Measurements of Aqueous Droplet Evaporation Rate As a Function of Solute Species

Measurements of aqueous droplet evaporation rate as a function of solute species

Nicole A. Combe

A thesis submitted in conformity with the requirements for the degree of Master of Science in Environmental Chemistry

Graduate Department of Chemistry University of Toronto

Measurements of aqueous droplet evaporation rate as a function of solute species

Nicole A. Combe

MSc. in Environmental Chemistry, Department of Chemistry, University of Toronto, 2016

Abstract

The water content of atmospheric particles determines their size and solute concentration, and thus their phase, gas uptake, reactivity, optical properties, and cloud- forming properties. I have measured the evaporation rate of water from binary and ternary solution droplets using an ultrasonic levitator, and developed a simple model to predict the change in droplet size as a function of solute concentration. The simple model agrees well with experimental results for solutions of simple, non-ammonium salts, and may be used for organic acids with parameterized water activity data. For ammonium chloride and ammonium sulfate droplets, the experimental evaporation rate of subsaturated solutions exceeds the simple model’s prediction. For ternary malonic acid/ammonium sulfate/water droplets, the effect of solutes on the evaporation rate of water from subsaturated solutions appears to be additive, and at higher concentrations a drastic reduction to evaporation rate is observed, suggesting that a highly viscous phase is formed.

Acknowledgements

I have been privileged to continue pursuing higher education at the University of Toronto, and to work with extraordinary people who have contributed immensely to my development as an environmental chemist and environmentally conscious citizen.

Firstly, I am thankful for the guidance, patience, and confidence afforded to me by Jamie Donaldson. I am fortunate to have worked with a supervisor who not only allowed me the space to learn and work through problems on my own, but was willing to help and work through them with me when I needed it. It has been an incredible opportunity to learn from Jamie and my committee members, Professors Jonathan Abbatt and Jennifer Murphy, and to do research made possible by funding from NSERC. I am further indebted to Jon Abbatt for his contributions to reviewing this thesis and interest in discussing my research.

My good fortune extends to the exceptional women I have shared the lab with: Alyson Baergen, Angela Hong, Laura Stirchak, Karen Morenz, and Kate Mill. Thank you for all of the great conversations about science and life, as well as the coffee and chocolate. I am always rooting for you!

It has truly been a privilege to be part of the environmental chemistry graduate cohort: a group of passionate scientists and inspiring human beings. I have learned so much from each of you, and greatly appreciated the lunchtime reminders that science is everywhere and it's awesome!

Ultimately, I am ineffably grateful to my family. Peter Sinclair, thank you for your unbounded friendship and support in everything, and for being a wonderful cat parent, especially when I was working late in the lab; you and Clark ensure that I laugh every single day.

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Table of Contents

Abstract ...... ii

Acknowledgements ...... iii

Table of Contents ...... iv

List of Tables ...... vii

List of Figures ...... viii

1 Introduction ...... 1 1.1 Aerosols & Droplets ...... 1 1.1.1 Size ranges & dynamic regimes ...... 1 1.1.2 Composition ...... 3 1.1.2.1 Inorganic salts ...... 3 1.1.2.2 Organic compounds ...... 4 1.1.3 Thermodynamic equilibrium in aerosol science ...... 4 1.1.3.1 Organic aerosols ...... 6 1.1.3.2 Mixed aerosol systems ...... 6 1.1.3.3 Liquid-liquid phase separation (LLPS) ...... 6 1.1.4 Kinetic limitations to water transport in highly viscous aerosols ...... 7 1.2 Single particle studies ...... 8 1.3 Thesis objectives ...... 10 1.4 References ...... 11

2 Thermodynamic & Kinetic Considerations ...... 17 2.1 Intersection of thermodynamics & kinetics in aerosol science ...... 17 2.2 Vapour pressure of water over aqueous solutions ...... 18 2.2.1 Raoult's law & ideality ...... 18 2.2.2 Aqueous solutions with non-volatile solutes ...... 19 2.2.2.1 van't Hoff factor ( ) & activity coefficient ( ) ...... 20 2.2.3 Saturated salt solutions ...... 20

2.3 Diffusion controlled evaporation from a droplet ...... 21 2.3.1 Simple models combining Maxwell's equation with equilibrium thermodynamics ...... 24 2.4 References ...... 26

3 Instrumentation & Methods ...... 27 3.1 Instrumentation ...... 27 3.1.1 Ultrasonic levitator ...... 27 3.1.2 Imaging - CCD camera & telecentric lens ...... 28 3.2 Methods ...... 30 3.2.1 Experimental procedure ...... 30 3.2.2 Chemicals ...... 31 3.2.3 Extended AIM (E-AIM) Aerosol Thermodynamics Model ...... 33 3.3 References ...... 34

4 Results ...... 35 4.1 Water droplets ...... 35 4.2 Binary inorganic salt/water droplets ...... 37 4.2.1 Binary simple salt/water droplets ...... 38 4.2.2 Binary ammonium salt/water droplets ...... 44 4.3 Binary malonic acid/water droplets ...... 48 4.4 Ternary malonic acid/ammonium sulfate/water droplets ...... 50 4.5 References ...... 53

5 Discussion ...... 54 5.1 Binary simple salt/water droplets ...... 54 5.2 Binary ammonium salt/water droplets...... 57 5.3 Binary malonic acid/water droplets ...... 59 5.4 Ternary malonic acid/ammonium sulfate/water droplets ...... 61 5.5 References ...... 64

6 Conclusions & Future Work ...... 67 6.1 Conclusions ...... 67 6.2 Future Work ...... 69 6.3 References ...... 70

Appendix ...... 71 A : Maintenance & cleaning of the ultrasonic levitator ...... 71 B : Simple model predictions of a solution's evaporation rate ...... 72

List of Tables

Table 3.1 Properties of solutes...... 32

Table 4.1 Ratios comparing the evaporation rates, in terms of change in surface area versus time, of an aqueous simple salt solution/distilled water (solution/water ) for 0-100 . Experimental range given is 95% confidence interval for n = 15...... 43

Table 4.2 Ratios comparing the evaporation rates, in terms of change in surface area versus time, of an aqueous simple salt solution/distilled water (solution/water ) for the 100 before crystallization. Experimental range given is 95% confidence interval for n = 15...... 44

Table 4.3 Ammonia vapour pressure above a saturated aqueous solution at 25°C...... 44

Table 4.4 Ratios comparing the evaporation rates, in terms of change in surface area versus time, of an aqueous ammonium salt solution/distilled water (solution/water ) for 0-100 . Experimental range given is 95% confidence interval for n = 15...... 45

Table 4.5 Ratios comparing the evaporation rates, in terms of change in surface area versus time, of an aqueous ammonium salt solution/distilled water (solution/water ) for the 100 before crystallization. Experimental range given is 95% confidence interval for n = 15...... 45

Table 4.6 Ratios comparing the evaporation rate, in terms of change in surface area versus time, of aqueous malonic acid/distilled water (solution/water ) for 0-100 . Experimental range given is 95% confidence interval for n = 15...... 50

Table 4.7 Ratios comparing the evaporation rates, in terms of change in surface area versus time, of aqueous malonic acid/distilled water (solution/water ) for the 100 before crystallization. Experimental range given is 95% confidence interval for n=5...... 50

Table 4.8 Ratios comparing the evaporation rate, in terms of change in surface area versus time, of malonic acid/ammonium sulfate/distilled water (solution/water ) for 0-100 . Experimental range given is 95% confidence interval for n = 15...... 52

Table 5.1 Water activity coefficients ( ) corresponding to the average concentration range for 0-100 ...... 55

Table 5.2 Comparison of moles of semi-volatile solute evaporated across 0-100 , as predicted by Eq. 15, to the difference in moles between the experimental data and the Eq. 11b prediction across 0-100 ...... 58

Table B.3 Variables in Eq. 11a and Eq. 11b describing the evaporation of water...... 72 vii

List of Figures

Figure 1.1 Aerosol size distribution in terms of number, surface area, and volume as a function of particle diameter (Robinson 2012)...... 2

Figure 2.2 Position ( ) and radius ( ) relative to the sphere...... 22

Figure 3.1 Schematic for the ultrasonic levitator and CCD camera set-up, viewed in the x,z plane...... 27

Figure 3.2 Illustration depicting how the image from a telecentric lens is independent of an object's distance...... 29

Figure 4.1 Evaporation of a distilled water droplet held in the ultrasonic levitator at 0% RH and 24.7°C (average temperature). Error bars span the 95% confidence interval corresponding to the number of measurements available at each time point (n = 3-15)...... 35

Figure 4.2 Experimental evaporation data for aqueous sodium chloride, deployed as a 1.2 droplet of 2 m solution: experimental data (green diamonds), predictions using Eq. 11a (red curve) and Eq. 11b (blue curve), and experimental evaporation data for distilled water as reference (black circles). Black arrow indicates where experimental droplets are expected to reach saturation, and error bars span the 95% confidence interval. Panels display (a) entire timescale, (b) initial 100 , and (c) final 200 before crystallization. Inset image shows visible crystallization; the final data point corresponds to the image preceding crystallization...... 39

Figure 4.3 Evaporation of aqueous sodium bromide, deployed as 1.2 droplets of 2 m solution: experimental data (green diamonds), prediction using Eq. 11a (red curve), and experimental evaporation data for distilled water as reference (black circles). Black arrow indicates where experimental droplets are expected to reach saturation, and error bars span the 95% confidence interval. Panels display (a) entire timescale, (b) initial 100 , and (c) 200 before crystallization...... 40

Figure 4.4 Evaporation of aqueous potassium chloride, deployed as 1.0 or 1.2 droplets of 2 m solution: experimental data (green diamonds), prediction using Eq. 11a (red curve), and experimental evaporation data for distilled water as reference (black circles). Black arrow indicates where experimental droplets are expected to reach saturation, and error bars span the 95% confidence interval. Panels display (a) entire timescale, (b) initial 100 , and (c) 200 before crystallization...... 41

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Figure 4.5 Evaporation of aqueous magnesium chloride, deployed as 1.2 droplets of 2 m solution: experimental data (green diamonds), prediction using Eq. 11a (red curve), and experimental evaporation data for distilled water as reference (black circles). Black arrow indicates where experimental droplets are expected to reach saturation, and error bars span the 95% confidence interval. Panels display (a) entire timescale, (b) initial 100 , and (c) 200 before crystallization...... 42

Figure 4.6 Evaporation of aqueous ammonium chloride, deployed as 1.2 droplets of 2 m solution: experimental data (green diamonds), predictions using Eq. 11a (red curve) and Eq. 11b (blue curve), and experimental evaporation data for distilled water as reference (black circles). Black arrow indicates where experimental droplets are expected to reach saturation, and error bars span the 95% confidence interval. Panels display (a) entire timescale, (b) initial 100 , and (c) 200 before crystallization...... 46

Figure 4.7 Evaporation of aqueous ammonium sulfate, deployed as 1.2 and 1.4 droplets of 1.9 m solution: experimental data (green diamonds), predictions using Eq. 11a (red curve) and Eq. 11b (blue curve), and experimental evaporation data for distilled water as reference (black circles). Black arrow indicates where experimental droplets are expected to reach saturation, and error bars span the 95% confidence interval. Panels display (a) entire timescale, (b) initial 100 , and (c) 200 before crystallization...... 47

Figure 4.8 Evaporation of aqueous malonic acid, deployed as a 1.2 droplet of 2 m solution: experimental data (green diamonds), prediction using Eq. 11a and (red curve), and experimental evaporation data for distilled water as reference (black circles). Black arrow indicates where experimental droplets are expected to reach saturation, and error bars span the 95% confidence interval. Panels display (a) entire timescale, (b) initial 100 , and (c) 200 before crystallization. Inset image shows visible formation of a precipitate...... 49

Figure 4.9 Evaporation of ternary malonic acid/ammonium sulfate/water, deployed as a 1.2 droplet of 2 m malonic acid and 0.8 m ammonium sulfate: experimental data (green diamonds). Experimental evaporation data for distilled water (black circles), aqueous malonic acid as (a) purple triangles and (b,c) purple curve, and aqueous ammonium sulfate as (a) yellow squares and (b,c) yellow curves are given as reference. Error bars span the 95% confidence interval. Panels display (a) entire timescale, (b) initial 100 , and (c) 200 before malonic acid precipitates...... 51

Figure 5.1 Molecular structure of malonic acid...... 60

Figure B.2 Spreadsheet relating droplet volume and solute concentration for 1.2 droplets of 2 m ammonium chloride...... 73

Figure B.3 E-AIM Model IV output for 1.2 droplets of 2 m ammonium chloride: input as . Volume(aq) is given in and partial pressures are given in . Activity coefficients are denoted as f_z for each species z in the system. .. 77

Figure B.4 Spreadsheet relating E-AIM Model IV output for droplet volume and solute concentration for 1.2 droplets of 2 m ammonium chloride...... 78

1 Introduction

1.1 Aerosols & Droplets

The atmosphere is not a single phase system, but rather a dynamic mixture of gases, liquids, and solids. Atmospheric particles, such as aerosols and droplets, are stable suspensions of condensed phase particles that control the liquid water content of the atmosphere (Finlayson-Pitts and Pitts 2000). The water content of atmospheric particles can vary drastically and is a major factor determining aerosol size, from solid salts and minerals to cloud and fog droplets that are up to 100x larger in diameter. By controlling aerosol size, the water content of aerosols determines the concentration of inorganic salts, organic compounds, and metals, and impacts aerosols' phase, trace gas uptake, aqueous phase reactions, cloud-forming properties, optical properties, and aerosols' effect on Earth's radiation budget (Andreae and Rosenfeld 2008; Rosenfeld et al. 2008; Hallquist et al. 2009; Mikhailov et al. 2009; Kolb et al. 2010; Abbatt et al. 2012).

1.1.1 Size ranges & dynamic regimes

Aerosols are dynamic atmospheric systems where the size of each particle is always in flux; thus, aerosol populations are polydispersed with respect to particle diameter. The size distribution of aerosols can be described in terms of particle number, surface area, and volume, with each yielding a different distribution profile (see Figure 1.1). When discussing aerosol populations, the range of particle diameters is often divided into two modes: the accumulation mode describes aerosols from 200-2500 , and the coarse mode describes aerosols in the 2500-10000 range. Above 10 , particles have taken up up a sufficient amount of water to be considered cloud or fog droplets (Finlayson-Pitts and Pitts 2000).

In aerosol dynamics, which considers the movement of aerosols and their interaction with the surrounding gas phase, particle size is discussed in terms of dynamic regime.

Dynamic regimes are classified in terms of Knudsen number ( ), which relates the gas phase mean free path ( ) to a characteristic length, such as a particle's diameter ( ):

Eq. 1

Using the Knudsen number, the gas suspending particles can be divided into three regimes: the free molecular regime, the transition regime, and the continuum regime. The free molecular regime describes particles on the same scale as molecules, >> 1, which interact with the surrounding gas as colliding bodies. Conversely, the continuum regime describes particles of << 1; these particles are significantly larger than the mean free path of the surrounding gas, and so the gas acts as a continuous fluid around the particle. The transition regime accounts for the particles that fall between the free molecular regime and the continuum regime, 1, which must be treated by a combination of molecular and macroscopic interactions. In air at 1 , the mean free path of gas molecules is on the order of tens of nanometres; thus, accumulation mode aerosols, coarse mode aerosols, and cloud droplets are all described by the continuum regime.

Figure 1.1 Aerosol size distribution in terms of number, surface area, and volume as a function of particle diameter (Robinson 2012).

1.1.2 Composition

Aerosols are composed of water, inorganic salts, condensed carbonaceous matter, and metals and metalloids from the Earth's crust. The primary, non-aqueous components of aerosols are often mixtures of inorganic salts and organic compounds; mixtures of sulfates and organic matter account for over 90% of accumulation mode aerosols by mass, with organic matter accounting for 20% to upwards of 80% of the aerosol mass fraction (Murphy et al. 1998; Murphy et al. 2006; Hallquist et al. 2009; Jimenez et al. 2009).

