Efflorescence and deliquescence of airborne particles

... Particles .………………………………………… 1.2 Deliquescence and Efflorescence of Airborne Particles …… 1.3 Experimental Measurements of DRH and ERH……………… 1.4 Investigation on DRH and ERH of Airborne Particles …… 1.5 Objectives………………………………………………………... size change of these aerosol particles 1.2 Deliquescence and Efflorescence of Airborne Particles The amount of water associated with airborne particles depends on the RH in atmosphere and the water... diagram of deliquescence and efflorescence processes 1.3 Experimental Measurements of DRH and ERH To understand the deliquescent and efflorescent behaviors of atmospheric particles, measurements of

EFFLORESCENCE AND DELIQUESCENCE OF AIRBORNE PARTICLES GAO YONGGANG (B. ENG., BEIJING UNIVERSITY OF CHEMICAL TECHNOLOGY) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CHEMICAL AND BIOMOLECULAR ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2007 ACKNOWLEDGEMENTS I want to express my gratitude to National University of Singapore who gave me financial support to complete my research work. I am deeply indebted to my supervisors Professor Shing Bor CHEN and Professor Liya E YU whose help, stimulating suggestions, critical evaluation, open-minded discussion and encouragement helped me in all the time of research and writing of this thesis. I would like to thank my committee members: Professor CHUNG, Tai-Shung Neal and Professor ZHAO, Xiu Song George who generously shared their knowledge and gave me constructive criticism and comments. I would also like to give my greatest appreciation to other postgraduate students in Professor CHEN’s research group: Dr. ZHOU Tong, Mr. ZHAO Guangqiang, Ms. ZHOU Huai and in Professor YU’s research group: Dr. YANG Liming, Mr. ZHOU Hu, Mr. SINGH Avinash, Mr. LIM Jaehyun, Ms. PAL Amrita, Mr. KUMAR Balasubramanian Suresh for their help and valuable discussions and comments. I wish to express my heartful thanks to the following kind people who gave me help and support for my experimental work: Mdm. CHIA Susan, Mdm. LI Xiang, Dr. YUAN Zeliang, Mdm. FAM Samantha, Mdm. KHOH Sandy, Mdm. SIEW Jamie, Mr. NG Kim Poi, Dr. XU Fujian, Dr. YANG Qian and Mr. YUAN Shaojun. I particularly thank Professor ZENG Huachun very much who allowed me to use AFM in his research lab. i Especially, I want to thank my parents and parents-in-law for their understanding, love and support. I would like to give my special thanks to my wife MEN Yali whose patient love and understanding enabled me to complete this research work. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS………………………………………………... i TABLE OF CONTENTS…………………………………………………... iii SUMMARY…………………………………………………………………. vi LIST OF TABLES………………………………………………………….. ix LIST OF FIGURES………………………………………………………… xi NOMENCLATURE………………………………………………………... xiv CHAPTER INTRODUCTION……………………………………… 1 1.1 Airborne Particles….…………………………………………... 1 1.2 Deliquescence and Efflorescence of Airborne Particles……… 3 1.3 Experimental Measurements of DRH and ERH……………… 4 1.4 Investigation on DRH and ERH of Airborne Particles………. 7 1.5 Objectives………………………………………………………... 9 1.6 Organization…………………………………………………….. 9 1 CHAPTER 2 EFFLORESCENCE RELATIVE HUMIDITY OF AIRBORNE AMMONIUM SULFATE AND SODIUM CHLORIDE PARTICLES……………………………... 11 2.1 Introduction……………………………………………………... 11 2.2 Basic Theories and ERH Prediction…………………………… 14 2.2.1 The Kelvin Effect on Relative Humidity…………………. 14 2.2.2 Homogeneous Nucleation in an Aqueous Droplet………... 15 iii 2.2.3 Homogeneous Nucleation Rate…………………………… 18 2.2.4 ERH Prediction…………………………………………… 18 2.2.4.1 Ammonium Sulfate Droplets………………………………….. 18 2.2.4.2 Sodium Chloride Droplets…………………………………….. 22 2.3 Experimental…………………………………………………….. 24 2.4 Results and Discussions………………………………………… 27 2.4.1 Ammonium Sulfate Particles……………………………... 27 2.4.2 Sodium Chloride Particles………………………………… 36 2.5 Conclusions……………………………………………………… 41 CHAPTER 3 EFFLORESCENCE RELATIVE HUMIDITY OF MIXED SODIUM CHLORIDE AND SODIUM SULFATE PARTICLES………………………………... 43 3.1 Introduction……………………………………………………... 43 3.2 Theories and ERH Prediction………………………………….. 45 3.3 Experimental……………………………………………………. 54 3.4 Results and Discussions………………………………………… 55 3.5 Conclusions……………………………………………………… 64 CHAPTER 4 EFFECTS OF ORGANICS ON EFFLORESCENCE RELATIVE HUMIDITY OF AMMONIUM SULFATE OR SODIUM CHLORIDE PARTICLES………………. 65 4.1 Introduction……………………………………………………... 65 4.2 Theories and ERH Prediction………………………………….. 67 4.3 Results and Discussions………………………………………… 75 4.4 Conclusions……………………………………………………… 84 iv CHAPTER 5 THEORETICAL INVESTIGATION OF SUBSTRATE EFFECT ON DELIQUESCENCE RELATIVE HUMIDITY OF NaCl PARTICLES……………………... 86 5.1 Introduction……………………………………………………... 86 5.2 Deliquescence of a Deposited Particle…………………………. 90 5.3 Results and Discussions………………………………………… 94 5.4 Conclusions……………………………………………………… 108 CHAPTER 6 CONCLUSIONS AND FUTURE WORK...…………... 109 6.1 Conclusions……………………………………………………… 109 6.2 Future Work…………………………………………………….. 111 BIBLIOGRAPHY…………………………………………………………... 113 APPENDICES………………………………………………………………. 135 Appendix A…………………………………………………………….. 135 Appendix B…………………………………………………………….. 136 LIST OF PUBLICATIONS………………………………………………... 137 v SUMMARY This work aims to investigate efflorescence relative humidity (ERH) of suspended particles and deliquescence relative humidity (DRH) of deposited particles by developing theoretical models with experimental validation. A classical homogeneous nucleation theory is employed to investigate the ERH of airborne ammonium sulfate (AS) particles with a wide size range, 8 nm – 17 µm, and ERH of airborne sodium chloride (NaCl) particles in sizes ranging from 6 nm to 20 µm at room temperature. The developed theoretical predictions are in good agreement with the experimentally measured values. For AS, the ERH first decreases with decreasing particle size, and reaches a minimum around 30% for an AS particle of 30 nm, before increases with decreasing nanometer-sized AS particles. It is for the first time that the Kelvin effect is shown to substantially affect the ERH of AS particles smaller than 30 nm, while the aerosol size is the dominant factor affecting the efflorescent behavior of AS particles larger than 50 nm. For NaCl, when particle sizes are larger than 70 nm, their ERH decreases with decreasing dry particle sizes, and reaches a minimum around 44% RH, otherwise the ERH increases with decreasing dry particle sizes (< 70 nm) because of the Kelvin effect. Compared with AS particles, the Kelvin effect on ERH is stronger for NaCl particles smaller than 30 nm, while the dry particle size exerts weaker influence on NaCl particles larger than 70 nm. The ERH of particles composed of mixed two inorganic components, sodium vi chloride and sodium sulfate (Na2SO4), was also investigated by building a formulation based on the previously developed theoretical model for ERH of single-component particles assuming that one salt nucleates much faster than the other, and the critical nuclei formation of the former controls the rate of efflorescence. The predicted ERHs agree favorably with the experimental data, except for particles containing Na2SO4 in a mole fraction of around 0.25. At this composition, the model built in this work underestimates the ERH, indicating factors involving interaction between solutes may need to be incorporated to better theoretically describe the particle behavior with this mixing ratio. Relative to particles larger than 40 nm, Kelvin effect more significantly affects particles smaller than 20 nm and containing a higher Na2SO4 mole fraction. Effects of water soluble organics (glycerol, levoglucosan, malonic acid, glutaric acid, maleic acid) on ERH of AS or NaCl particles were also theoretically investigated based on the same model framework. These water soluble organics (WSOs) appeared to suppress the ERH of AS and NaCl particles; decrease in ERH of mixed particles is more than 30% RH when the mole fraction of WSOs is larger than 0.5. However, the developed model only satisfactorily predicts the ERH of mixed particles comprising WSOs with low surface active nature (glycerol, levoglucosan, malonic acid). The ERH prediction, which is less than satisfactory, of mixed particles comprising WSOs with high surface active nature (glutaric acid, maleic acid) might be attributed to the assumptions (e.g., no interaction between solutes) of the model and the approach of estimating interfacial tension between nuclei and the mixed solution. The last part of this thesis work devotes to, for the first time, the theoretical vii exploration of the DRH of NaCl particles depositing on a substrate. The formulation incorporates the Kelvin effect with the assumption that the dry and wet particles are both spherical caps in shape. Unlike the deposited particles larger than 500 nm, the DRH of smaller particles can substantially depend on the particle size, contact angles, and surface tension between particles and atmosphere. At certain contact angles, small particles depositing on a substrate could deliquesce at a much lower RH, posing a potential corrosion problem for metallic substrates. viii LIST OF TABLES Table 1.1 Techniques used to measure DRH and ERH. 5 Table 1.2 Theoretical studies for DRH. 8 Table 2.1 Experimentally observed DRH and ERH of suspended (NH4)2SO4 and NaCl particles in different sizes. 12 Table 2.2 Calculated quantities as functions of molality at 298 K for an AS particle with a dry diameter of 100 nm. 21 Table 2.3 Experimentally obtained & theoretically calculated ERH. 34 Table 2.4 Calculated ERHs for AS particles with different diameters (induction time=1 s). 35 Table 2.5 Effect of induction time on the estimated ERH of AS particle with a dry diameter of 100 nm. 36 Table 2.6 Comparison of ERHs based on experimental observations (Hämeri et al., 2001) and theoretical prediction (this study). 39 Table 2.7 Calculated ERH for NaCl and (NH4)2SO4 particles with different dry mobility diameters. 41 Table 3.1 Physical properties of Na2SO4 and NaCl. 47 Table 3.2 Calculated physical quantities with varying water activity for the case of a dry particle with diameter of 1 µm and the NaCl-to-Na2SO4 mole ratio of 1:1. 53 ix Table 3.3 ERH comparison between prediction and experimental data in this study. The calculated nucleation rates of two salts at ERH are also shown. 56 Table 3.4 ERH comparison between prediction and experimental data of Lee and Chang (2002). The calculated nucleation rates of two salts at ERH are also shown. 58 Table 3.5 Variation of predicted ERH with dry diameter of mixed NaCl and Na2SO4 particles. The residence time is 15 min. 62 Table 3.6 Variation of predicted ERH with residence time for mixed NaCl and Na2SO4 particles with a dry diameter of 45 nm and xβ =0.5. 63 Table 3.7 Variation of ERH with σnuc-air for mixed NaCl and Na2SO4 particles with a dry diameter of 45 nm. The residence time is 60 s. 63 Table 4.1 Physical properties of salts and WSOs. 68 Table 4.2 Structures and group no. of WSOs. 74 Table 4.3 UNIFAC group interaction parameters. 74 Table 5.1 Available experimental DRHs of deposited (NH4)2SO4 and NaCl particles. 87 Table 5.2 DRHs of suspended NaCl particles in nanometer size. 88 x LIST OF FIGURES Figure 1.1 Schematic diagram of deliquescence and efflorescence processes. 4 Figure 1.2 Schematic illustration of TDMA measurement. 7 Figure 2.1 Variation of the Gibbs energy change for nucleation at three different values of supersaturation (S). ∆Gh* is 17 the barrier energy and critical radius. r * is the corresponding Figure 2.2 Schematic setup for ERH measurements of AS particles: (1) Mass flow controller; (2) and (3) RH measurement ports. 25 Figure 2.3 Effects of the flow rate of dry air on RH in the exposure tube. 26 Figure 2.4 Growth factor and efflorescence trends for AS particles with a dry-state diameter of (a) 8 nm, (b) 15 nm, (c) 30 nm, and (d) 50 nm. 30 Figure 2.5 Growth factor and efflorescence trends for AS particles with a dry-state diameter of (a) 43.7 nm, and (b) 47 nm. 31 Figure 2.6 Growth factor and efflorescence trends for AS particles with a dry-state diameter of (a) 5 µm and (b) 6 µm. 33 Figure 2.7 ERH of the NaCl particles with dry mobility diameter of 6 – 70 nm. 37 xi Figure 2.8 Growth factor of NaCl particles with a dry mobility diameter of (1) 6 nm, (2) 8 nm, (4) 10 nm, (4) 15 nm, (5) 20 nm, (6) 30 nm, (7) 40 nm, and (8) 60 nm. (Theoretical estimation in this study ( ― ) and experimental data from Biskos et al., 2006a ( □, ○)). 38 Figure 3.1 Flowchart for the calculation procedure of ERH. 52 Figure 3.2 Variation of ERH with the mole fraction of Na2SO4 (xβ) for mixed NaCl-Na2SO4 particles with average dry-state diameter of 45 nm. 57 Figure 3.3 Variation of ERH with the mole fraction of Na2SO4 (xβ) for mixed NaCl-Na2SO4 particles with dry-state diameters of 1 µm and residence time of 15 min. The experimental data are extracted from the work of Lee and Chang (2002). 59 Figure 4.1 Experimental and calculated ERHs of mixed (NH4)2SO4-glycerol particles with average dry diameter of 10 µm and observation time of 150 S. 76 Figure 4.2 Experimental and calculated ERHs of mixed (NH4)2SO4-levoglucosan particles with average dry diameter of 10 µm and observation time of 150 S. 77 Figure 4.3 Experimental and calculated ERHs of mixed (NH4)2SO4-malonic acid particles with average dry diameter of 10 µm and average observation time of 200 S. 78 Figure 4.4 Experimental and calculated ERHs of mixed (NH4)2SO4-glutaric acid particles with average dry diameter of 10 µm and observation time of 150 S. 79 Figure 4.5 Experimental and calculated ERHs of mixed NaCl-glutaric acid particles with average dry diameter of 10 µm and observation time of 150 S. 80 xii Figure 4.6 Experimental and calculated ERHs of mixed (NH4)2SO4-maleic acid particles with average dry diameter of 0.6 µm and residence time of 120 S. 81 Figure 4.7 Surface tension of aqueous WSO solution as a function of molality. 