Ultrafine Particle-Particle and Particle-Ion Interactions in Aerosol Reactors by Girish Sharma

Washington University in St. Louis Washington University Open Scholarship

Engineering and Applied Science Theses & Dissertations McKelvey School of Engineering

Spring 5-15-2020

Ultrafine arP ticle-Particle and Particle-Ion Interactions in Aerosol Reactors

Girish Sharma Washington University in St. Louis

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Recommended Citation Sharma, Girish, "Ultrafine arP ticle-Particle and Particle-Ion Interactions in Aerosol Reactors" (2020). Engineering and Applied Science Theses & Dissertations. 552. https://openscholarship.wustl.edu/eng_etds/552

This Dissertation is brought to you for free and open access by the McKelvey School of Engineering at Washington University Open Scholarship. It has been accepted for inclusion in Engineering and Applied Science Theses & Dissertations by an authorized administrator of Washington University Open Scholarship. For more information, please contact [email protected]. WASHINGTON UNIVERSITY IN ST LOUIS School of Engineering and Applied Sciences Department of Energy, Environmental, and Chemical Engineering

Dissertation Examination Committee: Pratim Biswas, Chair Michel Attoui Richard Axelbaum Peng Bai Rajan Chakrabarty, co-advisor

Ultrafine Particle-Particle and Particle-Ion Interactions in Aerosol Reactors by Girish Sharma

A dissertation presented to The Graduate School of Washington University in partial fulfillment of the requirements for the degree of Doctor of Philosophy

May 2020

Saint Louis, Missouri

Table of Contents

List of Figures ...... vii List of Tables ...... xvii Acknowledgements ...... xviii Abstract of the Dissertation ...... xxii Chapter 1. Introduction ...... 1 1.1 Background and Motivation ...... 2 1.1.1 Synthesis of ‘good’ aerosols ...... 2 1.1.2 Measurement of 1-10 nm sized particles ...... 4 1.1.3 Capture of ‘bad’ aerosols ...... 8 1.2 Dissertation Outline ...... 9 1.3 References ...... 10

Chapter 2. Collisional Growth Rate and Correction Factor for TiO2 Nanoparticles at High Temperatures in Free Molecular Regime ...... 17 Abstract ...... 18 2.1 Introduction ...... 19 2.2 Methods ...... 23 2.2.1 Experimental Set up ...... 23 2.2.2 Analysis ...... 27 2.3 Results and Discussion ...... 31 2.3.1 Dilution Ratio ...... 31

2.3.2 Lognormal PSD of spherical TiO2 nanoparticles ...... 32 2.3.3 Collisional correction factor ( ) at different temperatures ...... 34 2.4 Conclusions ...... 40 2.5 References ...... 41 Chapter 3. Molecular dynamics trajectory calculations for collisional growth rates of titania nanoparticles during gas-phase synthesis at high temperatures ...... 48 Abstract ...... 49 3.1 Introduction ...... 50 3.2 Methodology ...... 54

3.2.1 MD Trajectory Calculations ...... 54 3.2.2 Nanoparticle Equilibration and Collisions ...... 57 3.3 Results and Discussions ...... 58 3.3.1 Dipole Moment of Equilibrated Titania Nanoparticles ...... 58 3.3.2 Collisions of equally sized particles ...... 60 3.3.3 Collisions of unequally sized particles ...... 63 3.3.4 Comparison with experiments and models ...... 65 3.4 Conclusions ...... 67 3.5 References ...... 68

Chapter 4. Role played by charge in early stages (1-10 nm) of TiO2 particle formation and growth in premixed flames ...... 73 Abstract ...... 74 4.1 Introduction ...... 75 4.2 Methods ...... 78 4.2.1 Experimental Set-up ...... 78 4.2.2 Data inversion from Half-mini DMA ...... 80 4.2.3 Experimental Plan ...... 82 4.3 Results and Discussions ...... 83

4.3.1 Blank Flame Ions (Ar v/s N2) ...... 83

4.3.2 Effect of diluent on particle charging (N2 v/s Ar) ...... 85 4.3.3 Effect of sampling height on particle charging ...... 87 4.3.4 Effect of precursor concentration on particle charging ...... 91 4.4 Conclusions ...... 94 4.5 References ...... 95 Chapter 5. Modeling Simultaneous Coagulation and Charging of Nanoparticles at High Temperatures Using the Method of Moments...... 101 Abstract ...... 102 5.1 Introduction ...... 105 5.2 Model description ...... 107 5.2.1 Ion attachment coefficient ...... 107 5.2.2 Coagulation Coefficient ...... 110 5.2.3 Solving for simultaneous coagulation and charging using MoM ...... 112 5.2.4 Charging terms of the GDE ...... 115

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5.2.5 Coagulation terms of the GDE...... 116 5.2.6 Ion Balance ...... 119 5.3 Simulation Results and Comparison with the MdM ...... 119 5.3.1 Charging in a unipolar ion environment ...... 120 5.3.2 Charging in a bipolar ion environment ...... 124 5.4 Conclusions ...... 129 5.5 References ...... 129 Chapter 6. Numerical modeling of the performance of high flow DMAs to classify sub-2 nm particles ...... 134 Abstract ...... 135 6.1 Introduction ...... 136 6.2 Model Development...... 139 6.2.1 Configuration of Half-mini DMA ...... 139 6.2.2 Flow Regime Calculations ...... 139 6.2.3 Numerical Model ...... 142 6.3 Results and Discussions ...... 144 6.3.1 Flow Regime and Mach Number ...... 144 6.3.2 Flow, Electric and Concentration Fields ...... 146 6.3.3 Transfer Function of Half-Mini DMA compared to Nano DMA ...... 150 6.3.4 Performance under different q/Q ratios ...... 155 6.4 Conclusions ...... 160 Nomenclature ...... 162 6.5 References ...... 164 Chapter 7. Measurement of sub 3 nm flame-generated particles using ultrafine boosted butanol CPC ...... 169 Abstract ...... 170 7.1 Introduction ...... 171 7.2 Experimental Set Up ...... 174 7.2.1 Particle Generation ...... 175 7.2.2 Particle Measurement ...... 176 7.2.3 Experimental Plan ...... 178 7.3 Results and Discussions ...... 179 7.3.1 Nucleation of butanol vapors ...... 179

7.3.2 Effect of saturator temperature and capillary flow rate ...... 181 7.3.3 Effect of particle material ...... 185 7.4 Conclusions ...... 188 7.5 References ...... 189 Chapter 8. Characterization of Particle Charging in Low-temperature, Atmospheric- Pressure, Flow-through Plasmas ...... 195 Abstract ...... 196 8.1 Introduction ...... 199 8.2 Methods ...... 202 8.2.1 Particle Generation and Plasma Reactor ...... 202 8.2.2 Plasma Characterization ...... 204 8.2.3 Charge Distribution Measurement ...... 205 8.2.4 Characteristic Time Scale Analysis ...... 206 8.3 Results and Discussions ...... 213 8.3.1 Comparison of PSDs of different salts passing through plasma...... 213 1.2.1 Plasma Characterization ...... 215 8.3.2 Characterization of Particle Charging in RF and AC plasmas ...... 216 8.3.3 Characteristic Time Scale Analysis ...... 220 8.4 Conclusions ...... 223 8.5 References ...... 224 Chapter 9. Conclusions and Suggestions for Future Work ...... 230 9.1 Conclusions ...... 231 9.1.1 Improvement in the understanding of flame synthesis of 1-10 nm sized nanoparticles (Chapter 2, 3, 4 and 5) ...... 231 9.1.2 Insights on Particle Charging Models (Chapter 2, 3, 4 and 5) ...... 232 9.1.3 Classification and counting of 1-10 nm sized particles (Chapter 6 and 7) .... 238 9.1.4 Capture of suspended particulate matter (Chapter 8) ...... 239 9.2 Future Work ...... 240 9.2.1 Flame Synthesis of 1-10 nm sized nanoparticles ...... 240 9.2.2 Instrumentation...... 241 9.2.3 Plasma Reactor coupled with Electrostatic Precipitators ...... 242 9.3 References ...... 243 Appendix A. Supplemental Information for Chapter 3 ...... 246

Appendix B. Supplemental Information for Chapter 4 ...... 250 Appendix C. Supplemental Information for Chapter 5 ...... 253 Appendix D. Supplemental Information for Chapter 6 ...... 267 Appendix E. Supplemental Information for Chapter 8 ...... 280 Curriculum Vitae ...... 299

List of Figures

Figure 1-1: Early stages of particle formation and growth in a flame aerosol reactor ...... 3

Figure 1-2: a) Brownian diffusion in a differential mobility analyzer (DMA), b) picture of a half- mini DMA, c) Picture of a 1 nm- DMA...... 5

Figure 1-3: Condensational particle counter, and default operating conditions ...... 7

Figure 1-4: Different types of plasmas on a 2-D map of gas temperature, and electron density ... 8

600 °C and 800 °C) by using CO2 gas and a gas analyzer...... 23

Figure 2-2. Measured initial and final particle size distribution, before and after Furnace 2 for T =

400 °C. The PSD is fitted using lognormal particle size distribution for size range: A) dpg = 5-6 nm, and B) dpg = 6-8 nm...... 32

Figure 2-3. TEM images for initial and final particle size distribution for average geometric size

5-6 nm a) Initial at 823 °C, b) Final at 400 °C, c) Final at 600 °C, d) Final at 800 °C; and 6-8 nm e) Initial at 823 °C, Final at f) 400 °C, g) 600 °C, h) 800 °C ...... 33

Figure 2-4. Integral parameters of the size distribution function at three different temperatures 400

°C, 600 °C and 800 °C of Furnace 2, measured before, and after Furnace 2. The average geometric diameter for the experimental data is between 5-6 nm...... 35

Figure 2-5. Integral parameters of the size distribution function at three different temperatures 400

°C, 600 °C and 800 °C of Furnace 2, measured before, and after Furnace 2. The average geometric diameter for the experimental data is between 6-8 nm ...... 36

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Figure 2-6. Collisional correction factor ( ) as a function of temperature for two different particle size ranges compared with the different models for a Hamaker constant of 1.99×10-19 J...... 38

Figure 3-1. Schematic of nanoparticle collisions ...... 55

Figure 3-2. Simulated annealing of TiO2 Wulff structure with 252 atoms at high temperature to obtain a spherical TiO2 nanoparticle (dp ~ 1.8 nm) ...... 57

Figure 3-3. Time averaged dipole moment as a function of A) temperature, B) particle diameter.

...... 59

Figure 3-4. Collisional probability of particles of equal size (2.8 nm) as a function of normalized particle velocity, and impact parameter at 4 different temperatures of 500, 1000, 1500, 2000 K.

...... 60

Figure 3-5. Collisional correction factor for equally sized particles as a function of temperature62

Figure 3-6. Collisional probability of particles of unequal size (1.8 nm, 3.6 nm) as a function of normalized particle velocity, and impact parameter at 4 different temperatures of 500, 1000, 1500,

2000 K ...... 63

Figure 3-7. Collisional correction factor for unequally sized particles as a function of temperature

...... 64

Figure 3-8. Comparison of collisional correction factor as calculated through molecular dynamic simulations with experiments, and existing models...... 65

Figure 4-1. Schematic of the experimental set-up ...... 78

Figure 4-2. Positive and negative ions generated in the blank flame for CH4-O2-N2 and CH4-O2-

Ar with no precursor vapors of TTIP. Table 1 (test 1a)...... 83

Figure 4-3. Percentage of charged particles for CH4-O2-N2 and CH4-O2-Ar at low TTIP concentration (both polarities). Table 1 (test 1b)...... 86

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Figure 4-4. Effect of height above the burner on particle size distribution, and percentage of charged particles. Table 4.1 (test 2)...... 88

Figure 4-5. Total number concentration of charged particles, and total particles measured at different height above the burner. Table 1 (test 2)...... 90

Figure 4-6. Effect of precursor concentration on total particle size distribution, and percentage of charged particles at a fixed height above the burner (3.5 mm). Table 1 (test 3)...... 91

Figure 4-7. Comparison of percentage of charged particles, a) measured using method 1

(neutralizer, half-mini DMA, and electrometer) b) measured using method 2 (boosted butanol

CPC); c) calculated from Fuchs theory of charging. Table 4.1 (test 3)...... 93

Figure 5-1. Comparison between the ion-attachment coefficient given by the Fuchs theory (lines) and the simplified expression (symbols). a) and b) correspond to T = 1200 K whereas c) and d) corresponds to T = 2400 K. a) and c) show the ion-attachment coefficient for negative ions ... 110

Figure 5-2. Schematic diagram of the monodisperse model (MdM) and the method of moments

(MoM) ...... 114

Figure 5-3. Evolution of average (geometric) particle size as a function of time at two different temperatures using MoM and MdM, with and without charging effects in a unipolar ion environment. Subplots represent initial particle-to-ion concentration ratios of a) 0.01 for MoM b)

0.01 for MdM, c) 100 for MoM, and d) 100 for MdM. Note the different scales of the x-axes and y-axes...... 121

Figure 5-4. Evolution of normalized particle number concentration as a function of time at two different temperatures using MoM and MdM, with and without charging effects in a unipolar ion environment. Subplots represent initial particle-to-ion concentration ratios of a) 0.01 for MoM b)

0.01 for MdM, c) 100 for MoM, and d) 100 for MdM. Note the different scales of the x-axes and y-axes...... 122

Figure 5-5. Evolution of geometric standard deviation as a function of time at two different temperatures using MoM, with and without charging effects in a unipolar ion environment.

Subplots represent initial particle-to-ion concentration ratios of a) 0.01 b) 1, c) 100, and d) 1000.

Note the different scales of the x-axes and y-axes...... 123

Figure 5-6. Evolution of average (geometric) particle size as a function of time at two different temperatures using MoM and MdM, with and without charging effects in a bipolar ion environment. Subplots represent initial particle-to-ion concentration ratios of a) 0.01 for MoM b)

0.01 for MdM, c) 100 for MoM, and d) 100 for MdM. Note the different scales of the x-axes and y-axes...... 124

Figure 5-7. Evolution of normalized total particle number concentration as a function of time at two different temperatures using MoM and MdM, with and without charging effects in a bipolar ion environment. Subplots represent initial particle-to-ion concentration ratios of a) 0.01 for MoM b) 0.01 for MdM, c) 100 for MoM, and d) 100 for MdM. Note the different scales of the x-axes and y-axes...... 125

Figure 5-8. Effect of different ion concentration on the total particle number concentration as a function of time. Here, the particle concentration = 10^17 #/cm3...... 127

Figure 5-9. Evolution of normalized average particle size and percentage of charged particles as a function of ion concentrations ratio. Here, the particle concentration = 10^17 #/cm3...... 128

Figure 6-1. Schematic of the Half Mini DMA a) main geometry b) notations for sheath flow parameters...... 140

Figure 6-2. Flow regime in the working section. Black-solid line: Mach number vs. flow rate;

Blue-dashed line: velocity vs. flow rate...... 145

Figure 6-3. The flow fields of Half Mini DMA a) velocity magnitude field below the trumpet, and streamlines shown near the aerosol inlet and outlet slit (q = 9 lpm, Q = 136 lpm) b) different locations in the working section c) the axial velocity profile at different z as increasing q (Q = 136 lpm)...... 147

Figure 6-4. Electric field with the applied voltage (-300V) on the inner electrode...... 148

Figure 6-5. Convective flux (mol·m-2·s-1) fields of aerosol with increasing magnitude of the inner electrode voltage in working section (dp = 1.4 nm, q = 9 lpm, Q = 136 lpm)...... 149

Figure 6-6. a) Transfer function vs. voltage for two different values of dp. b) Comparison between the simulated and experimental peak voltages for different particle diameters...... 152

Figure 6-7. Comparison of transfer function (Ω) between Half Mini DMA and Nano DMA for sub-

2 nm particles. Ω only counts the particle transmission in the DMA work section...... 153

Figure 6-8. The comparison of Resolution (R) of Half Mini DMA and Nano DMA under different particle mobility sizes (q/Q=9/136)...... 154

Figure 6-9. Transfer function vs. voltage for Half Mini DMA a) q = 3 lpm b) q = 5 lpm...... 156

Figure 6-10. The simulation (Half Mini DMA) and theoretical transfer function for different q/Q

(q = 3 lpm) at dp = 1.4 nm under a) the non-diffusion theory (Knutson and Whitby 1975) b) the diffusion theory (Stolzenburg 1988; Stolzenburg and McMurry 2008)...... 158

Figure 6-11. The simulation and theoretical resolution of Half Mini DMA for different q/Q at dp

= 1.4 nm. Note that the simulation point denoted by triangular corresponding to q = 0.93 lpm and

Q = 230 lpm...... 160

Figure 7-1. Schematic of the experimental set-up ...... 175

Figure 7-2. Homogeneous nucleation of butanol vapors for different aerosol capillary flow rate and saturator temperature ...... 180

Figure 7-3. Effect of increasing saturator temperature on the measurement of THAB salt ions for boosted butanol CPC in comparison with electrometer. Capillary flow rate is kept fixed at 50 sccm.

...... 181

Figure 7-4. Effect of capillary flow rate on the CPC Counting Efficiency (%) at different saturator temperature for the measurement of THA+ ions ...... 182

Figure 7-5. CPC Counting Efficiency (%) for different ammonium alkyl halide salt ions as a function of mobility diameters at three different boosted CPC conditions...... 184

Figure 7-6. CPC Counting Efficiency (%) for titanium dioxide (TiO2) synthesized using a flame aerosol reactor, and soot particles synthesized using a McKenna burner for both polarities. .... 186

Figure 7-7. CPC Counting Efficiency (%) for four different types of positively charged particles/ions (< 2 nm) as a function of their mobility diameter. Here, the saturator temperature is

45°C and aerosol capillary flow rate is 70 sccm...... 187

Figure 8-1. Experimental setup for A) particle generation and particle charging in a low- temperature, atmospheric-pressure, flow-through plasma; B) measurement of particle size distribution, overall particle charge fraction, and multiply charged particle distribution ...... 203

Figure 8-2. Proposed mechanism for particle charging inside and outside the plasma volume. 206

Figure 8-3. Comparison of PSDs of different salts after passing through the RF plasma at different powers: A) sea salt, B) NaCl, C) MgSO4 (Test 1) ...... 213

Figure 8-4. Electron density, absorbed power, and electron temperature in a) RF and b) AC plasmas as a function of power and applied peak-to-peak voltage, respectively. (Test 2) ...... 215

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Figure 8-5. Charge fraction of particles as a function of particle diameter for a) RF plasma, and b)

AC plasma at different plasma powers and different initial particle size distributions. (Test 3) 217

Figure 8-6. Particle fraction with different positively, and negative charges (-3 to +3) for four different diameters, viz. a) 15 nm, b) 45 nm, c) 90 nm, d) 135 nm, e) 180 nm at four different RF plasma powers, and two different AC powers. (Test 4) ...... 218

Figure 8-7. A) Average charge acquired by particles in the plasma volume. B) Characteristic time scales for particle charging in the plasma volume and in the spatial afterglow region...... 221

Figure 9-1. Comparison of percentage of charged particles, a) measured using method 1

(neutralizer, half-mini DMA, and electrometer) b) measured using method 2 (boosted butanol

CPC); c) calculated from Fuchs theory of charging at different temperatures (25, 100, 500 C), and d) calculated from Boltzmann theory of charging at 500 C...... 236

Figure 9-2. Schematic to understand different charging mechanisms, during titania formation and growth in a flame reactor...... 237

Figure A-1. Maxwell Boltzmann velocity distribution for a nanoparticle of size 2 nm 246 Figure A-2 Collisional probability of particles of equal size (1.8 nm) as a function of normalized particle velocity, and impact parameter at 4 different temperatures of 500, 1000, 1500, 2000 K.

...... 247

Figure A-3. Collisional probability of particles of equal size (3.6 nm) as a function of normalized particle velocity, and impact parameter at 4 different temperatures of 500, 1000, 1500, 2000 K

...... 248

Figure A-4. Collisional probability of particles of unequal size (1.8 nm, 2.8 nm) as a function of normalized particle velocity, and impact parameter at 4 different temperatures of 500, 1000, 1500,

2000 K...... 249

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Figure B-1. Nascent flame-generated positively and negatively charged particle size distribution for CH4-O2-N2 and CH4-O2-Ar at low TTIP concentration...... 250

Figure B-2. Total PSD for CH4-O2-N2 and CH4-O2-Ar at low TTIP concentration ...... 250

Figure B-3. Effect of the sampling height above the burner on charged particle size distribution, and total particle size distribution, at a fixed precursor concentration...... 251

Figure B-4. Effect of four different precursor concentrations on charged particle size distribution, and total particle size distribution, at a fixed height above the burner (3.5 mm) ...... 252

Figure C-1. Comparison between the steady state charge distribution given by the Fuchs’ theory

(lines) and the simplified expression (Symbols). a) and b) correspond to T = 1200 K, whereas c) and d) correspond to T = 2400 K. a) and c) show the charge distribution of positively charged particles whereas b) and d) show the charge distribution of negatively charged particles...... 260

Figure C-2. Absolute Percentage Error for Park et al., 2005 and this work for both positive and negative ions at 1200 K...... 261

Figure C-3. Comparison between the exact correction factor for coagulation coefficient of charged particles and the fitted values...... 263

Figure C-4. Comparison of the model prediction with the experimental measurements from Alonso et al., 1998...... 264

Figure D-1. Different locations in the working section of Half Mini DMA...... 269

Figure D-2. The comparison of axial velocity profile at different locations with various p in the working section of Half Mini DMA...... 270

Figure D-3. Schematic of trumpet inlet part...... 271

Figure D-4. Streamlines with the flow field of trumpet at various Lin. (q = 9 lpm, Q = 136 lpm)

...... 272

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Figure D-5. The axial velocity profile at different h. (q = 9 lpm, Q = 136 lpm) ...... 272

Figure D-6. The axial velocity profile (vz) and relative difference (ε) at different z with various

Lin. (q = 9 lpm, Q = 136 lpm) ...... 273

Figure D-7. Resolution (a) and transfer function height (b) vs. Q/q (q = 3 lpm) for Half Mini DMA.

...... 274

Figure D-9. Effect of mesh number on the resolution of Half-Mini DMA. The simulation conditions correspond to dp = 1.4 nm, q = 9 lpm, Q = 136 lpm ...... 276

Figure D-10. The simulation data fitted by the Stolzenburg’s diffusive transfer function. The simulation conditions correspond to dp = 1.4 nm, q = 9 lpm, Q = 136 lpm...... 277

Figure D-11. The comparison of fitted and theoretical sigma as increasing Q ...... 278

Figure E-1. Lissajous plot of Ar-H2O dielectric barrier discharge driven at 22.7 kHz with MgSO4 particle flow...... 283

Figure E-2. Calculated waveforms for one period from one set of electrical measurements. a) The gas gap voltage Ug(t), b) the discharge current jr(t), c) the instantaneous impedance Zp and d) the instantaneous power...... 285

Figure E-3. Equivalent circuit representation for the radio-frequency plasma system. ‘Plasma off’ circuit shows the active components from the power supply unit (PSU), matching network, power probe and stray components while the plasma is unstruck. ‘Plasma on’ shows the additional capacitive and resistive contributions due to the plasma discharge. Courtesy of Paul Maguire. 287

Figure E-4. Comparison of the different methods for calculation of charge fraction ...... 290

Figure E-5. Average particle charge as a function of particle diameter for RF and AC plasmas calculated assuming different mean electron temperatures (0.5 – 2 eV)...... 293

Figure E-6. Evolution of electron and ion flux to the particle surface inside the plasma for dp = 90 nm ...... 294

Figure E-7. Evolution of particle charge inside the plasma for dp = 90 nm ...... 295

Figure E-8. Average particle charge as a function of particle diameter for RF/AC plasma Effect for different electron temperatures (0.5 – 2 eV) ...... 297

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List of Tables

Table 2-1. List of instruments and their role in the experiments ...... 24

Table 2-2. Dilution Ratio and residence time for Furnace 1 and Furnace 2 operated at different temperatures...... 31

Table 5-1. Fitting parameters for the correction factor ...... 112

Table 5-2. Parameters used in the simulation of particle simultaneous charging and coagulation.

...... 120

Table 6-1. Different variables used to understand the flow regime in the working section ...... 142

Table 7-1. Test plan for the experiments for different particles at different CPC operating conditions ...... 178

Table 8-1. Overall test plan for the experiments...... 212

Table 8-2. Parameters used for the calculation for characteristic time scales and average particle charge shown in Figure 8.7...... 222

Table D-1. Boundary conditions used in our simulation ...... 268

Table D-2. The comparison of Δp at different sheath inlet pressure...... 269

Table E-1. Effect of different mean electron temperatures on the characteristic times for particle charging in RF and AC plasmas...... 292

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Acknowledgements

I would like to express my deepest and most sincere gratitude to Prof. Pratim Biswas, my PhD advisor, for his guidance and support for my scientific research. I still remember when I first met him at IIT Bombay in December 2014. He has helped me tremendously in my PhD work as a great

‘guru’ would do. He introduced me to the wonderful world of aerosol science and engineering, and how it is an enabling knowledge which impacts the fields of air pollution, energy crises, environment, climate change, chemical engineering, drug delivery, agriculture, and so on. His energy levels are so amazing, that ‘almost every time’ after I meet him, I would come out very happy and motivated to work harder, and perform better. Several times during my PhD, Prof.

Biswas pointed out at problems in my work style, which I never realized were an issue. But, fixing those issues really increased my efficiency to work, and deliver results in a very optimistic and positive manner.

This paragraph will also talk about the other side of my mentor, Prof. Pratim Biswas. I have worked closely with him in different capacities, as his student in aerosol course, teaching assistant in aerosol course, several sessions in India through McDonnell Academy, several non-research type work in US, etc. Through each of these interactions, I realized how lucky I am to get an advisor who helped me to develop strong leadership skills, networking skills, apart from providing research guidance. I am extremely thankful to Prof. Biswas for his continued support in research, leadership, and life decisions.

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I am also lucky to have the guidance from Prof. Rajan Chakrabarty as my co-advisor, who would boost my confidence when I am down, and motivate me to perform better. Many of the times, we would have a quick chat in the lobby about topics ranging from research to politics to meditation to life. I am also thankful for him to teach me the advanced aerosol course, which motivated me further to pursue the fundamentals of aerosol science and engineering.

I would also like to extend my gratitude to Prof. Michel Attoui for teaching me very patiently on how to operate the condensational particle counters, Prof. Richard Axelbaum for teaching me the advanced concepts of combustion, which proved to be very useful in my research work, Prof. Peng

Bai for helpful discussions on decision making in life, Prof. Rohan Mishra for introducing me to molecular dynamics simulations which is also one of my PhD chapters, Prof. Mohan Sankaran for providing me with a new perspective towards research on plasmas, Prof. Carl Bender for teaching me the beautiful world of mathematics through asymptotic analysis and perturbation theory. I am also thankful to McDonnell Academy community which made me feel home all the time with wonderful smiles from Kristin, Carla, Angie, Laura, and Mary Wertch, as well as, career guidance

& advice on important issues from Prof. Jim Wertch, Prof. Mark Wrighton, and Prof. Kurt Dirks.

I would like to thank Teresa Sarai. I am so thankful to come in her contact, as she is so cheerful and happy, that you are bound to be happy after meeting her. Our discussions about job, life, career, family, research, PhD were very fruitful for me, and I am thankful that she could always find time for me for the discussion.

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I also feel lucky to have my better half, Priya Rathi around, who has been very patient with me, when the times were tensed during my PhD. I am also thankful to her for listening to my problems when I am really upset, hanging out with me to make me feel better, providing me food when I am hungry, discussing research in detail, listening to my practice presentations, coping up with me, and many more…

I am thankful to Vipassana meditation, teacher S N Goenka, and several meditators who improved my meditation practice, which resulted in high focus in work, tremendous increase in my efficiency to work with positive mindset. Here, I would again like to thank Prof. Rajan

Chakrabarty, and Prof. Pratim Biswas for allowing me to take some time off to practice 10-day silent meditation retreat. I would also appreciate the support of Priya Rathi, and my family members in supporting me.

My next thanks is to AAQRL family, which nurtures you from the day you join the lab, and trains you to make smart decisions in research, which translates directly to life. I am very thankful to be a part of this family, and would continue to be. The work environment in lab to work as a team on several projects really inculcates strong team building, leadership, mentorship qualities, and I am thankful to Prof. Biswas for keeping everyone together. AAQRL lab members, Dr. Yang Wang

(my first mentor, and very helpful throughout the five years of my PhD), Dr. Jiayu Li, Dr. Huang

Zhang (very hardworking, which motivated me to work hard as well!), Dr. Nathan Reed, Dr.

Tandeep Chadha, Mengda Zhang, Sukrant Dhawan (my PhD would not have been possible without this guy’s assistance in most importantly research, and less importantly daily discussions, daily

xx memes, and daily fun videos), Clayton Kacica (for being my comrade), and all others in AAQRL made my PhD journey very smooth and fun. I am also very thankful to the lab members at Complex

Aerosol Systems Research Laboratory for helpful discussions. Many thanks to the staff in the

EECE department, especially Kim, and Patty. I am also thankful to all my friends in USA, especially Eylul, Okyu, Necip, Rodrigo, and Eric, and India, especially Bhaiyee buoyz, who are my family. I am also thankful to Dr. Bharat Suthar and Dr. Akshay Gopan for their help in the initial part of my PhD and helping me to adjust in USA. I am also thankful to Krishna Upadhyay, my roommate for cooking food for me, which did help me to write probably one more paper!

I want to thank my funding agency, McDonnell International Scholars Academy for supporting me for my study and research at Washington University in St. Louis for 5 years.

Last, but not the least, I am very grateful to my parents, Ashok Kumar Sharma, and Saroj Kaushik; my sisters, Manusmriti, Deepti, and Jyotsana; my grandparents Om Prakash Kaushik, and Kanta

Kaushik for their support when I left for US to get a PhD. I will always be indebted to them for their unconditional love, and nurturing me to be what I am today.

Girish Sharma

Washington University in St Louis

May 2020

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ABSTRACT OF THE DISSERTATION

Ultrafine Particle-Particle & Particle-Ion Interactions in Aerosol Reactors

Girish Sharma

Doctor of Philosophy in Energy, Environmental & Chemical Engineering

Washington University in St Louis, 2020

Professor Pratim Biswas, Chair

Aerosol science and technology has enabled the material synthesis of ‘good’ nanoparticles, as well as, addressed the problem of air pollution by developing particle capture technologies for ‘bad’ nanoparticles. For material synthesis at industrial scale, flame aerosol reactors are extensively used for large-scale industrial production of ‘good’ nanoparticles. But, there exists a knowledge gap in understanding the early stages (1-10 nm) of particle formation and growth, which is necessary for tailoring the synthesized nanoparticles’ properties. To achieve this goal, measurement tools for the characterization of 1-10 nm particles are quintessential. On the other hand, to capture ‘bad’ particles, existing control technologies perform fairly well for particles > 200 nm, but fail to capture smaller nanoparticles.

My dissertation is divided into three sections. First section focuses on developing the understanding of early stages of particle formation and growth (1-10 nm) during material synthesis in flame reactors both through experiments and modeling. Second section focuses on developing measurement tools for precise measurement of 1-10 nm sized particles, both through measurements, and simulations. Third section focuses on investigating plasma reactors as a possible approach for particle capture in conjunction with electrostatic precipitators.

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Part 1a: In this part, spherical, neutral particle-particle interaction is studied, and collisional growth rate is calculated both through controlled furnace experiments, as well as, molecular dynamic simulations. Controlled experiments are performed at moderately high temperatures from 400 –

800 C; and it was found that the collisional growth rate is higher than predicted by kinetic theory of gases. Experiments show that there is higher enhancement in the collisional growth as compared to theories based on Hamaker constant. Following this, molecular dynamics simulations are performed to understand the interatomic forces that lead to this enhancement in collisional growth using LAMMPS. .

Part 1b: After focusing on particle-particle interactions in Part 1a, particle-ion interactions are studied both through experiments, and population balance modeling. Different factors like the effect of diluent in the flame (N2 v/s Ar), sampling height, and precursor concentration is evaluated on the percentage of charged particles. It is found that increasing the precursor concentration, and decreasing the sampling height leads to higher fraction of charged particles. To further understand the role played by charge, a population balance model for simultaneous charging and coagulation is developed using the method of moments.

Part 2: The measurement tools for the classification and counting of nanoparticles are developed in this section. For classification, the new half-mini differential mobility analyzer is set-up in the lab, with high voltage source, and blower with high flow rates (100-600 lpm), and calibrated using electrospray set-up. This instrument is then characterized using commercial software COMSOL

Multiphysics, and the simulated transfer function and resolution is compared with existing models, and experiments. This work provides a useful method to study the flow regimes and transfer function of a high flow DMA. On the other hand, for counting of nanoparticles less than 3 nm in

xxiii size, the detection efficiency of conventionally used instrument condensational particle counter

(CPC) is enhanced, and characterized for different composition of sub-3 nm particles.

Part 3: This part of the dissertation will discuss about the fundamental understanding of particle- ion interactions in a non-thermal plasma reactor, with a vision to incorporate plasma reactors in conjunction with the conventionally used electrostatic precipitators, thereby increasing their efficiency for particle capture. Premade, charge-neutral nanoparticles are introduced into the plasma. The charge fraction and distribution of the particles are examined at the reactor outlet for different mobility diameters (10-250 nm) as a function of plasma power and two different types of power sources, alternating current (AC) and radio-frequency (RF). We find that the overall charge fraction increases with increasing plasma power and diameter for the RF plasma. A similar increasing trend is observed for the AC plasma with increasing particle diameter in the range of

50-250 nm, but the charge fraction increased with decreasing particle diameter in the range of 10-

50 nm. The charge distribution is revealed to be bipolar with particles supporting multiple charges for both the RF and AC plasmas. Differences in the characteristic time scales for particle charging in the AC and RF plasmas are discussed which provide a possible explanation for the trends observed in the experiments.

xxiv

Chapter 1. Introduction

1.1 Background and Motivation

Aerosols can be broadly categorized into ‘good’ and ‘bad’ aerosols. ‘Good’ aerosols are nanoparticles synthesized for a variety of different products, like paints, pigments, sunscreens, drugs, food, tires, semiconductors, and so on [1-8]. These applications are possible due to particle size and morphology. The most commonly synthesized nanoparticles using aerosol route are titanium dioxide, carbon black , fumed silica [9, 10]. For instance, 9 million metric ton of titanium dioxide was produced in 2015 alone [11, 12]. On the other hand, aerosol technologies are developed to get rid of ‘bad’ nanoparticles, addressing the problem of suspended pathogens in the air [13], and polluted air [14, 15]. According to World Health organization, 91% of world population lives in poor air quality, and 7 million people die every year from exposure to polluted air [16]. Aerosol science and technology paves the way for the synthesis of variety of composite materials for various applications, as well as, capture particulate matter, thereby combating the problem of air pollution.

1.1.1 Synthesis of ‘good’ aerosols

Flame aerosol reactors (FLAR) have been extensively used to synthesize nanoparticles in gas- phase at high temperatures in a “bottom-up” approach [17]. This involves multiple processes taking place including precursor reactions, supersaturated vapor nucleation, vapor condensation, particle collisional growth [18] and charging [19, 20]. Although ﬂame synthesis is widely used for the production of nanoparticles on an industrial scale, a clear understanding of the early stages of particle formation and collisional growth is still elusive [21, 22].

The characteristic size dependent properties of nanometer sized particles differ from their bulk counterpart with the most significant effects occurring for 1-10 nm diameters. Due to very high specific surface area, and unique quantum confinement forces, sub-10 nm particles have found applications in catalysis [23], bio-medical imaging [24], Cerenkov radiation induced therapy [25] and semiconductor quantum dots [26]. On the other hand, flame aerosol reactor is a highly versatile approach to synthesize nanoparticles on a large scale, and sub-10 nm particles are the building blocks for larger particles. This further motivates us to investigate the particle formation, and growth in flame aerosol reactor, with a goal to synthesize particles with precise size, crystal phase and morphology on industrial scale [27].