1.1.2.1 Inorganic salts

2- Sulfate (SO4 ) is the predominant anion in atmospheric aerosols and is a secondary 2- product, primarily formed by aqueous phase oxidation of sulfite (SO3 ), which partitions with gas phase sulfur dioxide (SO2) (Calvert et al. 1985; Jimenez et al. 2009).

2- + SO2(g) + H2O(l) ↔ SO3 (aq) + 2H (aq)

The majority of sulfur dioxide is emitted by anthropogenic sources, such as fossil fuel burning; however, sulfur dioxide is naturally present in the atmosphere, released directly from volcanic emissions and indirectly by the oxidation of dimethyl sulfide from marine phytoplankton (Andreae and Crutzen 1997; Jacobson and High 2008). Thus, while sulfate aerosols may be concentrated in urban areas, they are also present in remote regions (Johnson and Kumar 1991; Jimenez et al. 2009; Gong et al. 2010). The pH of sulfate aerosols is controlled by the ambient relative humidity and neutralization by gas phase ammonia, and ammonia promotes the formation of new particles (Johnson and Kumar 1991; Kirkby et al. 2011).

Ammonia is the primary alkaline group in the atmosphere; it contributes to new particle formation and partitions with aqueous phase particles according to its Henry's law constant ( at 298 , Sander 1999). In the aqueous phase, ammonia is predominantly present as ammonium ( 9.25), the primary cation in atmospheric particles (Jimenez et al. 2009). Ammonia is emitted from natural sources around the globe, such as soils, vegetation, oceans, and animal excreta, and its major anthropogenic source is agriculture (Reis et al. 2009; Sutton et al. 2013).

Sea spray is another source of inorganic salts to aerosols, sending non-volatile solutes such as sodium, magnesium, calcium, potassium, chloride, bromide, and iodide ions into the atmosphere (Tang 1997).

1.1.2.2 Organic compounds

Organic matter accounts for 20% to upwards of 80% of the total aerosol mass; however, the sources, atmospheric processing, and removal of organic aerosols (OA) are still poorly characterized (Murphy et al. 1998; Decesari et al. 2000; Murphy et al. 2006; Hallquist et al. 2009; Jimenez et al. 2009; Ervens et al. 2011). Primary organic aerosols (POA) are directly emitted from anthropogenic sources, such as biomass burning and fossil fuel combustion, while secondary organic aerosols (SOA) are formed when oxidation products of anthropogenic and biogenic volatile organic compounds (VOCs) partition to particles. SOA account for a large fraction of OA in the atmosphere, and it is estimated that they contain 104-105 different organic compounds (Goldstein and Galbally 2007; Hallquist et al. 2009).

The discussion of OA can be simplified by dividing organic compounds into two classifications: hydrophobic and hydrophilic. Compounds in the hydrophilic fraction are referred to as water soluble organic compounds (WSOCs), and include low molecular weight carboxylic acids, dicarboxylic acids, alcohols, ketones, aldehydes, nitrates, and macromolecular humic acids (Saxena and Hildemann 1996; Facchini et al. 1999) Studies have found that a large fraction of organic acids in OA, including linear dicarboxylic acids, are generated through aqueous phase oxidation, although the majority of mechanisms and products remain unidentified (Sorooshian et al. 2007; Hallquist et al. 2009; Ervens et al. 2011; He et al. 2013). Therefore, understanding the influence of organic compounds on aerosol water content is of reciprocal importance.

1.1.3 Thermodynamic equilibrium in aerosol science

Aerosols are often discussed under the assumption that they are in instantaneous thermodynamic equilibrium with the surrounding atmosphere. This framework allows for the discussion of water uptake and loss in terms of hygroscopic behaviour: deliquescence, hygroscopic growth, and efflorescence. Deliquescence is the phase transition that occurs

5 when a solid substance, such as an inorganic salt, takes up water from the surrounding gas phase in order to be completely dissolved as a saturated solution. This occurs when the ambient relative humidity (RH) is equal to or greater than the water activity ( ) of the resulting saturated solution; this relative humidity is characteristic of the solute, and is called the deliquescence relative humidity ( ). As the ambient relative humidity increases above an aerosol's , hygroscopic growth describes the aerosol's water uptake. The degree of water uptake above an aerosol's is discussed using the diameter hygroscopic growth factor ( ), which is the ratio of the wet particle diameter at a given relative humidity to the dry particle diameter. rely on the aerosol reaching thermodynamic equilibrium at the given relative humidity. The deliquescence and hygroscopic growth of individual inorganic salts is generally considered to be well understood; the of common salts, such as ammonium sulfate, ammonium nitrate, and sodium chloride, have been tabulated, and their wet particle diameters are well-described by Köhler theory (Köhler 1936; Greenspan 1977; Tang and Munkelwitz 1994; Gysel et al. 2002; Mikhailov et al. 2004; Petters and Kreidenweis 2007).

When aerosols are exposed to decreasing relative humidity, dissolved species in aqueous solution will spontaneously crystallize when the ambient relative humidity is sufficiently low that the aerosol is saturated or supersaturated; this phase transition is referred to as efflorescence or crystallization. Efflorescence cannot be described by the same model as deliquescence because it can occur after a solution has reached a metastable state of supersaturation, wherein crystal nucleation and growth is a kinetic process. This results in a wide range of reported efflorescence relative humidity values ( ) for common salts; for example, ammonium nitrate has been reported to crystallize at 30% RH, as well as remain in a metastable aqueous state down to 0.05% RH (Gysel et al. 2002; Mikhailov et al. 2004). Recently, contact efflorescence has been reported for ammonium sulfate, ammonium nitrate, and sodium chloride particles, whereby efflorescence is initiated by a solid particle externally impacting the surface of a metastable aqueous droplet (Davis et al. 2015). Davis and his colleagues observed efflorescence upon a single collision, and demonstrated that crystallization of a salt can occur at any RH below the salt's . After contact efflorescence, particles remained crystalline at all relative humidities below their . This

6 highlights the need for further study of efflorescence in order to improve our understanding of the kinetic process, and subsequently atmospheric particle phase and liquid water content.

1.1.3.1 Organic aerosols

As single component aerosols, WSOCs can absorb water and exhibit a range of hygroscopic behaviour. Many WSOCs do not exhibit clear onset of deliquescence and efflorescence, as is observed for inorganic salts; instead, water uptake and loss is observed across the spectrum of relative humidity (Peng et al. 2001; Prenni et al. 2001; Choi and Chan 2002a; Demou et al. 2003; Zobrist et al. 2011; Liu et al. 2016). Recent research has shown that OA can be highly viscous at low relative humidity and/or low temperature, forming amorphous/glassy states with slow condensed phase diffusion (Mikhailov et al. 2009; Virtanen et al. 2010; Tong et al. 2011; Zobrist et al. 2011).

1.1.3.2 Mixed aerosol systems

Studies of mixed aerosol systems containing organic aerosol (OA) and inorganic salts have aimed to characterize their hygroscopicity, and have demonstrated that water uptake and loss depends on multiple factors, such as the ratio of organic and inorganic fractions, the physiochemical properties of the specific organics, and ambient conditions (Cruz and Pandis 2000; Choi and Chan 2002b; Brooks et al. 2002; Prenni et al. 2003; Wise et al. 2003; Braban and Abbatt 2004; Svenningsson et al. 2005; Sjogren et al. 2007; Hodas et al. 2015; Liu et al. 2016). Like binary WSOCs/water droplets, mixed aerosols containing WSOCs and inorganic salts can exhibit continuous water uptake and loss at low relative humidities, and are generally single phase mixtures above 60% RH (Marcolli and Krieger 2006; Murphy et al. 2006; Ciobanu et al. 2009; Bertram et al. 2011; Song et al. 2012a, 2012b; You et al. 2013, 2014; Zhou et al. 2014).

1.1.3.3 Liquid-liquid phase separation (LLPS)

Recent research has found that organic aerosols and mixed organic/inorganic aerosols can exist in more phases than simply aqueous or crystalline (Marcolli and Krieger 2006; Ciobanu et al. 2009; Virtanen et al. 2010; Bertram et al. 2011; Zobrist et al. 2011). Below 60% RH, non-ideal solutions containing organic aerosols and inorganic salts may undergo liquid-

7 liquid phase separation (LLPS), which is akin to salting-in and salting-out by electrolytes and results in the coexistence of a non-polar, organic phase and polar, electrolyte-rich phase in a single particle (Ciobanu et al. 2009; Bertram et al. 2011; Song et al. 2012; You et al. 2012, 2013, 2014). Phase separation can result in core-shell and engulfed particle morphologies, and is expected to be a common occurrence in tropospheric aerosols; LLPS is the product of many factors, including relative humidity, temperature, mole fraction of constituents, polarity of organic compounds in terms of oxygen-to-carbon ratio (O:C), particle size, surface tension effects, and ion diffusion (Marcolli and Krieger 2006; Ciobanu et al. 2009; Bertram et al. 2011; Song et al. 2012; You et al. 2013, 2014; Hodas et al. 2015). Coupled with OA formation of highly viscous, glassy states, the complex phase behaviour of LLPS may have significant implications for the partitioning and transport of water and semi-volatile solutes to and from particles in the atmosphere, discussed further in the following section.

1.1.4 Kinetic limitations to water transport in highly viscous aerosols

For particles in the continuum regime ( << 1), the evaporation and condensation of water is limited by diffusion in the gas phase. However, the formation of a highly viscous bulk aerosol or outer shell can drastically reduce condensed phase diffusion and control the mass transfer of water between the particle and gas phase (Mikhailov et al. 2009; Tong et al. 2011; Zobrist et al. 2011; Bones et al. 2012; Davies et al. 2012; Krieger et al. 2012). For coarse mode particles, Zobrist et al. (2011) determined that binary sucrose/water aerosols in an amorphous, glassy state can have condensed phase water diffusion coefficients as low as at 18°C, which is 6 orders of magnitude less than in pure water and consequently limits evaporation and condensation. Subsequently, Tong et al. (2011) found that aqueous sucrose droplets continue to slowly lose water and exist in disequilibrium for below their glass transition RH, 24% RH at 25°C. In the case of ternary droplets, Bones et al. (2012) determined that the time for ternary sucrose/sodium chloride/water droplets to reach equilibrium correlates with bulk viscosity, and 7 diameter droplets can take to reach equilibrium below 15% RH.

Bones and his colleagues also reported the formation of an aqueous outer shell following an increase in relative humidity from 20-40%. Sucrose/sodium chloride/water

8 droplets exist as highly viscous particles at 20% RH, but when the relative humidity is abruptly increased to 40%, water is taken up onto the surface of the viscous particle and solute begins dissolving; this condensation is driven by a difference between the water activity at the surface of the particle and in the surrounding gas phase. As the viscous core dissolves, the concentration of the outer shell increases and more water is accommodated at the surface in order to maintain equilibrium between the atmosphere and the developing aqueous phase. Separately, equilibrium is not reached within the particle until there is no longer a concentration gradient between the aqueous outer shell and inner core, and so the water uptake and size response of the particle is determined by the rate of solute dissolution into the aqueous phase.

Accumulation mode particles have also been considered, using models to scale viscosity and condensed phase diffusion with particle size (Bones et al. 2012; Price et al. 2015). Price et al. (2015) have predicted that decreasing viscous SOA particle diameter from 1000 to 100 will decrease the timescale for condensed phase diffusion by a factor of 100; however, this timescale can still be significant at low temperature. These studies highlight the importance of both understanding how highly viscous phases interact with the transport of water in aerosols, and quantifying how this affects equilibration time for atmospherically relevant particles.

1.2 Single particle studies

Single particle techniques are used in aerosol science to study and decouple the processes that govern particle size, composition, phase, and morphology. Measurements of single particles can be made by depositing particles on a surface, as well as suspending particles spanning 2 - 2 in electrodynamic, optical, and acoustic traps. These traps offer contactless observation of a spherical particle, and allow for direct observation of the particle's physical state. Thus, single particle techniques offer different information than ensemble measurements from flow-tube and chamber studies; ensemble measurements provide information about aerosols populations and distributions, and single particle measurements allow the same particle to be probed at a series of environmental conditions, and observations to be made in situ.

In aerosol science, instruments for contactless suspension of an individual particle include the electrodynamic balance (EDB), optical tweezers, and the ultrasonic levitator, which are described by Davis et al. (1990), Mitchem and Reid (2008), and Ali Al Zaitone and Tropea (2011), respectively. The EDB suspends charged particles, ranging from 10-100 in diameter, in an electric field; the EDB has been used to study both the hygroscopic behaviour of single and mutli-component aerosols and the evaporation kinetics of pure organic liquids and binary solutions (Tang and Munkelwitz 1989, 1991, 1993; Peng et al. 2001; Choi and Chan 2002a, 2002b; Zobrist et al. 2011). Optical tweezers are a more recent technique, which employ a single-beam laser to hold a single particle ranging from 2-100 in diameter in place, and are emerging in aerosol hygroscopicity and evaporation kinetics research (Tong et al. 2011; Bones et al. 2012; Davies et al. 2012, 2013a, 2013b). The ultrasonic levitator is has been less explored in aerosol science, as it suspends particles on the order of 100-1000 . However, since all particles above 250 in diameter are in the continuum regime, the ultrasonic levitator can be used to study the evaporation of atmospheric particles. Tuckermann and his colleagues have coupled an ultrasonic levitator with a CCD camera, infrared thermography, and Raman spectroscopy to measure the evaporation rates of pure organic droplets and the concentration gradient of binary dimethyl sulfoxide (DMSO)/water droplets (Tuckermann et al. 2002, 2005, 2009).

To date, the majority of liquid-liquid phase separation (LLPS) studies have been performed by depositing a single particle on a hydrophobically coated substrate and monitoring the phase with Raman spectroscopy. Zhou et al. (2014) demonstrated that the surface tension and polarity of the substrate can determine whether the organic or aqueous phase will be the outer shell in LLPS, which reinforces the need for contactless observation of phase separated particles (Krieger et al. 2012).

1.3 Thesis objectives

The water content of atmospheric particles determines aerosol size and solute concentration, and consequently influences aerosols' phase, trace gas uptake, aqueous phase reactions, optical properties, and cloud-forming properties. The water content of particles is often discussed in terms of hygroscopic behaviour at equilibrium; however, recent research has demonstrated the need for understanding the effect of organics on water transport to and from aerosols.

My research aims to take a bottom-up approach to this problem and develop a framework for understanding how the evaporation of water is affected by simple solute systems. To this end, I have measured the evaporation rate of water from binary and ternary solution droplets, developed a simple model to describe aqueous droplet evaporation rate, and applied this model to understand the effects of different solutes on evaporation rate. The evaporation rate of aqueous droplets on the order of 1 in diameter was measured for seven binary systems and one ternary system: sodium chloride, sodium bromide, potassium chloride, magnesium chloride, ammonium chloride, ammonium sulfate, malonic acid, and 2:1 malonic acid/ammonium sulfate by dry mass. In parallel, I developed a simple model to predict the evaporation rate of binary solution droplets by combining Maxwell's equation with the solution's evolving equilibrium vapour pressure, as described in Chapter 2. This model was then used to discuss the measured evaporation rates of both the binary and ternary droplets.

