies. The current malonic acid results are consistent with the measurements from Braban et al.,1 2 2 Brooks et al.,1 2 3 and Wise et al. 1 2 4 The results from Peng et al.1 2 1 appear to be 5 % RH lower than the current measurements. The current succinic acid results are consistent with the measurements by Peng et al.,121 Prenni et al.,1 2 0 and Wise et al.;124 however, the current results are approximately 7 % RH above the measurement at 298 K by Brooks et al. 1 2 3 For glutaric acid, the current results are consistent with the results reported by Brooks et al.,1 2 3 and the current results (when extrapolated to warmer temperatures) are consistent with the results reported by Cruz and Pandis,119 Peng et al.,121 and Wise et al. 1 2 4 Finally, the current results for adipic acid are consistent with the lower limits reported by Prenni et al. 1 2 0 and Brooks et al. 1 2 3 As mentioned above, the combined experimental results presented in Figure 3.4 — Figure 3.7 were obtained using submicrometre and supermicrometre particles as well as bulk solutions. The good agreement between these Chapter 3 58 results illustrates that there is no significant kinetic barrier to the deliquescence of dicarboxylic acid particles and that bulk thermodynamics can be used to predict the D R H of these particles. That is to say, the agreement between these experimental results suggests there is no significant size dependence to DRH measurements for these compounds. Braban et al. 1 2 2 recendy reached a similar conclusion for the malonic acid system. 3.3.3 Calculations of DRH We first calculated the D R H of the dicarboxylic acid particles using solubility data and by assuming the saturated solutions obey Raoult's law (ideal solution). Solubility data for malonic, succinic, and adipic acid where taken from Apelblat and Manzurola141 and solubility data for glutaric acid was taken from Stephen and Stephen.142 Apelblat and Manzurola141 reported solubility data from 298.15 to 278.15 K, and Stephen and Stephen reported solubility data from 318.95 to 276.55 K. The solubility data were fit to the following empirical equation: where is the solubility (mole fraction of the organic acid in a saturated solution) and Tis the temperature (in units of K). The parameters from the least squares analysis were used when calculating deliquescence. The empirical Equation 3.2 was chosen for this study because it fit the solubility data well (R2 ranged from 0.9963 to 0.9999) and because it gave realistic solubilities when extrapolated to low temperatures. In contrast, other equations we tried gave either negative solubilities when extrapolated to 243 K or solubilities that increased with decreasing temperature at low temperatures. The relative uncertainty of the solubility data for malonic, succinic, glutaric, and adipic acid are approximately 1 %, 1 %, 4 %, and 3 % respectively, based on the scatter in the data. Calculations based on solubility data and Raoult's law are shown in Figure 3.4 -Figure 3.7 (labelled ideal solution calculation). The uncertainties in the calculations due to the uncertainties in the solubility data are estimated to be less than 1 %. These calculations accurately describe the deliquescence of succinic acid and adipic acid, which is not surprising since these particles are dilute solutions at deliquescence. The calculation also appears to agree reasonably well with the glutaric acid measurements (the calculations fall within the error bars except for two data points); however for malonic acid the calculations are Chapter 3 59 significantly above the measurements at temperatures greater than 270 K, indicating that saturated solutions of malonic acid do not obey Raoult's law. We have also calculated the D R H of these dicarboxylic acid particles as a function of temperature using the solubility data described above and the original UNIQUAC (universal quasi-chemical) Functional Group Activity Coefficients (UNIFAC) model.143 The UNIFAC model is a group contribution method that is used for predicting thermodynamic properties of non-ideal solutions. Here we use the UNIFAC model to calculate the water activity of saturated solutions of dicarboxylic acids. Note that the water activity at saturation is equal to DRH divided by 100 % RH. The use of UNIFAC has been described in detail.1 4 3 1 4 5 In order to calculate the water activity of an organic-water solution using UNIFAC, group volume parameters, group area parameters, and group interaction parameters are required. For the first set of UNIFAC calculations shown in Figure 3.4 — Figure 3.7 (UNIFAC calculation 1) we used group volume, group area, and group interaction parameters from Reid et al. 1 4 6 For the second set of UNIFAC calculations shown in Figure 3.4 - Figure 3.7 (UNIFAC calculation 2) we used group volume and group area parameters from Reid et al. 1 4 6 and group interaction parameters from Peng et al.1 2 1 The calculations based on the interaction parameters from Reid et al. 1 4 6 deviate from the current glutaric acid results at temperatures greater than 285 K, and deviate significandy from the current malonic acid results over the entire temperature range studied. This is not surprising since recently it was shown that water activity predictions for malonic and glutaric acid based on parameters from Reid et al. 1 4 6 deviate from water activity measurements.121 In contrast, the calculations based on the parameters from Peng et al.1 2 1 agree statistically with the experimental results for glutaric acid, and the calculations are within 3 % of the experimental results for malonic acid. Despite the statistical agreement between most experimental data and the UNIFAC calculations presented in Figure 3.4 through Figure 3.7 (with group interaction parameters from Peng et al.), the overall trend of the current malonic acid D R H values shown in Figure 3.4 is poorly reproduced in these calculations. It has been noted before that UNIFAC does not account for interactions between disubstituted strongly polar functional groups in close proximity (less than three or four carbon atoms separation) and that UNIFAC is not well suited for estimating activity coefficients for such compounds.145,147'148 Poor agreement (statistically and in terms of general trends) between experimental results and UNIFAC Chapter 3 60 calculations has been observed in other studies (see, for example, Demou et al. and Saxena and Hildemann148). Further improvements to group interacdon parameters in UNIFAC may provide better agreement between UNIFAC calculations and experimental observations for compounds with closely positioned polar groups. We also calculated the D R H for these acids using interaction parameters reported by Ming and Russell,149 group volume and group area parameters from Reid et al.,1 4 6 and the solubility data described above. The results from this third set of UNIFAC calculations (not shown) fell between the results from the first two sets of UNIFAC calculations (UNIFAC calculation 1 and 2). The UNIFAC model combined with interaction parameters from Peng et al.1 2 1 gave the best statistical agreement with the current experimental results. The statistical agreement suggests that the UNIFAC model combined with appropriate interaction parameters should be a useful tool for estimating the deliquescence properties of multi-component organic particles found in the atmosphere. 3.3.4 DRH Values Below the Eutectic Temperature As mentioned above, at temperatures below the eutectic the vapour is supersaturated with respect to ice prior to deliquescence. At these temperatures ice may nucleate directiy on the solid organic particles prior to deliquescence if the solid organic particles are good ice nuclei. Furthermore, if these solid dicarboxylic acids are good ice nuclei then they may play an important role in ice cloud formation in the atmosphere. The eutectic temperature for each system was identified by determining the temperature at which the vapour pressure of ice equals the partial pressure of water over the saturated organic solution. The vapour pressure of ice as a function of temperature was calculated with the Goff and Gratch equation.128 The partial pressure of water over the saturated aqueous solutions as a function of temperature was determined from the current deliquescence results. Based on these results, the eutectic temperatures for malonic, succinic, glutaric, and adipic acid are 255.7, 273.2, 269.0, and 273.2 K, respectively. Also shown in Figure 3.4 - Figure 3.7 is the ice saturation line from the Goff and Gratch equation.128 This line illustrates the conditions at which the vapour becomes supersaturated with respect to ice. The region to the left of the ice saturation line in Figure 3.4 - Figure 3.7 is where ice, as opposed to liquid water, is the thermodynamically stable phase. Chapter 3 61 At temperatures below the eutectic temperature ice was not observed in any of the current experiments; instead, the particles underwent deliquescence to form metastable solution droplets. Furthermore, the measured D R H was in agreement with the DRH predicted with the UNIFAC model and interaction parameters from Peng et al.1 2 1 (see above). Deliquescence below the eutectic has also been observed for the malonic acid-water system,122 the ammonium sulphate-water system,136,150 and the sodium chloride-water system.125 The current measurements at temperatures below the eutectic indicate that solid dicarboxylic acids (with surface structures similar to the surface structures employed in this study) will not play an important role in ice cloud formation at temperatures above 243 K. These solid acids may be important in ice cloud formation at temperature below 243 K, or if the particles are preactivated or have significandy more defects than the particles in the current study.111 3.4 Summary and Conclusions Deliquescence relative humidities for malonic, glutaric, succinic, and adipic acid particles were determined for temperatures ranging from 293 to 243 K. Over this temperature range both succinic acid and adipic acid deliquesced at approximately 100 % RH. In contrast, the DRH for malonic acid at 293 K and 243 K was 73.7 % RH and 86.6 % RH respectively, and the D R H for glutaric acid at 293 K and 243 K was 91.0 % RH and 100 % RH respectively. The current results are in good agreement with previous studies which used bulk solutions, supermicrometre particles and submicrometre particles. This agreement suggests that there is no significant kinetic barrier or size dependence to the deliquescence of these dicarboxylic acid particles. The deliquescence measurements were compared with a series of calculations. The UNIFAC model combined with interaction parameters from Peng et al.1 2 1 gave the best statistical agreement with the experimental results. The statistical agreement suggests that the UNIFAC model combined with appropriate interaction parameters should be a useful tool for estimating the deliquescence properties of multi-component organic particles found in the atmosphere. At temperatures below the eutectic, ice was not observed in any of the current experiments, rather the particles underwent deliquescence to form metastable solution Chapter 3 62 droplets. This indicates that the solid organics studied are not good ice nuclei above 243 K and hence will probably not play a role in ice cloud formation at these temperatures. 3.5 References (101) USEPA "Air Quality Criteria for Particulate Matter," Rep. EPA/600/P-95/001, Washington, D. C , 1996, Office of Research and Development. 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Solubilities of Inorganic and Organic Compounds; Macmillan: New York, 1963; Vol. 1. (143) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. AIChE J. 1975, 21,1086. (144) Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using Unifac:A Group Contribution Method; Elsevier Scientific Pub. Co.: Amsterdam, 1977. (145) Fredenslund, A.; Sorensen, J. M. Group Contribution Estimation Methods. In Models for Thermodynamic and Phase Equilibria Calculations; Sandler, S. I., Ed.; Marcel Dekker: New York, 1994; pp 287-361. (146) Reid, R. C ; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill, 1987. (147) Demou, E.; Visram, H.; Donaldson, D. J.; Makar, P. A. Atmos. Environ. 2003, 37, 3529. (148) Saxena, P.; Hildemann, L. M. Environ. Sci. Technol. 1997, 31, 3318. Chapter 3 65 (149) Ming, Y.; Russell, L. M . AIChE J. 2002, 48,1331. (150) Fortin, T. J.; Shilling, J. E.; Tolbert, M. A. /. Geophys. Res. 2002, 107, art. no. 4088, doi: 10.1029/2001JD000677. Chapter 4 66 4. D E L I Q U E S C E N C E A N D C R Y S T A L L I Z A T I O N O F A M M O N I U M S U L F A T E P A R T I C L E S I N T E R N A L L Y M I X E D W I T H W A T E R -S O L U B L E O R G A N I C C O M P O U N D S 4.1 Introduction Aerosols can have a significant impact on climate, visibility, atmospheric chemistry, and health.151'152 Before the role of particles in these processes can be quantified, however, the phase and hygroscopic properties of atmospheric particles must be understood and accurately represented. This is because the phase and water content govern the total mass of airborne particles, the amount of light they scatter and absorb, and their reactivity. For example, Thornton et al. 1 5 3 have shown that N 2 O s reactivity on aerosol particles depends on the particle phase and water content. Martin et al. 1 5 4 have also shown that radiative forcing due to the direct aerosol effect varies by about 24 % depending on the physical state of ammonium + sulphate + nitrate particles. Studies have shown that aerosols can contain various ratios of inorganic to organic material, and this ratio depends on factors such as location.155 Also, composition measurements of single particles have shown that organic material is internally mixed with inorganic species in the troposphere.156,157 An average composition of urban fine particles, based on measurements at several sites, is 28 % sulphate, 31 % organic carbon, 8 % ammonium, 9 % elemental carbon, and 6 % nitrate by weight.155 Other field measurements suggest that the organic material typically accounts for 10-50 % of the fine particle mass.151 Despite the abundance of organic material present in aerosol particles, information about phase transitions and hygroscopic properties of organic and mixed organic-inorganic particles is not at a level comparable to inorganic particles.158 Hundreds of different organic species with a range of chemical and physical properties have been identified in atmospheric aerosols (see for example, Saxena and Hildemann159). However, Fuzzi et al. 1 6 0 have suggested that the water-soluble organic material in aerosol particles can be represented with mixtures of the following classes of A version of this chapter has been published. Parsons, M. T.; Knopf, D. A.; Bertram, A. K. Deliquescence and Crystallization of Ammonium Sulfate Particles Internally Mixed with Water-Soluble Organic Compounds,/. Phys. Chem. A, 2004, 108,11600 - 11608. Reproduced with permission from The Journal of Physical Chemistry A, 2004, 108,11600 - 11608. Copyright 2004 American Chemical Society. Chapter 4 67 organic species: dialkyl ketones, polyols, polyphenols, alkanedioic acids, hydroxyalkanoic acids, aromatic acids, and polycarboxylic acids. Two atmospherically relevant phase transitions are deliquescence and crystallization. Several groups have studied the deliquescence and crystallization of pure organic systems.161" 1 6 8 This work has shown that the deliquescence and crystallization properties of organic particles change significantiy with the type of organic compound. More recentiy, Marcolli et al.1 6 9 have shown that increasing the number of organic components in mixed solutions decreases the deliquescence relative humidity. Their study suggested that aerosol particles with numerous organic components are more likely to remain in the liquid state. Several research groups have also studied the deliquescence and crystallization of mixed organic-inorganic particles.170"184 A preliminary study suggested that the deliquescence and crystallization properties of inorganic particles only decreased slighdy when the mole fraction of organic was less than O.4.182 This conclusion was similar to some previous conclusions concerning the effects of organics on inorganic phase transitions.154'172 However, these conclusions are based on only a few organic species. As mentioned above, hundreds of different species with a range of chemical and physical properties have been identified in the atmosphere. Studies with other combinations of inorganic and organic compounds are needed. In the following we expand on a previous study182 by investigating the deliquescence and crystallization of ammonium sulphate particles internally mixed with organic species having a range of chemical and physical properties. These systematic studies are restricted to compositions between 0 and 0.6 dry organic mole fraction and focus on the effect of organics on the deliquescence and crystallization of ammonium sulphate particles. Previous measurements showed that glutaric acid only decreased the crystallization relative humidity and deliquescence relative humidity of pure inorganic particles by less than 10 % RH over this entire composition range.182 Here we determine if other condensed-phase organics found in the atmosphere behave in a similar manner over this range. The organics studied were malonic acid, glycerol, levoglucosan, and fulvic acid (see Table 4.1 for the chemical structures). These organics were selected to include several of the classes suggested by Fuzzi et al. 1 6 0 Sources of malonic acid, glycerol, and levoglucosan include biomass burning, tobacco smoke, and meat cooking.159'185"189 Fulvic acid has not been measured in atmospheric aerosols, but it has been suggested as a reasonable model for Chapter 4 68 polycarboxylic acids found in atmospheric aerosols. In addition to measuring deliquescence and crystallization, we compared the current measurements with thermodynamic and empirical calculations. These studies should provide further insight into the phase of atmospheric particles. Table 4.1: Structures of Organic Species Used in This Study Organic Compound [Class] Structure Malonic Acid [alkanedioic acid] HO O O A A OH Glycerol [polyol] OH Levoglucosan [polyol] Fulvic Acid [polycarboxylic acid] (proposed average structural model190) HO-HO-OH 4.2 Experimental The technique used in this study has been described in Chapter 3 (Parsons et al.191) and elsewhere.182 Here we give an overview of the technique with an emphasis on the experimental conditions and procedures specific to these measurements. Chapter 4 69 The apparatus consisted of an optical microscope coupled to a flow cell. The particles of interest were deposited on the bottom surface of the flow cell and monitored with the microscope (using unpolarized light). The bottom surface of the flow cell, which supported the particles, consisted of a hydrophobic polytetrafluoroethylene (PTFE) film annealed to a plain glass cover slide. Relative humidity with respect to water (RH) over the particles was controlled by a continuous flow of a mixture of dry and humidified N 2 . All observations were made at a temperature of 293.2 i 0.1 K with a carrier gas flow rate of about 400 cm3 min"1 at standard temperature and pressure. Images of the particles in the flow cell were captured at a regular interval (approximately every 15 s) by a digital video camera attached to the microscope. From the images we could determine if the particles were liquid or contained solid material. The temperature of the particles and the dew point or ice frost point of the carrier gas were also recorded and associated with each image. This data was converted into R H using the Goff and Gratch equations.192 During both deliquescence and crystallization experiments, the R H of the carrier gas over the sample particles was changed at a rate of approximately 0.4 % RH min"1. The uncertainty in measuring the R H of the carrier gas is ± 0.3 % RH, and the uncertainty in the reported deliquescence and crystallization results, based on the reproducibility of the data, is ± 2.1 % RH (95 % confidence level).164 Ammonium sulphate (Fisher, 99.8 %), malonic acid (Aldrich, 99 %), glycerol (Fisher, 99.9 %), levoglucosan (1,6-anhydro-P-D-glucopyranose, Fisher, 99+ %), and fulvic acid (International Humic Substances Society, Suwannee River reference) were all used as supplied. Fulvic acids are soluble in water at all pH values, which distinguishes these acids from humic acids. Bulk mixtures of various compositions were prepared gravimetrically and dissolved in purified 18.2 MQ water (Millipore Simplicity 185). All solutions were passed through a 0.02 urn filter (Whatman Anodisc 25) twice prior to use. Solutions were then passed through a glass nebulizer producing a stream of submicrometre particles. These particles were directed onto the bottom surface of the flow cell resulting in coagulation and the production of supermicrometre particles. Typically, between 5000 and 10000 particles were deposited on the bottom surface with a maximum diameter of about 15 urn. The diameter of particles monitored in the current experiments ranged from 5 — 15 um, with an average diameter of about 8 um. Chapter 4 70 Prior to the deliquescence experiments, the particles were first subjected briefly to approximately 0 % RH in order to crystallize the particles. The R H was then increased to 60 - 70 % RH and the deliquescence experiment started. At this R H the particles were partially solid. The total time required for a single deliquescence experiment was less than 30 minutes. In the crystallization experiments, the particles were exposed to decreasing R H starting at 25 - 40 % RH after being placed into the apparatus. The observed particles did not contain any solid material at the start of the experiments. Crystallization experiments lasted at most one hour from particle deposition to completion. Evaporation of the organic material during any experiment was not significant due to the large number of particles, and hence mass of material in the flow cell. This was confirmed by calculations of evaporation rates of the organics as well as separate experiments where we monitored particle size for extended periods of time at constant relative humidity of approximately 35 % RH. In these experiments, the particle size decreased by less than 2 % over two hours. 