84 Figure 5.1 Schematic of a deposited particle on a substrate before and after deliquescence. 91 Figure 5.2 Effect of surface tension on the DRH of suspended NaCl particles. The prediction is compared with experimental data of Biskos et al. (2006a) and Hämeri et al. (2001) and with the model of Russell and Ming (2002). 95 Figure 5.3 σCV effect on DRH variation with θ1 for deposited particles having a volume equivalent diameter (VED) of 63 nm at θ2=10o, 90o, and 180o. 97 Figure 5.4 Sketch of variations of Gibbs free energies of a deposited solid particle and its aqueous solution with relative humidity (Seinfeld and Pandis, 1998). The arrows indicate the directions of curve shift with decreasing contact angles, particle size or surface tension. 99 Figure 5.5 DRH of a deposited particle as a function of θ1 with σCV = 0.131 and 0.213 N/m and at θ2=10o, 90o, and 180o. 101 Figure 5.6 Variation of DRH with θ2 for different particle sizes at θ1=180o, 90o, 60o, and 10o. 103 Figure 5.7 Contour plots for DRH as a function of the contact angles (θ1 and θ2) for deposited NaCl particles with dry diameter: D=63 nm (a), 257 nm (b) and 555 nm (c). The value for each curve denotes the DRH in %. 106 xiii NOMENCLATURE A interfacial area AIM aerosol inorganic model ai activity of solute or solvent in a solution a0 solute activity of the saturated solution aij contact area between phase i and j amn UNIFAC group interaction parameters AS ammonium sulfate aw water activity Aγ Debye-Huckel constant C(D) Cunningham slip correction factor CCN cloud condensation nuclei CDRH complete deliquescence relative humidity CRH crystallization relative humidity D droplet diameter DAASS dry ambient aerosol size spectrometer Ddry dry particle diameter Dm,dry mobility diameter DRH deliquescence relative humidity Dv,dry volume equivalent diameter EA-TCD element analysis using thermal conductivity detection ECM electrical conductivity method EDB electrodynamic balance ERH efflorescence relative humidity ESEM environmental scanning electron microscope ETEM environmental transmission electron microscope xiv Fnuc-drop interaction energy per unit area across the interface between the nucleus and drop FTIR fourier transform infrared spectrometer G Gibbs free energy GC-TCD gas chromatography with thermal conductivity detection GF growth factor i molecule number of the solute in the nucleus I ionic strength Ikelvin Kelvin effect IN ice nuclei J formation rate for a unit volume of a critical nucleus in a supersaturated droplet J0 kinetic factor Jc critical nucleation rate KM Kusik and Meissner KB, k Boltzmann constant lpm litre per minute m salt molality MDRH mutual deliquescence relative humidity Msalt salt molar mass Mw water molar mass N, n molecule number NA Avogadro’s constant OM optical microscopy OPC optical particle counter p actual water vapor pressure pc water vapor pressure over droplet solution psol water vapor pressure over the aqueous solution xv pw water vapor pressure at saturation R molar gas constant, 8.314 J·mol-1·K-1 r radius of the nucleus r* critical nuclei radius RH relative humidity Ri curvature radii of i object R curvature radii RS Mie and raman spectroscopy RSMS rapid single-particle mass spectrometry S supersaturation ratio S* critical supersaturation SMPS scanning mobility particle sizer t induction time T absolute temperature TDMA tandem differential mobility analyzer TnDMA tandem nano-differential mobility analyzer UF-DMA ultrafine tandem differential mobility analyzer UNIFAC UNIQUAC Functional Group Activity Coefficients VED volume equivalent diameter v volume of a molecule Ve particle volume at efflorescence Vw molar volume of pure water wf mass fraction WSOs water soluble organics x mole fraction of water or solute in the solution zi absolute charge number of ion species i α, β solutes in water solution γ activity coefficient xvi θ contact angle ∆G change in Gibbs free energy ∆Gh* free energy barrier ∆µ chemical potential difference µ chemical potential of a species ρsalt density of salt ρsol, ρi density of solution i ρw water density σ interfacial tension χ shape factor xvii CHAPTER 1 Introduction 1.1 Airborne Particles Airborne particles, also called to atmospheric aerosols or atmospheric particles, are suspensions of solid or liquid particles in a gas phase. In the atmosphere, concentrations of airborne particles can be up to 107~108 cm-3 (Seinfeld and Pandis, 1998) with a size ranging from several nanometers to tens of micrometers. Airborne particles can be attributed to various sources, such as volcano eruptions, industrial emissions, sea spray, and various combustion processes. Airborne particles consist of multiple components, such as inorganic salts (ammonium sulfate, sodium chloride, ammonium chloride, etc), organic species (alkanedioic acids, hydroxyalkanoic acids, aromatic acids, etc), crustal species (silicon, calcium, aluminum, etc), metal oxides, and water (Seinfeld and Pandis, 1998). Inorganic salts and organic species account for 25~50% and 20~60%, respectively, of fine airborne particles without water by mass depending on locations (Gray et al., 1986; Heintzenberg, 1989; Rogge et al., 1993; Alfarra et al., 2004). Airborne particles have many effects on the atmospheric environment, such as visibility degradation. The visibility, generally denotes visual range, is reduced by the absorption and scattering of light by both gases and aerosol particles. The absorption of light is sometimes contributed to atmospheric colorations, whereas the light 1 scattering by aerosols is the main reason causing the degradation of visibility (Seinfeld and Pandis, 1998). Atmospheric particles also influence the earth climate via altering the radiation balance through direct and indirect mechanisms. The direct forcing is induced by scattering and absorption of solar and infrared radiation from the aerosol particles themselves. The indirect forcing is induced by the effect of aerosol particles, acting as cloud condensation nuclei (CCN) or ice nuclei (IN) which play an important role on cloud formation and precipitation efficiency, cloud albedo, and optical depth (Seinfeld and Pandis, 1998; Rosenfeld, 2000). In addition, atmospheric particles have significant effects on human health (Dockery et al., 1993; Sidhu et al., 1997; Donaldson et al., 1998) and corrosion of electronic materials and devices (Sinclair, 1988; Sinclair et al., 1990; Frankenthal et al., 1993; Litvak et al., 2000). Uptake and losing of water by aerosols under different relative humidity conditions can be important for abovementioned effects, mainly due to the size and phase changes of airborne particles. During water condensation and evaporation, most inorganic salts (e.g. ammonium sulfate, sodium sulfate and sodium chloride) and some organic species (e.g. glutaric acid, L-glycine, L-glutamine and succinic acid) have the deliquescent and efflorescent/crystallization behaviors, two main atmospheric processes, which are contributed to phase transition between solid and liquid and size change of these aerosol particles. 2 1.2 Deliquescence and Efflorescence of Airborne Particles The amount of water associated with airborne particles depends on the RH in atmosphere and the water absorption property of airborne particles. Figure 1.1 schematically shows the deliquescent and efflorescent behaviors of airborne particles. When RH increases from a lower level, particles remain at almost a dry state (from a to b) until a sufficiently high RH, deliquescence RH (DRH), under which dry particles substantially absorb water (water condensation) suddenly to become large droplets (from b to c). As RH further increases, the droplets will continue to grow in size (from c to d). On the other hand, as RH decreases airborne droplets decrease in size (d to e) through continuous water evaporation and remain at a metastable and supersaturated state until a low RH, efflorescence RH (ERH) or crystallization RH (CRH), at which supersaturated droplets undergo spontaneous crystallization (liquid (e) to solid (a)). The hysteresis process (cycle a-b-c-e-a) plays an important role of affecting particle phase (solid or liquid or a combination of both), size, mass and optical properties (Cziczo et al., 1997; Seinfeld and Pandis, 1998; Martin et al., 2003). In other words, whether the airborne particles exist in a solid or liquid state depends on RH and RH history in air. Hence, understanding the deliquescent and efflorescent behaviors of airborne particles well is important to understand and simulate atmospheric processes affecting air quality, visibility, cloud and fog formation, climate change, etc (Seinfeld and Pandis, 1998). 3 d Particle Diameter c e Efflorescence a b Deliquescence Solid phase Relative Humidity Figure 1.1 Schematic diagram of deliquescence and efflorescence processes. 1.3 Experimental Measurements of DRH and ERH To understand the deliquescent and efflorescent behaviors of atmospheric particles, measurements of DRH and ERH of airborne particles have been taken place, which are summarized in Table 1.1. Employed techniques are based on the effect of water absorption and evaporation on particle mass, optical properties and diameter, or based on images and conductivity of airborne particles. Thereof, the direct measurement of particle diameter can be carried out via dry ambient aerosol size spectrometer (DAASS), ultrafine tandem differential mobility analyzer (UF-DMA), tandem 4 nano-differential mobility analyzer (TnDMA), or tandem differential mobility analyzer (TDMA). In current work, a TDMA system was used for experimental studies (Chapters 2 and 3). TABLE 1.1: Techniques used to measure DRH and ERH. Technique Abbr. Basis References Electrodynamic balance EDB Mass Tang et al., 1986 Choi and Chan, 2002 Mie and raman spectroscopy RS Optical Jordanov and Zellner, 2006 Optical particle counter OPC Optical Hand et al., 2000 Fourier transform infrared spectrometer FTIR Optical Han and Martin, 1999 Schlenker et al., 2004 Nephelometry or dual-nephelometry Optical Rood et al., 1985 McInnes et al., 1998 Environmental transmission electron ETEM Image Wise et al., 2005 ESEM Image Ebert et al., 2002 OM Image Pant et al., 2006 Thermal Lee and Hsu, 1998 microscope Environmental scanning electron microscope Optical microscopy Element analysis using thermal EA-TCD conductivity detection Gas chromatography conductivity with thermal GC-TCD conductivity detection Electrical conductivity method ECM Thermal Chang and Lee, 2002 conductivity Lee and Chang, 2002 Electrical Yang et al., 2006 conductivity Dry ambient aerosol size spectrometer DAASS Size Stanier et al., 2004 Ultrafine tandem differential mobility UF-DMA Size Hämeri et al., 2001 TnDMA Size Biskos et al., 2006a TDMA Size Cruz and Pandis, 2000 analyzer Tandem nano-differential mobility analyzer Tandem differential mobility analyzer Prenni et al., 2003 5 Figure 1.2 shows the schematic measurement principle of TDMA which basically consists of two differential mobility analyzers (DMAs) equipped with electrostatic classifiers and one condensation particle counter (CPC). DMA1 is used to select monodisperse particles from polydisperse particles according to their electrical mobility. Hence, the measured diameter of particles is considered as electrical mobility equivalent diameter defined as the diameter of a singly charged spherical particle with the same electrical mobility as the particle being detected (Seinfeld and Pandis, 1998). When initial polydisperse particles are in dry phase, monodisperse particles with known size are then exposed to high RH to induce growth of particles by water condensation in an exposure tubing; when initial polydisperse particles are in liquid phase, the monodisperse particles can be exposed to high or low RH to increase or decrease size via water condensation or water evaporation in an exposure tubing. At the outlet of the exposure tubing, size of the monodisperse particles is detected via DMA2 and counted by a CPC. A DMA coupled with a CPC are also called as scanning mobility particle sizer (SMPS). To avoid diffusional broadening of the DMA transfer function, the investigated particles should be larger than 30 nm (Hagwood et al., 1999); otherwise, the investigation of particles smaller than 30 nm should be conducted by UF-DMA or Nano-DMA (Hämeri et al., 2001; Biskos et al., 2006a). 6 Figure 1.2 Schematic illustration of TDMA measurement. 1.4 Investigation on DRH and ERH of Airborne Particles Laboratory investigations on DRH and ERH of airborne particles have been carried out for several decades using various experimental tools as shown in Table 1.1, including single inorganic particles, e.g., (NH4)2SO4, NaCl, Na2SO4 (Orr et al., 1958; Tang et al., 1977; Tang and Munkelwitz, 1994; Cziczo et al., 1997; Biskos et al., 2006a), single organic particles, e.g., glutaric acid, maleic acid, malonic acid (Choi and Chan, 2002a; Braban et al., 2003) and mixed particles, e.g., Na2SO4-NaCl, HH4Cl-NaCl, NaCl-glutaric acid, (NH4)2SO4-glutaric acid (Ha et al., 2000; Lee and Chang, 2002; Choi and Chan, 2002b). Theoretical investigation on DRH of airborne particles has also been developed as shown in Table 1.2. Thereof, only models 10–12 investigated how particle size affects DRH, namely, Kelvin effect. 