1.4 References

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He, C., Liu, J., Carlton, A.G., Fan, S., Horowitz, L.W., Levy, H., Tao, S.: Evaluation of factors controlling global secondary organic aerosol production from cloud processes. Atmos. Chem. Phys. 13, 1913–1926 (2013). Hodas, N., Zuend, A., Mui, W., Flagan, R.C., Seinfeld, J.H.: Influence of particle-phase state on the hygroscopic behavior of mixed organic–inorganic aerosols. Atmos. Chem. Phys. 15, 5027–5045 (2015). Jacobson, D., High, C.: Wind Energy and Air Emission Reduction Benefits: A Primer. , Golden, Colorado (2008). Jimenez, J.L., Canagaratna, M.R., Donahue, N.M., Prevot, A.S.H., Zhang, Q., Kroll, J.H., DeCarlo, P.F., Allan, J.D., Coe, H., Ng, N.L., Aiken, A.C., Docherty, K.S., Ulbrich, I.M., Grieshop, A.P., Robinson, A.L., Duplissy, J., Smith, J.D., Wilson, K.R., Lanz, V.A., Hueglin, C., Sun, Y.L., Tian, J., Laaksonen, A., Raatikainen, T., Rautiainen, J., Vaattovaara, P., Ehn, M., Kulmala, M., Tomlinson, J.M., Collins, D.R., Cubison, M.J., Dunlea, J., Huffman, J.A., Onasch, T.B., Alfarra, M.R., Williams, P.I., Bower, K., Kondo, Y., Schneider, J., Drewnick, F., Borrmann, S., Weimer, S., Demerjian, K., Salcedo, D., Cottrell, L., Griffin, R., Takami, A., Miyoshi, T., Hatakeyama, S., Shimono, A., Sun, J.Y., Zhang, Y.M., Dzepina, K., Kimmel, J.R., Sueper, D., Jayne, J.T., Herndon, S.C., Trimborn, A.M., Williams, L.R., Wood, E.C., Middlebrook, A.M., Kolb, C.E., Baltensperger, U., Worsnop, D.R.: Evolution of Organic Aerosols in the Atmosphere. Science (80-. ). 326, 1525–1529 (2009). Johnson, S.A., Kumar, R.: Composition and Spectral Characteristics of Ambient Aerosol at Mauna Loa Observatory. J. Geophys. Res. 96, 5379–5386 (1991). Kirkby, J., Curtius, J., Almeida, J., Dunne, E., Duplissy, J., Ehrhart, S., Franchin, A., Gagné, S., Ickes, L., Kürten, A., Kupc, A., Metzger, A., Riccobono, F., Rondo, L., Schobesberger, S., Tsagkogeorgas, G., Wimmer, D., Amorim, A., Bianchi, F., Breitenlechner, M., David, A., Dommen, J., Downard, A., Ehn, M., Flagan, R.C., Haider, S., Hansel, A., Hauser, D., Jud, W., Junninen, H., Kreissl, F., Kvashin, A., Laaksonen, A., Lehtipalo, K., Lima, J., Lovejoy, E.R., Makhmutov, V., Mathot, S., Mikkilä, J., Minginette, P., Mogo, S., Nieminen, T., Onnela, A., Pereira, P., Petäjä, T., Schnitzhofer, R., Seinfeld, J.H., Sipilä, M., Stozhkov, Y., Stratmann, F., Tomé, A., Vanhanen, J., Viisanen, Y., Vrtala, A., Wagner, P.E., Walther, H., Weingartner, E., Wex, H., Winkler, P.M., Carslaw, K.S., Worsnop, D.R., Baltensperger, U., Kulmala, M.: Role of sulphuric acid, ammonia and galactic cosmic rays in atmospheric aerosol nucleation. Nature. 476, 429–433 (2011). Köhler, H.: Nucleus in Growth of Hygroscopic Droplets. Trans. Faraday Soc. 32, 1152–1161 (1936). Kolb, C.E., Cox, R.A., Abbatt, J.P.D., Ammann, M., Davis, E.J., Donaldson, D.J., Garrett, B.C., George, C., Griffiths, P.T., Hanson, D.R., Kulmala, M., McFiggans, G., Pöschl, U., Riipinen, I., Rossi, M.J., Rudich, Y., Wagner, P.E., Winkler, P.M., Worsnop, D.R., O’ Dowd, C.D.: An overview of current issues in the uptake of atmospheric trace gases by aerosols and clouds. Atmos. Chem. Phys. 10, 10561–10605 (2010). Krieger, U.K., Marcolli, C., Reid, J.P.: Exploring the complexity of aerosol particle properties and processes using single particle techniques. Chem. Soc. Rev. 41, 6631 (2012).

Liu, Q., Jing, B., Peng, C., Tong, S., Wang, W., Ge, M.: Hygroscopicity of internally mixed multi- component aerosol particles of atmospheric relevance. Atmos. Environ. 125, 69–77 (2016). Marcolli, C., Krieger, U.K.: Phase Changes during Hygroscopic Cycles of Mixed Organic/Inorganic Model Systems of Tropospheric Aerosols. J. Phys. Chem. A. 110, 1881– 1893 (2006). Mikhailov, E., Vlasenko, S., Martin, S.T., Koop, T., Pöschl, U.: Amorphous and crystalline aerosol particles interacting with water vapor: conceptual framework and experimental evidence for restructuring, phase transitions and kinetic limitations. Atmos. Chem. Phys. 9, 9491–9522 (2009). Mikhailov, E., Vlasenko, S., Niessner, R., Pöschl, U.: Interaction of aerosol particles composed of protein and salts with water vapor: hygroscopic growth and microstructural rearrangement. Atmos. Chem. Phys. 4, 323–350 (2004). Mitchem, L., Reid, J.P.: Optical manipulation and characterisation of aerosol particles using a single-beam gradient force optical trap. Chem. Soc. Rev. 37, 756–769 (2008). Murphy, D.M., Cziczo, D.J., Froyd, K.D., Hudson, P.K., Matthew, B.M., Middlebrook, A.M., Peltier, R.E., Sullivan, A., Thomson, D.S., Weber, R.J.: Single-particle mass spectrometry of tropospheric aerosol particles. J. Geophys. Res. 111, D23S32 (2006). Murphy, D.M., Thomson, D.S., Mahoney, M.J.: In Situ Measurements of Organics, Meteoritic Material, Mercury, and Other Elements in Aerosols at 5 to 19 Kilometers. Science (80-. ). 282, 1664–1669 (1998). Peng, C., Chan, M.N., Chan, C.K.: The Hygroscopic Properties of Dicarboxylic and Multifunctional Acids: Measurements and UNIFAC Predictions. Environ. Sci. Technol. 35, 4495–4501 (2001). Petters, M.D., Kreidenweis, S.M.: A single parameter representation of hygroscopic growth and cloud condensation nucleus activity. Atmos. Chem. Phys. 7, 1961–1971 (2007). Prenni, A.J., DeMott, P.J., Kreidenweis, S.M.: Water uptake of internally mixed particles containing ammonium sulfate and dicarboxylic acids. Atmos. Environ. 37, 4243–4251 (2003). Prenni, A.J., DeMott, P.J., Kreidenweis, S.M., Sherman, D.E., Russell, L.M., Ming, Y.: The Effects of Low Molecular Weight Dicarboxylic Acids on Cloud Formation. J. Phys. Chem. A. 105, 11240–11248 (2001). Price, H.C., Mattsson, J., Zhang, Y., Bertram, A.K., Davies, J.F., Grayson, J.W., Martin, S.T., O’Sullivan, D., Reid, J.P., Rickards, A.M.J., Murray, B.J.: Water diffusion in atmospherically relevant α-pinene secondary organic material. Chem. Sci. 6, 4876–4883 (2015). Reis, S., Pinder, R.W., Zhang, M., Lijie, G., Sutton, M.A.: Reactive nitrogen in atmospheric emission inventories. Atmos. Chem. Phys. 9, 7657–7677 (2009). Robinson, N.: Synthetic aerosol distribution in number area and volume space, https://en.wikipedia.org/wiki/File:Synthetic_aerosol_distribution_in_number_area_and_volu me_space.png.

Rosenfeld, D., Lohmann, U., Raga, G.B., O’Dowd, C.D., Kulmala, M., Fuzzi, S., Reissell, A., Andreae, M.O.: Flood or Drought: How Do Aerosols Affect Precipitation? Science. 321, 1309– 1313 (2008). Sander, R.: Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry, http://www.mpch- mainz.mpg.de/~sander/res/henry.html. Saxena, P., Hildemann, L.M.: Water-Soluble Organics in Atmospheric Particles: A Critical Review of the Literature and Application of Thermodynamics to Identify Candidate Compounds. J. Atmos. Chem. 24, 57–109 (1996). Sjogren, S., Gysel, M., Weingartner, E., Baltensperger, U., Cubison, M.J., Coe, H., Zardini, A.A., Marcolli, C., Krieger, U.K., Peter, T.: Hygroscopic growth and water uptake kinetics of two- phase aerosol particles consisting of ammonium sulfate, adipic and humic acid mixtures. J. Aerosol Sci. 38, 157–171 (2007). Song, M., Marcolli, C., Krieger, U.K., Zuend, A., Peter, T.: Liquid-liquid phase separation and morphology of internally mixed dicarboxylic acids/ammonium sulfate/water particles. Atmos. Chem. Phys. 12, 2691–2712 (2012)(a). Song, M., Marcolli, C., Krieger, U.K., Zuend, A., Peter, T.: Liquid-liquid phase separation in aerosol particles: Dependence on O:C, organic functionalities, and compositional complexity. Geophys. Res. Lett. 39, L19801 (2012)(b). Sorooshian, A., Lu, M.L., Brechtel, F.J., Jonsson, H., Feingold, G., Flagan, R.C., Seinfeld, J.H.: On the Source of Organic Acid Aerosol Layers Above Clouds. Environ. Sci. Technol. 41, 4647– 4654 (2007). Sutton, M.A., Reis, S., Riddick, S.N., Dragosits, U., Nemitz, E., Theobald, M.R., Tang, Y.S., Braban, C.F., Vieno, M., Dore, A.J., Mitchell, R.F., Wanless, S., Daunt, F., Fowler, D., Blackall, T.D., Milford, C., Flechard, C.R., Loubet, B., Massad, R., Cellier, P., Personne, E., Coheur, P.F., Clarisse, L., Van Damme, M., Ngadi, Y., Clerbaux, C., Skjøth, C.A., Geels, C., Hertel, O., Wichink Kruit, R.J., Pinder, R.W., Bash, J.O., Walker, J.T., Simpson, D., Horváth, L., Misselbrook, T.H., Bleeker, A., Dentener, F., de Vries, W.: Towards a climate-dependent paradigm of ammonia emission and deposition. Philos. Trans. R. Soc. B. 368, 20130166 (2013). Svenningsson, B., Rissler, J., Swietlicki, E., Mircea, M., Bilde, M., Facchini, M.C., Decesari, S., Fuzzi, S., Zhou, J., Mønster, J., Rosenørn, T.: Hygroscopic growth and critical supersaturations for mixed aerosol particles of inorganic and organic compounds of atmospheric relevance. Atmos. Chem. Phys. Discuss. 5, 2833–2877 (2005). Tang, I.N.: Thermodynamic and optical properties of mixed-salt aerosols of atmospheric importance. J. Geophys. Res. 102, 1883–1893 (1997). Tang, I.N., Munkelwitz, H.R.: Evaporation Kinetics of Ammonium Chloride Solution Droplets in Water Vapor. J. Colloid Interface Sci. 128, 289–295 (1989). Tang, I.N., Munkelwitz, H.R.: Simultaneous Determination of Refractive Index and Density of an Evaporating Aqueous Solution Droplet. Aerosol Sci. Technol. 15, 201–207 (1991).

Tang, I.N., Munkelwitz, H.R.: Composition and Temperature Dependence of the Deliquescence Properties of Hygroscopic Aerosols. Atmos. Environ. 27, 467–473 (1993). Tang, I.N., Munkelwitz, H.R.: Water activities, densities, and refractive indices of aqueous sulfates and sodium nitrate droplets of atmospheric importance. J. Geophys. Res. 99, 18801 (1994). Tong, H.J., Reid, J.P., Bones, D.L., Luo, B.P., Krieger, U.K.: Measurements of the timescales for the mass transfer of water in glassy aerosol at low relative humidity and ambient temperature. Atmos. Chem. Phys. 11, 4739–4754 (2011). Tuckermann, R., Bauerecker, S., Cammenga, H.K.: IR-Thermography of Evaporating Acoustically Levitated Drops. Int. J. Thermophys. 26, 1583–1594 (2005). Tuckermann, R., Bauerecker, S., Neidhart, B.: Evaporation rates of alkanes and alkanols from acoustically levitated drops. Anal. Bioanal. Chem. 372, 122–127 (2002). Tuckermann, R., Puskar, L., Zavabeti, M., Sekine, R., McNaughton, D.: Chemical analysis of acoustically levitated drops by Raman spectroscopy. Anal. Bioanal. Chem. 394, 1433–1441 (2009). Virtanen, A., Joutsensaari, J., Koop, T., Kannosto, J., Yli-Pirilä, P., Leskinen, J., Mäkelä, J.M., Holopainen, J.K., Pöschl, U., Kulmala, M., Worsnop, D.R., Laaksonen, A.: An amorphous solid state of biogenic secondary organic aerosol particles. Nature. 467, 824–827 (2010). Wise, M.E., Surratt, J.D., Curtis, D.B., Shilling, J.E., Tolbert, M.A.: Hygroscopic growth of ammonium sulfate/dicarboxylic acids. J. Geophys. Res. 108, 1–8 (2003). You, Y., Renbaum-Wolff, L., Bertram, A.K.: Liquid–liquid phase separation in particles containing organics mixed with ammonium sulfate, ammonium bisulfate, ammonium nitrate or sodium chloride. Atmos. Chem. Phys. 13, 11723–11734 (2013). You, Y., Renbaum-Wolff, L., Carreras-Sospedra, M., Hanna, S.J., Hiranuma, N., Kamal, S., Smith, M.L., Zhang, X., Weber, R.J., Shilling, J.E., Dabdub, D., Martin, S.T., Bertram, A.K.: Images reveal that atmospheric particles can undergo liquid-liquid phase separations. Proc. Natl. Acad. Sci. 109, 13188–13193 (2012). You, Y., Smith, M.L., Song, M., Martin, S.T., Bertram, A.K.: Liquid–liquid phase separation in atmospherically relevant particles consisting of organic species and inorganic salts. Int. Rev. Phys. Chem. 33, 43–77 (2014). Zhou, Q., Pang, S.F., Wang, Y., Ma, J.B., Zhang, Y.H.: Confocal Raman Studies of the Evolution of the Physical State of Mixed Phthalic Acid/Ammonium Sulfate Aerosol Droplets and the Effect of Substrates. J. Phys. Chem. B. 118, 6198–6205 (2014). Zobrist, B., Soonsin, V., Luo, B.P., Krieger, U.K., Marcolli, C., Peter, T., Koop, T.: Ultra-slow water diffusion in aqueous sucrose glasses. Phys. Chem. Chem. Phys. 13, 3514–3526 (2011).

2 Thermodynamic & Kinetic Considerations

2.1 Intersection of thermodynamics & kinetics in aerosol science

Aerosols are often discussed in terms of thermodynamic equilibrium, which is underpinned by the assumption that all species instantaneously partition and reach equilibrium between the gas, liquid, and solid phase. In the case of water, the thermodynamic equilibrium framework assumes that the water activity of aqueous aerosols is always in equilibrium with the relative humidity of the surrounding gas phase. Based on this framework, the hygroscopic properties of aerosols are generally studied as a function of relative humidity, assuming that equilibrium is reached between changes in relative humidity (eg. Tang and Munkelwitz 1993; Cruz and Pandis 2000; Choi and Chan 2002; Prenni et al. 2003; Sjogren et al. 2007; Hodas et al. 2015).

The limitations of this framework are exemplified by the common treatment of efflorescence. Efflorescence is generally acknowledged to be driven by crystal nucleation and growth, which a kinetic process. This implies that if an aerosol has not crystallized below its , then it should not be assumed to be in equilibrium, but rather in a metastable state. However, aerosols are often assigned an efflorescence relative humidity ( ), which corresponds to the ambient relative humidity at which aerosols are observed to crystallize. Because efflorescence is driven by crystal nucleation whereas deliquescence is the result of reaching thermodynamic equilibrium, the two processes exhibit an observed hysteresis as a function of relative humidity. However, this does not confirm that the water activity of aerosols is actually in equilibrium with the ambient relative humidity between the and during efflorescence-mode experiments.

Recent studies of mixed organic/inorganic aerosols have identified the need to acknowledge and address the limitations of assuming near-instantaneous equilibrium when studying aerosols (Sjogren et al. 2007; Mikhailov et al. 2009; Tong et al. 2011; Vaden et al. 2011; Zobrist et al. 2011; Bones et al. 2012; Davies et al. 2012). Sjogren et al. (2007) determined that ternary adipic acid/ammonium sulfate/water aerosols, 4-20 in diameter, can require residence times beyond 40 to reach equilibrium when relative humidity is held constant at 85% RH. When the residence time for these aerosols was reduced to 4 , typical

18 of many hygroscopic growth studies, up to a 7% reduction in the measured hygroscopic growth factor was observed when compared to the measurements made at equilibrium. Kinetic limitations to equilibrium are also being studied for metastable, amorphous phase aerosols, as low molecular diffusivity in the condensed phase may increase the time it takes for water to reach equilibrium with the gas phase (Tong et al. 2011; Zobrist et al. 2011; Bones et al. 2012; Davies et al. 2012). This highlights the need for an increased understanding of the interplay between thermodynamics and kinetics, especially in the context of mixed organic/inorganic aerosols.