Research gaps:

Figure 1-1: Early stages of particle formation and growth in a flame aerosol reactor

Conventionally, for the synthesis of titania nanoparticles, collisional growth is considered a dominant mechanism in a flame reactor, but, recent studies [21, 22, 28, 29] have shown that a high percentage of particles are charged in a flame reactor, as shown in Figure 1.1. These charged clusters then further interact to form larger particles. So, in addition to neutral particle-neutral particle interactions, there are charged-particle, charged-particle interactions taking place, as well.

At the same time, ions continue to charge the particles through particle-ion collisions. This simultaneous charging and coagulation is not understood well as it takes place in a time scale of less than 1 second.

1.1.2 Measurement of 1-10 nm sized particles

To understand the particle formation and growth, it is important to measure their particle size distribution. The conventional instrument that is used for this measurement, consists of three parts, first a neutralizer to charge the particles to a known charge distribution [30]. Once the particles are charged with a known charge distribution, they are classified based on their mobility, using a differential mobility analyzer [31-34] . Differential mobility analyzers classify the particles based on the balance between the drag force and the electrical force. The classified particles are then counted by growing them in size by condensing vapors on the particles [35, 36]. This is a standard procedure to first charge, then classify, and then count these particles, and works very well for 5 nm to 1 um sized particles [22, 37, 38]. Scanning mobility particle sizer (SMPS), which is a combination of the neutralizer, differential mobility analyzer, and a condensational particle counter, can be used to measure the particle size distribution [39].

Research gaps:

Figure 1-2: a) Brownian diffusion in a differential mobility analyzer (DMA), b) picture of a half-mini DMA, c) Picture of a 1 nm- DMA

As the particle size becomes smaller, the classification is hampered due to Brownian diffusion, as the diffusion coefficient increases, as the particle size decreases.

kT kTC D  fd3 p where, 퐷 is the diffusion coefficient, 퐶 is the Cunningham slip correction factor, 푇 is the temperature, f is the drag force, 푘 is the Boltzmann constant, µ is the viscosity, and 푑푝 is the particle diameter.

For sub-2 nm particles, the DMA transfer function is broadened due to high diffusivity of these particles [40]. High flow DMAs, like the Half Mini DMA (Figure 1.2), attempt to solve this problem by decreasing the residence time considerably in the working section of the DMA. The sheath flow in the Half Mini DMA, is therefore much higher than that of other typical DMAs [32,

41, 42]. As a result, the flow can reach sonic conditions in the working section [37]. Moreover, the length of the working section of Half Mini DMA is reduced significantly as compared to the TSI- short [43] or Nano DMA [42]. These two improvements decrease the residence time of small particles traversing through the DMA, which greatly inhibit the diffusion loss to achieve a better resolution and stronger voltage signal for sub-2 nm particles [44]. Hence, it is of great significance to investigate its performance, such as the flow behavior of both sheath gas and aerosol, the electrostatic field, and most importantly, the transfer function.

After classifying the particles, it is important to count their number concentration, in order to get the particle size distribution. These particles can be counted using a condensational particle counter

(CPC), which grows the particles by condensation of super-saturated vapors on them [35]. These particles then grow to larger droplets, so that laser can detect them. Another approach to count the particles is to measure total current from the charged particles using an electrometer [45]. Both the approaches have their limitations. Electrometer requires fairly high particle number concentration for accurate measurements because of the minimum current that can be detected, and can only detect charged particles. Moreover, if the concentration of the positive ions and negative ions are equal, electrometer will detect no signal. In contrast, CPCs are highly sensitive and have high signal-to-noise ratio, as they count individual particles, and can count neutral as well as charged particles.

Figure 1-3: Condensational particle counter, and default operating conditions

The major limitation of the CPC is the detection limit for minimum particle size [46], which is limited by the Kelvin equation.

4휎푣 푆 = exp ( 푚) 푑푝푘푇

Where, 푆 is the saturation ratio, 휎 is the surface tension, and 푣푚 is the molecular volume. The important research question here is to investigate if butanol based conventional CPCs can be modified in order to activate and count sub-3 nm particles.

1.1.3 Capture of ‘bad’ aerosols

Figure 1-4: Different types of plasmas on a 2-D map of gas temperature, and electron density

Electrostatic precipitators (ESPs) are widely used as particulate control devices in industry and coal power plants to capture fine aerosol particles from emissions. In an ESP, ions are typically produced by a corona discharge, which is a type of plasma created by partial breakdown of a gas in the presence of a relatively strong electric field [47]. The efficiency of an ESP depends mainly on its ability to charge particles and the charging, and thus removal of smaller sized particles, has been a challenge in corona-based devices [15]. Other types of plasmas that are formed by complete gas breakdown contain higher concentration of ions [48, 49], as shown in Figure 1.4 [50].

Plasma is considered the fourth state of matter, which constitutes more than 99.9 % of the universe

[51]. As energy is supplied to solids, they convert to liquid state, and when more energy is supplied, it leads to the formation of gaseous state. Additional energy to gaseous state leads to ionization of

gas phase, which is still charge-neutral, and is termed as plasma [52]. It consists of free electrons, ions, radicals, and meta-stable species. It is important to note here that the plasmas may or may not be in thermal equilibrium, which can lead to different electron and gas temperatures.

Research gaps:

Plasma community has worked on several problems related to nanoparticle synthesis [53-55], space, astronomy, ionosphere [56], TV displays [57], semiconductor device fabrication [58], etc, and a detailed understanding of different types of plasmas is developed. On the other hand, aerosol scientists have developed electrostatic precipitators for particle capture technologies using the DC corona . But, there is a research gap in the application of different types of plasmas in conjunction with electrostatic precipitators, which may enhance particle charging.

1.2 Dissertation Outline

This dissertation has three main objectives:

1. To investigate particle-particle and particle-ion interaction in a flame, and furnace aerosol

reactor (1-10 nm) through controlled experiments and modeling

2. To evaluate the performance of instruments for the classification: Half-mini DMA, and

counting: boosted butanol CPC of 1-10 nm sized particles

3. To characterize particle charging in low-temperature atmospheric-pressure, flow-through

plasmas for development of particle capture technologies

The three objectives are studied and described in the 7 chapters of the dissertation. Each chapter is self-contained, with and introduction, methodology, results, discussion, and conclusions section.

Chapter 2-5 develops the understanding for the particle Chapter 2 and Chapter 3 investigates collisional growth rates for titania nanoparticles (1-10 nm) at high temperatures in free molecular regime through controlled experiments, and molecular dynamics simulations, respectively.

Chapter 4 and Chapter 5 develops the understanding of simultaneous charging and coagulation at high temperature flame reactors (1-10 nm) through controlled experiments, and population balance modeling, respectively. Chapter 6 evaluate the performance of high resolution differential mobility analyzers through COMSOL simulations, whereas Chapter 7 investigates the possibility of using a boosted butanol based CPC to measure sub- 3 nm particles from electrospray, flame aerosol reactor, and Mckenna burner. Chapter 8 aims at developing the understanding of particle charging in a low temperature, atmospheric pressure RF/AC plasma.

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Chapter 2. Collisional Growth Rate and Correction Factor for TiO2 Nanoparticles at High Temperatures in Free Molecular Regime

The results of this paper have been published in Girish Sharma, Sukrant Dhawan, Nathan Reed, Rajan Chakrabarty, Pratim Biswas, (2019) Collisional growth rate and correction factor for TiO2 nanoparticles at high temperatures in free molecular regime, Journal of Aerosol Science, Volume 127, Pages 27-37, DOI: 10.1016/j.jaerosci.2018.10.002

Abstract

Flame and furnace aerosol reactors are used extensively for the synthesis of nanoparticles at high temperatures (800-2000 K), however, there is a limited understanding of the early stages of particle growth by collision at these temperatures. An experimental set-up to quantify the collisional growth rate and collisional correction factor (relative to the kinetic theory of gases) for flame synthesized TiO2 nanoparticles in the free molecular regime is described. Spherical charge-neutral nanoparticles with precise control of size are selected from a flame aerosol reactor (FLAR), and then passed through a downstream furnace reactor tube maintained at a high temperature. Initial and final particle size distributions (PSD) are measured using a scanning mobility particle sizer

(SMPS), and the PSD is represented by a lognormal distribution. The general dynamic equation

(GDE) for simultaneous coagulation and diffusive deposition is solved numerically for a laminar pipe flow using the method of moments. By comparing the experimental data with the model prediction, a correction factor to collisional growth rate is calculated. It was found that for particles in the size range 5-8 nm, there was significant enhancement in the collisional growth rate for TiO2 nanoparticles at 400°C. This enhancement in growth rate decreased as temperature increased (upto

800°C). The collisional correction factor values are compared to that of three existing models in the literature which predict similar trends with temperature, however, these models under-predict the value of the collisional correction factor. Reasons for these deviations from existing models are elucidated.

2.1 Introduction

Flame aerosol reactors (FLAR) have been extensively used to synthesize nanoparticles in gas- phase at high temperatures in a “bottom-up” approach [1-5]. This involves multiple processes taking place including precursor reactions, supersaturated vapor nucleation, vapor condensation, and particle collisional growth. Although flame synthesis is widely used for the production of nanoparticles on an industrial scale, a clear understanding of the early stages of particle formation and collisional growth is still elusive.

Collisional growth, or coagulation, is a process where small particles collide with each other to form larger particles. This process depends on the diffusion coefficient of the colliding particles, which depends on temperature and particle size. As temperature increases, the particle diffusion coefficient increases, and therefore particles have a higher probability to collide. It is very important to quantify this rate, as it determines the shape and structure of the final product.

For instance, if collision occurs faster than coalescence, fractal-like structures are formed, otherwise, spherical particles are formed [6]. Therefore, it is of great interest to accurately predict the rate of collisional growth, and its dependence on particle size and temperature.

A widely used approach to determine the collision frequency function in the free molecular regime is to correct the expression derived from kinetic theory [7] by a factor[8]. This correction factor depends on a variety of inter-particle forces, such as van der Waals force between two neutral particles [9]. Several models have been proposed to understand the role played by the attractive forces. For monotonically attractive potentials, enhancement in collisional growth rate is reported in the literature. Fuchs and Sutugin (1965) proposed a critical impact parameter [8] for the colliding particles, which increases as attractive potentials increase, causing an enhancement

in collisional growth rates. The calculation procedure assumes that the particles approach each other at constant average thermal speed and ignores the role played by the distribution of speeds.

Improving the above model, Marlow and co-workers [10-14] derived an expression for enhancement in collisional growth rates due to van der Waals forces of attraction, accounting for the initial distribution of velocities. Several researchers solved Fokker-Plank equations to predict the collisional correction factor. Sceats (1989) predicted that there is an increase in collisional rates due to attractive forces [15], whereas some literature report that in the limiting case of the free molecular regime, the particles might not stick together on collision, and therefore decrease the overall rate [16, 17]. Several approaches to calculate collisional growth rates were reviewed [9,

18, 19]. and it was concluded that the collisional correction factor can be greater than or less than

1, depending on the dominance of attractive or repulsive forces. A final distinct method to calculate the free molecular collisional correction factor used mean first passage time calculations [20].

They developed a simple relationship to determine the collisional growth rate in the gas phase in the influence of singular contact potentials [21], and predicted enhancement in collisional growth rate.

In addition to models, several experiments have also been performed to study the collisional growth in the free molecular regime. Fuchs and Sutugin (1965) measured the rate of collisional growth for NaCl particles of 5 nm and 9 nm diameter, by comparing the total particle number concentration before and after passing through a tube. Enhancement in collisional growth rates was observed [8]. Following this, the coagulation of NaCl, ZnCl2 and Ag aerosol particles having geometric mean diameter of 5-40 nm using a metal pipe, with improved instruments including a differential mobility analyzer (DMA) with a condensation nucleus counter (CNC) [22,

23]. The experimental data matches well with several models mentioned before, which predicted

enhancement in collisional growth rate. However, clarity on the initial shape of the particles especially for the room temperature experiments, and unavailability of appropriate instrumentation to measure sub 10 nm particles accurately may result in potential inaccuracies.

While there are several experiments and models to understand collisional growth rate at room temperatures, few studies consider the effect of high temperatures. There is an indication of enhancement in collisional growth in high temperature flame aerosol reactors in the literature [24], but detailed studies have not been conducted to establish relationships. This problem arises because chemical reaction, particle formation [25, 26], particle charging [27, 28], and particle growth take place at very small time scales (usually less than 1 second). This creates difficulty in particle measurement and characterization, and model development. To overcome this difficulty, a tubular reactor is used at high temperatures [29, 30]. The experiments were performed to find the coagulation efficiency of soot nanoparticles as small as 2-4 nm. It was found that coagulation is very ineffective due to low sticking coefficients, for this size range, especially at high temperatures. These experimental findings were supported by numerical model [16, 17]. However, this study did not consider the role played by particle charge, and particle morphology in collisional growth. Moreover, the particle size distributions were bimodal with a wide spread, leading to inaccuracies in collisional correction factor calculations. Another set of studies aimed to develop an understanding of collisional growth rate at high temperatures used molecular dynamics simulations [31, 32]. This study predicted enhancement in collisional growth rate of TiO2 nanoparticles, sized range 2-3.5 nm from 273-1673 K, due to dipole-dipole interactions in addition to van der Waals force.

The collisional correction factor strongly depends on material properties, and influenced by inter-particle forces. The literature also reports that there is a lack of systematic experiments at

high temperatures such as encountered in flame and furnace aerosol reactors to study the rate of collisional growth of nanoparticles. While a number of factors influence the early stages of collisional growth rate such as that of ions [28, 33], the focus of this work was to study the role of temperature for collisional growth of neutral particles at elevated temperature. An experimental set-up is developed to quantify the collisional growth rate and collisional correction factor (as compared to the kinetic theory of gases) for TiO2 nanoparticles in the free molecular regime. This is achieved by selecting spherical charge-neutral nanoparticles with precise control of size from a flame aerosol reactor (FLAR), and passing them through a ceramic tube at a high temperature.

Initial and final particle size distributions (PSD) are measured using a scanning mobility particle sizer (SMPS). The general dynamic equation (GDE) for simultaneous coagulation and diffusive deposition is solved numerically for a laminar pipe flow using the method of moments. Comparing the experimental data with the model prediction, a correction factor to collisional growth rate is reported for titania nanoparticles. This is also compared to various model predicted values reported in the literature.

2.2 Methods

2.2.1 Experimental Set up

Figure 2.1a

Figure 2-1. (a) Experimental set up to study collisional growth rate of spherical TiO2 nanoparticles at different temperatures. (b) Characterization of Furnace 1 (at 823 °C), and Furnace 2 (at 400 °C, 600 °C and 800 °C) by using CO2 gas and a gas analyzer. Figure 2.1a shows a schematic diagram of the experimental setup, including a flame aerosol reactor (FLAR), dilution probe, charged particle remover (CPR), and Furnace 1 to obtain spherical charge neutral TiO2 nanoparticles; Furnace 2 to provide additional residence time for collisional

growth at different temperatures; and an SMPS (with a nano DMA) for the measurement of the

PSD. A list of different instruments/reactors used in the experiments, and their role are summarized in Table 2.1. A premixed flat flame was used in this study, due to its high stability, one- dimensionality, and broad usage. A detailed description of the setup is described elsewhere

(Wang., et al., 2017b). The gases entering the FLAR were composed of methane (CH4, Airgas

Inc., Radnor, PA, USA) at 1.3 lpm, oxygen (O2, Airgas Inc.) at 2.8 lpm, and nitrogen (N2, Airgas

Inc.) at 8 lpm. These flow rates were controlled by mass flow controllers (MKS Inc., Andover,

MA, USA).

Sno Instrument Role Nano-Differential Mobility Analyzer (n- Classify particles as a function of mobility 1 DMA) size 2 Condensation Particle Counter (CPC) Measure particle number concentration Provide fixed high temperature 3 Furnace 1 environment (823 °C) Provide variable high temperature 4 Furnace 2 environment (400 °C, 600 °C, 800 °C) 5 Charged Particle Remover (CPR) Remove charged ions and particles

6 Gas Analyzer Measure CO2 gas concentration 7 Tunneling Electron Microscope (TEM) Observe the shape of the particles

Table 2-1. List of instruments and their role in the experiments

To synthesize TiO2 nanoparticles of precise size, a bypass flow of N2 was passed through a bubbler containing titanium isopropoxide (TTIP, Sigma-Aldrich Inc., > 97 %) at a stable temperature of 20 °C. Subsequently, this mixture was fed to the flame, where TiO2 is produced through thermal decomposition, hydrolysis, and combustion of TTIP. The bypass flow is tuned (2-

6 lpm) to get the desired particle size distribution.

Flame synthesized TiO2 particles are sampled using a sampling probe, placed horizontally in a flame, at a dilution flow rate of 36 lpm controlled by a mass flow controller (MKS Inc.,

Andover, MA, USA), which corresponds to a dilution flow of 300. The sampled TiO2 nanoparticles are then passed through a charged particle remover (CPR), which removes the ions and charged particles. CPR consists of a tube, 3/8 inch diameter, with a central rod, which is 1/16 inch diameter. Voltage of 1.5 kV, applied across the central rod and outer tube, removes all the charged particles. Complete removal of charged particles is verified by measuring total particle number concentration using scanning mobility particle sizer (SMPS) without a neutralizer. This is very important to ensure charge-neutral particles for the experimental design, because charged particles can alter the collisional growth rate significantly [34].

The charge neutral stream of particles, thus obtained, is then passed through a ceramic tube

(Alumina AD-998, 90 cm long and 1.9 cm ID) in Furnace 1 (Lindberg Blue M). Furnace 1 is maintained at a constant temperature of 823 °C to ensure that the particles sinter completely.

Another ceramic tube (Alumina AD-998, 84 cm long and 1.9 cm ID) is kept in Furnace 2 (Lindberg

Blue M), and was heated between 400 and 800 °C. PSD is measured at two points, first at the exit of Furnace 1, i.e. at the entrance of Furnace 2; and second at the exit of Furnace 2. Both the measurements are performed after diluting the high temperature aerosol stream exiting the furnaces with room temperature air. The particles can get charged at high temperatures due to thermionic emission from the particles, or ceramic tubes releasing charges [35]. In this work, we measured the fraction of charged particles after Furnace 1 and Furnace 2, and found that more than

99 % of the particles were charge-neutral, at 800 °C and lower temperatures. When the temperature

was further increased to 1000 °C, we found that the ceramic tube generated the additional particles.

Therefore, we restricted our final temperature to 800 °C.

The dilution ratio is calculated before measuring PSD, in both the furnaces, at relevant furnace temperatures by using CO2 and a Horriba PG-250 Portable Gas Analyzer as shown in

Figure 2.2. 1b. In the gas analyzer, CO2 concentration is measured using two pyroelectric element sensors. Different flow rates (1-2 lpm at STP) of CO2 gas were passed through the furnace. The inlet flow rate is measured with the help of a calibrated mass flow controller (MKS Inc., Andover,

MA, USA). The furnace is operated at a fixed temperature, and the exiting flow is then diluted with the dilution air of 12.5 lpm at STP. The CO2 concentration in the exit stream is measured, and the dilution ratio is calculated.

After diluting the exiting flow, a scanning mobility particle sizer (SMPS) is used to measure the PSD. SMPS consists of a neutralizer, which uses a radioactive source (Kr-85) to charge the particles, a nano-differential mobility analyzer (TSI DMA Model 3085), where particles are classified according to their electrical mobilities, and a condensation particle counter (CPC) to count the total number concentration of the classified particles. The data measured by the SMPS is corrected for diffusional loss in the instrument, using circular tube penetration efficiency for aerosols [36]. This is quite important for particle sizes smaller than 10 nm because of their high diffusion coefficient.

Transmission electron microscopy (TEM, FEI Tecnai Spirit) is used to characterize the shape and to confirm the size of the colliding TiO2 nanoparticles. TEM images are analyzed by

using ImageJ software (Rasband, W.S., ImageJ, U. S. National Institutes of Health, Bethesda,

Maryland, USA). Samples are collected on a 300-mesh copper TEM grid using a custom electrostatic precipitator [37]. Nanoparticle size and shape were characterized for each PSD and all different temperatures.

2.2.2 Analysis

In the free molecular regime, in the absence of inter-particle potentials, kinetic theory of gases (KTG) defines the rate of collisional growth (  ) as:

1 112 622 3 6kTb  1 1  11  (v , v ')      v33  v '  (2.1) 4' P vv 

where, kb is the Boltzmann constant, T is the temperature, P is the particle density, v and v' denote the volume of the two colliding particles. The collisional growth rate due to shear flow is found to be 7 orders of magnitude smaller than the Brownian coagulation rate given by Eq. 2.1, and is therefore not considered here.

In actual practice, coagulation rarely occurs in the absence of inter-particle forces. There is a coulombic force between two charged particles, image potential between charged and uncharged particles, and van der Waals force between two neutral particles [19]. This can influence the collisional growth rate significantly, and can either increase or decrease the overall collisional growth rate. To quantify the effect of inter-particle potentials, the collisional correction factor ( 

) is estimated by Eq. 2.2.

   EXP/ MOD (2.2) KTG

Where, EXP/ MOD denotes the collisional growth rate as measured by experiments or through

modeling, and KTG denotes the collisional growth rate as given by the kinetic theory of gases. The magnitude of  depends on the inter-particle forces. If attractive forces dominate over repulsive forces  1, whereas if repulsive forces dominate  1.

Collisional correction factor is calculated by solving the population balance equations, undergoing simultaneous collisional growth and diffusive deposition in a laminar flow in a cylindrical tube. Many experiments in FLAR and FUAR reported in earlier work [38, 39] indicate that the aerosol PSD is nearly lognormal. Therefore, population balance equations can be simplified in the form of three moment balance equations [1, 40, 41] as shown in Eq. 2.3.

 r 2  M B     2U 1  0  1 r M  B M   M 2 avg  2    1/ 3 2 2 / 3  0  R  z r r  r   r 2  M B     2U 1  1  1 r M  B M avg  2    2 / 3 2 1/ 3  (2.3)  R  z r r  r   r 2  M B     2U 1  2  1 r M  B M   2M 2 avg  2    5 / 3 2 4 / 3  1  R  z r r  r 

Where, U avg is the average gas velocity in the furnace tube corrected for thermal expansion of the gas at different temperatures, r is the radial distance inside the tube, R is the radius of the tube,

n is the PSD function, z is the axial distance inside the tube, B1 is the particle diffusivity constant,

and B2 is the slip correlation constant for diffusion, and  are the coefficients for the rate of collisional growth, as given by the kinetic theory of gases, for zeroth and second moment, respectively [42].

The initial conditions for Eq. 2.3 are obtained from the initial PSD entering the ceramic tube in Furnace 2. The partial differential equations are also subjected to boundary conditions,

d M r R 0and Mr 00 for q = 0, 1 and 2. Subjected to these initial and boundary q dr q conditions, three coupled partial differential equations are solved by using an explicit finite- difference scheme at 11 radial points across the tube. This gives a set of 33 coupled ordinary differential equations (ODEs). These equations are then solved by a stiff ODE solver in MAPLE,

and M0 , M1 and M 2 are calculated as a function of both r and z . Following this, the cup mixing

average ( Mq, avg ) of the moments inside the tube at any location, , is calculated by Eq. 2.4.

R M( r , z ) U (1 r2 ) r d r  q avg 0 Mzq, avg () R (2.4) U(1 r2 ) r d r  avg 0

In experiments, an additional mass is lost due to the thermal gradient towards the end of the Furnace 2, which leads to thermophoretic force on the particles towards the tube surface. Since, in the free molecular regime, thermophoretic loss is found to be size independent [6], only the total

number concentration ( Ntot ) is reduced, here. This is achieved by comparison between the final

PSD and the total mass concentration obtained through simulation, and through experiments.

Based on this, the following correction scheme is proposed to balance the mass in both experiments and simulations, given by Eq. 2.5.

EXP TH EXP Mtot NNtot tot SIM (2.5) M tot

TH EXP Here, Ntot is the total number concentration after thermophoretic correction, Ntot is the

EXP experimentally measured total number concentration, Mtot denotes the experimentally measured

SIM total mass concentration, whereas Mtot denotes the total mass concentration based on the simulation.

Collisional correction factor ( ) is calculated by comparing the experimental measurement with the model prediction for final PSD. The value of is chosen such that the final total number concentration obtained experimentally (after thermophoretic correction), matches with the total final number concentration predicted by the model. The same procedure is repeated for different furnace temperatures for two different particle size ranges, and the collisional correction factor is obtained as a function of particle size and temperature.

2.3 Results and Discussion

The method to calculate the dilution is described first. Following this, measurements of initial and final PSD, before and after Furnace 2 are discussed. TEM images are also presented for each measurement. The collisional correction factor values obtained through experiments, are compared to that of three existing models in the literature.

2.3.1 Dilution Ratio

Both the furnaces are characterized at relevant temperatures, using CO2 gas and a gas analyzer to measure CO2 concentration.

Table 2.2 shows the dilution ratio for different temperatures for both the furnaces. Note that the dilution ratio is not calculated according to the furnace temperature and gas thermal expansion, because the temperature at the furnace exit can be much lower than the set point. This temperature drop occurs due to the furnace end effects, and the mixing of dilution flow with the exiting flow from the furnace. This is also evident in Table 2.2, where there is no significant change in the dilution ratios at different temperatures.

Temperature Residence Dilution Furnace (°C) Time (s) Ratio 1 823 - 7.86 2 400 4.57 8.41 2 600 3.53 8.25 2 800 2.87 7.91

Table 2-2. Dilution Ratio and residence time for Furnace 1 and Furnace 2 operated at different temperatures.

2.3.2 Lognormal PSD of spherical TiO2 nanoparticles

Figure 2-2. Measured initial and final particle size distribution, before and after Furnace 2 for T = 400 °C. The PSD is fitted using lognormal particle size distribution for size range: A) dpg = 5-6 nm, and B) dpg = 6-8 nm. Figure 2.2a and Figure 2.2b show the experimental data corresponding to geometric mean diameter of 5-6 nm and 6-8 nm, respectively. Different initial PSD is obtained by adjusting the bypass N2 flow rate (2-8 lpm) that contains TTIP vapors in the premixed flame. Both Figure 2.2a and Figure 2.2b show that the peak corresponding to the final PSD shifts towards the right, with

decrease in the total particle number concentration indicating collisional growth. The average values and error bars are calculated from 10 different measurements for initial and final PSD using

SMPS. The low error indicates that the TTIP bubbler, the premixed flame, and Furnace 1 and

Furnace 2 have stabilized to produce a steady state PSD, which is critical for our experiments.

Moreover, lognormal PSD fits the experimental data very well with errors less than 5%, which suggests that the combined residence time in the flame, probe, and Furnace 1 is sufficient to get a lognormal particle size distribution [38]. This justifies our assumption to represent initial and final

PSD by three parameters for lognormal PSD, i.e. Ndtot,, pg and  g .

Figure 2-3. TEM images for initial and final particle size distribution for average geometric size 5-6 nm a) Initial at 823 °C, b) Final at 400 °C, c) Final at 600 °C, d) Final at 800 °C; and 6-8 nm e) Initial at 823 °C, Final at f) 400 °C, g) 600 °C, h) 800 °C Figure 2.3(a-f) represents the TEM images for initial and final PSD, at three different temperatures (400 °C, 600 °C and 800 °C) for average mean geometric size of 5-6 nm, and 6-8 nm. Most of the particles are found to be completely spherical, except for some partially sintered

particles. At lower temperature (400 °C), the number of partially sintered particles is greater as compared to high temperature (800 °C). Figure 2.3f shows the least perfectly sintered particles because of the increase in size (~8 nm) in addition to the decrease in temperature. This can be explained by the exponential dependence of characteristic sintering time on temperature and quartic dependence on particle size for TiO2 nanoparticles [43, 44]. Another possible reason for the partially sintered particles could be the collisions in the latter part of the tube of Furnace 2, therefore, the particles do not have enough residence time at high temperature after collision to sinter completely. Nonetheless, majority of the particles are sintered, and therefore the assumption of spherical particles in the modeling analysis to calculate the collisional correction factor is justified.

2.3.3 Collisional correction factor ( ) at different temperatures

Figure 2.4 and Figure 2.5 represent the average value for the three parameters Ndtot, pg and

 g , and normalized total mass concentration for initial and final PSD, both obtained from 10 experimental data sets at each temperature, and PSD predicted by Model 1 and Model fit. Model

1 and Model fit represent predicted final PSD using the population balance model for as unity and best fit, respectively. To obtain the model predicted final PSD, and for initial PSD are used as an input to the model.

Figure 2-4. Integral parameters of the size distribution function at three different temperatures 400 °C, 600 °C and 800 °C of Furnace 2, measured before, and after Furnace 2. The average geometric diameter for the experimental data is between 5-6 nm. experimentally measured initial PSD; experimentally measured final particle size distribution; model predicted PSD assuming the value of collisional correction factor as unity; model predicted PSD with a fitted value of collisional correction factor; …...... thermophoretic correction to the final PSD.

Figure 2-5. Integral parameters of the size distribution function at three different temperatures 400 °C, 600 °C and 800 °C of Furnace 2, measured before, and after Furnace 2. The average geometric diameter for the experimental data is between 6-8 nm experimentally measured initial PSD; experimentally measured final particle size distribution; model predicted PSD assuming the value of collisional correction factor as unity; model predicted PSD with a fitted value of collisional correction factor; …...... thermophoretic correction to the final PSD.

The experimental final PSD shows a 5-32% mass lost due to diffusional and thermophoretic loss in the tube of Furnace 2. On the other hand, Model 1 shows that the mass lost due to diffusion varies between 4-10% of the initial mass. Therefore, the additional mass loss is attributed to thermophoretic loss, and the number concentration of experimental final PSD is corrected using Eq. 2.5. This is important to ensure mass balance between the experimental final

PSD, and model prediction of final PSD, and highlighted in both Figure 2.4 and Figure 2.5.

At all the three temperatures, the total number concentration predicted by Model 1 is much greater than the experimental value for the final total number concentration. In terms of geometric mean diameter, Model 1 predicts smaller particles as compared to the measured geometric mean diameter. This clearly shows that Model 1 under-predicts the collisional growth rate. To match the measured final PSD with the Model fit prediction of PSD, different values of collisional correction factor ( 1) are used. It is important to note that matching of the final total number concentration, and not the geometric mean diameter, is used as a criterion. This is done to avoid the errors due to incomplete sintering of these particles in Furnace 2, as shown in Figure 2.3.

Figure 2.4 represents the experimental and model data, for particles in the size range between 5-6 nm, whereas Figure 2.5 represents the data for particles in the size range between 6-

8 nm. Even though the Model fit prediction for the total number concentration, and the total mass concentration matched the experimental data, the Model fit prediction of mean geometric diameter is less than the experimental value, because the particles are assumed to be perfectly spherical in the model. Although TEM imaging shows that the particles are close to being spherical, there are

some partially sintered particles. Furthermore, the model fit predicts slightly larger g as compared

to the experiments. The possible reason for this can be the result of cup mixing average of the three

moments in the model, to obtain final PSD. These larger values of the Model fit prediction of  g further contribute to smaller values of Model fit prediction of final geometric diameter to ensure mass balance.

Figure 2-6. Collisional correction factor ( ) as a function of temperature for two different particle size ranges compared with the different models for a Hamaker constant of 1.99×10-19 J.

Collisional correction factor calculated through experiments for 5-6 nm sized particles (this work); experiments for 6-8 nm sized particles (this work); molecular dynamics simulations for 2 nm sized particles, which includes both van der Waals forces, and dipole moment; ; Marlow’s formula, which considers only van der Walls forces; ……….. mean first passage time calculations, which considers only van der Waals forces of attraction.

Figure 2.6 shows the average values for collisional correction factor ( ) as a function of temperature of the furnace for the two different cases of particle size range. Average value for is obtained by repeating the above discussed set of 10 experiments for initial and final PSD, three times for each temperature. These values are compared with three different models for collisional correction factor from the literature [13, 20, 31]. Marlow (1980) derived an analytical expression, taking into consideration the initial distribution of velocities, whereas Ouyang et al. (2012) performed mean first passage time calculations in the presence of singular contact potentials like van der Waals (vdW) forces of attraction. Both the models are independent of particle size in the free molecular regime, and are a function of Hamaker constant and temperature only. Another model [31] for collisional correction factor performed MD simulations to understand the effect of dipole-dipole attraction in TiO2 nanoparticles, in addition to vdW forces. Unlike, the other two models, this model depends on the particle size as well.

Figure 2.6 shows the comparison of the experimental data with the three models. A value

-19 of 1.99×10 J is used here for the Hamaker constant of TiO2 [45]. The experimental results differ significantly from the models, where only vdW forces of attraction are considered. Possible reasons could be the inaccurate value of Hamaker constant for nanoparticles in this size range [46], as the Hamaker constant is assumed to be independent of the particle size. Furthermore, it is calculated for rutile TiO2 in aqueous medium, whereas flame-synthesized TiO2 nanoparticles in 5-

10 nm size range are close to anatase [47], and the experiments are performed in the gas-phase.

Another possible reason that can contribute to such high values for  , at lower temperature, is the role played by dipole-dipole attractions for TiO2 nanoparticles. These interactions can increase significantly, especially at low temperatures as shown in Figure 2.6.

This model predicts higher value of collisional correction factor for 2 nm sized particles than the other two model. It is important to note that according to the results of MD simulations, increase in size after 2.5 nm decreases the collisional correction factor, which suggests that the model would predict lower value of collisional correction factor for 5-8 nm sized particles. The possible reason for the deviation of experimental data from models is the assumption of constant value of collisional correction factor for the lognormal PSD with a geometric standard deviation, where there are collisions between unequal sized particles. The interaction forces for unequal sized particles can be higher as compared to equal sized particles. This can further contribute to the large average experimental values for the collisional correction factor. To reproduce the experimental data through modeling more accurately, the collisions of unequal sized particles will be studied, in future, through molecular dynamics simulations.

2.4 Conclusions

Collisional growth of selected flame-synthesized spherical, charge-neutral TiO2 nanoparticles with a geometric mean diameter of 5-8 nm have been studied at three different furnace temperatures, 400 °C, 600 °C, and 800 °C in a ceramic tube with laminar flow. The changes in PSD, at the outlet of the tube, have been compared with the population balance model for simultaneous coagulation and diffusive deposition corrected for thermophoretic losses at different temperatures. It was observed that the collisional growth of TiO2 nanoparticles proceeded

faster than the theoretical prediction obtained using the kinetic theory of gases, and the collisional correction factor ( ) was estimated for this system.

The collisional correction factor increased with a decrease in temperature, indicating an important role played by inter-particle forces of attraction. At a lower temperature of 400 °C, the overall attractive forces between particles tend to increase the collisional growth rate, and coagulation proceeds faster than the theoretical prediction obtained using the kinetic theory of gases. As the temperature increases to 800 °C, the collisional correction factor decreases, but is still greater than unity. This suggests that the attractive forces continue to dominate over repulsive forces at high temperatures as well. Comparison with other models suggest that the models under- predict the collisional correction factor. The possible reason for this could be the assumption of constant value of collisional correction factor for the lognormal PSD with a geometric standard deviation, and/or the lack of accurate value for Hamaker constant for sub 10 nm TiO2 nanoparticles.

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Technology, 2006. 40(5): p. 309-319.

44. Buesser, B., A. Grohn, and S.E. Pratsinis, Sintering rate and mechanism of TiO2

nanoparticles by molecular dynamics. The Journal of Physical Chemistry C, 2011.