7 TABLE 1.2: Theoretical studies for DRH. No. 1 Model SCAPE2 Particle component + + 2+ References + + - NH4 /Na /Ca /Mg /K /NO3 / 2- - 2- SO4 /Cl /CO3 2 3 ISORROPIA EQUISOLVII + + + + Kim et al., 1993a and b Kim and Seinfeld, 1995 - - 2- NH4 /Na /NO3 /SO4 /Cl 2+ + + Nenes et al., 1998 - NH4 /Na /Ca /Mg /K /NO3 / Jacobson et al., 1996 SO42-/Cl-/CO32- Jacobson et al., 1999 + + - 2- - Ansari and Pandis, 1999 + + - 2- - Clegg et al., 1998a and b + + 2+ + + 2+ + + - 2- - Topping et al., 2005 + + - 2- - NH4 /Na /NO3 /SO4 /Cl Amundson et al., 2006 10 NaCl Mirabel et al., 2000 11 NaCl Djikaev et al., 2001 12 Electrolytes Wexler and Seinfeld, 1991 13 NaCl/(NH4)2SO4/Malonic acid Russell and Ming, 2002 14 Electrolytes and organics Clegg et al., 2001 15 Electrolytes and organics Raatikainen and Laaksonen, 2005 16 Organics/mixed salt and organic Clegg and Seinfeld, 2006 4 5 GFEMN AIM2 (Model III) NH4 /Na /NO3 /SO4 /Cl NH4 /Na /NO3 /SO4 /Cl Wexler and Clegg, 2002 6 EQSAM + + - NH4 /Na /Ca /Mg /K /NO3 / 2- - SO4 /Cl 7 8 9 MESA ADDEM UHAERO Metzger et al., 2002 Trebs et al., 2005 - 2- - NH4 /Na /Ca /NO3 /SO4 /Cl NH4 /Na /NO3 /SO4 /Cl Zaveri et al., 2005 However, except the work of ERH of bulk (NH4)2SO4-H2SO4 solution by Amundson et al. (2006), theoretical investigation rarely incorporates Kelvin (size) effect to study ERH of airborne single and mixed particles. In addition, all models in Table 1.2 are for suspended particles, while no theoretical model is available to investigate substrate effects on DRH of deposited particles, which is important because atmospheric particles can easily deposit on surface during random movement. A substantial water sorption of deposited particles can eventually lead to surface corrosion, a serious problem in the electronic industry (Sinclair et al., 1990; Frankenthal et al., 1993; Litvak et al., 2000). Although Ebert et al. (2002) and Wise et al. (2005) experimentally investigated the DRHs of microsized deposited 8 ammonium sulfate and sodium chloride particles using Environmental Scanning Electron Microscope (ESEM) and Transmission Electron Microscope (ETEM), respectively, they observed the DRH close to those of big (>100 nm) suspended particles and reported unnoticeable substrate effect on DRH. Hence, more studies on smaller ( 10 mol/kg. Otherwise, the empirical equation of Tang et al. (1986) is employed: 23 1 2 a w = exp[-0.03604 × m + 0.01649 × (1 + 1.37 × m ) - 0.01649 × 4.60517 1 2 × log(1 + 1.37 × m ) - 0.01649 1 2 - 1.1601× 10 -3 × m 2 - 2.6572 (2.26) (1 + 1.37 × m ) × 10 × m + 1.7029 × 10 -5 × m 4 ] -4 3 Note that the molality of a saturated NaCl solution is 6.143 mol/kg at 298 K. The procedure of ERH prediction is identical to ammonium sulfate. 2.3 Experimental To investigate the size change in the suspended AS particles under decreasing RH, a tandem differential mobility analyzer (TDMA) system was employed as Figure 2.2 shows, which consists of an electrostatic classifier (Model 3080L, TSI Inc., USA), an exposure chamber, and a scanning mobility particle sizer (Model 3034 SMPS, TSI Inc., USA). AS particles were produced through the atomization of a solution containing 0.2 wt% of (NH4)2SO4 (purity >99%, Merck, Germany). They were carried by air through the aerosol generation system followed by the particle size classifier with an aerosol-to-sheath flow rate of 0.1. The resulting mono-dispersed wet AS particles with a size around 80 nm at a flow rate of 1±0.1 lpm were then mixed with a dry air stream (RH 70 nm). The dry particle size and the induction time during homogeneous nucleation are the two major factors affecting the accuracy of theoretically predicted ERH. According to the induction time adopted in this study, the estimated ERH could be somewhat higher than the actual value. 42 CHAPTER 3 Efflorescence Relative Humidity of Mixed Sodium Chloride and Sodium Sulfate Particles 3.1 Introduction Inorganic salts account for 25~50% of fine aerosol mass (Heintzenberg, 1989). Since atmospheric particulates contain a complicated chemical composition, understanding deliquescent and efflorescent behaviors of multi-component particles is important to elucidate their effects on air quality, visibility degradation and climate change (Seinfeld and Pandis, 1998). Deliquescent behavior of particles composed of multicomponents, such as NaCl-Na2SO4, NH4Cl-NH4NO3, NaCl-NaNO3, and Na2SO4-(NH4)2SO4, has been investigated experimentally (Tang, 1997; Ha et al., 2000; Chang and Lee, 2002; Lee and Chang, 2002) and theoretically (Potukuchi and Wexler, 1995; Nenes et al., 1998; Topping et al., 2005; Amundson et al., 2006). Among these studies, two types of deliquescence relative humidity (DRH) of the multi-component particles are reported: (1) the mutual deliquescence relative humidity (MDRH) at which solid particles partially dissolve in the absorbed water, and (2) the complete deliquescence relative humidity (CDRH) at which particles complete deliquescence and become homogeneous airborne droplets. The MDRH is 43 lower than the minimum DRH of all components in their individual pure solutions, and is independent of particle composition. Unlike MDRH, CDRH depends substantially on the fractions of individual components in mixtures. Efflorescence of a multi-component particle is more complicated than that of a single component particle. The latter involves only homogeneous nucleation, whereas additional heterogeneous nucleation may occur for the former. Schlenker et al. (2002) reported that ammonium bisulfate or ammonium nitrate, which cannot crystallize in its pure solution (no ERH), actually crystallize through heterogeneous nucleation in a multicomponent solution after crystals of other species are formed through homogeneous nucleation. Ge et al. (1996) investigated the chemical composition of particles dried from KCl-NaCl, KI-KCl, and (NH4)2SO4-NH4NO3 mixture solutions at different mole ratios using rapid single-particle mass spectrometry (RSMS). They found that a dried multi-component particle consists of a pure salt surrounded by mixed salt coating, and the core-shell arrangement depends on the salt mixing ratios. These two studies suggest that homogeneous nucleation plays a key role in the crystallization of a multi-component solution. For the ensuing heterogeneous nucleation of other salts, the formed crystal of the first salt must be sufficiently large to act as a heterogeneous inclusion (Braban and Abbatt, 2004). The necessity of a sufficiently large crystal is supported by the observed decrease in ERH of NH4NO3 when the crystal size becomes too small (Han et al., 2002). Since both ensuing heterogeneous nucleation and crystal growth occur rapidly, one can assume that the formation of the critical nuclei of the first salt controls the rate of efflorescence. 44 Accordingly, homogeneous nucleation theory may be promising for ERH prediction of a particle consisting of more than one salt. This approach has been applied to investigate how H2SO4, which cannot crystallize, affects ERH of (NH4)2SO4 (Amundson et al., 2006). In this work, attempt is given to predict the ERH of binary mixed salt particles using homogeneous nucleation theory. NaCl and Na2SO4 were selected as tested components because: (1) these two salts exhibit distinctive ERHs, 58% RH for Na2SO4 and 48% RH for NaCl, facilitating observations of changes in resultant ERH, and (2) available experimental data of micron-sized particles containing these two salts at various mixing ratios (Tang, 1997; Chang and Lee, 2002; Lee and Chang, 2002) provide a basis to further verify the theoretical prediction for particles in micron size in this study. The theoretical model previously developed for a single salt particle in Chapter 2 is modified for the application of binary NaCl-Na2SO4 particles, before the trend in ERH of NaCl-Na2SO4 particles is presented. ERH measurements for NaCl-Na2SO4 particles down to 40 nm were conducted to verify the theoretical calculations. This is the first theoretical investigation on the ERH of mixed NaCl-Na2SO4 particles with different mixing ratios supported with experimental data. 3.2 Theories and ERH Prediction To facilitate theoretical analysis, the rate of the crystallization process at ERH of a droplet of mixed NaCl and Na2SO4 solution is hypothesized to be mainly controlled 45 by homogeneous nucleation of one salt. This hypothesis is discussed in detail based on comparison between theoretical prediction and experimental data in the next section. Following the prior formulation in Chapter 2, the nucleation rate at an RH is calculated by J = J 0e − ∆Gh* K BT (3.1) where ∆G = * h 3 16πσ drop − nuc v c 3( K B T ln S ) 2 2 (3.2) is the Gibbs energy barrier, and the prefactor J 0 is estimated to be 2.8×1038 m-3s-1 for NaCl and 1.7×1038 for Na2SO4 by applying the method of Richardson and Snyder (1994) and Onasch et al. (2000). In equation 3.2, vc is the volume of a NaCl or Na2SO4 molecule; K B T is the thermal energy; S = a / a0 is the supersaturation ratio between a and a0 , representing solute activity in supersaturated and saturated mixed salt solutions, respectively; and σ drop− nuc is the interfacial tension between a NaCl or Na2SO4 nucleus and the supersaturated mixed salt solution. The nucleation rate Jc at the ERH can be estimated by Jc = 1 Ve t (3.3) where Ve is the corresponding volume of the supersaturated droplet of the mixed salt solution, and t is the nucleation induction time (Onasch et al., 2000; Söhnel and Garside, 1992). Because the actual induction time is difficult to measure, the estimated residence time for t according to experimental setup and flow rate for particle efflorescence is adopted (Onasch et al., 2000). Since the employed residence 46 time could be longer than the actual induction time, the predicted ERH could be overestimated. To determine the nucleation rate and ERH, one needs to calculate various thermodynamic properties. Let the subscripts w, α and β denote water, NaCl and Na2SO4, respectively. Given a spherical dry particle consisting of the two salts with mass equal to Wα and Wβ, simple volume additivity (Tang and Munkelwitz, 1994; Chan et al., 2006) is adopted to determine the diameter D0 and density ρdry of dry particles using the individual crystal densities as shown in Table 3.1. TABLE 3.1: Physical properties of Na2SO4 and NaCl. Parameters Na2SO4 3 νc (m ) 8.8×10 ρsalt (kg/m3)a Msalt (g/mole) msaturation (mole/kg) a b NaCl -29 4.48×10-29 2680 2165 142.0 58.44 1.978 6.143 Obtained from Lide et al. (2006). b Calculated values according to the solubility from Lide et al. (2006). For a droplet resulting from water uptake and salt dissolution, the salt molalities mα and mβ can be determined by specifying the water activity and using the Zdanovskii-Stokes-Robinson (ZSR) relationship (Robinson and Stokes, 1965), mβ mα + =1 mα ,o (a w ) m β ,o (a w ) (3.4) where mi,o(aw) is the molality for the corresponding single-salt solution with the same water activity aw. Equation 3.4 has been commonly employed by many researchers (Nenes et al., 1998; Chan and Ha, 1999; Ha et al., 2000; Topping et al., 2005) and 47 more accurate than other models, e.g., the KM model (Kusik and Meissner, 1978), the Pitzer model (Pitzer and Kim, 1974). AIM model developed by Clegg et al. (1998) considered the interactions of the solutes, but for system of mixed NaCl-Na2SO4, the model is only valid for concentrations from infinite dilution to moderate supersaturation, namely, valid for RH higher than 60% RH. Although AIM model can also be extrapolated to lower RH, the standard deviation between experiment and prediction is comparable to ZSR mixing rule. In addition, this study focused on much supersaturated solution, namely, much lower RH, so in order to facilitate theoretical formulation, AIM model was not chosen in this calculation. The correlations for mi,o(aw) are given in Appendix A. The total salt molality is hence m = mα + m β , and the water mass Ww can be calculated from the molality and molecular weight of either salt. The density ρ of the mixed salt solution is estimated by the equation of Tang (1997), 1 ρ = ⎛ Wα Wβ ⎞ 1 ⎜ ⎟ + (Wα + Wβ ) ⎜⎝ ρ α ρ β ⎟⎠ (3.5) where ρi is the density of the corresponding single salt solution with molality m. The correlations for ρi are given also in Appendix A. The growth factor defined as the diameter ratio of wet to dry particle is D ⎡ ρ dry (Ww + Wα + Wβ ) ⎤ GF = =⎢ ⎥ D0 ⎢⎣ ρ (Wα + Wβ ) ⎦⎥ 1/ 3 (3.6) Note that sodium sulfate in mixed salt solution crystallizes to anhydrous salt (Na2SO4), because a supersaturated solution droplet under ambient conditions rarely crystallizes to the decahydrate, Na2SO4·10H2O (Cohen et al., 1987; Tang and Munkelwitz, 1994). 