2.2 Vapour pressure of water over aqueous solutions

2.2.1 Raoult's law & ideality

The vapour pressure of solutions was first described by Raoult using empirical observations. The resulting empirical relationship (Eq. 2) can be coupled with the definition of a solution's chemical potential at equilibrium (Eq. 2b) in order to relate the chemical potential of a solution to the mole fractions of its components (Eq. 2c).

Eq. 2a

Eq. 2b

Eq. 2c

In the above equations, is the partial pressure of component i, is the equilibrium vapour pressure of pure component i, is the chemical potential of the solution, is the chemical potential of pure component i at equilibrium between the liquid and gas phase, is the ideal gas constant, is the temperature of the gas phase, and is the mole fraction of component i in solution.

Raoult's law describes an ideal solution wherein the partial vapour pressure of each component is equal to the product of its equilibrium vapour pressure and mole fraction in

19 solution. Since Raoult's law can be applied to each component in an ideal solution, the total vapour pressure of the solution ( ) is the sum of each component's contribution:

Eq. 2d

An ideal solution assumes that the interactions between every molecule in the mixture are the same, regardless of whether or not they are the same species. This is reflected in Raoult's law as each component only affects the vapour pressure of the others through dilution; whereas in a real solution, the vapour pressure will also be affected by the intermolecular interactions between the different components.

The difference in intermolecular interactions of a real solution versus an ideal solution can be accounted for using activity coefficients ( ), which reflect whether a component in solution will experience more or less intermolecular attraction relative to an ideal solution. When 1, there is a relative increase in intermolecular attraction, which corresponds to the component being less volatile than predicted by an ideal solution. Conversely, 1 reflects a decrease in intermolecular attraction, resulting in the component being more volatile. Since the activity coefficient accounts for the phenomenon whereby the presence of a different species contributes different molecular interactions to a solution, the degree of each species' deviation from ideality is dependent on the solution concentration:

2.2.2 Aqueous solutions with non-volatile solutes

For aqueous solutions with non-volatile solutes, the total vapour pressure of the solution is exerted solely by water and corresponds to the product of water's equilibrium vapour pressure and mole fraction, which can also be given in terms of the total mole fraction of solutes ( ).

Eq. 2e

Equation Eq. 2e illustrates that above an ideal, binary aqueous solutions of non- volatile solutes, the vapour pressure of water will be suppressed by a factor equal to its mole

20 fraction. If equilibrium conditions change and water evaporates from the solution, the solution will become increasingly concentrated as the mole fraction of water decreases; consequently, the vapour pressure will also decrease.

2.2.2.1 van't Hoff factor ( ) & activity coefficient ( )

Inorganic salts are relatively non-volatile solutes that are ubiquitous in the atmosphere and further complicate Raoult's law due to their dissociation when dissolved in water (Shaw 1978). Dissociation can be incorporated into Raoult's law as the van't Hoff factor ( ), which reflects the concentration of solute particles after a substance is dissolved relative to the concentration calculated using dry mass. For example, substances that do not dissociate upon dissolution have , such as sucrose, whereas binary ionic compounds that dissociate completely in water, such as sodium chloride, have . When , the increased concentration of solute consequently decreases the mole fraction of water:

Eq. 2f

As discussed in Chapter 2.2.1, the activity coefficient ( ) is a thermodynamically derived factor that accounts for deviations from ideal behaviour in a liquid mixture. In the case of aqueous salt solutions where water is the only volatile species, equation Eq. 2f can be extended to include water's activity coefficient ( ):

Eq. 2g

The water activity coefficient for a salt solution is dependent on the salt species and concentration; thus, to be used in Eq. 2g, the water activity coefficient must be available for the corresponding water mole fraction.

2.2.3 Saturated salt solutions

Once a binary salt solution has reached saturation, its solute concentration is fixed as any additional solute will precipitate. Consequently, a saturated solution's water activity is fixed at a given temperature, and so its water vapour pressure is constant and characteristic of the salt. This vapour pressure is often discussed in terms of relative humidity ( ):

Eq. 3

Where, as before, is the partial vapour pressure of water and is the equilibrium vapour pressure of pure water at the given temperature. The relative humidity above a saturated salt solution is referred to as its deliquescence relative humidity ( ).

When discussing aerosols, saturated salt solutions are relevant as they occur at the onset of deliquescence. Deliquescence is the process by which a solid substance takes up water from the surrounding gas phase in order to be completely dissolved, forming a saturated solution. In order for deliquescence to occur, the relative humidity of the surrounding gas must be equal to or greater than the particle's ; if the relative humidity is greater than the , the solution will continue taking up water until it is in equilibrium with the surrounding gas. Therefore, is a parallel expression to the equilibrium relative humidity above a saturated solution.

Eq. 4

2.3 Diffusion controlled evaporation from a droplet

For aerosols and droplets in the continuum regime, the evaporation of a stationary, single component particle is controlled by diffusion of the evaporating species away from the condensed phase into the gas phase. A particle's dynamic regime is determined by its

Knudsen number ( ), which is proportional to the ratio of the gas phase mean free path ( ) and diameter of the particle ( ):

Eq. 1

When << 1, the particle is significantly larger than the mean free path of the surrounding gas, and so the gas acts as a continuous fluid around the particle. Therefore, the limiting factor to evaporation is the escape of molecules from the relatively stationary condensed phase into the flowing gas phase, which is described by Fick's first law of diffusion.

Fick's first law describes diffusive flux moving across a gradient from high to low chemical potential. The diffusive flux of a gas ( ) is expressed as the product of its diffusivity

( ) and concentration gradient in terms of position ( φ/ ):

Eq. 5

This relationship can be adapted to describe evaporation from the surface of a sphere through an equivalent expression describing the diffusive flux in terms of the change in moles of evaporating species in the condensed phase per unit time ( / ) with respect to surface area:

Eq. 6

Combining equations Eq. 5 and Eq. 6 returns an expression for the concentration gradient ( φ/ ), where it is important to define the position, , as originating from the same point as the sphere's radius, (see Figure 2.2).

Eq. 7

Figure 2.2 Position ( ) and radius ( ) relative to the sphere.

When considering the gas phase concentration of the evaporating species near the surface of the sphere, . This yields an expression for the difference in gas concentration near the surface versus that in the ambient atmosphere, which is considered to be consistent from an infinite distance up to the region at the surface (Eq. 8c); this is known as Maxwell’s equation (Fuchs 1959).

Eq. 8a

Eq. 8b

Eq. 8c

In order to apply Maxwell’s equation to experimental observations, equation 8c can be reconfigured to describe diffusion controlled evaporation from a sphere in terms of the condensed phase volume (Eq. 9a) or surface area (Eq. 9b). Similarly, the gas phase concentration of evaporating species at the surface of the sphere can be described in terms of its pressure using the ideal gas law.

Eq. 9a

Eq. 9b

In the equations above, is the molar mass of the evaporating species, is the density of the evaporating species, and are the partial pressures of the evaporating species at the surface of the sphere and in the ambient atmosphere, and and are the temperatures of the gas phase at the surface of the sphere and in the ambient atmosphere, respectively.

It should be noted that the rate of change of a sphere's volume with respect to time is dependent on both the gas phase concentration of the evaporating species at the surface of the sphere and the radius of the sphere. Therefore, describing diffusion controlled evaporation in terms of surface area is optimal as it removes the dependence on radius so that the rate of change is solely a function of the evaporating species' concentration.

This raises another consideration as, even in the form of equation Eq. 9b, the application of Maxwell’s equation is limited because the gas phase concentration at the surface cannot be measured. Therefore, the gas phase concentration at the surface is assumed to be equivalent to the species’ equilibrium vapour pressure; as the gas at the surface diffuses away into the ambient atmosphere, more molecules will leave the liquid phase for the gas phase in order to maintain the equilibrium vapour pressure. Evaporation will continue until the pressure of the evaporating species at the surface is no longer depleted by diffusion, due to reaching equilibrium with the ambient partial pressure of the evaporating species: .

2.3.1 Simple models combining Maxwell's equation with equilibrium thermodynamics

For pure liquids, the equilibrium vapour pressure is constant at constant temperature, allowing in equation Eq. 9b to be replaced by a constant ( for water):

Eq. 10

Based on Eq. 10, the rate of change of a sphere's surface area with respect to time is constant. Therefore, the evaporation rate of a pure liquid droplet, in terms of surface area versus time, is expected to be a linear so long as the ambient pressure remains constant.

For aqueous solutions of non-volatile solutes, the use of equilibrium vapour pressure is complicated by the fact that it depends on concentration, which is no longer constant with time. Therefore, an expression for the aqueous solution's partial vapour pressure as a function of mole fraction of solvent (water) must be used for in equation Eq. 9b. Either equation Eq. 2f or Eq. 2g can be used, but equation Eq. 11b requires that the solvent activity coefficient is known as a function of concentration.

Eq. 11a

Eq. 11b

Equations Eq. 11a and Eq. 11b illustrate that at a given time, the instantaneous slope of surface area versus time is determined by the mole fraction of solute.

Once a salt solution reaches saturation, the equilibrium vapour pressure of water is equal to the salt's deliquescence relative humidity. In terms of evaporation, the instantaneous evaporation rate above a saturated solution can be described by allowing equation Eq. 4 to be used for in equation Eq. 9b:

Eq. 11c

2.4 References

Bones, D.L., Reid, J.P., Lienhard, D.M., Krieger, U.K.: Comparing the mechanism of water condensation and evaporation in glassy aerosol. Proc. Natl. Acad. Sci. U. S. A. 109, 11613– 11618 (2012). Choi, M.Y., Chan, C.K.: The Effects of Organic Species on the Hygroscopic Behaviors of Inorganic Aerosols. Environ. Sci. Technol. 36, 2422–2428 (2002). Cruz, C.N., Pandis, S.N.: Deliquescence and Hygroscopic Growth of Mixed Inorganic-Organic Atmospheric Aerosol. Environ. Sci. Technol. 34, 4313–4319 (2000). Davies, J.F., Haddrell, A.E., Miles, R.E.H., Bull, C.R., Reid, J.P.: Bulk, Surface, and Gas-Phase Limited Water Transport in Aerosol. J. Phys. Chem. A. 116, 10987–10998 (2012). Fuchs, N.A.: Evaporation and Droplet Growth in Gaseous Media. Pergamon Press Ltd., Oxford (1959). Hodas, N., Zuend, A., Mui, W., Flagan, R.C., Seinfeld, J.H.: Influence of particle-phase state on the hygroscopic behavior of mixed organic–inorganic aerosols. Atmos. Chem. Phys. 15, 5027–5045 (2015). Mikhailov, E., Vlasenko, S., Martin, S.T., Koop, T., Pöschl, U.: Amorphous and crystalline aerosol particles interacting with water vapor: conceptual framework and experimental evidence for restructuring, phase transitions and kinetic limitations. Atmos. Chem. Phys. 9, 9491–9522 (2009). Prenni, A.J., DeMott, P.J., Kreidenweis, S.M.: Water uptake of internally mixed particles containing ammonium sulfate and dicarboxylic acids. Atmos. Environ. 37, 4243–4251 (2003). Shaw, D.T. ed: Fundamentals of Aerosol Science. John Wiley & Sons (1978). Sjogren, S., Gysel, M., Weingartner, E., Baltensperger, U., Cubison, M.J., Coe, H., Zardini, A.A., Marcolli, C., Krieger, U.K., Peter, T.: Hygroscopic growth and water uptake kinetics of two- phase aerosol particles consisting of ammonium sulfate, adipic and humic acid mixtures. J. Aerosol Sci. 38, 157–171 (2007). Tang, I.N., Munkelwitz, H.R.: Composition and Temperature Dependence of the Deliquescence Properties of Hygroscopic Aerosols. Atmos. Environ. 27, 467–473 (1993). Tong, H.J., Reid, J.P., Bones, D.L., Luo, B.P., Krieger, U.K.: Measurements of the timescales for the mass transfer of water in glassy aerosol at low relative humidity and ambient temperature. Atmos. Chem. Phys. 11, 4739–4754 (2011). Vaden, T.D., Imre, D., Beránek, J., Shrivastava, M., Zelenyuk, A.: Evaporation kinetics and phase of laboratory and ambient secondary organic aerosol. Proc. Natl. Acad. Sci. U. S. A. 108, 2190–2195 (2011). Zobrist, B., Soonsin, V., Luo, B.P., Krieger, U.K., Marcolli, C., Peter, T., Koop, T.: Ultra-slow water diffusion in aqueous sucrose glasses. Phys. Chem. Chem. Phys. 13, 3514–3526 (2011).

3 Instrumentation & Methods

3.1 Instrumentation

Figure 3.1 Schematic for the ultrasonic levitator and CCD camera set-up, viewed in the x,z plane.

3.1.1 Ultrasonic levitator

Single droplets were suspended for contactless observation using an ultrasonic levitator purchased from tec5 Technology for Spectroscopy. The ultrasonic levitator operates at 100 , which corresponds to a longitudinal wave with = 3.46 at 25 °C in ambient air. A standing longitudinal wave is generated by a piezoelectric transducer and reflected back along the z-axis by a concave reflector (see Figure 3.1). The position of the reflector can be adjusted via the micrometer in order to control the interference of the incident and reflected waves. Constructive interference occurs when the distance between the piezoelectric transducer and the reflector ( ) is an integer multiple of 0.5∙ :

Eq. 12

The integer multiple, , corresponds to the number of pressure nodes present in the standing wave. At 100 and L 8.7 , which corresponds to a micrometer setting of 2.5, five pressure nodes exist ( = 5); however, only the central nodes can be used for levitation as the two outer nodes are subject to destabilizing effects from the transducer and

28 reflector (tec5 Technology for Spectroscopy 1995). The central node, = 3, was used for all tests.

The size limits for levitation are dependent on the sample’s density and surface tension, and are independent of the ultrasonic frequency. However, there exists an optimal droplet diameter (dopt), which minimizes the ultrasonic power required for levitation, related to ultrasonic frequency: dopt = λ/3 (tec5 Technology for Spectroscopy 1995).

The power supply unit can generate 0.65-5 Watt radio frequency (RF) power, given as HF-power in arbitrary units on the digital display. When the LED is green, the transducer is oscillating at its resonance frequency and so interference can be controlled by the reflector distance. For all tests, the HF-power setting was maintained at 3.3; however, it could be temporarily increased in order to re-stabilize a droplet that had begun to oscillate.

The ultrasonic levitator is enclosed in a single-walled, glass processing chamber: 70 mm inner diameter and 2 wall thickness. The chamber has three open windows and a bore hole in the sample plane; two windows lie along the x-axis, and the third window and bore hole are situated along the y-axis. Nitrogen gas was flowed into the processing chamber at 500 in order to maintain near 0% relative humidity around the droplet. The window between the droplet and CCD camera was left open, and the other two windows were closed using Parafilm in order to reduce variations in turbulence and diffusion of water vapour into the chamber.

3.1.2 Imaging - CCD camera & telecentric lens

Images of the levitated droplets were collected using a charge-coupled device (CCD) camera (PixeLINK, PL-B952, Color, 1/3” CCD sensor). To remove the dependence of image magnification on object distance, an object-space telecentric lens was used (Edmund Optics, 63-732, 2X, 110 WD). An object-space telecentric lens has its entrance pupil at infinity and aperture positioned at the rear focal point, resulting in a parallel projection that is independent of distance (see Figure 3.2). The telecentric lens used has 2X magnification, which, coupled with the 1/3” CCD sensor, results in a 2.4 field of view.