115(22): p. 11030-11035.

45. Ackler, H.D., R.H. French, and Y.-M. Chiang, Comparisons of Hamaker Constants for

Ceramic Systems with Intervening Vacuum or Water: From Force Laws and Physical

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47. Zhao, B., et al., Ultrafine anatase TiO2 nanoparticles produced in premixed ethylene

stagnation flame at 1atm. Proceedings of the Combustion Institute, 2005. 30(2): p. 2569-

2576.

Chapter 3. Molecular dynamics trajectory calculations for collisional growth rates of titania nanoparticles during gas-phase synthesis at high temperatures

Girish Sharma, Sukrant Dhawan, Rohan Mishra, & Pratim Biswas. (2020) Molecular dynamics trajectory calculations for collisional growth rates of titania nanoparticles during gas-phase synthesis at high temperatures, Journal of Nanoparticle Research, in preparation

Abstract

Flame and furnace aerosol reactors have been widely used to synthesize titania nanoparticles in gas-phase at high temperatures, both on lab as well as industrial scale, However, there is a limited understanding about the early stages of particle formation and their growth mechanism in gas phase. In this work, molecular dynamics trajectory calculations are used to investigate the collisional growth rate of titania nanoparticles in a detailed manner. First, nanoparticle is constructed and equilibrated through simulated annealing, to ensure that there is no bias, or inconsistencies in the equilibration procedure. We find that our approach for equilibration results in particles with low dipole moment which captures the experimental conditions closely.

Following this, particle trajectory based molecular dynamics simulations are set up, where the particles are given random orientations, different velocities sampled from Maxwell Boltzmann velocity distribution, and different impact parameters (푏), to calculate the probability of collision on a 2-dimensional 푏 − 푣 scale. The collisional correction factor is calculated from these simulations for equal and unequal sized particles at different temperatures. We found that unequal sized particles have higher collisional correction factor as compared to equal sized particles. The comparison with respect to existing models, previous molecular dynamic simulations, and experiments is presented, which predict similar trend with respect to temperature, but differ in the actual values for the collisional correction factor. Reasons for this deviation from existing models are elucidated.

3.1 Introduction

Flame aerosol technology has been widely used in industry for the synthesis of a wide range of nanoparticles, including reinforcement materials for polymers like carbon black, and refractive pigments like titanium dioxide [1-4]. Although, industrial scale synthesis of nanoparticles usually focus on the synthesis of particles with sizes over 100 nm, understanding of early stages of particle formation and growth is still elusive [5-8]. It is important to investigate the synthesis of sub-10 nm particles for two main reasons. First, smaller particles are the building blocks for larger particles

[9, 10] , and second, nanometer sized particles have found applications in drug delivery, imaging, etc. [11, 12].

Conventional understanding of particle formation and growth in a flame reactor suggests that, multiple processes, like precursor reaction, supersaturated vapor nucleation, condensation, and collisional growth, take place which affects the size and properties of synthesized particles. It is very important to quantify the overall collisional growth rate, as it determines the characteristics of the final product. Recent studies focused on sub-10 nm particles have found that that along with particle-particle collisions, the interaction of particles with charged species in flame also influence the collisional growth rates of the particles [13, 14]. The simultaneous particle-particle and particle-ion interactions makes it difficult to independently determine the effect of both phenomena on growth rate via experiments [10].

In the free molecular regime, kinetic theory of gases is commonly used to calculate the collisional growth rate of the particles, which is directly proportional to the relative mean thermal velocity, and collisional cross sectional area of the colliding particles [15], and is given as:

8휋푘푏푇 2 훽푖푗,퐾푇퐺 = √ (푎푖 + 푎푖) 푚푖푗

where, 훽푖푗,퐾푇퐺 is the collisional growth rate given by kinetic theory of gases, 푘푏 is the Boltzmann constant, 푚푖푗 is the reduced mass, 푎푖 and 푎푗 represent the radius of entities 푖 and 푗, respectively.

But, several experiments have found that the collisional growth rate for sub-10 nm sized particles is different from that predicted by the kinetic theory of gases. Fuchs and Sutugin, 1965 [16] found that there is enhancement in the collisional growth rate of NaCl particles of size 5 nm, and 9 nm as compared to the growth rates predicted by kinetic theory of gases. Similar values of enhancement were reported for NaCl, ZnCl2, and Ag nanoparticles having geometric mean diameter of 5-40 nm [17, 18]. These experiments were performed at room temperature and the deviation from KTG predicted collisional growth rate was explained through the presence of inter- particles forces.

The interparticle forces, and hence the deviation from KTG predicted growth rate, are function of temperature, however there are a few controlled experiments to measure collisional growth rate of

1-10 nm sized particles at high temperatures. Tsantilis et al. observed that there is enhancement in collisional growth of titania nanoparticles in high temperature flame reactors through population balance modeling [19]. D’Alessio ansd co-workers used a tubular reactor to quantify the collisional growth rate for soot particles. It was reported that 2-4 nm sized soot particles have low sticking coefficients, and they tend to bounce back [20-22], which decreases the overall rate of collisional growth at high temperatures. On the other hand, controlled experiments for titania nanoparticles showed an enhancement in collisional growth [10]. All the experimental findings show that the

collisional growth rate is not only dependent on particle size and temperature, but also on the material properties.

Several models have been proposed to understand the role of inter-particle forces on particle collisions. Fuchs and Sutugin, 1965 [16] proposed a critical impact parameter for the colliding particles based on the attractive potential, where the particles are assumed to approach each other at their mean thermal velocity. As an improvement to this model, accounted for the distribution of initial velocities to calculate the enhancement in collisional growth rate due to Vander Waals forces of attraction. Several other approaches like solving Fokker Plank equations [23] and mean-passage time calculations [24], also predicted an increase in the collisional growth rates. On the other hand, some literature reports that in the limiting case of the free molecular regime, the particles might bounce back, and decrease the overall collisional growth rate [25, 26]. The calculation of the collisional growth rate in the gas-phase was reviewed in the past by [27-30] and based on the experimental evidence, it was concluded that the collisional correction factor could be greater than or less than 1, depending on the dominance of attractive or repulsive forces.

The focus of this paper is to investigate the collisional growth rate of titania nanoparticles through molecular dynamics trajectory calculations. In the past, the experimental work on calculating the collisional correction factor for titania nanoparticles reported that the enhancement is dependent both on particle size and temperature [10]. As the temperature decreases, the collisional correction factor increases for 5-10 nm sizes particles. A similar trend is observed in another study based on molecular dynamics simulations for understanding collisional growth rate of titania nanoparticles

[31, 32]. It was found that for titania nanoparticles sized 2-3.5 nm, there is enhancement in collisional growth rate, which can be as high as a factor of 8.56 for 2.5 nm particles at 273 K. The

high value of enhancement is contributed to dipole-dipole interactions in addition to van der Waals forces.

But, there are drawbacks for both the experiments, as well as, molecular dynamics simulation for titania nanoparticles, performed in the past. In these controlled experiments, the particles were not perfect spheres due to incomplete sintering, especially at lower temperatures (400 °C), and the particle size distribution was not monodisperse. In addition to this, the diffusive and thermophoretic losses of the particles were not measured directly, but estimated using empirical models. On the other hand, previous molecular dynamics calculation for collisional growth rate did not take into account the role played by velocity distribution of particles, and also the approach to equilibrate titania nanoparticles was inconsistent. The nanoparticles were constructed by randomly excising the excess atoms to ensure charge neutrality, which lead to high initial dipole moments in that study. Therefore, the nanoparticle construction created a bias in the collisional growth rates. Some other gaps in the previous MD work included inaccurate calculation for the mean particle velocities, and lack of calculations for the case of collisions between particles of different sizes.

In this work, first the titania nanoparticles of different sizes are equilibrated at high temperatures using a new approach of simulated annealing to ensure nanoparticle construction with low dipole moment, that replicates experiments. Following this, particle collisions are simulated with different initial velocities, impact parameter and orientations to compute the collisional probability. The collisional correction factor is calculated for different particle sizes, and temperatures. Finally, the comparison with exiting models, and experiments is discussed with future directions.

3.2 Methodology

3.2.1 MD Trajectory Calculations

Molecular dynamics simulations were performed using an open source software LAMMPS (Large scale Atomic/Molecular Massively Parallel Simulator) using a GPU (NVIDIA Tesla K20X) at the

Center for high performance computing at Washington University in St Louis. The performance of GPU was found to be ~35 times faster than CPU, which made these detailed simulations possible. To simulate titania nanoparticles equilibration, and collisions, Matsui-Akaogi (MA) potential [33] used. This potential is widely accepted for studying titania nanoparticle sintering, and growth, and has been validated by x-ray absorption spectra data [34, 35]. The MA potential, 푈푖푗, is given as

푞푖푞푗 퐶푖퐶푗 퐴푖 + 퐴푗 − 푟푖푗 푈푖푗 = − 6 + 푓(퐶푖 + 퐶푖) exp ( ) 푟푖푗 푟푖푗 퐵푖 + 퐵푗

where, the three terms on the right-hand side represent electrostatic (Coulomb), dispersion (vdW), and repulsion interactions, respectively. The last two terms constitute a Buckingham potential. The values of particle charges 푞, and the parameters 퐴, 퐵 and 퐶 of atom 푖 (or 푗) are listed elsewhere

[32]. Even though MA potential is unable to capture some structural issues like nucleation for phase transformation inside the nanoparticle, but we believe that these potentials are suitable for characterization of collisional growth rates as a function of equilibration temperature and particle size.

Figure 3-1. Schematic of nanoparticle collisions Figure 3.1 shows the typical simulation set-up for the calculation of collisional growth rate, and the collisional correction factor based on the molecular dynamics trajectory calculations. The orientation-averaged collisional probability as a function of initial relative velocity (v) between the two particles, and the impact parameter (b) is calculated which is then used to calculate the collision rate enhancement. This is achieved by first, generating different orientations by rotating equilibrated clusters through a rotation matrix composed of normalized random numbers. These orientations are important to remove the effect of orientations on final collisional growth rate calculation.

Then, the equilibrated titania nanoparticles, with known velocities of all the atoms of titanium and oxygen, are given initial relative velocity towards each other. This velocity is sampled from the

Maxwell Boltzmann velocity distribution corresponding to the equilibration temperature, and size of the particle. Eight equal spaced values of the velocities on logarithm scale are chosen to span the complete velocity distribution. The impact parameter (푏) is varied from 푏 = 0.5(푑푝1 + 푑푝2)

Å to 푏 = 30 + 0.5(푑푝1 + 푑푝2) Å, and it is found to encompass all the realistically possible collision and miss scenarios. The two nanoparticles were kept at different distances in x- direction,

and simulations were repeated for different values of this distance. It indicated that the distance greater than 3(푑푝1 + 푑푝2) does not influence particle trajectories, as the interactive forces involved at this distance are very small.

These trajectories either leads to collision between the two particles or they miss each other. Each set of trajectory calculations results in determination of 푃(푏, 푣), the orientation-averaged probability of collision for a specified equilibration temperature of the particles of specified size

[36]. The collisional probability as a function of impact parameter (푏), and velocity of collision

(푣) can be used to calculate the collisional growth rate of the particles, as follows,

∞ ∞ 푚 3 푚 푣2 2 3 푖푗 푖푗 훽푖푗,푀퐷 = 8휋 ∫ ∫ 푃(푏, 푣) 푣 √( ) exp (− ) 푏 푑푏 푑푣 0 0 2휋푘푏푇 2푘푏푇

Where, 훽푖푗,푀퐷 denotes the collisional growth rate as calculated by the molecular dynamics trajectory calculations, and this expression is adopted from (Hogan), where the condensational rate coefficient is calculated. The collisional correction factor is given by,

훽푖푗,푀퐷 Collisional Correction Factor = 훽푖푗,퐾푇퐺

A value of greater than 1 for the collisional correction factor would indicate that the attractive forces are dominant, whereas a value of less than 1 would mean that the repulsive forces are dominant

3.2.2 Nanoparticle Equilibration and Collisions

To equilibrate the nanoparticles, we constructed a large Wulff structure of titania nanoparticles in anatase crystal phase with oxygen atoms double the number of titania atoms. The conventional approach involves excising a spherical structure from the large crystal lattice, and removing the excess titanium or oxygen atoms from the surface in order to ensure charge-neutrality. This approach could lead to inconsistencies due to biased structures, non-uniformity, and issues with repeatability. Therefore, instead of excising a spherical structure from this large crystal lattice, we develop a different approach to excise a smaller Wulff structure with charge-neutrality. This structure is then annealed at high temperatures in order for it to sinter and form a spherical titania nanoparticle.

Figure 3-2. Simulated annealing of TiO2 Wulff structure with 252 atoms at high temperature to obtain a spherical TiO2 nanoparticle (dp ~ 1.8 nm)

Figure 3.2 shows that the Wulff structure of titania nanoparticle was first equilibrated in an NVT

(canonical) ensemble at a high temperature T = 3000 K with a step size of 1 fs with a total simulation time of 7 ns. The motion of all the atoms was monitored via a Velocity-Verlet algorithm. It is found that for all the particle sizes, in consideration in this work, the nanoparticle sinters completely to become spherical in shape. Following this, the temperature is decreased at a rate of 125 K/ns in an NVT ensemble. Finally, the spherical nanoparticle is equilibrated for 5 ns at different equilibration temperatures so that the final structure is relaxed appropriately before collisions. The nanoparticles considered here are composed of 252 (1.8 nm), 858 (2.8 nm), 2040

(3.6 nm) and 3990 (4.2 nm) atoms with number of oxygen atoms twice the number of titanium atoms. These nanoparticles were equilibrated at four different temperatures, 500, 1000, 1500 and

2000 K.

For the nanoparticle collisions, the trajectory simulations are performed using LAMMPS with the

Velocity-Verlet algorithm in an NVE framework, in order to keep the energy conserved in these simulations. A time step of 1 fs is used in these simulations and they are carried out until the collision event occurs or one of the nanoparticle leaves the simulation domain without collision.

3.3 Results and Discussions

3.3.1 Dipole Moment of Equilibrated Titania Nanoparticles

Figure 3.3 shows the calculated value of time averaged dipole moment of the equilibrated titania nanoparticles for 5 ns. Figure 3.3a shows the effect of temperature on the dipole moment, for both the calculations for this work for 1.8 nm sized particle, and the previous molecular dynamics simulation work [31, 32], which were performed for 2 nm sized particle. As temperature increases,

Figure 3-3. Time averaged dipole moment as a function of A) temperature, B) particle diameter.

the time averaged dipole moment does not change much, but for the previous work it decreases significantly. We argue that in these simulations, the high dipole moment comes as an artifact because of the particle construction, and equilibration approach, whereas in this work, simulated annealing ensures that the equilibrated spherical nanoparticle represents the liquid like amorphous titania nanoparticle at such high temperatures At high temperatures, the dipole moment reported previously matches well with the calculated values, as the particle gets sufficient energy to relax and equilibrate in previous as well as this work. Therefore, the bias is more prominent at lower temperatures.

Figure 3.3b compares the time averaged dipole moment as a function of particle diameter at a temperature of 500 K. Both the approaches show linear increase in the dipole moment as a function of particle diameter, but the previous MD simulations show a much higher value as compared to

the simulated annealing approach. The random excision, and insufficient equilibration are the factors that contribute to this behavior.

3.3.2 Collisions of equally sized particles

Figure 3-4. Collisional probability of particles of equal size (2.8 nm) as a function of normalized particle velocity, and impact parameter at 4 different temperatures of 500, 1000, 1500, 2000 K.

Once the nanoparticles were equilibrated, their collisions were studied in detail. Figure 3.4 shows the collisional probability of particles of equal size (2.8 nm - 2.8 nm) on a b-v scale at 4 different temperatures (500-2000 K). The red color indicates collisional probability of 1, whereas blue color represents zero collisional probability. The x-axis denotes the initial velocity of impaction, normalized with respect to the velocity mean thermal velocity, whereas y-axis denoted the impact parameter minus the average size of particle collisions. The simulations resulted in either a collision or a miss case, but none of the collisions led to dissociation of the original nanoparticle or bouncing of the surface. This is because the impaction velocities were chosen reasonably around the relative mean thermal velocity, and the additional degree of freedom of the nanoparticle would take up the kinetic energy of impaction.

First observation from Figure 3.4 is that there is enhancement in the rate of collisional growth as the effective collisional cross section area is increased due to interactive forces. The collisional probability decreases, as the normalized velocity increases and the impact parameter increases.

This is quite obvious as the particles with smaller relative velocities spend more time in the vicinity of each other, and the particles with smaller impact parameter are close to each other, allowing interactive forces to attract them towards each other, resulting in higher collisional probability.

There is no sharp change in probability as can be seen from Figure 4, as the collisional probability is obtained by averaging the collisions between particles with different orientations for a fixed size, and temperature, and the collisional probability values are interpolated to obtain this plot. It can also be observed that as the temperature increases, the overall area corresponding to the red color decreases, suggesting lower collisional probability, and therefore lower collisional correction factor. The reader is referred to supplementary information for the collisional probability on b-v scale for collisions between 1.8 nm – 1.8 nm sized particles, and 3.6 nm – 3.6 nm sized particles.

Figure 3-5. Collisional correction factor for equally sized particles as a function of temperature

Figure 3.5 summarizes the simulations for the calculation of the collisional growth rate between the particles of same size, at 4 different temperatures. It can be observed that as the temperature increases the collisional growth rate decreases, which is similar to the prediction of several previous models. But all the empirical or theoretical models only report the limiting case of free molecular regime, and fail to quantify the collisional correction factor for different sizes. On the

other hand, even controlled experiments cannot study collisional growth rates for monodisperse particles. Therefore, molecular dynamics simulations provide accurate values for the collisional correction factors as a function of system temperature, and particle diameter.

3.3.3 Collisions of unequally sized particles

Figure 3-6. Collisional probability of particles of unequal size (1.8 nm, 3.6 nm) as a function of normalized particle velocity, and impact parameter at 4 different temperatures of 500, 1000, 1500, 2000 K

Figure 3-7. Collisional correction factor for unequally sized particles as a function of temperature

Figure 3.6 shows the collisional probability of particles of unequal sizes (1.8 nm – 3.6 nm) as a function of normalized particle velocity and impact parameters. The trends with respect to the normalized velocity and the impact parameter is found to be the same as Figure 3.4. The overall collisional probability also decreases with respect to the increasing temperatures. The reader is referred to supplementary information for the collisional probability on b-v scale for collisions between 1.8 nm – 2.8 nm sized particles, and 2.8 nm – 3.6 nm sized particles. Figure 3.7 shows the collisional correction factor for unequally sized particles at three different temperatures. The trend with respect to temperature is again found to be consistent with previous findings. As the

ratio between the two particles increases, the collisional correction factor increases. Previously, several models [27, 28] have indicated similar trend, but the value was not quantified systematically as a function of particle size. It can be concluded that even though the collisional correction factor increases between the particles of different sizes it is not significantly higher than for the collisions between the same sized particles.

3.3.4 Comparison with experiments and models

Figure 3-8. Comparison of collisional correction factor as calculated through molecular dynamic simulations with experiments, and existing models.

Figure 3.8 compares the molecular dynamics trajectory calculations in this work (1.8 nm, 2.8 nm,

3.6 nm), with the previous molecular dynamics simulations (2 nm), first mean passage time model

(limiting free molecular regime), and the experimental results (5 nm, polydispersed) obtained in the past for titania nanoparticles. First, enhancement is observed in all the modeling and experimental findings for the titania nanoparticle collisions, and as the temperature increases the collisional correction factor decreases. Second, the molecular dynamics based trajectory calculations are closely followed by the mean passage time calculations, whereas the previous MD simulations, and experiments show a much higher value for the collisional correction factor.

There are shortcomings for both the experiments, as well as, previous molecular dynamics simulations. Even though these experiments were performed in a very controlled manner, there were some limitations. The particle size distribution measured was based on the assumption of complete sintering of the nanoparticles, which might not be the case, especially at lower temperatures. Incomplete sintering can lead to higher collisional cross sectional area, and therefore, higher collisional growth rates, and higher calculated values for the collisional correction factor. Moreover, the particle size distribution was not monodisperse but lognormal, which could contribute further to increase the collisional correction factor experimentally. On the other hand, the previous molecular dynamic simulations involved inconsistencies in the dipole moment calculations. But, at the same time it is worth mentioning that all the trajectory based molecular dynamics calculations are performed for spherical titania particles, which are amorphous. The effect of different crystal structures on the collisional correction factor of titania nanoparticles will be studied in the future.

3.4 Conclusions

Collisional growth rate of titania nanoparticles in gas phase at high temperatures is investigated through molecular dynamics trajectory calculations. A new approach of simulated annealing to construct and equilibrate titania nanoparticles is proposed. We find that this approach removes several inconsistencies, and bias of dipole moment, which were present in previous molecular dynamic simulations. The equilibrated titania nanoparticle collisions are then studied by tracking their trajectories. The particles either collide and stick or miss each other; no case of particle bouncing or dissociation is observed. The orientation-averaged collisional probability is found to increase with decrease in the impact parameter (b) and collision velocity (v). The collisional correction factor, calculated from the 2-dimensional b-v map of collisional probability, is found to decrease with increasing temperature for both equal and unequal sized particles. As compared to equal sized particles, unequal sized particles were found to have a higher collisional correction factor, which increases with higher differences in their particle sizes. Finally, the trajectory calculations MD approach is compared with previous models, and experiments. A simple model based on mean passage time calculations is able to explain the detailed MD results, whereas the experiments and previous MD simulations found a much higher value for collisional correction factor. The reasons for these inconsistencies could be the shortcomings of experiments like assumption of complete sintering, and previous MD simulations like bias in dipole moment calculations, which can artificially increases the collisional correction factor. Nevertheless, molecular dynamics trajectory calculations provide accurate quantification of the collisional growth rates, which is crucial for improving the understanding of the early stages of particle formation and growth in high temperature gas-phase synthesis.

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Chapter 4. Role played by charge in early stages (1-10 nm) of TiO2 particle formation and growth in premixed flames

Girish Sharma, Mengda Zhang, Xiaoqing You, & Pratim Biswas. Role played by charge in early stages (1-10 nm) of TiO2 particle formation and growth in premixed flames, Combustion and Flame, in prep

Abstract

The charge on particles plays an important role in the early stages of nanomaterial formation and growth in high temperature material synthesis from flame aerosol reactors. Thus, it is important to study the charging characteristics of sub-10 nm particles. With the development of measurement tools like high-resolution differential mobility analyzers coupled with electrometer, and boosted butanol CPC; the particle size distribution and percentage of charged particles can be measured by two different approaches. In this work, the effect of diluent in the flame (N2 v/s Ar), sampling height, and precursor concentration is evaluated. The percentage of charged particles is higher with

Ar as diluent, as compared to N2. This percentage decreases as height above the burner increases, with positive particles smaller in size as compared to negative particles, owing to different charging mechanisms. Increasing precursor concentration increases the particle size for both neutral and charged particles, as well as the percentage of charged particles. The two measurement approaches, neutralizer-half-mini-DMA-electrometer, and boosted butanol CPC complement each other. They agree well for particles larger than 2 nm, but owing to their limitations, provide the lower and upper bounds for average charge fraction for sub 2 nm particles, respectively.

4.1 Introduction

Flame aerosol reactors (FLAR) are the backbone of the gas-phase synthesis of nanoparticles at high temperatures in a “bottom-up” approach [1-4]. Several processes like precursor reactions, homogeneous/heterogenous nucleation, particle-particle collisions, agglomeration, etc take place in relatively short time scale (~ µs to ms). Although flame synthesis is widely used for the production of nanoparticles on an industrial scale, a clear understanding of the early stages of particle formation and growth is still elusive [5].

The characteristic size dependent properties of nanometer sized particles differ from their bulk counterpart with the most significant effects occurring for 1-10 nm diameters. Due to very high specific surface area, and unique quantum confinement forces, sub-10 nm particles have applications in catalysis [6], bio-medical imaging [7], Cerenkov radiation induced therapy [8] and semiconductor quantum dots [9]. On the other hand, flame aerosol reactor is a highly versatile approach to synthesize nanoparticles on a large scale. This further motivates us to investigate the particle formation, and growth in flame aerosol reactor, with a goal to synthesize particles with precise size, crystal phase and morphology on industrial scale [10].

Few researchers have studied the synthesis process of sub-10 nm particles from flame systems in the past, but several researchers have worked on understanding the soot nucleation, and growth.

Maricq measured the charged particle size distributions (PSDs) and charge fractions of soot particles in premixed ethylene flames by nano-differential mobility analyzer (DMA) and condensation particle counter (CPC) [11]. It was found that they were either neutral or singly charged with both polarity, and the charge fraction increased with increase in mobility diameter.

These measurements were limited to particles larger than 3 nm, due to the low activation efficiency

of CPC and high diffusion loss and low resolution of nano-DMA used in these studies [12, 13]. To shed light on sub-3 nm soot particles, Sgro et al. [14, 15] used a higher resolution TapCon DMA coupled with an electrometer to investigate charged particles, and found that the experimental data agreed well with the Boltzmann charge distribution. Recently, nascent soot particle size distributions down to 1 nm were measured using a 1 nm scanning mobility particle sizer (SMPS), but charge fractions were not reported [16].

To counteract the diffusion broadening of DMA transfer functions, high resolution DMA (Half- mini DMA) with new conﬁgurations and high sheath ﬂow rates (> 100 lpm) was designed [17,

18], which signiﬁcantly reduced the residence time and diffusional loss of classiﬁed particles. By applying an electrometer downstream of the Half-mini DMA, Wang et al. measured sub-3 nm

TiO2 particles from flame reactors successfully [19]. In order to activate sub-3 nm particles in

CPC, several instruments have been developed like particle size magnifiers, which uses diethylene glycol (DEG) as working fluid to grow the particles, and can measure particle size distribution by changing the capillary flow rates. Jingkun et al. [20] developed a two stage CPC, which is now commercialized by TSI, to measure particles as small as 1 nm. On the other hand, several researchers [21, 22] have improved the existing butanol CPC, by increasing the super-saturation, and therefore activating sub-3 nm particles. It has been be argued that this is relatively better approach to activate particles, as butanol is less chemistry dependent than DEG [23].

Previous measurements using enhanced particle detectors provided valuable information about

TiO2 cluster measurements. Wang et al. [24] reported that for CH4 + O2 + N2 flame, majority (>

90 %) of the sub 3 nm clusters were charged; either positively with hydrocarbon group attached to

- TiO2, or negatively with NO3 group attached to it. This was the first study to look at both the physical, and chemical aspects of sub 3 nm particles using enhanced particle detectors, but the

evolution of charge fractions, and particle size distributions to larger particle sizes remained unanswered in this study. Sharma et al. [25] investigated the collisional growth rate of TiO2 particles (4-10 nm) through controlled furnace experiments, whereas Yan et al. [26] studied the effect of dipole-dipole interactions on the collisional growth rate for TiO2 particles through molecular dynamic simulations. Both the studies independently found higher collisional growth rate than predicted by kinetic theory of gases, and proposed a correction factor. These growth rates are important for solving the population balance equations [27, 28]. To further understand the relative effect of particle-particle and particle-ion interactions, simultaneous coagulation and charging models were developed and simulated for flame conditions [25, 29]. It was found that as many as 50% of the particles are charged through diffusion charging mechanism only, depending on the ratio of particle to ion concentrations in the flame. It was also reported that as the particles exit the high ion concentration environment close to the flame front, charged particles coagulate to significantly reduce the charge fraction.

Therefore, all the previous literature on understanding particle formation and growth from molecular clusters to sub-10 nm particles is focused on soot particles. On the other hand, during the synthesis of titania nanoparticles from a flame aerosol reactor, researchers measured a high fraction of charged particles for sub-2 nm sized particles. But several questions remain unanswered like how this high particle charge fraction in sub-2 nm range translates to larger particles (2-10 nm), effect of different diluents (N2 v/s Ar), charging/discharging mechanisms after particles exit the high temperature flame region for this particle size range.

In this work, the role of particle charge in the early stages (< 10 nm) of TiO2 nanoparticle formation and growth is elucidated. High resolution DMA, with electrometer was used to measure particle size distributions for both charged, and neutral particles; whereas a boosted butanol CPC was used

to measure the average charge fraction. This instrumentation was used to study the particle size distribution and percentage of charged particles for different diluents in flame (N2 v/s Ar), height above the burner, and precursor concentrations.

4.2 Methods

4.2.1 Experimental Set-up

Figure 4-1. Schematic of the experimental set-up

Figure 4.1 shows a schematic diagram of the experimental set-up for the measurement of particle size distribution, and charge distribution from the flame aerosol reactor. The experimental setup consisted of a premixed flat flame burner, a high-dilution sampling system, and sub-10 nm particle measurement instruments.

A premixed flat flame was used for this study to generate 1-10 nm TiO2 nanoparticles, due to its high stability, quasi-one-dimensionality, and broad usage. The cold mixture gas consisted of methane (CH4, > 99.5 %, Linde AG) and oxygen (O2, > 99.95%, Linde AG) with either Nitrogen

(N2, > 99.95 %, Linde AG) or Argon (Ar, > 99.95 %, Linde AG) as diluent. A set of mass flow controllers (MKS Inc.) maintained the total flow rates of CH4, O2, and N2/Ar. The velocity of cold gas is kept at 60 cm/s, and flame equivalence ratio at 1. A detailed description of the set-up is provided elsewhere [30]. The dilution sampling system consists of a stainless steel sampling tube with a 0.16 mm sampling orifice embedded in the stagnation plate. TiO2 particles were drawn into the sampling tube through the orifice and diluted immediately by a 30 L/min nitrogen flow in the tube. The appropriate dilution ratio (~800) was determined and used in this work for eliminating chemical reactions and limiting particle coagulation in the sampling tube [31, 32]. The maximum flame temperature, without precursor, is calculated using Chemkin-Pro [33] and kinetic model of

USC Mech II [34].

The sampled particles from the flame were measured by two methods. Method 1 consisted of Kr-

85 neutralizer to impart a known charge to the particles, Half-mini DMA to classify the particles, and electrometer to count them. When the total particle size distribution is measured, the flow through the neutralizer is maintained at 5 lpm, whereas to measure the charged particle size distribution the neutralizer is bypassed, and the inlet flow to the Half-mini DMA is maintained at

9 lpm. It is assumed that the neutralizer results in particles with a steady-state charge distribution

[35, 36], but this assumption is revisited in the discussion section. Both positive, and negative polarities applied on the inner electrode of the Half-mini DMA were used for the measurements of total and charged particle size distribution. Total particle size distribution inferred from negative particles at the outlet of neutralizer is used for the calculation of the percentage of charged particles

as a function of particle size, due to higher mobility of negative ions in a neutralizer, which prefers to achieve Fuchs charge distribution with less residence time [37].

Method 2 consisted of a charged particle remover to remove all the charged particles; a secondary dilution system, and boosted butanol CPC. Charged particle remover (CPR) was a 3/8 inch diameter tube with a central rod of 1/16 inch diameter. Voltage of 0.5 kV, applied across the central rod and outer tube, was able to remove all the charged particles, as verified by measuring total particle number concentration using SMPS without a neutralizer. A secondary dilution system provided dilution ratio between 20 and 300 to satisfy the measurement limit of CPC. A butanol based CPC from TSI (Model 3776) was boosted by changing the capillary flow rate to 69 sccm, and saturation temperature to 45 °C [21, 22]. These conditions ensured the measurement of sub 2 nm particles with high counting efficiency. When the CPR was turned off, both charge-neutral, and charged particles were measured, whereas when it turned on, only charge-neutral particles were measured. The percentage of charged particles was calculated by the two measurements separately.

4.2.2 Data inversion from Half-mini DMA

The raw current data from electrometer, as a function of Half-mini DMA voltage is inverted to the size distribution function in the flame, using Eqn. 4.1.

퐼 푙푛10 × 푑푁 푞푎 × 푒 = ± × 퐷푅, 푑ln푑푝 휂퐻푀 × Ω × 휂푑푖푓푓 × 푓 (4.1)

where 퐼 is the raw current measured from the electrometer, 푞푎is the aerosol flow rate, 푒 is the elementary charge, 휂퐻푀 is the penetration efficiency of the Half-mini DMA, 훺 is the diffusive

± transfer function, 휂푑푖푓푓 is the penetration efficiency in connecting tubing [38], 푓푖 is the steady state charge fraction given by Fuchs theory of charging for positive and negative ions [35, 37], DR is the dilution ratio calculated by the pressure drop across the sampling tube.

The penetration efficiency of Half-mini DMA is given by the empirical expression obtained by

Cai et al. [39], which is based on the experiments performed for different aerosol flow rates, and particle sizes.

푏휂 퐶휂 휂퐻푀 = 푎휂 × exp (− 2) × exp (− ), (4.2) 푑푝 푑푝 × 푞푎

where 푎휂, 푏휂 and 푐휂 are coefficients equal to 0.82, 2.57 and 1.56, respectively; 푞푎 is the aerosol flow rate .

The diffusive transfer function (훺) accounting for diffusion is given by Eqn. 4.3 [40].

푍̃ − (1 + 훽) 푍̃ − (1 − 훽) 휀 ( ) + 휀 ( ) 휎 ̃ √2훿 √2훿 훺(푍, 훽, 훿, 휎) = , (4.3) √2훽(1 − 훿) 푍̃ − (1 + 훽훿) 푍̃ − (1 − 훽훿) −휀 ( ) − 휀 ( ) [ √2훿 √2훿 ]

−푥2 Where, 휀(푥) = 푥 ∙ erf(푥) + 푒 /√휋; 휎 = 퐺퐷푀퐴 ∙ 퐷̃. 퐺퐷푀퐴 is the non-dimensional geometry factor and 퐷̃ is the non-dimensional particle diffusion coefficient [40], 훽 and 훿 are given as follows:

푞푠 + 푞푎 훽 = 푄 + 푄 푚 푐 (4.4)

푞푠 − 푞푎 훿 = (4.5) 푄푚 + 푄푐

where 푞푠, 푞푎, 푄푚 and 푄푐 are aerosol sampling outlet flow rate, aerosol inlet flow rate, main excess air outlet flow rate and clean sheath air inlet flow rate.

4.2.3 Experimental Plan

Table 1 shows the experimental test plan with three objectives. The first objective was to understand the effect of different diluent (N2 and Ar) for both blank flame, and flame with TTIP

(titanium tetraisopropoxide) feed as precursor. The second objective was to study the effect of the sampling height above the burner (3.5 mm – 24.0 mm) with constant TTIP flow. The third objective was to study the effect of TTIP precursor concentration in the flame on particle charging,

4.3 Results and Discussions

4.3.1 Blank Flame Ions (Ar v/s N2)

Figure 4-2. Positive and negative ions generated in the blank flame for CH4-O2-N2 and CH4-O2-Ar with no precursor vapors of TTIP. Table 1 (test 1a).

Figure 4.2 shows the particle size distribution for both positive and negative charged ions generated in the blank flame, which refers to the condition when no precursor vapors of TTIP are introduced in the flame. Two different diluents (N2 and Ar) were studied with equivalence ratio 1, and the flame conditions were chosen to keep the similar calculated maximum flame temperatures, so as to isolate the effect of temperature on the measurements. The calculated maximum flame temperatures for N2 and Ar were 2318 K and 2315 K, respectively.