4.3 Results and Discussion Shown in Figure 4.1, Panels A - D, and Figure 4.1, Panels E - H , are images recorded during a typical deliquescence and crystallization experiment, respectively. Figure 4.1, Panels A - D, correspond to images of mixed malonic acid (Mai) + ammonium sulphate particles (dry malonic acid mole fraction, x'Miii = 0.240, where x'Mal = moles Mai / (moles Mai + moles ammonium sulphate)) recorded while the R H was increased from 76.3 to 78.2 %. In a system with two components plus water, a solid can exist in equilibrium with an aqueous solution over a range of R H as can be seen in Figure 4.1, Panels A - C. The results we report refer to when the particles fully deliquesced. In other words, the current results correspond to when the given solids completely dissolved in the particles. In the following we refer to this as the complete deliquescence relative humidity (DRH*) as done previously.193 DRH* occurred between Panels C and D in Figure 4.1. Knowledge of the conditions at which particles fully deliquesce is important for predicting if particles are partially or completely solid in the atmosphere. This, in turn, is important for predicting the chemistry and physics of atmospheric aerosol particles. For example, in order to predict Chapter 4 71 when ice nucleates on or in atmospheric particles, one first needs to know if the particles are pure liquids or contain solid material. The presence of solids can shift the mode of ice nucleation from homogeneous to heterogeneous and lower the supersaturation required for ice formation. Chapter 4 72 ( A ) O ° Q ^ • A - — ^ O o ° ^ o , — O ( B ) © ° | £ 5 ) o ° o © D ° ( F ) ~ o w o , o ( C ) r ^ ° Q o ° < G > DP 6 ® 0 o ( D ) o ° Q ^ ) O ° ) ) _ — - m o ° <") W €5 0 . Figure 4.1: Images of ammonium sulphate + malonic acid particles ( V ^ = 0.240) during deliquescence at RH equal to (A) 76.3 % RH, (B) 77.2 % RH, (C) 77.7 % RH, (D) 78.2 % RH, and during crystallization at RH equal to (E) 30.4 %RH, (F) 29.3 % RH, (G) 29.2 % RH, (H) 28.1 % RH. Bars indicate a distance of 10 um. Chapter 4 73 Figure 4.1, Panels E - H correspond to images of mixed malonic acid + ammonium sulphate particles (with the same x'Msl as noted above) as the R H was decreased from 30.4 to 28.1 % RH. Due to the stochastic nature of nucleation, all the particles did not crystallize at the same RH. The crystallization results we report below refer to the R H when half the particles have crystallized (CRH50) and also the range over which crystallization was observed. We were unable to determine from the images of the particles if they were completely or partially solid after crystallization had occurred. In a future study we will use FTIR-microscopy to investigate if the particles are completely or partially solid after crystallization. Also note that in our experiments we cannot determine if the solid particles are crystalline or amorphous. Previous studies have shown that solid particles of the compounds used in this study are crystalline.170,194 4.3.1 DRH * of Mixed Ammonium Sulfate + Organic Particles Shown in Figure 4.2 are the current DRH* results for mixed ammonium sulphate ((NH4)2S04) and malonic acid (Mai) particles together with previous measurements of this system. In these experiments, (NH 4) 2S0 4 and Mai can precipitate at low RH, and the lowest DRH* for this system occurs at the eutonic composition.195 At the eutonic composition, the solution is saturated with respect to both ammonium sulphate and malonic acid. The eutonic composition for the (NH 4) 2S0 4 + Mai system was previously determined to be x'ua — 0.645.171 When x'ua is less than the eutonic composition, as is the case in the current experiments, complete deliquescence corresponds to the R H at which (NH 4) 2S0 4 is saturated in the liquid ternary solution. It is possible that other salts, in addition to (NH 4) 2S0 4 (such as letovicite or ammonium malonate), can precipitate in this system at low RH, since malonic acid is a weak acid. Here we assume that these other salts are of minor importance as the iC, for malonic acid is small (piC, = 2.85196). This assumption appears to be consistent with measurements by Braban and Abbatt.170 Chapter 4 74 Figure 4.2: Measured and predicted DRH* for the (NH4)2S04 + Mai system as a function of dry Mai mole fraction, dUsA = moles Mai / (moles Mai + moles (NH4)2S04). (•) This study; (V) Brooks et al.;171 (A) Choi and Chan;176 (•) Prenni et al.;183 (O) Wise et al.;184 (--) Calculations 1; (•••••) Calculation 2; (—) Calculation 3. Calculations are described within the text. Also shown in Figure 4.2 are results from other groups that have studied complete deliquescence of the (NH 4) 2S0 4 + Mai system. The current results are in agreement with these previous studies, which were performed with bulk solutions,171'184 supermicrometre particles,176 and submicrometre particles.183 These previous studies were carried out at temperatures ranging from 293 to 303 K. The agreement between the combined results for the (NH 4) 2S0 4 + Mai system suggests that there is no size dependence to the deliquescence of these particles, similar to the findings of Parsons et al.1 6 4 (see Section 3.3.2) and Braban et al.1 6 1 The results show that DRH* decreases continuously with an increase in organic mole Chapter 4 75 fraction over the range of compositions studied; however, this decrease is small (within the uncertainty of the measurements) when the dry organic mole fraction is less than approximately 0.35. In other words, the results are not statistically different. DRH* of (NH 4) 2S0 4 in the presence of glycerol (Gly) is reported in Figure 4.3. Gly is miscible in water and does not crystallize at room temperature. Hence, there is no eutonic composition for this system, and the current results correspond to complete deliquescence of (NH 4) 2S0 4 in the liquid ternary solution. Similar to the (NH 4) 2S0 4 + Mai results, DRH* decreases continuously with an increase in dry organic mole fraction, and this decrease is small (within the uncertainty of the measurements) when the dry mole fraction of Gly (x'Gly) is less than approximately 0.35. Also shown in Figure 4.3 are results from Choi and Chan176 who studied DRH* of supermicrometre particles with an electrodynamic balance. The results from Choi and Chan176 are approximately 4 % RH higher than the current measurements. The reason for this small difference is unclear. Chapter 4 76 Figure 4.3: Measured and predicted DRH* for the (NH4)2S04 + Gly system as a function of dry Gly mole fraction, = moles Gly / , (moles Gly + moles (NH4)2S04). (•) This study; (A) Choi and Chan;176 (--) Calculation 1; (•••••) Calculation 2; (—) Calculation 3. Calculations are described within the text. Figure 4.4 shows the DRH* results for mixed (NH 4) 2S0 4 + levoglucosan (Lev) particles. For comparison, the deliquescence relative humidity of pure levoglucosan particles is approximately 81.5 % RH. This value was determined using the same procedure that we used to determine DRH* of mixed inorganic-organic particles. The eutonic composition for the (NH 4) 2S0 4 + Lev system has not been measured but based on the current data we suggest that it is greater than or equal to a dry Lev mole fraction, x'Uv, of 0.6 + 0.1, as this composition corresponds to the lowest DRH* measured in the current experiments. Similar to (NH 4) 2S0 4 + Mai and (NH 4) 2S0 4 + Gly, DRH* decreases continuously with an increase Chapter 4 77 in organic mole fraction. No other group has measured DRH* for the (NH 4) 2S0 4 + Lev system. Figure 4.4: Measured and predicted DRH* for the (NH4)2S04 + Lev system as a function of dry Lev mole fraction, x1^ = moles Lev / (moles Lev + moles (NH4)2S04). (•) This study; (--) Calculation 1; (•••••) Calculation 2. Calculations are described within the text. Fulvic acids are a class of compounds with a range of functional groups depending on the source and isolation method. DRH* measurements of (NH 4) 2S0 4 internally mixed with fulvic acid (Ful) are plotted as a function of dry Ful mass fraction, w'F^ (primary horizontal axis) and dry Ful mole fraction, (secondary horizontal axis) in Figure 4.5. Chapter 4 78 The dry Ful mole fraction scale is approximate and was calculated using an estimated molecular weight of 645 g mol"1.197 ~\ 1 1 1 1 < 1 < 1 « 1 > r 0.0 0.1 0.2 0.3 0.4 0.5 0.6 + H h Ful + H h 0.0 0.025 0.05 0.075 0.1 0.15 0.2 0.25 x' Ful Figure 4.5: Measured and predicted DRH* for the (NH4)2S04 + Ful system as a function of dry Ful mass fraction, w?Vui = mass Ful / (mass Ful + mass (NH4)2S04). (•) This study; (V) Brooks et al.;173 (A) Chan and Chan;174 (--) Calculation 1; and (•••••) Calculation 2. Calculations are described within the text. The secondary scale of dry Ful mole fraction, A ' F u 1 = moles Ful / (moles Ful + moles (NH4)2S04), is approximate and based on an estimated molecular weight of 645 g mol"1 for this particular fulvic acid sample.197 Chapter 4 79 Brooks et al. 1 7 3 and Chan and Chan174 also measured water uptake of mixed (NH 4) 2S0 4 + Ful particles using submicrometre and supermicrometre particles, respectively. These results are also included in Figure 4.5 and are in agreement with the current observations of DRH*. As shown, DRH* for these particles does not change significandy up to 0.5 dry Ful mass fraction. This is not surprising as 0.5 dry Ful mass fraction corresponds to less than 0.2 dry Ful mole fraction. When mole fraction is known, this is the better variable than weight fraction for comparing DRH* values, as DRH* is linear with mole fraction, assuming ideality.154 When considering the dry Ful mole fraction, DRH* for (NH 4) 2S0 4 + Ful changes by about the same amount as for (NH 4) 2S0 4 + Mai, Lev, or Gly. In Figure 4.6, we compare the measurements of DRH* for all the systems we investigated (solid symbols). In addition, Figure 4.6 shows previous measurements from this laboratory of DRH* for (NH 4) 2S0 4 + glutaric acid (Glut) particles.182 This figure shows that DRH* values for the different systems are not statistically different from pure ammonium sulphate when the dry organic mole fraction is less than approximately 0.35. At a dry organic mole fraction of 0.6, the maximum deviation between the systems is approximately 10 % RH. This is discussed in more detail below. Chapter 4 80 Figure 4.6: Summary of the DRH* (filled symbols) and CRH50 (open symbols) results for (NH4)2S04 + organic systems from the current study and from previous work.182 (•, •) pure (NH4)2S04; (•, O) (NH4)2S04 + Mai; (A, A) (NH4)2S04 + Gly; (•, V) (NH4)2S04 + Lev; (•) (NH4)2S04 + Ful; and (•, O) (NH4)2S04 + Glut. Data is plotted in terms of water-soluble organic material (WSOM) mole fraction, A'VPSOM = moles WSOM / (moles WSOM + moles inorganic). The two overlapping hatched regions correspond to WSOM mole fraction in remote (marine) and urban aerosol particles as discussed within the text. Shaded regions show variation of data between each system. 4.3.2 Thermodynamic Calculations of DRH * as a Function of Composition In addition to measuring DRH*, the DRH* results are compared with thermodynamic calculations. This comparison provides a test of the accuracy and validity of these calculations for predicting the thermodynamic properties of inorganic-organic particles in the atmosphere. Chapter 4 81 As discussed above, the DRH* results for (NH 4) 2S0 4 + Mai and (NH 4) 2S0 4 + Gly correspond to complete deliquescence of (NH 4) 2S0 4. We assume that the current DRH* results for (NH 4) 2S0 4 + Lev and (NH 4) 2S0 4 + Ful also correspond to complete deliquescence of (NH 4) 2S0 4. This assumption is reasonable considering the range of concentrations studied and the trend in the measured DRH* data (DRH* either remains constant or decreases monotonically with the addition of organic material). We calculated complete deliquescence of ammonium sulphate as a function of composition by first determining the concentrations of the liquid ternary solutions that are saturated with respect to ammonium sulphate, and then by predicting the RH above each of these saturated solutions (see below for more details). In the first series of calculations we assumed the solutes behave ideally. In this case, the solubility of ammonium sulphate (in terms of molality) in the liquid ternary solutions equals the solubility of ammonium sulphate in pure water. Also assuming ideality of the solutes, the R H above the saturated solutions, and hence DRH* of ammonium sulphate, can be predicted with the following equation (see Section 2.2 above):169 4.1 R H = 100 %RH-« W = 100%RH-exp where <aw is the water activity, M w is the molecular weight of water (0.0L8 kg mol"1), and ntj is the molality of the solute j in the solution. Here we assume the inorganic salt is completely dissociated in the mixed solutions. Shown in Figure 4.2 through Figure 4.5 (labelled Calculation 1) are predictions of DRH* as a function of composition calculated with Equation 4.1 and assuming the solutes behaved ideally. For these calculations a solubility of 5.71 mol kg"1 at 293.15 K was used based on the Aerosol Inorganics Model by Clegg et al.198" 200 Clearly, Calculation 1 substantially underestimates DRH* for all systems even when the dry organic mole fraction is zero (pure ammonium sulphate particles). This is not surprising as electrolyte solutions depart significandy from ideality even in dilute solutions. The second set of calculations was based on a simplified version of a recent model by Clegg et al. 1 9 3 Their model relies upon existing models of inorganic-water198'200 and organic-water201 solutions in combination with thermodynamically consistent terms that take into account the interactions between ions and organic molecules. This method is analogous Chapter 4 82 to the model of Pitzer202 where binary and ternary interactions between species in solution are summed to give the activity coefficients of the species. In the model by Clegg et al.,193 the molal activity coefficients of an ion (y} and an organic solute (yn) in a liquid ternary solution are given as follows:193 4.2 ln(^.) = A \n{y. [ion - water]) + A \n(yi [ion - organic]) 4.3 ln(/„) = A ln(x„ [organic - water]) + A ln(/„ [ion - organic]) Each A term can be calculated independentiy and represents the contribution to the activity coefficient from ion-water, organic-water or ion-organic terms.193 The model by Clegg et al. 1 9 3 provides a relationship for the water activity with respect to the osmotic coefficient of the solution, <j>, as given by:193 \ If 4.4 V n J m; V J + ( r - 1 ) V ' // V J J Here, <fl is the osmotic coefficient contribution from the ionic-water interactions of the solution, <fl' is the contribution from the organic-water interactions, and <ff" is the contribution from ion-organic interactions.193 Equations 4.2 — 4.4 can be used to calculate the activity coefficients and osmotic coefficients for the liquid ternary solutions saturated with respect to ammonium sulphate. Then the RH above the liquid ternary solutions at complete deliquescence of ammonium sulphate can be calculated with the following equation (see Section 2.2 above): ( 4.5 R H = 100%RH-* W =100%RH-exp m, j J J where <j) is given by Equation 4.4. Shown in Figure 4.2 through Figure 4.5 are predictions based on Equations 4.4 and 4.5. For these calculations (labelled Calculation 2) we set the ion-organic interactions terms in Equations 4.2 - 4.4 to zero, as these parameters are not known for the systems studied. In this case, the solubility of ammonium sulphate in the liquid ternary solutions used in Equation 4.5 equals the solubility in pure water (5.71 mol kg"1). The first term in Equation 4.4 was determined with the mole fraction based model of Clegg et al., 1 9 8 , 1 9 9 and the second term in Equation 4.4, which is the contribution Chapter 4 83 from the organic solute to the osmotic coefficient, was set to zero. This is equivalent to assuming that the organic-water mixtures form ideal solutions. As shown in Figure 4.2 through Figure 4.5, Calculation 2 reproduces the current data up to 0.4 dry organic mole fraction. At higher dry organic mole fractions, the calculations slighdy under predict the measurements. The third set of calculations was similar to the second set of calculations except that the second term in Equation 4.4, - 1), was calculated with the UNIFAC (Universal Quasi-Chemical Functional Group Activity Coefficients) model.201 UNIFAC is a group contribution method that can be used for predicting thermodynamic properties of non-ideal aqueous organic solutions. Interaction parameters from Reid et al.203.were used in the UNIFAC calculations. Shown in Figure 4.2 and Figure 4.3 (labelled Calculation 3) are predictions based on this method. This procedure was not used to predict DRH* of (NH 4) 2S0 4 + Lev and (NH 4) 2S0 4 + Ful as the original UNIFAC model does not include interaction parameters for ring structures. Calculations 1—3 were also applied to previous measurements of DRH* of the (NH 4) 2S0 4 + Glut system.182 Shown in Figure 4.7 are the previous results as well as these thermodynamic calculations. The experimental results from other groups are also included for completeness.176,194 Similar to the other organic systems studied, Calculation 1 deviates significandy from measurements of DRH*. Both Calculations 2 and 3 agree with the measurements up to about 0.2 dry Glut mole fraction, but underestimate the measurements at higher dry Glut mole fractions. Chapter 4 84 Figure 4.7: Comparison of thermodynamic calculations with previously measured values of DRH* for (NH4)2S04 + Glut as a function of dry Glut mole fraction, ^ G l M = moles Glut / (moles Glut + moles (NH4)2S04). (—) Calculation 1; (•••••) Calculation 2; (—) Calculation 3; (•) Pant et al.;182 (V) Brooks et al.;171 (A) Choi and Chan;176 (O) Wise et al.184 Calculations are described within the text. Within the uncertainty of the measurements Calculations 2 and 3 reproduce the current data up to an organic mole fraction of 0.4 for (NH 4) 2S0 4 + Mai, (NH 4) 2S0 4 + Gly, and (NH 4) 2S0 4 + Lev. The maximum deviation between the current measurements and the calculations occurs for the (NH 4) 2S0 4 + Glut system. For this system, Calculations 2 and 3 were approximately 7 and 5 % RH below the measurements, respectively. Also, for all the systems we considered Calculation 3 was slightly better than Calculation 2. Chapter 4 85 4.3.3 Crystallisation of Ammonium Sulphate in Aqueous Organic Solutions Figure 4.8, Panels A — C, shows the current CRH measurements of (NH 4) 2S0 4 + Mai, (NH 4) 2S0 4 + Gly, and (NH 4) 2S0 4 + Lev. Also shown in Figure 4.8, Panel D, for comparison purposes, are data for (NH 4) 2S0 4 + Glut particles from a previous study.182 The data points in Figure 4.8 correspond to CRH50 and the vertical bars associated with each point correspond to the range over which crystallization was observed. 60 50 40 30 a 20 10 0 • • < • 1 1 (A) A t (C) i • l 1 l 1 l 1 l ' l 1 l (D) + J -cr- -Cr-TT-- D - ' 0 A' * O* • 1 h : * j : n 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Gly Figure 4.8: Crystallization of (A) (NH4)2S04 + Mai, (B) (NH4)2S04 + Gly, and (C) (NH4)2S04 + Lev from the current study and (D) (NH4)2S04 + Glut from previous work182 as a function of dry organic mole fraction, ^ 0 l g i m i c = moles organic / (moles organic + moles (NH4)2S04). Data points represent CRH50 and vertical bars indicate the range over which crystallization was observed. (O) this study; (•) Pant et al.;182 (•) Braban;194 (*) Braban and Abbatt;170 (A) Choi and Chan.176 Dashed lines represent a ARH offset of 45.2 % RH from the measured DRH* data sets as discussed in the text. Values of 0 % RH signify some or all particles were not observed to crystallize under dry conditions. 