48 The NaCl and Na2SO4 activities in the mixed salt solution are calculated by aα = (γ α mα / mα0 ) 2 (3.7) a β = 4(γ β m β / m β0 ) 3 (3.8) where γi is the activity coefficient of salt i; mi0 is the standard state of solution, 1. According to Bromley (1973), the activity coefficient can be calculated by 1 log γ α = − Aγ z1 z 2 I 2 1+ I 1 2 + z1 z 2 F1 F2 [ + ] z1 + z 2 z1 z 2 (3.9) + z1 z 3 F1 F3 [ + ] z1 + z 3 z1 z 3 (3.10) 1 log γ β = − Aγ z1 z 3 I 2 1+ I 1 2 where the subscripts 1, 2 and 3 represent Na+, Cl-, and SO4-2, respectively. zi is the absolute charge number of ion species i, and Aγ is the Debye-Huckel constant equal to 0.511 kg0.5mol-0.5 at 298.15K. The functions in (3.9) and (3.10) are given by Aγ I F1 = X 21 log γ 120 + X 31 log γ 130 + 1 2 1+ I ( z1 z 2 X 21 + z1 z 3 X 31 ) 1 2 (3.11) 1 F2 = X 12 log γ 120 + Aγ I 2 1+ I 1 2 z1 z 2 X 12 (3.12) z1 z 3 X 13 (3.13) 1 F3 = X 13 log γ 130 + Aγ I 2 1+ I 1 2 with X ij = ( where I = zi + z j 2 )2 mi I (3.14) 1 3 ∑ mi z i2 is the ionic strength, and γ ij0 is the mean ionic activity 2 i =1 49 coefficient of the pair i-j (binary activity coefficient) for a solution containing only i and j ions at I equal to that of the mixed salt solution. The binary activity coefficient γ ij0 is calculated from equations of Kusik and Meissner (1978), C = 1 + 0.055q exp(−0.023I 3 ) log Γ* = − 0.5107 I 1 + CI 1 2 1 2 (3.15) (3.16) B = 0.75 − 0.065q (3.17) Γ 0 = [1 + B(1 + 0.1I ) q − B]Γ * (3.18) log γ ij0 = z i z j log Γ 0 (3.19) where q is equal to 2.23 and -0.19 for NaCl and Na2SO4, respectively (Kim et al., 1993). In order to calculate supersaturation ratio S in equation 3.2, the saturation activity of each salt in the mixed salt solution ao is assumed to take the value for the corresponding single salt solution at the same temperature and pressure (Yu et al., 2003). The interfacial tension between a critical nucleus of each salt and the supersaturated mixed salt solution ( σ drop− nuc ) can be estimated using Young’s equation with the assumption of a zero contact angle (Amundson et al., 2006), namely, σ drop − nuc = σ nuc − air − σ drop − air (m) (3.21) At a known m, the ionic strength of the mixed salt solution can be written as I = I α + I β , and σ drop− air is then calculated using the simple mixing rule (Hu and Lee, 2004): σ drop − air = yα σ α , 0 + y β σ β , 0 (3.22) 50 where yα = I α / I , y β = I β / I , and σ i ,0 is the surface tension of the corresponding single salt solution at the same I. In this study, the formula of Pruppacher and Klett (1978) is adopted to calculate the surface tension of a NaCl solution, σ α , 0 = 0.072 + 0.0017m (3.23) The surface tension of a Na2SO4 solution is expressed by the formula of Li et al. (1999), σ β ,0 = σ w − RT ln a w (V N A )1 / 3 (3.24) 2 w where σ w and Vw are the surface tension and molar volume of pure water, respectively, and N A is Avogadro’s constant. For each salt, σ nuc − air can be determined from the experimental measured ERH for the single salt solution and the corresponding fitted σ drop− nuc and evaluated σ drop− air . Accordingly, the calculated σ nuc − air are found to be 0.169 N/m for Na2SO4, and 0.197 N/m for NaCl. Taking into account the Kelvin effect, the relative humidity is determined by RH = 100 × a w exp( 4M wσ drop − air RTρ w D ) (3.25) where D is the droplet diameter, M w and ρ w the molar mass and density of water, R the molar gas constant, T the absolute temperature. To facilitate ERH prediction, Jα and Jβ are first calculated for the two salts using equation 3.1 at various values of aw. The ERH determination is then conducted by an iterative method developed in the previous work (Chapter 2) to ensure identical nucleation rates calculated from equations 3.1 and 3.3. The flowchart is shown in Figure 3.1 and the prediction process starts with a randomly specified aw (99.5%, Merck, German) and Na2SO4 (purity>99%, Merck, German) in seven different molar proportions of 1:3, 1:2, 1:1, 2:1, 3:1, 4:1, and 9:1, in addition to pure NaCl (0% Na2SO4) and pure Na2SO4 (0% NaCl). To generate mono-dispersed particles, aerosolized salt particles were carried by compressed air through a neutralizer before they entered an electrostatic classifier (3080L, TSI Inc., USA). For individual batch measurements, droplets in monomodal distribution (66-72 nm ± 10 nm) were introduced into the exposure chamber in a consistent flow rate (1 ± 0.01 lpm) for more than 10 min under 90% RH. Once the size distribution of salt droplets reached a steady state, RH in the exposure chamber was decreased by adjusting flow rates of dry air ( 0.25 , and vice versa for x β < 0.25 (Tables 3.3 and 3.4). This justifies the assumption made in the formulation that each salt undergoes homogeneous nucleation separately at an early stage, and successful nucleation leading to ensuing crystal growth requires nuclei in a critical size. Since one salt nucleates and forms critical nuclei much faster, the other salt could undergo heterogeneous nucleation with the crystal of the first salt as a substrate. Therefore, the formation of critical nuclei of the first salt is the rate-controlling process for the experimentally observed efflorescence. Accordingly, the first salt shall appear in the core of the formed dry particle with the second salt enriched over the surface layer (Ge et al., 1996). For the case of x β = 0.25, however, the ratio of nucleation rate of Na2SO4 to NaCl becomes smaller than 200 (Table 3.4) or even down to less than 20 (Table 3.3). Relative to the experimental data, the noticeable underestimation of the predicted ERH could be justified by two possible reasons. First, it implies that the abovementioned process may be less than applicable to predict ERH around this composition. A proposed scenario is as follows. When the homogeneous nucleation rates of two salts become sufficiently close, nuclei of one salt smaller than their critical sizes, which can form and disappear constantly, may suffice to trigger heterogeneous nucleation of the other salt, and vice versa. This is in contrast to the necessity of formation of nuclei larger than the critical size as seeds for ensuing heterogeneous nucleation, a central assumption in the formulation of this study. Since overcoming the energy barrier estimated from the homogeneous nucleation is not required, crystallization can take 60 place at a RH higher than predicted values obtained based on the formulation in the present study. In this case, the effloresced dry particles could consist of a homogeneous mixture. The second possible reason is the inadequacy of the empirical mixing rule of activities (equation 3.4) ignoring the interactions of the two solutes, which become important at high concentrations because of the nonlinear nature of sodium sulfate. The inaccuracy in the calculated water activity could be significant in particular for xβ around 0.25, where the ionic strengths of the two solutes are comparable (Chan et al., 1997; Clegg et al., 1997). With the limited experimental data, it is attempted to estimate the range for xβ, within which the prediction for ERH may not be as accurate. To take into account the composition precision for prepared samples, IC method was used to test the prepared mixed solutions with xβ of 0.2, 0.25, and 0.33 (three solutions for each of the mole fractions), and obtained the standard deviation of 0.011, 0.016, and 0.038, respectively. Hence, this range is crudely estimated to be to be from 0.18 to 0.37. Because the theoretical model takes into account Kelvin effect, the dependence of ERH on particle size is also theoretically examined. Since ERH decreases with decreasing residence time, a constant residence time of 15 min is employed, as an example, to calculate ERHs. Table 3.5 shows that ERH decreases when particle size decreases from 1 µm to 100 nm, while a reverse trend is seen for smaller particles (< 100 nm). For all mixing ratios, the difference of ERH over particle size range 40 nm-1 µm is no more than 1.4% RH. Such a small difference is difficult to be verified through experimental measurements, which usually have errors of at least 2% RH. 61 Similar to the experimental observation of Biskos et al. (2006a), the increase in ERH with decreasing dry diameter starts when the particle size has been decreased to 40 nm. The increase becomes substantial in particular for particles smaller than 20 nm. The differences in ERH between 10 and 40 nm are more than 5.8% RH, and the difference increases with increasing Na2SO4 mole fraction as shown in the last column of Table 3.5. The greater increase in ERH for an increased Na2SO4 fraction is attributed to the higher water activity for Na2SO4 than for NaCl, because the exponential factor representing the Kelvin effect in equation 3.24 is comparable for NaCl and Na2SO4 for a given dry diameter from the calculation. TABLE 3.5: Variation of predicted ERH with dry diameter of mixed NaCl and Na2SO4 particles. The residence time is 15 min. ERH (%) Particle 1 µm 100 nm 40 nm 20 nm 10 nm ∆ERHa 1.00 58.1 57.8 59.2 62.0 68.7 9.5 0.90 57.8 57.6 58.8 61.7 68.3 9.5 0.75 56.8 56.6 57.9 60.7 67.2 9.3 0.50 53.6 53.5 54.6 57.2 63.2 8.6 0.10 45.7 45.3 46.0 48.0 52.6 6.6 0.00 46.4 45.7 46.5 48.1 52.3 5.8 Diameter xβ a Difference of ERH between 10-nm and 40-nm particles, (ERH10-nm – ERH40-nm). Finally, the sensitivity of predicted ERH to residence time and to surface tension between nuclei and air is addressed. In principle, the nucleation induction time could be approached experimentally by gradually reducing the residence time and monitoring the occurrence of efflorescence at a fixed RH. This can be done, for 62 example, with a well designed exposure chamber having an adjustable length. Unfortunately, the chamber used in the present study lacks this flexibility. To examine the sensitivity of the current model to the residence time, a 45-nm mixed particle with xβ = 0.5 is selected, as an example, to calculate the ERH using different values for the residence time, and the results are shown in Table 3.6. It is found that the current model for mixed Na2SO4-NaCl particles is not so sensitive to the residence time ranging widely from 0.1 to 3600 s. The sensitivity of predicted ERH to the surface tension between nuclei and air (σnuc-air) is analyzed by making the surface tension deviate slightly away from the inferred σnuc-air (0.197 and 0.169 N/m for NaCl and Na2SO4). The results in Table 3.7 indicate that the prediction in this study is strongly sensitive to σnuc-air. Since σnuc-air is used to calculate σnuc-drop, a change in σnuc-air can considerably alter the Gibbs energy (equation 3.2) and then ERH. Therefore, an accurate experimental measurement for σnuc-air is critical for validation of the present formulation. TABLE 3.6: Variation of predicted ERH with residence time for mixed NaCl and Na2SO4 particles with a dry diameter of 45 nm and xβ =0.5. t (s) 0.1 1 10 20 40 60 80 100 1200 3600 ERH (%) 52.4 53 53.5 53.6 53.7 53.9 53.9 53.9 54.4 54.6 TABLE 3.7: Variation of ERH with σnuc-air for mixed NaCl and Na2SO4 particles with a dry diameter of 45 nm. The residence time is 60 s. σnuc-air (α/β) 0.183/0.155 0.190/0.162 xβ 0.197/0.169 0.204/0.176 0.211/0.183 ERH (%) 0.1 49.2 47.1 45.3 43.1 40.8 0.5 59.0 56.4 53.9 51.1 48.4 63 3.5 Conclusions A theoretical model is built to predict the ERHs of particles containing mixed NaCl and Na2SO4 at various molar ratios, and shows satisfactory agreement with experimental values, except for the cases with a Na2SO4 mole fraction of around 0.25. The general agreement supports the hypothesis that for mixed salt particles, efflorescence is controlled by the homogeneous nucleation of one salt, whose nucleation rate is much higher than that of the other. However, at mixing ratios where the individual nucleation rates of two salts are close enough to each other, the theoretical formulation underestimates ERH as compared to the experimental data. For this unique case, the attribution is twofold: (1) the hypothesized mechanism – homogeneous nucleation of one salt followed by heterogeneous nucleation – cannot well describe the efflorescence process and requires further investigation; (2) the mixing rule of activities used is inadequate for accurate prediction. For this case, because the heterogeneous nucleation may take place at early stage and two solutes may trigger nucleation each other, the application of heterogeneous nucleation theory should be a way to improve the prediction. However, current model is not suitable for heterogeneous nucleation, so Monte Carlo and Molecular Dynamics simulation may be potential ways. Relative to particles larger than 40 nm, the Kelvin effect plays an important role in the ERHs of mixed NaCl-Na2SO4 particles smaller than 40 nm, and becomes substantial for sizes below 20 nm. In addition, the higher the Na2SO4 mole fraction, the larger the increase in ERH. 64 CHAPTER 4 Effects of Organics on Efflorescence Relative Humidity of Ammonium Sulfate or Sodium Chloride Particles 4.1 Introduction It has be identified that organic compounds can constitute 50% or more of the particle mass (Chow et al., 1994; Murphy et al., 1998); especially for tropospheric aerosols, organic species may be up to 90% of the total mass (Kanakidou et al., 2005). Since atmospheric particles are most likely to be mixtures of organic and inorganic components (Chow et al., 1994; Henning et al., 2005; Clegg and Seinfeld, 2006), it is important to understand the effects of organic compounds on phase transitions and chemical properties of aerosols, which have a profound impact on air quality, light scattering and climatic change (Seinfeld and Pandis, 1998). Smog chamber experiments (Forstner et al., 1997a and b) and field studies (Gray et al., 1986; Schroder et al., 1991; Pandis et al., 1992; Blando et al., 1998) have indicated that organic compounds cover a wide range of carbon numbers and functional groups, and a large fraction of organic aerosols is water soluble (Saxena and Hildemann, 1996; Zappoli et al., 1999). Many of the water soluble organics (WSOs) 65 tend to act as surfactants (surface active) in nature (Andrews and Larson, 1993; Choi and Chan, 2002b). Fuzzi et al. (2001) suggested that water soluble organics in aerosols can be represented by dialkyl ketones, polyols, polyphenols, alkanedioic acids, hydroxyalkanoic acids, aromatic acids, and polycarboxylic acids. Accordingly, dicarboxylic acids are the most commonly found in atmospheric aerosols (Rohrl and Lammel, 2001; Yao et al., 2002; Narukawa et al., 2002). Deliquescent behavior of particles composed of inorganic salt and WSOs, such as (NH4)2SO4 mixed with glutaric acid, malonic acid, maleic acid, glycerol, or levoglucosan, and NaCl with glutaric acid, has been investigated experimentally (Choi and Chan, 2002b; Brooks et al., 2003; Prenni et al., 2003; Wise et al., 2003; Braban et al., 2004; Pant et al., 2004; Parsons et al., 2004; Marcolli and Krieger, 2006) and theoretically (Clegg et al., 2001; Raatikainen and Laaksonen, 2005; Clegg and Seinfeld, 2006). These studies found that deliquescence relative humidity (DRH) decreased first and then increased with increasing the fraction of organic species, and minimum DRH and its corresponding mole ratio of inorganic to WSO (eutonic composition) altered with salt and organic species. Efflorescent behaviors of mixed particles have been experimentally investigated as well (Choi and Chan, 2002b; Brooks et al., 2003; Pant et al., 2004; Braban et al., 2004; Parsons et al., 2004; Parsons et al., 2006). Efflorescence relative humidity (ERH) was found to gradually decrease with the fraction of organics until ERH disappeared if the pure WSOs do not effloresce at all. Otherwise, the ERH of mixed particles decreases first from ERH of pure inorganic particle to a minimum and then 66 increases to ERH of the pure WSO particle, when the mole fraction of WSO is increased from 0 to 1. Two examples for such WSOs are for glutaric acid with ERH of 22~36% (Pant et al., 2004) and maleic acid with ERH of 14~20% (Brooks et al., 2003) However, no theoretical model is available to predict ERH of mixed inorganic-WSO particles. Thus, in this work, attempt is given to a formulation with the assumption that formation of critical nuclei of the first component controls the rate of efflorescence. Similar formulation has successfully predicted ERH of mixed NaCl-Na2SO4 particles in Chapter 3. In this study, (NH4)2SO4 and NaCl were selected as inorganic salts, and glutaric acid, malonic acid, maleic acid, glycerol and levoglucosan were selected as WSOs/surfactants, because these salts and WSOs exist commonly in atmospheric aerosols and experimental data are available to verify the theoretical prediction. In current study, the three acids were treated as nondissociating components, because of their low degrees of dissociation (Clegg and Seinfeld, 2006). This is the first work to theoretically predict ERH of mixed inorganic-WSO particles with different mixing ratios. 