It was found that the blank flame with N2 (CH4 + O2 + N2) as diluent consisted of both positive and negative ions, which was also observed previously [29, 42]. Argon flame (CH4 + O2 + Ar) was found to produce slightly more positive ions in blank flame as compared to nitrogen flame. These ions showed a broader peak with particle size for nitrogen flame, suggesting multiple species whereas the ion concentration peak is relatively sharp for argon flame. On the other hand, negative ions were observed in nitrogen flame (CH4 + O2 + N2) only, and they were absent in Argon flame

(CH4 + O2 + Ar). Since the flame is charge-neutral, the dominant negative charge carriers were electrons for both Ar and N2 flame, but more in N2 flame. The source of ions in the flame is attributed to be chemical, and thermal ionization [43], where the former is more dominant in the specific flame conditions in this study [24]. Previous mass spectrometric analysis of nitrogen flame has shown very similar size distribution for both positive and negative ions, with former composed

+ - of several hydrocarbon species (CxHyOz ) and latter composed of nitrate ions (NO3 ) [24].

- It can be argued that these ions, especially NO3 , can be formed in the dilution probe, where nitrogen concentration is very high. However, the temperature was measured in the probe to be <

500 K, which was low enough to quench majority of the chemical reactions. Furthermore, measurements were also performed for particle size distribution with Ar as dilution gas in the

probe, and the size distribution did not change significantly. Therefore, we conclude that the reported size distributions of ions represent the ions in the flame.

4.3.2 Effect of diluent on particle charging (N2 v/s Ar)

When TTIP is introduced to the flame, both charged and neutral particles are measured from the flame. Figure 4.3 shows the comparison of the percentage of charged particles in the flame for N2 and Ar as diluent. It is important to note that the precursor loading was kept constant for this comparison, which is evident from the near identical corresponding particle size distribution reported for both the flames, as shown in the SI (Figure B1).

Figure 4-3. Percentage of charged particles for CH4-O2-N2 and CH4-O2-Ar at low TTIP concentration (both polarities). Table 1 (test 1b).

The percentage of charged particles were found to be higher for Ar than N2 flame; which can be explained by higher concentration of ions in the former. Figure 4.3 also shows that the positively charged particles are relatively smaller in size as compared to negatively charged particles.

The possible reasoning behind this could be different charging mechanisms to gain charge for each polarity. Previous mass spectrometric studies focused on sub 2 nm particles have shown that positively charged particles are composed of TiO2 attached with organic groups, and negatively

- charged particles are composed of TiO2 groups attached with NO3 . This indicated a strong particle-ion interactions in the flame. In addition to previous measurements, Figure 4.2 in this work showed that positive charge carriers were mainly positive ions; whereas negative charge carriers were mainly electrons in the blank flame. Therefore, we speculate that particle charging by direct impact of electrons [44, 45] and ion-diffusion [37] were dominant mechanisms for particle acquiring negative charge, whereas incomplete precursor decomposition [42, 46] and ion-diffusion

[29, 37] contributed to positive charge on the particles. This also explains differences in the charge fraction (Figure 4.3) as well as, charged particle size distribution (Figure B2)

4.3.3 Effect of sampling height on particle charging

Figure 4.4 shows the PSD, and percentage of positive, negative and total charged particles at different sampling heights above the burner (HAB). Both positive and negative polarity of the

Half-mini DMA led to similar total PSD, even for sub 2 nm particles, probably due to overall low total particle concentration. Besides, the particle size distribution did not charge significantly with sampling height. This is explained by comparing the characteristic time of coagulation (~ seconds) with the residence time (~ milliseconds), since no persistent nucleation takes place, when TiO2 is formed from TTIP.

Figure 4-4. Effect of height above the burner on particle size distribution, and percentage of charged particles. Table 4.1 (test 2).

Figure 4.4 also shows the corresponding percentage of charged particles for each height, and the particle size distribution for the charged particles in the flame is included in the SI (Figure B3). In contrast to PSD, the percentage of charged particles decreased as the measurements were performed farther from the flame front. The particles very close to the flame front acquire charge as there is continuous generation of ions/electrons in this region due to chemical ionization and charging of particles. As the distance from the flame increases, the concentration of flame ions decreases significantly, reducing particle-ion collision probability. The acquired particle charge can then be reduced by loss of ions/electrons to the surrounding medium or coagulation of charged particles among themselves. The enhanced coagulation of a percentage of charged particles will not change the overall PSD with height significantly, because of their relatively small contribution to particle diameter. Another important thing to note here is that the percentage of charged particles for positive charge were consistently smaller than that for negative charge, which follows the same trend as described earlier. The dominance of different charging mechanisms for different polarities is a possible reason for this trend.

Figure 4.5 summarizes the effect of sampling height on particle number concentration. The total number concentration of the particles did not change significantly with height, and the calculated total number concentration for both positive and negative polarity seems to agree well with each other. On the other hand, the charged particle concentration for both the polarities decreased with increase in sampling height. Very close to the flame (HAB = 3.5 mm), the negatively charged particle concentration is almost 3 times of positively charged particles due to the dominant role played by electrons close to the flame. The electrons are easier to diffuse and charge the particles, as compared to ions, which have a relatively lower diffusion coefficient [45]. As the height

increases, charged particles of both polarities have similar total number concentration, because the electrons are quickly lost due to their high mobility.

Figure 4-5. Total number concentration of charged particles, and total particles measured at different height above the burner. Table 1 (test 2).

4.3.4 Effect of precursor concentration on particle charging

Figure 4-6. Effect of precursor concentration on total particle size distribution, and percentage of charged particles at a fixed height above the burner (3.5 mm). Table 1 (test 3).

Figure 4.6 shows the effect of increase in precursor concentration on particle size distributions, and percentage of charged particles. As the precursor concentration was increased from low to high, particle size distribution shifted to the right, due to the formation of larger particles. The percentage of charged particles also increased with increase in precursor loading in the flame.

Both positive and negative charged particles were found to grow in size, as precursor loading was increased. Negatively charged particles constituted single peak for all the cases, whereas for positively charged particles, two peaks were observed at high precursor loading. This further bolsters our hypothesis that for negatively charged particles electrons impaction is the more dominant pathway for particle charging; whereas for positively charged particles, sub 2 nm particles are formed by incomplete decomposition of precursor, and larger particles are formed by diffusion charging of large ions in the flame. Moreover, as the precursor concentration was increased, larger particles with more surface area were formed, and therefore increasing the probability of particle-ion, and particle-electron collisions. This provides a possible explanation for the observed high percentage of charged particles. The reader is directed to SI, Figure B4, for the details on the charged particle size distribution for both the polarities.

Figure 4-7. Comparison of percentage of charged particles, a) measured using method 1 (neutralizer, half-mini DMA, and electrometer) b) measured using method 2 (boosted butanol CPC); c) calculated from Fuchs theory of charging. Table 4.1 (test 3).

Figure 4.7 summarizes the measurements of different precursor loading on the percentage of charged particles. Here, the x-axis shows the geometric mean diameter of the particle size distribution measured for different precursor loading. This figure also compares the measurements from method 1 comprising of neutralizer, half-mini DMA, and electrometer; measurements from method 2 comprising of charged particle remover (CPR), and boosted butanol CPC; and calculations from Fuchs theory of charging.

Method 1 and Fuchs theory of charging suggest that the percentage of charged particles increases, as the geometric mean diameter increases; whereas method 2 suggests an opposite trend. The two measurement methods seems to flatten out for particles larger than 2 nm, but disagree with each other for sub-2 nm particles. Both the measurements showed their biases in the calculation of the percentage of charged particles. Method 1 was limited because of inability of sub 2 nm particles to reach steady state Fuchs charge distribution. Assuming that the particles would be more charged before they enter the neutralizer, the reported values for the percentage of charged particles depicts the lower-limit of measurement. On the other hand, the measurements from method 2 are limited due to preferential activation, and detection of sub 2 nm charged particles over neutral particles in boosted butanol CPC [47]. This approach tends to overestimate the overall percentage of charged particles, and can therefore be considered as an upper limit. This interpretation of the upper and lower limit of charged percentage is further supported by the convergence of the percentage of charged particles measured by the two methods for particles > 2 nm.

4.4 Conclusions

The role played by ions in particle growth and charging is investigated by studying the effect of diluent (CH4+O2+N2 v/s CH4+O2+Ar), sampling height, and precursor concentration. When Ar is used as diluent, there is higher ion/electron concentration in the flame than nitrogen, and therefore when precursor is introduced, higher percentage of particles acquire charge. This percentage is higher close to the flame front (3.5 mm), with ~3 times more negatively charged particles than positive charged, but as the sampling height is increased, their concentrations decreased, and were roughly equal. The mobility diameter of positively charged particles is found to be consistently

smaller in size than their counterpart. Based on our measurements, the dominant charging mechanism is incomplete precursor degradation and particle-ion interactions for positive particles, whereas electron impaction dominates for negative particles. On the other hand, increase in precursor concentration lead to increase in particle size, with higher percentage of charged particles. Both the measurement approaches, neutralizer-Half-mini DMA-electrometer (method 1) and boosted CPC measurements (method 2) show higher average charge percentage when compared with the Fuchs’ theory of charging. More importantly, they diverge from each other for sub-2 nm particles, but agree well for particles larger than 2 nm. We conclude that owing to inherent limitations, neutralizer-Half-mini DMA-electrometer and boosted CPC measurements complement each other, and represent the lower and upper limit of the percentage of charged particles, respectively. Future studies are needed to fully understand particle-particle and particle- ion interactions in flame aerosol reactors to realize the application of controlled sub-10 nm material synthesis.

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42. Wang, Y., et al., Application of Half Mini DMA for sub 2 nm particle size distribution measurement in an electrospray and a flame aerosol reactor. Journal of Aerosol Science, 2014.

71: p. 52-64.

43. Fialkov, A.B., Investigations on ions in flames. Progress in Energy and Combustion

Science, 1997. 23(5): p. 399-528.

44. Ziemann, P.J., D.B. Kittelson, and P.H. McMurry, Effects of particle shape and chemical composition on the electron impact charging properties of submicron inorganic particles. Journal of aerosol science, 1996. 27(4): p. 587-606.

45. Romay, F.J. and D.Y. Pui, Free electron charging of ultrafine aerosol particles. Journal of aerosol science, 1992. 23(7): p. 679-692.

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Chapter 5. Modeling Simultaneous Coagulation and Charging of Nanoparticles at High Temperatures Using the Method of Moments

Girish Sharma, Yang Wang, Rajan Chakrabarty, Pratim Biswas, (2019) Modeling simultaneous coagulation and charging of nanoparticles at high temperatures using the method of moments, Journal of Aerosol Science, Volume 132, Pages 70-82. DOI: 10.1016/j.jaerosci.2019.03.011

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Abstract

A large number of chemically and thermally ionized species are produced in flames. During flame synthesis of nanoparticles, these ions collide with the particles as do the particles amongst themselves. Both charging and particle-particle collisions decide the particle size distribution, but existing models in flame synthesis often do not consider the coupling of these two effects. In this work, a model simulating simultaneous charging and coagulation is developed using the method of moments (MoM), with the help of asymptotic methods and perturbation theory. This model considers different charged states, as well as the particle size distribution in each charged state and their interactions. To achieve this, first, a simplified polynomial expression for the charging coefficient is derived from Fuchs’ theory. This expression is found to be in good agreement with the complete Fuchs theory expression at high temperatures in the free molecular regime. Next, this expression is used in the general dynamic equation for simultaneous charging and coagulation to derive population balance equations of volume moments. A simplified modeling method, named the monodisperse model (MdM), was used to compare the simulation results. Both the MoM and

MdM showed good agreement in different simulated cases. It was found that for constant bipolar ion environment, the collisional growth increases as the ion concentration increases, and flattens out for high ion concentration (>108 #/cm3). Simulated results also showed that for a unipolar ion environment, MoM predicted that the particle growth by collisions would be more suppressed, resulting in particles with a lower polydispersity index. The simplified expressions for the ion- attachment coefficient used in the MoM works well at high temperatures in the free molecular regime, and that MdM is able to capture the physics of the system well.

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Nomenclature

q,  char Ion-attachment coefficient between an ion (+/-) and a particle with charge q Charge on the particle T Temperature of the system A (q,T),B (q,T) Function of charge ( ) and temperature ( ) in the ion-attachment coefficient p Constant for charging coefficient m Maximum charge acquired by a particle e Elementary charge

 0 Vacuum permittivity

c  Thermal velocity of an ion (+/-) K Conductivity of the particle  Mean free path of ions (+/-)

nq (v,t) Size distribution function for particles of charge

q th M k (v,t) k volume moment of particles of charge k k = 0,1,2 represents 0th, 1st , and 2nd moment of lognormal size distribution

 E Potential energy to thermal energy ratio for the Coulombic potential

Q1,Q2 ,Q3 Fitting parameters for coagulation coefficient of charged particles

B2 , b2 Constants for coagulation coefficient ~ ~ brownian(v,v) Coagulation coefficient between neutral particles of size v and v for Brownian motion

 i, j (v,v~) Coagulation coefficient between particles of size v and , with charges i and j i, j Charge on a particle

N  Number concentration of positive ions ion N  Number concentration of negative ions ion

  Ion recombination coefficient

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N p,0 Initial particle number concentration

Ni,0 Initial ion concentration

q d pg Geometric mean diameter of particles of charge q

q Ntot Total concentration of particles with charge

q  g Geometric standard deviation of particles with charge

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5.1 Introduction

Flame processes have been widely to produce a variety of nanoparticles [1-3]. The particles are formed through nucleation and grow at high temperatures in flame conditions [4-6]. Understanding the growth of nanoparticles is of great importance in controlling their size and shape [7], which are parameters of great interest for energy [8, 9], environmental [6], and biomedical applications

[10]. This understanding is not yet complete because of the difficulties in the accurate measurement of particles below 3 nm [11, 12]. Moreover, experiments show that a large fraction of particles thus produced are charged [12-14], possibly resulting from the high concentrations of both positive and negative ions in the flame, which can be as high as 1010 #/cm3 [15]. Therefore, as particles coagulate, ions can attach to them affecting their overall rate of growth.

In the past, detailed aerosol dynamics models have been developed to understand coagulation, aggregation, and sintering, including the discrete-sectional model [16, 17], moving sectional model

[18] and the method of moments [19]. These models neglected the effect of charging on coagulation rates of particles in a flame environment. When the characteristic time of coagulation is comparable to the characteristic time of charging, models have to account for both phenomena.

There are a few studies on simultaneous coagulation and charging. Oron and Seinfeld (1989) proposed a detailed 2-dimensional sectional model for charge and size and simulated it for both unipolar and bipolar ion environments [20]. Based on these models, Fujimoto et al. (2003) proposed a 2-dimensional discrete-sectional model for charge and size [21]. This model was then used to simulate the formation and growth of titania nanoparticles at 500 oC in a unipolar ion environment. It was found that the product titania’s average diameter, geometric standard deviation, and concentration are affected greatly. Even though these models are detailed, they are

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computationally demanding. A large number of coupled ordinary differential equations must be solved simultaneously, and the complex expression for the ion-attachment coefficient must be calculated at each time step.

One simple monodisperse model has been proposed to study the effect of simultaneous charging and coagulation in flame conditions [22]. This model is easy to solve computationally because the number of ordinary differential equations is reduced significantly. However, the calculations for the complex form of the ion-attachment coefficient given by the Fuchs expression at different temperatures are still computationally demanding. Park et al., 2005 [23] used a simple expression for ion-attachment coefficient derived from Keefe et al., 1959 [24]; and solved the moment balance equations for simultaneous charging and coagulation for singly charged particles in bipolar ion environments. However, the ion-attachment coefficient used in this study is much lower as compared to Fuchs theory [25]. In addition, none of the above models have been used to systematically understand the effect of charging in flame conditions. Recently Wang et al. (2017c) used a monodisperse model to explain trends in the presence of bipolar and unipolar ions in a flame environment [26]. It was found that particle coagulation is highly suppressed in unipolar ion environments. A simple time scale analysis was also proposed by comparing the characteristic time scales of charging and coagulation. MdM captures simultaneous charging and coagulation in flame conditions but does not take into account the size distribution of the particles. Hence, a model considering both the evolution of the particle size distribution and simultaneous coagulation and charging is needed to accurately capture the particle dynamics during combustion.

This work develops such a model, based on the method of moments (MoM), to simulate the simultaneous particle charging and coagulation at high temperatures. Simplified polynomial

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expressions for the ion-attachment coefficients as a function of particle volume are proposed with the help of asymptotic methods and perturbation theory. These expressions are validated at high temperatures and are found to be in good agreement with the exact Fuchs theory formulation.

These expressions are then used in the population balance equation and closed-form equations of particle volume moments are derived. These equations are solved under various conditions in unipolar and bipolar ion environments. Finally, the MoM simulation is compared with the MdM to evaluate the performance of the simulation methods.

5.2 Model description

5.2.1 Ion attachment coefficient

The ion-attachment (charging) coefficient is given by the Fuchs expression for charging [27]. In order to apply the method of moments to the general dynamic equation involving simultaneous charging and coagulation, the charging coefficient needs to be simplified to a polynomial function of the size of the particles. According to Fuchs’ theory, the charging coefficient is a complex function of the charges carried by the particle, particle size, particle conductivity, and the system temperature, as given by Eq. (5.4).

 2         c   exp i  i  k T      b  i  (5.1)  1        i   1 exp i    c   / 4D  exp x dx   i     kbT  0  kbT   

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1 8k T k TZ  16 2 D   M  2 Here, c   b , D   b and     , m e 3 c   M  m 

 The collision probability,i , for the ion-attachment coefficient is

2  b      min,i  (5.2) i      

2 2  2   bmin,i  ra 1 i  ra  (5.3)  3kbT  e 2  i a 3  i r    K  (5.4) 4 r 2 2 2 0  2r r  a 

It is important to note that the expression for ion-attachment coefficient involves minimization of the apsoidal distance, b for the calculation of collisional probability, ; calculation of integrals, and exponentials, which are a function of particle size or volume. In this work, simplified polynomial expressions for the ion-attachment coefficient are derived with the help of asymptotic methods and perturbation theory [28]. The final expression in Eq. (5.5) is presented here, and the reader is referred to the supplementary material for a detailed derivation of the expression.

2 1 q,  3  3  char ~ A (q,T)v  B (q,T)v ,q  0 (5.5) 2 1 0,  3  2  char ~ A (0,T )v  B (0,T )v ,q  0 where

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2 2 3   32 c K  pq  A( q , T ) 2  1   1   , q  0 4 pq1  pq  2q  3  1 2   1  33 c p 1 2  K    B( q , T ) 2   p 1  , q  0 4 pq1  pq  31 K 3 2 q 1  4q (5.6) 2 q 2 3 3 A(0, T ) c , q 0 4 B (0,T ) c  pK , q 0 e2 1 p  4 0 kTb

In Eq. (5.5), A (q,T) and B (q,T) represent the functions of the charge, q , and temperature, T .

Further, v denotes the volume of the particle, p denotes a constant for charging coefficient, K denotes the conductivity of the particles, c  denotes the mean thermal velocity of ions, and  denotes the mean free path of the ions. Note that in Eq. (5.6), and are not functions of the size of the particle.

Eq. (5.5) is valid at high temperatures in the free molecular regime. Figure 5.1 shows a comparison between the exact expression given by Fuchs Eq. (C27) and the simplified expression given by

Eq. (5.5). The plot clearly shows that for small particles ( d p  15 nm), Eq. (5.5) almost overlaps the exact expression. In addition, the effects of temperature, the charge on the particle, and the polarity of the ion are also well captured by the simplified expression. Another way to look at the validity of the expression is to plot the steady state charge distribution using both the expressions, as shown in Figure C1. This figure also indicates good agreement with the Fuchs theory of charging.

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5.2.2 Coagulation Coefficient

The coagulation coefficient of particles in the free molecular regime is given by the kinetic theory of gases for collisions among molecules that behave like rigid elastic spheres [29]. This coagulation coefficient for uncharged particles can then be represented as a function of v and v~ , as shown in Eq. (5.7):

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1/2 112 11 33 (5.7) brownian (,)v v B2   v  v vv  

1 1  3  6  6k Tv  2  b 1  v m In Eq. (5.7), B2      , where 1 and 1 denote the volume and mass of a  4   m1  background gas molecule respectively [30].

For the interaction between charged particles, a correction factor is applied [31].

i, j coag (di ,d j )  W(zi , z j )brownian (di ,d j ) (5.8) where, W  1 E for attractive potentials, and W  exp E  for repulsive potentials and

2  zi z j e  E  . In these equations, zi is the number of elementary charges on the 2 0di  d j kbT particle, di is the size of the particle with zi elementary charges,  is the relative permittivity of

the medium,  0 is the dielectric constant of vacuum, and e is the elementary charge.

The correction factor W is then fitted with the help of a polynomial function to get Eq. (5.9). The detailed fitting is shown in the Appendix, and the final expression is presented here.

1 1 2 1 1 1 W  Q i, jv 3  v~ 3   Q i, jv 3  v~ 3   Q i, j (5.9) 1   2   3

The fitting parameters ( Q1,Q2 ,Q3 ) are summarized in Table 5.1 for different values of  E . Q1,Q2

and Q3 are a function of charge on the two particles, given by i and j , and the temperature of the system, T . Combining Eq. (5.8) and Eq. (5.9), we get Eq. (5.10), which further simplifies to Eq.

(5.11).

1 1 2 1 1 1 i, j ~ ~   3 ~ 3   3 ~ 3    (v,v )  brownian (v,v )Q1 i, jv  v   Q2 i, jv  v   Q3 i, j (5.10)      

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1 1 1 1 2 i, j  1 1    (v,v~)  B b   Q i, j Q i, jv 3  v~ 3   Q i, jv 3  v~ 3   (5.11) 2 2  1 1  1 2 3   v 2 v~ 2      

Here, b2 is adopted from Park et al., 2005 [23] and is given by Eq. (5.12):

2 b i,  j 1  0.867exp  1.01  i  0.867exp  1.01  j  0.33exp  0.211  i 2  g g  g  g   g   (5.12) 2  0.33exp  0.211j  0.644exp 0.512  i  j   g   g g 

 E Q1 Q2 Q3

 E  0 0 0 1 1   3  E  0 0 2p  | ij | 1  6  2 1 3 3 2      0.6  E  0 2p   | ij |  2p  | ij | 1  6   6  2 1 3 3 2      3.0  E  0.6 0.3432 p   | ij | 1.0132 p  | ij | 0.7987  6   6 

3.0  E 0 0 0

Table 5-1. Fitting parameters for the correction factor

5.2.3 Solving for simultaneous coagulation and charging using MoM

During nanoparticle charging, the number concentration of the ions changes and the charges of the particles change. At the same time, charged and neutral particles coagulate to form larger particles.

Both charging and coagulation occur simultaneously and can be represented by the general dynamic equation (GDE), Eq. (5.13) [32]. Ions can also be lost to the particles or recombine among themselves. The balance of the ion concentration is represented by Eq. (5.9):

 q  q  q n (v,t)  n (v,t)  n (v,t) (5.13) t t charging t coagulatio n

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p       qq,  N q  N N  N n v, t (5.14)  ion ion ion ion     t qp

The charging and coagulation terms of the GDE are represented in Eq. (5.15) and Eq. (5.16) respectively. The first and second terms in Eq. (5.15) represent the loss of the particles of size v and charge q when they collide with positively or negatively charged ions respectively. The third term represents the increases number of particles of size and charge when particles of charge q 1 collide with positively charged ions. The fourth term represents the gain in particles of size

and charge when particles of charge q 1 collide with negatively charged ions. The first term of the coagulation part of the GDE represents the gain in the particle number concentration due to collisions between particles of size v and charge i with particles of size v  v and charge q  i .

The second term represents the loss due to coagulation of particles of charge and size with particles of all other sizes and charges. The charge on the particle is assumed to vary from  m to  m .

 q q,  q q,  q n (v,t)   N ion n (v,t)  N ion n (v,t) t charging (5.15) q1,  q1 q1,  q1  N ion n (v,t)  N ion n (v,t)  1 v nq(,),(,)(,) v t   i, q i v v  v  n i v  t n q i v  v  t dv  t coagulation 2 i 0 (5.16) m   nq ( v , t )   q, i ( v , v ) n i (,) v  t dv  im 0

Eq. (5.13–5.16) are a set of coupled integro-differential equations. The simplest model, MdM, assumes a monodisperse particle size distribution, which simplifies Eq. (5.13–5.16) to a set of

4m 4ordinary differential equations [26]. Although the MdM for coagulation only has been shown to agree with the detailed discrete-sectional model [17, 33] and the MoM [30] for

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coagulating systems, it is not clear if the agreement would hold for simultaneous charging and coagulation. In this work, Eq. (5.14–5.16) are integrated to get a closed form moment balance for

q q q three moments ( M 0 ,M1 , and M 2 ) for each charge q . Although it is now required to solve a set of 6m5 ordinary differential equations, it is still computationally faster than the two-dimensional discrete-sectional formulation. Note that the value of m , which is the maximum charge a particle can acquire, is assumed to be 4 in this work. Figure 5.2 shows the schematic comparison of MoM and MdM.

Figure 5-2. Schematic diagram of the monodisperse model (MdM) and the method of moments (MoM)

The polynomial functions of the ion-attachment coefficient and the coagulation coefficient are respectively substituted in Eq. (5.15) and Eq. (5.16). The equations are then integrated to get a set of ordinary differential equations for the three moments [30]. For each charge , the total particle

q q number concentration Ntot , the geometric average diameter d pg , and the geometric standard

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q q q q deviation g can be derived from M 0 , M1 , and M 2 , as shown in Eq. (5.17–5.19). A generalized

th q expression to calculate the k volume moment, M k is represented by Eq. 5.20.

q q Ntot  M 0 (5.17)

1 3 q  6 q 3/ 2 q 2 q 1 2  d pg  M0  M1  M 2  (5.18)  

 q q  2 q 1 M M ln   ln  0 2  (5.19) g 9 q 2  M1  

k q q q9 22 q Mk M0  v g exp k ln  g (5.20) 2

5.2.4 Charging terms of the GDE

The value of ion-attachment coefficient from Eq. (5.5) can be used to derive Eq. (5.21) from Eq.

1 1 (5.15). The ion-attachment coefficient shows dependence on v 2 or v 3 as the value of q changes.

Therefore, the value of  in Eq. (5.21) can be equal to 1 2 or 1 3 . The generalized representation of the value of is shown in Eq. (5.22). Eq. (5.21) is then integrated after multiplying with v k to obtain Eq. (5.23).

2 2   3    3   q  A (q,T)v   q  A (q,T)v   q n (v,t)   N ion n (v,t)  N ion n (v,t) t         charging  B (q,T)v   B (q,T)v  (5.21) 2 2   3    3   A (q 1,T)v   q1  A (q 1,T)v   q1  N ion n (v,t)  N ion n (v,t)          B (q 1,T)v   B (q 1,T)v  1   , when q 0 2 (5.22) 1   , when q 0 3

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q In Eq. (5.23), M k (v,t) with k = 0, 1, and 2 represents the zeroth, first, and second volume moment of the lognormal particle size distribution for each charge q .

 q   q   A (q,T)M 2  A (q,T)M 2  q  k    k   3 3 M k (v,t)   N ion   N ion  q t charging  q    B (q,T)M  k   B (q,T)M  k    (5.23)  q1  q1  A (q 1,T)M 2   A (q 1,T)M 2   k   k  3  3    N ion   N ion  q1  q1  B (q 1,T)M  k   B (q 1,T)M  k     

5.2.5 Coagulation terms of the GDE

Similar to the charging terms of the GDE, the expression for the coagulation coefficient, Eq. (5.16), is applied to the coagulation terms of the GDE described by Eq. (5.11). The resultant equation is then integrated after multiplying with v k to obtain Eq. (5.24), Eq. (5.25), and Eq. (5.26) for k = 0,

1, and 2 respectively.

 i j i j i j QijMM1(,)(,) 1 0 QijMM 2  1 0 MM  1 1 i  j  q  ij2  6 2 3   b2 (,)gg m  i  m i j i j i j m  j  m Q( i , j ) M M  2 M M  M M 3 1 0 1 1 2 1 6 3 6 3 2 q qi i q i q M 0 MM01 MMMM1 0 1 1  B2   (5.24) t Q(,) q i2  Q (,)qi 6 2 3 coag 1 qi 2 q i q i MM10 MMMM1 0 1 1 2 6 2 3  b (,)qi  2 ggq i q i q i m  i  m MMMMMM1 02 1 1  2 1   6 3 6 3 2 Q3 (,) q i  MMMMMMi q2 i q i q 1 0 1 1 2 1 6 3 6 3 2

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ij i j i j MM10 MMMM5 0 1 1   Q(,)(,) i j2  Q i j 6 2 3 12i j i j i j MMMMMM1 1  4  1  1  1 i  j  q   ij 2 3 2 6 b (,)   2 gg i j i j i j  m  i  m MMMMMM7 02 5 1 1 2 m  j  m   Q(,) i j 6 6 3 2 3  3 i j i j i j  2MMMMMM4 1  1 1  5 1  q   3 6 6 3 2  M1   B2  (5.25) t  qi q i q i  coag MM10 MMMM5 0 1 1    Q(,)(,) q i2  Q q i 6 2 3  12q i q i q i   MMMMMM1 1  4  1  1  1  2 3 2 6  b (,)qi  2 ggq i q i q i m  i  m MMMMMM7 02 5 1 1 2  6 6 3 2 3 Q3 (,) q i  q i q i q i 2MMMMMM4 1  1 1  5 1 3 6 6 3 2 

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 ij i j i j MM30 MMMM11 0 3 1 2 6 2 3 i j i j i j QijMM( , ) Qij ( , )  2 MM  2 MM 1 1 2 2 5 1 1 4 2 6 2 3 ij i j i j 2MM11 MMMM1 2 7 1 i  j  q ij2 6 3 2  b2 (,)gg m  i  m i j i j i j m  j  m MMMMMM2 13 0 11 1 3 2 6 6 3 2 3 ij i j i j q Q3( i , j ) 2 M 7 M 1 42MMMM5 4 1 5 (5.2 M 2   B 6 6 3 2 3 t 2  coag i j i j i j 6) MMMMMM1 2 2 7 1  8 1 6 3 6 3 2  qi q i q i MM21 MMMM11 0 3 1  2 6 2 3 Q12(,)(,) q i Q q i  MMMMq i q i  MMqi 3 0 7 1 21 2 3 2 6  b (,)qi  2 ggq i q i q i m  i  m MMMMMM13 02 11 1 3 2  6 6 3 2 3 Q3 (,) q i  q i q i q i 2MMMMMM7 1  2 1  8 1 3 6 6 3 2

0 0 0 It can be easily shown that Eq. (5.24-5.26) simplifies to the moment balance of M 0 , M1 , and M 2 for uncharged particles in the free molecular regime, which are identical to the equations proposed by Lee et al., 1984. Further model validation with the experimental measurements from Alonso et al., 1999 [34] is discussed in the supplementary material. Eq. (5.23) and Eq. (5.24-5.26) are then

q combined to get Eq. (5.27) for the overall change in M k for simultaneous charging and coagulation.

 q  q  q M k   M k   M k  (5.27) t t char t coag

It is important to note here that these equations are derived with the assumption of lognormal particle size distribution for both charged and neutral particles. A more detailed approach of

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Lagrange interpolation of moments can also be used, where particle size distribution is not constrained to be lognormal [35].

5.2.6 Ion Balance

The ion balance on the positive and negative ions is given by Eq. (5.28). The first term represents rate of generation of the ions, the second term represents the loss of particles due to recombination, and the third term represents the loss of ions due to their attachment on the particles.

1   i  i   A (i,T )M 2  B (i,T)M 1    3 3  im   m          i  i N   q  N N  N  A (i,T)M 2  B (i,T )M 1  (5.28) ion ion ion ion  3 3 t  i1    0  0   A (0,T)M 2  B (0,T)M 1   3 2   

5.3 Simulation Results and Comparison with the MdM

The set of ordinary differential equations Eq. (5.21) and Eq. (5.22) were solved simultaneously

q using VODE solver in Python®. The overall mass balance was checked by summing M1 over all charges and was found to be constant at each time step for the entire simulation time. This simulation time of 1 second was chosen to describe the flame conditions because it corresponds to typical residence time of particles at high temperatures. The particle size distributions for each charge and ion concentration were then evaluated under different initial conditions, using MoM.

Following this, the results were compared with the MdM for both unipolar and bipolar ion environments. The parameters used in the simulation are summarized in Table 5.2.

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Parameter Values 103-1010 #/cm3 Initial Positive Ion Concentration ( Ni,t0 ) 103-1010 #/cm3 (bipolar)/0 #/cm3 (unipolar) Initial Negative Ion Concentration ( Ni,t0 )

Positive Ion Mobility and Mass 1.54 cm2/Vs and 140 amu Negative Ion Mobility and Mass 1.97 cm2/Vs and 70 amu 108 / 1010 / 1012 / 1013 #/cm3 Initial Particle Concentration (all neutral) ( N p,t0 ) Initial Particle Diameter 0.4 nm/ 1 nm Temperature 1200 / 2400 K Ion Recombination Coefficient 10-13 m3/s

Table 5-2. Parameters used in the simulation of particle simultaneous charging and coagulation.

5.3.1 Charging in a unipolar ion environment

The changes in average geometric diameter and particle number concentration with time are shown in Figure 5.3 and Figure 5.4 respectively.

Figure 5.3a and Figure 5.3c show the results obtained using the MoM, while Figure 5.3b and Figure

5.3d show the results obtained using the MdM for same initial conditions. In Figure 5.4, the particle size growth is hampered over time because most of the particles acquire similar charges, which leads to repulsive forces. The same trend can be seen for both MdM and MoM, because the number concentrations drop by similar ratios. Even though the trend is similar, MoM predicts the coagulation of charged particles to be even less than for MdM. Possibly, the particles are charged faster in MoM, which includes the particle size distribution unlike to MdM where a fixed size is assumed. As shown earlier, the ion- attachment coefficient increases as the size of the particles increases. Therefore, in MoM, the larger particles become more charged while the smaller particles remain less charged. Overall, compared with the MdM, MoM predicts that more particles acquire

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charge. Therefore, we conclude that the inclusion of the size distribution in the model favors more charging.

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Figure 5-5. Evolution of geometric standard deviation as a function of time at two different temperatures using MoM, with and without charging effects in a unipolar ion environment. Subplots represent initial particle-to-ion concentration ratios of a) 0.01 b) 1, c) 100, and d) 1000. Note the different scales of the x- axes and y-axes.

Figure 5.5 shows the change in geometric standard deviation as a function of time using MoM for different initial particle-to-ion concentration ratios. Geometric standard deviation approaches 1.35 in free molecular regime for the coagulation of neutral particles [36]. This can be observed in the

Figure 5.5c and 5.5d, where particle initial number concentration is high enough for the particles to coagulate and reach a self-preserving size distribution. Figure 5.5 also shows that when unipolar charging effects are incorporated, the geometric standard deviation follows the same trend, but settles at a lower value. The possible explanation is that the charging probability of smaller particles is less than that of larger particles, resulting in less charged fraction of smaller size

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particles. These particles are scavenged by the larger particles, and therefore the geometric standard deviation reduces as compared to 1.35. Therefore, unipolar charging environment should be exploited further to synthesize more monodisperse particles experimentally.

5.3.2 Charging in a bipolar ion environment

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Figure 5.6a and Figure 5.6b show the increases in average geometric particle diameter for MoM and MdM respectively, as a function of time at two different temperatures in a bipolar

environment. At the very low particle concentration ( N p,o Ni,o  0.01 ), there are negligible increases in particle diameter. Both MoM and MdM predict only very small changes in particle diameter due to charging when compared to the base case of coagulation-only. In the other case

where the particle number concentration is high ( N p,o Ni,o 100 ), Figure 5.6c and Figure 5.6d

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show that the evolution of particle size for MoM and MdM are similar and there is a negligible effect of charging. As expected, there is a little effect of a bipolar ion environment when the ion concentration is much lower than the particle concentration. As time increases, the ion concentration reduces even further as the oppositely charged ions recombine. The effect of temperature is also studied which shows similar trends. Figure 5.7 represents decrease in the total number concentration of particles as a function of time, is another way to represent the effect of bipolar ions on particle growth.