00 Chapter 4 87 CRH50 data for the (NH 4) 2S0 4 + Ful system was not measured because of experimental difficulties. For particles of pure (NH 4) 2S0 4, (NH 4) 2S0 4 + Mai, (NH 4) 2S0 4 + Gly, and (NH 4) 2S0 4 + Lev, the contact angle with the PTFE surface was approximately 90 °. In contrast, the contact angle between (NH 4) 2S0 4 + Ful particles and the PTFE surface was close to 0 ° at RH less than approximately 50 % RH, which is close to the expected CRH values for this system. Under these circumstances, we could not rule out the possibility that excessive contact with the PTFE surface would initiate crystallization in these particles, thus we did not determine the CRH values for (NH 4) 2S0 4 + Ful particles. As shown in Figure 4.8, Panels A - D, pure (NH 4) 2S0 4 (dry organic mole fraction = 0) crystallized over the range 37.1 - 34.3 % RH, and half the particles were crystalline at 35.0 % RH in this study. This is in good agreement (within 3 % RH) with most previous studies measuring homogeneous crystallization of pure (NH 4) 2S0 4 using various techniques (see for example, Cziczo et al.,2 0 4 Martin,205 and Tang and Munkelwitz206). Based on this, it is suggested that the crystallization of (NH 4) 2S0 4 is not affected by the presence of the PTFE surface supporting the particles in the current experiments and crystallization occurred by homogeneous nucleation. Also shown in Figure 4.8 are measurements of crystallization reported by other groups. Choi and Chan1 7 6 studied crystallization of (NH 4) 2S0 4 + Mai, (NH 4) 2S0 4 + Gly, (NH 4) 2S0 4 + Glut particles and obtained values significandy above the current results. This difference cannot be explained by particle size, as similar sizes were used in both experiments. One explanation is that the particles in the Choi and Chan176 experiments contained trace amounts of contamination that acted as a heterogeneous nucleus for crystallization. Braban,194 and Braban and Abbatt170 studied the crystallization of (NH 4) 2S0 4 + Glut and (NH 4) 2S0 4 + Mai particles, respectively, and obtained results that are lower than ours; however, this difference can be explained by differences in particle size. Classical nucleation theory predicts that the crystallization relative humidity decreases with the volume of the particle, and the particle volume in the experiments by Braban, 1 9 4 and Braban and Abbatt170 was approximately 5 orders of magnitude less than the particle volume in the current studies. Not included in Figure 4.8, Panel A, are results by Hameri et al. 1 7 8 and Prenni et al. 1 8 3 Both groups studied crystallization of submicrometre (NH 4) 2S0 4 + Mai particles using a Chapter 4 88 tandem differential mobility analyzer. Hameri et al. 1 7 8 did not observe crystallization of particles with a composition of 0.5 dry malonic acid mole fraction, and Prenni et al. 1 8 3 did not observe crystallization of particles with a composition of about 0.3 dry malonic acid mole fraction. These results are consistent with the current measurements when the difference in particle size is taken into account. As expected, the results in Figure 4.8, Panels A - D, show that the CRH50 decreases with increasing dry organic mole fraction for all the mixed inorganic-organic systems studied. However, there are significant differences between each system. For example, at a dry organic mole fraction of about 0.5, (NH 4) 2S0 4 + Mai particles did not crystallize even at 0 % RH, whereas (NH 4) 2S0 4 + Glut particles crystallize at approximately 30 % RH. In Figure 4.6 we compare the results of DRH* and CRH50 for all the systems in this study and a previous study.182 This figure shows that the CRH50 results vary significandy from system to system at large dry organic mole fractions. Also the variation in the CRH50 results are considerably larger than the variation in the DRH* results. For example at 0.6 dry organic mole fraction, DRH* varies by at most 10 % RH, whereas the CRH JO results vary by 25 % RH. This wide variation in CRH50 results can be reasoned with classical nucleation theory. As mentioned earlier, we suggest that the current CRH50 results correspond to homogeneous nucleation. According to classical nucleation theory, the rate of homogeneous nucleation, / h o m , in an aqueous solution can be expressed as the following (see Section 2.4 and the Appendix):207,208 4-6 Jhom = a0 exp 16flyV AG' [ 3k3T3(lnS)2 kT J where a0 is the pre-exponential factor, vis the molecular volume, ^is the interfacial tension, k is the Boltzmann constant, T is the temperature, S is the supersaturation, and AG' is the activation energy for molecular motion across the cluster-matrix interface, which is a function of the viscosity of the solution.207 Based on Equation 4.6, one possible explanation for the variation in the CRHS0 results is that the interfacial tension varies significantly from system to system at high organic mole fractions. This could lead to considerably different nucleation rates at similar RH. Another possible explanation is that at low R H and high dry organic mole fractions, viscosity may be significant and vary from system to system. In this case, viscosity will limit the rate of nucleation (through AG'). Yet another possible Chapter 4 89 explanation is that the supersaturation at a given R H varies significantly with the type of organic material, due to non-ideal behaviour. Colberg et al. 2 0 9 have shown that the R H of crystallization for H 2 S 0 4 / N H 3 / H 2 0 aerosol particles can be estimated by subtraction of a constant relative humidity (ARH) from the DRH* curves. We have also recendy used this procedure to predict the CRH50 of (NH 4) 2S0 4 + Glut particles and found that this procedure works well for a Glut mole fraction of less than O.4.182 Shown as dashed lines in Figure 4.8, Panels A - D, are predictions of CRH50 based on this procedure. For these predictions a A R H offset of 45.2 % RH was used. Clearly, CRH50 for (NH 4) 2S0 4 + Mai, Gly, or Lev is significandy below these curves even with low organic content. We conclude that this procedure is not appropriate for most of the systems we studied. 4.3.4 Atmospheric Implications Here we estimate the effect of organics on the deliquescence and crystallization of inorganic particles in remote (marine) and urban areas by comparing the DRH* and CRH50 results with literature estimates of the amount of water-soluble organic material (WSOM) in these areas. Based on several field studies, Heintzenberg155 estimated that the average composition of fine aerosol particles in remote (marine) areas is 11 % organic carbon (by mass), 22 % sulphate, and 3 % nitrate, and the average composition of fine aerosol particles in urban areas is 31 % organic carbon (by mass), 28 % sulphate, and 6 % nitrate. Furthermore, we estimate that the fraction of organic carbon that is water-soluble is between 41 - 80 % (by mass) in remote areas and between 29 - 66 % (by mass) in urban areas, based on measurements of water-soluble organic carbon in the troposphere.210"216 These values should be considered as rough estimates as they are based on limited data. From the numbers presented above we calculate that the average dry WSOM mole fraction is about 0.21 - 0.35 in remote (marine) areas and 0.28 - 0.47 in urban areas. (Here the dry WSOM mole fraction is defined as moles WSOM / (moles WSOM + moles inorganic). In order to calculate the dry WSOM mole fraction from the % organic carbon, we followed the procedure outlined by Martin et al. 1 5 4 Briefly, the mass of ammonium was not considered when calculating the dry WSOM mole fraction as it was assumed that the sulphate and nitrate occur as molecular units combined with ammonium or protons. Also, it was assumed Chapter 4 90 that each organic molecule contained an average of five carbon atoms, which is consistent with measured organic molecular weights in remote aerosol particles.213 Nevertheless, further studies are needed to verify the accuracy of this number. The two overlapping hatched regions in Figure 4.6 (labelled Urban and Remote) represent the range of dry WSOM mole fractions we calculated for urban and remote (marine) areas above. For the remote (marine) region, the measured DRH* values do not deviate significandy from the D R H of pure ammonium sulphate (the difference is less than the uncertainty of the measurements). Based on this, we conclude the organics, on average, are only a minor perturbation on the D R H of the pure inorganic particles in remote (marine) areas. Even for the urban region the difference in DRH* from D R H of pure ammonium sulphate is small. This difference ranges from 0 - 7 % RH, which is close to the uncertainty of the current measurements. In contrast, the organics appear to have a larger effect on the crystallization of inorganic particles. For the remote (marine) region, the difference between the CRH50 of pure (NH 4) 2S0 4 and the mixed inorganic-organic ranges from about 0 -15 % RH and depends on the type of inorganic-organic particle. This difference is extended to about 0 - 2 5 % RH in the urban region. If we also consider the measurements by Braban,194 and Braban and Abbatt,170 this difference is even larger. We conclude that the organics on average may decrease the CRH50 of pure inorganic particles significandy and this effect depends on the type of organic material. Recendy Martin et al. 1 5 4 estimated that an upper limit to the average dry WSOM mole fraction in the atmosphere is approximately 0.27. This value was determined by converting atmospheric mass burdens of sulphate, nitrate, and organic material from the IPCC SCI scenario for 2000217 into relative global mole burdens. If we compare this value with the current DRH* and CRH50 data, we obtain similar conclusions to the conclusions reached above for remote (marine) regions. That is, the organics are only a minor perturbation to the D R H of inorganic particles. This is the same conclusion reached previously by Martin et al.1 5 4 based on a more limited data set. In contrast, organics may decrease the CRH50 of inorganic particles slighdy and this decrease will depend on the type of organic material. Several limitations to the discussions above need to be considered. First, the discussions above are based on average dry organic mole fractions. In reality, atmospheric particles have a broad range of dry organic mole fractions, and some areas will have significandy higher water-soluble organic content than represented in Figure 4.6 (see for Chapter 4 91 example, Aklilu and Mozurkewich218). For a more accurate description, this variable in the dry organic mole fraction needs to be considered. Second, the effect of surfactants, heterogeneous nucleation, and mass transfer were not considered. Studies are needed to determine if these factors can affect the phase transitions of mixed inorganic-organic particles in the atmosphere. Third, to determine the average dry organic mole fractions in the atmosphere, we assumed that each organic molecule contained five carbon atoms as done previously.154 As mentioned above, further studies are needed to verify the accuracy of this estimate. Fourth, as indicated above, particle size is important for crystallization. The current results of CRH50 should be considered as upper limits for these systems since this study used particle sizes greater than typically found in the atmosphere. The R H of crystallization for inorganic particles is not very sensitive to particle size, but initial comparisons suggest that the CRH50 of inorganic-organic particles vary significantly with particle size. Finally, these conclusions are still based on a limited data set. Studies of other inorganic-organic particles that are relevant to the atmosphere are needed. 4.4 Conclusions We have measured DRH* of four, atmospherically relevant internally mixed inorganic-organic systems. The current measurements agree well with previous results and show that DRH* has little dependence on the type of organic material. DRH* of (NH 4) 2S0 4 decreases with increasing organic content, but remains within 10 % RH of pure (NH 4) 2S0 4 for each of the systems we have studied up to a dry organic mole fraction of 0.6. The thermodynamic calculations based on a simplified version of the model from Clegg et al. 1 9 3 are in agreement with measured values of DRH* up to dry organic mole fraction of approximately 0.4 for most of the systems studied. The conclusions from crystallization measurements made for (NH 4) 2S0 4 + Mai, (NH 4) 2S0 4 + Gly, and (NH 4) 2S0 4 + Lev show that even for particles with dry organic mole fraction as low as 0.2, crystallization behaviour for internally mixed inorganic-organic particles depends on type of organic material. Therefore, mixed inorganic-organic systems may be more likely to exist as liquid particles. 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C R Y S T A L L I Z A T I O N O F A Q U E O U S I N O R G A N I C - M A L O N I C A C I D P A R T I C L E S : N U C L E A T I O N R A T E S , D E P E N D E N C E O N S I Z E , A N D D E P E N D E N C E O N T H E A M M O N I U M - T O - S U L P H A T E R A T I O 5.1 Introduction Aerosols, suspensions of solid or liquid particles in a gas, may play a significant role in the Earth's atmosphere. For example, aerosol particles influence the chemistry of the atmosphere by providing a medium for heterogeneous reactions.219'220 Aerosol particles also affect climate direcdy by absorbing and scattering solar radiation and indirecdy by acting as ice nuclei or cloud condensation nuclei.219"222 Atmospheric aerosol particles can undergo several types of phase transitions. An example of an atmospherically relevant phase transition is crystallization, which here refers to the crystallization of a solute in an aqueous solution droplet at a low relative humidity (in this case water is considered the solvent). An example of crystallization includes the formation of crystalline ammonium sulphate from an aqueous ammonium sulphate droplet at a low relative humidity (RH). This process is also often called efflorescence. Here the general term crystallization is used rather than efflorescence since the latter term implies that water will completely evaporate from a droplet after crystallization, which is not always the case for a multi-component particle even at low RH. 2 2 3 Crystallization is a kinetic process due to the free energy barrier associated with nucleation of a solute in aqueous solution droplets. As a result, aerosol particles typically do not crystallize at the same R H as they deliquesce.221 (Deliquescence refers to when particles take up water to form solution droplets.) In the absence of a heterogeneous nucleus, crystallization occurs by homogeneous nucleation. Knowledge of the conditions required for crystallization of atmospheric particles is necessary to predict the phase of the particles. This information is, in turn, necessary to A version of this chapter has been published. Parsons, M. T.; Riffell, J. L.; Bertram, A. K. Crystallization of Aqueous Inorganic-Malonic Acid Particles: Nucleation Rates, Dependence on Size, and Dependence on Ammonium-to-Sulphate Ratio, J. Phys. Chem. A, 2006, 110, 8108 -8115. Reproduced with permission from The Journal of Physical Chemistry A, 2006,110, 8108 - 8115. Copyright 2006 American Chemical Society. Chapter 5 97 predict the reactivity of particles, the amount of light they scatter and absorb, and their ability to act as ice nuclei.219'221 Field measurements have shown that a majority of the fine particulate mass (particles less than 2 urn in diameter) in the troposphere consists of sulphate, ammonium, and nitrate ions, as well as organic material.219'220 An average composition of urban fine particles, based on measurements at several sites, is 28 % sulphate, 31 % organic carbon, 8 % ammonium, 9 % elemental carbon, and 6 % nitrate by weight.224 Organic material is believed to contribute approximately 20 - 50 % to the total fine aerosol mass at continental mid-latitudes.225 Also, composition measurements of single particles have shown that organic material is often internally mixed with sulphate in the troposphere.226"230 Over the past approximately 25 years the homogeneous crystallization of aqueous inorganic droplets such as aqueous (NH 4) 2S0 4 has been studied extensively (see, for example, the review by Martin221 and references therein). More recendy, researchers have investigated the homogeneous crystallization of aqueous inorganic particles internally mixed with organic surfactants231,232 as well as aqueous inorganic particles internally mixed with water soluble organic material (i.e., mixed aqueous organic-inorganic particles).223'232"244 Nevertheless, more research is needed on this topic in order to completely understand crystallization in aqueous organic-inorganic particles in the atmosphere. In particular, a better fundamental understanding of the underlying physical chemistry is needed. In the following, the crystallization of aqueous inorganic-malonic acid particles is investigated using an electrodynamic balance made in-house, with the general aim of improving the fundamental understanding of crystallization of aqueous inorganic-organic particles. Malonic acid (Mai) was chosen for these studies since it is typically one of the most abundant dicarboxylic acids observed in field studies and because dicarboxylic acids are a significant component of condensed phase organic material found in the troposphere.245"247 In the first series of measurements, the crystallization of aqueous (NH 4) 2S0 4-Mal particles with diameters between 10 and 30 um was investigated. Specifically, the R H at which 50 % of the particles partially or completely crystallized was determined, which is referred to as the 50 % crystallization relative humidity (CRH50) for the remainder of the document. The crystallization of these aqueous particles has been investigated previously by several groups, but some of the results are in disagreement.223,237'243 Chapter 5 98 In the second series of measurements, the CRH50 was investigated for aqueous (NH4)3H(S04)2-Mal and aqueous NH 4 HS0 4 -Mal particles, also with diameters between 10 and 30 [im. Most previous studies on the crystallization of aqueous inorganic-organic particles have used (NH 4) 2S0 4 as the inorganic component. In this case the ammonium-to-sulphate ratio is two. In the troposphere, however, the ammonium-to-sulphate ratio can vary from two to zero.222 Studies on inorganic-organic particles with ammonium-to-sulphate ratios less than two are needed. In the third series of measurements, the effect of particle size on the crystallization R H (CRH) values of aqueous (NH 4) 2S0 4 particles and aqueous (NH 4) 2S0 4-Mal particles was investigated, and homogeneous nucleation rates as a function of R H from the crystallization data were determined. The homogeneous nucleation rate, / h o m , is defined as the number of nucleation events (of solid ammonium sulphate) per unit volume of aqueous solution per unit time. Note this value is also often referred to as the homogeneous nucleation rate coefficient in the atmospheric literature. Previous laboratory studies suggest that the CRH of aqueous inorganic droplets relevant for the atmosphere (such as aqueous (NH 4) 2S0 4 and NaCl droplets) are not very sensitive to particle size (see, for example, Martin221, Cziczo et al.,2 4 8 Onasch et al.,2 4 9 and references therein). Also, previous studies that combined results from several laboratories suggest that the nucleation rate of crystalline (NH 4) 2S0 4 in aqueous (NH 4) 2S0 4 particles is a strong function of RH. 2 4 9 However, the size dependence of CRH and the homogeneous nucleation rates as a function of R H for aqueous inorganic-organic particles have not been investigated. Information on the size dependence and nucleation rates is necessary to accurately extrapolate laboratory results to the atmosphere and to understand the crystallization process in general. These data can also serve as a test for theories on homogeneous nucleation. Often classical nucleation theory has been used to describe nucleation in aqueous inorganic particles (see, for example, Martin221, Onasch et al.,2 4 9 Oatis et al.,2 5 0 and Richardson and Snyder251). In the following, classical nucleation theory is also used to analyze the current nucleation rate data for aqueous (NH 4) 2S0 4 particles. From the analysis the interfacial tension between the crystalline ammonium sulphate critical nucleus and an aqueous ammonium sulphate solution was determined. Finally, the atmospheric implications of all these results are discussed. Chapter 5 99 5.2 Experimental An electrodynamic balance (EDB) was used to study the crystallization of single levitated, charged droplets (see Figure 5.1, Panel A). The EDB is a double-ring electrode configuration with two end cap electrodes, based on the configuration used by the Agnes group at Simon Fraser University,252"254 which in turn was adapted from that reported by Davis et al. 2 5 5 An AC potential (2.3 kV, 100 to 700 Hz) was applied to the double-ring electrodes and DC potentials (-10 to -100 V) were applied to the end cap electrodes to balance the gravitational forces on the charged particles. Chapter 5 100 Figure 5.1: Panel A: Electrodynamic balance (EDB) and optical system for determining the phase of levitated particles. Panel B: Image of the elastically scattered light from a completely liquid aqueous (NH4)2S04-Mal particle recorded prior to crystallization at 35.7 % RH. Panel C: Image of the elastically scattered light from the same particle recorded after crystallization at 29.6 % RH. The EDB was located inside a stainless steel chamber and operated at atmospheric pressure and ambient temperature with all measurements performed between 295 and 300 K (as measured with a thermocouple inside the EDB). The stainless steel chamber was located in the optical path of a transmission optical microscope (not shown in Figure 5.1, Panel A) with a 15 x objective (numerical aperture = 0.4 and resolution « 0.6 urn). The optical Chapter 5 101 microscope with a white light source was used to measure pardcle diameter with an uncertainty of about ± 1 [xm. Each pardcle was assumed to be spherical to calculate its volume. The phase of each pardcle was determined by analyzing the pattern of the elastically scattered light from a He-Ne laser (i.e., the angular distribution of light scattered by the particles). Radiation from a linearly polarized 10 mW He-Ne laser was used to illuminate the levitated particles. The scattered light was imaged on a charge coupled device (CCD) camera using a lens system as shown in Figure 5.1, Panel A. Both the laser beam and CCD camera were in the horizontal plane and the CCD camera was positioned at an angle of 90 ° with respect to the laser beam. The lens system and CCD camera were adjusted so that the image of the particle was out of focus, resulting in a pattern from the elastically scattered light. If the particles are completely liquid the elastically scattered light gives sharp lines (a fringe pattern). If the particles contain solid material, the pattern is irregular and fluctuates with a high frequency. Shown in Figure 5.1, Panels B and C, are images recorded before and after crystallization. Panel B shows an image of the scattered light for an aqueous (NH 4) 2S0 4-Mal particle prior to crystallization (the fringe pattern confirms that the particle is completely liquid). Panel C shows an image of the scattered light for the same particle just after crystallization (the irregular pattern confirms that the particle contains solid material). From the images of the scattered light, it was possible to determine direcdy if the particles were completely liquid or contained solid material. This method is similar to the method used by others in the past to elucidate the phase of single levitated particles.256"259 Note that this method cannot distinguish between particles that are partially solid and particles that are completely solid from the scattering images. Also, in our experiments we cannot determine if the solid particles are crystalline or amorphous. Previous studies have shown that solid particles of the compounds used in this study are crystalline.223,260 Solutions used in this study were prepared gravimetrically, dissolved in 18.2 MQ water (Millipore Simplicity 185), and filtered twice with a 0.02 |4,m filter (Whatman Anodisc 25) before use. Chemicals used were: Mai (Aldrich, 99 %), (NH 4) 2S0 4 (Fisher, 99.8 %), N H 4 H S 0 4 (Alfa Aesar, 99.9 %), and aqueous H 2 S0 4 (Alfa Aesar, 50.0 % v/v). Particles were introduced to the system from a drop-on-demand particle generator (MicroFab Technologies, Inc.) loaded with a solution prepared as discussed above. A voltage pulse was applied to the piezoelectric material of the droplet generator, which caused Chapter 5 102 the material to constrict around a glass tube inside the droplet generator and eject a droplet through an orifice at the end of the glass tube. The glass tube in the pardcle generator used in this study had an orifice diameter of 30 [Jim. Charging of the droplets occurred by induction. Different droplet sizes (10-30 [im in diameter) were produced by varying the voltage applied to the piezoelectric material in the particle generator. The R H in the chamber, which was monitored with a dew point hygrometer at both the inlet and the oudet of the chamber, was controlled by the continuous flow of a mixture of dry and humidified N 2 (99.999 %, Praxair). Total flow rates ranged from 150 to 200 cm3 min - 1 at standard temperature and pressure. Upon trapping a single particle, the R H in the chamber was increased to above 85 % RH to ensure the particle was completely liquid. The R H inside the trap was then adjusted to about 5 - 10 % RH above the estimated CRH for the particle and then slowly decreased at a rate of -0.2 % RH min"1. The deliquescence R H (DRH) was also measured after some crystallization experiments by increasing the R H at a rate of 0.2 % RH min"1. Each particle was observed for a maximum of about one hour. R H uncertainty for individual measurements was about + 1 % RH at low R H (near the CRH) and about ± 3 % RH at high R H (near the DRH) based on the accuracy of the R H monitoring equipment. 