4.2 Theories and ERH Prediction As mentioned, the major hypothesis is that the rate of the crystallization process of a droplet of mixed component solution at ERH is controlled by homogeneous nucleation of one component, analogous to the prior formulation in Chapter 3. The 67 nucleation rate at an RH is calculated by J = J 0e − ∆Gh* K BT (4.1) where ∆G = * h 3 16πσ drop − nuc v c 2 (4.2) 3( K B T ln S ) 2 is the Gibbs energy barrier, and the prefactor J 0 is estimated by applying the method of Richardson and Snyder (1994) and Onasch et al. (2000). In equation 4.2, v c is the molecular volume of a component; K B T is the thermal energy; S = a / a0 is the supersaturation ratio between a and a0 , representing the solute activity in supersaturated and saturated mixed solutions, respectively; and σ drop− nuc is the interfacial tension between the nucleus and the supersaturated mixed solution. J 0 and v c for the studied salts and WSOs are shown in Table 4.1. TABLE 4.1: Physical properties of salts and WSOs. -3 -1 3 M (g/mole)a ρsalt (kg/m3)a Chemicals vc (m ) Jo (m s ) (NH4)2SO4 NaCl glycerol 1.0×1038 1.24×10-28 132.14 1769 5.83 38 4.48×10 -29 58.44 2165 6.14 1.21×10 -28 92.09 1260 ∞ -28 162.10 1640 >2.4c 2.8×10 38 1.3×10 37 levoglucosan 9.4×10 1.64×10 glutaric acid 1.0×1038 1.54×10-28 132.11 1429 12.0 malonic acid 1.4×10 38 1.06×10 -28 104.06 1630 7.1 1.3×10 38 1.20×10 -28 116.07 1609 6.9 maleic acid a msaturation(mole/kg)b Obtained from Lide et al. (2006). b Calculated values according to the solubility from Lide et al. c (2006) except specified data. From reference Topping et al. (2007). The nucleation rate Jc at the ERH can be estimated by Jc = 1 Ve t (4.3) 68 where Ve is the corresponding volume of the supersaturated droplet of the mixed solution, and t is the nucleation induction time (Söhnel and Garside, 1992; Onasch et al., 2000). Because the actual induction time is difficult to measure, the estimated residence time (according to experimental setup and flow rate for particle efflorescence) or observation time (according to the reported time rate of change of RH during an experiment) is adopted for t (Onasch et al., 2000). Since the employed residence time or observation time could be longer than the actual induction time, the predicted ERH could be overestimated. To determine the nucleation rate and ERH, one needs to calculate various thermodynamic properties. Let the subscripts w, α and β denote water, salt and WSO, respectively. Given a spherical dry particle consisting of one salt and one WSO with mass equal to Wα and Wβ, simple volume additivity (Tang and Munkelwitz, 1994; Chan et al., 2006) is adopted to determine the diameter D0 and density ρdry of dry particles using the individual crystal densities as shown in Table 4.1. For a droplet resulting from water uptake and components dissolution, the solute molalities mα and mβ can be determined by specifying the water activity and using the Zdanovskii-Stokes-Robinson (ZSR) relationship (Robinson and Stokes, 1965) mβ mα + =1 mα ,o (a w ) m β ,o (a w ) (4.4) where mi,o(aw) is the molality for the corresponding individual component solution with the same water activity aw. Equation 4.4 has been identified to be valid for mixed salt and WSO (Choi and Chan, 2002b; Marcolli et al., 2004; Chan et al., 2006; 69 Svenningsson et al., 2006; Marcolli and Krieger, 2006). Recently, the AIM model was improved to incorporate interaction parameters of salts with organics (Clegg and Seinfeld, 2006); the water activity prediction showed good agreement with experimental data of deliquescence process, namely, the model can yield satisfactory results for dilute to moderate concentration system, but for higher supersaturated solution, water activity deviation between prediction and experiment was larger than that calculated using ZSR mixing rule. ADDEM developed by Topping et al. (2005) also applied the principle of ZSR mixing rule and generated good results of water activity. The empirical expressions of mi,o(aw) for the two salts are given in Chapter 2, and the relations between mi,o and aw for WSOs are given by aw=xwγw, where xw is the water mole fraction in solution and γw is the water activity coefficient calculated using UNIFAC (UNIQUAC Functional Group Activity Coefficients) model (Fredenslund et al., 1975; Poling et al., 2000). The total solute molality is hence m = mα + m β , and the water mass Ww can be calculated from the molality and molecular weight of either solute component. The density ρ of the mixed salt-WSO solution is estimated by the equation of Tang (1997), 1 ρ = ⎛ Wα Wβ ⎞ 1 ⎜ ⎟ + (Wα + Wβ ) ⎜⎝ ρ α ρ β ⎟⎠ (4.5) where ρi is the density of the corresponding individual component solution with molality m. The correlations for ρi of two salts are given in Chapter 2, and ρi for WSO solution is simply estimated by the mass-averaged value between water and WSO (Cruz and Pandis, 2000; Peng et al., 2001; Choi and Chan, 2002b; Chan et al., 70 2006). The growth factor defined as the diameter ratio of wet to dry particle is D ⎡ ρ dry (Ww + Wα + Wβ ) ⎤ GF = =⎢ ⎥ D0 ⎢⎣ ρ (Wα + Wβ ) ⎦⎥ 1/ 3 (4.6) When calculating the solute activities in mixed solution, it is difficult to couple the inorganic and organic species (Clegg et al., 2001; Topping et al., 2007). Organic species has dissociation equilibrium in aqueous solution, and the dissociation equilibrium varies with concentration, especially in much supersaturated solution. How dissociated and non-dissociated organics interact with inorganic species is still in the progress of study. Thus, in this study, the CSB approach of Clegg et al. (2001) is adopted, which ignores interactions between the inorganic ions and organic solutes. Namely, the activity calculation for one solute is done as if the other were absent (Clegg and Seinfeld, 2006; Topping et al., 2007). Accordingly, aα can be calculated using model of Ally et al. (2001) shown in Chapter 2, and aβ is given by relation aβ=xβγβ, where xβ is the solute mole fraction in the solution and γβ is the solute activity coefficient calculated by the UNIFAC model. In order to calculate supersaturation ratio S in equation 4.2, the saturation activity of each solute in the mixed solution ao is assumed to take the value for the corresponding individual component solution at the same temperature and pressure (Yu et al., 2003). The interfacial tension between a critical nucleus of each component and the supersaturated mixed solution ( σ drop− nuc ) can be estimated using Young’s equation as 71 follows. Consider a planar surface of solute solid, on which a drop of the mixed rests with contact angle θ2, Young’s equation states σ drop − nuc = σ nuc − air − cos θ 2 ⋅ σ drop − air (m) (4.7) For each solute, σ nuc − air can be inferred from the experimental measured ERH for its pure solution. One can then determine σ nuc− drop (s ) denoting the surface tension between this solute and its pure σ nuc − air = σ nuc −drop ( s ) + cos θ1 ⋅ σ drop ( s )− air (m ERH ) , where mERH solution from is the molality corresponding to ERH of the pure solute particle. Accordingly, equation 4.7 can be transformed to σ drop − nuc = σ nuc − drop ( s ) + cos θ1 ⋅ σ drop ( s )− air (m ERH ) − cos θ 2 ⋅ σ drop − air (m) (4.8). For a single-salt system, θ1 can be approximated to be zero, because of high affinity between the hydrophilic solid and liquid (Amundson et al., 2006). For a salt nucleus surrounded by a mixed solution, the WSO tends to behave as surfactant (Andrews and Larson, 1993; Choi and Chan, 2002b). It has been reported that when the WSO concentration is higher than 10-3 molality, the contact angle θ2 almost vanishes due to the formation of a surfactant bilayer, leading to high solid-liquid affinity (Li and Gu, 1985; Sabatini and Knox, 1992; Karagunduz et al., 2001; Rosen, 2004). Therefore, equation 4.8 becomes σ drop − nuc = σ nuc − drop ( s ) + σ drop ( s )− air (m ERH ) − σ drop − air (m) (4.9). For a WSO nucleus surrounded by the mixed solution, θ1 and θ2 are both unknown, although the presence of salt in WSO solution in principle causes θ2>θ1 (Davis et al., 2003). Thus equation 4.8 cannot be used to calculate σ drop− nuc . 72 However, a lower limit for σ drop− nuc can be deduced from the following equation (Rosen, 2004), σ drop − nuc = σ nuc − air + σ drop − air − 2 Fdrop −nuc (4.10) where Fdrop − nuc represents the interaction energy per unit area across the interface between the nucleus and drop, and is supposedly larger for better affinity between the nucleus and the solution (Rosen, 2004). When more salt is present in WSO solution, σ drop−air will increase, and Fdrop − nuc will decrease due to the higher hydrophilicity of the salt. It can then be concluded that σ drop− nuc should be larger than σ nuc− drop (s ) , for which the salt is absent. This deduction indicates that cos θ1 ⋅ σ drop ( s ) − air (mERH ) − cos θ 2 ⋅ σ drop − air (m) should be positive in equation 4.8, so one can regard σ nuc− drop (s ) as a lower-limit of σ drop− nuc . At a known m, σ drop−air of the mixed solution can be estimated by a simple additive approach (Topping et al., 2007), σ drop − air = σ w + ∆σ inorg + ∆σ WSO (4.11) where ∆σ inorg and ∆σ WSO are the deviations from the surface tension of pure water ( σ w ) caused by the inorganic salts and WSOs, respectively. The expressions for the surface tensions of aqueous solutions are provided in Chapter 2 for (NH4)2SO4 and NaCl and in Appendix B for WSOs. Because the UNIFAC model is based on interactions among structural groups to calculate activity coefficients of water and solutes in mixed solution, the molecular structures and group interaction parameters of WSOs are tabulated in Table 4.2 and Table 4.3, respectively. Other physical parameters used in the UNIFAC model are 73 available in the literature (Fredenslund et al., 1975; Poling et al., 2000). TABLE 4.2: Structures and group no. of WSOs. WSO Structure Group (group no.) glycerol HO-CH2-CH(OH)-CH2-OH OH(3); CH2(2); CH(1) levoglucosan OH(3); CH(4); O CH2O(1); O OH CHO(1) OH OH glutaric acid HOOC-(CH2)3-COOH COOH(2); CH2(3) malonic acid HOOC-CH2-COOH COOH(2); CH2(1) maleic acid HOOC-CH=CH-COOH COOH(2); CH=CH(1) TABLE 4.3: UNIFAC group interaction parameters.a Group n CHxb CH=CH OH H2O CH2O/CHO COOH Group interaction parameters, amn Group m CHx CH=CH OH H2O CH2O/CHO COOH a 0 86.02 986.5 1318 251.5 663.5 -35.36 0 524.1 270.6 214.5 318.9 c 28.06 224.39c 156.4 457 0 265.87 300 496.1 -467.42c 0 540.5 -69.29c 83.36 26.51 237.7 -314.7 0 664.6 1264 c c -338.5 0 315.3 -103.03 -145.88 Obtained by Poling et al. (2000) except the specified. b x can be 0, 1, 2 3. c Modified parameters obtained from the fitting of UNIFAC model to experimental data by Peng et al. (2001). Taking into account the Kelvin effect, the relative humidity is determined by RH = 100 × a w exp( 4M wσ drop − air RTρ w D ) (4.12) where D is the droplet diameter, M w and ρ w the molar mass and density of water, R the molar gas constant, and T the absolute temperature. To predict ERH of mixed salt-WSO particles, Jα and Jβ (if WSO has ERH) are 74 first calculated for the two components using equation 4.1 at various values of aw. The ERH determination is then conducted by the iterative method developed in Chapter 2 to ensure identical nucleation rates calculated from equations 4.1 and 4.3. The detailed ERH prediction procedure has been described in Chapter 3. 4.3 Results and Discussions Figure 4.1 to 4.6 show the theoretically predicted ERHs as a function of xWSO for mixed (NH4)2SO4-glycerol, (NH4)2SO4-levoglucosan, (NH4)2SO4-malonic acid, (NH4)2SO4-glutaric acid, NaCl-glutaric acid and (NH4)2SO4-maleic acid, respectively. Also plotted are the experimental data from several prior works (Choi and Chan, 2002b; Brooks et al., 2003; Pant et al., 2004; Braban et al., 2004; Parsons et al., 2004; Parsons et al., 2006). In Figure 4.4, the predicted ERHs of mixed particles with x glutaric acid =(0.3, 0.45) are not shown because they become negative and unreasonable. For mixed particles with x glutaric x maleic acid acid =(0.8, 0.9) in Figure 4.5 and =(0.6, 0.8) in Figure 4.6, because J α is close to J β in these ranges, the model of this study can no longer give accurate prediction as detailed in Chapter 3. In all figures, each vertical bar represents the range of RH over which crystallization was observed experimentally. The results in Figure 4.1-4.3 show that ERH of mixed inorganic-WSO particles gradually decreases with increasing xWSO for WSOs without ERH. In contrast, when the pure WSO has ERH, the ERH of mixed particles decreases to a minimum and then gradually increases towards the ERH of the pure 75 WSO as shown in Figure 4.4-4.6. However, in Figure 4.6, the experimental ERH of mixed particles with xmaleic =0.77 is unusually higher than those for other xmaleic. This is probably due to the impurity in particles. 