In certain flame conditions, ions are continuously produced by chemical ionization while they continue to recombine as well, which can cause a constant ion concentration. To understand such a system, we assumed the particle concentration to be constant (1017 #/cm3) for particles of size 1 nm for a simulation time of 4 seconds at T = 1200 K, and solved the population balance equations.

MoM was simulated for different ion concentrations in the flame.

Figure 5.8 shows the effect of different ion concentrations on the total particle number concentration as a function of time. It is observed that the ion concentration less than 106 #/cm3 seems to have a little effect on the total particle concentration, but as the ion concentration increases, the overall rate of coagulation increases, and the particle number concentration drops even further. Figure 5.9 compares the final number concentration with coagulation and charging

both included in the simulation, normalized to the coagulation-only case, NNtot__ coag char tot coag , as a function of ion concentration. Figure 5.9 also shows the percentage of charged particles as the ion concentration increases. It is observed that as the ion concentration increases to 107 #/cm3, there is a sharp increase in the percentage of charged particles, which seems to flatten out on further

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increasing the ion concentration. Similar trend of flattening is observed for the total number concentration.

Figure 5-8. Effect of different ion concentration on the total particle number concentration as a function of time. Here, the particle concentration = 10^17 #/cm3.

In a constant bipolar ion environment, increase in the ion concentration leads to increase in the charging of neutral particles, thereby increasing the concentration of both positively, and negatively charged particles. Oppositely charged particles experience attractive force, whereas the particles of same charge experience repulsive force. The interplay between the attractive and repulsive forces decides the overall rate of collisional growth. The collision of opposite charged particles lead to the formation of neutral particles of larger size, which then get charged by ion- particle collision, and the process continues. After increasing the ion concentration beyond 107

#/cm3, the percentage of charge particles reach a steady value. This value represents the balance

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between the attractive and repulsive forces in the bipolar constant ion environment. The normalized final particle number concentration also follows similar trend, and begins to flatten out at high ion concentration.

Figure 5-9. Evolution of normalized average particle size and percentage of charged particles as a function of ion concentrations ratio. Here, the particle concentration = 10^17 #/cm3.

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5.4 Conclusions

The Fuchs charging theory is coupled with method of moments (MoM) aerosol dynamics model to simulate bipolar/unipolar ion environments at high temperatures. The complex expression for the ion-attachment coefficient in Fuchs’ charging theory is first simplified to obtain polynomial expressions as a function of volume of the particle. These expressions are then used to simulate aerosol dynamics coupled with charging at high temperatures in the MoM. Closed form expressions for three volume moments are derived. The results from the MoM agree well with the monodisperse model (MdM). MoM predicts that in a unipolar ion environment, particle growth is suppressed slightly more than predicted by the MdM, and the size distribution is less polydisperse as compared to the case where charging effects are not considered. This difference is significant even for 1000 times lower ion concentration as compared to particle concentration. For constant bipolar ion environment, the collisional growth increases as the ion concentration increases, and flattens out for higher ion concentration. Simulation with MoM could provide further insights by including the size distribution. To conclude, MdM is reasonably able to capture the physics of simultaneous coagulation and charging in bipolar ion environments, whereas in unipolar ion environments, MdM predicts less charging and more coagulation than MoM.

5.5 References

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Chapter 6. Numerical modeling of the performance of high flow DMAs to classify sub-2 nm particles

Girish Sharma*, Huang Zhang*, Yang Wang, Shuiqing Li & Pratim Biswas (2019) Numerical modeling of the performance of high flow DMAs to classify sub-2 nm particles, Aerosol Science and Technology, 53:1, 106-118, DOI: 10.1080/02786826.2018.1549358

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Abstract

While there are several computational studies on differential mobility analyzers, there is none for high flow differential mobility analyzers (DMA) to classify nanoparticles less than 3 nm. A specific design of a high flow differential mobility analyzer, a Half Mini DMA, is investigated to predict its performance through numerical modeling in the incompressible flow regime. The governing equations for flow field, electric field and aerosol transport are solved using COMSOL

5.3. The transfer function of the Half Mini DMA is compared with that of a Nano DMA (TSI

3085). The results show that both the height of the transfer function and resolution (R) of the Half

Mini DMA are much better than those of Nano DMA in sub-2 nm particle size range. Finally, the transfer function of Half Mini DMA is evaluated for different values of aerosol flow rate to the sheath flow rate (q/Q). Comparison of the simulated transfer function with existing models from

Knutson-Whitby [1] and Stolzenburg [2] is also elucidated. It is found that the former model overestimates the resolution; whereas the latter is close to the simulation results for q/Q above

0.067. This work provides a useful method to study the flow regimes and transfer function of a high flow DMA.

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6.1 Introduction

Differential mobility analyzers have been extensively used to measure and classify particles over a wide range of sizes, from micrometers down to nanometers [1, 3]. Since the introduction of

DMAs, several studies have employed them to understand the airborne particle size distribution, and environmental pollutants [4]. On the other hand, DMAs serve as a unique technique to synthesize particles with a strict control of size [5] using different aerosol reactors [6]. Several researchers have also used tandem DMAs to understand the collisional growth and charge distribution of particles in the atmosphere [7], as well as several aerosol reactors [8-10].

There is a growing interest to extend the lower limit of DMAs to measure nanoparticles made of a cluster of few molecules. To achieve this, different types of DMAs have been developed, namely Caltech radial DMA (RDMA), nanoRDMA, the Grimm nanoDMA and the Karlsruhe-

Vienna DMA [11]. These high resolution DMAs have been used for the measurement of sub-2 nm particles in a variety of applications, such as atmospheric nucleation of aerosols [12], determination of gas phase protein densities [13], understanding the early stages of particle formation and growth in aerosol reactors [14-16], quantifying sub-2 nm filtration efficiency of fibrous filters [17, 18].

However, for sub-2 nm particles, the DMA transfer function is broadened due to high diffusivity of these particles [3]. High flow DMAs, like the Half Mini DMA, attempt to solve this problem by decreasing the residence time considerably in the working section of the DMA. A short residence time implies that a high voltage is required to classify these particles, thereby, increasing the resolving power (R) [19, 20]. It is important to note that residence time is but one factor in

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determining R. Stolzenburg (1988) [2] and, later, Flagan (1999) [21], showed that the Peclet number for migration can be reduced to neV/kT. The sheath flow in the Half Mini DMA, is therefore much higher than that of other typical DMAs [1, 22, 23]. As a result, the flow can reach sonic conditions in the working section. Moreover, the length of the working section of Half Mini

DMA is reduced significantly as compared to the TSI-short [22] or Nano DMA [24]. These two improvements decrease the residence time of small particles traversing through the DMA, which greatly inhibit the diffusion loss to achieve a better resolution and stronger voltage signal for sub-

2 nm particles [14]. Hence, it is of great significance to investigate its performance, such as the flow behavior of both sheath gas and aerosol, the electrostatic field, and most importantly, the transfer function. Few studies [25-27] have analyzed the DMA transfer function through experiments using a tandem configuration, where the first DMA was used to classify and obtain monodisperse aerosols under a constant voltage, and the second DMA was used in scanning mode to obtain the size distribution of the classified aerosols to determine the resolution. At the same time, the numerical approach provides a convenient way to predict the performance of the Half

Mini DMA, as well as to optimize the DMA design.

Chen and Pui (1997) [28] developed a comprehensive model to predict the performance of the

DMA for nanoparticle measurements. In this model, the flow field is described by Navier Stokes equations assuming axisymmetric geometry and steady state, and Laplace’s equation is used to describe the electric potential. The aerosol flow is regarded as the continuous phase to obey the convective diffusion formulation. This model was used to get the optimized design for Nano DMA.

Hagwood (1999) [29] proposed a Monte-Carlo based methodology for particle Brownian motion for parabolic and plug flow in a DMA. Deye et al. (1999) [30] used a commercial computational fluid dynamics (CFD) software FLUENT to model the two-dimensional axisymmetric

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computational domain coupled with a particle trajectories routine in a DMA. Song et al. (2006)

[31] solved the Langevin equation for particle motion and used a commercial CFD solver to obtain the flow and electric field to study the performance of the Long DMA. Mamakos, Ntziachristoset, and Samaras (2007) [32] numerically solved the convective diffusion equation of particles based on the given flow and electric field, to evaluate the Knutson-Whitby triangular transfer function and the Stolzenburg diffusive transfer function in long and Nano DMAs. Martínez-Lozano and

Labowsky (2009) [33] solved the same equations from Chen and Pui (1997) [28] by a commercial software COMSOL to verify performance of their isopotential Nano DMA. All these studies are focused on the understanding of the transfer function for relatively low flow rates in the working section. To the best of our knowledge, no effort has been made to numerically predict the performance of high flow DMAs like a Half Mini DMA. As the flow could reach the sonic conditions in the working section of these high flow DMAs [19], previous numerical models cannot be applied directly, as all the models are based on incompressible flow assumption. The diffusion coefficient and the drag force coefficient are typically estimated for incompressible flow conditions [34]. Further, it is also meaningful to understand the flow regime in the working section for experimental operations or structure optimization.

In this paper, first, a scaling law analysis is performed to determine the flow regime in the working section of a design of a high flow DMA, the Half Mini DMA. Details of the numerical model are then described. The transfer function of the Half Mini DMA is compared with that of a conventional Nano DMA (TSI 3085). The performance of both the DMAs are evaluated under different flow rate ratios.

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6.2 Model Development

The configuration of a 4/2 type (short bullet) Half Mini DMA is described in detail. The Half Mini

DMA is operated in a wide range of sheath flow rates ranging from 25 lpm [27] to over 700 lpm

[19]. Therefore, it is imperative to establish the flow regime as the details of the numerical model will accordingly have to be established. In this paper, the Half Mini DMA is modeled for the incompressible flow regime. Several researchers [14-16, 27, 35, 36] have operated the Half Mini

DMA with moderately high sheath flow rates (≤ 250 lpm). Moreover, with the new design of Half

Mini DMA [37], resolution as high as 25 is obtained for sheath flow rates of ~ 150 lpm. This further motivates us to model the Half Mini DMA in the incompressible flow regime.

6.2.1 Configuration of Half-mini DMA

Figure 6.1(a) shows the schematic of the 4/2 type (short bullet) Half Mini DMA. The length of the working section L, is 4 mm, and the difference between the outer radius (Rout = 6 mm) and inner radius (Rin = 4 mm) of the DMA is 2 mm. The width of the aerosol inlet silt is 0.254 mm (0.01")

[20]. The upstream laminar sheath flow mixes with the annular injection of aerosol flow before it comes into the working section. Different voltages can be applied to the inner cylindrical electrode to let the particles with the corresponding mobility exit through the aerosol outlet slit, while the sheath flow exits through the working section and then to the diffuser.

6.2.2 Flow Regime Calculations

A scaling law analysis is used to distinguish the sheath flow regime in the working section. Since clean air is used as the sheath gas, it is assumed that it is an ideal gas, and the flow is isentropic from the entrance to the exit [19, 38]. The parameters of sheath gas are shown in Figure 6.1(b),

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where ρ, p, T, u, M and A are respectively, gas density, pressure, temperature, velocity, Mach number and cross-section area. The subscript 1, 2 and 3 denote the positions at the sheath flow inlet, the working section and the sheath flow outlet, respectively.

Figure 6-1. Schematic of the Half Mini DMA a) main geometry b) notations for sheath flow parameters.

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For the sheath gas in the working section (cross-section 2) and the exit (cross-section 3), the mass continuity equation can be described by Equation (6.1),

휌2푢2퐴2 = 휌3푢3퐴3. (6.1)

As the assumption that the sheath flow is isentropic [38], the relation between u2 and u3 or ρ2 and

ρ3 can be given as follows

1 훾−1 1+ M2 2 푢3 M3 2 2 = ( 훾−1 2) , (6.2) 푢2 M2 1+ M 2 3

1 훾−1 1+ M2 훾−1 휌3 2 2 = ( 훾−1 2) , (6.3) 휌2 1+ M 2 3

where γ is the adiabatic index of the sheath gas. Equations (6.2-6.3) are solved to obtain the Mach number at any cross-section, which determines the flow compressibility of the sheath gas with different flow rates. Combining Equations (6.1-6.3), we get

훾+1 훾−1 1+ M2 2(훾−1) 퐴3 M2 2 2 = ( 훾−1 2) . (6.4) 퐴2 M3 1+ M 2 3

Here T3 is assumed to be the atmospheric temperature (293 K), and Table 6.1 lists all the known variables. Therefore, M2 is calculated as a function of the sheath flow rate Q3 (Q3 = Q).

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2 Q3 (lpm) A2 (m ) u3 γ T3 (K) M3

100-740 2 2 Q /A 1.4 293 푢3 π(푅표푢푡 − 푅푖푛) 3 3 √훾푅푔푇3

Table 6-1. Different variables used to understand the flow regime in the working section

6.2.3 Numerical Model

The sheath flow is described by the constant-density (or incompressible) Navier Stokes equations which are included in the supplementary material. In order to decrease the computational time without reducing the numerical accuracy, a two-dimensional axisymmetric geometry is selected

[28, 33]. For boundary conditions of the flow fields, both the inlet and outlet aerosol flow rates are set equal to q. At the aerosol inlet, the initial velocity profile is set as the mean speed corresponding the aerosol flow rate (q) over the area of the inlet surface. The orientation of the jet for the aerosol flow is normal to the inlet surface. The flow rate at the aerosol outlet and the sheath outlet is set to be q and Q, respectively. For the sheath flow inlet, the gauge pressure is set to be zero as the boundary condition. The effect of gauge pressure and the inlet length of the trumpet on the flow field discussed in detail in the supplementary material.

When solving for the electric field, the electric potential φ is obtained by solving the Laplace’s equation as given below:

∇2휑 = 0. (6.5)

The electric intensity E vector is given as

푬 = −∇휑. (6.6)

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For the boundary conditions for Equation (6.5), the inner electrode is assigned a negative voltage, and the outer surface is grounded.

The aerosol particles are assumed to be in continuous phase in the DMAs. This implies that they are a component of the fluid phase, and not in the transition or free molecular regime. The convective diffusion equation used to describe the number concentration (N) of the particles is given as

2 (풖 + 푍푝푬) ∙ ∇푁 = 퐷∇ 푁, (6.7)

where Zp and D are the particle electric mobility and the particle diffusion coefficient, respectively, which are calculated as

퐶푠푙𝑖푝푛푒 푍푝 = , (6.8) 3휋휇푑푝

푘푇퐶 퐷 = 푠푙𝑖푝, (6.9) 3휋휇푑푝

where Cslip is the slip correction factor provided in Friedlander (2000), n is the number of elementary charges on the particle, e is the elementary charge, μ is the dynamic viscosity of sheath gas, dp is the particle mobility diameter, k is the Boltzmann constant, and T is the sheath flow temperature assumed to be 293 K here. The boundary conditions for the aerosol number concentration, N, is set to zero at the wall. N is assumed to be uniformly distributed at the aerosol inlet, and the gradient of N is assumed to be zero at the aerosol outlet, the inlet and outlet of the

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sheath flow. The Navier Stokes equations and Equations (6.5-6.9) are solved using the commercial

CFD software COMSOL 5.3. The simulation zone is discretized using a free triangular mesh with a finer mesh for the zone between the inlet and outlet of the DMA. A sensitivity analysis of mesh size is performed first, and the reader is referred to the supplementary material for details on refined mesh, optimal mesh size, and numerical diffusion considerations.

6.3 Results and Discussions

This section describes the sheath flow rates for compressible and incompressible flow regimes, followed by the discussion of the results from the numerical model. First, the flow, electric, and particle concentration fields are examined. Then, the transfer function and performance of the Half

Mini DMA is compared with the Nano DMA.

6.3.1 Flow Regime and Mach Number

Figure 6.2 shows the change in Mach number (M2) and gas velocity (u2) in the working section as a function of the sheath flow rate (Q). Owing to the translation of random thermal energy (퐶푝푇0)

푢2 into directed kinetic energy (퐶 푇 + ) as the gas is accelerated to high velocity by a large pressure 푝 2 drop, the temperature (T) and density (ρ) change while the mass is conserved. As a result, Mach number and velocity do not vary in the same way, and the curves deviate from one another. The incompressible flow is defined as the regime where resulting density and temperature change are sufficiently small that they can be neglected. The consideration of temperature is important here, because it determines the speed of sound, which is the normalizing factor used in calculating the

Mach number (M). Figure 6.2 also points out for the incompressible flow regime i.e. M < 0.3, Q should be less than 368 lpm. The highest flow rate simulated in this work is 230 lpm, thus

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validating the incompressible flow regime assumption. This value of sheath flow rate used is consistent with several experimental studies [14-16, 27, 35, 36]. On the other hand, there are several studies where the maximum reported value of Q (Qmax_rep) is about 740 lpm [39]; thus requiring compressible flow simulations. This is the subject of a following paper to be done by the authors.

1.0 0.9 (740,0.88) 300 0.8 250 0.7 0.6 200 2 0.5

M 150 (m/s) incompressible flow region 2 0.4 u 0.3 100 0.2 368 lpm 50 0.1 230 lpm 0.0 0 100 200 300 400 500 600 700 The studied region in this paperQ (lpm)

Figure 6-2. Flow regime in the working section. Black-solid line: Mach number vs. flow rate; Blue-dashed line: velocity vs. flow rate.

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6.3.2 Flow, Electric and Concentration Fields

Figure 6.3(a) shows the sheath flow field within the lower part of trumpet and the whole cylindrical region for q = 9 lpm and Q = 136 lpm [14]. The aerosol inlet and outlet sections are enlarged to show the velocity magnitude and streamline. Figure 6.3(b) illustrates the axial velocity profiles at different locations. Figure 6.3(c) shows that the axial velocity profile of the main flow (Q = 136 lpm) within the working section of the DMA is flat, with two boundary layers at the inner and outer electrode. As q increases, the boundary layer thickness increases towards the outer wall, and decreases slightly towards the inner wall. This is due to the larger radial inertia of the entering aerosol jet, which pushes the main sheath flow towards the inner electrode. Figure 6.4 shows the contour of electric potential and streamline of electric field with a -300 V applied voltage. The electric field is found to be uniform in the working section.

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147

Figure 6-4. Electric field with the applied voltage (-300V) on the inner electrode.

Figure 6.5 illustrates the convective flux for the aerosol as a function of increasing applied voltage. Increasing the voltage directs the flow direction of charged particles towards the inner electrode.

The transfer function (Ω) is the key parameter to determine the DMA performance. Ω is defined as the ratio of inlet to outlet aerosol convective flux as

∬ 푁풗∙푑풔 훺 = 푒푥𝑖푡 , (10) ∬𝑖푛 푁풗∙푑풔

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where 풗 and 푑풔 are the particle flow velocity and surface element [28]. It is important to note that the calculated Ω considers only the working section of both the Half Mini and Nano DMA [1, 28,

33].

A dimensionless mobility of the classified particles (푍̃) is defined as the ratio of the particle mobility (Z) to the centroid electrical mobility (푍∗) of the transfer function

푍 푍̃ = . (6.11) 푍∗

Figure 6-5. Convective flux (mol·m-2·s-1) fields of aerosol with increasing magnitude of the inner electrode voltage in working section (dp = 1.4 nm, q = 9 lpm, Q = 136 lpm).

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6.3.3 Transfer Function of Half-Mini DMA compared to Nano DMA

The centroid electrical mobility (푍∗) is given by

∗ 푄 푅표푢푡 푍 = ∗ ln ( ) , (6.12) 2휋퐿푉 푅𝑖푛

In Equation (6.12), 푉∗ is the voltage where Ω reaches its maximum value. Hence, the DMA resolution (R) is defined as

푍∗ 푅 = , (6.13) ∆푍푓푤ℎ푚

where ∆푍푓푤ℎ푚 is the full width of the transfer function at 50% of its maximum value [21].

Here, our simulation conditions for the flow rates (q = 9 lpm and Q = 136 lpm) and the particle mobility sizes are assumed to be same as the experimental case 1 and 3 by Wang et al. (2014) [14].

The particles are assumed to carry a single elementary charge. Figure 6.6(a) shows the transfer function with increasing applied voltage to classify particles of different dp. It can be observed that the larger particles need a larger applied voltage for classification. The transfer functions are triangular in shape with the appearance of tails on both sides, and rounding of the top, due to the high diffusion coefficient of sub-2 nm particles. In Figure 6.6(b), the simulation peak voltages, at which the transfer function is maximum for each particle diameter, are compared with the experimental data [14]. The changing trend of the simulation and experimental data agrees well, and the relative errors between the simulation and the experimental voltages are below 5.7%. Two mechanisms may explain this difference. First, the direction of the aerosol flow through its inlet

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slit may not be perfectly axisymmetric in the experiments, but our model assumes the aerosol flow to be symmetric in two-dimensional computational domain. Second, the flow rate in experiment was not measured directly, but was calculated based on the mobility values of monodisperse organic ions [40]. The difference of the gas properties used in the experiment and simulation may also contribute to this small deviation.

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(a) d =1.4 nm 90 p

dp=1.8 nm 80 dp=2.0 nm 70

(%)  40

0 200 300 400 500 600 700 800 Peak Voltage Peak Voltage Voltage (V) Peak Voltage

(b) 800 Simulation Exp. Data (Wang et al., 2014) 700

600

500

Peak Voltage (V) Voltage Peak 400

300

1.4 1.5 1.6 1.7 1.8 1.9 2.0

dp(nm)

Figure 6-6. a) Transfer function vs. voltage for two different values of dp. b) Comparison between the simulated and experimental peak voltages for different particle diameters.

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Figure 6-7. Comparison of transfer function (Ω) between Half Mini DMA and Nano DMA for sub-2 nm particles. Ω only counts the particle transmission in the DMA work section.

Figure 6.8 shows resolution (R) for sub-2 nm particles for both the Half Mini and Nano DMA. It is found that, for dp = 1.4 nm, the simulated R of Half Mini DMA equals 11.4, which is close to the experimental value of 10 [14]. For the Half Mini DMA, R goes up gradually from dp = 0.7 nm to 2 nm. On the other hand, R for a Nano DMA increases with dp linearly. For the dp range from

0.7 to 2.0 nm. The value of R of the Half Mini DMA is greater than 9.4, while R of the Nano DMA varies from 1.4 to 4.5, which clearly shows that the resolution is much better for the classification of sub-2 nm particles.

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Half Mini DMA 12 Nano DMA

R 6

0.8 1.2 1.6 2.0

dp (nm)

Figure 6-8. The comparison of Resolution (R) of Half Mini DMA and Nano DMA under different particle mobility sizes (q/Q=9/136).

It should be noted that the recent experimental work [27] shows the transmission of sub-2 nm particles of Half Mini DMA are much lower than those calculated by our simulations, indicating that the particle loss in other sections of the DMA play an important role. In this study, the transmission efficiency of sub-2 nm particles for both the Half Mini DMA and Nano DMA were constrained to the working sections only. This is due to the lack of detailed information of the inlet and outlet configuration, and the corresponding dimensions; and more importantly, the

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computational burden caused by adding an asymmetrical aerosol inlet to the simulated geometry.

Therefore, in our numerical model, the particle loss in the inlet annular chamber and the outlet aerosol tube is not considered.

Further, because of the axisymmetric geometry of our model in this paper, the influence of non- uniform aerosol inlet flow on the Half Mini DMA transfer function was not evaluated. Attention should be paid here that a non-uniform distribution of the aerosol inlet flow would result in a local change of voltage-mobility relationship, where the classified particles become less monodisperse, reducing the DMA resolution. The non-uniform distribution is important for previous versions of the Half Mini DMA, which is greatly improved in the newer models by using a circular ring at the aerosol inlet [20].

6.3.4 Performance under different q/Q ratios

To evaluate the performance of Half Mini DMA under different flow rates, the ratio of q to Q is varied. The particle mobility size is fixed at 1.4 nm and q is chosen to be 3 lpm and 5 lpm. Figure

6.9 shows the transfer function versus DMA voltage for increasing Q. It is found that as V increases, the maximum value of transfer function decreases. This verifies numerically the changing trend of the experimental data reported in Figure 6.4 of de la Mora and Kozlowski (2013)

[19].

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(a) 80 Q q=qin=qout=3 lpm 70 60 50

(%) 40

 30 20 10 0 50 100 150 200 250 300 Voltage (V)

(b) 90 Q q=qin=qout=5 lpm 80 70 60 50

(%)  40 30 20 10 0 100 200 300 400 500 Voltage (V)

Figure 6-9. Transfer function vs. voltage for Half Mini DMA a) q = 3 lpm b) q = 5 lpm. Figure 6.10 compares the simulated transfer function to the theoretical transfer function by

Knutson and Whitby (1975) [1, 2, 42]and Stolzenburg (Stolzenburg 1988; Stolzenburg and

McMurry 2008). Figure 6.10(a) shows that the peak values for Ω are 100% for all the Knutson-

Whitby transfer functions which are triangular in shape, and do not consider the effect of diffusion.

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The width of each triangle shrinks with decreasing q/Q. The simulated resolutions in Figure 6.10(a) are 7.3 and 18.4, which are both smaller than 10 and 40, as predicted by Knuston-Whitby for q/Q

= 1/10 and 1/40, respectively. It is important to note that even though the resolution for the case with q/Q = 1/40 is greater than that with q/Q = 1/10; the overall height of the transfer function is lower. The decrease in the height of the transfer function is attributed to the tail occupying an additional area. In order to keep the total area under the curve constant, the peak height decreases to compensate for this increase in area. Now, for a high sheath flow rate, and q/Q = 1/40, the width of the triangular transfer function is smaller as compared to that for q/Q = 1/10. Therefore, the appearance of the tail will lead to larger drop in the overall height to keep the overall area constant.

Figure 6.10(b) compares the simulated transfer function to the Stolzenburg diffusive transfer function. The height of the Stolzenburg transfer function decreases as q/Q is reduced, which is consistent with our modeling results. Ωmax for Stolzenburg transfer function is as high as 70% and

50% at q/Q = 1/10 and 1/40, respectively, however, the simulation results show the maximum value of 80% and 65% with higher width of the transfer function. This shows that our modeling results predict higher particle transmission ability of the working section of the Half Mini DMA than the theoretical prediction by Stolzenburg (1988) [2].

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(a) 100 Simu. q/Q = 1/10 90 Simu. q/Q = 1/40 Theo. q/Q = 1/10 80 Theo. q/Q = 1/40 70 60

 50  40 30 20 10 0 0.8 0.9 1.0 1.1 ~-1 Z

(b) 80 Simu. q/Q = 1/10 Simu. q/Q = 1/40 70 Theo. q/Q = 1/10 Theo. q/Q = 1/40 60

 40  30

0 0.8 0.9 1.0 1.1 1.2 ~ Z-1

Figure 6-10. The simulation (Half Mini DMA) and theoretical transfer function for different q/Q (q = 3 lpm) at dp = 1.4 nm under a) the non-diffusion theory (Knutson and Whitby 1975) b) the diffusion theory (Stolzenburg 1988; Stolzenburg and McMurry 2008).

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Figure 6.11 compares the simulated and theoretical values by Stolzenburg (1988) [2] for resolution (R) at different q/Q. R is 7.3 and 7.8 for q = 3 and 5 lpm, respectively at q/Q = 0.1, while

R increases to 18.4 and 19.6 for q = 3 and 5 lpm, respectively at q/Q = 0.025. The theoretical R closely follows the trend with the simulated R. Particularly, for higher values of q/Q, the simulated

R agrees very well with the theoretical values. A possible reason for this slight deviation at high Q could be that there still exists small intrinsic numerical diffusion issues with the computational code. Besides, some assumptions of the theoretical derivation of the diffusion transfer function, such as the neglecting of diffusion in the streamwise direction, and the neglecting of cross-stream shear[42] , could cause higher prediction of R than that obtained by models. The largest Q that could be obtained by the convergent solution of COMSOL here is 230 lpm. It was found that the simulated R for q/Q = 0.93/230 is 30.4, whereas it is found to be larger than 50 for the same q/Q but Q ~ 740 lpm (de la Mora and Kozlowski 2013; de la Mora and Barrios-Collado 2017). This mismatch may be due to the compressible flow at Q ~ 740 lpm, as compared to our simulations which are performed in the incompressible flow regime. To further this understanding, future work will be focused on modeling the compressible sheath flow in high flow DMAs.

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Simu. q = 3 lpm Simu. q = 5 lpm 30 Theo. q = 3 lpm Theo. q = 5 lpm Simu. q = 0.93 lpm

R 20

0.00 0.02 0.04 0.06 0.08 0.10 q/Q

Figure 6-11. The simulation and theoretical resolution of Half Mini DMA for different q/Q at dp = 1.4 nm. Note that the simulation point denoted by triangular corresponding to q = 0.93 lpm and Q = 230 lpm.

6.4 Conclusions

A numerical model is developed to predict the performance of a high flow DMA, the Half Mini

DMA (Rout = 6 mm, Rin = 4 mm, L = 4 mm) for the first time. A numerical model is developed to solve the flow field, electric field, coupled with the aerosol transport, and the equations are solved by COMSOL 5.3. The simulation is done in the incompressible flow regime for a sheath flow rate

(Q) less than 368 lpm (corresponding to M = 0.3). The electric field is found to be uniform in the working section. Then, the transfer function of Half Mini DMA is evaluated, and the simulated

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peak voltages and resolution are found to be in good agreement with the experimental values. For particles in the sub-2 nm range, the height of the transfer function of the Half Mini DMA is over

5.8 times larger than that of a Nano DMA at dp = 0.7 nm. Even for 1.8 nm particles, the ratio of these two heights is still more than 2.7 times for q/Q = 9/136. The resolution of both Half Mini

DMA and Nano DMA increases with increasing dp. But the resolution of Half Mini DMA is much better that that of Nano DMA. For example, the magnitude of R is less than 2 at dp = 0.7 nm for a

Nano DMA, but R is over 9 for the same dp for the high flow Half Mini DMA.

The transfer function of the Half Mini DMA is investigated under different q/Q. The height of the transfer function is found to decrease as the magnitude of Q increases at fixed q. The comparison of the simulated transfer function with the theoretical models by Kunston and Whitby

(1975) and Stolzenburg (1988) shows that the height of the simulated transfer function Ω is higher than that obtained by Stolzenburg’s theoretical model where particle diffusion was considered.

The simulated resolution of the Half Mini DMA closely follows the trend with the Stolzenburg’s theoretical model, but predicts slightly lower resolution for smaller values of q/Q. This deviation can be attributed to the intrinsic numerical diffusion of the particle transport computational codes, and some assumptions, such as neglecting of diffusion in the streamwise direction, and neglecting of cross-stream shear in Stolzenburg’s theoretical model.

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Nomenclature A: area of the cross-section of DMA, m2

-1 -1 Cp: specific heat capacity at constant pressure, J·kg ·K

Cslip: slip correction e: elementary charge, C

E: electric field intensity, V/m dp: particle mobility diameter, nm ds: surface element, m2

D: diffusion coefficient, m2/s g: gravity acceleration, m/s2 k: Boltzmann constant, m2·kg·s-2·K-1

L: length of the working section of DMA, mm

M: Mach number of the sheath gas n: number of elementary charges on the particle

N: particle concentration, #/m3 p: pressure of the sheath gas, Pa q: aerosol flow rate, lpm qin: aerosol flow rate at inlet slit, lpm qout: aerosol flow rate at outlet slit, lpm

Q: sheath flow rate, lpm

Qmax_report: maximum sheath flow rate of a pump reported in the literature, lpm

Rg: ideal gas constant, J/(kg·K)

Rin: radius of the inner cylinder of DMA, mm

Rout: radius of the outer cylinder of DMA, mm

R: DMA resolution

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T: temperature of the sheath gas, K

T0: upstream stagnation temperature of the sheath gas, K u: velocity magnitude of the sheath gas, m/s u: velocity of the sheath gas, m/s v: velocity of the particles, m/s

V: DMA voltage on the inner electrode, V

* V : DMA voltage at Ωmax, V

Z: classified particle electrical mobility, cm2/(V·s)

푍̃: non-dimensional classified particle electrical mobility

Z*: transfer function centroid electric mobility, cm2/(V·s)

2 Zp: particle electric mobility, cm /(V·s)

γ: adiabatic index of the sheath gas

μ: dynamic viscosity of sheath gas, Pa·s

ρ: density of the sheath gas, kg/m3

φ: electric potential, V

∆푍푓푤ℎ푚: full width of the transfer function at 50% of its maximum value

Ω: transfer function

Ωmax: height of transfer function (or the maximum value of Ω)

Subscript

1: sheath inlet

2: working section

3: sheath outlet

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resolution for 1–30 nm particles: Design and fabrication considerations. Journal of

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20. de la Mora, J.F., Expanded flow rate range of high-resolution nanoDMAs via improved

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Chapter 7. Measurement of sub 3 nm flame- generated particles using ultrafine boosted butanol CPC

Girish Sharma, Mengda Wang, Michel Attoui, Xiaoqing You, Pratim Biswas. (2020) Measurement of sub 3 nm flame generated particles using ultrafine boosted butanol CPC. Aerosol Science and Technology (2020), in preparation

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Abstract

While condensation particle counters (CPCs) are routinely used to measure particle number concentrations for 3-1000 nm particles, there detection efficiency for sub-3 nm particles remain relatively poor. In this study, we evaluate the performance of ultrafine butanol based CPC (TSI

3776) for the measurement of alkyl ammonium halide ions, and flame-generated particles of titanium dioxide (TiO2) and soot. Homogenous nucleation of butanol vapors, and detection efficiency of THAB ions are systematically evaluated for a range of saturator temperature, 39-

45°C, and capillary flow rate, 30-70 sccm. We find that the optimal conditions with minimal background corresponds to saturator temperature of 45°C and capillary flow rate of 70 sccm.

Flame generated particles of TiO2 and soot were activated more readily than the alkyl ammonium halide salts of similar mobility diameters, especially in the sub-1.6 nm mobility size range, whereas above 1.6 nm the detection efficiency is independent of particle material, but depends on particle size. The negatively charge on the particles is found to promote their activation with butanol vapors leading to higher activation efficiencies than positively charged particles. Finally, the importance of butanol as working fluid, and its calibration for precise measurement of sub-3 nm particles is discussed. This will enable the researchers to perform experiments using ‘conventional’ CPC in boosted conditions for the understanding of early stages of particle formation and growth in different aerosol reactors.

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7.1 Introduction

Early stages of particle formation and growth (1-5 nm) have attracted attention of aerosol scientists for several decades [1]. For atmospheric aerosol, it is important to study the nucleation of new particles from molecular clusters, as they play a crucial role in cloud formation, climate change and suspended particulate matter [2]. Ultrafine particles generated through fossil fuel combustion involves both primary [3] as well as secondary formation pathways [4]. The secondary aerosol formation from precursor vapors is not only limited to fossil fuel combustion, but also diesel/gasoline engines [5] and 3D printers [6]. On the other hand, gas-phase synthesis of nanoparticles in a ‘bottom-up’ approach has recently received tremendous attention due to their unique thermal, acoustic, electrical, and optical properties. The material synthesis involve precursor to particle conversion, which form the building blocks for larger particles. Therefore, a better understanding of particle formation using real time measurements would envisage the development of future particle capture technologies to clean air pollution [7], as well as, synthesis of ultrafine particles with precise control of size, morphology, and chemical composition [8, 9].