5.3 Results and Discussion 5.3.1 Crystallisation of Aqueous (NHJ^O^Mal Particles Shown in Figure 5.2 are the CRH50 results obtained for particles of (NH 4) 2S0 4 mixed with Mai with diameters between 10-30 (xm. As mentioned above, CRH50 refers to the R H at which 50 % of the particles are partially or completely crystallized. From this type of information one can predict the range over which particles in the atmosphere will be completely liquid and the range over which they will contain some solid material. This information is, in turn, important for predicting the ice nucleation properties and the light scattering properties of aerosols. For example, if the particles are completely liquid, then ice nucleation in the particles will occur by homogeneous nucleation. However, if the particles contain some solid material (either partially crystalline or fully crystalline), then ice nucleation can occur by heterogeneous nucleation. The presence of solids can shift the mode of ice Chapter 5 103 nucleation from homogeneous to heterogeneous and lower the supersaturation required for ice formation. Also note that since the experimental technique cannot distinguish between partially or completely crystalline particles, it was not possible to determine from the current results if malonic acid crystallizes after the crystallization of ammonium sulphate. However, previous measurements by Braban et al. 2 2 3 suggest that crystalline ammonium sulphate is a poor heterogeneous nucleus for the crystallization of malonic acid. 50-45-40-35-X 30-a: 25-o a: 20-oc 15-10-5-0-Figure 5.2: CRH50 of (NH4)2S04-Mal particles as a function of x!Mai = (moles Mai) / (moles Mai + moles (NH4)2S04). Key: (*) Braban and Abbatt;223 (A) Choi and Chan;237 (•) Parsons et al.243 (Chapter 4), (O) Current data. The vertical bars indicate the range of RH over which crystallization was observed for the current data. Values of 0 % RH indicate that less than 50 % of the particles crystallized, even under dry conditions. Chapter 5 104_ In Figure 5.2, the composition of the particles are described by the dry mole fraction of Mai, = moles Mai / (moles Mai + moles inorganic). Since crystallization is a stochastic process, droplets with the same x'Mai did not always crystallize at the same RH. The open circles in Figure 5.2 represent the CRH50 of the particles, and the vertical bars associated with these symbols represent the range of R H over which crystallization was observed for all particles tested. 14-55 individual crystallization events were observed at each composition. Note that the data points at 0 % RH indicate that less than 50 % of the particles crystallized, even under dry conditions. Also included in Figure 5.2 are the results from previous measurements using droplets suspended on a hydrophobic surface discussed in Chapter 4 (Parsons et al.243) as well as the previous measurements that used an E D B 2 3 7 and an aerosol flow tube.223 The current results are in good agreement with the previous measurements obtained with particles on a hydrophobic surface discussed in Chapter 4 (Parsons et al.243). This confirms that the previous measurements in Chapter 4 (Parsons et al.243) were not influenced by the surface supporting the particles. The current results are significantiy lower (with 95 % confidence) than previous EDB measurements, which utilized 1 0 - 1 5 um particles with xMai = O.5.237 This conclusion is based on a Student's t-test, which takes into account the statistics of the current measurements and the statistics of the previous measurements. The particles studied in the previous EDB measurements237 may have contained trace amounts of impurities that acted as heterogeneous nuclei for the crystallization process. The results for the submicrometre particles by Braban and Abbatt223 appear to be slighdy lower than the current results; however, this small difference can be explained by differences in particle size. Classical nucleation theory predicts that the crystallization relative humidity decreases with the volume of the particle, and the particle volume in the experiments by Braban and Abbatt223 was approximately 5 orders of magnitude less than the particle volume in the current study. The results from other studies on submicrometre particles (not shown in Figure 5.2) are also consistent with the current measurements if the difference in particle size is taken into account.238,244 See Chapter 4 (Parsons et al.243), Section 4.3.3, for a full discussion. Chapter 5 105 5.3.2 Crystallisation of Aqueous (NH4)3H(S04)2-Mal andNH4HS04-MalParticles Shown in Figure 5.3 are the CRH50 values obtained for (NH4)3H(S04)2-Mal and NH 4 HS0 4 -Mal with particle diameters between 10-30 um. 6 -10 individual crystallization events were observed at each composition. Also included in Figure 5.3 are the current results for (NH 4) 2S0 4-Mal for comparison. As noted above, the data points at 0 % RH indicate that less than 50 % of the particles crystallized, even under dry conditions, and the vertical bars associated with the symbols represent the range of R H over which crystallization was observed for all particles tested. 4 5 1 40-35-30-X 25-• 20-15-10-5-0--> r " i 1 r i 0 - A A 0 A — i 1 1 ' 1 ' 1 1 1 1 1 • i 0.0 0.1 0.2 0.3 0.4 0.5 0.6 x' Mai Figure 5.3: CRH50 of inorganic-Mai particles as a function of x!Mai = (moles Mai) / (moles Mai + moles (NH4)2S04). Key: (•) (NH4)2S04-Mal; (O) (NH4)3H(S04)2-Mal; (A) NH 4HS0 4-Mal. The vertical bars indicate the range of RHovet which crystallization was observed for the current data. Values of 0 % RH indicate that less than 50 % of the particles crystallized, even under dry conditions. Chapter 5 106 First the current results for pure aqueous N H 4 H S 0 4 and (NH 4) 3H(S0 4) 2 particles (xMai = 0) a r e briefly discussed. Several groups have investigated the crystallization of these inorganic particles248'261"268 and the current results are in reasonable agreement with most previous data. For example, for an ammonium-to-sulphate ratio of 1.0, Spann and Richardson269 and Cziczo et al. 2 4 8 did not observe crystallization under dry conditions and Tang and Munkelwitz268 noted that crystallization was not observed for some particles under dry conditions, and was observed at an R H as high as 22 % RH for other particles. For an ammonium-to-sulphate ratio of 1.5 the current observed CRH50 was 30.9 ± 2.7 % RH. Tang and Munkelwitz268 observed crystallization from 44 - 35 % RH, and Spann and Richardson269 observed crystallization at a value of 35 % RH. However, Martin et al. 2 6 5 estimated that crystallization occurred over the range of 26 - 21 % RH (+ 3 % RH), which agrees with the current measurements when the uncertainties are considered. The D R H for the pure inorganic particles has also been measured in the current study, and the measurements are consistent with calculations.270,271 The current values of CRH50 as a function of x'ml show that for ammonium-to-sulphate ratios of 1.5 and 2.0, malonic acid decreases the CRH50 of the pure inorganic particles by less than 7 % RH when x'Ma] < 0.25. For x M a ] ~ 0.5, malonic acid can modify the CRH50 by up to 35 % RH. For an ammonium-to-sulphate ratio of 1.0, the presence of Mai does not significantiy modify the CRH50 for the entire range of x'Mll studied. For these particles, crystallization was not observed with the exception of two aqueous N H 4 H S 0 4 particles at about 3 % RH. Note that the piC, for Mai is 2.85.272 Hence, Mai is negligibly dissociated in supersaturated aqueous inorganic-Mai solutions. For example, in a 5 M aqueous solution of Mai (close to the concentration of Mai in the aqueous inorganic-Mai particles in the current experiments), < 2 % of the malonic acid is dissociated, and the amount dissociated is reduced in an acidic solutions. Chapter 5 107_ 5.3.3 Crystallisation of Aqueous (NH4)^04 and Aqueous (NH4)^S04-Mal Particles as a Function of Varticle Si\e Shown in Figure 5.4 are results from crystallization measurements as a function of particle volume (V) and diameter (D) for aqueous (NH 4) 2S0 4 and aqueous (NH 4) 2S0 4-Mal particles with x'Mai = 0.36. Note that Figure 5.4 does not report the CRH50, rather each data point represents one observed crystallization event. For clarity, error bars have not been included in this figure. As mentioned above, the uncertainty in R H at which the particles crystallize is approximately ± 1 % RH and the uncertainty associated with determining the particle diameter is ± 1 (im. The results shown in Figure 5.4 illustrate that the CRH for aqueous (NH 4) 2S0 4 particles is rather insensitive to particle size as expected. Based on a fit to the data, the CRH of aqueous (NH 4) 2S0 4 particles decreases by 1 ± 1 % RH (95 % confidence) when the volume decreases by an order of magnitude. As mentioned above, previous laboratory results suggest that the C R H of aqueous inorganic particles, such as (NH 4) 2S0 4, that are typically found in the atmosphere are relatively insensitive to particle volume (see, for example, Martin,221 Cziczo et al.,2 4 8 Onasch et al.,2 4 9 and references therein). The current results are consistent with these suggestions. Chapter 5 108 Dhim] 6 8 10 15 20 30 40 50 V[10"16m3] Figure 5.4: CRH of single particles as a function of particle volume, V, for (NH4)2S04 and (NH4)2S04-Mal particles. Key: (O) (NH4)2S04; (•) (NH4)2S04-Mal = 0.36). The top abscissa indicates the diameter, D, of each particle. The uncertainty in RH at which the particles crystallize is approximately ± 1 % RH and the uncertainty associated with deteirrririing the particle diameter is ± 1 fjim. Each data point represents one observed crystallization event. Solid lines are linear fits to each data set to guide the eye and dashed lines are the 95 % confidence bands associated with each linear fit. In contrast, the CRH for (NH 4) 2S0 4-Mal particles with x'Msi = 0.36 is more sensitive to particle size. Based on a fit to these data, the CRH for (NH 4) 2S0 4-Mal particles decreases by 6 ± 3 % RH (95 % confidence) when the volume decreases by an order of magnitude. These are the first size dependent measurements of the CRH of atmospherically relevant aqueous inorganic-organic particles. Chapter 5 109 5.3.4 Nucleation Rates in Aqueous (NHJ^O,, and Aqueous (NHJ^O^Mal Particles For aqueous (NH 4) 2S0 4 and aqueous (NH 4) 2S0 4-Mal (x M a ] = 0.36), 55 and 39 crystallization events were observed, respectively. Shown in Figure 5.5 is the number of particles remaining completely liquid, N, as a function of RH. Note that the data illustrated in Figure 5.5 is the same data shown in Figure 5.4, but presented in a different way. From the information shown in Figure 5.5 one can determine homogeneous nucleation rates of solid ammonium sulphate in aqueous (NH 4) 2S0 4 and aqueous (NH 4) 2S0 4-Mal droplets (see below). There appears to be a discontinuity at about 25 % RH in Figure 5.5, Panel B. However a discontinuity is not evident in Figure 5.4, which displays the same data as in Figure 5.5 but in a different format. Hence, the discontinuity in Figure 5.5, Panel B, is likely due to noise in the data. Chapter 5 110 Figure 5.5: Panel A: number of particles remaining completely liquid, N, as a function of if/7 for (NH4)2S04. Panel B: number of particles remaining completely liquid, N, as a function of RH for (NH4)2S04-Mal ( A ^ = 0.36). As mentioned above, the homogeneous nucleation rate, / h o m , is defined as the number of nucleation events of solid per unit volume of solution per unit time. The homogeneous nucleation rate in liquid droplets can be described with the following equation, corresponding to first-order kinetics:221'273 M J ^ { R H ) = r i N ( m ) jhom\ J V-N{RH) dRH Chapter 5 111 where N(RH) is the total number of liquid particles (not including droplets that have crystallized), and the product V-N(RH) is the total volume of liquid particles (again, not including droplets that have crystallized), dN(RH) is the number of droplets observed to crystallize between R H and (RH - dRH), and r is the rate of change of the RH, which is -0.2 % RH min 4 in the current experiments. Equation 5.1 assumes that the rate limiting step is nucleation of the solute and that only one nucleation event leads to the solidification of the droplet, which is a reasonable assumption for the conditions used in this study. dAT(RH)/dRH was determined by obtaining N versus R H from the current experimental data. N versus R H is illustrated in Figure 5.5. Then at each data point diV(RH)/dRH was calculated by the central difference approximation, which is a numerical method for differentiation. V-N(RH) was determined by summing the volume of all the liquid droplets (not including droplets that have partially or completely crystallized) at each CRH measurement. From dN(RH)/dRH and V-N(RH) one may determine / h o m using Equation 5.1. Shown in Figure 5.6 is / h o m versus R H for aqueous (NH 4) 2S0 4 and aqueous (NH4)2S04-Mal particles ( x ^ = 0.36) calculated using Equation 5.1 and the current crystallization results (Figure 5.5). Clearly, / h o m for aqueous (NH 4) 2S0 4 particles increases rapidly with a decrease in R H for R H values less than approximately 40 % RH. In contrast, the homogeneous nucleation rate of solid (NH 4) 2S0 4 in aqueous (NH 4) 2S0 4-Mal particles (xMai = 0-36) is less sensitive to RH, as can be seen by the slower increase in Jhom with a decrease in RH. Chapter 5 112 RH [% RH] Figure 5.6: Homogeneous nucleation rate, Jhom, as a function of RH for the (NH4)2S04 and (NH4)2S04-Mal systems. Key: (O) (NH4)2S04; (•) (NH4)2S04-Mal (x"M3l = 0.36); lines are to guide the eye and have no physical meaning. The trends observed in Figure 5.6 are consistent with the size dependent results shown in Figure 5.4. If / h o m is a very strong function of RH, then one would expect that the CRH is a weak function of particle size. This is because a small change in R H will compensate for a large change in droplet volume. However, if / h o m is a weaker function of RH, then one would anticipate that the CRH is a stronger function of particle size. In this case the R H would have to change significantly to compensate for a large change in droplet volume, based on the kinetics of homogeneous nucleation in aqueous droplets. 5.3.5 Analysis of the Nucleation Rates Using Classical Nucleation Theory In the following, classical nucleation theory and the nucleation rates obtained in the aqueous (NH 4) 2S0 4 experiments are used to calculate the interfacial tension between a Chapter 5 113 crystalline (NH 4) 2S0 4 critical nucleus and an aqueous (NH 4) 2S0 4 solution. Note that this same analysis was not carried out for aqueous (NH 4) 2S0 4-Mal particles due to a lack of information on the thermodynamic properties of concentrated (NH 4) 2S0 4-Mal solutions. According to classical nucleation theory the homogeneous nucleation rate can be described by the following equation (see Section 2.4 and the Appendix):274 5.2 /hom - « h o m • e X P A C ^ l + AG' kT where ahom is the pre-exponential factor, T is the temperature, k is the Boltzmann constant, A G ^ is the free energy of formation of a critical nucleus, and A G ' is the activation energy for molecular motion across the cluster-matrix interface, which is a function of the viscosity of the solution.274 For solids crystallizing from solutions at constant temperature and assuming a spherical critical nucleus, the free energy of formation of a critical nucleus is given by:274 5.3 16^KV2 3(kT In Sf where / i s the interfacial tension between the crystalline (NH 4) 2S0 4 critical nucleus and an aqueous (NH 4) 2S0 4 solution, vis the molecular volume (124 A 3 for (NH 4) 2S0 4), 2 6 9 Tis the temperature, and S is the supersaturation.249 S is described by the following equation: 5.4 S=-solute where « s o l u t c is the activity of the solute and a^lute is the activity of the solute in a saturated solution. S was obtained directly from the model by Clegg et al. 2 7 0 , 2 7 1 for aqueous (NH4)2SO For convenience, Equation 5.2 can be rewritten as: 5.5 where: /hom — /o.hom ' e X P AG, hom kT 5.6 /o.hom — ^hom ' e X P ( A G ^ V kT j Combining Equations 5.3 and 5.5 gives the following: Chapter 5 114 _ ( 1 6 a y V " Equation 5.7 suggests that the nucleation rate is a strong function of supersaturation. Ahom is expected to be relatively insensitive to changes in supersaturation and temperature, at least over a relatively narrow range of these variables.275"278 In Figure 5.7, Panel A, In / h o m versus T"3 -(In S)'2 is plotted for aqueous (NH 4) 2S0 4 particles, and the straight line is a linear least squares fit to all the data. At first glace it appears that the data fit reasonably well to a straight line. Upon closer inspection, however, it appears that perhaps the fit of a single straight line to the whole data set may not be appropriate. To explore this further, in Figure 5.7, Panel B, In / h o m versus T 3 -(ln S)'2 is plotted again, but in this case the first 10 % of the crystallization events were not included in the least squares linear fit analysis. In other words, all crystallization events that occurred at T 3-(lni)" 2 > 3.25 x 10"9K"3 were neglected. Figure 5.7, Panel B, also shows the 95% prediction bands from the linear fit. There are four data points at T 3 -(In i ) " 2 > 3.25 X 10"9 K"3 that are systematically outside the 95 % prediction limits, suggesting these data do not fit the straight line shown in Figure 5.7, Panel B. A possible explanation is that/0 ) h o m or y vary significandy with a change in S. Alternatively the first 10 % of the crystallization events occurred by heterogeneous nucleation. In the literature there are many studies where nucleation data also do not fall on a single line when In / h o m is plotted versus T3 -(In J)"2 (or versus (In S)'2 for isothermal experiments).274'279"281 Often these data in the literature exhibit two different kinetic regions, and the trend is attributed to homogeneous nucleation at high supersaturations and heterogeneous nucleation at low supersaturations. However, the small quantity of data that fall outside the 95 % prediction bands in Figure 5.7, Panel B, precludes the ability to make any strong conclusions on the applicability of classical nucleation theory and the underlying assumptions to the current experimental results. In the future, the current apparatus may be automated so that hundreds of crystallization events can be observed routinely. This should provide a better test of the assumptions involved in classical nucleation theory. Chapter 5 115 Figure 5.7: Natural logarithm of the