While the size of the collected image is not affected by distance, objects outside of the lens’s working distance (110 ± 1 ) are out of focus. Therefore, the position of the ultrasonic levitator was fixed and the camera was moved along the x-axis to optimize focus. In order to optimize the image’s contrast, a light was directed onto a white background placed behind the droplet. Images were collected as Bitmap files using the PixeLINK Capture OEM software. The exposure time and gain were held constant for all images: 500 and 11.41 , respectively. When necessary, lighting and contrast were adjusted by changing the position of the lamp.

Figure 3.2 Illustration depicting how the image from a telecentric lens is independent of an object's distance.

The area of a 1/3” CCD sensor corresponds to 1024 x 768 pixels; combined with the 2.4 field of view, each pixel is equivalent to 2.34 in distance. The horizontal and vertical diameters of the droplet ( and , respectively) were measured from the collected Bitmap files using Image J, public domain image processing software. Due to the sound-radiation pressure along the z-axis, the levitated droplet was flattened with respect to the z-axis and deformed into an oblate spheroid. Therefore, the eccentricity (e) of the droplet was considered when calculating its surface area ( ):

Eq. 13

Eq. 14

Where and are the horizontal and vertical radii of the levitated droplet, respectively. The difference between the horizontal and vertical diameters was generally less than 10%: thus, 0 0.45.

The systematic uncertainty in the diameter measurements was determined by imaging levitated nylon balls, 1.6 diameter, purchased from Polysciences, Inc. The average diameter of a nylon ball, measured using digital vernier calipers, was compared to the experimental diameter extracted from 15 images; the experimental diameter was <1% larger than the diameter measured using vernier calipers. The nylon balls are solid white and scatter more light than the transparent droplets, resulting in less well-defined edges in the images; therefore, the error for the nylon balls is expected to be larger than the error for the droplets. The precision of the experimental diameter measurements of nylon balls was 0.06% for one standard deviation. Based on these results, systematic uncertainty was not included in the error analysis.

3.2 Methods

3.2.1 Experimental procedure

Droplets were suspended in the ultrasonic levitator by pulling them from the tip of a microlitre syringe with a stainless steel, beveled needle (Hamilton Model 701, 26s gauge, point style 2). Droplets ranging from 1.0-1.8 were ejected onto the tip of the syringe and placed in the standing acoustic wave at the midpoint between the piezoelectric transducer and the reflector. To remove the droplet from the syringe tip, the micrometer controlling the reflector position was decreased from 2.5 while the syringe was slowly moved up and down until the droplet could be detached. Once the droplet was suspended in the centre node, the reflector was repositioned to 2.45-2.50 in order to optimize the droplet’s stability and symmetry at HF-power 3.3. The difference between the horizontal and vertical diameters was generally maintained to be less than 10%.

The first image of the suspended droplet was captured 60 after the droplet was ejected onto the syringe tip. This was meant to standardize the amount of time each droplet was exposed to evaporation before the first image, set as t = 0 . From t = 0 , images were

31 collected at regular time intervals. The aqueous salt droplets were imaged until crystallization was visible; some particles remained stable during crystallization, allowing for clear images of the solid phase to be collected, but many particles became unstable. Distilled water droplets were imaged for 400 , which generally corresponded to a total change in surface area that was comparable to the solution droplets.

The relative humidity and temperature of the atmosphere around the droplet are required for Maxwell's equation (see Chapter 2.3). By suspending the droplet in a stream of dry nitrogen flowing into the chamber at 0.5 standard litres per minute (SLPM) at 25°C, the relative humidity of the gas surrounding the droplet is assumed to be 0%; therefore, . The temperature of the surrounding gas is both a crucial factor and tricky measurement: crucial in that it is a factor not only as temperature, but it also determines the saturation vapour pressure of water. The temperature inside the processing chamber was measured before and after each test using a thermohygrometer, and was generally maintained between 23-26°C; however, it could not be directly monitored during the evaporation trials because the ultrasonic field affects its probe, causing inaccurate measurements.

Fifteen replicate trials were run for each solution that was studied. Distilled water trials were also run in conjunction with each aqueous solution's trials in order to account for any temporal variations in the system, which could be the result of changes to the ultrasonic power or acoustic streaming. Generally, a distilled water droplet was tested between each solution trial, and each day's initial and final trial was distilled water.

3.2.2 Chemicals

Table 3.1 lists the compounds that were tested as solutes and provides some aqueous properties. The van't Hoff factor ( ) corresponds to the number of units (ions) that a compound is expected to produce upon dissolution. All aqueous solutions were prepared using salt that had been dried at 120°C for >12 hours, and the distilled water provided on tap in the lab, Lash Miller 315.

Binary solutions, containing one solute species and water, were tested for each compound. The initial concentration of each test solution was 2.0 moles of solute per

32 kilogram of water (m), except for ammonium sulfate which had an initial concentration of 1.9 m. The initial concentration was chosen as a compromise between a sufficiently concentrated solution, which suppresses the water vapour pressure so that it can be differentiated from distilled water, and a sufficiently dilute solution that allows tests to run for longer times before salt crystallization.

A ternary solution of malonic acid/ammonium sulfate/water was also tested. The solute composition was chosen based on the results from Braban and Abbatt (2004): 2:1 malonic acid to ammonium sulfate by dry mass, which is equivalent to 2.5:1 malonic acid to ammonium sulfate by moles. The initial concentration of the primary component, malonic acid, was the same concentration used for the binary solutions (2.0 m), and the concentration of ammonium sulfate was set relative to that (0.8 m).

Table 3.1 Properties of solutes. Solubility in Deliquescence Molar Mass van't Hoff Compound Water at 25°C Relative Humidity (g/mol) factor ( ) (mol/kg water)1 at 25°C (%)1 Sodium Chloride 58.442 2 6.15 75.8 NaCl Sodium Bromide 102.89 2 9.19 58.6 NaBr Potassium Chloride 74.551 2 4.77 84.32 KCl Magnesium Chloride 95.211 3 5.88 32.82 MgCl2 Ammonium Chloride 53.491 2 7.39 78.3 NH4Cl Ammonium Sulfate 132.14 3 5.78 81.2 (NH4)2SO4 Malonic Acid 104.06 1.033 7.074 745 CH2(COOH)2 1 CRC Handbook of Chemistry and Physics (Haynes 2015) 2 Greenspan (1977) 3 Predicted by E-AIM Model IV (Friese and Ebel 2010): http://www.aim.env.uea.ac.uk/aim/aim.php 4 At 20°C 5 Brooks et al. (2002)

3.2.3 Extended AIM (E-AIM) Aerosol Thermodynamics Model

The Extended AIM (E-AIM) Aerosol Thermodynamics Model, developed by Simon L. Clegg, Peter Brimblecombe, and Anthony S. Wexler, is an online, community model for predicting partitioning in aqueous solution aerosol particles using parameterized equations based on current literature. Model IV was used to obtain volume properties, solution densities, mole fractions, vapour pressures, and activity coefficients for aqueous solutions containing sodium chloride, ammonium chloride, and ammonium sulfate. These outputs were coupled with Eq. 11b in order to predict the rate of change of an aqueous salt droplet's surface area with respect to time (see Appendix B).

E-AIM can be accessed at http://www.aim.env.uea.ac.uk/aim/aim.php.

3.3 References

Braban, C.F., Abbatt, J.P.D.: A study of the phase transition behavior of internally mixed ammonium sulfate – malonic acid aerosols. Atmos. Chem. Phys. 4, 1451–1459 (2004). Brooks, S.D., Wise, M.E., Cushing, M., Tolbert, M.A.: Deliquescence behavior of organic/ammonium sulfate aerosol. Geophys. Res. Lett. 29, (2002). + + Friese, E., Ebel, A.: Temperature Dependent Thermodynamic Model of the System H -NH4 - + 2- - - Na -SO4 -NO3 -Cl -H2O. J. Phys. Chem. A. 114, 11595–11631 (2010). Greenspan, L.: Humidity Fixed Points of Binary Saturated Aqueous Solutions. J. Res. Natl. Bur. Stand. Sect. A Phys. Chem. 81A, 89–96 (1977). Haynes, W.M. ed: CRC Handbook of Chemistry and Physics. Taylor and Francis Group, LLC (2015). tec5 Technology for Spectroscopy: Ultrasonic Levitator Manual, (1995).

4 Results

4.1 Water droplets

In Chapter 2.3.1, diffusion controlled evaporation from a pure liquid droplet was described by a simple model combining Maxwell’s equation and the equilibrium vapour pressure of the evaporating species (Eq. 10). Based on this equation, surface area is expected to be a linear function of time for a pure liquid droplet. This has been reproducibly observed during the evaporation of water droplets held in the ultrasonic levitator at 0% RH.

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Using the slope of the first 100 , the experimental evaporation rate of a water droplet, in terms of the change in surface area with respect to time, was determined to be at 0% ambient RH and 24.7°C, averaged over 151 trials. The first 100 were used to determine the evaporation rate in order to parallel the conditions of the binary aqueous droplets (see Chapter 4.2).

The evaporation rate of a water droplet under the given conditions can also be predicted using Eq. 10; this requires the binary gas diffusion coefficient for water in nitrogen gas ( ), which is at 25°C (Cussler 1997). Equation 10 yields a theoretical value for a water droplet’s change in surface area with time at 0% RH and 24.7°C: .

The difference between the experimental and theoretical evaporation rates of a water droplet can be attributed to experimental factors that are not encapsulated in the Maxwell equation: eg. acoustic streaming and wind factors (Shaw 1978; Tuckermann et al. 2002; Ali Al Zaitone and Tropea 2011). The Maxwell equation also lacks consideration of heat transfer from the droplet as water evaporates and assumes that the temperature at the surface of the droplet ( ) is constant. The good linear fit of the experimental data suggests that the temperature at the surface of 1 diameter droplets is relatively constant, which is supported by IR-thermography by Tuckermann et al. (2005). Error in the relative humidity measurement is not expected to contribute significantly to this difference, as ±1% RH only affects the theoretical evaporation rate by ±1% (see Eq. 10). The difference can be accounted for by a correction factor, :

Eq. 14a

It is assumed that the correction factor is independent of temperature across the narrow temperature range of these experiments. This was tested by comparing the average correction factor, calculated from each water trial (Eq. 14b), to the correction factor calculated from the average experimental evaporation rate and the theoretical rate for the average trial temperature (Eq. 14c). The correction factors determined from these calculations are indistinguishable.

Eq. 14b

Eq. 14c

Due to the potential for temporal variations in the system, distilled water tests were run in conjunction with the trials for each salt in order to optimize the accuracy of the correction factor and evaporation ratio between salt solutions and distilled water. Therefore, all reported evaporation ratios and the distilled water evaporation data in each figure correspond to the distilled water trials run alongside the salt being discussed.

4.2 Binary inorganic salt/water droplets

As discussed in Chapter 2.3.1, the simple model combining Maxwell's equation and a solution's equilibrium vapour pressure is complicated for aqueous solutions of non-volatile solutes, such as inorganic salts. This is due to the solution becoming increasingly concentrated as water evaporates, consequently suppressing the equilibrium vapour pressure of water. Therefore, surface area as a function of time is not expected to be linear for binary aqueous droplets of inorganic salts. Instead, the rate of change of surface area with respect to time would be expected to decrease as the solution becomes more concentrated and its equilibrium vapour pressure is further suppressed. In order to determine whether combining Maxwell's equation and water's equilibrium vapour pressure can be used to predict the evaporation of binary aqueous solution of relatively non-volatile solutes, six inorganic salts were tested: sodium chloride, sodium bromide, potassium chloride, magnesium chloride, ammonium chloride, and ammonium sulfate.

The evaporation rate of unsaturated, binary salt/water droplets was predicted using Eq. 11a and Eq. 11b (see Figure 4.2); Eq. 11a incorporates the van't Hoff factor, and Eq. 11b employs both the van't Hoff factor and water activity coefficient. These predictions require density information for the aqueous salt solution across the range of observed concentrations in order to relate droplet volume to the mole fractions of salt and water (see Appendix B). They also depend on the correction factor, , which scales the prediction so that it accounts for experimental factors and thus is comparable to the experimental data.

Eq. 11a and Eq. 11b were used to predict evaporation until the solution concentration reached saturation; the prediction curves in Figure 4.2 - Figure 4.8 stop once saturation is reached. Once the droplet has reached saturation, the equilibrium vapour pressure of water

38 is no longer dependent on concentration, and can be predicted using the deliquescence relative humidity ( ), as shown in Eq. 11c.

4.2.1 Binary simple salt/water droplets

Figure 4.2 displays the experimental evaporation data for an aqueous sodium chloride droplet, overlaid onto the Eq. 11a and Eq. 11b predictions, which show good agreement. As previously discussed, the evaporation rate in terms of surface area versus time is not expected to be linear; therefore, linear approximations were used to extract evaporation rates that could be compared to distilled water. The linear approximations were taken across 100 , which was chosen as a balance between optimizing the number of data points included in the line and minimizing the range being approximated. The average slope of these linear approximations was compared to the average slope for water at the corresponding droplet diameter range as the ratio of aqueous salt solution/distilled water: hereon referred to as the solution/water evaporation rate ratio ( ) (see Table 4.1 and Table 4.2).

The same analysis was performed for the other inorganic salts that were tested: sodium bromide, potassium chloride, and magnesium chloride (see Figure 4.3, Figure 4.4, and Figure 4.5). Predictions using Eq. 11a were also generated for these salts; bromide, potassium, and magnesium ions are not included in E-AIM Model IV (Friese and Ebel 2010), so activity coefficients were not readily available.

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The figures show good agreement between the experimental data and Eq. 11a predictions for 150 . Magnesium chloride, the only salt tested here, exhibits enhanced suppression to the evaporation rate before saturation, as predicted by Eq. 11a.

Table 4.1 gives the solution/water s, determined from linear approximations of evaporation rate taken across 0-100 , compared to distilled water. In all four cases, the Eq. 11a prediction is within the 95% confidence interval.

Table 4.2 lists solution/water s for the 100 preceding visible crystallization. While the experimental data may deviate from the Eq. 11a prediction after 150 , Table 4.2 illustrates that the evaporation rate of each aqueous solution approaches the evaporation rate predicted by the and Eq. 11c during the final 100 before crystallization.

Eq. 11a Eq. 11b van't Experimental prediction of prediction of Compound Hoff solution/water solution/water solution/water factor ( )

Sodium Chloride 2 0.91 0.91 0.92 ± 0.04 NaCl Sodium Bromide 2 0.92 -- 0.90 ± 0.03 NaBr Potassium Chloride 2 0.93 -- 0.93 ± 0.05 KCl Magnesium Chloride 3 0.86 -- 0.86 ± 0.03 MgCl2

Eq. 11c prediction of Experimental Compound solution/water solution/water Sodium Chloride 0.7581 0.79 ± 0.04 NaCl Sodium Bromide 0.5861 0.61 ± 0.02 NaBr Potassium Chloride 0.8432 0.91 ± 0.02 KCl Magnesium Chloride 0.3282 0.47 ± 0.02 MgCl2

1 CRC Handbook of Chemistry and Physics (Haynes 2015) 2 Greenspan (1977)

4.2.2 Binary ammonium salt/water droplets

Ammonium is the dominant cation in atmospheric particles, present as ammonium sulfate, ammonium nitrate, and ammonium chloride (Jimenez et al. 2009). Consequently, the evaporation of aqueous ammonium sulfate and ammonium chloride droplets was also investigated. Ammonium is considered to be a semi-volatile solute, as it can partition to the gas phase as ammonia; Table 4.3 lists the ammonia vapour pressure above saturated aqueous solutions, which is 5 orders of magnitude less than that of water.

Table 4.3 Ammonia vapour pressure above a saturated aqueous solution at 298 .

Compound Ammonia Vapour Pressure (Pa)1

-1 Ammonium Sulfate (NH4)2SO4 3.9 10

-2 Ammonium Nitrate NH4NO3 5.0 10

-2 Ammonium Chloride NH4Cl 5.1 10

1 E-AIM Model IV (Friese and Ebel 2010)

Based on their van't Hoff factors, ammonium chloride and ammonium sulfate would be predicted to exhibit similar behaviour to the =2 and =3 salts studied in Chapter 4.2, respectively. However, neither ammonium salt exhibited suppression to the evaporation rate during the first 300 (see Figure 4.6, Figure 4.7, and Table 4.4); instead the evaporation of both solutions seems to be indistinguishable from that of distilled water droplets. Yet for the final 100 before crystallization, both ammonium salts approach the evaporation rate predicted by their and Eq. 11c (see Table 4.5).