80 Experimental data (Choi and Chan, 2002) Experimental data (Parsons et al., 2004) Calculated ERH 70 60 ERH (%) 50 40 30 20 10 0 -10 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 xglycerol Figure 4.1 Experimental and calculated ERHs of mixed (NH4)2SO4-glycerol particles with average dry diameter of 10 µm and observation time of 150 S. 76 80 Experimental data (Parsons et al., 2004) Calculated ERH 70 60 ERH (%) 50 40 30 20 10 0 -10 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 xlevoglucosan Figure 4.2 Experimental and calculated ERHs of mixed (NH4)2SO4-levoglucosan particles with average dry diameter of 10 µm and observation time of 150 S. 77 80 Experimental data (Braban and Abbatt, 2004) Experimental data (Parsons et al., 2004) Experimental data (Parsons et al., 2006) Experimental data (Choi and Chan, 2002) Calculated ERH 70 60 ERH (%) 50 40 30 20 10 0 -10 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 xmalonic acid Figure 4.3 Experimental and calculated ERHs of mixed (NH4)2SO4-malonic acid particles with average dry diameter of 10 µm and average observation time of 200 S. 78 80 Experimental ERH (Pant et al., 2004) Experimental ERH (Choi and Chan, 2002) Calculated ERH 70 60 ERH (%) 50 40 30 20 10 0 -10 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 xglutaric acid Figure 4.4 Experimental and calculated ERHs of mixed (NH4)2SO4-glutaric acid particles with average dry diameter of 10 µm and observation time of 150 S. 79 80 Experimental ERH (Pant et al., 2004) Experimental ERH (Choi and Chan, 2002) Calculated ERH 70 60 ERH (%) 50 40 30 20 10 0 -10 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 xglutaric acid Figure 4.5 Experimental and calculated ERHs of mixed NaCl-glutaric acid particles with average dry diameter of 10 µm and observation time of 150 S. 80 80 Experimental ERH (Brooks et al., 2003) Calculated ERH 70 60 ERH (%) 50 40 30 20 10 0 -10 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 xmaleic acid Figure 4.6 Experimental and calculated ERHs of mixed (NH4)2SO4-maleic acid particles with average dry diameter of 0.6 µm and residence time of 120 S. 81 The comparison shown in Figure 4.1-4.6 reveals that the model of this study can satisfactorily predict the ERH of ammonium sulfate mixed with glycerol, levoglucosan or malonic acid. However, for (NH4)2SO4-glutaric acid, NaCl-glutaric acid and (NH4)2SO4-maleic acid, the predicted ERHs do not quantitatively agree with experimental data. Note that the ERHs of mixed (NH4)2SO4-glutaric acid and NaCl-glutaric acid particles at high WSO mole fractions are controlled by WSOs (the right part of solid line in Figure 4.4 and 4.5), and calculated using the lower-limit of interfacial tension between the WSO nuclei and mixed solution, in principle leading to an underestimated energy barrier (see equation 4.2) and hence an overpredicted ERH. Based on a similar lower limit, however, the predicted ERH of mixed (NH4)2SO4-maleic acid controlled by maleic acid (the right part of solid line in Figure 4.6) is always much lower than experimental data. The possible reasons are (1) the temperature difference between 273K for experiment and 298K for calculation and (2) impurity in mixed solution. The ERHs of mixed particles at low WSO fractions are controlled by inorganic salts. The predicted ERHs (the left parts of solid lines in Figure 4.4 to 4.6) are always lower than experimental data. Possible explanations are twofold. First, the assumption of no interaction between inorganic salts and WSOs may not be suitable for these three mixed cases. Glutaric and maleic acids may substantially increase the salt activity in solution and consequently the supersaturation ratio (S). This leads to a decline of the Gibbs free energy expressed in equation 4.2, thereby making efflorescence occur at a higher RH. Since the formulation in this study has ignored 82 interaction effects at all, it can underestimate ERH. Second, the calculation of interfacial tension between salt nuclei and mixed solution may not be suitable for these three cases. Figure 4.7 shows surface tension of WSO solution as a function of xWSO . It can be found that glutaric and maleic acids are more surface active than the other three WSOs, so the true interfacial tension could be smaller than the calculated value using equation 4.9. A decline in the interfacial tension can decrease the energy barrier in given by equation 4.2 and thus increase the ERH of mixed particles. For mixed (NH4)2SO4-maleic acid, the temperature difference between 273K for experiment and 298K for calculation may also be responsible for the discrepancy. Note that experimental ERHs obtained by Choi and Chan (2002b) are higher than other data in the literature, probably due to the presence of impurity in the mixed particles (Pant et al., 2004; Parsons et al., 2006; Chan et al., 2006). 83 0.07 σdrop-air 0.06 0.05 0.04 Glycerol Levoglucosan Malonic acid Glutaric acid Maleic acid 0.03 0.02 0 10 20 30 40 50 60 70 80 90 100 110 m Figure 4.7 Surface tension of aqueous WSO solution as a function of molality. 4.4 Conclusions The theoretical model in this study can predict suppression of crystallization of ammonium sulfate and sodium chloride particles caused by WSOs that do not effloresce in the absence of salt. The ERH of mixed salt-WSO particle gradually decreases with increasing mole fraction of WSO. For an efflorescible WSO, however, the ERH of mixed particles decreases to a minimum and then increases towards the ERH of pure the WSO. Quantitatively, the model of this study can only satisfactorily predict the ERH of mixed particles comprising WSOs that are weakly surface active, such as glycerol, levoglucosan and malonic acid. For WSOs with 84 stronger surface active nature, e.g., glutaric and maleic acids, the inaccurate prediction might be attributed to the calculation method for the interfacial tension between salt nuclei and mixed solution, and the assumption of no interaction between salt and WSOs. Thus, an accurate experimental or theoretical method should be developed to obtain the actual interfacial tension between nuclei and mixed solution to improve the model. In addition, the model is not applicable for water insoluble organics, so if one wants to investigate the effect of water insoluble organics, the heterogeneous nucleation should be considered. 85 CHAPTER 5 Theoretical Investigation of Substrate Effect on Deliquescence Relative Humidity of NaCl Particles 5.1 Introduction The hygroscopic properties of airborne particles have received increasing attention because of the subsequent effects on atmospheric visibility and earth’s climate (Xu et al., 1998; Lightstone et al., 2000; Cruz et al., 2000; Martin et al., 2001). While most studies examined the water sorption of suspended particles (Tang et al., 1978; Shulman et al., 1997; Cruz et al., 2000; Hämeri et al., 2000 and 2001; Choi and Chan, 2002; Gysel et al., 2002; Biskos et al., 2006a), little effort has been devoted to investigating the hygroscopic behavior of particles deposited on a substrate. The hygroscopicity of deposited particles is important because substantial water sorption can lead to surface corrosion, a serious problem for electronic devices (such as printed circuit boards) (Sinclair et al., 1990; Frankenthal et al., 1993; Litvak et al., 2000) in contact with potentially corrosive particles (Sinclair et al., 1990; Frankenthal et al., 1993; Baboian et al., 2000; Zhang et al., 2005). Therefore, to minimize costly failure in the usage of electronics, it is necessary to understand the hygroscopicity of deposited particles. 86 Table 5.1 shows the limited available experimental works investigating (NH4)2SO4 and NaCl particles on three types of substrates (Ebert et al., 2002; Wise et al., 2005). The resultant deliquescence relative humidity (DRH) of deposited particles with sizes ranging from 0.1 to 20 µm are between 75% RH and 80% RH (Table 5.1), consistent with the DRH of suspended micron-size (NH4)2SO4 and NaCl particles (Tang and Munkelwitz, 1984; Cohen et al., 1987; Cziczo et al., 1997). Therefore, the substrates appear to have a very weak effect on the hygroscopicity of deposited particles. This result can be attributed to the large particle sizes examined in the studies because both experimental observations (Table 5.2) and theoretical simulation for suspended NaCl particles (Russell and Ming, 2002) consistently show an increase of DRH with the decreasing particle size for particles smaller than 60 nm. Hence, for small deposited particles, a noticeable size effect on deliquescence is also expected. TABLE 5.1: Available experimental DRHs of deposited (NH4)2SO4 and NaCl particles. Particle size (µm) 0.1-20 a Materials (NH4)2SO4 Substrates Stainless steel NaCl 0.1-4 a DRH(%) 79.8±1.5 Methods References b ESEM Ebert et al., 2002 ETEMc Wise et al., 2005 77.5±1.3 (NH4)2SO4 Carbon, 80-81 NaCl Formvar/Carbon 75-77 type TEM grid a Reported in references (Ebert et al., 2002; Wise et al., 2005). b Environmental Scanning Electron Microscope. c Environmental Transmission Electron Microscope. 87 TABLE 5.2: DRHs of suspended NaCl particles in nanometer size. Particle size (nm) 8 NaCl DRH(%) 80.9±2 10 82.4±2 15 81.3±2 30 75.6±1 50 76.0±1 6 a Materials NaCl 87±2.5 8 84±2.5 15 80±2.5 20 (77-78)±2.5 30 77±2.5 60 (76-77)±2.5 Methods UF-DMA References a TnDMAb Hämeri et al., 2001 Biskos et al., 2006a Ultrafine tandem differential mobility analyzer. b Tandem nano-differential mobility analyzer. For suspended particles, Mirabel et al. (2000) made theoretical prediction for DRH by equalizing the free energies for a dry particle and a droplet, in which the solid has completely dissolved. This approach was later modified by Russell and Ming (2002), who allowed for a thin water layer coated on the particle, replacing the aforementioned dry state. The wetted particle was handled under the capillarity approximation. A more thermodynamically rigorous theory was formulated by Djikaev et al. (2001). This two-dimensional model calculated the free energy of a composite particle consisting of a partly dissolved solid core and a surrounding solution shell. Treating the radii of the solid core and the composite particle as two independent variables, the authors were able to draw a contour plot for the free energy at a given relative humidity, and determine the equilibrium path from a dry particle to a droplet. The important findings are: (1) deliquescence is not prompt 88 (Hämeri et al., 2000) when RH is not high enough, reflected by a metastable coated particle having a local minimum of free energy along the path, corresponding to the initial water uptake; (2) a dramatic particle growth associated with complete dissolution can occur, provided that the droplet state has a lower free energy than the uncoated state and the metastable state, and the energy barrier can be overcome; (3) at sufficiently high RH, the energy barrier and the metastable state both disappear, and the deliquescence becomes prompt; (4) Hysteresis is predictable for the reverse process (efflorescence). Quantitative agreement between theory and experiment depends greatly on the accuracy of physical parameters, such as surface tension, activities, etc. The predicted metastable composite particle can justify the use of a wetted particle in the work of Russell and Ming (2002), but their equalization of free energies would, in principle, underpredict DRH. Nevertheless, acceptably good agreement with DRH experiment has been achieved by using appropriate values of surface tension (Russell and Ming, 2002). In fact, the method of Mirabel et al. (2000) becomes equivalent to that of Russell and Ming (2002), when an “effective” surface tension between solid and vapor is adopted instead. More detailed arguments will be given later in Section 5.3. Up to now, all the available thermodynamic models are applicable to predict the DRH only for suspended particles (Mirabel et al., 2000; Djikaev et al., 2001; Russell and Ming, 2002). The present study, for the first time, examines the trend in DRH of deposited particles. The DRH in the present study is defined as the relative humidity, at which a dramatic increase in particle size takes place. In view of 89 methodology simplicity and qualitative elucidation, the theory of Mirabel et al. (2000) is extended with the assumptions that both the particle and droplet are spherical caps in shape, having different contact angles from the substrate. Because of scarce experimental data for verification of this theoretical work, possible experimental techniques and measurements are also suggested as a future work. 5.2 Deliquescence of a Deposited Particle According to the Wulff theorem, the shape of a crystal on a substrate depends on the wetting condition: no wetting, imperfect wetting, or perfect wetting (Defay et al., 1966; Mutaftschiev, 2001). To facilitate the theoretical formulation, it is assumed that a deposited solid particle exhibits the shape of a spherical cap satisfying Young’s equation, analogous to a droplet on a substrate. The advantage of this assumption is that it is unnecessary to know the surface tension between the particle and the substrate, as will be shown in the following derivation. Although a spherical cap can represent the shape of a nucleus formed on a substrate (Richardson and Snyder, 1994; Lightstone et al., 2000; Onasch et al., 2000; Mirabel et al., 2000; Han et al., 2002; Liu, 2002), it is stated that the shape of a particle depends on the deposition process, and does affect DRH. 90 State I (crystal) State II (liquid) θ2 θ1 RI RII Figure 5.1 Schematic of a deposited particle on a substrate before and after deliquescence. Figure 5.1 shows the schematic of a deposited particle before (State I) and after (State II) deliquescence, where θ1 and θ2 are the contact angles, and RI and RII are the curvature radii for the two states. The free energies of the two states are expressed respectively as G I = Nµ1V + n2 µ 2C + σ CV a CV + σ CS a CS + σ SV ( A − a CS ) (5.1) G II = n1 µ1 + n2 µ 2 + ( N − n1 ) µ1V + σ LV a LV + σ LS a LS + σ SV ( A − a LS ) (5.2) where N is the number of water molecules in the vapor of state I ; n1 is the number of water molecules in solution; n2 