homogeneous nucleation rate, Jhom, as a function of 7*3(ln S)~2 (where S is the supersaturation as defined in Equation 5.4 and Tis temperature) for (NH4)2S04 particles. The solid line in Panel A is a linear fit to the complete data set. The solid line in Panel B is a linear fit to the data, excluding the data from the first 10 % of particles to crystallize (i.e., excluding the data with T3(ln 5)"2 > 3.25 x 10"9 K"3). Dashed lines in Panel B indicate the 95 % prediction band associated with the linear fit. Chapter 5 116 To be conservative, both of the linear fits in Figure 5.7, Panels A and B, were used to determine / 0 > h o m and y. From the intercept and slope of the lines in these figures, / 0 , h o m and y were determined, and the upper and lower limits determined from these two fits are reported. Based on this procedure, the upper and lower limits to In / O h o m are 129 and 74, and the upper and lower limits to y are 0.070 and 0.053 J m"2. Note that this analysis also takes into account the uncertainty in the fit parameters (95 % confidence). Table 5.1 compares the range of values for In / 0 ,hom a n ^ /obtained from the linear fits in both Figure 5.7, Panels A and B, to values obtained in previous studies. Within uncertainty limits, the current result for y agrees with y from Mohan et al. 2 8 2 However, y from Onasch et al. 2 4 9 is outside of the uncertainty limits and lower than y obtained from the current study. Onasch et al. 2 4 9 measured the R H at which aqueous particles crystallized and then from an estimate of the induction time and an estimate of J0 they calculated a homogeneous nucleation rate (at one relative humidity) and an interfacial tension. Onasch et al.2 4 9 did not measure nucleation rates over a range of relative humidity. In the current experiments, nucleation rates were measured over a range of relative humidity. From an analysis of the current experimental results, both J0 and the interfacial tension were obtained. Table 5.1: Classical Nucleation Theory Parameters Current Study Mohan et al. 2 8 2 Onasch et al. 2 4 9 T[K] 295 - 300 298 298 ln(/o,hom/m" 3 s1) 74-129 - -/Qm-2] 0.053 - 0.070 0.05829572 0.052 5.4 Conclusions and Atmospheric Implications For aqueous (NH 4) 2S0 4-Mal particles, the current results obtained with an EDB were in agreement with the previous experiments in Chapter 4 (Parsons et al.243) that utilized particles suspended on a hydrophobic surface. This confirms that the hydrophobic support used previously does not influence the crystallization measurements. The current values of CRH50 show that for ammonium-to-sulphate ratios of 1.5 and 2.0, Mai decreases the CRH50 of the inorganic particles by less than 7 % RH when x'Mai < Chapter 5 117 0.25. For x M a l ~ 0.5, Mai can decrease the CRH50 of the inorganic particles by up to 35 % RH. These results are consistent with results in previous work that focused on (NH4)2S04-glutaric acid and NaCl-glutaric acid particles242 and (NH4)2S04-organic particles (Chapter 4; Parsons et al.243): on average, organics may change the CRH50 of pure inorganic particles, but only if the mole fraction of the organics is large. See Chapter 4 (Parsons et al.243) for a detailed discussion in terms of the atmospheric implications of this finding. For an ammonium-to-sulphate ratio of 1.0, the presence of Mai does not significantiy modify the CRH50 for the entire range of xMi>i studied. The size dependent measurements show that the CRH for aqueous (NH 4) 2S0 4 particles is not a strong function of particle volume, consistent with previous conclusions (see, for example, Martin,221 Cziczo et al.,2 4 8 Onasch et al.,2 4 9 and references therein). The CRH for aqueous (NH 4) 2S0 4 particles is also expected to be relatively insensitive to observation time as the CRH depends on both volume and time based on the kinetics of homogeneous nucleation. For aqueous (NH 4) 2S0 4-Mal particles with x'Mal = 0.36 the CRH was a stronger function of particle size. The CRH for the (NH 4) 2S0 4-Mal particles with xMi\ ~ 0-36 is also expected to be a stronger function of observation time than in the case of aqueous (NH 4) 2S0 4 particles. The size dependence for organic concentrations less than and greater than x'MstS — 0.36 may be investigated in a future publication from this laboratory. Preliminary results suggest that the CRH for (NH 4) 2S0 4-Mal particles is not a strong function of size for particles with x'UA < 0.25. However, further work is needed to confirm this. In the atmosphere the volume and time for crystallization may be significantly different than in the laboratory. Hence, differences in size and observation time should be considered when extrapolating laboratory crystallization results to atmospheric scenarios. For pure aqueous inorganic particles, CRH values determined in the laboratory (with different volumes and observation times compared to the atmosphere) can be used to direcdy predict the CRH in the atmosphere with reasonable accuracy without correcting for a difference in volume or time. This is because the CRH for these types of particles is rather insensitive to volume and, most likely, time. This simplifies predictions of crystallization in the atmosphere. However, the current results for aqueous (NH 4) 2S0 4-Mal particles with xMai = 0-36 suggest that for certain organic mole fractions the CRH can depend strongly on Chapter 5 118 particle size. In this case, ideally one would measure / h o m in the laboratory over a wide range of R H values and then use these values to predict the R H at which droplets crystallize in the atmosphere. The benefits of using/ h o m to predict crystallization in the atmosphere compared to using just CRH values determined in the laboratory have been discussed previously in the literature.221 The current studies further emphasize the need for determining / h o m for certain organic mole fractions. Further work is needed to determine the range of organic concentrations where crystallization depends strongly on particle size. The current homogeneous nucleation rate data show that / h o m in aqueous (NH 4) 2S0 4 is a stronger function of R H than / h o m in aqueous (NH 4) 2S0 4-Mal (x'm] = 0.36). These observations are consistent with the size dependent data and can be used to rationalize the size dependent results discussed above. The reason that the homogeneous nucleation rate in (NH4)2S04-Mal particles is a weaker function of R H may be related to viscosity. At low R H and high organic mole fractions, viscosity may become significant and influence the nucleation rate (through AG'). When analyzing the homogeneous nucleation rates for aqueous (NH 4) 2S0 4 particles, Equation 5.7 was used with the assumption that A G ' does not change significandy with a change in R H (see above). For aqueous (NH 4) 2S0 4-Mal particles, the viscosity could increase significandy (increasing AG') as the R H decreases. This would result in / h o m being less dependent on RH. Experimental studies on the viscosities and supersaturations in mixed inorganic-organic aqueous solutions as a function of R H would be useful to help explain these observations. The current combined results should be an interesting test for theories of homogeneous nucleation. 5.5 References (219) Finlayson-Pitts, B. J.; Pitts, J. N . Chemistry of the Upper and Lower Atmosphere: Theory, Experiments and Applications; Academic Press: San Diego, CA, 2000. (220) Seinfeld, J. H.; Pandis, S. N . Atmospheric Chemistry and Physics: From Air Pollution to Climate Change; Wiley: New York, 1998. (221) Martin, S. T. Chem. 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W.; Osman, M. M. Krist. Tech. 1973, 8, 471. (278) Walton, A. G. Nucleation in Liquids and Solids. In Nucleation; Zettiemoyer, A. C , Ed.; M. Dekker: New York, 1969; pp 225-327. (279) Mullin, J. W.; Ang, H..M. Faraday Discuss. 1976, 61, 141. (280) Hendriksen, B. A.; Grant, D. J. W. /. Cryst. Growth 1995, 156, 252. (281) Sohnel, O.; Mullin, J. W. /. Cryst. Growth 1978, 44, 377. (282) Mohan, R.; Kaytancioglu, O.; Myerson, A. S. /. Cryst. Growth 2000, 217, 393. Chapter 6 122 6. C R Y S T A L L I Z A T I O N O F A Q U E O U S A M M O N I U M S U L P H A T E P A R T I C L E S I N T E R N A L L Y M I X E D W I T H S O O T A N D K A O L I N I T E : C R Y S T A L L I Z A T I O N R E L A T I V E H U M I D I T I E S A N D N U C L E A T I O N R A T E S 6.1 Introduction Aerosol particles are abundant in the atmosphere, and these pardcles can undergo several types of phase transitions. An example of an atmospherically relevant phase transition is crystallization, which here refers to the crystallization of a solute in an aqueous solution droplet at low values of relative humidity (in this case water is considered the solvent). An example of crystallization includes the precipitation of crystalline ammonium sulphate in an aqueous ammonium sulphate droplet at low values of relative humidity. This last process is also often called efflorescence. Crystallization is a kinetically controlled process due to the free energy barrier associated with nucleation of a crystalline solid in an aqueous solution. As a result, crystallization of aqueous particles typically does not occur at the same relative. humidity (RH) as deliquescence, which refers to when particles take up water to form solution droplets. In the absence of heterogeneous nuclei, crystallization occurs by homogeneous nucleation; otherwise, crystallization can occur by heterogeneous nucleation. Knowledge of the conditions required for crystallization of atmospheric aqueous particles is necessary to predict if particles in the atmosphere are solid, liquid, or mixtures of solid and liquid. This information is, in turn, necessary to predict the rates of heterogeneous reactions occurring on and in particles, the amount of light particles scatter and absorb, and their ability to act as ice nuclei.283'286 A version of this chapter has been published. Pant, A; Parsons, M. T.; Bertram, A. K. Crystallization of Aqueous Ammonium Sulfate Internally Mixed with Soot and Kaolinite: Crystallization Relative Humidities and Nucleation Rates, / . Phys. Chem. A, 2006, /10, 8701 - 8709. Reproduced with permission from The Journal of Physical Chemistry A, 2006,110, 8701 - 8709. Copyright 2006 American Chemical Society. Chapter 6 123 Field measurements have shown that a majority of the fine particulate mass (less than 2 um in diameter) in the troposphere consists of sulphate, ammonium, and nitrate ions, as well as organic material.287 The crystallization of aqueous inorganic particles, such as aqueous (NH 4) 2S0 4 particles, has been studied extensively in the past (see for example Martin284 and references therein). More recendy, researchers have started to study the crystallization of aqueous organic and aqueous organic-inorganic particles due to the atmospheric abundance of these types of particles (see for example Braban and Abbatt,288 Brooks et al.,2 8 9 Choi and Chan,290 Cruz and Pandis,291 Hansson et al.,2 9 2 Lightstone et al.,2 9 3 Marcolli et al.,2 9 4 Mikhailov et al.,2 9 5 Pant et al.,2 9 6 Parsons et al.,2 9 7 Prenni et al.,2 9 8 and references therein). Aqueous particles in the atmosphere may also contain solid material, such as soot and mineral dust, which could lower the free energy barrier to nucleation of crystalline material, and hence change the crystallization R H (CRH) values of the aqueous particles. In this case the particles can crystallize by heterogeneous nucleation in addition to homogeneous nucleation. See Lightstone et al.,2 9 3 Dougle et al.,2 9 9 Even et al.,3 0 0 Han and Martin,301 Han et al.,3 0 2 Martin et al.,3 0 3 Oatis et al.,3 0 4 Onasch et al.,3 0 5 and Richardson and Snyder306 for studies on crystallization of aqueous particles containing heterogeneous nuclei relevant for the atmosphere. There is now evidence that a large fraction of sulphate particles in the troposphere contain soot material (i.e., sulphate and soot are often internally mixed).307 3 1 0 For example, Posfai et al. 3 0 9 found that in the polluted north Atiantic marine boundary layer about 50 % of the smallest and 90 % of the larger (approximately 1 um in diameter) sulphate particles contained soot. They concluded that internally mixed soot and sulphate appear to comprise a globally significant fraction of aerosols in the troposphere. Two recent studies have investigated the effect of soot and carbon black on the crystallization of aqueous inorganic particles. Dougle et al. 2 9 9 found that the addition of soot from the combustion of diesel fuel did not modify the CRH of aqueous ammonium nitrate particles or aqueous particles consisting of 2:1 internal mixtures by weight of ammonium nitrate to ammonium sulphate, and Even et al. 3 0 0 found that Talens Indian ink (a type of carbon black) did not modify the CRH of aqueous sodium chloride particles. However, the studies by Dougle et al.2 9 9 and Even et al. 3 0 0 only investigated two types of soot and a limited number of solution compositions. More studies similar to those by Dougle et al. 2 9 9 and Even et al. 3 0 0 are still needed to establish categorically that soot does not modify the CRH values of aqueous Chapter 6 124 inorganic particles relevant for the atmosphere. First, studies need to be carried out with different types of soot. Soot in the atmosphere may have a range of properties (size, chemical composition, porosity, etc.) depending on the source. Some types of soot may be good heterogeneous nuclei for crystallization and other types of soot may not. Second, studies of other atmospherically relevant aqueous compositions would be beneficial, as soot may influence the crystallization of some inorganic salts but not others. . There is also abundant evidence that mineral dust particles can be internally mixed with sulphate and nitrate.307'308,311"315 For example, Liu et al. 3 1 4 and Lee et al. 3 0 8 found that mineral dust particles in the Atlanta region often contain sulphate and nitrate indicating aged dust. Recent studies suggest that components of mineral dust can lower the free energy barrier to nucleation of crystalline material, and hence modify the R H at which aqueous inorganic particles crystallize.301"305 Nevertheless, more work in this area is needed to fully quantify the effect of mineral dust on crystallization of aqueous droplets in the atmosphere. For example, the crystallization of aqueous droplets in the presence of kaolinite, illite, and montmorillonite, which are major components of mineral dust,316,317 has not been investigated. Mineral dust particles are abundant in the atmosphere. This dust is largely produced from the Gobi and Saharan deserts 3 1 8 , 3 1 9 then transported over long distances becoming coated with sulphates and other electrolytes.320 These mineral dust particles are believed to have a significant effect on the Earth's radiation budget by absorbing and scattering solar and infrared radiation. Dust particles and dust particles coated with sulphates can also indirecdy affect climate by acting as ice nuclei.321,322 Furthermore, modeling studies have suggested that these mineral dust particles can modify the oxidative capacity of the atmosphere.323 In order to better understand the role of mineral dust in the atmosphere, knowledge of the hygroscopic properties (including crystallization) of dust particles coated with sulphates would be beneficial. In the following we use optical microscopy to investigate the crystallization of aqueous ammonium sulphate droplets containing soot and kaolinite. For comparison purposes we also investigated the crystallization of aqueous ammonium sulphate droplets free of solid material. We determined the range over which crystallization occurred and the R H at which 50 % of the particles crystallized as a function of droplet size for aqueous ammonium sulphate droplets and aqueous ammonium sulphate droplets internally mixed Chapter 6 125 with kaolinite or soot. In addition, we determined the homogeneous nucleation rates (number of nucleation events per unit volume of the aqueous droplet per unit time) of crystalline ammonium sulphate in aqueous ammonium sulphate droplets free of solid material and the heterogeneous nucleation rates (number of nucleation events per unit surface area of solid material per unit time) of crystalline ammonium sulphate in aqueous ammonium sulphate droplets containing kaolinite. We also parameterized the homogeneous and heterogeneous nucleation rates using classical nucleation theory. In this analysis we determined the interfacial tension between a crystalline ammonium sulphate critical nucleus and an aqueous solution of ammonium sulphate and the contact angle between a solid ammonium sulphate critical nucleus and a kaolinite surface. From the combined results, we discuss if soot or kaolinite can modify the CRH values of aqueous ammonium sulphate droplets in the atmosphere. This combined analysis provides insight into the kinetics of nucleation in aqueous solutions in addition to crystallization of aqueous droplets in the atmosphere. 6.2 Experimental The apparatus consisted of an optical microscope coupled to a flow eel] 2 9 6-2 9 7-3 2 4-3 2 5 The apparatus used in this study is similar to the apparatus we used previously to measure crystallization and deliquescence of organic and mixed organic-inorganic particles,296,297'325 except that images of the particles recorded during the crystallization experiments were analyzed with digital analysis software in the current study. This allowed us to routinely monitor the phase and size of many individual particles during the crystallization experiments. The particles of interest (aqueous ammonium sulphate droplets with or without solid material, depending on the experiment) were deposited on the bottom surface of the flow cell and monitored with the optical microscope (using polarized light). For the experiments involving aqueous droplets without solid material, droplets with diameters ranging from 5-30 urn were investigated. For the experiments involving aqueous droplets with solid inclusions, only droplets with diameters ranging from 1 0 - 3 0 um were investigated to ensure the droplets were significandy larger than the size of the solid inclusions. The bottom surface of the flow cell, which supported the particles, consisted of a hydrophobic polytetrafluoroethylene (PTFE) film annealed to a glass cover slide. R H over Chapter 6 126 the particles was controlled by a continuous flow of a mixture of dry and humidified N 2 gas. R H uncertainty for individual measurements was about ± 1 % RH based on the accuracy of the R H monitoring equipment. Three different samples of n-hexane soot were used in these studies (provided by D. M. Smith, University of Denver). The first sample was produced by burning n-hexane under ambient conditions in an open vessel, resulting in a diffusion flame. The second and third samples were generated using an apparatus designed for producing premixed flames with variable air to fuel ratios. Previous measurements have shown that there is a linear relationship between the state of soot surface oxidation and the air to fuel ratio.325 Properties of n-hexane soot have been documented by Smith and co-workers.326,327 The kaolinite particles used in the current experiments were purchased from Fluka Chemika (purum; natural grade). Listed in Table 6.1 is the Brunauer, Emmett, and Teller (BET) surface area per unit mass and average primary particle size of the solid materials investigated. Table 6.1: Properties of Soot and Kaolinite Particles Used in these Experiments Solid Inclusion BET Surface Area Average Primary Particle Size _ _ _ _ _ K g 1 ] dxm] n-Hexane soot (diffusion flame) 89 ± 2a 0.05 - 0.1 (spheroids)3 n-Hexane soot (Air : Fuel = 0.53) 100 ± 2b 0.05 - 0.1 (spheroids)b n-Hexane soot (Air : Fuel = 2.4) 156 ± l l b 0.05 - 0.1 (spheroids)b Kaolinite ~ 9C ~ 2.1c ' a Akhter et al. 3 2 7 b Chughtai et al. 3 2 6 0 From vendor. Aqueous ammonium sulphate droplets internally mixed with solid material were prepared by first making a solution of 10 g L 1 ammonium sulphate in water. 