Eq. 11a Eq. 11b van't Experimental prediction of prediction of Compound Hoff solution/water solution/water solution/water factor ( )

Ammonium Chloride 2 0.91 0.93 1.03 ± 0.03 NH4Cl Ammonium Sulfate 3 0.88 0.92 1.02 ± 0.09 (NH4)2SO4

Eq. 11c prediction of Experimental Compound solution/water 1 solution/water Ammonium Chloride 0.783 0.79 ± 0.01 NH4Cl Ammonium Sulfate 0.812 0.82 ± 0.04 (NH4)2SO4

1 CRC Handbook of Chemistry and Physics (Haynes 2015)

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(b) 5.1 (c) 3.9

5.0 3.7

) ) 2 2 4.9 3.5 4.8 3.3 4.7 3.1 4.6 2.9 4.5 2.7

4.4 2.5 Surface Area (mm Area Surface Surface Area (mm Area Surface 4.3 2.3 4.2 2.1 4.1 1.9 0 50 100 200 250 300 350 400 Time (s) Time (s)

Eq. 11a only accounts for water vapour pressure suppression as the result of dissociated solutes, and does not account for deviations from solution ideality or any loss of semi-volatile solutes. Eq. 11b incorporates the water activity coefficients obtained using E- AIM Model IV into the water vapour pressure. Along with activity coefficients, E-AIM was also used to obtain mole fractions of each component in both the aqueous and gas phase, and the vapour pressure of each volatile species. Therefore, the mole fraction of solute used in Eq. 11b reflects the loss of solute to the gas phase.

4.3 Binary malonic acid/water droplets

Malonic acid is semi-volatile in aqueous solution; its partial vapour pressure is on the order of (Pope et al. 2010). Peng et al. (2001) observed 3% solute loss per hour for 10-15 diameter aqueous particles at 50% RH, room temperature, and ambient pressure.

The evaporation of aqueous malonic acid droplets displays clear suppression to the evaporation rate relative to distilled water, well before saturation (see Figure 4.8). A prediction for malonic acid was generated using Eq. 11a, density information from Hyvärinen et al. (2006), and values from the CRC Handbook of Chemistry and Physics (Haynes 2015). When the concentration of malonic acid is m, less than 3% is expected to be dissociated, which corresponds to . However, the degree of suppression for 0-100 is in the same range observed for the inorganic salts that do not contain ammonium, and the evaporation ratio predicted based on is at the upper bound of the 95% confidence interval (see Table 4.6). For all 15 replicate trials, formation of a precipitate was observed after 430-480 , and the linear approximation of evaporation rate agrees with the equilibrium vapour pressure above a saturated solution.

(a) 5.5

5.0

)

2 4.5

4.0

3.5

3.0

Surface Area (mm Area Surface 2.5

2.0

1.5 0 50 100 150 200 250 300 350 400 450 500 Time (s)

(b) 5.2 (c) 3.5

5.1 3.3

) ) 2 2 5.0 3.1 4.9 2.9 4.8 2.7 4.7 2.5 4.6 2.3

4.5 2.1 Surface Area (mm Area Surface Surface Area (mm Area Surface 4.4 1.9 4.3 1.7 4.2 1.5 0 50 100 250 300 350 400 450 Time (s) Time (s)

Eq. 11a prediction Eq. 11a prediction Experimental of solution/water of solution/water Compound solution/water using using

Malonic Acid 0.95 0.92 0.92 ± 0.03 CH2(COOH)2

Eq. 11c prediction of Experimental Compound solution/water 1 solution/water Malonic Acid 0.74 0.71 ± 0.06 CH2(COOH)2

1 Brooks et al. (2002)

4.4 Ternary malonic acid/ammonium sulfate/water droplets

The evaporation of ternary malonic acid/ammonium sulfate/water droplets was monitored and compared to the evaporation of distilled water, aqueous malonic acid, and aqueous ammonium sulfate (see Figure 4.9). The solution/water during the initial 100 is similar to aqueous malonic acid (see Table 4.8); however beyond that time, the evaporation rate slows drastically. Of the 15 replicate trials, 4 trials were run for 15 minutes and 11 trials were run for 20 minutes, and crystallization was not visible during any of these trials.

(a) 5.5

5.0

)

2 4.5

4.0

3.5

3.0

Surface Area (mm Area Surface 2.5

2.0

1.5 0 200 400 600 800 1000 1200 Time (s)

(b) 5.2 (c) 3.5

5.1 3.3

) ) 2 2 5.0 3.1 4.9 2.9 4.8 2.7 4.7 2.5 4.6 2.3

4.5 2.1 Surface Area (mm Area Surface Surface Area (mm Area Surface 4.4 1.9 4.3 1.7 4.2 1.5 0 50 100 250 300 350 400 450 Time (s) Time (s)

Experimental Compound solution/water

Malonic Acid 0.92 ± 0.03 CH2(COOH)2 Ammonium Sulfate 1.02 ± 0.09 (NH4)2SO4 Ternary droplet 0.91 ± 0.04

4.5 References

Ali Al Zaitone, B., Tropea, C.: Evaporation of pure liquid droplets: Comparison of droplet evaporation in an acoustic field versus glass-filament. Chem. Eng. Sci. 66, 3914–3921 (2011). Brooks, S.D., Wise, M.E., Cushing, M., Tolbert, M.A.: Deliquescence behavior of organic/ammonium sulfate aerosol. Geophys. Res. Lett. 29, (2002). Cussler, E.L.: Diffusion: Mass Transfer in Fluid Systems (2nd ed.). Cambridge University Press, New York (1997). + + Friese, E., Ebel, A.: Temperature Dependent Thermodynamic Model of the System H -NH4 - + 2- - - Na -SO4 -NO3 -Cl -H2O. J. Phys. Chem. A. 114, 11595–11631 (2010). Greenspan, L.: Humidity Fixed Points of Binary Saturated Aqueous Solutions. J. Res. Natl. Bur. Stand. Sect. A Phys. Chem. 81A, 89–96 (1977). Haynes, W.M. ed: CRC Handbook of Chemistry and Physics. Taylor and Francis Group, LLC (2015). Hyvärinen, A.P., Lihavainen, H., Gaman, A., Vairila, L., Ojala, H., Kulmala, M., Viisanen, Y.: Surface Tensions and Densities of Oxalic, Malonic, Succinic, Maleic, Malic, and cis-Pinonic Acids. J. Chem. Eng. Data. 51, 255–260 (2006). Jimenez, J.L., Canagaratna, M.R., Donahue, N.M., Prevot, A.S.H., Zhang, Q., Kroll, J.H., DeCarlo, P.F., Allan, J.D., Coe, H., Ng, N.L., Aiken, A.C., Docherty, K.S., Ulbrich, I.M., Grieshop, A.P., Robinson, A.L., Duplissy, J., Smith, J.D., Wilson, K.R., Lanz, V.A., Hueglin, C., Sun, Y.L., Tian, J., Laaksonen, A., Raatikainen, T., Rautiainen, J., Vaattovaara, P., Ehn, M., Kulmala, M., Tomlinson, J.M., Collins, D.R., Cubison, M.J., Dunlea, J., Huffman, J.A., Onasch, T.B., Alfarra, M.R., Williams, P.I., Bower, K., Kondo, Y., Schneider, J., Drewnick, F., Borrmann, S., Weimer, S., Demerjian, K., Salcedo, D., Cottrell, L., Griffin, R., Takami, A., Miyoshi, T., Hatakeyama, S., Shimono, A., Sun, J.Y., Zhang, Y.M., Dzepina, K., Kimmel, J.R., Sueper, D., Jayne, J.T., Herndon, S.C., Trimborn, A.M., Williams, L.R., Wood, E.C., Middlebrook, A.M., Kolb, C.E., Baltensperger, U., Worsnop, D.R.: Evolution of Organic Aerosols in the Atmosphere. Science (80-. ). 326, 1525–1529 (2009). Peng, C., Chan, M.N., Chan, C.K.: The Hygroscopic Properties of Dicarboxylic and Multifunctional Acids: Measurements and UNIFAC Predictions. Environ. Sci. Technol. 35, 4495–4501 (2001). Pope, F.D., Tong, H.J., Dennis-Smither, B.J., Griffiths, P.T., Clegg, S.L., Reid, J.P., Cox, R.A.: Studies of Single Aerosol Particles Containing Malonic Acid, Glutaric Acid, and Their Mixtures with Sodium Chloride. II. Liquid-State Vapor Pressures of the Acids. J. Phys. Chem. A. 114, 10156–10165 (2010). Shaw, D.T. ed: Fundamentals of Aerosol Science. John Wiley & Sons (1978). Tuckermann, R., Bauerecker, S., Cammenga, H.K.: IR-Thermography of Evaporating Acoustically Levitated Drops. Int. J. Thermophys. 26, 1583–1594 (2005). Tuckermann, R., Bauerecker, S., Neidhart, B.: Evaporation rates of alkanes and alkanols from acoustically levitated drops. Anal. Bioanal. Chem. 372, 122–127 (2002).

5 Discussion

5.1 Binary simple salt/water droplets

The results presented in Chapter 4 demonstrate that the ultrasonic levitator and CCD camera with telecentric lens can be used to obtain surface area time series for aqueous droplets of sodium chloride, sodium bromide, potassium chloride, and magnesium chloride, and determine the suppression of the evaporation rate of water from aqueous droplets of a non-volatile solute. By comparing these surface area time series to predictions generated by simple models combining Maxwell's equation with a solution's vapour pressure through Eq. 11a, Eq. 11b, and Eq. 11c, the evaporation of water from aqueous droplets containing relatively non-volatile solutes can be modelled. For all four salts, the profile of surface area versus time generated by agrees well with the experimental results (see Figure 4.2 - Figure 4.5). Numerical predictions for the linear approximation of evaporation rate across 0-100 and 100 before crystallization, from Eq. 11a and Eq. 11c, respectively, are within the experimental 95% confidence interval (see Table 4.1 and Table 4.2).

For sodium chloride, activity information retrieved from E-AIM was used with Eq. 11b to generate a second profile of surface area versus time and a numerical prediction for the evaporation ratios at 0-100 . The profiles generated by Eq. 11a and Eq. 11b were within 4% at their most separated, and the solution/water for 0-100 were both 0.91. The concentration of sodium chloride is expected to increase from 2.3-2.9 m across 0-100 , which corresponds to less than a 1% deviation from ideality: = 0.997-0.990. Using parameterized activity equations developed by Cohen et al. (1987), the water activity coefficients for sodium bromide and potassium chloride were calculated for their respective concentration ranges corresponding to 0-100 (see Table 4.1); these salts are also predicted to exhibit minimal deviation from ideality with respect to water.

Table 5.1 Water activity coefficients ( ) corresponding to the average concentration range for 0-100 .

Average Average concentration concentration corresponding corresponding Compound at at to conc. at to conc. at (m) (m) Sodium Chloride 2.3 2.9 0.9971 0.9901 NaCl Sodium Bromide 2.3 3.0 0.9882 0.9672 NaBr Potassium Chloride 2.2 2.7 1.0022 1.0012 KCl

1 E-AIM Model IV (Friese and Ebel 2010) 2 Cohen et al. (1987)

Based on these results, a simple model using either Eq. 11a, which employs the van't Hoff factor, and Eq. 11b, which incorporates both the van't Hoff factor and water activity coefficient, can be used to predict the evaporation of water from subsaturated aqueous solutions of non-volatile solutes when the water fraction does not deviate significantly from ideality.

The evaporation rate of water continued to decrease as each solution became increasingly concentrated, and the solution/water during the 100 before crystallization approached the salt's deliquescence relative humidity ( ). Based on the initial concentration of the droplets and diameter measurements, the solutions were expected to be supersaturated during the 100 before crystallization; however, the solution/water was within 8% of the for sodium chloride, sodium bromide, and potassium chloride. This suggests that the evaporation of water from a supersaturated solution can be described by combining Maxwell's equation and the solution's deliquescence relative humidity (Eq. 11c).

In the case of magnesium chloride, the solution/water was 43% larger than the . Based on the initial concentration and volume of the droplets, the magnesium chloride droplets were expected to reach saturation 90 before crystallization became visible, so

56 the solute concentration during the 100 before crystallization should also correspond to a supersaturated solution. Magnesium chloride is very hygroscopic, making it difficult to obtain truly anhydrous salt, so it is possible that the salt used to prepare the test solutions contained some water, resulting in a lower initial concentration than expected. However, the salt used to prepared the test solutions would need to be more than 5% water by mass before the droplets would be expected to reach saturated less than 50 before crystallization, which is unlikely since the salts were dried at 100°C for >12 hours before the test solutions were prepared. Taking linear approximations across the 50 before crystallization, the solution/water is still 28% larger than the , suggesting that there may be another contributing factor.

The efflorescence behaviour of magnesium chloride has been observed to be different than that of other inorganic salts studied here. In an aerosol study by Cziczo and Abbatt (2000), the efflorescence of aqueous magnesium chloride aerosols was monitored using infrared spectroscopy to observe phase changes in the aerosols. The authors reported differences in the aqueous magnesium chloride spectrum, relative to the spectrum of pure water, that suggest the formation of a hydrate, likely MgCl2∙6H2O. When the relative humidity was below the (33% RH) and a hydrate was present, introducing small amounts of water vapour to the system demonstrated that the aerosols still exhibit immediate water uptake and return to aqueous magnesium chloride; this suggests that the formation of a hydrate prevents magnesium chloride from fully crystallizing, as the solid phase is not expected to take up water and deliquesce until 33% RH.

Therefore, the evaporation of water from supersaturated binary droplets containing simple salts that undergo complete crystallization can be predicted by combining Maxwell's equation with the solution's (Eq. 11c), as shown by aqueous sodium chloride, sodium bromide, and potassium chloride droplets. Since the droplets are expected to be supersaturated during the final 100 before crystallization, the fact that the solution/water approaches the implies that the vapour pressure of water above a supersaturated solution is similar to its deliquescence relative humidity, and that supersaturated, metastable droplets may not be in equilibrium with the surrounding gas phase. In the case of salts that

57 can form hydrates, such as magnesium chloride, the evaporation of water from supersaturated solutions is not adequately described by Eq. 11c.

5.2 Binary ammonium salt/water droplets

Ammonium salts are prevalent in atmospheric particles around the globe, with ammonium comprising up to 16% of the aerosol mass fraction (Jimenez et al. 2009). Ammonium is a semi-volatile solute in aqueous solution, showing partitioning between aqueous and gas phase ammonia. The Henry's law constant for ammonia is on the order of M/ at 298 , which corresponds to ammonia equilibrium vapour pressures on the order of above the aqueous ammonium salt droplets studied here (Sander 1999; E-AIM Model IV).

Based on Eq. 11a and Eq. 11b, the solution/water s of aqueous ammonium chloride and ammonium sulfate droplets are expected to be 0.9 for the initial 100 ; however, the experimental results show that their evaporation rates are indistinguishable from that of distilled water droplets (see Table 4.4). Eq. 11a only accounts for water vapour pressure suppression due to the colligative properties of dissociated solutes, and so is not expected to fully capture the evaporation of aqueous droplets containing semi-volatile solutes. Eq. 11b is somewhat more robust as it employs the water activity coefficient, which accounts for deviations from solution ideality, as well as the mole fractions predicted by E- AIM, which consider the partitioning of semi-volatile solutes to the gas phase. The predictions using Eq. 11b do seem to capture that the solution/water of aqueous ammonium chloride and ammonium sulfate droplets are indistinguishable, as observed in the experimental solution/water s. Based on Eq. 11b, the fact that the solution/water s appear to be the same suggests that the water activities of the two aqueous ammonium salts are very similar, despite ammonium sulfate contributing more solute ions to solution. However, Eq. 11b does not account for the contribution of evaporating solutes to the change in surface area.