is the number of the salt molecules; µ1V is the chemical potential of water vapor; µ 2C is the chemical potential of solid crystal; µ1 is the chemical potential of water in solution; µ 2 is the chemical potential of solute in solution; A is the surface area of substrate; σ ij denotes the interfacial tension between phase i and j, which can be L (droplet), V (gas), S (substrate) or C 91 (crystal). For a spherical cap with contact angle θ and curvature radius R , its volume and surface areas are given by 3 1 V = π R (1 − cos θ ) 2 (2 + cos θ ) 3 2 a iV = 2π R (1 − cos θ ) 2 a iS = π R sin 2 θ (5.3) (5.4) (5.5) where i can be L or C. The relation among the interfacial tensions is described by Young’s equation: σ SV = σ CS + σ CV cos θ1 = σ LS + σ LV cos θ 2 (5.6) The chemical potentials for different species are expressed by µ1 = µ10 + kT ln a1 (5.7) µ1V = µ10 + kT ln p p∞0 (5.8) µ 2 = µ 20 + kT ln a2 a2 (5.9) where a1 and a 2 are the water and the solute activity in the droplet; a 2 is the solute activity in a bulk saturated solution; p is the water vapor pressure with p∞0 being the corresponding saturation value; kT is the thermal energy. The volumes of the crystal and droplet can be related to the molecular volumes as n2 v c and n1v1 + n2 v2 , where v c is the molecular volume of solid crystal; v1 and v2 are the partial molecular volume of water and solute in the solution, respectively (Mirabel et al., 2000). In the model of Mirabel et al. (2000), deliquescence occurs when the two states have an identical free energy. Following this criterion and assuming the solution is 92 ideal, the equation is obtained, 1 3σ LV g − 3σ CV v 2 c3 ⎡ 2 − 3 cos θ 1 + cos 3 θ 1 ⎤ 3 13 23 ⎢ ⎥ g x2 3 ⎣ 2 − 3 cos θ 2 + cos θ 2 ⎦ 1 3 (5.10) ⎡ ⎤ x2 3 LV +x ⎢ ⎥ g kTn ln( ) − 2σ v1 (1 − x 2 ) = 0 3 x2 ⎣ π (2 − 3 cos θ 2 + cos θ 2 ) ⎦ 2 3 2 1 3 1 3 2 with g = v1 − ( v1 − v 2 ) x 2 where x2 is the molar fraction of solute in the droplet, x 2 is the corresponding value in a bulk saturated solution, and σ LV is a function of x 2 . Note that when θ1 = θ 2 = 180 o , equation 5.10 reduces to that for suspended particles. For a spherical cap of solution, one can easily modify the available derivation (Seinfeld and Pandis, 1998) to obtain the corresponding Köhler equation and calculate the relative humidity: RH = 100 × a1 exp( 2σ LV v1 kT R ) (5.11) where R is the curvature radius. For deposited NaCl particles, v1 = 3.03 × 10 −29 m3; v 2 = 4.48 × 10 −29 m3; v c = 4.48 × 10 −29 m3. These parameters are calculated based on the corresponding densities and the solubility in water (35.9g NaCl/100ml water, i.e., x2 =0.0996) (Lide, 2006). The surface tension, which depends on concentration, is given by (Pruppacher and Klett, 1997) σ LV = 0.072 + 0.0017 × m (5.12) where m is the molality of NaCl. As for σ CV , the available values reported in the 93 literature cover a wide range, spanning from 0.09 to 0.348 N/m (Mirabel et al., 2000; Djikaev et al., 2001; Russell and Ming, 2002). Mirabel et al. (2000) chose four values: 0.1, 0.112, 0.2 and 0.271 N/m for their theoretical study, Russell and Ming (2002) used 0.213 N/m, while Djikaev et al. (2001) deduced 0.348 N/m. The effect of σ CV on DRH and how to obtain an effective value accounting for the initial water coating (a wetted particle) (Russell and Ming, 2002) will be discussed in detail in Section 5.3. After numerically solving equation 5.10 for x 2 , the water activity in the droplet is determined and then the DRH from equation 5.11. When m < 13 mol/kg, the water activity in droplet solution is estimated by equation 2.26. Otherwise, the equation 2.17 is used. For NaCl solution, Ally et al. (2001) reported c A = 3.813 ± 0.2598 and q = 2.845 ± 0.332 . In the present formulation, it is found that at a given temperature, x 2 can be affected by θ1, θ2, σ CV and n 2 , so can DRH. The results for the individual effects are presented and discussed in the following section, where the size of a dry particle represents the volume-equivalent diameter (VED). 5.3 Results and Discussions Predicted DRH for suspended particles is quite sensitive to σCV, in particular for small particles (Mirabel et al., 2000). As discussed in Section 5.2, the reported values of σCV for NaCl span a considerable range. To investigate its effect, the 94 calculated DRH against particle size for suspended particles ( θ1 = θ 2 = 180 o ) for several values of σCV is plotted in Figure 5.2 and compared with available experimental data. 150 Experimental data (Hämeri et al., 2001) Experimental data (Biskos et al., 2006a) Experimental data (Biskos et al., 2006a) Model (Russell and Ming, 2002) This study (σCV=0.271 N/m) This study (σCV=0.213 N/m) This study (σCV=0.131 N/m) This study (σCV=0.112 N/m) This study (σCV=0.1 N/m) 140 130 DRH (%) 120 110 100 90 80 70 60 50 8.6 nm 0 20 40 60 D (nm) 80 100 120 Figure 5.2 Effect of surface tension on the DRH of suspended NaCl particles. The prediction is compared with experimental data of Biskos et al. (2006a) and Hämeri et al. (2001) and with the model of Russell and Ming (2002). For suspended NaCl nanoparticles, Hämeri et al. (2001) and Biskos et al. (2006a) systematically investigated the particle-size dependence of DRH using an ultrafine-DMA and tandem nano-DMAs. Note that the filled and open circles shown in Figure 5.2 are the experimental data of Biskos et al. (2006a) for particles generated by a vaporization-condensation method and an electrospray technique, 95 respectively. The experimental data reveal that DRH decreases with the particle size, and can be expressed by an empirical equation: DRH ( Dm ) = 213Dm−1.6 + 76 with Dm being the dry particle mobility diameter (nm) for 6 nm ≤ Dm ≤ 60 nm (Biskos et al., 2006a). Also included in the figure is DRH calculated by the wetted particle model using σLC=0.029 N/m, σLV =0.083 N/m, and the measured partial molar volume (Line 6 of Figure 3 in the published paper of Russell and Ming (2002)), showing a good agreement with experiment. Interestingly, the theoretical prediction with σCV =0.131 N/m in this study compares favorably with the experimental data, too, except for Dm< 8.6 nm. The above comparison implies that 0.131 N/m can be regarded as an effective surface tension accounting for the initial water coating, although the formulation is based on a dry particle. It can be understood by comparing the free energies of the two initial states for a suspended particle; σCV aCV in the dry state will be replaced by σLV aLV + σLC aLC + n1L µ1L in the coated state. When the water layer is comparatively thin enough (i.e., small n1L and aLV ≈ aLC≈ aCV), the change of chemical potential for n1L water molecules after deliquescence has a negligible effect on the DRH calculation. This can also explain why the prediction worsens for D < 8 nm. Therefore, σCV =0.131 N/m is employed to calculate DRH for most of the cases, where the NaCl particles are greater than 8.6 nm. Note that for sufficiently large particles, DRH is only weakly affected by σCV, although the results are not shown in Figure 5.2. 96 VED= 63 nm 100 θ2=10 95 o 0.1 N/m 0.131 N/m 0.213 N/m 0.271 N/m 90 85 RH (%) 80 75 70 65 60 55 50 45 40 100 θ2=90o 95 90 85 RH (%) 80 75 70 65 60 55 50 45 40 100 θ2=180 95 o 90 85 RH (%) 80 75 70 65 60 55 50 45 40 0 20 40 60 80 100 θ1 (o) 120 140 160 180 Figure 5.3 σCV effect on DRH variation with θ1 for deposited particles having a volume equivalent diameter (VED) of 63 nm at θ2=10o, 90o, and 180o. 97 Figure 5.3 shows DRH as a function of θ1 at various θ2 for particles with VED of 63 nm. The calculated DRH is lower for larger σCV, similar to that of suspended particles (Mirabel et al., 2000), and increases with decreasing θ1. In fact, when θ1 approaches zero, DRH converges to the same value, independent of σCV. The weaker σCV effect at smaller θ1 can be understood as follows. Using equations 5.4–5.6, equation 5.1 can be rewritten as G I = Nµ + n 2 µ + π ( v 1 c 2 3n2 v c π 2 3 ) σ CV 1 3 (2 − 3 cos θ1 + cos θ1 ) + σ SV A 3 (5.13) Note that the third term on the right-hand side of equation 5.13 represents the surface energy change (mechanical work) after the particle is deposited. When θ1 decreases, this term decreases and actually vanishes at θ1=0, where the free energy becomes unaffected by σCV. From equation 5.13, it is also found that the relative magnitude of chemical to mechanical work (i.e., the ratio of the second to third term) is proportional to n12 / 3 , indicative of increasing importance of the mechanical work when the particle decreases in size. Figure 5.4 sketches how the free energies for a solid particle and a corresponding solution droplet vary with RH (Seinfeld and Pandis, 1998). At low RH, the free energy of solid particle is lower than that of the corresponding solution droplet, so the dry particle remains thermodynamically stable. When RH increases, the free energy of the solution droplet decreases, and becomes equal to that of the solid particle at a certain RH, which is regarded as DRH in the present study. As RH 98 further increases, the free energy of the solution droplet is lower than that of the dry state, and thereby the solid particle spontaneously absorbs water to form a solution droplet (Seinfeld and Pandis, 1998). An increase in σCV or θ1 means an upward shift of the dash-dotted line (GI) in Figure 5.4, leading to a crossover at a lower RH. Gibbs free energy (J ) Deposited aqueous solution (GII) Deposited solid particle (GI) DRH 50 75 100 RH (%) Figure 5.4 Sketch of variations of Gibbs free energies of a deposited solid particle and its aqueous solution with relative humidity (Seinfeld and Pandis, 1998). The arrows indicate the directions of curve shift with decreasing contact angles, particle size or surface tension. Figure 5.5 plots DRH as a function of θ1 for six particle sizes ranging from 20 to 555 nm for two values of σCV : 0.131 and 0.231 N/m. Only for small particles, does the variation in θ1 substantially influence DRH; when the particle size is larger than 555 nm, θ1 hardly affects DRH. At a given σCV, DRH may exhibit opposite trends with varying particle size, depending on both θ1 and θ2 (see Figure 5.5). The 99 crossover region appears to shift toward a greater value of θ1 when θ2 is increased, and may disappear for certain cases, such as that shown in Figure 5.5(c). The complicated behavior can be explained by how the free energies change when the particle size is varied. Depending on θ1, θ2 and σCV, both GI and GII (equations 5.1 and 5.2) decrease with decreasing particle size, but at different rates, leading to a complex trend in the crossover shift shown in Figure 5.4. 100 (1) σ RH (%) 90 CV (2) σ =0.131 N/m θ2=10o （a） 90 80 80 70 70 60 60 50 50 555nm 257nm 119nm 63nm 44nm 20nm 40 30 20 RH (%) 10 θ2=90 RH (%) o 90 80 80 70 70 60 60 50 50 40 40 30 30 θ2=180o （c） 100 90 90 80 80 70 70 60 60 50 50 40 60 θ2=90o （e） θ2=180o （f） （b） 90 20 （d） 20 100 0 o θ2=10 30 10 40 =0.213 N/m 40 100 100 CV 80 100 θ1 (o) 120 140 160 180 40 0 20 40 60 80 100 θ1 (o) 120 140 160 Figure 5.5 DRH of a deposited particle as a function of θ1 with σCV = 0.131 and 0.213 N/m and at θ2=10o, 90o, and 180o. 101 180 The variation of DRH with θ2 is presented in Figure 5.6 for σCV =0.131 N/m, where one can again see a significant effect only for small particles. A decrease in θ2 lowers the free energy of the droplet as demonstrated by the re-arranged equation 5.2: G II = ( N − n1 ) µ1v + n2 µ 2 + n1 µ1 + π[ 3(n1v1 + n2 v 2 ) π 2 3 ] σ LV 1 3 (2 − 3 cos θ 2 + cos θ 2 ) + σ SV A 3 (5.14), leading to a lower DRH which can be visualized in Figure 5.4. For larger particles, because the chemical potential terms dominate over the influence of surface tension (the 4th term of equation 5.14), the effect of θ2 on the DRH becomes weaker. In addition, Figure 5.6 shows that the location of the crossover region with respect to θ2 depends on the θ1 value, which can also be understood from the different change rates of GI and GII as particles vary in size. From Figures 5.5 and 5.6, one can find that for sufficiently small particles, the DRH could be substantially lowered when θ2 is small, but θ1 is not small. It corresponds to a case where small particles in a nearly spherical shape are deposited on a hydrophilic substrate. This finding suggests that corrosion associated with deliquescent deposited aerosol may take place at a rather low RH. 102 RH (%) 100 100 σCV=0.131 N/m; θ1=180o 90 80 80 70 70 60 40 50 40 30 30 100 RH (%) o 60 555nm 257nm 119nm 63nm 44nm 20nm 50 100 σCV=0.131 N/m; θ1=60o 90 90 80 80 70 70 60 60 50 50 40 40 30 CV σ =0.131 N/m; θ1=90 90 0 20 40 60 80 100 θ2 (o) 120 140 160 180 30 σCV=0.131 N/m; θ1=10o 0 20 40 60 80 100 θ2 (o) 120 140 160 Figure 5.6 Variation of DRH with θ2 for different particle sizes at θ1=180o, 90o, 60o, and 10o. To the best of the knowledge, there exist only two experimental works examining the DRH of deposited particles (100 nm - 20 µm) with the results shown in Table 5.1. Verifying the theoretical prediction requires the interfacial properties in terms of θ1, θ2, and σCV measured experimentally along with the DRH, which unfortunately could not be provided by these two studies using environmental-TEM or 103 180 environmental-SEM. To roughly estimate the range of θ1, one can use the DRH contour plots shown in Figure 5.7. For instance, using the measured θ2=60o for a large NaCl solution drop on a TEM grid, the θ1 range is found to be 16o~80o for D=257 nm from the data in Table 5.1 and Figure 5.7(b). 180 (a) 160 90 140 θ2(o) 120 85 100 80 80 75 60 70 40 65 20 20 40 60 80 100 θ1(o) 120 140 160 180 104 180 (b) 160 79 140 78 θ2(o) 120 77 100 76 80 75 60 74 40 73 20 72 20 40 60 80 100 θ1(o) 120 140 160 180 105 180 (c) 160 77.0 140 76.5 θ2(o) 120 76.0 100 75.5 80 75.0 60 74.5 40 20 74.0 20 40 60 80 100 θ1(o) 120 140 160 180 Figure 5.7 Contour plots for DRH as a function of the contact angles (θ1 and θ2) for deposited NaCl particles with dry diameter: D=63 nm (a), 257 nm (b) and 555 nm (c). The value for each curve denotes the DRH in %. 