18.2 MQ water from a Millipore Simplicity 185 water purification system was used to make the solutions. The aqueous solutions were mixed with n-hexane soot or kaolinite and then placed in an ultrasonic bath for ~30 min to make a stable suspension. In all cases the mass ratio of soot or kaolinite to ammonium sulphate was 0.01. Aqueous droplets containing solid material Chapter 6 127 were created by passing these suspensions through a concentric flow pneumatic nebulizer that had a large liquid capillary opening to avoid plugging of the nebulizer by the solid material. Droplets from the nebulizer were directed to the bottom surface of the flow cell where they impacted on the PTFE surface and coagulated to form supermicrometre droplets. The contact angle between aqueous ammonium sulphate droplets and aqueous droplets containing solid material on the PTFE surface was close to 120°. In these experiments we could not measure precisely the size of the inclusions in individual droplets. We assumed that the kaolinite and the soot particles were randomly distributed in the droplets in the same proportion as in the bulk solutions. We verified that each droplet contained solid material in the soot and kaolinite experiments by monitoring individual droplets with a 50 x objective lens. It was clear from these tests that all aqueous ammonium sulphate droplets investigated contained solid particulates, and the solid was present both within the bulk and close to the interface of the aqueous ammonium sulphate droplets. The solid particulates within the bulk of the droplets moved in all directions whereas solid particulates near the interface of the droplets moved along the interface of the droplets. This movement is likely from Brownian motion. During a crystallization experiment the flow cell was maintained at a temperature of 293.2 ± 0.1 K and the R H was decreased at a rate of 0.5 % RH minute"1. The R H was monitored with a dew point hygrometer. Images of the particles were recorded every 15 s with a corresponding dew point measurement (from the hygrometer). From the images, the size of each droplet and also the R H at which each droplet crystallized was determined with image analysis software (Northern Eclipse). The CRH values of the droplets could be clearly determined from the images as solid particles appear very bright under polarized light. Note that in our experiments we cannot determine if the solid particles are crystalline or amorphous. Previous studies have shown that solid particles of the compounds used in this study are crystalline.288'328 Shown in Figure 6.1 is a plot of the change of the intensity of the light reflected by a single aqueous ammonium sulphate droplet with kaolinite during a crystallization experiment determined with the image analysis software. The change in intensity was calculated by taking the derivative of the intensity with respect to RH. At 46.3 % RH, the change in intensity deviates significantly from zero, indicating that the droplet had crystallized. From plots similar to Figure 6.1 we determine the CRH of each droplet. Chapter 6 128 Crystallization 50 52 RH [% RH] Figure 6.1: Change in the intensity of the light reflected by a single aqueous ammonium sulphate droplet containing kaolinite as a function of RH during a crystallization experiment. At 46.3 % RH, the change in intensity deviates significantly from zero, indicating that the droplet crystallized. 6.3 Results and Discussions 6.3.1 Crystallisation of Aqueous Ammonium Sulphate Droplets and Droplets Containing Soot or Kaolinite Shown in Figure 6.2 are examples of results from typical R H cycles (i.e., experimental runs). Each data set corresponds to a single R H cycle, and each data point corresponds to a single crystallization event. This figure is included to illustrate the type of results obtained in an R H cycle, and should not be used exclusively to compare the Chapter 6 129 crystallization of different droplet types, since it does not take into account the fact that different droplet sizes were often used in the different R H cycles. RH [% RH] Figure 6.2: Examples of results from typical RH cycles (i.e., experimental runs). The fraction of particles remaining liquid during the experimental run is given by N/N0i where N is the number of particles remaining liquid and iV0 is the total number of particles. Each data set corresponds to a single RH cycle, and each data point corresponds to a single crystallization event. During the experiments the relative humidity was decreased at a rate of 0.5 % RH minute"1. Key: (•) aqueous ammonium sulphate; and aqueous ammonium sulphate internally mixed with: (O) n-hexane soot (diffusion flame); (O) n-hexane soot (Air : Fuel = 0.53); (A) n-hexane soot (Air : Fuel = 2.4); (•) kaolinite. The solid inclusion to ammonium sulphate mass ratio was 0.01 in these experiments. Chapter 6 130 For each particle type we carried out several R H cycles or experiments. For aqueous ammonium sulphate droplets without solid material, three cycles were carried out for a total of 172 droplets. For aqueous ammonium sulphate droplets with n-hexane soot, six cycles were performed for a total of 350 droplets. For aqueous ammonium sulphate droplets with kaolinite, six cycles were performed for a total of 225 droplets. The results from all these measurements are summarized in Figure 6.3, Panel A. This figure takes into account particle size, and hence can be used to compare direcdy the results from the different particle types. In Figure 6.3, Panel A, we have plotted, as a function of droplet diameter, D, the R H at which 50 % of the particles crystallized (i.e., the median), which we refer to as CRH50. Figure 6.3, Panel A, was generated by sorting the crystallization data into bins according to the particle size (with a bin width of about 3 [im over the range of 5 to 25 urn, and a bin width of 5 urn over the range of 25 to 30 um). Then for each bin, the CRH50 was calculated if the number of nucleation events in the bin was greater than 5. The symbols in Figure 6.3, Panel A, correspond to CRH50 values at the average diameter for each size bin and the vertical bars indicate the 20th and 80th percentiles of the CRH data in each size bin. This method of presenting the crystallization data is similar to Koop et al. 3 2 9 Chapter 6 131 D[um] Figure 6.3: (A) CRH50 as a function of aqueous droplet diameter, Z>, for the current data and (B) comparison of current CRH50 data for aqueous ammonium sulphate droplets free of solid material with CRH data from previous studies. Key: aqueous ammonium sulphate: (•) current data; (•) Han and Martin;301 (•) Badger et al.;330 (•) Brooks et al.;331 (A) Cziczo et al.;332 (•) Onasch et al.;333 (<) Orr et al.;334 (*) Parsons et al.33S (Chapter 5); aqueous ammonium sulphate internally mixed with: (O) n-hexane soot current data (diffusion flame); (O) n-hexane soot current data (Air : Fuel = 0.53); (A) n-hexane soot current data (Air : Fuel = 2.4); (•) kaolinite current data. The vertical bars indicate the 20* and 80th percentiles of the CRH data in each particle size bin. Chapter 6 132 For pure ammonium sulphate (open squares in Figure 6.3) the CRH50 ranges from 35 to 38 % RH depending on particle size. In Figure 6.3, Panel B, the current results for aqueous ammonium sulphate free of solid material are compared with results from the literature using submicrometre particles301'330'334 and previous size dependent measurements, which utilized an electrodynamic trap and supermicrometre particles (Chapter 5; Parsons et al.335). The current results are in good agreement with most of these previous studies. Based on this, it is suggested that the crystallization of pure ammonium sulphate is not significandy affected by the presence of the PTFE surface supporting the particles in the current experiments. Furthermore the results in Figure 6.3 show that the CRH50 does not change significandy with particle size. This is consistent with conclusions made previously in the literature based on comparisons of results from different laboratories, (see for example Badger et al.,3 3 0 Brooks et al.,331 Cziczo et al.,3 3 2 Han and Martin,301 Martin,284 Onasch et al.,3 0 5 Onasch et al.,3 3 3 and Orr et al.334) and also a recent detailed study of the effect of particle size on crystallization carried out in this laboratory with an electrodynamic balance (see Chapter 5, Parsons et al.335). Figure 6.3, Panel A, shows that the crystallization results for aqueous ammonium sulphate droplets containing soot (with a mass ratio of soot to ammonium sulphate equal to 0.01) are statistically equivalent to the results for aqueous ammonium sulphate droplets with no solid particulates. This indicates that n-hexane soot is not an effective nucleus for crystallization of ammonium sulphate. As mentioned in the introduction, the effects of soot or carbon black on the crystallization of aqueous inorganic droplets have been investigated in two other studies. Dougle et al.2 9 9 found that the addition of soot from the combustion of diesel fuel did not influence crystallization of aqueous ammonium nitrate droplets or aqueous droplets consisting of 2:1 internal mixtures by weight of ammonium nitrate to ammonium sulphate. Also, Even et al. 3 0 0 found that Talens Indian ink (a type of carbon black) did not influence the crystallization of aqueous sodium chloride droplets. The current results give further support that soot does not influence the crystallization of aqueous inorganic droplets. Figure 6.3, Panel A, also shows that kaolinite (with a mass ratio of kaolinite to ammonium sulphate equal to 0.01) does induce crystallization of ammonium sulphate, increasing the CRH50 values by approximately 10 % from those of the aqueous ammonium Chapter 6 133 sulphate droplets with no solid particulates. Also the CRH50 increases slightiy as the droplet size increases. This is because the larger droplets have a larger surface area available for heterogeneous nucleation. This study is the first to investigate the effect of kaolinite on the CRH of aqueous ammonium sulphate droplets. Others have investigated the effect of other types of solid inorganic material on the CRH of aqueous ammonium sulphate droplets.301'303"305 The results from these other studies as well as the current results for kaolinite are summarized in Table 6.2. Comparing the CRH values in Table 6.2, it is clear that some solid inorganic materials act as better heterogeneous nuclei than others. For example, it appears that A1 20 3, Zr0 3 , and T i 0 3 are significantly better heterogeneous nuclei than kaolinite as the CRH values are higher for these inorganic solids compared with kaolinite CRH values, despite the fact that the surface area available for heterogeneous nucleation per droplet was lower in these previous experiments compared with the current kaolinite experiments. (Note, to compare results from different experiments the difference in surface area should be considered. This is discussed in more detail below.) Chapter 6 134 Table 6.2: Comparison of Measurements of the CRH of Aqueous Ammonium Sulphate Droplets Containing Inorganic Solids Solid Inclusion Temperature [K] CRH [% RH] Surface Area of Solid Inclusion per Droplet [m2] Observation Time [s] Reference None 293.2 34.3 ± 1 -42.5 ± 1 0 ~ 120 Current study Kaolinite 293.2 42.4 ± 1 -50.1 ± 1 (0.8-20) x 10"10 ~ 120 Current study A1 20 3 298 57 8 x 10 1 3 120 Han and Martin301 Z r 0 3 298 59 8 x 10"13 120 Han and Martin301 T i 0 2 298 65 8 x 10 1 3 120 Han and Martin301 Hemadte 298 35-59 (0.1 - 6) x 10'13 120 Martin et al. 3 0 3 Corundum 298 33-53 (0.1-3) x 10 1 3 120 Martin et al. 3 0 3 Mullite 298 43 2 x 10 4 3 120 Martin et al. 3 0 3 Amorphous Silica 298 35 2 x 10"13 120 Martin et al. 3 0 3 BaS0 4 298 45.8 3 x 10 1 4 < 1 Oatis et al. 3 0 4 CaC0 3 298 48.5 2 x 10 1 3 < 1 Oatis et al. 3 0 4 CaC0 3 298 46.6-49.4 (8 - 10) x 10"13 < 1 Onasch et al. 3 0 5 6.3.2 Nucleation Rates from Experimental Data From the crystallization results discussed above, we determine the homogeneous nucleation rates of crystalline ammonium sulphate in aqueous ammonium sulphate droplets (free of solid material) and the heterogeneous nucleation rates of crystalline ammonium sulphate in aqueous ammonium sulphate droplets containing kaolinite. A similar analysis was not performed for aqueous ammonium sulphate droplets containing soot since soot did not significandy influence the CRH values of the aqueous ammonium sulphate droplets. In Chapter 6 135 Sections 3.3 and 3.4 the nucleation rates are parameterized using classical nucleation theory, and the parameters from this analysis are used in Section 6.4 to predict the impact of kaolinite on the CRH50 of aqueous ammonium sulphate particles in the atmosphere. From the data for aqueous ammonium sulphate droplets without solid material, we calculated the homogeneous nucleation rate, / h o m , which is the number of nucleation events per unit volume of aqueous solution per unit time. Note this is also often referred to as. the homogeneous nucleation rate constant in the atmospheric literature. / h o m can be calculated with the following equation, corresponding to first-order kinetics:284'335,336 61 I (FJI) r dN(RH) A o m V ) T/ . N ( jRH) d R H where N(RH) is the total number of liquid droplets (not including droplets that have crystallized), and the product V-N(RH) is the total volume of liquid droplets (again, not including droplets that have crystallized), dN(RH) is the number of droplets observed to crystallize between R H and (RH - dRH), and r is the rate of change of the RH, which is -0.5 % RH min'1 in these experiments. Equation 6.1 assumes that the rate limiting step for crystallization is nucleation of the solute and that only one nucleation event leads to the solidification of the droplet, which is a reasonable assumption for the current conditions. Equation 6.1 also assumes that crystallization is dominated by homogeneous nucleation rather than heterogeneous nucleation by foreign nuclei or heterogeneous nucleation on the PTFE substrate supporting the particles. We calculated dAT(RH)/dRH by first plotting N versus R H (the plot is similar to Figure 6.2 except that the total number of liquid droplets, N, is plotted instead of N/N0). Then at each R H measurement, we calculated dN(RH)/dRH by the central difference approximation, which is a numerical method for differentiation. V-N(RH) was determined by summing the volume of all the liquid droplets (not including droplets that have crystallized) at each CRH measurement. The volume of each droplet was calculated from the droplet diameter immediately before crystallization and the contact angle between aqueous ammonium sulphate droplets and the PTFE surface. Shown in Figure 6.4 is an image of an aqueous ammonium sulphate droplet on the PTFE surface prior to crystallization, recorded with a CCD camera coupled to a microscope held in the same plane as the PTFE surface. As mentioned above the contact angle between aqueous ammonium sulphate droplets and the PTFE surface was close to 120°, and this Chapter 6 136 angle does not change significandy with droplet composition or over the range of R H values investigated in these experiments. When calculating the volume of the droplets, we took into account the fact that the droplets form a spherical cap (i.e., a sphere truncated by a plane) on the PTFE surface. From diV(RH)/dRH and V-N(RH) we determine / h o m using Equation 6.1. Shown in Figure 6.5 is a plot of / h o m versus R H for pure ammonium sulphate droplets, calculated using Equation 6.1 and the current crystallization results. Note that / h o m (which has units of m"3 s"1) corresponds to the left ordinate in Figure 6.5. Figure 6.4: Side view of an aqueous ammonium sulphate solution droplet on a P T F E substrate. The contact angle of the droplet on the P T F E substrate was about 120 ° for all systems studied. Chapter 6 137 Figure 6.5: Nucleation rates as a function of relative humidity. The open squares correspond to the nucleation rates (Jhom) of solid ammonium sulphate in aqueous ammonium sulphate droplets determined in this study (corresponding to the left ordinate). The solid circles correspond to nucleation rates (J^"1) of solid ammonium sulphate in aqueous ammonium sulphate droplets containing kaolinite (corresponding to the right ordinate). From the crystallization data for aqueous ammonium sulphate droplets internally mixed with kaolinite, we calculated the heterogeneous nucleation rate on kaolinite, /^ t o 1 , which we define as the number of nucleation events of crystalline ammonium sulphate per unit surface area of solid kaolinite per unit time. / ^ ° ' can be described with the following equation, corresponding to first-order kinetics:336 J " y A^-N(RH) dRH The surface area of kaolinite per liquid droplet, Akaoi, was calculated from knowledge of the BET surface area per unit mass of the kaolinite material, the volume of the aqueous droplet Chapter 6 138 (taking into account the spherical cap geometry), and the composition of the aqueous droplets as a function of RH, which can be determined from the model by Clegg et al. 3 3 7 , 3 3 8 Akaol-N(RH) corresponds to the total surface area (of kaolinite) available for heterogeneous nucleation in the experiments (not including the surface area of kaolinite in droplets that have crystallized). /^ t ° ' is determined with a method similar to the method used to determine / h o m (see above) except Ak!lol-N(RH) is used in place of V-N(RH). It should be noted that Equation 6.2 applies only when heterogeneous nucleation dominates over homogeneous nucleation, which is the case under the current experimental conditions. Shown in Figure 6.5 is a plot of / ^ ° ' as a function of R H calculated with Equation 6.2 and the current experimental results. Note that / ^ ° ' (which has units of m"2 s"1) corresponds to the right ordinate in Figure 6.5. 6.3.3 Classical nucleation theory parameters from Jhom From the homogeneous nucleation rates calculated above, we determined the interfacial tension between an ammonium sulphate critical nucleus and an aqueous ammonium sulphate solution. According to classical nucleation theory the homogeneous nucleation rate, / h o m , can be described by the following equation (see Section 2.4 and the Appendix):339 ( A G ^ ' + A G ' ^ V  fel J where, a^om is pre-exponential factor, T is the temperature, k is the Boltzmann constant, A G ^ is the free energy of formation of a critical nucleus, and AG' is the activation energy for molecular motion across the cluster-matrix interface.339 Assuming a spherical critical nucleus, the free energy of formation of a critical nucleus is given by:339 6.4 Acr = !6a?fV' hom 3(kT In Sf where, /is the interfacial tension between the crystalline ammonium sulphate critical nucleus and an aqueous ammonium sulphate solution, v is the molecular volume (124 A 3 for ammonium sulphate340), Tis the temperature, and Sis the supersaturation defined as: Chapter 6 139 6.5 S = sat ^solute where a s o l u t c is the activity of the solute, and a*£latc is the acdvity of solute in a saturated solution. Combining Equations 6.3 and 6.4 gives the following: 6 6 /hom = /o.hom • e X p| where: ( \6ny\z A 3^ 3T 3(lnJ') A 7 r f A G ' l 6 - 7 /o.hom = « h o m • e X P ~ V kT J The nucleation rate described by Equation 6.6 exhibits a strong dependence on the supersaturation due to the quantity (In S)2 that appears in the exponential term. J0 h o m is expected to be relatively insensitive to changes in temperature and supersaturation, at least over a relatively narrow range of these variables.341"344 In Figure 6.6, we have plotted In/ h o m versus (In S)'z for aqueous (NH 4) 2S0 4 particles. The thermodynamic model by Clegg et al. 3 3 7 , 3 3 8 was used to calculate S in the aqueous ammonium sulphate droplets. Note that In / h o m corresponds to the left ordinate in Figure 6.6. Interestingly, the In / h o m data in Figure 6.6 do not seem to fall perfectiy on a straight line. A possible explanation is that / 0 > h o m or yvary significandy with a change in S. In the literature there are many studies where nucleation data also do not fall on a single line when In / h o m is plotted versus (In S)'2 (see for example Mullin,3 3 9 Hendrickson and Grant,345 Mullin and Ang, 3 4 6 and Sohnel and Mullin347). Often the data in the literature exhibit two different kinetic regions and the trend is attributed to homogeneous nucleation at high supersaturations and heterogeneous nucleation at low supersaturations. When calculating y in these previous studies, nucleation rates at high supersaturation were only considered, and nucleation rates at low supersaturations (which potentially may have been influenced by heterogeneous nucleation) were not included in the analysis.339,345"347 We follow a similar procedure here. Chapter 6 140 Figure 6.6: Nucleation results as a function of supersaturation. The open squares correspond to the nucleation rates QnJhom) of solid ammonium sulphate in aqueous ammonium sulphate droplets (corresponding to the left ordinate). The solid circles correspond to nucleation rates QnJ^) of solid ammonium sulphate in aqueous ammonium sulphate droplets containing solid kaolinite (corresponding to the right ordinate). The lines are linear fits to the data (neglecting the first 13 % of crystallization events of aqueous ammonium sulphate droplets without solid material). To determine In J0 h o m and y, we neglected the first 13 % of the crystallization events. In other words, we neglected all crystallization events that occurred at (In S)'2 > 0.085, or R H values > 37.7 % RH. A linear fit to the results excluding the first 13 % of the crystallization events is included in Figure 6.6. Over the range of (In S)'2 < 0.085 the data fit well to a straight line when In / h o m is plotted versus (In S)'2. The In / O h o m and /values determined from the intercept and slope of this line are given in Table 6.3. The uncertainties given for In/ O i h o m and / come from the 95 % confidence limits of the intercept and slope from the linear fit. Also included in Table 6.3 are /0,hOm a n < ^ 7 determined in other studies. The parameters Chapter 6 141 determined from Figure 6.6 are in good agreement (within limits of uncertainty) with the values from Chapter 5 (Parsons et al.335). The Rvalue determined in the current study is greater than the ^values determined by Onasch et al. 3 0 5 and Mohan et al. 3 4 8 This discrepancy is likely due to the assumptions made in calculating y in these previous studies. Onasch et al. 3 0 5 measured the R H at which aqueous particles crystallized and then from an estimate of the induction time and an estimate of/ O h o m they calculated a homogeneous nucleation rate (at one RH) and y. Mohan et al. 3 4 8 estimated y based on a measurement of the spinodal curve concentration. Note that in the work in Chapter 5 (Parsons et al.335), two kinetic regions in the experimental data were not clearly discernable. This may be because heterogeneous nucleation by foreign impurities was less of an issue in the previous experiments in Chapter 5 (Parsons et al.335) where droplets suspended in an electrodynamic balance were studied. Table 6.3: Classical Nucleation Theory Parameters for Aqueous Ammonium Sulphate with and without Kaolinite Determined from Experimental Results Parameter Current Data Mohan et al. 3 4 8 Onasch et al. 3 0 5 Parsons et al. 3 3 5 (Chapter 5) T[K] 293.2 ± 0.1 298 298 295 - 300 In (/0,hom / m"3 s"1) 111 ±10 - - 74-129 In CCl / s-') 3 5 ± 2 -yflm2] 0.064 ±0.003 0.05829572 0.052 0.053-0.070 6[°\ 59 ± 2 6.3.4 Classical Nucleation Theory Parameters from J kaol het From the heterogeneous nucleation rate on kaolinite ( / " ) we determined the contact angle between an ammonium sulphate critical nucleus and the kaolinite surface. Based on classical nucleation theory the heterogeneous nucleation rate on kaolinite can be described with the following equation (see Section 2.4 and the Appendix):339 6.8 he. = « h « ' e XPj crit.hom kT Chapter 6 142 Where aha is the pre-exponential factor for heterogeneous nucleation and (f> is described by the following equation:339 , (2 + cosc?)