To estimate the potential change in surface area due to evaporation of semi-volatile solute, Eq. 8c can be rearranged in order to solve for the rate of change in moles of

58 evaporating species with respect to time from a sphere (Eq. 15). Eq. 15 can be used to estimate the number of moles of semi-volatile solute that are lost to the gas phase during the initial 100 . This can subsequently be compared to the difference in the number of moles between the experimental data and the Eq. 11b prediction in order to determine to what extent this difference can be attributed to loss of solute (see Table 5.2). E-AIM Model IV predicts that ammonia and hydrochloric acid partition from aqueous ammonium chloride in comparable amounts, with some protons remaining in solution, whereas only ammonia is expected to partition from aqueous ammonium sulfate.

Eq. 15

The binary nitrogen at 25°C, and for hydrochloric acid in air at 23°C (Tang et al. 2014); the E-AIM Model IV output was used to obtain the partial vapour pressure of the volatile solute, and the ambient vapour pressure of the volatile solute is assumed to be 0.

Table 5.2 Comparison of moles of semi-volatile solute evaporated across 0-100 , as predicted by Eq. 15, to the difference in moles between the experimental data and the Eq.

11b prediction across 0-100 .

Evaporating Difference in moles Moles of semi-volatile Compound semi-volatile Experimental data - solute evaporated solute Eq. 11b prediction

Ammonium Chloride NH3

NH4Cl HCl

Ammonium Sulfate NH3 (NH4)2SO4

The comparison in Table 5.2 implies that while there is some evaporation of semi- volatile solutes from aqueous ammonium salt droplets, it is 5 orders of magnitude less than what is required to explain the experimental results. It should also be noted that the ammonium salts were deployed as 1.2 droplets of 2 m solution, which corresponds to

moles of dry salt. This means that 50% and 25% of the semi-volatile solutes from ammonium chloride and ammonium sulfate, respectively, would need to be lost during the first 100 in order to close the gap between the experimental results and predicted evaporation rates. Thus, the evaporation of semi-volatile solutes alone cannot explain the experimental evaporation rates observed for the ammonium salts.

The experimental finding that the evaporation of aqueous ammonium sulfate droplets is indistinguishable from the evaporation of distilled water is supported by previous work by Drisdell et al. (2009), which determined that the evaporation coefficient of subsaturated aqueous ammonium sulfate is indistinguishable from the evaporation coefficient of pure water. These results imply that subsaturated concentrations of ammonium sulfate do not affect the evaporation rate of water even though the vapour pressure of water is significantly reduced (Tang and Munkelwitz 1994); this has also been illustrated here through the comparison of experimental evaporation rates and predictions based on the equilibrium vapour pressure of water.

Once the droplets became supersaturated, the solution/water during the final 100 before crystallization approached the ammonium salt's deliquescence relative humidity ( ). For both ammonium chloride and ammonium sulfate, the solution/water of the final 100 was within 1% of the . This further supports the hypothesis that evaporation of semi-volatile solutes is not responsible for the difference between the experimental and predicted evaporation rates, because if a significant fraction of the solutes was lost then the solution would be too dilute to approach saturation, and consequently the .

5.3 Binary malonic acid/water droplets

Malonic acid, the C3 dicarboxylic acid, is among the most common dicarboxylic acids in the atmosphere (C2-C4), and is predominantly generated as a secondary product from oxidation in both the gas and aqueous phases (Kawamura and Ikushima 1993; Chebbi and Carlier 1996; Blando and Turpin 2000; Kerminen et al. 2000; Hallquist et al. 2009). Low molecular weight dicarboxylic acids are highly water soluble, and have been detected in clouds, fog, and precipitation (Chebbi and Carlier 1996). Malonic acid shows similar

60 hygroscopicity to some inorganic salts; however, unlike inorganic salts, it exhibits continuous water uptake and evaporation without step-wise deliquescence or efflorescence between 10- 90% RH (Peng et al. 2001; Yeung and Chan 2010). At 24°C, the equilibrium vapour pressure of water is measured as 74% RH above saturated malonic acid solutions, which is reflected by a steep, but continuous, increase in water uptake when scanning across relative humidity in the deliquescence mode (Brooks et al. 2002; Demou et al. 2003).

Malonic acid has equal to 2.85 and 5.70 for its primary and secondary dissociation (Haynes 2015). Based on , less than 3% of malonic is expected to be dissociated at concentrations above 2 m, corresponding to . However, the solution/water for 0-100 is centred in the same range as the inorganic salts that do not contain ammonium, while is at the upper bound of the 95% confidence interval (see Table 4.6).

Figure 5.1 Molecular structure of malonic acid.

It is unlikely that malonic acid exhibits increased dissociation in droplets. Rather, it could be that its molecular structure affects the solution ideality. In its neutral form, malonic acid has six sites that can participate in hydrogen bonding, which would increase molecular attraction in solution and result in In order to generate a prediction that matches the experimental solution/water for malonic acid, the water activity coefficient would need to be approximately 0.95 across 0-100 . Peng et al. (2001) measured the water activity

( ) of malonic acid aerosols as a function of mass fraction of solute ( ); based on their experimental results, the water activity coefficients of the aqueous malonic acid droplets studied here are expected to be in the range of 0.93-0.87. This supports the case for increased intermolecular attraction in aqueous malonic acid as a significant factor affecting the vapour pressure of water, and this is likely true for other polar organic compounds as well. Therefore, Eq. 11a is not sufficient for predicting the evaporation of aqueous malonic

61 acid, but Eq. 11b may yield a more accurate result when water activity coefficients are available as a function of concentration.

Formation of a precipitate was observed at 450 for aqueous malonic acid droplets (see Figure 4.8). The equilibrium relative humidity over saturated malonic acid is 74% (Brooks et al. 2002), which is approached by the experimental solution/water during the final 100 . Again, the droplets are expected to be supersaturated during the final 100 before crystallization, so the fact that the evaporation of water from supersaturated malonic acid can be described by Eq. 11c supports the idea that the vapour pressure of water above supersaturated solutions is similar to their deliquescence relative humidity, and so metastable droplets may not be in equilibrium with the surrounding gas phase.

5.4 Ternary malonic acid/ammonium sulfate/water droplets

Aerosols are multi-component systems, thus it is not sufficient to solely study solutes as binary mixtures with water. The growing body of literature investigating organics that have been measured in the condensed phase highlights the importance of understanding the effect of organic compounds, such as dicarboxylic acids, on the water content of inorganic salts (Brooks et al. 2002; Choi and Chan 2002; Wise et al. 2003; Braban and Abbatt 2004; Sjogren et al. 2007; Ling and Chan 2008; Yeung and Chan 2010; Wong et al. 2014; Hodas et al. 2015; Liu et al. 2016). Recent studies have shown that organics do not solely influence the thermodynamically controlled hygroscopic properties of aerosols, but also affect their temporal response to changes in humidity (Sjogren et al. 2007; Mikhailov et al. 2009; Bones et al. 2012). Many organic compounds have been observed to form a metastable, highly viscous phase aerosols upon the evaporation of water, maintaining residual water rather than crystallizing (Ling and Chan 2008; Virtanen et al. 2010; Zobrist et al. 2011). These amorphous phases can have low molecular diffusivity, which imposes kinetic limitations on the uptake and evaporation of water and consequently increases the time it takes for aerosols to reach equilibrium (Tong et al. 2011; Zobrist et al. 2011; Bones et al. 2012; Davies et al. 2012). For example, Zobrist et al. (2011) found that aqueous sucrose aerosols in a highly viscous, glassy state can have condensed phase water diffusion coefficients as low as at 291 , which is 6 orders of magnitude less than in pure water.

Braban and Abbatt (2004) studied phase changes in ternary malonic acid/ammonium sulfate/water aerosols and observed that aerosols containing 25-90% malonic acid by dry mass exhibit suppressed efflorescence, retaining water below 1% RH. Therefore, this system was chosen for study in order to observe whether the evaporation of water from a ternary droplet differs from binary droplets of its solutes. Neither binary malonic acid nor ammonium sulfate droplets exhibited kinetic limitations to diffusion in the condensed phase, even as supersaturated solutions, and so do not seem to form a significant viscous phase as the only solute.

As presented in Chapter 4.4, surface area versus time data were collected for aqueous droplets of 2:1 malonic acid/ammonium sulfate by dry mass. The initial molality of malonic acid was conserved between the binary and ternary droplets, so the mole fraction of malonic acid was relatively unchanged and the mole fraction of ammonium sulfate in the ternary droplets was 60% less than the binary droplets. For the initial 100 , the experimental solution/water was within the same range as the binary malonic acid/water droplets. Binary ammonium sulfate/water droplets did not exhibit any suppression to the evaporation rate of distilled water during the initial 100 , which suggests that a lower concentration of ammonium sulfate would not suppress the evaporation rate either. Considering the behaviour of the binary droplets, the evaporation rate for the initial 100 of aqueous 2:1 malonic acid/ammonium sulfate by dry mass suggests that the contributions of solutes in mixed systems may be additive rather than synergistic at subsaturated concentrations.

Approaching 450 , by which time binary malonic acid droplets were nearing solid formation, the evaporation rate of the ternary droplets decreased dramatically (see Figure 4.9). During 450-550 , the evaporation rate was 22% of the initial rate, and by 800-900 , evaporation had slowed to less than 3% of the initial rate. The ternary droplets persisted as liquid droplets at 0% ambient relative humidity beyond 20 minutes, with no visible indication of precipitation. Because dry nitrogen was continually being flowed passed the droplets, removing evaporated water, the drastic reduction to evaporation rate cannot be the result of slow gas phase diffusion. This suggests the formation of a viscous solution that kinetically limits condensed phase diffusion of water.

Bones et al. (2012) reported a similar phenomenon, where ternary sucrose/sodium chloride/water coarse mode particles exhibited inhibition of condensed phase water diffusion during evaporation below 50% RH, which they attributed to a highly viscous phase that was uniform in composition. The formation of a single, highly viscous phase is also supported by You et al. (2013), who reported that ternary particles of malonic acid/ammonium sulfate, ammonium nitrate, or sodium chloride/water do not appear to undergo liquid-liquid phase separation (LLPS). These considerations lead to the conclusion that a similar highly viscous state is achieved for the ternary malonic acid/ammonium sulfate/water droplets studied here.

5.5 References

Blando, J.D., Turpin, B.J.: Secondary organic aerosol formation in cloud and fog droplet: a literature evaluation of plausibility. Atmos. Environ. 34, 1623–1632 (2000). Bones, D.L., Reid, J.P., Lienhard, D.M., Krieger, U.K.: Comparing the mechanism of water condensation and evaporation in glassy aerosol. Proc. Natl. Acad. Sci. U. S. A. 109, 11613– 11618 (2012). Braban, C.F., Abbatt, J.P.D.: A study of the phase transition behavior of internally mixed ammonium sulfate – malonic acid aerosols. Atmos. Chem. Phys. 4, 1451–1459 (2004). Brooks, S.D., Wise, M.E., Cushing, M., Tolbert, M.A.: Deliquescence behavior of organic/ammonium sulfate aerosol. Geophys. Res. Lett. 29, (2002). Chebbi, A., Carlier, P.: Carboxylic Acids in the Troposphere, Occurence, Sources and Sinks: A Review. Atmos. Environ. 30, 4223–4249 (1996). Choi, M.Y., Chan, C.K.: The Effects of Organic Species on the Hygroscopic Behaviors of Inorganic Aerosols. Environ. Sci. Technol. 36, 2422–2428 (2002). Cohen, M.D., Flagan, R.C., Seinfeld, J.H.: Studies of Concentrated Electrolyte Solutions Using the Electrodynamic Balance. 1. Water Activities for Single-Electrolyte Solution. J. Phys. Chem. 91, 4563–4574 (1987). Cziczo, D.J., Abbatt, J.P.D.: Infrared Observations of the Response of NaCl, MgCl2, NH4HSO4, and NH4NO3 Aerosols to Changes in Relative Humidity from 298 to 238 K. J. Phys. Chem. A. 104, 2038–2047 (2000). Davies, J.F., Haddrell, A.E., Miles, R.E.H., Bull, C.R., Reid, J.P.: Bulk, Surface, and Gas-Phase Limited Water Transport in Aerosol. J. Phys. Chem. A. 116, 10987–10998 (2012). Demou, E., Visram, H., Donaldson, D.J., Makar, P.A.: Uptake of water by organic films: The dependence on the film oxidation state. Atmos. Environ. 37, 3529–3537 (2003). Drisdell, W.S., Saykally, R.J., Cohen, R.C.: On the evaporation of ammonium sulfate solution. Proc. Natl. Acad. Sci. U. S. A. 106, 18897–18901 (2009). + + Friese, E., Ebel, A.: Temperature Dependent Thermodynamic Model of the System H -NH4 - + 2- - - Na -SO4 -NO3 -Cl -H2O. J. Phys. Chem. A. 114, 11595–11631 (2010). Hallquist, M., Wenger, J.C., Baltensperger, U., Rudich, Y., Simpson, D., Claeys, M., Dommen, J., Donahue, N.M., George, C., Goldstein, a. H., Hamilton, J.F., Herrmann, H., Hoffmann, T., Iinuma, Y., Jang, M., Jenkin, M.E., Jimenez, J.L., Kiendler-Scharr, A., Maenhaut, W., McFiggans, G., Mentel, T.F., Monod, A., Prévôt, A.S.H., Seinfeld, J.H., Surratt, J.D., Szmigielski, R., Wildt, J.: The formation, properties and impact of secondary organic aerosol: current and emerging issues. Atmos. Chem. Phys. 9, 5155–5236 (2009). Haynes, W.M. ed: CRC Handbook of Chemistry and Physics. Taylor and Francis Group, LLC (2015).

Hodas, N., Zuend, A., Mui, W., Flagan, R.C., Seinfeld, J.H.: Influence of particle-phase state on the hygroscopic behavior of mixed organic–inorganic aerosols. Atmos. Chem. Phys. 15, 5027–5045 (2015). Jimenez, J.L., Canagaratna, M.R., Donahue, N.M., Prevot, A.S.H., Zhang, Q., Kroll, J.H., DeCarlo, P.F., Allan, J.D., Coe, H., Ng, N.L., Aiken, A.C., Docherty, K.S., Ulbrich, I.M., Grieshop, A.P., Robinson, A.L., Duplissy, J., Smith, J.D., Wilson, K.R., Lanz, V.A., Hueglin, C., Sun, Y.L., Tian, J., Laaksonen, A., Raatikainen, T., Rautiainen, J., Vaattovaara, P., Ehn, M., Kulmala, M., Tomlinson, J.M., Collins, D.R., Cubison, M.J., Dunlea, J., Huffman, J.A., Onasch, T.B., Alfarra, M.R., Williams, P.I., Bower, K., Kondo, Y., Schneider, J., Drewnick, F., Borrmann, S., Weimer, S., Demerjian, K., Salcedo, D., Cottrell, L., Griffin, R., Takami, A., Miyoshi, T., Hatakeyama, S., Shimono, A., Sun, J.Y., Zhang, Y.M., Dzepina, K., Kimmel, J.R., Sueper, D., Jayne, J.T., Herndon, S.C., Trimborn, A.M., Williams, L.R., Wood, E.C., Middlebrook, A.M., Kolb, C.E., Baltensperger, U., Worsnop, D.R.: Evolution of Organic Aerosols in the Atmosphere. Science (80-. ). 326, 1525–1529 (2009). Kawamura, K., Ikushima, K.: Seasonal Changes in the Distribution of Dicarboxylic Acids in the Urban Atmosphere. Environ. Sci. Technol. 27, 2227–2235 (1993). Kerminen, V.-M., Ojanen, C., Pakkanen, T., Hillamo, R., Aurela, M., Meriläinen, J.: Low- Molecular-Weight Dicarboxylic Acids in an Urban and Rural Atmosphere. J. Aerosol Sci. 31, 349–362 (2000). Ling, T.Y., Chan, C.K.: Partial crystallization and deliquescence of particles containing ammonium sulfate and dicarboxylic acids. J. Geophys. Res. Atmos. 113, 1–15 (2008). Liu, Q., Jing, B., Peng, C., Tong, S., Wang, W., Ge, M.: Hygroscopicity of internally mixed multi- component aerosol particles of atmospheric relevance. Atmos. Environ. 125, 69–77 (2016). Mikhailov, E., Vlasenko, S., Martin, S.T., Koop, T., Pöschl, U.: Amorphous and crystalline aerosol particles interacting with water vapor: conceptual framework and experimental evidence for restructuring, phase transitions and kinetic limitations. Atmos. Chem. Phys. 9, 9491–9522 (2009). Peng, C., Chan, M.N., Chan, C.K.: The Hygroscopic Properties of Dicarboxylic and Multifunctional Acids: Measurements and UNIFAC Predictions. Environ. Sci. Technol. 35, 4495–4501 (2001). Sander, R.: Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry, http://www.mpch- mainz.mpg.de/~sander/res/henry.html. Sjogren, S., Gysel, M., Weingartner, E., Baltensperger, U., Cubison, M.J., Coe, H., Zardini, A.A., Marcolli, C., Krieger, U.K., Peter, T.: Hygroscopic growth and water uptake kinetics of two- phase aerosol particles consisting of ammonium sulfate, adipic and humic acid mixtures. J. Aerosol Sci. 38, 157–171 (2007). Tang, I.N., Munkelwitz, H.R.: Water activities, densities, and refractive indices of aqueous sulfates and sodium nitrate droplets of atmospheric importance. J. Geophys. Res. 99, 18801 (1994).