106 Finally, feasible laboratory experiments are briefly reviewed and suggested to measure the contact angles, and interfacial properties of nanosized particles on substrates. To determine the contact angles of deposited dry and wet particles, in-situ measurements using tapping-mode AFM appears to be one of the most promising techniques, because of its strength of providing three dimensional images, in particular for a contact angle smaller than 90o (Herminghaus et al., 1997; Pompe et al., 1998; Wang et al., 2002a, 2002b and 2005). Wang et al. (2002a and b) reported the contact angles of 10.8o and 22o for nanosized water droplets on mica and stainless steel (SUS 304), respectively. They also found that the contact angels appear to decrease with decreasing particle sizes, which is consistent with the observations of micron-sized droplets (Ueda et al., 2003). Because the surface properties of a substrate can affect the contact angles (Adamson and Gast, 1997; Wang et al., 2002b; Ponsonnet et al., 2003; Hennig et al., 2004), one should take into account the composition, roughness, homogeneity, and the preparation method for the substrate surface when designing experiments. For instance, the contact angle of a water droplet on Formvar (a kind of coating on a TEM grid) can vary from 50o to 83o (Pruppacher and Klett, 1978; Hennig et al., 2004), while it can become as small as 35o if a carbon film is used as the substrate (Mattia et al., 2006). In addition, since the methods of depositing particles on a substrate may also affect the interfacial properties (contact angle and surface tension) (Adamson and Gast, 1997), a consistent experimental preparation and execution is important to obtain reproducible data. 107 5.4 Conclusions The model of Mirabel et al. (2000) has been extended to study the deliquescence of particles deposited on a substrate. To facilitate the formulation and calculation, it has been assumed that the particle, dry or wet, is in a shape of spherical cap. For deposited particles smaller than 100 nm, the DRH substantially depends on the particle size, the contact angles, and the surface tension between the dry particle and the atmosphere, whereas the substrate effect is insignificant for large particles (> 500 nm). Depending on the contact angles, small particles depositing on a substrate could deliquesce at a much lower RH, posing a potential corrosion problem for the substrate. Although the formulation in this study is based on spherical caps, it can be easily modified to investigate a deposited particle with experimentally measured shape, dimensions and σCS. In the future, more experimental investigation providing the shape or contact angles in parallel with corresponding DRH for deposited particles smaller than 100 nm is needed to verify the present theoretical understanding of the deliquescent behavior. 108 CHAPTER 6 Conclusions and Future Work 6.1 Conclusions The theoretical models based on classical nucleation theory have been successfully developed to investigate ERHs of single-inorganic particles ((NH4)2SO4 and NaCl), and multi-inorganic particles (mixed Na2SO4-NaCl), and study effects of WSOs on ERH of (NH4)2SO4 and NaCl particles. The main findings are summarized below: (1) The theoretical model satisfactorily predicts ERHs of suspended (NH4)2SO4 particles with the diameter of 8 nm to 17 µm and NaCl particles with the diameter of 6 nm to 20 µm. (2) The ERHs of suspended (NH4)2SO4 and NaCl particles first decrease with the dry particle size and then start to increase when the dry particle size is smaller than 30 nm for (NH4)2SO4 particles and 70 nm for NaCl particles. (3) The Kelvin effect plays an important role in raising the ERH of suspended particles smaller than 30 nm for (NH4)2SO4 and 70 nm for NaCl, whereas the dry particle size is the most dominant factor influencing the ERH of suspended particles larger than 50 nm for (NH4)2SO4 and 70 nm for NaCl. (4) Compared to (NH4)2SO4 particles, the Kelvin effect raises the ERH of smaller NaCl particles (70 nm) less significantly. (5) The predicted ERHs of mixed NaCl-Na2SO4 particles at various molar ratios show satisfactory agreement with experimental values, except for the cases with a Na2SO4 mole fraction of around 0.25. (6) The ERH of mixed NaCl-Na2SO4 particles is controlled by the homogeneous nucleation of one salt, whose nucleation rate is far much higher than that of the other. (7) At mixing ratios where the individual nucleation rates of two salts are close enough to each other, the theoretical formulation of this study underestimated ERH as compared to the experimental data. For these unique cases, the hypothesized mechanism of homogeneous nucleation of one salt followed by heterogeneous nucleation may not be appropriate for the efflorescence process. Further investigation is required in the future. (8) Kelvin effect plays a more important role in the ERHs of mixed NaCl-Na2SO4 particles smaller than 20 nm. Furthermore, the higher the Na2SO4 mole fraction, the stronger the Kelvin effect. (9) The theoretical model predicts that non efflorescible WSOs with surface active nature suppress the ERHs of suspended (NH4)2SO4 and NaCl particles; the drop of ERH can be as large as 30% RH when the mole fraction of WSOs is more than 0.5. (10) The theoretical model can satisfactorily predict the ERH of mixed particles comprising WSOs with weak surface active nature, e.g., glycerol, 110 levoglucosan and malonic acid, but not for WSOs with strong surface active nature, e.g., glutaric and maleic acids. In this thesis, a thermodynamic model has also been formulated to examine the deliquescence of deposited NaCl particles on a substrate. The major discovery is: (1) The DRH of deposited NaCl particles smaller than 100 nm substantially relies on the particle size, the contact angles between particles and substrates, and the surface tension between the dry particle and the atmosphere. (2) The substrate effect is insignificant for NaCl particles larger than 500 nm. (3) Small NaCl particles deposited on a substrate with certain contact angles could deliquesce at a much lower RH than suspended particles, thereby posing a potential corrosion problem for the substrate. 6.2 Future Work In the future, several studies on theoretical model and experiment can be carried out: 1. Current ERH prediction model can be improved from several facets: (1) Because prediction is very sensitive to the interfacial tension between nuclei and surrounding supersaturated solution, it is very important to develop an accurate theoretical or experimental method for the interfacial tension, especially for organics with strong surface active nature. (2) In ERH prediction model, the surface tension of solution was calculated by the empirical equation; once empirical equations for some species are not 111 available, this model cannot be applied to prediction. Thus, developing a theoretical method to calculate the surface tension of solution will be useful to apply this model to more species. (3) Applying more existing models of water and solute activities in ERH prediction model to make comparison. Because some models are very complicated, it will be helpful and time-saving to get the programme code of calculation from owners. 2. In order to verify the theoretical result that a minimum ERH exists, the ERH of particles can be experimentally detected from tens of micro-meter to several nano-meters using good hygrometer with high precision. At the same time, the length-adjustable exposure tubing can be designed to experimentally investigate residence time effects on ERH of suspended large and small particles. 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(2001), and equation A1 is a polynomial obtained by combining the work of Ally et al. (2001) and Tang et al. (1986), which have all been detailed in Chapter 2. 135 APPENDIX B Empirical equations for surface tension of aqueous WSO solutions (1) The formula of Li and Lu (2001) is used to calculate the surface tension of an aqueous glutaric acid, malonic acid or maleic acid solution: 1 ) 1 + k i ai σ drop − air = σ w + RTΓiwo ln( (B1) where ai is solute activity calculated by the UNIFAC model; Γiwo and ki are the saturated surface excess and the adsorption equilibrium constant for solute i, respectively. The parameter values are listed in Table B1 (Topping et al., 2007): Table B1: Parameter value for Γiwo and ki. Compound glutaric acid malonic acid maleic acid Γiwo ki 0.00296865 0.00055578 0.00163897 139.4950309 2108.971823 293.1181882 (2) The fitted equation for aqueous levoglucosan solution is (Svenningsson et al., 2006) σ drop − air = σ w − 0.0028 ⋅ 298.15 ln(1 + 0.813 ⋅ C ) (B2) where C is the number of moles of carbon atom per kg of water. (3) The polynomial equation for glycerol, according to the experimental data (Romero and Paez, 2006), is σ drop − air = 241.39 ⋅ x 6 - 849.29 ⋅ x 5 + 1198.6 ⋅ x 4 − 851.94 ⋅ x 3 + 313.37 ⋅ x 2 − 60.872 ⋅ x + 71.742 (B3) where x is the mole fraction of glycerol in its aqueous solution. 136 LIST OF PUBLICATIONS Y. Gao, L. E. Yu, and S. B. Chen. Effects of Organics on Efflorescence Relative Humidity of Ammonium Sulfate or Sodium Chloride Particles. Submitted to Atmospheric Environment. Y. Gao, L. E. Yu, and S. B. Chen. Efflorescence Relative Humidity of Mixed NaCl-Na2SO4 Particles. Journal of Physical Chemistry A, 111, 10660, 2007. Y. Gao, L. E. Yu, and S. B. Chen. Theoretical Investigation of Substrate Effect on Deliquescence Relative Humidity of NaCl Particles. Journal of Physical Chemistry A, 111, 633, 2007. Y. Gao, S. B. Chen, and L. E. Yu. Efflorescence Relative Humidity of Airborne Sodium Chloride Particles: A Theoretical Investigation. Atmospheric Environment, 41, 2019, 2007. Y. Gao, S. B. Chen, and L. E. Yu. Efflorescence Relative Humidity for Ammonium Sulfate Particles. Journal of Physical Chemistry A, 110, 7602, 2006. 137 [...]... cloud and fog formation, climate change, etc (Seinfeld and Pandis, 1998) 3 d Particle Diameter c e Efflorescence a b Deliquescence Solid phase Relative Humidity Figure 1.1 Schematic diagram of deliquescence and efflorescence processes 1.3 Experimental Measurements of DRH and ERH To understand the deliquescent and efflorescent behaviors of atmospheric particles, measurements of DRH and ERH of airborne particles. .. diameter of 10 µm and observation time of 150 S 77 Figure 4.3 Experimental and calculated ERHs of mixed (NH4)2SO4-malonic acid particles with average dry diameter of 10 µm and average observation time of 200 S 78 Figure 4.4 Experimental and calculated ERHs of mixed (NH4)2SO4-glutaric acid particles with average dry diameter of 10 µm and observation time of 150 S 79 Figure 4.5 Experimental and calculated... Growth factor and efflorescence trends for AS particles with a dry-state diameter of (a) 43.7 nm, and (b) 47 nm 31 Figure 2.6 Growth factor and efflorescence trends for AS particles with a dry-state diameter of (a) 5 µm and (b) 6 µm 33 Figure 2.7 ERH of the NaCl particles with dry mobility diameter of 6 – 70 nm 37 xi Figure 2.8 Growth factor of NaCl particles with a dry mobility diameter of (1) 6 nm,... sulfate and sodium chloride) and some organic species (e.g glutaric acid, L-glycine, L-glutamine and succinic acid) have the deliquescent and efflorescent/crystallization behaviors, two main atmospheric processes, which are contributed to phase transition between solid and liquid and size change of these aerosol particles 2 1.2 Deliquescence and Efflorescence of Airborne Particles The amount of water... mixed NaCl-Na2SO4 particles with dry-state diameters of 1 µm and residence time of 15 min The experimental data are extracted from the work of Lee and Chang (2002) 59 Figure 4.1 Experimental and calculated ERHs of mixed (NH4)2SO4-glycerol particles with average dry diameter of 10 µm and observation time of 150 S 76 Figure 4.2 Experimental and calculated ERHs of mixed (NH4)2SO4-levoglucosan particles with... or liquid or a combination of both), size, mass and optical properties (Cziczo et al., 1997; Seinfeld and Pandis, 1998; Martin et al., 2003) In other words, whether the airborne particles exist in a solid or liquid state depends on RH and RH history in air Hence, understanding the deliquescent and efflorescent behaviors of airborne particles well is important to understand and simulate atmospheric processes... and calculated ERHs of mixed NaCl-glutaric acid particles with average dry diameter of 10 µm and observation time of 150 S 80 xii Figure 4.6 Experimental and calculated ERHs of mixed (NH4)2SO4-maleic acid particles with average dry diameter of 0.6 µm and residence time of 120 S 81 Figure 4.7 Surface tension of aqueous WSO solution as a function of molality 84 Figure 5.1 Schematic of a deposited particle... µ chemical potential of a species ρsalt density of salt ρsol, ρi density of solution i ρw water density σ interfacial tension χ shape factor xvii CHAPTER 1 Introduction 1.1 Airborne Particles Airborne particles, also called to atmospheric aerosols or atmospheric particles, are suspensions of solid or liquid particles in a gas phase In the atmosphere, concentrations of airborne particles can be up to... is 15 min 62 Table 3.6 Variation of predicted ERH with residence time for mixed NaCl and Na2SO4 particles with a dry diameter of 45 nm and xβ =0.5 63 Table 3.7 Variation of ERH with σnuc-air for mixed NaCl and Na2SO4 particles with a dry diameter of 45 nm The residence time is 60 s 63 Table 4.1 Physical properties of salts and WSOs 68 Table 4.2 Structures and group no of WSOs 74 Table 4.3 UNIFAC group... water associated with airborne particles depends on the RH in atmosphere and the water absorption property of airborne particles Figure 1.1 schematically shows the deliquescent and efflorescent behaviors of airborne particles When RH increases from a lower level, particles remain at almost a dry state (from a to b) until a sufficiently high RH, deliquescence RH (DRH), under which dry particles substantially