(l-cosc?)2 6.9 0 — 4 6 is the contact angle between the crystalline critical nucleus and the surface of kaolinite. For convenience, we define /<^°'t as: 6-10 / S - « h e t - e x p f - 4 ^ N V kT J The combination of Equations 6.4 and 6.8-6.10 gives an expression for the heterogeneous nucleation rate in terms of the interfacial tension and the contact angle: ( 6 4 -t j kaol 7 kaol _ - 1 1 / he . = /o,het • e X P " 16 / r /V (2 + cos«9)(l-cos<9)2 v 3k3T3 (in Sf 4 In Figure 6.6, we have plotted In / ^ ° ' versus (In S)'2. Note that In /^ t ° ' corresponds to the right ordinate in Figure 6.6. A linear fit to the results is included in Figure 6.6. It appears that the data fit well to a single straight line. From the slope and intercept of In J^°] versus (In S)'2 we determined In and 6 for kaolinite. These values are given in Table 6.3. The uncertainties given for In and 6 come from the 95 % confidence limits of the intercept and slope from the linear fit, respectively. Note that we used the y value determined from the homogeneous nucleation measurements when calculating 6 from the slope of the line. 6.4 Atmospheric Implications 6.4.1 Atmospheric Implications of the Soot Studies It is clear from Figure 6.3 that n-hexane soot particles do not influence the CRH values of ammonium sulphate under the current experimental conditions (observation time and soot surface area). In these experiments the average soot surface area per 30 [im droplet was 4 X 10"8 m2, according to the average BET surface area per unit mass for n-hexane soot given in Table 6.1. Based on data from several field studies, Blake and Kato 3 4 9 found that Chapter 6 143 the average diameter of soot particles in the atmosphere is approximately 0.2 um and they estimated that the average atmospheric soot particle surface area was 4 x 10'12 m 2 (assuming a fractal geometry with the total volume of a soot particle composed of 20 nm spheres). Hence, the average atmospheric soot particle surface area is approximately 4 orders of magnitude less than the surface area used in the current experiments. Soot did not influence the CRH values in the current experiments, so it is unlikely that soot will influence crystallization of atmospheric aqueous droplets (if the soot particles have the same chemical and physical properties as the soot particles investigated in the current studies). 6.4.2 Atmospheric Implications of the Kaolinite Studies It is clear from Figure 6.3 that kaolinite does influence the CRH values of ammonium sulphate in the current experiments. To put these measurements into an atmospheric context, we calculated the R H at which 50 % of aqueous ammonium sulphate droplets internally mixed with kaolinite particulates will crystallize (i.e., CRH50) using atmospherically relevant times and kaolinite particulate sizes. We used diameters ranging from 0.1 to 5 um for atmospherically relevant kaolinite particulate sizes, which is approximately the size range of mineral dust in the atmosphere (see for example, Usher et al.350). Residence times of aerosols in the atmosphere are approximately a week. For this discussion, however, it is more appropriate to consider the temporal variation of R H in the atmosphere. In the continental boundary layer, the R H is often low in the summer and there is a strong diurnal cycle, and the diurnal variation often exhibits a continuously changing relative humidity covering a R H range of typically more than 10 %. For these calculations we will assume that the particles are held at a constant R H for approximately 8 hours, which is a simplification to the true diurnal variation. We also assume that each aqueous ammonium sulphate droplet is internally mixed with a single kaolinite particulate. Finally we assume that the fraction of aqueous ammonium sulphate droplets crystallized can be calculated with the following equation: 6.12 F(RH,/) = l - e x p [ - f c l ( R H ) - ^ k a o l + / h o m (RH)-F) - / ] where F(RH,/) is the fraction of ammonium sulphate particles that have crystallized. This equation is consistent with classical nucleation theory and the statistics of nucleation.339'351 To calculate the nucleation rate of crystalline ammonium sulphate on kaolinite in aqueous Chapter 6 144 ammonium sulphate droplets, we use the parameters listed in Table 6.3. Shown in Figure 6.7 is the R H at which 50 % of aqueous ammonium sulphate droplets containing a kaolinite inclusion with diameter, D k a o l , will crystallize (i.e., the CRH50) under the conditions mentioned above (i.e., t — 8 hours). As an example, the CRH50 of aqueous ammonium sulphate droplets with a kaolinite particulate 0.1 um in diameter will be 41.4 ± 0.5 % RH. Note that the CRH50 is independent of the aqueous ammonium sulphate droplet size since heterogeneous nucleation dominates for this size range of kaolinite inclusion. For comparison, the CRH50 of 0.5 um diameter aqueous ammonium sulphate droplets free of solid material will be 34.3 + 0.5 % RH, assuming an observation time of 8 hours, using the parameters in Table 6.3, and setting A equal to zero in Equation 6.12 to calculate the homogeneous nucleation rate. Also note that Figure 6.7 suggests that the CRH50 of aqueous ammonium sulphate droplets in the atmosphere will depend strongly on the size of the kaolinite particulate, increasing by about 6 % RH with an increase in the diameter of the kaolinite particulate by one order of magnitude or an increase in kaolinite surface area of two orders of magnitude. This trend is also observed in the current CRH50 data presented in Figure 6.3, Panel A. Based on Figure 6.3, Panel A, the CRH50 for droplets with kaolinite increases by approximately 3 % RH when the kaolinite surface area increases by a factor of nine. (In the current experiments we assume that the surface area of kaolinite per unit volume in the droplets is independent of droplet size, and hence an increase in volume by a factor of nine also leads to an increase in surface area of kaolinite by a factor of nine.) This observed increase is consistent with the predictions in Figure 6.7. Chapter 6 145 Figure 6.7: The calculated size of a kaolinite inclusion needed to crystallize 50 % (i.e., the CRH50) of the aqueous ammonium sulphate droplets in the atmosphere (solid line). The calculation assumes that every aqueous ammonium sulphate droplet contains a single, spherical kaolinite inclusion with diameter, -Dkao„ and surface area, A^^, and that the relevant time in the atmosphere for crystallization is approximately 8 hours, which is a simplification to the diurnal cycle of RH (see text). Calculations were carried out using Equation 6.12 and the parameters listed in Table 6.3. The dashed lines indicate the uncertainty of the calculation based on the uncertainty of the parameters given in Table 6.3. A few caveats to the above discussion should be mentioned at this point. First, kaolinite typically only represents 5 to 10 % of the total mass of mineral dust particles in the atmosphere,350 and the other components of mineral dust may also influence CRH50. To accurately predict the effect of mineral dust on crystallization, the entire composition of the dust needs to be considered. This work is a starting point for this analysis. Second, we Chapter 6 146 assumed in the above calculations that each aqueous ammonium sulphate droplet is internally mixed with a kaolinite particulate. This, of course, is an upper limit. Equation 6.12 should only be used to predict the crystallization relative humidity of ammonium sulphate particles that contain kaolinite inclusions (i.e., kaolinite particles with ammonium sulphate coatings); it should not be used to predict the crystallization relative humidity of the entire aerosol population. In regions far removed from large dust sources, a majority of ammonium sulphate particles will not contain mineral dust, although the majority of the mineral dust particles may contain ammonium sulphate. Third, this analysis assumes that the results can be described by classical nucleation theory. This provided a straightforward method to parameterize the current data and extrapolate the results to atmospheric scenarios but suffers from the assumptions inherent to classical nucleation theory. Several others in the past have also used classical nucleation theory to analyze and interpret crystallization results as well as ice nucleation measurements (see for example Hung et al.,3 5 2 Lightstone et al.,2 9 3 Oatis et al.,3 0 4 Onasch et al.,3 0 5 Richardson and Snyder,306 and Tang and Munkelwitz353). Nevertheless, more work, similar to the work by Martin and colleagues,301,303'352 is needed to determine the general applicability of classical nucleation theory to the heterogeneous crystallization of atmospheric particles. Results by Martin et al. 3 0 3 and Han and Martin301 show that an active site model is needed to precisely describe nucleation of crystalline ammonium sulphate and ammonium nitrate on hematite and corundum inclusions. Ice nucleation results on mineral dust cores by Hung et al.3 5 2 also showed some deviation from ideal classical nucleation theory, in that smaller particles had a higher surface-normalized nucleation rate. However, the deviation from classical nucleation theory only resulted in a small uncertainty when calculating important variables like average freezing temperatures.352 Until further information is available, the classical nucleation analysis discussed above provides an initial estimate of the effect of kaolinite on the crystallization of aqueous ammonium sulphate droplets. 6.5 Conclusions and Summary The current results show that the CRH50 of aqueous ammonium sulphate droplets free of solid material does not depend strongly on droplet size, in agreement with previous work conducted with droplets suspended in an electrodynamic balance shown in Chapter 5 Chapter 6 147 (Parsons et al. ). In addition, the results show that soot did not influence the CRH50 of aqueous ammonium sulphate particles under the current experimental conditions (observation time and soot surface area per droplet). In contrast, kaolinite increased the CRH50 of the aqueous ammonium sulphate droplets by approximately 10 % RH. From the crystallization results we determined the homogeneous nucleation rates of crystalline ammonium sulphate in aqueous ammonium sulphate droplets and the heterogeneous nucleation rates of crystalline ammonium sulphate in aqueous ammonium sulphate droplets containing kaolinite. In addition, we parameterized these rates using classical nucleation theory. Based on this analysis, the interfacial tension between an ammonium sulphate critical nucleus and an aqueous ammonium sulphate solution, y, is 0.064 ± 0.003 J m"2 (in agreement with previous measurements in Chapter 5 (Parsons et al.335)), and the contact angle between an ammonium sulphate critical nucleus and a kaolinite surface, 0, is 59 ± 2 °. The current laboratory results were also used to determine if soot or kaolinite will influence the CRH values of aqueous ammonium sulphate droplets in the atmosphere. Based on these results, we argue that soot will not influence the crystallization of aqueous ammonium sulphate particles in the atmosphere. Additionally, using y determined from the current homogeneous measurements and 0 determined from the current kaolinite measurements, we argue that kaolinite can significandy influence the crystallization of aqueous ammonium sulphate droplets in the atmosphere. 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C O N C L U D I N G R E M A R K S 7.1 Conclusions This thesis has described the deliquescence and crystallization phase transitions of organic, inorganic, mixed organic-inorganic, and mixed inorganic-solid particles. The goals outlined in Chapter 1 were achieved using complementary techniques including optical microscopy, particles in a flow cell, and particles in an electrodynamic balance. Specifically, using optical microscopy with particles in a flow cell, the deliquescence and crystallization phase transitions were studied for pure and mixed organic and inorganic particles over a range of temperature or particle composition. And using optical microscopy with particles in an electrodynamic balance (EDB), the crystallization phase transition was studied with pure and mixed organic and inorganic particles over a range of particle composition. The deliquescence results were compared to various thermodynamic predictions and calculations. The crystallization results were analyzed in terms of the kinetics of nucleation and classical nucleation theory. In Chapter 3, the deliquescence relative humidity values for malonic, glutaric, succinic, and adipic acid particles were determined as a function of temperature. The D R H results for these compounds are in good agreement with previous studies that used bulk solutions, supermicrometre particles and submicrometre particles. This agreement suggests that there is no significant kinetic barrier or size dependence to the deliquescence of these dicarboxylic acid particles. The deliquescence measurements were compared with a series of calculations. The results of these calculations suggest that the UNIFAC (universal quasi-chemical functional group activity coefficients) model combined with appropriate interaction parameters should be a useful tool for estimating the deliquescence properties of multi-component organic particles found in the atmosphere. At temperatures below the eutectic, ice was not observed in any of these pure dicarboxylic acid particles, rather the particles underwent deliquescence to form metastable solution droplets. This indicates that the solid organics studied are not good ice nuclei above 243 K and hence will probably not play a role in ice cloud formation at these temperatures. Chapter 7 153 In Chapter 4, DRH* and CRH50 values of four atmospherically relevant internally mixed inorganic-organic systems were measured as functions of particle composition. These measurements agree well with previous results and show that DRH* has litde dependence on the type of organic material. DRH* of ammonium sulphate decreases with increasing organic content, but remains within 10 % RH of the D R H for pure ammonium sulphate over the range of compositions studied for each internally mixed ammonium sulphate-organic system. Thermodynamic calculations based on a simplified version of the model from Clegg et al. 3 5 4 were in agreement with measured values of DRH* up to moderate organic mole fractions for most of the systems studied. Crystallization measurements made for ammonium sulphate particles internally mixed with malonic acid, glutaric acid, glycerol, or levoglucosan showed that even for particles with a low organic mole fraction, crystallization behaviour for internally mixed inorganic-organic particles depended on type of organic material. Therefore, mixed inorganic-organic systems may be more likely to exist as liquid particles. It was estimated that organic compounds on average are only a minor perturbation on the DRH* of the pure inorganic particles in the atmosphere; whereas, the organic compounds on average may significantly decrease the CRH values of pure inorganic particles in the atmosphere and this effect depends on the type of organic material. In Chapter 5, the CRH values of mixed inorganic-malonic acid particles were measured as a function of particle size and as a function of particle composition. It was shown that for aqueous ammonium sulphate-malonic acid particles, the results obtained with an EDB were in agreement with the experiments that utilized particles suspended on a hydrophobic surface in Chapter 4, which confirmed that the hydrophobic support did not influence the crystallization measurements in Chapter 4. On average, malonic acid reduces the CRH50 of pure inorganic particles, but only if the organic mole fraction is large. The size dependent measurements show that the CRH values for aqueous ammonium sulphate particles are not a strong function of particle volume and subsequendy estimated to not be a strong function of observation time. For aqueous ammonium sulphate-malonic acid particles the CRH values were a stronger function of particle size and subsequendy estimated to be a stronger function of observation time. For pure aqueous inorganic particles, CRH values determined in the laboratory (with different volumes and observation times compared to the atmosphere) can be used to directly predict the CRH values in the atmosphere with reasonable accuracy without correcting for a difference in volume or time, simplifying Chapter 7 154 predictions of crystallization in the atmosphere. However, for certain organic mole fractions the CRH values can depend strongly on particle size, emphasizing the need for determining homogeneous nucleation rates for certain organic mole fractions to predict the CRH values of these particles in the atmosphere. The homogeneous nucleation data for ammonium sulphate was parametrized using classical nucleation theory, and should also be an interesting test for theories of homogeneous nucleation. In Chapter 6, the homogeneous and heterogeneous crystallization of ammonium sulphate particles was studied with soot and kaolinite as solid heterogeneous nuclei. The results showed that the CRHJO of aqueous ammonium sulphate droplets free of solid material does not depend strongly on droplet size, in agreement with the findings in Chapter 5. In addition; under the experimental conditions (observation time and solid surface area per droplet), the CRH50 of aqueous ammonium sulphate particles was not influenced by soot, but was increased by kaolinite. The homogeneous nucleation rates were determined for crystalline ammonium sulphate in aqueous ammonium sulphate droplets and the heterogeneous nucleation rates were determined for crystalline ammonium sulphate in aqueous ammonium sulphate droplets containing kaolinite. The homogeneous and heterogeneous nucleation rates were parametrized using classical nucleation theory. Based on the results in Chapter 6, it was argued that soot will not influence the crystallization of aqueous ammonium sulphate particles in the atmosphere and that kaolinite can significandy influence the crystallization of aqueous ammonium sulphate droplets in the atmosphere. The combined results in this thesis present an improved understanding of phase transitions in particles. This information can be applied to atmospheric aerosol particles and, in turn, used to help understand the effects of particles in the atmosphere discussed in Chapter 1. 7.2 Considerations for Future Work A number of further studies are possible to help explain the results or to reduce the application limitations of the results in this thesis. The following are suggestions for further studies that would have a great impact on the results from each chapter in this thesis: 1. In Chapter 3, it was found that UNIFAC could predict the deliquescence R H of organic compounds with reasonable accuracy provided appropriate Chapter 7 155 interaction parameters are available. Further work to improve the interaction parameters for a broad range of compounds that are observed in the atmosphere would be useful. 2. In Chapter 4, variation of the CRH50 results between types of organic compounds was observed. Experimental studies on the viscosities and supersaturations in mixed inorganic-organic aqueous solutions as a function of R H would be useful to help explain these observations. 3. In Chapter 5, it was speculated that the CRH values for ammonium sulphate-malonic acid particles are not a strong function of size for particles with litde organic material. Further work is needed to determine the range of organic concentrations in mixed organic-inorganic particles where crystallization depends strongly on particle size and if this trend is common to other organic compounds in the atmosphere. 4. In Chapter 6, the atmospheric implications of heterogeneous nucleation by kaolinite are limited in application due to the fact that kaolinite typically represents 5 to 10 % of the total mass of mineral dust particles.355 Other components of mineral dust may also influence CRH values and, therefore, further research on the other components of mineral dust (pure and mixed) is needed to improve the overall understanding of heterogeneous nucleation in atmospheric particles. 