Tang, M.J., Cox, R.A., Kalberer, M.: Compilation and evaluation of gas phase diffusion coefficients of reactive trace gases in the atmosphere: Volume 1. Inorganic compounds. Atmos. Chem. Phys. 14, 9233–9247 (2014). Tong, H.J., Reid, J.P., Bones, D.L., Luo, B.P., Krieger, U.K.: Measurements of the timescales for the mass transfer of water in glassy aerosol at low relative humidity and ambient temperature. Atmos. Chem. Phys. 11, 4739–4754 (2011). Virtanen, A., Joutsensaari, J., Koop, T., Kannosto, J., Yli-Pirilä, P., Leskinen, J., Mäkelä, J.M., Holopainen, J.K., Pöschl, U., Kulmala, M., Worsnop, D.R., Laaksonen, A.: An amorphous solid state of biogenic secondary organic aerosol particles. Nature. 467, 824–827 (2010). Wise, M.E., Surratt, J.D., Curtis, D.B., Shilling, J.E., Tolbert, M.A.: Hygroscopic growth of ammonium sulfate/dicarboxylic acids. J. Geophys. Res. 108, 1–8 (2003). Wong, J.P.S., Liggio, J., Li, S.-M., Nenes, A., Abbatt, J.P.D.: Suppression in droplet growth kinetics by the addition of organics to sulfate particles. J. Geophys. Res. Atmos. 119, 222–232 (2014). Yeung, M.C., Chan, C.K.: Water Content and Phase Transitions in Particles of Inorganic and Organic Species and their Mixtures Using Micro-Raman Spectroscopy. Aerosol Sci. Technol. 44, 269–280 (2010). You, Y., Renbaum-Wolff, L., Bertram, A.K.: Liquid–liquid phase separation in particles containing organics mixed with ammonium sulfate, ammonium bisulfate, ammonium nitrate or sodium chloride. Atmos. Chem. Phys. 13, 11723–11734 (2013). Zobrist, B., Soonsin, V., Luo, B.P., Krieger, U.K., Marcolli, C., Peter, T., Koop, T.: Ultra-slow water diffusion in aqueous sucrose glasses. Phys. Chem. Chem. Phys. 13, 3514–3526 (2011).

6 Conclusions & Future Work

6.1 Conclusions

The evaporation rate of water from droplets on the order of 1 mm in diameter was measured for eight different solutions: sodium chloride, sodium bromide, potassium chloride, magnesium chloride, ammonium chloride, ammonium sulfate, malonic acid, and 2:1 malonic acid/ammonium sulfate by dry mass. In parallel, a simple model was developed to describe the evaporation rate of water from binary solution droplets by combining Maxwell's equation with the solution's evolving vapour pressure.

For binary droplets containing non-volatile inorganic salts, the simple model using Eq. 11a, which employs the van't Hoff factor to account for solute dissociation, generates evaporation profiles and numerical predictions for the solution/water evaporation rate ratios ( s) that agree very well with the experimental measurements. For sodium chloride, E- AIM Model IV output was coupled with Eq. 11b in order to improve the simple model by considering deviations from solution ideality. Since the water fraction in aqueous sodium chloride has less than 10% deviation from ideality across the entire concentration range, including saturation, incorporating the water activity coefficient into the simple model does not have a significant effect on its predictions. Therefore, a simple model using either Eq. 11a or Eq. 11b can be used to predict the evaporation of water from relatively ideal, subsaturated aqueous solutions of non-volatile solutes.

Binary droplets containing ammonium chloride and ammonium sulfate revealed that, despite ammonium salt's suppression of the water vapour pressure, the evaporation rates of 2.5 m aqueous droplets are indistinguishable from those of distilled water. The simple model using Eq. 11b, which includes water activity coefficients and mole fractions based on partitioning of semi-volatile solutes to the gas phase, predicts that the solution/water s of the ammonium salts will be less than 1 due to the reduction of water vapour pressure by solute ions; thus, the prediction does not agree with the experimental results. However, Eq. 11b does seem to capture the relative solution/water s of aqueous ammonium chloride and ammonium sulfate droplets, which were observed to be indistinguishable from each

68 other despite their different van't Hoff factors. The experimental finding that the evaporation of aqueous ammonium sulfate droplets is indistinguishable from the evaporation of water cannot be attributed to loss of semi-volatile solute, and is supported by previous work by Drisdell et al. (2009). These results imply that subsaturated concentrations of ammonium sulfate do not affect the evaporation rate of water even though they significantly reduce its vapour pressure. Further research is required to determine the mechanism of this effect.

Binary malonic acid/water droplets were tested in order to elucidate any differences from the evaporation behaviour of aqueous inorganic salt droplets, and highlighted the need to account for deviations from solution ideality. Based on the of malonic acid, its van't Hoff factor is expected to be ; however, the experimental results suggest that the water vapour pressure may be suppressed by more than a factor of 1.03. Based on the water cycle of malonic acid published by Peng et al. (2001), the water activity of the aqueous malonic acid droplets is expected to deviate from ideality by 93-87%, which would significantly reduce the predicted evaporation rate. Therefore, with access to a parameterization for water activity as a function of malonic acid concentration, the Eq. 11b model could be used to describe the evaporation of water from binary malonic acid/water droplets.

Precipitation was visible for all of the binary droplets, including malonic acid; based on the initial concentration of the droplets and diameter measurements, all droplets were expected to be supersaturated during the final 100 before crystallization. The solution/water during the 100 before crystallization approached the deliquescence relative humidity ( ), and was within 8% of the for all solutes except magnesium chloride. In the case of magnesium chloride, the solution/water during the final 100 was 43% larger than the , which may be the result of hydrate formation (Cziczo and Abbatt 2000). The results presented here suggest that the evaporation of water from supersaturated binary droplets can be predicted by combining Maxwell's equation with the solution's (Eq. 11c) for solutes that do not form hydrates, which implies that

69 supersaturated, metastable droplets may not be in equilibrium with the surrounding gas phase.

Particles in the atmosphere are not binary solutions, so the framework for discussing the evaporation of water from solution droplets must be expanded to describe more complex systems; as a next step, ternary malonic acid/ammonium sulfate/water droplets were studied as a combination of two binary systems. Considering the behaviour of the binary droplets, the evaporation rate for the initial 100 of aqueous 2:1 malonic acid/ammonium sulfate by dry mass suggests that the contributions of solutes in mixed systems may be additive rather than synergistic at subsaturated concentrations. At increased concentrations, the evaporation rate of the ternary droplets decreased dramatically, and they persisted as metastable liquid droplets with no visible indication of precipitation beyond 20 minutes at 0% RH. Based on the results from Bones et al. (2012) and You et al. (2013), the persistence of a liquid phase suggests the formation of a viscous solution wherein condensed phase diffusion of water is drastically reduced, which in turn kinetically limits the evaporation of water.

6.2 Future Work

The results of this research highlight the importance of continuing to resolve the effects of organic aerosols on the evaporation of water from droplets. Before more complex systems are investigated, our understanding of the ternary malonic acid/inorganic salt/water systems should be improved. In order to confirm that the contributions of solutes are additive at subsaturated concentrations, different ratios of malonic acid to ammonium sulfate should be tested, as well as mixtures of malonic acid and sodium chloride. These systems will also provide more information about whether the formation of metastable, viscous droplets is a function of solute species, solute concentration ratio, or both.

Once the evaporation of water from ternary malonic acid/inorganic salt/water droplets is better understood, a survey of ternary droplets containing different organic compounds and inorganic salts should be performed. This survey will determine whether the relationships and models developed to describe ternary malonic acid/ammonium sulfate/water droplets can be applied to other ternary systems.

6.3 References

Bones, D.L., Reid, J.P., Lienhard, D.M., Krieger, U.K.: Comparing the mechanism of water condensation and evaporation in glassy aerosol. Proc. Natl. Acad. Sci. U. S. A. 109, 11613– 11618 (2012). Cziczo, D.J., Abbatt, J.P.D.: Infrared Observations of the Response of NaCl, MgCl2, NH4HSO4, and NH4NO3 Aerosols to Changes in Relative Humidity from 298 to 238 K. J. Phys. Chem. A. 104, 2038–2047 (2000). Drisdell, W.S., Saykally, R.J., Cohen, R.C.: On the evaporation of ammonium sulfate solution. Proc. Natl. Acad. Sci. U. S. A. 106, 18897–18901 (2009). Peng, C., Chan, M.N., Chan, C.K.: The Hygroscopic Properties of Dicarboxylic and Multifunctional Acids: Measurements and UNIFAC Predictions. Environ. Sci. Technol. 35, 4495–4501 (2001). You, Y., Renbaum-Wolff, L., Bertram, A.K.: Liquid–liquid phase separation in particles containing organics mixed with ammonium sulfate, ammonium bisulfate, ammonium nitrate or sodium chloride. Atmos. Chem. Phys. 13, 11723–11734 (2013).

Appendix

A: Maintenance & cleaning of the ultrasonic levitator

When working with aqueous solutions, salt may be deposited on the piezoelectric transducer and reflector when a droplet bursts or is removed from the standing wave. This salt can be removed immediately after the test by gently wiping down the transducer and reflector surfaces using a Q-tip that has been wetted with distilled water. This is preventative maintenance, and should be practiced regularly to limit the formation of small, unobservable salt deposits.

On a routine basis, the levitator should be cleaned more thoroughly. To do this, the processing chamber is dismantled by removing the four screws securing the top plate; the top plate, which includes the micrometer and reflector, and the glass tube of the processing chamber can then be removed. The reflector and underside of the top plate can be cleaned using Kimwipes and distilled water, and the glass tube can be washed using dish detergent. With these components removed, the piezoelectric transducer and foam sound absorbers can be accessed. The transducer surface can be cleaned using Kimwipes and distilled water, and the underside and base of the transducer can be cleaned using Q-tips and distilled water. The foam sound absorbers, which serve to dampen stray acoustic resonance within the processing chamber, should also have any salt deposits removed using Kimwipes and distilled water. Over time, salt and organic acids may corrode the piezoelectric transducer and foam sound absorbers, requiring them to be replaced. Spare parts and servicing can be ordered through tec5 USA.

It has been observed that salt deposits, visible or invisible, can affect the evaporation rate of water from a levitated droplet. The mechanism for this in unclear, but is suspected to be the result of a change to the ultrasonic power or acoustic streaming experienced by the droplet.

B: Simple model predictions of a solution's evaporation rate

Simple model predictions were created using Eq. 11a and Eq. 11b (see Chapter 2 for derivation):

Eq. 11a

Eq. 11b

Table B.3 Variables in Eq. 11a and Eq. 11b describing the evaporation of water.

Variable Units Definition

Surface area of the droplet Time

Gas diffusion coefficient Molar mass of water Density of water Gas constant

Equilibrium vapour pressure of water -- van't Hoff factor

-- Total mole fraction of solute

-- Water activity coefficient for mole fraction

Temperature at the surface of the droplet

Ambient partial pressure of water

Ambient temperature

For the experiments described here, the evaporating species is water and the ambient partial pressure of water was maintained near 0% RH; therefore, . For the evaporation of water, the temperature at the surface of the droplet can be treated as constant (Tuckermann et al. 2005); therefore, the change in surface area with respect to time is a function of the solute mole fraction.

Simple model using Eq. 11a - Ammonium chloride

In order to generate a curve for surface area versus time, the evolving vapour pressure of water must be predicted using the mole fraction of solute ( ). The mole fraction of solute depends on the droplet volume, thus the prediction starts with a volume series that begins at the average droplet volume for The moles of solute in the droplet can be calculated using the initial volume and concentration of the droplets deployed to the ultrasonic levitator, assuming that the solute is not volatile. Using a parameterized equation relating aqueous ammonium chloride molality and molarity to solution density, the molality of the droplet can be calculated for each volume. Molality can then be converted to solute mole fraction, from which the product of and water vapour pressure above droplets at each volume can be calculated.

Figure B.2 Spreadsheet relating droplet volume and solute concentration for 1.2 droplets of 2 m ammonium chloride.

Using the relationship for surface area and solute mole fraction, Eq. 11a can be rearranged to solve for the change in time corresponding to the change in surface area for each consecutive droplet volume (Eq. B.2). The corresponding change in time is calculated using the average solution vapour pressure of water across the change in surface area, and

is calculated for the average ambient temperature of the aqueous ammonium chloride trials using the Antoine equation (Antoine 1888).

Eq. B.1

The results can be expressed as an evaporation profile, surface area time series. In order to compare the predicted evaporation profile to the experimental results, the solution vapour pressure of water must be scaled by the experimental correction factor, (see Chapter 4.1).

Eq. B.2

The solution/water evaporation rate ratio ( ) for the initial 100 can then be determined by the same method used for the experimental solution/water s: linear approximations taken across 0-100 .

Simple model using Eq. 11b - Ammonium chloride

The simple model using Eq. 11b employs the same process as Eq. 11a for determining the change in time corresponding to the change in surface area for each consecutive droplet volume, except that it uses E-AIM Model IV output for volume, solute mole fraction, and the water activity coefficient (Friese and Ebel 2010). The moles of solute input to E-AIM are determined from the initial volume and concentration of the droplets deployed to the ultrasonic levitator; E-AIM Mode IV then outputs the aqueous phase volume, number of moles, density, surface tension, molality, mole fraction, activity coefficient, and partial pressure for a system in thermodynamic equilibrium at a specified relative humidity and temperature (see Figure B.3).

E-AIM Model IV accounts for partitioning of semi-volatile solutes to the gas phase; therefore, the output mole fractions account for loss of ammonia to the gas phase. After the initial partitioning, the solution droplet becomes acidic and the partial pressure of ammonia decreases by two orders of magnitude; as a result, the number of moles of aqueous ammonium is predicted to decrease by less than 2% during the initial 100 .

By the same process as for Eq. 11a, the time between each consecutive surface area can be summed, yielding an evaporation profile as a time series. Again, in order to compare the predicted evaporation profile to the experimental results, the solution vapour pressure of water must be scaled by the experimental correction factor, , and the solution/water for the initial 100 can then be determined using linear approximations taken across 0-100 .

Eq. B.2

Figure B.4 Spreadsheet relating E-AIM Model IV output for droplet volume and solute concentration for 1.2 droplets of 2 m ammonium chloride.

B: References

Antoine, C.: Tensions des vapeurs; nouvelle relation entre les tensions et les températures pressure and temperature. Comptes Rendus des Séances l’Académie des Sci. 107, (1888). Friese, E., Ebel, A.: Temperature Dependent Thermodynamic Model of the System H+-NH4+- Na+-SO42--NO3--Cl--H2O. J. Phys. Chem. A. 114, 11595–11631 (2010). Tuckermann, R., Bauerecker, S., Cammenga, H.K.: IR-Thermography of Evaporating Acoustically Levitated Drops. Int. J. Thermophys. 26, 1583–1594 (2005).