Several measurement tools have been developed to investigate sub-3 nm particles in the atmosphere, combustion sources, and aerosol reactors [10, 11]. For the measurement of particle size distribution, different types of state-of-the-art differential mobility analyzers have been developed which can classify particles as small as 1 nm in mobility diameter with high resolution

[12-14]. Once classified, these particles can be counted using a condensational particle counter

(CPC), which grows the particles by condensation of super-saturated vapors on them [15]. These particles then grow to larger droplets, so that laser can detect them. Another approach to count the

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particles is to measure total current from the charged particles using an electrometer. Both the approaches have their limitations. Electrometer requires fairly high particle number concentration for accurate measurements because of the minimum charge that can be detected, and can only detect charged particles. In contrast, CPCs are highly sensitive and have high signal-to-noise ratio, as they count individual particles, and can count neutral as well as charged particles. The major limitation of the CPC is the detection limit for minimum particle size.

In order to extend the detection limit of CPC, several modifications like different working fluid, two-stage growth with a ‘booster CPC’ are proposed to the conventional design of laminar CPCs.

In a typical CPC, butanol [15] or water [16] is used as the working fluid. In accordance with the

Kelvin equation, this can be replaced with high surface tension fluid, which can lower the size detection limit of the CPCs [17]. [18] proposed that this detection limit can be lowered by using a two-stage CPC, where in first stage, particle activation and growth takes place, and in second stage, particles grow further so that laser can detect them. It was found that sub-2 nm particles can be activated and measured using diethylene glycol (DEG), and oleic acid as the working fluid for the first stage. [19] combined a 2-stage DEG/butanol CPC with TSI DMA 3085 to measure the particle size distribution of particles down to 1 nm in mobility diameter. Another instrument was developed using the same 2-stage concept, Airmodus PSM, which can measure particle size distribution down to 1 nm [20]. Sub-2 nm particles of different materials like ammonium sulfate, sodium chloride, silver, tungsten oxide, etc were measured, and the activation efficiency of these particles was found to be chemistry dependent. It was concluded that sound characterization of particle source and particle counter with respect to a classifier and electrometer set-up is essential for precise measurement of sub-2 nm particle size distribution.

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In contrast, several researchers have instead focused on the existing CPCs, with a goal to measure sub-2 nm particles. In this approach, two parameters, super-saturation and residence time, are adjusted by changing saturator/condenser temperatures, and capillary aerosol flow rate in order to promote sub-3 nm particle/clusters activation, and detection by CPCs. [21] modified TSI CPC

3025A by changing the saturator temperature from 37°C to 44°C, and capillary flow rate from

0.30 to 0.47 lpm, and measured 2 nm particles with 20-50 % detection efficiency. [22] performed a detailed study by deploying a nano-CPC battery to compare four different types of CPCs, which were calibrated with 7 different types of materials using three different working fluids, butanol, water, and DEG. It was concluded that different material is activated differently depending on the working fluid, and the activation efficiency is dependent on both material of the particle, as well as, the particle size. Very recently, it was reported that butanol is less chemistry dependent as compared to DEG, and particles as small as 1 nm can be detected using a boosted butanol CPC

Model 3776, but the detection efficiency was not quantified [23-25]. [26] showed that instead of increasing the saturator temperature, decreasing the condenser temperature can promote higher activation of sub-2 nm particles.

The material dependence of the particles clearly show that it is absolutely important to calibrate the system with respect to material, and operating conditions of the CPC to achieve precise measurements. Moreover, researchers involved in combustion are really interested in the early stages (sub 3 nm) of particle formation and growth for both desirable [27-30] and undesirable particles [31, 32]. But, to the best of our knowledge, boosted CPCs are not calibrated for flame-

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generated particles. In the absence of proper guidelines for the operation of boosted CPC, several researchers, in spite of existing butanol based CPC, are unable to perform sub-3 nm particle measurements.

Therefore, the focus of this work is to measure sub-3 nm flame-generated particles by using a butanol based CPC 3776, and report its detection efficiency. First, mobility standards of alkyl ammonium halides are generated using an electrospray to narrow down the optimal operating conditions for the butanol based CPC. Following this, combustion generated sub-3 nm particles are measured for both soot, using a Mckenna burner, and titanium dioxide using a flame aerosol reactor. The effect of polarity of the particles, material properties, and operating conditions on the detection efficiency of the particles is compared.

7.2 Experimental Set Up

Figure 7.1 shows the experimental set-up to characterize the detection efficiency of boosted butanol CPC with respect to an electrometer. This set-up has been widely used in previous works by several researchers [22, 23, 26]. First, particles/clusters were generated using different particle generation approaches, followed by particle classification using a high resolution Half-mini DMA.

These size-classified particles were then measured by an electrometer and a boosted butanol CPC to calculate the particle detection efficiency.

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Figure 7-1. Schematic of the experimental set-up

7.2.1 Particle Generation

The aerosol particles were generated using three different approaches. First, electrospray was used to generate alkyl ammonium halide ions. The solutions for electrospray were prepared using four different mobility standards, tetra-heptyl ammonium bromide (THAB), tetra-butyl ammonium iodide (TBAI), tetra-methyl ammonium iodide (TMAI), tetra-dodecyl ammonium bromide

(TDDAB) [33]. All these salts were purchased from Sigma Aldrich. The electrospray was operated with constant flow of air in the electrospray chamber, and the liquid was pumped by applying a

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constant pressure difference. Charged particles/clusters were generated through the capillary needle maintained at a voltage of 3 kV.

Flame aerosol reactor was used to synthesize titanium dioxide (TiO2) nanoparticles of controlled size distribution. A bypass flow of N2 was passed through a bubbler containing titanium isopropoxide (TTIP, Sigma-Aldrich Inc., > 97 %) at a stable temperature of 20 °C. Subsequently, this mixture was fed to the flame, where TiO2 is produced through thermal decomposition, hydrolysis, and combustion of TTIP. The bypass flow is tuned (2-6 lpm) to get the desired particle size distribution ranging from mobility diameter as small as 1.2 nm to particles as large as 5 nm in mobility diameter [28, 34].

Soot particles are generated by a commercial McKenna burner with a stainless steel outer layer and 60-mm diameter bronze porous sintering plug. A shroud nitrogen gas, at 25-30 cm/s, shields the burner-stabilized-stagnation flame from surrounding air [32]. A stainless steel sampling tube with a 0.16 mm sampling orifice is embedded in the stagnation plate. Soot particles are drawn into the sampling tube through the orifice and their particle size distribution is controlled by adjusting the flame equivalence ratio.

7.2.2 Particle Measurement

The generated particles are classified using a closed-loop half-mini DMA, and are measured using an electrometer, and boosted butanol CPC from TSI (Model 3776). Half-mini DMA was operated

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at high sheath flow rates to classify particles based on their mobility, and was calibrated using

THAB salt ions [13, 14, 35]. The classified particles were distributed in two parallel streams to electrometer and boosted butanol CPC. The electrometer (TSI 3068B) measured the current generated by the charged particles, and can be easily converted to the number concentration, which is used as the concentration reference. Electrometer inlet flow rate is maintained at 6-9 lpm depending on the experiment. The other stream to boosted butanol CPC (TSI 3776) measures the particle number concentration detected by the laser in optics section.

The flow rate entering the CPC is 1.5 lpm, of which 1.2 lpm is bypassed and the balance goes to the optics region. It is controlled by a critical orifice of fixed flow rate of 0.3 lpm, due to the operation constraint of nozzle design in optics region. In the default settings of the CPC, the sheath flow rate in the condenser is 250 sccm, and the capillary flow rate is 50 sccm. The sheath flow ensures that the particles are not lost due to radial diffusion in the condenser region. The variable orifice in line with the sheath flow allows the user to modify the capillary flow rate in the range from 30 sccm to 70 sccm, and this flow is displayed on the main screen of butanol CPC.

The detection efficiency (휂푑푒푡) of the CPC (%) is calculated as the ratio of the measured number concentration by boosted butanol CPC (푁퐶푃퐶) to the reference concentration from electrometer

(푁퐸푙푒푐), and is given by:

푁퐶푃퐶 휂푑푒푡 = × 100 푁퐸푙푒푐

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It is important to note that the detection efficiency of the CPC is calculated through experiments, but is not the same as the activation efficiency of the particles. The detection efficiency includes both the activation of the particles as well as their diffusion loss in the capillary or tubing, and is given as the product of the two efficiencies.

휂푑푒푡 = 휂푎푐푡 휂푑푖푓푓

7.2.3 Experimental Plan

Test Particle Saturator Capillary Particle Material Mobility diameter # Charge Temperature flow rate 30, 40, 50, 1 Filtered air - - 39-45°C 60, 70 sccm Tetra-heptyl 1.47 nm (monomer) 30, 40, 50, 2 ammonium bromide + 39-45°C 60, 70 sccm (THAB) 1.78 nm (dimer) Tetra-methyl 1.05 nm (monomer) 3 ammonium iodide + 44, 45°C 60, 70 sccm (TMAI) 1.20 nm (dimer) Tetra-butyl ammonium 1.24 nm (monomer) 4 + 44, 45°C 60, 70 sccm iodide (TBAI) 1.55 nm (dimer)

Tetra-dodecyl 1.4 nm (monomer) 5 ammonium bromide + 44, 45°C 60, 70 sccm (TDDAB) 2.03 nm (dimer) Flame generated ions Particle size 6 + 45°C 70 sccm (no precursor) distribution Titanium dioxide Particle size 7 +/- 45°C 70 sccm (TiO2) distribution Particle size 8 Soot +/- 45°C 70 sccm distribution Table 7-1. Test plan for the experiments for different particles at different CPC operating conditions

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Table 7.1 summarizes the plan for experiments for particles of different materials at different CPC operating conditions. First, homogeneous nucleation of butanol vapors is quantified as a function of boosted CPC conditions. Then, the optimal operating conditions for maximum detection efficiencies with minimal background from homogeneous nucleation are determined. This is followed by evaluating the effect of polarity, material properties on the detection efficiency of the butanol CPC in boosted conditions.

7.3 Results and Discussions

7.3.1 Nucleation of butanol vapors

We initially measured the particles generated by homogenous nucleation of butanol vapors for different operating conditions of the boosted butanol CPC. To assess the range of operating conditions that can be considered for our experiments, filtered air with no particles was used at the inlet of the CPC. Figure 7.2 shows the measured number concentration for the filtered air at different saturator temperatures (39-45°C) and capillary flow rates (30-70 sccm). It was found that the increase in saturator temperature from 39°C to 45°C increased the butanol nucleation as higher concentration of particles was detected. This is consistent with previous findings that as the difference between saturator temperature and the condenser temperature increases, the super- saturation increases, which promotes homogenous nucleation [26]. Moreover, increasing the capillary flow rate decreased the homogeneous nucleation due to lower residence time in the supersaturated region. A value of 10 particles/cc was considered as an acceptable homogeneous nucleation rate in this study, as shown in Figure 7.2 [23]. Therefore, all the CPC operating

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conditions for less than 10 p/cc can be considered for the detection of particles from different aerosol generators.

Figure 7-2. Homogeneous nucleation of butanol vapors for different aerosol capillary flow rate and saturator temperature

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7.3.2 Effect of saturator temperature and capillary flow rate

Figure 7-3. Effect of increasing saturator temperature on the measurement of THAB salt ions for boosted butanol CPC in comparison with electrometer. Capillary flow rate is kept fixed at 50 sccm.

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Figure 7.3 shows the effect of increasing saturator temperature on the measurement of THAB salt ions for boosted butanol CPC in comparison with the electrometer. In these experiments, the capillary flow rate was kept fixed at the default setting of 50 sccm. Three different peaks in

+ + + Figure7.3 corresponds to THA , (THAB)THA , and (THAB)2THA with mobility sizes of 1.47 nm, 1.78 nm, and 1.97 nm, respectively [33]. It was found that increasing the saturator temperature increases the boosted CPC signal for all the three ions due to higher super-saturation. It is important to note here that even though the saturator temperature of 43°C and above shows higher signal for boosted CPC than lower saturator temperatures, the homogenous nucleation could influence the background as highlighted in Figure 7.2. Nevertheless, detection of sub-2 nm particles is observed in boosted conditions as compared to the default CPC settings.

Figure 7-4. Effect of capillary flow rate on the CPC Counting Efficiency (%) at different saturator temperature for the measurement of THA+ ions

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The particle number concentration measured from the boosted CPC can be compared to the calculated number concentration from the electrometer current signal to get the CPC counting efficiency. Figure 7.4 shows the counting efficiency as a function of capillary flow rate at different saturator temperatures for THA+ ions. We found that as the saturator temperature was increased or the capillary flow was decreased, the CPC counting efficiency increased. Figure 7.4 consists of both the acceptable and unacceptable regions for the operation of boosted CPC due to homogeneous nucleation. In the acceptable region, high saturator temperature of 44°C and 45°C, at high capillary flow rate of 60 sccm and 70 sccm were found to have highest detection efficiency.

Therefore, for further experiments, only three sets of operating conditions (Ts, f) for boosted CPC were tested viz. Ts = 45°C, f = 70 sccm; Ts = 44°C, f = 70 sccm; and Ts = 44°C, f = 60 sccm.

The overall detection efficiency depends on both the activation efficiency (ηact), as well as, the penetration efficiency (ηdiff) of these ions/particles. High super-saturation due to high saturator temperature and high residence time due to low capillary flow rates increased the activation efficiency of these ions (ηact). On the other hand, low residence time due to high capillary flow reduces diffusion losses, and increases the diffusive transmission (ηdiff). A balance between the two parameters dictates the overall detection efficiency.

Residence time in the capillary region significantly influences the particle penetration efficiency.

For instance, at a capillary flow rate of 30 sccm, 50% of 2 nm particles are lost in the capillary

[15]. Even at a capillary flow rate of 70 sccm, which is the highest that can be achieved in the existing design of the TSI CPC 3776, as many as 60% of 1 nm particles are lost [23, 36]. Moreover,

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increasing the capillary flow rate decreased the sheath flow, which can lead to higher radial diffusion loss in the condenser region. In order to resolve this limitation, nozzle in the optical head needs to be designed to accommodate higher flow rates than 0.3 lpm.

Figure 7-5. CPC Counting Efficiency (%) for different ammonium alkyl halide salt ions as a function of mobility diameters at three different boosted CPC conditions.

Figure 7.5 shows that the CPC counting efficiency increases as the mobility diameter increases.

The monomer and dimer ions of alkyl ammonium halide ions were considered for the calculation of the CPC counting efficiency at three different boosted CPC conditions. The reader is referred to Table 7.1 for the different salt ions considered here. The counting efficiency was found to

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increase with increase in particle size due to ease of activation, as well as, high penetration of relatively larger particles. The best counting efficiency for all the particle sizes considered here was found for high capillary flow of 70 sccm and saturator temperature of 45°C. Even though, it has been previously reported that increasing the capillary flow beyond 60 sccm could adversely affect the particle transmission due to lower sheath flow contributing to radial losses [23], but in this work, we found that higher capillary flow rate continues to increase the counting efficiency.

7.3.3 Effect of particle material

Figure 7.6 shows the CPC counting efficiency for two different flame generated particles of both the polarities. The boosted CPC is operated at the capillary flow rate of 70 sccm and saturator temperature of 45°C to ensure high detection efficiency. The particle size distribution for titanium dioxide and soot particles begins at 1.2 nm and 1.5 nm of mobility diameter, respectively. It was found that the CPC counting efficiency follows a typical ‘S-curve’ for both the flame generated particles, with ~90% detection for 3 nm particles. The negatively charged particles activated slightly more than positively charged particles, especially for sub-2 nm particles, probably due to butanol vapors preferential condensation on the former. Similar trends for polarity dependence have also been reported previously with tungsten oxide, sodium chloride and silver particles [20,

22].

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Figure 7-6. CPC Counting Efficiency (%) for titanium dioxide (TiO2) synthesized using a flame aerosol reactor, and soot particles synthesized using a McKenna burner for both polarities.

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Figure 7-7. CPC Counting Efficiency (%) for four different types of positively charged particles/ions (< 2 nm) as a function of their mobility diameter. Here, the saturator temperature is 45°C and aerosol capillary flow rate is 70 sccm.

Figure 7.7 shows the comparison of the counting efficiency of positively charged particles composed of different materials from different aerosol generators. The boosted CPC was operated at the capillary flow rate of 70 sccm and saturator temperature of 45°C for all the particles. For the particles larger than 1.6 nm in mobility size, the CPC counting efficiency was found to be similar for alkyl ammonium halide ions, titania, and soot particles. In contrast, for particles smaller than

1.6 nm in mobility diameter, there were differences in the counting efficiencies of titanium dioxide, flame generated ions without any precursor, and alkyl ammonium halide salt ions. Alkyl

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ammonium halide ions, which are considered relatively difficult to activate due to less solubility in water were found to be least activated. On the other hand, titanium dioxide particles and flame- generated organic ions which are readily soluble in water were found to activate more easily.

This clearly shows that butanol is not very chemistry dependent, especially for particles larger than

1.6 nm in mobility diameter. This has also been reported previously when candle generated particles, tungsten oxide, etc were considered [22]. While DEG is used in the 1 nm SMPS which involves a 2-stage CPC, it is reported to be more chemistry dependent than butanol [22, 37, 38].

Nevertheless, proper calibration is quintessential for both butanol and DEG based CPCs to ensure accurate measurement of the particle size distribution for sub-2 nm charged particles. As butanol based CPCs are readily available as an ‘existing’ instrument in aerosol laboratories, the user can make some reversible changes in the operating conditions of the CPC to successfully measure sub-

2 nm particles with minimal background.

7.4 Conclusions

Detection efficiency of boosted butanol CPC has been systematically characterized for sub-3 nm alkyl ammonium halide ions and flame-generated particles. Optimal conditions for the operation of boosted butanol CPC are determined under the assumption that the acceptable homogenous nucleation limit is 10 p/cc. We find that the maximum detection efficiency for sub 3 nm particles is achieved at the saturator temperature of 45°C and capillary flow rate of 70 sccm, with background homogeneous nucleation rate of < 5 p/cc. Flame-generated particles, as small as 1.2 nm in mobility diameter for titanium dioxide, and 1.5 nm for soot were found to be activated using

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the optimal operating condition. The negatively charged particles were activated slightly more than the positively charged due to difference in the interactive forces with the butanol vapors. Particles of different materials larger than 1.6 nm are activated with similar efficiency, whereas sub 1.6 nm are dominated by their composition. This establishes the applicability of butanol CPC in boosted conditions for the measurement of sub-3 nm particles, but at the same time, reinforces the importance of appropriate calibration for their precise measurement. The researchers with existing butanol CPCs can perform sub-2 nm measurements to study early stages of particle formation and growth in different aerosol reactors.

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detection with a laminar flow ultrafine condensation particle counter. Aerosol Science and

Technology, 2009. 43(1): p. 81-96.

19. Jiang, J., et al., Electrical mobility spectrometer using a diethylene glycol condensation

particle counter for measurement of aerosol size distributions down to 1 nm. Aerosol

Science and Technology, 2011. 45(4): p. 510-521.

20. Kangasluoma, J., et al., Remarks on ion generation for CPC detection efficiency studies in

sub-3-nm size range. Aerosol Science and Technology, 2013. 47(5): p. 556-563.

21. Kuang, C., et al., Modification of laminar flow ultrafine condensation particle counters for

the enhanced detection of 1 nm condensation nuclei. Aerosol Science and Technology,

2012. 46(3): p. 309-315.

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22. Kangasluoma, J., et al., Sub-3 nm particle size and composition dependent response of a

nano-CPC battery. Atmospheric Measurement Techniques, 2014. 7(3): p. 689.

23. Attoui, M., Activation of sub 2 nm singly charged particles with butanol vapors in a

boosted 3776 TSI CPC. Journal of Aerosol Science, 2018. 126: p. 47-57.

24. Kangasluoma, J. and M. Attoui, Review of sub-3 nm condensation particle counters,

calibrations, and cluster generation methods. Aerosol Science and Technology, 2019: p.

1-34.

25. Attoui, M. and J. Kangasluoma, Activation of sub 2 nm Water Soluble and Insoluble

Standard Ions with Saturated Vapors of Butanol in a Boosted TSI Ultrafine CPC.

Atmosphere, 2019. 10(11): p. 665.

26. Barmpounis, K., et al., Enhancing the detection efficiency of condensation particle

counters for sub-2 nm particles. Journal of Aerosol Science, 2018. 117: p. 44-53.

27. Wang, Y., et al., The high charge fraction of flame-generated particles in the size range

below 3nm measured by enhanced particle detectors. Combustion and Flame, 2017. 176:

p. 72-80.

28. Wang, Y., et al., Observation of incipient particle formation during flame synthesis by

tandem differential mobility analysis-mass spectrometry (DMA-MS). Proceedings of the

Combustion Institute, 2017. 36(1): p. 745-752.

29. Wang, Y., et al., Influence of flame-generated ions on the simultaneous charging and

coagulation of nanoparticles during combustion. Aerosol Science and Technology, 2017.

51(7): p. 833-844.

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30. Sharma, G., et al., Modeling simultaneous coagulation and charging of nanoparticles at

high temperatures using the method of moments. Journal of Aerosol Science, 2019. 132: p.

70-82.

31. Carbone, F., M. Attoui, and A. Gomez, Challenges of measuring nascent soot in flames as

evidenced by high-resolution differential mobility analysis. Aerosol Science and

Technology, 2016. 50(7): p. 740-757.

32. Tang, Q., et al., Nascent soot particle size distributions down to 1 nm from a laminar

premixed burner-stabilized stagnation ethylene flame. Proceedings of the Combustion

Institute, 2017. 36(1): p. 993-1000.

33. Ude, S. and J.F. De la Mora, Molecular monodisperse mobility and mass standards from

electrosprays of tetra-alkyl ammonium halides. Journal of Aerosol Science, 2005. 36(10):

p. 1224-1237.

34. Sharma, G., et al., Collisional growth rate and correction factor for TiO2 nanoparticles at

high temperatures in free molecular regime. Journal of Aerosol Science, 2019. 127: p. 27-

37.

35. Zhang, H., et al., Numerical modeling of the performance of high flow DMAs to classify

sub-2 nm particles. Aerosol Science and Technology, 2018: p. 1-13.

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chemical engineering. 2000, Oxford University Press, New York.

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Airmodus A20 fine condensation particle counters. Aerosol science and technology, 2015.

49(8): p. 674-681.

38. Kangasluoma, J., et al., Sizing of neutral sub 3 nm tungsten oxide clusters using Airmodus

Particle Size Magnifier. Journal of Aerosol Science, 2015. 87: p. 53-62.

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Chapter 8. Characterization of Particle Charging in Low-temperature, Atmospheric- Pressure, Flow-through Plasmas

Girish Sharma*, Nabiel Abuyazid*, Sukrant Dhawan, Sayali Kshirsagar; Mohan Sankaran, Pratim Biswas. (2020) Characterization of particle charging In low-temperature, atmospheric- pressure, flow-through plasmas. Journal of Physics D, 2020, (Accepted).

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Abstract While plasmas are now routinely employed to synthesize or remove nano- to micron-sized particles, the charge state (polarity and magnitude) of the particles remains relatively unknown. In this study, charging of nanoparticles was systematically characterized in low-temperature, atmospheric-pressure, flow-through plasmas previously applied for synthesis. Premade, charge- neutral nanoparticles of MgSO4, NaCl, and sea salt were introduced into the plasma to decouple other effects such as the reactive vapor precursor, and MgSO4 was selected as the focus because of its stability (i.e., no evaporation) in the plasma environment. The charge fraction and distribution of the particles was examined at the reactor outlet for different particle diameters (10-

250 nm) as a function of plasma power and two different types of power sources, alternating current (AC) and radio-frequency (RF). We find that the overall charge fraction increases with increasing plasma power and diameter for the RF plasma. A similar increasing trend was observed for the AC plasma with increasing particle diameter in the range of 50-250 nm, but the charge fraction increased with decreasing particle diameter in the range of 10-50 nm. The charge distribution was revealed to be bipolar with particles supporting multiple charges for both the RF and AC plasmas, but the RF plasma produced a higher fraction of multiple charges. Differences in the characteristic time scales for particle charging in the AC and RF plasmas provide a possible explanation for the trends observed in the experiments.

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Nomenclature

A Cross-sectional area for flow (m2)

+ -1 푐푖표푛 Thermal velocity of positive ions (m s ) 퐷 Diffusivity of particle (m2 s-1)

− 2 -1 퐷푒 Diffusion coefficient of electrons (m s ) + 2 -1 퐷푖표푛 Diffusion coefficient of ions (m s ) 푒 Elementary charge (C)

ℎ Plank’s constant (m2 kg s-1)

-2 -1 퐽푒 Electron flux density to the particle surface (# m s )

-2 -1 퐽푖 Ion flux density to the particle surface (# m s ) 푘 Boltzmann constant (m2 kg s-2 K-1)

퐾 Particle conductivity (0-1)

푚푒 Mass of electron (kg)

푚푖 Mass of ion (kg)

-3 푛푒 Electron number concentration (# m )

-3 푛푖 Ion number concentration (# m )

-3 -1 푛(푑푝, 푞, 푥, 푡) PSD function as a function of diameter, charge, space and time (# m m )

-3 푛푖,0 Initial number concentration of positive charged ions (# m ) 〈푄〉 Average charge on the particle

푅푝 Plasma resistance (Ω)

± -3 -1 푆 Rate of loss of ions/electrons to the wall (# m s )

푇푒 Temperature of electron (K)

푇푖 Temperature of ion (K)

푇푔 Temperature of gas (K)

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푢 Convective velocity (m s-1)

-1 푣푒 Mean thermal velocity of electrons (m s )

-1 푣푖 Mean thermal velocity of ions (m s )

± 3 -1 훽 (푣, 푞) Rate of collision of particle of charge 푞 with ions/electrons (m s )

훿 Limiting sphere radius (m)

-3 -1 4 2 휀0 Vacuum permittivity (m kg s A ) θ Space-time (s)

휆퐷 Debye length (m)

휆푖 Mean free path of ions (m)

2 −1 −1 µe Electron mobility (m V s )

3 -1 휉 Recombination rate of ions and electrons (m s )

2 휎푖 Collisional cross section area of ions (m ) 휏 Space time (s)

휏1 Characteristic time of charging inside the plasma (s)

휏2 Characteristic time of charging outside the plasma (s) 휙(푟) Potential energy of particle as a function of 푟 (J)

휙푝 Surface potential energy of particle (J)

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8.1 Introduction

The charging of nano- to micron-sized particles in the gas phase is of fundamental importance to aerosol science and related technologies including instrumentation [1], materials synthesis [2], pollution control [3], and indoor air filtration [4]. For example, electrostatic classification of aerosol particles by scanning mobility particle sizing (SMPS) involves initially exposing the particles to ions produced by ionizing radiation from a radioactive source (neutralizers), followed by diffusion charging. To obtain the size distribution of particles, it is essential that the charging distribution imparted by the neutralizer is well-defined and known [5]. Alternatively, electrostatic precipitators (ESPs) are widely used as particulate control devices in industry and coal power plants to capture fine aerosol particles from emissions. In an ESP, ions are typically produced by a corona discharge, which is a type of plasma created by partial breakdown of a gas in the presence of a relatively strong electric field [1]. The efficiency of an ESP depends mainly on its ability to charge particles and the charging, and thus removal of smaller sized particles, has been a challenge in corona-based devices[6]. Other types of plasmas that are formed by complete gas breakdown contain higher concentration of ions [7, 8], but have yet to be explored for particle charging to realize ESP applications.

Plasmas have also been increasingly studied for the synthesis of nanoparticles in the gas phase from a vapor precursor by homogeneous (i.e., substrate-free) nucleation. A variety of low- temperature, glow-like plasma sources characterized by complete gas breakdown have been reported at different operating pressures ranging from vacuum [9] to atmospheric [10, 11], and with different power couplings including direct-current (DC) [12], alternating current (AC) [11],

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radio-frequency (RF) [10], and microwave [13]. Flow-through, atmospheric-pressures systems are easily integrated with SMPS and the particle diameter distributions have been measured on line to correlate process conditions such as precursor concentration, reactor residence time, and plasma power to the as-grown particle diameter. Nanoparticles are also deposited by ESP for off line materials analysis by microscopy or producing thin films for applications. While particle charging is known to be important either inside the plasma for its influence on agglomeration [14] or outside of the plasma for measurement and application, our current understanding in these types of plasmas is very limited.

Several models have been developed over the years to explain particle charging in a plasma

[15-21]. The simplest model is based on orbital motion-limited (OML) theory, which via the electron and ion currents to the particle surface provides an estimate of the steady-state charge

[15]. Corrections to OML theory have been developed over the years by accounting for high particle density, secondary electron emission [20] due to thermoionization and photoionization, ion trapping [17-19], and charge fluctuations [18]. Particles are expected to charge negatively inside a plasma because of the higher mobility of electrons compared to other charged species, but the magnitude or even possibly the polarity of charge can change as these different effects are considered. The particle charging may also be different outside of the plasma, as they exit through what is referred to as the spatial afterglow, or flowing afterglow [22-25]. This afterglow, similar to temporal ones, refers to the region outside the electrodes where ionization no longer takes place, but plasma species remain [26]. On a fundamental level, the quasi-neutrality assumption may not hold in the afterglow, i.e., the electron and ion density may not be equal, which could lead to substantial differences in their respective fluxes to the particle surface. Additionally, because particles are initially charged in the plasma before passing through the afterglow, the final charge

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state (polarity and magnitude) could be even more complex. Couedel et al. [23] and Wörner et al.

[24] measured the charge distributions of particles in the temporal afterglow of a low-pressure plasma and independently showed negatively-charged particles. In contrast, Chen et al. [25] and

Sankaran et al. [22] observed the presence of bipolarly charged silicon nanoparticles after the spatial afterglow of a low-pressure RF plasma and an atmospheric-pressure DC microplasma, respectively. Particle charging therefore remains unresolved and comprehensive characterization of the charge state is yet to be reported.

In this work, we systematically characterized particle charging in low-temperature, atmospheric-pressure, flow-through plasmas similar to those that have been previously reported for synthesis [27]. The plasma reactor used in this work features the ability to switch between different power couplings without any other changes to the system. Premade nanoparticles of sodium chloride (NaCl), sea salt, and magnesium sulfate (MgSO4) generated by atomization were introduced in the plasma to decouple particle nucleation and growth from reactive vapors, and isolate particle charging. Of these materials, MgSO4 was selected as a focus of this study because of its stability in the plasma to evaporation. The overall charge fraction and charge distribution in terms of polarity and magnitude were compared for both RF and AC power coupling and were measured as a function of particle diameter and plasma power. The results were supported by analyzing the characteristic timescales for charging.

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8.2 Methods

8.2.1 Particle Generation and Plasma Reactor

The overall experimental setup is schematically illustrated in Figure 8.1. Aerosolized nanoparticles were produced using an atomizer (TSI Aerosol Generator Model 3076) with argon

(Ar) as the carrier gas (≥ 99.998% pure, Sigma Aldrich). The Ar flow rate entering the atomizer was controlled by a mass flow controller. The Ar flow expands through an orifice to form a high- velocity jet, which atomizes the liquid solution to generate a fine spray of droplets. These droplets were passed through two diffusion dryers to evaporate the water from the droplets, and obtain dry salt particles. The particle size distribution was tuned by varying the salt concentration. Three

− + 2− 2+ different salts, sea salt (mass fraction: 55% chloride (Cl ), 31% Na , 8% sulfate (SO4 ), 4% Mg ,

+ 2+ 1% K , 1% Ca and <1% other, Sigma Aldrich), NaCl (≥ 99% pure, Sigma Aldrich), and MgSO4

(≥ 99% pure, Sigma Aldrich), were chosen because of their different boiling points, which would be expected to lead to different volatilities in the plasma. Two different initial particle size distributions (PSDs) characterized by geometric mean diameters (dpg) of 25-30 nm and 75-80 nm of each material were generated. As the salt particle generated through droplets are spherical [28], particle mobility diameter measured through SMPS was assumed to be same as the particle volumetric diameter and is simply referred to as the particle diameter. Downstream of the diffusion dryers, a bypass stream was connected to a vacuum pump to maintain a total gas flowrate of 1 lpm through the plasma. In order to ensure that the particles entering the plasma were initially neutral, a charged particle remover (CPR1) operated at a fixed voltage of 1.5 kV was used to trap particles of either charge polarity, and the elimination of charged particles was confirmed by SMPS without a neutralizer.

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Figure 8-1. Experimental setup for A) particle generation and particle charging in a low-temperature, atmospheric- pressure, flow-through plasma; B) measurement of particle size distribution, overall particle charge fraction, and multiply charged particle distribution

The plasma reactor was a simple flow-through system consisting of a clear fused quartz tube

(ID: 2 mm, OD: 3.2 mm) and two metal ring electrodes, one for high voltage and one for electrical ground, on the outside in a parallel configuration with a spacing of 2 cm. The plasma was ignited by a high voltage AC power supply (PVM500-4000, Amazing1 Inc.). For RF operation, an additional electrode was electrically connected to a RF power supply (RF-3 XIII purchased from

RF VII Inc.) through a homemade L-type matching network and switched after ignition.

Downstream of the plasma, the aerosol flow was diluted by air; for smaller particles (dpg 25-30 nm) with lower total number concentration, the dilution flowrate was 2 lpm and for larger particles

(dpg 75-80 nm) with higher total number concentration, the dilution flowrate was 6 lpm.

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8.2.2 Plasma Characterization

Electrical characterization of the AC plasma was performed through standard Lissajous analysis [29]. Briefly, the analysis is based on measuring the voltage and charge waveforms and assuming a simplified equivalent circuit model for dielectric barrier discharges [30], calculating the energy deposited for a single period, the capacitances associated with each phase of the discharge, the instantaneous power, and instantaneous resistance. Additional details of these calculations are provided in the Supporting Information. The electron density, ne, was then obtained from the average resistance, using a 1-D plasma fluid model:

푑 (8.1) 푛푒 = 퐴푒휇푒푅푝

where d is the electrode distance, A is the reactor cross-sectional area, e is the elementary charge, µe is the electron mobility [30], and 푅푝 is the plasma resistance. This model assumes that the discharge current through the gas is dominated by the electron flux and ignores the ionic contribution. Furthermore, the electron flux is approximated by a drift-diffusion formulation where the diffusion component is assumed to be negligible in a strong electric field environment [31].

Electrical characterization of the RF plasma was performed using an RF power probe

(Octiv Poly, Impedans Ltd.). The power probe is needed to measure the voltage and current

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waveforms in a RF plasma because of stray impedances in the high-frequency circuit. We again developed a simplified equivalent circuit model to calculate the plasma resistance, and similarly to the AC plasma, estimated the electron density from the plasma-fluid model shown in Eqn. 8.1.

Additional details of these calculations are provided in the Supporting Information.

8.2.3 Charge Distribution Measurement

The total fraction (i.e., either polarity) of charged aerosol particles exiting the plasma reactor was obtained using a second charge particle remover (CPR2) and SMPS, as shown in Figure 8.1b.

Similar to CPR1, CPR2 trapped particles of either charge polarity and the elimination was confirmed by SMPS. The PSD of the charged particles was measured by the following procedure.

First, the PSD was measured with both the plasma and CPR2 off; this PSD corresponds to the PSD of the initial particles entering the plasma. Then, the PSD was measured with the plasma and CPR2 on; this PSD corresponds to the fraction of neutral particles. Subtracting the PSD of the neutral fraction from the initial particles yielded the PSD and total fraction of charged particles.

To obtain the charge distribution on the particles and characterize multiple charging, a TDMA setup was applied following previous reports [9]. Briefly, the setup consists of two DMAs, a neutralizer, and a condensation particle counter (CPC), as shown in Figure 1b. The first DMA

(DMA1) separates particles of a fixed mobility, but the classified particle stream could contain different diameters depending on their charge state. These particles are then passed through a neutralizer to obtain a Fuchs charge distribution [5, 32, 33], followed by the second DMA

(DMA2). Particles with the same mobility were therefore separated by their charge and diameter and finally counted by the CPC. The relative peak heights were used to calculate the charge

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distribution. In this study, the aerosol flow was 2.5 lpm, and the sheath flow in the DMA was 10-

16 lpm, depending on the number concentration of the particles at that particle diameter. The CPR2 was operated at a fixed voltage of 1.5 kV.