5. In general, a better understanding of the composition of aerosol particles in the atmosphere would be beneficial for applying the results in this thesis and future results of this type to atmospheric scenarios. In this manner, laboratory studies on the phase transitions of particles can focus on both the types and mixing ratios of compounds to better represent atmospheric aerosol particles in laboratory studies. Various extensions of the projects described in this thesis are also possible. Using flow cell microscopy, the temperature dependence of mixed organic-inorganic crystallization could be obtained to gain insight to the competition between viscosity and supersaturation in particles and the effect of each on crystallization. As temperature is decreased in these systems, viscosity may increase to hinder crystallization and supersaturation may increase to enhance crystallization. Also, a study with mixed organic-inorganic particles with solid Chapter 7 156 inclusions is possible using flow cell microscopy. Organic compounds in such particles may coat the solid inclusion, possibly influencing the effectiveness of the solid as a site for heterogeneous nucleation. Another possible investigation involves the phase transitions, hygroscopic properties, and chemical characterization of particles levitated in the EDB at various stages of a reaction by controlling the flow of gas phase reagents through the EDB. It has already been shown in this thesis that phase transitions are readily observable using the EDB. Also, previous studies with EDBs have investigated the hygroscopic properties of single particles by monitoring the mass of the particle relative to the mass of the dry particle (see, for example, Tang and Munkelwitz356 or Onasch et al.357) in a manner that would be easily attainable after minor modifications to the EDB equipment as described in this thesis. Preliminary tests using a Fourier transform infrared microscope coupled to the EDB have also shown that infrared absorption spectra can be obtained for a single levitated particle, providing insight to the chemical composition of the particle (also see Weritz et al.358). Combining these techniques would allow one to simulate aerosol particle processing that occurs in the atmosphere while monitoring the effects of the reaction on the physical and chemical properties of the particle. Undoubtedly, there is an assortment of possibilities for future work on the physical chemistry of atmospheric aerosol particles. 7.3 References (354) Clegg, S. L.; Seinfeld, J. H.; Brimblecombe, P./. Aerosol Sci. 2001, 32, 713. (355) Usher, C. R.; Michel, A. E.; Grassian, V. H. Chem. Rev. 2003, 103, 4883. (356) Tang, I. N . ; Munkelwitz, H. R. /. Geophys. Res. 1994, 99,18801. (357) Onasch, T. B.; McGraw, R.; Imre, D.J. Phys. Chem. A 2000, 104,10797. (358) Weritz, F.; Simon, A.; Leisner, T. Environ. Sci. Pollut. Res. 2002, 92. Appendix 157 A . A P P E N D I X A.1 Summary of Previous Studies The following tables list other studies that investigated deliquescence or crystallization phase transitions of organic or mixed organic-inorganic systems, and the crystallization of inorganic compounds in the presence of solid material. Table A.1: Summary of Organic and Mixed Organic-Inorganic Phase Transition Studies Type of Organic Organic Compound Inorganic Phase Transition(s) Particle size Reference Compound Compound Studied3 Alkane Tetracosane Sodium chloride DRH(xJ, CRH(xorg) 0.1 um Hansson et al. 3 5 9 Alcohol 1,8-octanediol — DRH, CRH 1' Bulk (film) Demou et al.3 6 0 Glycerol Ammonium sulphate DRH, CRH 10 - 20 um Choi and Chan361 • Sodium chloride DRH, CRH 10 - 20 um Choi and Chan361 Polyethylene glycol Ammonium sulphate DRH, CRH 2 - 20 u m Marcolli and Krieger362 Monocarboxylic Octanoic acid Sodium chloride DRH(xo r g), CRH(xJ 0.1 jam Hansson et al. 3 5 9 acid Laurie acid Sodium chloride DRH(x0 I g), CRH(xorg) 0.1 urn Hansson et al. 3 5 9 Palmitic acid Ammonium sulphate DRH(xJ, CRH 0.1 - 0.5 um Garland et al. 3 6 3 Dicarboxylic acid Oxalic acid — DRH(T) Bulk Brooks et al. 3 6 4 DRH;CRH 10 - 20 um, bulk Peng et al. 3 6 5 DRH(T), CRH 0.5 um, bulk Braban et al. 3 6 6 CRH*5 0.05-0.1 um Prenni et al. 3 6 7 Ammonium sulphate DRH Bulk Wise et al. 3 6 8 DRH(7>org) Bulk Brooks et al. 3 6 4 DRH(xo r g), CRH" 0.1 um Prenni et al. 3 6 9 Table A.1 (continued) B Type of Organic Organic Compound Inorganic Compound Compound Phase Transition(s) Studied2 Particle size Reference Dicarboxylic acid Malonic acid — DRH Bulk Peng et al.3 6 5 DRH(T) Bulk Brooks et al.3 6 4 Hansen and Beyer370 DRH, CRH Bulk (film) Demou et al.3 6 0 DRH(T), CRH 0.5 um, bulk Braban et al.3 6 6 CRH" 0.085 um Prenni et al.3 6 7 Ammonium sulphate DRH Bulk Wise et al.3 6 8 DRHCT,xot^ Bulk Brooks et al. 3 6 4 DRH, CRH 10-20 um Choi and Chan361 DRH(xJ, CRH* 0.1 jam Prenni et al.3 6 9 DRH(xo r g), CRH(xJ 0.5 um Braban and Abbatt371 CRH* 0.1 um Hameri et al.3 7 2 Sodium chloride DRH, CRH 10-20 um Choi and Chan361 U 1 Table A.1 (continued) Type of Organic Organic Compound Inorganic Phase Transition(s) Particle size Reference Compound Compound Studied2 Dicarboxylic acid Succinic acid — DRH 0.05 - 0.1 u m Prenni et al.3 6 7 DRH(T) Bulk Brooks et al.3 6 4 DRH,C CRH 10-20 um, bulk Peng et al.3 6 5 Ammonium sulphate DRH Bulk Wise et al.3 6 8 0.1 um Hameri et al.3 7 2 0.1 um Prenni et al.3 6 9 DRH(T,xJ Bulk Brooks et al.3 6 4 DRH, CRH 10-20 um Choi and Chan361 Ammonium nitrate DRH(XtJ, CRH(xorg) 14-16 umd Lightstone et al. 3 7 3 Sodium chloride DRH, CRH 10-20 um Choi and Chan361 Maleic acid — DRH(T) Bulk Brooks et al.3 6 4 DRH, CRH 15-20 um Choi and Chan374 Ammonium sulphate DRH Bulk Wise et al.3 6 8 DRH(T,^ Bulk Brooks et al.3 6 4 DRH(x^,CRH(xJ 0.5 um Brooks et al.3 7 5 Table A.1 (continued) Type of Organic Organic Compound Inorganic Phase Transition(s) Particle size Reference Compound Compound Studied3 Dicarboxylic acid Glutaric acid — DRH 10 - 20 um Choi and Chan374 DRH(T) Bulk Brooks et al. 3 6 4 CRH'' 0.1 um Prenni et al.3 6 7 Ammonium sulphate DRH Bulk Wise et al. 3 6 8 DRH(*J 0.1 um Cruz and Pandis376 Prenni et al.3 6 9 DRH(T,xJ Bulk Brooks et al. 3 6 4 DRH, CRH 10 - 20 um Choi and Chan361 DRH(xJ, CRH(xJ 2 - 20 um Pant et al. 3 7 7 Sodium chloride DRH(xorg) 0.1 um Chen and Lee378 Cruz and Pandis376 DRH, CRH 10 - 20 um Choi and Chan361 DRH(xJ, CRH(xJ 2 - 20 um Pant et al. 3 7 7 Table A.1 (continued) Type of Organic Compound Organic Compound Inorganic Compound Phase Transition(s) Studied1 Particle size Reference Dicarboxylic acid Adipic acid — DRH0 0.05 - 0.1 urn Prenni et al.3 6 7 DRH(T) Bulk Brooks et al. 3 6 4 Ammonium sulphate DRH(*o r g) 0.1 um Hameri et al. 3 7 2 Prenni et al.3 6 9 DRH(7>org) Bulk Brooks et al. 3 6 4 Pinonic acid Ammonium sulphate 0.1 um Cruz and Pandis376 Sodium chloride DRH(xot^ 0.1 um Cruz and Pandis376 Phthalic acid Ammonium sulphate DRH 0.1 um Hameri et al. 3 7 2 Polycarboxylic acid Citric acid Sodium chloride DRH, CRH 10-20 um Choi and Chan361 Fulvic acid (Nordic — DRH, CRH 0.1 um Gysel et al.3 7 9 aquatic reference) Fulvic acid (Suwannee Ammonium' sulphate DRH(xo r g) 0.1 um Brooks et al. 3 8 0 River reference) Chan and Chan381 DRH, CRH 10 - 20 um Sodium chloride DRH, CRH 10 - 20 jam Chan and Chan381 Table A.1 (continued) Type of Organic Organic Compound Inorganic Phase Transition(s) Particle size Reference Compound Compound Studied2 Polycarboxylic acid Humic acid (Aldrich) Ammonium sulphate DRH(xo r g), CRH(xorg) 0.5 umd Badger et al. 3 8 2 Humic acid (Fluka) — DRH 0.05 - 0.2 um Brooks et al.3 8 0 Ammonium sulphate 0.1 um Brooks et al.3 8 0 Humic acid Ammonium sulphate DRH(*J 0.1 urn Brooks et al.3 8 0 (Leonardite standard) Badger et al.3 8 2 DRH, CRH 0.5 umd Humic acid (Nordic — DRH, CRH 0.1 um Gysel et al.3 7 9 aquatic reference) Chan and Chan381 Ammonium sulphate DRH, CRH 10-20 um Sodium chloride DRH, CRH 10 - 20 um Chan and Chan381 Humic acid (Pahokee Ammonium sulphate DRH(xo r g) 0.1 um Brooks et al. 3 8 0 peat reference) Polyacrylic acids Ammonium sulphate DRH(xo r g) 0.1 um Brooks et al.3 8 0 Keto-carboxylic acidPyruvic acid Sodium chloride DRH(xorg) 0.1 um Chen and Lee3 7 8 Multi-functional L-Malic acid DRH(T) Bulk Brooks et al. 3 6 4 acid Ammonium sulphate DRH Bulk Wise et al.3 6 8 DRH(T,xorg) Bulk Brooks et al. 3 6 4 Table A.1 (continued) Type of Organic Compound Organic Compound Inorganic Compound Phase Transition(s) Studied3 Particle size Reference Protein Bovine serum albumin — DRH, CRH 0.1 um Mikhailov et al. 3 8 3 Sodium chloride DRH(xo r g), CRH(xOIB) 0.1 um Mikhailov et al. 3 8 3 Organic salt Sodium formate — DRH, CRH 20 um Peng and Chan384 Sodium acetate — DRH, CRH 20 um Peng and Chan384 Sodium oxalate — CRH 20 um Peng and Chan384 Ammonium oxalate — CRH 20 um Peng and Chan384 Sodium succinate — DRH, CRH 20 um Peng and Chan384 Sodium pyruvate — DRH, CRH 20 um Peng and Chan384 Sodium methanesulphonate — DRH, CRH 20 um Peng and Chan384 Humic acid sodium salt — DRH, CRH 0.1 um Gysel et al.3 7 9 a All measurements at one composition and room temperature unless otherwise noted. b Upper limit of C R H only. c Lower limit of deliquescence R H only. d Size estimated from experimental description. Table A.2: Summary of Mixed Solid-Inorganic Crystallization2 Studies Type of Solid Solid Inclusion Inorganic Solid Inclusion Reference Inclusion Compound Size Dicarboxylic acid Succinic acid Ammonium nitrate 3.1 - 5.2 um Lightstone et al. 3 7 3 Mineral dust A1 2 0 3 Ammonium sulphate 0.5 um Han et al. 3 8 5 components Han et al.3 8 6 Amorphous silica Ammonium nitrate 0.3 um Ammonium sulphate 0.28 um Martin et al.3 8 7 Corundum Ammonium nitrate 0.15-0.3 urn Han et al.3 8 6 Ammonium sulphate 0.05 - 0.28 um Martin et al.3 8 7 Hematite Ammonium nitrate 0.2 - 0.4 um Han et al.3 8 6 Ammonium sulphate 0.05 - 0.45 um Martin et al.3 8 7 Mullite Ammonium nitrate 0.3 um Han et al.3 8 6 Ammonium sulphate 0.28 um Martin et al.3 8 7 T i 0 2 Ammonium sulphate 0.5 um Han et al.3 8 5 Z r 0 2 Ammonium sulphate 0.5 Um Han et al.3 8 5 Table A.2 (continued) Type of Solid Inclusion Solid Inclusion Inorganic Compound Solid Inclusion Size Reference Solid salt Black carbon BaSCX CaCO, KC1 Na 2S0 4 Talens Indian Ink Soot Ammonium sulphate 0.1 um Ammonium sulphate 0.225 um 0.518-0.664 um Cesium chloride 2 um Potassium fluoride 2 um Sodium chloride 2 um Sodium nitrate 2 um Sodium chloride 0.025 umb Ammonium nitrate 0.05 umb Oatis et al. 3 8 8 Oatis et al.3 8 8 Onasch et al. 3 8 9 Richardson and Snyder390 Richardson and Snyder390 Richardson and Snyder390 Richardson and Snyder390 Even et al.3 9 1 Dougle et al. 392 a All measurements at room temperature. b Solid primary particle size. Appendix 167 A.2 Classical Nucleation Theory Details and Considerations Classical nucleation theory provides a method to determine the activation energy of forming a stable nucleus in an aqueous solution (i.e., the height of the kinetic barrier to nucleation shown in Figure 2.8), AG^j, , as discussed in Section 2.4, and relate this value to the homogeneous nucleation rate, / h o m > and the heterogeneous nucleation rate, Jha, as discussed in Chapters 4 through 6. According to classical nucleation theory and assuming the formation of a spherical solute cluster, the overall change in Gibbs free energy in homogeneously forming the solute cluster, A G h o m , is given by:393'394 A.1 A G h o m = 17trlSKr AG V + 4nrA2ustcj where AG V and yis the volume based Gibbs free energy and the surface area based interfacial tension associated with forming a solute cluster of radius, r c l u s t e r, respectively, as discussed in Section 2.4. Note that y is the interfacial tension between the crystalline solute cluster and the surrounding solution, as opposed to the bulk interfacial tension between bulk solid solute and a surrounding solution, and therefore cannot be determined with bulk methods. The height of the kinetic barrier to forming a solute cluster in a solution is given by A G ^ , at a critical solution cluster radius, r^xa. The following equations are used to derive the expression for AGc"'m . First, r^ta is found by setting the derivative of A G h o m (Equation A.l) with respect to reiser equal to zero and solving for r™Kt :393,394 A.2 4 ^ ( C e j A G v + 8 < : c r r = 0 A crit A " 5 duster ~ A ^ Next, combining Equations A . l and A.3 gives AG^"m as:393'394 A.4 AG™ -™9L 3(AG.) AG V can be found by considering the chemical potential of the solute cluster, // c l u s t c r, i 394 given by: Appendix 168 d A A C I, — ,," I v ^cluster • ^ V • * , /"cluster /"cluster ' j " ^cluster where -/4cluster is the surface area of the solute cluster and //° l u s t e r is the chemical potential of the solute cluster in its standard state. #duster is the number of moles in the cluster, which is related to the density of the cluster, /? d u s t c r, the volume of the cluster, VclusK„ and the molecular weight of the cluster, M c l u s t e r , by: A iC M Pcluster^cluster ^duster - ~ •'"cluster and A.7 d « d u s t e r = ^ ^ d K d u s t e r cluster Combining Equations A.5 and A.7 gives ,394 vM dA A Q n ,,° i ' cluster cluster • n - ° /"cluster — /"cluster ~*~ , T , /^ cluster cluster dA where £ l H H £ L is found from the derivatives of AAwm and K d u s t e r with respect to r d u s t c r, d ^cluster which gives: dA, A.9 cluster ^ ^cluster c^luster Combining Equations A.8 and A.9 gives: A 10 II — 11° ^M^cluster A a U /"cluster - /"cluster + Pcluster'cluster Now consider the chemical potential of the solute in aqueous solution, // s o l u t e, given by:394 A- 1 1 /"solute = /"solute + R T m Solute Where R is the universal gas constant, T is temperature, //° o l u t e is the chemical potential of the solute in aqueous solution in its standard state, and <2solute is the activity of the solute in the aqueous solution. Equilibrium between the solute in aqueous solution and the solute cluster requires Equations A. 10 and A. 11 to be equal such that:394 Appendix 169 A-12 2 y M d u s t " - + . ^ l n « s o l u t e Pcluster ^ cluster If r c l u s t e r is very large (i.e., bulk solid in equilibrium with the solution) then:394 where tfss*[ute is the activity of the solute in a saturated solution. Combining Equations A. 12 and A. 13 gives:394 A.14 2 r M c l u s l e r = RT In ^ sat 0 T a Acluster cluster solute where the ratio of activities is the supersaturation, S: A.15 S = " sat solute Combining Equations A.3, A.14, and A.15 with r d u s t e r equal to r°°'sKr and solving for AG V 394 gives: A.16 AG = - N A ^ c i u s , e r kTlnS M l v ± cluster where NA is Avagadro's number and k is Boltzmann's constant. Note also that:394 Yl -^APclustet _ J _ ^cluster V where vis the molecular volume of the solid. Finally, combining Equations A.4, A.16, and A. 17 gives the final result: A.18 AG_* =• 1 6 ^ V hom 3k2T2(lnS)2 An Arrhenius type equation can be applied to the nucleation process, in which a stable nucleus forms within a homogeneous solution, in the form of:393 ( A G ^ A-19 / h o m =a h o mexp - — V kT J where / h o m is the homogeneous nucleation rate as discussed in Chatpers 4 through 6, is a pre-exponential factor, and AG is an activation energy. AG can be separated into the Appendix 170 activation energy for forming a stable nucleus, AG^' m > a n d t n e activation energy for molecular motion across the cluster-matrix interface, AG' : 3 9 3 A.20 AG = AG™1 + AG' Combining Equations A. 19 and A.20 gives:3 hom .393 ( A / - c n l , A /"I \ A ' 2 1 /hom = « h o m e X P A G h c l + AG' And combining Equations A.18 and A.21 gives: 393 A - 2 2 /hom = /o.hom e X p| where: f 16ny3v2 3k3T3 (in Sf . „ r ( AG' A - 2 3 /o.hom = « h o m e X P - T Z T V kl An equation similar to Equation A . l can be written for the heterogeneous nucleation process. According to classical nucleation theory and assuming the formation of a spherical cap solute cluster on a flat solid surface, the overall change in Gibbs free energy in heterogeneously forming the solute cluster, AG h e t , is given by:394 A 0 / f AG h e t =^ d 3 u s t e r (2 + cosc?)(l-cosc9)2AGv A.24 3 + ^ d u s t e r S i n GJ /cluster-solid ~ Sin fff 7 s o l u t i o n_ s o l i d + 2 ^ ^ (l - COS Ofr where r c l u s t e r is the radius of curvature of the spherical cap, 9 is the contact angle between the solute cluster (with spherical cap geometry) and the flat solid surface, ^ c l u s t e r. s o U d is the interfacial tension between the crystalline solute cluster and the solid surface, and 7soiutjon.soud is the interfacial tension between the solution and the solid surface. In a similar manner as above, setting the derivative of A G h e t (Equation A.24) with respect to r c l u s t e r equal to zero, and with the use of Young's equation, it can be shown that:393'394 A-25 AG£ = A G £ . * where AGhc°' is the activation energy for forming a stable nucleus on a flat solid surface and * is a factor between 0 and 1 given by:393'394 Appendix 171 A.26 (2 + cosc?Xl-cosc?)2 An equation similar to Equation A.21 can be written for the heterogeneous nucleation rate:393 r A.27 /he, = «h=e e x P A G £ + AG' kT where a h e t is a pre-exponential factor. Combining Equations A.l8, A.25, A.26, and A.27 gives the result:393,394 A.28 where: A.29 /het ~ /o.hee e X P i \dny\2 (2 + cos c?Xl-cosc9): 2 \ 3k3T\lnS)2 /o.he, = « h e , e X P AG kT Homogeneous and heterogeneous nucleation rates obtained in the studies described in this thesis were obtained experimentally without the use of the assumptions inherent to classical nucleation theory. Rather, classical nucleation theory was used throughout this thesis as a convenient method to parametrize the homogeneous and heterogeneous nucleation rates obtained experimentally to gain insight into the nucleation process. Numerous assumptions are involved in the above equations for classical nucleation theory, thus limiting the appropriateness of the theory for use in solute nucleation in general. For example, in parametrizing the experimental results of homogeneous and heterogeneous nucleation rates in this thesis, it was necessary to assume / O h o m (cchom and A G ' ) , / 0 h c t (a h e t and AG'), y, and 0 are all constant for each system considered. It has been shown394"397 that this assumption is reasonable over narrow ranges of temperature and supersaturation, such as was used in this thesis. However, in mixed organic-inorganic particles similar to those used in this thesis, viscosity may become more significant with lower R H and affect the nucleation rate through A G ' . Nevertheless, the combined results of homogeneous and heterogeneous nucleation rates presented in this thesis may be an interesting test for theories of nucleation. Appendix 172 A.3 References (359) Hansson, H.-C; Rood, M. J.; Koloutsou-Vakakis, S.; Hameri, K.; Orsini, D.; Wiedensohler, A.J. Atmos. Chem. 1998, 31, 321. (360) Demou, E.; Visram, H.; Donaldson, D. J.; Makar, P. A. Atmos. Environ. 2003, 37, 3529. (361) Choi, M. Y.; Chan, C. K. Environ. Sci. Technol. 2002, 36, 2422. (362) Marcolli, C ; Krieger, U. K. /. Phys. Chem. A 2006, /10, 1881. (363) Garland, R. M.; Wise, M. E.; Beaver, M. R.; DeWitt, H. L.; Aiken, A. C ; Jimenez, J. L.; Tolbert, M. A. Atmos. Chem. Phys. 2005, 5, 1951. (364) Brooks, S. D.; Wise, M. E.; Cushing, M.; Tolbert, M. A. Geophys. Res. Lett. 2002, 29, 1917. (365) Peng, C ; Chan, M. N . ; Chan, C. K. Environ. Sci. Technol. 2001, 35, 4495. (366) Braban, C. F.; Carroll, M. F.; Styler, S. A.; Abbatt, J. P. D. /. Phys. Chem. A 2003, 107, 6594. (367) Prenni, A. J.; DeMott, P. J.; Kreidenweis, S. M.; Sherman, D. E.; Russell, L. M.; Ming, Y.J. Phys. Chem. A 2001, 105, 11240. (368) Wise, M. E.; Surratt, J. D.; Curds, D. B.; Shilling, J. E.; Tolbert, M. A. /. Geophys. Res. 2003, 108, art. no. 4638, doi: 10.1029/2003JD003775. (369) Prenni, A. J.; DeMott, P. J.; Kreidenweis, S. M. Atmos. Environ. 2003, 37, 4243. (370) Hansen, A. R.; Beyer, K. D. /. Phys. Chem. A 2004, 108, 3457. (371) Braban, C. F.; Abbatt, J. P. D. Atmos. Chem. Phys. 2004, 4,1451. (372) Hameri, K.; Charlson, R.; Hansson, H.-C. AIChE J. 2002, 48,1309. (373) Lightstone, J. M.; Onasch, T. B.; Imre, D.; Oatis, S. /. Phys. Chem. A 2000, 104, 9337. (374) Choi, M. Y.; Chan, C. K. /. Phys. Chem. A 2002, 106, 4566. (375) Brooks, S. D.; Garland, R. M.; Wise, M. E.; Prenni, A. J.; Cushing, M.; Hewitt, E.; Tolbert, M. A.J. Geophys. Res. 2003, 108, art. no. 4487, doi: 10.1029/2002JD003204. (376) Cruz, C. N. ; Pandis, S. N . Environ. Sci. Technol. 2000, 34, 4313. (377) Pant, A.; Fok, A.; Parsons, M. T.; Mak, J.; Bertram, A. K. Geophys. Res. Lett. 2004, 31, art. no. L12111, doi: 10.1029/2004GL020025. (378) Chen, Y.-Y.; Lee, W.-M. G. /. Environ. Sci. Health A 2001, 36, 229. Appendix 173 (379) Gysel, M.; Weingartner, E.; Nyeki, S.; Paulsen, D.; Baltensperger, U.; Galambos, I.; Kiss, G. Atmos. Chem. Phys. 2004, 4, 35. (380) Brooks, S. D.; DeMott, P. J.; Kreidenweis, S. M. Atmos. Environ. 2004, 38, 1859. (381) Chan, M. N . ; Chan, C. K. Environ. Sci. Technol. 2003, 37, 5109. (382) Badger, C. L.; George, I.; Griffiths, P. T.; Braban, C. R; Cox, R. A.; Abbatt, J. P. D. Atmos. Chem. Phys. 2006, 6, 755. (383) Mikhailov, E.; Vlasenko, S.; Niessner, R.; Poschl, U. Atmos. Chem. Phys. 2004, 4, 323. (384) Peng, C. G.; Chan, C. K. Atmos. Environ. 2001, 35, 1183. (385) Han, J. H.; Martin, S. T. / . Geophys. Res. 1999, 104, 3543. (386) Han, J. H.; Hung, H. M.; Martin, S. T. / . Geophys. Res. 2002, 107, art. no. 4086, doi: 10.1029/2001JD001054. (387) Martin, S. T.; Han, J. H.; Hung, H. M. Geophys. Res. Lett. 2001, 28, 2601. (388) Oatis, S.; Imre, D.; McGraw, R; Xu, J. Geophys. Res. Lett. 1998, 25, 4469. (389) Onasch, T. B.; McGraw, R.; Imre, D. /. Phys. Chem. A 2000, 104,10797. (390) Richardson, C. B.; Snyder, T. D. Langmuir 1994, 10, 2462. (391) Even, A.; ten Brink, H. M.; Khlystov, A.; Smekens, A.; Berghmans, P.; van Grieken, R. / . Aerosol Sci. 2000, 31, S336. (392) Dougle, P. G.; Veefkind, J. P.; ten Brink, H. M. / . Aerosol Sci. 1998, 29, 375. (393) Mullin, J. W. Crystallisation, 4th ed.; Butterworth-Heinemann: Oxford, U.K. and Boston, MA, 2001. (394) Walton, A. G. Nucleation in Liquids and Solids. In Nucleation; Zettlemoyer, A. C , Ed.; M. Dekker: New York, 1969; pp 225-327. (395) Granberg, R. A.; Ducreux, C ; Gracin, S.; Rasmuson, A. C. Chem. Eng. Sci. 2001, 56, 2305. (396) Kashchiev, D. Nucleation. In Science and Technology of Crystal Growth; van der Eerden, J. P., Bruinsma, O. S. L., Eds.; Kluwer Academic Publishers: Netherlands, 1995; pp 53-66. (397) Mullin, J. W.; Osman, M. M. Krist. Tech. 1973, 8, 471. 

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