8.2.4 Characteristic Time Scale Analysis

Figure 8-2. Proposed mechanism for particle charging inside and outside the plasma volume. Figure 8.2 provides a qualitative picture of our proposed mechanism for particle charging in a low-temperature, atmospheric-pressure plasma environment, highlighting the two important regions. In the first stage, the initially neutral aerosol particles enter the plasma, where particle charging is controlled by the flux of electrons and ions to its surface, thermoionization, and photoionization. In the second stage, the charged particles exit the plasma volume and their charge is perturbed by the spatial afterglow region. We suspect that the ion density is higher as compared to electron density in the afterglow region and consequently, the particles may become neutralized

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or positively charged, as previously reported [34, 35]. If particles become bipolarly charged, agglomeration by Coulombic attraction could be enhanced, leading to neutral aggregated particles

[15, 25, 36, 37].

In support of the experimental characterization of particle charging in a plasma, a characteristic time scale analysis was carried out. Based on the above picture, particle charging was analyzed by the two different stages. Assuming that the emission processes (thermo- and photoionization) are relatively less significant compared to charging by electrons and ions, the charge of a particle (Q) as a function of space-time (τ) inside the plasma volume is given by [38]

푑푄 (8.2) = 휋푑2(퐽 − 퐽 ) 푑τ 푝 푖 푒

where 퐽푒 and 퐽푖 are the electron and ion flux density to the particle surface, respectively, and can be described by the following equations [38]

1 푒휙푝 퐽푒 = 푛푒푣푒 exp ( ) (8.3) 4 푘푇푒

휋 휆푖 푒휙푝 (8.4) 퐽푖 = √ 푛푖푣푖 ( ) | | 2 푑푝 푘푇푖

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where 푣푒 and 푣푖 are the electron and ion velocities, respectively, 푇푖 is the mean ion temperature, k is the Boltzmann’s constant, 휆푖 = 푘퐵푇푖/√2휎푖푃 is the mean free path of ions, and 휙푝 is the surface potential of the particle given by [38]

푒푄 푑푝 휙푝 = exp (− ) (8.5) 2휋휀0푑푝 2휆퐷

and 휆퐷 is the Debye length and is given by

휀 푘푇 0 푒 (8.6) 휆퐷 = √ 2 푛푒푒

Qualitatively, the flux of electrons to the particle surface is higher than that of ions due to the higher mobility of electrons as compared to ions and thus particles very quickly (i.e., at initial times after entering the plasma) charge negatively. As the negative charge increases, the electron flux to the particle surface decreases because of Coulombic repulsion, and concomitantly, the ion flux to the particle surface increases because of Coulombic attraction. Eventually, the electron and ion flux to the particle surface become equal (퐽푖 = 퐽푒) and the particle obtains an equilibrium charge. The characteristic space-time in the first stage to attain this equilibrium charge, 휏1, is given by

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2 8 휆퐷 휏1 = √ (8.7) 휋 휆푖푣푖

The second stage, where particles exit the plasma and interact with a spatial afterglow, was modeled assuming the Fuchs theory of particle charging, where the governing equations for ion and electron concentrations are given by [39]

∞ 휕 (푛 ) = −푆+ − ∑ 훽+(푑 , 푞) 푛 푛(푑 , 푞, 푥, τ) − 휉푛 푛 − ∇. 푛 푢 휕τ 푖 푝 푖 푝 푖 푒 푖 푞=−∞ (8.8)

+ 2 + + 퐷푖표푛∇ 푛푖

∞ 휕 (푛 ) = −푆− − ∑ 훽−(푑 , 푞) 푛 푛(푑 , 푞, 푥, τ) − 휉푛 푛 − ∇. 푛 푢 휕τ 푒 푝 푒 푝 푖 푒 푒 푞=−∞ (8.9)

− 2 + 퐷푒 ∇ 푛푒

where 푆+ or 푆− are the loss rate of ions/electrons to the walls, the second term in the sum on the

RHS is the rate of electrons loss by their attachment onto particles, the third term is ion loss due to the recombination between ions of different polarities, and the fourth and fifth terms account for the variation of ions due to convective transport, and diffusion, respectively. As electrons have higher mobility than ions, the model assumes that more electrons are lost to the wall than ions in

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this exit region and the particles predominantly collide with ions, resulting in neutralization or positive charging. The number concentration of particles of different charges [39] is given by

휕 (푛(푑 , 푞, 푥, τ)) = 훽+(푑 , 푞 − 1, 푥, τ)푛+푛(푑 , 푞 − 1, 푥, τ) 휕τ 푝 푝 푖 푝 (8.10)

+ + 2 −훽 (푑푝, 푞, 푥, τ)푛푖 푛(푑푝, 푞, 푥, τ) − ∇. 푛(푑푝, 푞, 푥, τ)푢 + 퐷∇ 푛(푑푝, 푞, 푥, τ)

where the first term on the RHS is the generation rate of a particle with 푞 charges by the attachment of a positive ion to the particle with 푞 − 1 charges, the second term is the loss rate of the particle with 푞 charges due to the attachment of positive ions, and the third and fourth terms account for the variation of 푞 charged particles due to convective transport and diffusion, respectively. The

+ attachment coefficient of ions to the particle, 훽 (푑푝, 푞), with diameter 푑푝 and elementary charge,

푞, is given by [32, 40]

+ 2 ( ( ) ) + 휋푐푖표푛휉훿 푒푥푝 −휙 훿 /푘푇 훽 (푑푝, 푞) = + 푐 휉훿2 푑 /2훿 (8.11) 1 + 푒푥푝(−휙(훿)/푘푇) 푖표푛 푝 푒푥푝(−휙(푑 /2푥)/푘푇) 푑푥 + ∫0 푝 2퐷푖표푛푑푝

+ where, 푐푖표푛 is the thermal velocity of ions (m/s), 휉 is the collision coefficient between positive ions and negative ions, 훿 is the limiting-sphere radius, 푇 is the gas temperature, and 푥 is a dimensionless variable ranging from 0 to 푑푝/2훿.

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Eq. 8.11 is obtained by dividing the space around the particle into two regions by the limiting- sphere of radius, 훿, which is concentric to the particle, and is on the order of one ion mean free path larger than the particle radius. Outside the limiting sphere, the charge carriers move according to the continuum diffusion-mobility equation. Once the ions enter the limiting sphere, they are assumed to travel like in vacuum, without collisions with gas molecules. To calculate the ion- aerosol combination coefficients, the macroscopic diffusion-mobility flux outside the limiting sphere is set equal to the microscopic flux inside the limiting sphere. This method of flux matching then provides the necessary boundary condition for the diffusion-mobility equation [32, 40].

The electrostatic potential energy 휙(푟) at distance 푟 from the center of particle, is given by

2 3 푒 푖 푑푝 휙(푟) = { − 퐾 } (8.12) 2 2 2 4휋휀0 푟 16푟 (푟 − (푑푝/2) )

where 푖 is the number of elementary charges on the particle, and is positive if the charges of the ion and the particle are of the same sign. For a perfectly conducting particle, K = 1, and for a non- conducting particle, K = 0. The first term in Eq. 8.12 accounts for the Coulomb interaction

(attractive or repulsive) between the ion and the particles, and the second term accounts for the attractive potential due to the polarization interaction of a sphere with a point charge. The expression for limiting-sphere radius, 훿, is given by

3 5 2 3 2 5/2 푑푝 1 2휆푖 1 4휆푖 2휆푖 2 4휆푖 훿 = 2 { (1 + ) − (1 + 2) (1 + ) + (1 + 2) } (8.13) 8휆푖 5 푑푝 3 푑푝 푑푝 15 푑푝

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Finally, the characteristic charging space-time in the second stage, 휏2, is estimated from the ion density and attachment coefficient of ions by

1 휏2 = + + (8.14) 훽 (푑푝, 푞)푛푖,0

Table 8.1 summarizes the range of experimental conditions that were studied including plasma operating conditions and instrumental parameters.

Plasma Test Objective Salts Approach Source

Sea Salt, Compare the PSD for different Neutralizer, Classifier, Long 1 NaCl, RF salts exiting the plasma DMA, CPC MgSO4

Lissajous Analysis, Plasma Calculate absorbed power, AC fluid Model, Saha Equation plasma density, and electron 2 MgSO temperature from set points in 4 Plasma fluid Model, Saha instruments RF Equation

Study the size dependent CPR2, Neutralizer, Classifier, 3 charge fraction for various MgSO4 RF Long DMA (large PSD), Nano plasma powers DMA (Small PSD), CPC

Study the multiple charge AC CPR2, Classifier, Long fraction (-3 to +3) for 5 Tandem DMA (large PSD), MgSO 4 different particle sizes 4 Nano Tandem DMA (Small (15,45,90,135,180 nm) RF PSD), CPC

Table 8-1. Overall test plan for the experiments

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8.3 Results and Discussions

8.3.1 Comparison of PSDs of different salts passing through plasma

Figure 8-3. Comparison of PSDs of different salts after passing through the RF plasma at different powers: A) sea salt, B) NaCl, C) MgSO4 (Test 1)

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We initially measured PSDs of different materials passing through the plasma reactor to assess their stability within a plasma environment. In general, the RF plasma has a higher plasma density than the AC plasma and particles that are stable in the RF plasma are expected to also be stable in the AC plasma. Figure 8.3 shows PSDs of sea salt, NaCl, and MgSO4 generated from the atomizer after passing through a RF plasma operated at different powers. The initial PSD measured with the plasma off is not exactly the same for the three salts, but exhibit similar total number concentrations and geometric mean diameters. When the plasma is turned on and the particles are exposed to the plasma environment, the PSDs of sea salt and sodium chloride change substantially, notably with the appearance of an additional peak that increases in number concentration relative to the original peak with increasing power. A similar shift in the PSDs of aerosol particles flowing through a low-pressure plasma reactor has been previously reported and shown to be the result of evaporation of the injected particles and re-nucleation of new smaller particles [38, 41]. A higher number concentration of smaller diameter particles is also observed for sea salt than NaCl, which can be correlated to the lower melting point and increased volatility of sea salt. In comparison, the

PSD for MgSO4 shows almost no change even at the highest powers tested, consistent with its higher melting point and lower volatility relative to both sea salt and NaCl. The small decrease in the number concentration with increasing power can be attributed to particle loss at the exit of the plasma reactor from electro- or thermophoresis [42]. Based on these results, MgSO4 was determined to be the most stable in terms of PSD and contamination from evaporation, and therefore, chosen as the focus of our study to characterize solely particle charging in the plasma.

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1.2.1 Plasma Characterization

Figure 8-4. Electron density, absorbed power, and electron temperature in a) RF and b) AC plasmas as a function of power and applied peak-to-peak voltage, respectively. (Test 2)

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We next characterized the plasma powered by both AC and RF, in the presence of MgSO4 particles to obtain plasma properties. Plasma density and electron temperature are inputs for evaluating an estimate of the characteristic timescales for charging in these systems. Figure 8.4 shows the absorbed power, electron density, and electron temperature estimated from our electrical characterization and corresponding analysis for the AC and RF plasmas. For the AC plasma, the absorbed power was calculated using both I-V measurements and Lissajous analysis and found to agree very well. The electron density and electron temperature did not vary substantially with increasing power, with the values of ~ 3×1011 #/m3 and 0.37 eV, respectively. Similar trends of absorbed power and electron temperature are observed for the RF plasma, with the latter being estimated to be roughly 0.51 eV. The absorbed power in the RF case is roughly an order of magnitude higher than the AC plasma, and therefore the electron density of ~ 1×1014 #/m3 is as expected, also 2-3 order of magnitude higher than the AC plasma. These calculated values are supported by the higher visual intensity and the expected improved power coupling for RF as compared to AC plasmas.

8.3.2 Characterization of Particle Charging in RF and AC plasmas

The charge state of particles exiting the plasma was initially characterized by the total charge fraction. Figure 8.5 shows the charge fraction of MgSO4 particles exiting the AC and RF plasmas as a function of particle diameter at different powers. The charge fraction is found to increase with plasma power for both AC and RF power, but much less so for AC. Figure 8.5a shows that for the

RF plasma, the charged particle fraction increases with increasing particle diameter. For the AC plasma, Figure 8.5b shows a similar trend for particle diameters > 40 nm, but for particles < 40 nm, the trend reverses, and the charged particle fraction increases as the particle diameter

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decreases. Moreover, the charged fraction is higher for the AC than for the RF plasma in this diameter range (10-40 nm). At the larger diameters, the propensity for more charging can be attributed to the higher surface area available for the ions and electrons to attach.

Figure 8-5. Charge fraction of particles as a function of particle diameter for a) RF plasma, and b) AC plasma at different plasma powers and different initial particle size distributions. (Test 3)

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We next characterized the charge state of the particles flowing through the plasma by the charge distribution. Figure 8.6 shows the charge distribution of MgSO4 particles exiting the AC and RF plasmas for both polarities from +3 to -3 charges at different powers. As particle diameter increases, more and more particles acquire multiple charges, which is consistent with the trends observed by the total charge fraction. A higher fraction of particles acquire multiple charges for the RF plasma as compared with the AC plasma. Overall, at all diameters and all powers for both the AC and RF plasmas, the particles reach a bipolar charge distribution. A possible explanation is that particles are initially charged negatively inside the plasma volume, and then neutralized or charged positively in the spatial afterglow where there is a higher ion flux to the particles due to diffusive losses of electrons. An additional important factor that can contribute to this trend is the loss of highly-charged negative particles to the walls by electrophoresis.

Another clear trend that can be observed in Figure 8.6a is that for RF coupling, the particle charge is preferentially negative for smaller-sized particles at higher power. As particle diameter increases, the fraction of negatively charged particles decreases, while the fraction of positively charged particles increases. For example, 45 nm particles are preferentially negatively charged, whereas 180 nm particles are preferentially positively charged. Again, we suggest that a possible explanation is the difference in charging mechanisms between the plasma volume and spatial afterglow region. In this case, larger-sized particles will have more negative charge in the plasma volume because of their larger surface area and the resulting ion flux to their surface in the spatial afterglow could be higher, leading to more neutralization and/or more positive charging.

Analogously, smaller particles will have less negative charge in the plasma volume, the ion flux to their surface will be lower, and less neutralization or positive charging will occur.

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For the RF plasma at lower power, majority of the charged particles have single charge of both polarities. This finding can be supported by the smaller spatial afterglow region observed during experiments, which could decrease the space-time for charging effects in this region. As shown in

Figure 8.6b, the AC plasma similarly produces singly charged particles at low powers because of a smaller spatial afterglow region. It is important to note that in these measurements, the charge fraction of particles with ±4 elementary charges and higher charges was not assumed to be important and can be justified with the low charge fraction of ±3 elementary charges measured at all of the studied conditions.

8.3.3 Characteristic Time Scale Analysis

To support the experimental results, a characteristic time scale analysis was performed. The parameters used for these calculations are listed in Table 8.2. Literature values were assumed for the neutral gas temperatures in the AC [43] and RF [44] plasmas. The mean electron temperatures in these types of plasmas operating at atmospheric pressure are typically in the range of 0.5 to 2 eV [45-47]. The characteristic times for particle charging and the amount of particle charge acquired in the first stage of plasma were calculated for 0.5, 1.0, 1.5, and 2.0 eV, and are detailed in the Supplementary Information. In general, we did not find significant dependence on electron temperature and therefore, we assumed a value of 1.0 eV for the analysis discussed here.

Figure 8.7a shows the calculated steady-state charge acquired by the particles inside the plasma volume for both the AC and RF plasmas. It can be clearly seen that the negative charge acquired by the particles increases with particle diameter for both the RF and AC plasmas. Figure 8.7b shows the characteristic times calculated from Eqn. 8.7 for charging inside the plasma volume.

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Charging of the particles in the plasma is very fast: 9.8 ns for RF plasma and 22.7 µs for AC plasma. These time scales, when compared with the residence time in the plasma region of ~ 3.8 ms, indicates that the particles will acquire the steady-state charge fraction shown in Figure 8.7a, before exiting the plasma volume.

Figure 8-7. A) Average charge acquired by particles in the plasma volume. B) Characteristic time scales for particle charging in the plasma volume and in the spatial afterglow region.

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Plasma Electron Temperature Ion Concentration Gas Temperature (#/cm3) (°C) RF 1.0 eV 1e14 1000 °C AC 1.0 eV 3e11 150 °C

Table 8-2. Parameters used for the calculation for characteristic time scales and average particle charge shown in Figure 8.7.

Figure 8.7b also shows the characteristic times calculated from Eqn. 8.14 for charging downstream of the plasma in the spatial afterglow. The charging in the spatial afterglow of the AC plasma is found to be 3 orders of magnitude slower than the RF plasma. Moreover, as the particle diameter decreases, the characteristic time increases, which is a possible explanation for the higher charge fraction of smaller particles passing through the AC plasma as compared to the RF plasma

(see Figure 8.5). The relative time scales also suggest that for the AC plasma, smaller particles should not exhibit a bipolar charge distribution; instead these particles should be predominantly negatively charged. However, this is inconsistent with our experimental results which show a bipolar distribution (see Figure 8.6). A possible explanation for this could be the loss of highly negatively charged particles to the reactor walls due to electrophoresis. Also, the characteristic time scale analysis does not account for the possibility of charge distributions of particles of the same diameter.

From our study, two key factors that determine the charge on the particles are plasma power and residence time, both in the plasma volume and the spatial afterglow. Plasma power has an important role in both the plasma volume and the spatial afterglow, whereas the residence time is more important in the spatial afterglow than in the plasma volume. Higher plasma powers give

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rise to higher plasma densities, which promotes charging, and therefore more multiply charged particles. On the other hand, the loss of negative charge on the particles in the spatial afterglow is highly dependent on the particles’ transit time. The characteristic time scale for charging in the spatial afterglow depends on the residual ion density and its polarity, which is generally positive in plasmas. However, depending upon the gas composition, negative ions may also be present which could change the charging and will be a focus of future work.

8.4 Conclusions

Particle charging has been systematically characterized for low-temperature, atmospheric- pressure, flow-through plasmas with AC and RF power coupling. The overall fraction of particles that is charged is found to be higher and shows an opposite trend of increasing with decreasing particle diameter for the AC plasma as compared with the RF plasma. We invoke a two-stage charging mechanism and based on a characteristic time scale analysis, suggest that while particles are predominantly charged negative in the plasma volume for both AC and RF plasmas, the charging time in the spatial afterglow of an AC plasma is slower than a RF plasma, leaving more particles charged. The characteristic time in the second stage for attaining the equilibrium charge increases with decreasing particle diameter which may also explain the higher charge fraction of smaller diameter particles for the AC plasma. On the other hand, the charge state of the particles is observed to be bipolar for both the AC and RF plasma, with more multiply charged particles for the RF plasma, which is not currently addressable by the two-stage charge mechanism. Future studies are needed to fully address these complex issues and could lead to better understanding of particle charging in these plasma sources and control over charging for applications such as ESPs.

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Chapter 9. Conclusions and Suggestions for Future Work

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9.1 Conclusions

9.1.1 Improvement in the understanding of flame synthesis of 1-10 nm sized nanoparticles (Chapter 2, 3, 4 and 5)

Chapter 2 and 3:

Collisional growth rate of nanoparticles at high temperatures was found to be a function of particle size, and temperature of the system. For titania nanoparticles, enhancement in collisional growth rate was observed both through controlled experiments, as well as, molecular dynamics simulations. Controlled experiments were performed using a furnace aerosol reactor operated at fixed temperatures. Molecular dynamics based model was developed based on simulated annealing for nanoparticle equilibration, and trajectory calculations for collisions to calculate the collisional correction factor. This collisional correction factor (enhancement) increases as temperature, and/or size decreases. Some inconsistencies in the experimental findings, and modeling simulations were elucidated. This understanding of collisional growth rate of neutral particles shows there is a significant role played by interactive forces in the collisional growth of sub-10 nm titania nanoparticles.

Chapter 4 and 5:

In a flame system, typically particle-particle and particle-ion interactions take place simultaneously in time scale of less than a second. We measured the percentage of charged particles and found the upper and lower limits for the charge fraction. Moreover, the charge fraction for Argon flame was found to be higher than nitrogen flame, suggesting former involves

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higher ion/electron concentration in the flame than latter. Complementary to this, the simulations for particle-particle and particle-ion interactions suggest similar trends for particle charging. For unipolar ion environments, the particle size distribution could be more monodisperse than polydisperse. This is an important finding, as several researchers have failed to control standard deviation of particle size, during flame synthesis of nanoparticles.

Overall these two chapters provide with tools, and knowledge to guide the researchers to investigate the synthesis of particles from flames in the size range from 1-10 nm with precise control of size, and morphology.

9.1.2 Insights on Particle Charging Models (Chapter 2, 3, 4 and 5)

The particle charge in the gas-phase systems (flame reactors/dusty plasmas) can vary by a variety of mechanisms-ion and electron fluxes collected by the particles via collisions and charge transfer

[1, 2], photo-ionization [3], thermionic emissions, chemical ionization [4], and so on. Most widely studied mechanism in aerosol charging in gas-phase is diffusion charging, which occurs as a result of random thermal motion of ions and particles, which leads to ion/particle collisions and the particles become charged by capturing ions.

Different Charging Theories

Several theories for the bipolar diffusion charging of spherical aerosol particles have been reviewed [5-12]. Classical charging theories can be divided into two groups: one approach extends the equilibrium gas kinetic theory to the collision of particles with ions and postulates that the

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charge distribution follows Boltzmann statistics [13-15]. The other approach is based on the steady-state ion flux towards a sphere calculated from the diffusion-mobility equation; this flux is then related to the ion-aerosol combination coefficients [12], thus allowing for the calculation of the charge distribution on the aerosol particle [16-18].

The conventional charging of aerosol particles using air ions is fundamentally a non-equilibrium process. As pointed out by Fuchs (1963) [19] in his well-known criticism of the equilibrium hypothesis of Keefe et al. (1959) [13], this non-equilibrium behavior is brought about by the absence of desorption of the adsorbed ions from the particle surface. The often employed

Boltzmann law for bipolar charging is thus not a consequence of equilibrium considerations, but is only a mathematical approximation to the steady state charge distributions obtained through the method of non-equilibrium kinetics in the continuum regime [20].

According to Fuchs’ theory, the charging coefficient is a complex function of the charges carried by the particle, particle size, particle conductivity, and the system temperature, as given by Eq.

(9.1-9.4).

 2         c   exp i  i  k T      b  i   1    (9.2)     i   1 exp i    c   / 4D  exp x dx   i     kbT  0  kbT   

1   2  8kbT  kbTZ  16 2 D  M  c   , D  and       Here, m e 3 c  M  m  ,

  The collision probability, i , for the ion-attachment coefficient is

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2  b      min,i  (9.2) i      

2 2  2   bmin,i  ra 1 i  ra  (9.3) 3k T  b 

e 2  i a 3  i r    K  (9.4) 2 2 2 4 0 r   2r r  a 

On the other hand, Boltzmann equilibrium distribution, commonly known as the Boltzmann Law, describes the equilibrium charge distribution of particles as,

2 푛푞 (푒푞) = exp [− ] (9.5) 푛0 2휋휀푑푝푘푇

where, 푛푞 is the concentration of particles carrying 푞 elementary charges.

Mayya (1994) [21] showed that if true equilibrium existed via charge carrier adsorption and desorption, the obtained charge distributions would differ significantly from the presently known distributions including the Boltzmann law. Most importantly, they would show concentration dependence even for symmetric bipolar charging. On the other hand, in a hypothetical environment where there is aerosol charging in the presence of a large number of free-electrons at sufficiently high temperatures, continual charge carrier adsorption/desorption and thus the establishment of equilibrium are physically possible. Due to their large mobility, unipolar charging with free electrons gives rise to an order of magnitude higher charges on particles at relatively short times than ionic charging would. However, irreversible electron absorption cannot go on indefinitely, especially for small particles (< 10 nm size) of low work function materials or at higher

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temperatures like in a flame aerosol reactor. The system would then attain a limiting or a final state, describable in terms of equilibrium properties [11, 21, 22].

Model Predictions v/s Experimental Measurements

Figure 9.1 compares the percentage of charged particles in a flame aerosol reactor using the two experimental approaches of neutralizer, half-mini DMA, and electrometer, and boosted butanol

CPC with Fuchs and Boltzmann theory of charging. Fuchs theory predictions for the charge fraction depends on the mass, and mobility of the flame ions, and flame temperature. Here, the experimentally measured values of ion mass, and mobility are used [1, 2] for the calculations, while different temperature values are considered. We found that when the temperature of 100 C is simulated in the Fuchs theory, it shows a reasonable comparison with the experimentally measured percentage of charged particles using Method 1. Even higher value of temperature (500

C) as input to the model shows even higher prediction from Fuchs theory. It is again important to note here there Fuchs theory only considers interactions between the particles and ions in a bipolar ion environment, and ignores other charging mechanisms.

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Figure 9-1. Comparison of percentage of charged particles, a) measured using method 1 (neutralizer, half-mini DMA, and electrometer) b) measured using method 2 (boosted butanol CPC); c) calculated from Fuchs theory of charging at different temperatures (25, 100, 500 C), and d) calculated from Boltzmann theory of charging at 500 C.

The Boltzmann theory predictions for the percentage of charged particles is also shown as a reference in this figure for T = 500 C, which is found to under-predict the experimental findings.

This was quite expected because of equilibrium assumptions in its formulation.

Particle Charging Mechanisms in Flames

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Figure 9-2. Schematic to understand different charging mechanisms, during titania formation and growth in a flame reactor.

Figure 9.2 provides a schematic to understand the importance of different charging mechanisms during flame synthesis of titania nanoparticles in flame aerosol reactor. Ions are formed in the flame due to chemical ionization of methane, oxygen, argon/nitrogen and titania precursor. This leads to the formation of ions of both polarities, as well as, electrons, which recombine with each other, but also gets generated continuously. These ions can diffuse and charge the particles in the flames through diffusion charging depending on ion mass & mobility, and flame temperature, whereas electrons can adsorb/desorb on the particle surface depending on the electron concentration, charge on the particle, as well as the particle work function [22]. At very high temperatures, particles can also undergo thermal ionization, but, as per our experimental finding, we do not see that to be the case, as the particle charge distribution is bipolar. In order to support

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this argument, we performed time scale analysis for titania nanoparticles thermal emissions, 휏(푑푝), as per the procedure described previously [23].

−1 푒2 4휋푚 푘2푇2 푒2 (푉 + 2 푒 2퐶 (9.6) 휏(푑푝) = {휋푑푝 3 (1 + ) exp ( )} ℎ 2휋휀푑푝푘푇 푘푇

Where, 푚푒 is the mass of electron, 푘 is the Boltzmann constant, ℎ is the plank constant, 푒 is the elementary charge, 푉 is the work function of material making up the particle, which is 7.96 eV

[24]. It is found that the characteristic time for thermal charging is 5-8 orders of magnitude higher than the residence time in the flame for titania nanoparticles in 1-10 nm size range. For instance, for a flame temperature of 2000 K, and particle size of 5 nm, the characteristic time for thermal emissions was found to be ~ 104 seconds.

9.1.3 Classification and counting of 1-10 nm sized particles (Chapter 6 and 7)

Chapter 6:

Half-mini DMA, a high flow DMA, was investigated here for the classification of sub-2 nm particles. It was found that the flow is in the incompressible regime. The transfer function of Half- mini DMA and Nano-DMA was compared, and it was found that the former has much better resolution, and transmission efficiency than the latter. Stolzenburg model for diffusive transfer function closely explains the experimental data. This work opens up the way to comprehensively characterize the performance of Half-mini DMA.

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Chapter 7:

Boosted butanol based CPC performance was evaluated for sub-3 nm particles, and we found that with appropriate calibration for different types, and sizes of the particles, the boosted CPC can be used for their measurement with minimal background. The maximum detection efficiency for sub

3 nm particles was achieved at the saturator temperature of 45°C and capillary flow rate of 70 sccm. Flame-generated particles, as small as 1.2 nm in mobility diameter for titanium dioxide, and

1.5 nm for soot were found to be activated using the optimal operating condition. The negatively charged particles were activated slightly more than the positively charged due to difference in the interactive forces with the butanol vapors. This is important as butanol based CPCs are commonly available in the aerosol research laboratories, and therefore can be easily used by researchers to do sub-3 nm measurements.

9.1.4 Capture of suspended particulate matter (Chapter 8)

In this work, atmospheric pressure plasma reactor was evaluated for the first time to enhance particle charging, and therefore particle capture. ESPs fail to charge particles efficiently in ultrafine size range, and therefore plasma reactor was explored to achieve high particle charging for sub-

100 nm particles. The charge state of the particles is observed to be bipolar for both the AC and

RF plasmas, with more multiply charged particles for the RF plasma. This work lays the fundamental foundation for the future applications like using a plasma reactor in conjunction with an ESP.

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9.2 Future Work

9.2.1 Flame Synthesis of 1-10 nm sized nanoparticles

While the experiments and simulations in Chapter 2, 3, 4 and 5 focused on developing in-depth understanding on the particle-particle and particle-ion interactions in the flame system, the future direction should be to focus on utilizing this information of collisional growth and charging in order to synthesize 1-10 nm sized particles with controlled particle sizes, and morphology. The unipolar ion environment should be explored further in the experiments, probably through external fields assisted combustion and material synthesis. This could promote the synthesis of particles with a monodisperse size distribution.

In addition to applications, the fundamental understanding of collisional growth could be refined, based on the drawbacks of the experiments, and molecular dynamics simulations listed in Chapter

3. The effect of crystal structure of nanoparticles, as well as, the role of defects, and surface charge on collisional growth rate should be evaluated. This is important so that the gap between the experiments and models for collisional growth rate can be bridged, and the physics behind these collisions revealed. Another important suggestion for future work is to ensure proper capture of sub-10 nm particles from flames, and prevention of their future agglomeration, before they are used in different applications.

Regarding the charging models for flame synthesis of sub-10 nm particles, there are several models for understanding particle-particle interactions, particle-ion interactions (non-equilibrium

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process), particle-electron interactions at high temperatures (equilibrium process), but there has been little understanding of the combined effect of these charging mechanisms, especially when there are external electric fields present. This makes the overall charging process, and the final charge acquired by particles a little more complicated to predict in plasma systems, thermal like a flame reactor (Chap 2-5), or non-thermal plasma reactor (Chap 8). As a future direction, a robust model which incorporates the effect of all the possible particle charging scenarios, with simultaneous effects of particle-ion interaction, particle-electron interactions, particle-particle interactions, chemical ionization of molecular clusters, direct ionization of particles (thermo/photo induced), screening effect due to high ion concentration environment (importance of Debye length) in the framework of non-equilibrium charging process should be investigated in greater detail to understand the experimental data accurately. Moreover, this will also shed light on the relative importance of different charging mechanisms in different aerosol systems.

9.2.2 Instrumentation

For the instrumentation of sub-10 nm particles, particle classification based on size, and composition, as well as, particle number concentration should be determined precisely. In Chapter

6, only the working section of the Half-mini DMA was evaluated for particle classification, but a comprehensive study involving the inlet section (with rings), working section, and outlet section could be undertaken using Solid works, and design tools. This study will develop a better understanding of the transmission efficiency in different sections of the instrument, which would aim in optimizing the design of the high resolution DMAs in the future. Another important

241

direction would be to review the transfer functions of different high flow DMAs both through experiments, as well as, numerical simulations.

For the counting of sub-3 nm particles using a boosted butanol based CPC 3776, the focus should be on the daunting task of the appropriate calibration of neutral particles, which is an open research question. Another very interesting work would be to develop the understanding of butanol condensation on sub-3 nm particles using molecular dynamics simulations, and understanding in detail, the effect of particle material, morphology, charge, etc. The physics behind the process of preferential condensation of butanol vapors on negatively charged ions/particles as compared to positively charged ions/particles is not understood well.

9.2.3 Plasma Reactor coupled with Electrostatic Precipitators

In Chapter 8, plasma reactor was explored as a possible charging tool for the development of particle capture technologies. In this work, only the flow-through Ar plasmas were considered for controlled study, but to realize ESP applications, enhancement in particle charging should be studied in air. For this purpose, a cross-flow configuration for particle charging should be explored, where plasma jet (Ar) charges the particle stream (air) in a cross flow configuration. Second, the effect of different gas compositions on particle charging should be explored, as different gases preferentially acquire charge of different polarities. This could be useful in enhancing the unipolar charging of the particles, which is very important for their capture in an electrostatic precipitator.

Third, the effect of different types of particles should be considered, as particle with low conductivity might behave very differently, and have lower charge fractions. Third, a design to include a plasma reactor in conjunction with an electrostatic precipitator may be tested to enhance

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the overall charging efficiency of the particles. While doing so, one should be careful of the total energy expense in this modified electrostatic precipitator

9.3 References

1. Wang, Y., et al., Influence of flame-generated ions on the simultaneous charging and

coagulation of nanoparticles during combustion. Aerosol Science and Technology, 2017.

51(7): p. 833-844.

2. Sharma, G., et al., Modeling simultaneous coagulation and charging of nanoparticles at

high temperatures using the method of moments. Journal of Aerosol Science, 2019. 132:

p. 70-82.

3. Jiang, J., M.-H. Lee, and P. Biswas, Model for nanoparticle charging by diffusion, direct

photoionization, and thermionization mechanisms. Journal of electrostatics, 2007. 65(4):

p. 209-220.

4. Biswas, P., Y. Wang, and M. Attoui, Sub-2nm particle measurement in high-temperature

aerosol reactors: a review. Current Opinion in Chemical Engineering, 2018. 21: p. 60-

66.

5. Hidy, G.M. and J.R. Brock, The dynamics of aerocolloidal systems: International reviews

in aerosol physics and chemistry. Vol. 1. 2016: Elsevier.

6. Fuchs, N. and A. Sutugin, High-dispersed aerosols, in Topics in current aerosol

research. 1971, Elsevier. p. 1.

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7. Whitby, K. and B. Cantrell. Fine particles. in International Conference of Environmental

Sensing and Assessment, Las Vegas, NV, Institute of Electrical and Electronic Engineers.

1976.

8. Liu, B.Y.H. and D.Y.H. Pui, On unipolar diffusion charging of aerosols in the continuum

regime. Journal of Colloid and Interface Science, 1977. 58(1): p. 142-149.

9. Wen, H.Y., G.P. Reischl, and G. Kasper, Bipolar diffusion charging of fibrous aerosol

particles—I. charging theory. Journal of Aerosol Science, 1984. 15(2): p. 89-101.

10. Gopalakrishnan, R., P.H. McMurry, and C.J. Hogan Jr, The bipolar diffusion charging of

nanoparticles: A review and development of approaches for non-spherical particles.

Aerosol Science and Technology, 2015. 49(12): p. 1181-1194.

11. Mayya, Y.S. and B.K. Sapra, Variation of the aerosol charge neutralization coefficient in

the entire particle size range. Journal of Aerosol Science, 1996. 27(8): p. 1169-1178.

12. Hoppel, W.A. and G.M. Frick, Ion—Aerosol Attachment Coefficients and the Steady-

State Charge Distribution on Aerosols in a Bipolar Ion Environment. Aerosol Science

and Technology, 1986. 5(1): p. 1-21.

13. Keefe, D., P.J. Nolan, and T.A. Rich. Charge equilibrium in aerosols according to the

Boltzmann law. in Proceedings of the Royal Irish Academy. Section A: Mathematical and

Physical Sciences. 1959. JSTOR.

14. Matsoukas, T., On the electrostatic energy of charged aerosols. Journal of Aerosol

Science, 1995. 26(1): p. 147-150.

15. Matsoukas, T., Charge distributions in bipolar particle charging. Journal of Aerosol

Science, 1994. 25(4): p. 599-609.

244

16. Hoppel, W.A. and G.M. Frick, Comment on the Comparison of Measured and Calculated

Values of Ion Aerosol Attachment Coefficients. Aerosol Science and Technology, 1989.

11(3): p. 254-258.

17. Hoppel, W.A. and G.M. Frick, The Nonequilibrium Character of the Aerosol Charge

Distributions Produced by Neutralizes. Aerosol Science and Technology, 1990. 12(3): p.

471-496.

18. Keefe, D. and P.J. Nolan, Influence of image forces on combination in aerosols.

Geofisica pura e applicata, 1961. 50(1): p. 155-160.

19. Fuchs, N.A., On the stationary charge distribution on aerosol particles in a bipolar ionic

atmosphere. Geofisica pura e applicata, 1963. 56(1): p. 185-193.

20. Filippov, A.V., Charge distribution among non-spherical particles in a bipolar ion

environment. Journal of Aerosol Science, 1994. 25(4): p. 611-615.

21. Mayya, Y.S., On the “Boltzmann Law” in bipolar charging. Journal of Aerosol Science,

1994. 25(4): p. 617-621.

22. Mayya, Y.S. and W. Holländer, Statistical mechanics of equilibrium charging of metallic

aerosol particles with free-electrons at elevated temperatures. Journal of Aerosol

Science, 1995. 26(7): p. 1041-1054.

23. Balthasar, M., F. Mauß, and H. Wang, A computational study of the thermal ionization of

soot particles and its effect on their growth in laminar premixed flames. Combustion and

flame, 2002. 129(1-2): p. 204-216.

24. Kashiwaya, S., et al., The work function of TiO2. Surfaces, 2018. 1(1): p. 73-89.

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Appendix A. Supplemental Information for Chapter 3

Figure A-1. Maxwell Boltzmann velocity distribution for a nanoparticle of size 2 nm

246

Figure A-2 Collisional probability of particles of equal size (1.8 nm) as a function of normalized particle velocity, and impact parameter at 4 different temperatures of 500, 1000, 1500, 2000 K.

247

Figure A-3. Collisional probability of particles of equal size (3.6 nm) as a function of normalized particle velocity, and impact parameter at 4 different temperatures of 500, 1000, 1500, 2000 K

248

Figure A-4. Collisional probability of particles of unequal size (1.8 nm, 2.8 nm) as a function of normalized particle velocity, and impact parameter at 4 different temperatures of 500, 1000, 1500, 2000 K.

249

Appendix B. Supplemental Information for Chapter 4

Figure B-2. Total PSD for CH4-O2-N2 and CH4-O2-Ar at low TTIP concentration

Figure B-1. Nascent flame-generated positively and negatively charged particle size distribution for CH4-O2-N2 and CH4-O2-Ar at low TTIP concentration.

250

Figure B-3. Effect of the sampling height above the burner on charged particle size distribution, and total particle size distribution, at a fixed precursor concentration.

251

Charged PSD Total PSD

Figure B-4. Effect of four different precursor concentrations on charged particle size distribution, and total particle size distribution, at a fixed height above the burner (3.5 mm)

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Appendix C. Supplemental Information for Chapter 5

1. Derivation of the collision probability for the ion-attachment coefficient

 The collision probability, i , for the ion-attachment coefficient is

2  b      min,i  (C.3) i      

2 2  2   bmin,i  ra 1 i  ra  (C.4)  3kbT 

e 2  i a 3  i r    K  (C.5) 4 r 2 2 2 0  2r r  a 

The expression for the radius of the limiting sphere  is

5 2 3 5 a 3 1    1      2    2      1   1 1   1   (C.6)  2 5  a  3  a  a  15  a            

In the free molecular regime, where   a , Eq. (C.4) simplifies to

  2     a (C.7) 3

Using Eq. (C.1) and Eq. (C.5),

b2  4 a    ~ min 1 i 2    (C.8)   3  

Now, let us look at two cases: a. i = 0 and K  0

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In this case, the particles are neutral but the image potential is non-zero.

e 2  a 3  0 r   K  (C.9) 4 2 2 2 0  2r r  a 

2 2  2   b0  r 1 0  r (C.10)  3kbT 

 2 3   2 2 2 e a 1 1 b0 ~ r 1 K    (C.11) 3k T 4 2  2  2 2 r 2 r 2  a 2  b 0   a   

2 2 4 1 e For   a ,     2 a2 ~  and p  , kbT 4 0

3 2 2  a  1 1  b0 ~ r 1 pK  4  2 2 2  (C.12)  3  r r  a 

1 1 Since 4  2 2 2 , the expression for b0 can be further simplified to  r r  a 

a 3 b 2 ~ r 2  pK (C.13) 0 3r 2  a 2 

To get the values for the minimum apsoidal distance, ra , and for bmin,0 , Eq. (C.11) is differentiated and equated to zero, yielding

1 5  1 3 pK 4 a 4 pK 4 4     (C.14) ra ~ a       3  2  3 

3 4 b 2 ~ a 2  a 2 pK (C.15) min,0 3

 Combining Eq. (C.6) and Eq. (C.13), a simplified polynomial expression for 0 is derived.

254

2  a  pK   0 ~ 2 1 2  (C.16)   3a 

b. i  0and K

In this case, a simplified expression is derived for charged particles, where the value of K is non- zero. From Eq. (C.2) and Eq. (C.3), we get

3 2 2  2pi 2 pi a  1 1  bi ~ r 1    pK  4  2 2 2  (C.17)  3 3r 3  r r  a 

1 1 Since 4  2 2 2 , the above expression can be further simplified as  r r  a 

2  2pi  2Xapi pKa b ~ X 2 a 2 1   i    2 (C.18)  3  3 3X 1

In the above expression, X  ar. To get the minimum value, Eq. (C.16) can be differentiated, but no closed form solution can be obtained because the resultant polynomial is a quintic equation.

Perturbation theory is then used to obtain the roots.

 pi   2pi   pK  pi X 5   X 4  2X 3   X 2  1 X ~ (C.19)  3a   3a   3a  3a

First, the unperturbed solution of the above equation (K=0) is evaluated.

2 2  pi  X 0 1 X 0 1  X 0    0 (C.20)  3a 

The solution to the above equation is assumed to be of the form

X ~ X 0  K X1  KX 2 (C.21)

Plugging the value of X from Eq. (C.19) in Eq. (C.17) leads to

255

5  pi  4 3 X 0  K X 1  KX 2    X 0  K X 1  KX 2   2X 0  K X 1  KX 2   3a  (C.22)  2 pi  2  pK  pi   X 0  K X 1  KX 2   1 X 0  K X 1  KX 2  ~  3a   3a  3a

Using the binomial theorem, the following expression is derived:

2  pi  2 1 5 K X 1  5KX 2 10KX 1   1 4 K X 1  6KX 1  4KX 2   3a 

2  2 pi  2 2  21 3 K X 1  3KX 1  3KX 2   1 2 K X 1  2KX 2  KX 1  (C.23)  3a   pK  pi  1 X 0  K X 1  KX 2  ~  3a  3a

Collecting the coefficients of K0 , K , and K from Eq (C.21), and equating them to zero gives

the expression for X 2 . Therefore,

p K X ~ 1 3a (C.24) pi 2 |1 | 3a

In order to obtain a polynomial expression for the collision coefficient, and thereby obtain the charging coefficient with reasonable accuracy, Eq. (C.22) is simplified further.

K X 1 ~ 1 (C.25) 2 | i |

2 From Eq. (C.23) and Eq. (C.16), an expression for bmin,i is derived as follows:

2 2 bmin,i ~ C1a C2a (C.26)

In Eq. (C.24), the constants C1 and C2 are as follows.

256

2 2  r   2 p | i |   K   2 p | i |  C   a  1   1  1  1      a   3   2 | i |   3        (C.27) pK 2  r  2 p  K  K   C    a  p | i |  1  | i | 2 2  2     r   3  a  3     2 | i |  3 a  1   K       2 1 1   a     2 | i |        

 The simplified polynomial expression for i is therefore

C a 2  C a  4 a    ~ 1 2 1 i 2    (C.28)   3  

2. Derivation of the ion-attachment coefficient

The expression for the ion-attachment coefficient is given by

 2         c   exp i  i  k T      b  i   1    (C.29)     i   1 exp i    c   / 4D  exp x dx   i     kbT  0  kbT   

1 8k T k TZ  16 2 D   M  2 Here, c   b , D   b and     m e 3 c   M  m 

Eq. 27 is simplified further to obtain

2 c        i i        (C.30) f   c 4D  i g 

Here

  i   f   exp  (C.31)  kbT 

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 1      i  x  g  exp dx (C.32)   k T  0  b 

Now, let us look at the two cases again.

a. i = 0 and K  0

   Since 1 as T   , then kbT

   1 e 2  a 3       f   ~ 1 ~ 1 K 2 (C.33) k T k T 4    2 2  b b 0  2   a 

This gives

3  pK a  8 a  f   ~ 1 4 1   (C.34) 2   3  

Similarly, the expression g   can be simplified to

 1    1 3 4   i  x  pK a x  8 a  g   exp dx ~ 1 1 dx       3  0  kbT  0 2   3     (C.35) pK a3  8 a  ~ 1  3 1   10   3  

     Clearly,  c 4D g i << f  , therefore

  2   4 a    2  c   0 1    c    0  3   0 ~ ~ f    pK a 3  8 a  1  3 1   (C.36) 2   3   3 2  4 a K p a  ~ c     1   0       3  2   3 

From Eq. (C.14) and Eq. (C.34) and binomial expansion,

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  2 1   2 pK 3 2 i ~ c a 1 2  ~ A0,T v  B0,T v (C.37)  3a  where

2  3  3 A0,T     c   4  (C.38) B0,T   c  pK

b. i  0and K

The expression for charged particles can be easily obtained, as shown in case a.

2  4 a  c   1    3  i     i ~ 2 (C.37) pi 1  pi  1      2   

Using Eq. (C.37) and Eq. (C.26),

2 1  3 3 (C.38) i ~ Ai,Tv  Bi,Tv

Here

2  3  3   c   4  Ai,T   C1 2 pi 1  pi  1     2   

1 (C39)  3  3   c   4  Bi,T   C2 2 pi 1  pi  1     2   

259

Therefore, Eq. (C.34) and Eq. (C.38) represent the simplified polynomial form of the ion- attachment coefficient. This expression is a reasonable approximation for the Fuchs expression in the free molecular regime at high temperatures.

Figure C1 shows a comparison between the steady state charge distribution using Fuchs theory and the simplified expression.

Figure C-1. Comparison between the steady state charge distribution given by the Fuchs’ theory (lines) and the simplified expression (Symbols). a) and b) correspond to T = 1200 K, whereas c) and d) correspond to T = 2400 K. a) and c) show the charge distribution of positively charged particles whereas b) and d) show the charge distribution of negatively charged particles.

260

3. Comparison with previous work:

The ion-attachment coefficient used in this work for the derivation of the moment balance equations is different from previously reported by Park et al.,

2005. The two expressions for the ion-attachment coefficient are compared with the ion-attachment coefficient given by the complete

Fuchs theory. It is found that the ion-attachment expression from Park et al, is much lower as compared to that from Fuchs theory. Figure C3 shows the absolute error for the ion- attachment coefficient used by Park et al., 2005; and this work for different particle sizes. It can be clearly seen that the absolute error Figure C-2. Absolute Percentage Error for Park et al., 2005 and this for Park et al., 2005 is much higher work for both positive and negative ions at 1200 K. as compared to this work, especially for sub-10 nm particles.

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4. Formulation of the coagulation coefficient for charged particles

Here, the expression for the coagulation coefficient of charged particles is fitted in the range

from 0.4 nm to 10 nm to account for the correction factor W . For attractive potentials ( E  0 ),

the correction factor is given by Eq. (C.40a), whereas for repulsive potentials ( E  0 ), the correction factor is given by Eq. (C.40b).

W  1 E (C.40a)

W  exp E  (C.40b)

2  zi z j e where  E  . 4 0 ai  a j kbT

The two expressions for W are fitted for different ranges of  E and a polynomial fit is obtained

as shown in Figure C2.  E is then converted to the size of the two colliding particles as shown in

Eq. (C.41).

1 1 2 1 1 1 W  Q i, jv 3  v~ 3   Q i, jv 3  v~ 3   Q i, j (C.41) 1   2   3

In the above expression, v and v~ denote the size of the two colliding particles.

Figure C2 shows the fit for for different values of . The polynomial fit is shown to closely

predict the exact formulation. The fitting parameters ( Q1,Q2 ,Q3 ) are summarized in Table 5.1

for different values of . Q1 ,Q2 and Q3 are a function of charge on the two particles, given by i and j , and the temperature of the system, T .

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Figure C-3. Comparison between the exact correction factor for coagulation coefficient of charged particles and the fitted values. 5. Model Validation

The model has been validated by ensuring the following:

a. For uncharged particles, the ordinary differential equations for moment balance can be

simplified to the three moment balance equations as described by Lee et al., 1984. This is

also validated by performing simulations for uncharged particles, which gives identical

results a Lee et al., 1984.

b. The overall volume concentration of the particles for simultaneous coagulation and

charging is found to be conserved.

c. The moment model is also validated by comparison with the monodisperse model for

both bipolar and unipolar cases in the manuscript.

263

d. To further validate the model, bipolar charging and coagulation was simulated for the

conditions specified by Alonso et al. (1998). Figure C3 shows the comparison of the

charged particle size distribution with the measurements. There is reasonable agreement

between the model predictions, and the measurements. Similar agreement is obtained by

the moment model (Park et al., 2005) and sectional model (Alonso et al., 1998).

Figure C-4. Comparison of the model prediction with the experimental measurements from Alonso et al., 1998.

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Nomenclature

 Ion-attachment coefficient i i Charge on the particle c  Thermal velocity of the ion m  Mass of the ion Z  Mobility of the ion D  Diffusion coefficient of the ion Ionic mean free path  e Elementary charge  Collision probability  i Limiting sphere radius   Electrostatic potential energy of an ion in the field of the particle i r Distance of the ion from the center of the particle Apsoidal distance ra Impact parameter bi Minimum impact parameter bmin,i K Conductivity of the particle Dielectric constant of a vacuum  0 M Mass of the background gas a Radius of the particle p Constant for charging coefficient A q,T, B  (q,T) Function of charge q and temperature T

 E Potential energy to thermal energy ratio for the Coulombic potential

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References: Alonso, M., Hashimoto, T., Kousaka, Y., Higuchi, M., & Nomura, T. (1998). Transient bipolar charging of a coagulating nanometer aerosol. Journal of Aerosol Science, 29(3), 263- Lee, K. W., Chen, J., Gieseke, J. A. (1984). Log-Normally Preserving Size Distribution for Brownian Coagulation in the Free-Molecule Regime. Aerosol Sci. Technol. 3:53-62. Park, S., Lee, K., Shimada, M., & Okuyama, K. (2005). Coagulation of bipolarly charged ultrafine aerosol particles. Journal of aerosol science, 36(7), 830-845.

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Appendix D. Supplemental Information for Chapter 6

1. Navier Stokes equations

For steady flow, the continuity equation is

∇ ∙ 풖 = 0, (D1) and the momentum equation is

1 풖 ∙ ∇풖 = − ∇푝 + 휈∇2풖 + 품, (D2) 휌 where u is the velocity of sheath flow, ν is the kinetic viscosity of sheath gas, and g is the gravity due to acceleration.

2. Boundary condition for sheath flow inlet

2.1 Pressure boundary condition

In our calculation, the boundary condition for the inlet sheath flow is constrained by pressure.

휕푣푧 It is reasonable to assume that vr = 0, vθ = 0, = 0 at the sheath inlet, where vz, vr and vθ are 휕푧 axial, radial and tangential velocity of the sheath gas. By using these assumptions in the Navier-

휕푝 Stokes equation, it is shown that = 0 at the sheath inlet, indicating that p is only a function of z 휕푟 here. It is known that it is the pressure drop (Δp), not the gauge pressure itself, that drives the incompressible gas flow. So we let the gauge pressure (p) = 0, assuming the sheath inlet is atmosphere environment. This setting of boundary conditions is simulating a Half Mini DMA

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operated under an open loop while the sheath flow is being drawn from the sheath outlet of the

DMA. Table D1 summarizes the boundary conditions in our simulation.

Sheath flow inlet Gauge pressure = 0

Sheath flow outlet Flow rate = Q

Aerosol flow inlet Uniform velocity

Aerosol flow outlet Flow rate = q

Table D-1. Boundary conditions used in our simulation

For the sheath flow inlet, different boundary conditions were also explored – uniform inlet velocity profile, parabolic velocity profile, and sheath flow rate as Q, but they all failed to converge.

1.2 Effect of inlet pressure of sheath flow on the flow field

The effect of inlet gauge pressure of the sheath flow is analyzed on the flow field. We compared the flow simulation results for different gauge pressure at sheath flow inlet, which are p = -100,

100, -1000, +1000. Table D2 gives the pressure drop (Δp) between the sheath flow inlet and outlet.

We can see that the absolute difference between each magnitude of pressure is within 1.2 Pa.

The comparison of Δp at different sheath inlet pressure.

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p (Pa) 0 100 -100 1000 -1000

Δp (Pa) 1345.8 1346.0 1345.8 1346.7 1347.0

Table D-2. The comparison of Δp at different sheath inlet pressure.

Because our interest is on the flow field in the working section of the Half Mini DMA, we compared the axial velocity at different locations that are shown in Figure D1. Figure D2 displays the axial velocity at different z locations in the working section of the DMA. It is seen that the influence of the inlet pressure p on vz is insignificant, because vz profiles for different inlet pressure nearly collapse to one curve at different locations.

Figure D-1. Different locations in the working section of Half Mini DMA.

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Figure D-2. The comparison of axial velocity profile at different locations with various p in the working section of Half Mini DMA.

1.3 Effect of inlet length of the trumpet on the flow field

In order to understand whether the flow goes through a corner within the flow field, we simulated the flow field with different Lin, and the axial velocity profile at different h (Figure D3). Figure D4 shows the streamlines within the flow field in the trumpet part. Indeed, the corner region would disappear as Lin increases. Figure D5 shows the axial velocity profile (vz) along the radial axis at different h. vz is found to be greater than zero in the range of r from 12.5 mm to 18 mm. However, the velocity at the corner is very low, and the maximum vz is only 0.12 m/s for h1-4. Because our interest is in the flow field within the working section, we also investigated how the corner region would change the flow field there. Figure D6 shows the axial velocity profile from z1 to z4 as we increase Lin. The red circles show the relative difference (ε) between the simulation results of Lin

270

= 0 mm and 45 mm. vz profiles at the same z for different Lin almost overlap each other, except in the regions near r = 4.25 mm and 5.5 mm. But still, ε is below 3.5 % in these two regions. Hence, we conclude that the influence of Lin on the flow field in the working section is small. We used Lin

= 2 mm in our manuscript, because a longer Lin leads to more computational burden. Further, setting Lin = 2 mm is more helpful in obtaining a convergent result than Lin = 0 mm when Q is above 150 lpm. The influence of the laminarization screen will be considered in our future modeling work.

Figure D-3. Schematic of trumpet inlet part.

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Figure D-4. Streamlines with the flow field of trumpet at various Lin. (q = 9 lpm, Q = 136 lpm)

0 Lin = 2 mm h -2 0

h1 -4 0.15 vz_max = 0.12 m/s h2 -6 0.10 h3

(m/s)

z 0.05

(m/s)

v h

-8 4 v

-10 0.00

-0.05 -12 13 14 15 16 17 18 r (mm) -14 0 2 4 6 8 10 12 14 16 18 r (mm)

Figure D-5. The axial velocity profile at different h. (q = 9 lpm, Q = 136 lpm)

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Figure D-6. The axial velocity profile (vz) and relative difference (ε) at different z with various Lin. (q = 9 lpm, Q = 136 lpm)

3. Influence of particle size and q/Q on transfer function

The diffusion of sub-2 nm particles and q/Q play important roles in retaining the triangular shape of the transfer functions. Figure D7 displays the resolution and transfer function height (Ωmax) as a function of Q/q (q = 3 lpm) for the Half Mini DMA. In Figure D7(a), we can see that the theoretical resolution curve given by Knutson and Whitby (1975) is equal to Q/q, and the simulation values of R are all below the theoretical curve. Increasing the sheath flow rate Q does increase R. Furthermore, R increases with particle sizes. In Figure D7(b), we can see that all simulation height of the transfer function is below the theoretical value (100%) in Knutson and

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Whitby’s theoretical model. Ωmax reduces as Q/q increases. In addition, larger particles have higher transmission efficiency in the working section of the Half Mini DMA.

(b) 90 dp = 0.7 nm d = 1 nm 80 p dp = 1.4 nm

(%)

max  60

40 10 20 30 40 50 60 Q/q

(a) d = 0.7 nm 60 p dp = 1 nm

50 dp = 1.4 nm Knutson-Whitby (1975) 40

R 30

10 20 30 40 50 60 Q/q

Figure D-7. Resolution (a) and transfer function height (b) vs. Q/q (q = 3 lpm) for Half Mini DMA.

4. Mesh Size and Numerical Diffusion

Since the Peclet number is much larger than the Reynolds number, numerical diffusion can lead to artificial broadening of the transfer function. This can cause the model to predict lower

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resolution in the simulations. To ensure that the effect of numerical diffusion is minimal, mesh sensitivity analysis is performed to find the optimal mesh size. Moreover, the mesh is refined in the particle transport zone, which further reduced the effect of numerical diffusion. Figure D8 shows the comparison of non-refined mesh and the refined mesh. It is evident that there is more diffusion broadening of the particle convective flux for non-refined mesh.

Figure D-8. The convective flux of particles with non-refined (left) and refined (right) mesh. The simulation conditions correspond to dp = 1.4 nm, q = 9 lpm, Q = 136 lpm, inner electrode voltage is -318 V Figure D9 shows the sensitivity analysis, where the resolution is calculated for increasing mesh number for both refined and non-refined mesh. This analysis is performed for dp = 1.4 nm, q = 9 lpm, Q = 136 lpm. It is found that the resolution increases as the mesh size increases; but it flattens out on further increase in the mesh number. It is important to note that as the mesh size increases, the computational load for the simulations also increases. Keeping this in mind, an optimal mesh number is chosen as 4.18×105, where the resolution for this case is found to be 11.40. Further increase in mesh size to 6.24×105 increases the resolution to 11.45 (relative error < 0.5 %). This

275

further convinces the authors that numerical diffusion is not confounding the results for the transfer function in their simulations.

11 mesh chosen in this study 10

R 8 Refined mesh Non-refined mesh 7

4 1x105 2x105 3x105 4x105 5x105 6x105 Mesh number

Figure D-9. Effect of mesh number on the resolution of Half-Mini DMA. The simulation conditions correspond to dp = 1.4 nm, q = 9 lpm, Q = 136 lpm

5. Comparison of simulated and theoretical diffusive transfer function

At the aerosol exit, the non-dimensional form of the standard deviation (휎푡ℎ푒표) is expressed as

휎푡ℎ푒표 = 퐺퐷푀퐴 ∙ 퐷̃. 퐺퐷푀퐴 is the non-dimensional geometry factor and 퐷̃ is the non-dimensional particle diffusion coefficient (Stolzenburg and McMurry, 2008). To compare our simulation results with the theoretical value for the standard deviation, our simulation data points are fitted using the

Stolzenburg’s formulation of diffusive transfer function in non-dimensional form, as given by

Equation (D3).

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푍̃ −(1+훽) 푍̃ −(1−훽) 휀 ( 푝 ) + 휀 ( 푝 ) 휎 훺 (푍̃ , 훽, 훿, 휎) = [ √2훿 √2훿 ] (D3) where 푑 푝 2훽(1−훿) 푍̃ −(1+훽훿) 푍̃ −(1−훽훿) √ −휀 ( 푝 ) − 휀 ( 푝 ) √2훿 √2훿

−푥2 휀(푥) = 푥 ∙ erf(푥) + 푒 /√휋, 휎푓푖푡푡푒푑 is fitting the value of 휎 in Equation (D3). Figure D10 shows the fitted transfer function to the simulated data points.

90 Simulation data 80 Fitted curve 70 60

(%) 50

 40 30 20 10 0 0.6 0.8 1.0 1.2 1.4 ~-1 Z

Figure D-10. The simulation data fitted by the Stolzenburg’s diffusive transfer function. The simulation conditions correspond to dp = 1.4 nm, q = 9 lpm, Q = 136 lpm.

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0.035 q = 3 lpm q = 5 lpm 0.030

0.025 increasing Q

fitted

 0.020

0.015

0.010 0.010 0.015 0.020 0.025 0.030 0.035

theo

Figure D-11. The comparison of fitted and theoretical sigma as increasing Q

Figure D11 compares 휎푡ℎ푒표 and 휎푓푖푡푡푒푑 for different flow conditions. It is found that there is a close match between the two values. The difference between them is contributed due to the non- idealities in the flow. It is important to note that the Stolzenburg’s theoretical model for calculating

휎푡ℎ푒표 assumes uniform slug flow or fully-developed Poiseuille flow in the DMA (Stolzenburg,

1988). The simulated flow fields, as can be seen in Figure 6.3(c) shows a boundary layer near both inner and outer electrode. In Figure D11, there is more mismatch for higher aerosol flow (q) due to more radial component. This leads to the thickening of boundary layer (Figure 6.3(c)) near the inner electrode, and therefore more deviation from the flow configuration, assumed by

Stolzenburg.

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References

Knutson, E., and Whitby, K. (1975). Aerosol Classification by Electric Mobility: Apparatus, Theory, and Applications. J. Aerosol Sci., 6:443–451. Stolzenburg, M. R. (1988). An Ultrafine Aerosol Size Distribution Measuring System. University of Minnesota: Minneapolis, MN. Stolzenburg, M. R. and McMurry, P. H. (2008). Equations Governing Single and Tandem DMA Configurations and a New Lognormal Approximation to the Transfer Function. Aerosol Sci. Technol., 42:421-432.

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Appendix E. Supplemental Information for Chapter 8

1. Detailed Plasma Characterization Approach

1.1 Plasma fluid model

The plasma fluid model is used to obtain electron density from external circuit measurements, voltage and current. Detailed discussion is present in Raizer [1] and Ochkin [2]. The model starts by assuming a drift-diffusion approximation to the charged species flux in a cylindrical tube along the axial direction x:

푑푛 휞 = ∓휇 푛 푬 − 퐷 푒,𝑖 ≈ ∓휇 푛 푬 (E.1) 푒,푖 푒,푖 푒,푖 푒,푖 푑푥 푒,푖 푒,푖

In reality, the flux of charged species is energy dependent but this equation serves as a good first- order approximation. The first term is the drift contribution of the flux and it is proportional to the electrical field strength and the electrical mobility of the charge species. The second term is the diffusion term. In the atmospheric pressure plasma case, the diffusion term is ignored because of the strong electric fields necessary to induce gas breakdown at high pressures. The conductive current density through the gas jg is the sum of the ion and electron flux multiplied by its respective charge:

푗푔(푥, 푡) = 푒(훤푖 − 훤푒) (E.2)

280

We relate the total current density j0 as the sum of the conductive current and the displacement current density:

휕푬 휀 + 푗 = 푗 (E.3) 표 휕푡 푔 표

From the relation that the electric field is the derivative of voltage with respect to distance, the voltage between electrodes is introduced into the working equation. Integrating across the electrode distance d with the statement that the total current is independent of axial position, the equation becomes:

휕푉(푡) 1 푑 휀 + ∫ 푗 (푡)푑푥 = 푗 (E.4) 표 휕푡 푑 0 푔 표

The conductive current jg can be expanded into the charged species flux contribution and separated from the total current equation. To simplify the charged species flux, we assume that the ionic contribution is minor compared to the electronic contribution due to higher electron mobility. By integrating the electric field term across the electrode distance, the equation now consists of voltage and current associated with the gas discharge:

1 푑 푉(푡) 푖 (푡) = 푒휇 푛 ∫ 푬(푥, 푡)푑푥 = 푒휇 푛 (E.5) 푔 푑 푒 푒 0 푒 푒 푑

푉(푡) 퐼 (푡) = 퐴푟푒푎 × 푖 (푡) = 퐴푟푒푎 × (푒휇 푛 ) (E.6) 푔 푔 푒 푒 푑

Rearranging for electron density ne,

281

푑퐼푐(푡) 풅 풏풆 = = (E.7) 퐴푒휇푒푉(푡) 푨풆흁풆푹풑

However, the conductive current Ig(t) cannot be measured directly and it must be inferred from the external I-V characteristic. As shown in equation E.4, the displacement current contribution needs to be subtracted from the total current in order to obtain the conductive current Ig. Typically, this is done by measuring the circuit I-V characteristics when the discharge is on and off and making a subtractive argument to obtain the I-V characteristic of the discharge.

1.2 Lissajous analysis for dielectric barrier discharge plasma

The application of Lissajous figures to DBD reactors is developed as a means to interpret the electrical measurements. This has become a well-established method of extracting key information about the plasma such as energy dissipated per cycle and charge deposited per cycle. The Lissajous figure for DBDs plots the charge waveform against the voltage waveform across the electrodes.

Gas discharges are simply another circuit component and it can be represented electrically with an equivalent circuit model [3]. Typically, a gas discharge is represented as having a resistive component and a capacitive component. The most common experimental approach is to insert a test capacitor with known capacitance in series with the plasma on the ground side. The charge waveform is calculated from the voltage measurement across the inserted capacitor. Further discussion is provided by Pipa and Brandenburg [3]. Presented in Figure E.1 is an example of a

Lissajous plot obtained from experimental data.

282

Figure E-1. Lissajous plot of Ar-H2O dielectric barrier discharge driven at 22.7 kHz with MgSO4 particle flow.

The Lissajous is a visualization of the discharge behavior during a single cycle. The curve can be divided into two distinct phases, plasma on and plasma off. The ideal shape for a DBD is a parallelogram as depicted by the dashed lines in Figure E1. However, non-idealities may occur that distort the shape. The slope of the curves for each phase is related to a characteristic capacitance. The capacitance for the plasma off phase is the capacitance of the total system Ccell.

In this phase, no charge transfer is taking place and the system behaves as an ideal capacitor.

During the plasma on phase, the capacitance is governed by the dielectric material, denoted as Cd.

The plasma-fluid model is also used to obtain experimental values for electron density in the DBD reactor by calculating the plasma impedance. The gas gap voltage and the discharge current is needed to calculate the plasma impedance. The experimentally determined dielectric capacitance

283

can be used to calculate the voltage across the gas gap. The measured circuit voltage V(t) is a sum of the voltage across the dielectric Ud(t) and the voltage across the gas gap Ug(t). Ud(t) can be determined from the charge by dividing the dielectric capacitance. Equation 8 is used to calculate

Ug(t). Using the experimental data from Figure 1, the calculated gas gap voltage waveform is shown in Figure 2a.

푄(푡) 푈푔(푡) = 푉(푡) − 푈푑(푡) = 푉(푡) − (E.8) 퐶푑

In order to obtain the discharge current, we calculate the system current i(t) by taking the time derivative of the charge waveform Q(t). The system current is a sum of the discharge current jr(t) and the displacement current through the gas gap jg(t), equation E.9. Further manipulating equation

E.9 such that the equation is in terms of circuit measurements, we obtain equation E.10. The resulting discharge current waveform is shown in Figure E2b.

푑푈 (푡) 푗 (푡) = 푖(푡) − 푗 (푡) = 푖(푡) − 퐶 푔 (E.9) 푟 푔 푔 푑푡

1 푑푄(푡) 푑푉(푡) 푗푟(푡) = ( 퐶 ) [ − 퐶푐푒푙푙 ] (E.10) 1− 푐푒푙푙 푑푡 푑푡 퐶푑

The instantaneous impedance Z(t) over one period can be obtained by dividing the gas gap voltage waveform by the discharge current waveform. As observed in Figure E2c, the resulting graph looks reasonably constant for the most part with some stark discontinuities. These discontinuities are characterized first by a sudden decrease in instantaneous impedance followed by a sharp increase before returning to the steady value. The spikes may be associated with discharge filaments, where

284

a highly conductive channel forms due to a high concentration of charge carriers are confined into a small volume. Further study is needed to interpret these features. The average impedance is used to calculate the electron density.

The area enclosed by the Lissajous curve is the energy associated with each cycle. The power associated with the discharge is obtained by multiplying the energy for each cycle and the driving frequency. For the case presented in Figure 8.1, the power dissipated over one cycle is 4.19 W.

285

Instantaneous power P(t) can be calculated from the gas gap voltage and the discharge current as shown in Figure 8.2d. By taking the average of P(t), we obtain a similar value to the one obtained from the Lissajous area, 4.16 W. This good agreement provides support for the method presented above to determine gas gap voltage and discharge current.

1.3 Radio-frequency plasma electron density calculation

The current and voltage measurements for the RF plasma requires specialized devices due to non- idealities of circuit components at high frequency and practical challenges associated with using conventional voltage and current probes. We used an RF power probe, Impedans Octiv Poly, to determine the absorbed power and I-V characteristics for the RF plasma. Electrical measurements are taken for the plasma on and plasma off. The plasma off case is taken by switching on the power supply without striking the plasma. This is possible for the RF plasma because the voltage output for the RF power supply is not large enough to spontaneously breakdown the gas. Instead, an ignition is required as the spark generates enough charged carriers to start the electron avalanche mechanism that sustains the RF discharge.

Measurements provided by the power probe needs to be analyzed in order to obtain the desired voltage and current information associated with the RF discharge. More details can be found from the Impedans website. The power probe provides instantaneous current measurements as a complex number, separating the imaginary and the real components. It should be mentioned that the power probe uses proprietary signal processing to convert signals measured in the time- domain into values in the frequency-domain. From this mathematical processing, amplitudes of

286

the current and voltage waveforms are computed and used to calculate other quantities. For the

RF plasma analysis, the important measurements are voltage, real current and imaginary current.

The system circuit contributions to the measured I-V values need to be subtracted to obtain the I-

V characteristics specific to the discharge. To do this, we assume a simple equivalent circuit for the RF plasma system for when the plasma is off and on, Figure E.3.

The important values to determine are plasma resistance Rp and plasma capacitance Cp. We need to account for external circuit contributions from the matching network and the power probe as well as any stray contributions. We assume that there are minor inductance contributions and the circuit behavior is dominated by resistive and capacitive components. The circuit representation is

287

depicted in Figure E3 for the plasma on and off condition. While the plasma is on, the measured electrical values can be attributed to the combined effect of the entire system. The external circuit contribution can be measured when the plasma is off. For the RF plasma, the plasma off condition represents when the RF power source is set to the desired power but the plasma if left unstruck.

This happens because the RF power source does not supply enough voltage to induce spontaneous breakdown, unlike the kHz power source. Performing circuit analysis on both plasma on and off conditions, we can calculate the plasma resistance Rp from electrical measurements. We begin with the expression for the system impedance while the plasma discharge is on. The circuit impedance is composed of two parallel contributions, the plasma impedance Zp and the stray impedance Zs. This can be represented mathematically,

−1 푉퐴 1 1 푍푐 = = ( + ) (E.11) 퐼퐴 푍푝 푍푠

Where VA is the measured ‘plasma on’ voltage and IA is the measured ‘plasma on’ complex current.

From the plasma off equivalent circuit, we can obtain an expression for the stray impedance.

푉퐵 푍푠 = (E.12) 퐼퐵

Where VB is the measured ‘plasma off’ voltage, and IB is the measured ‘plasma off’ complex current.

288

Combining equations E.11 and E.12 and rearranging, we can obtain an expression for the plasma impedance Zp, equation E.13. The current is a complex number. It has real and imaginary components. To simplify the math, the voltage and current product is reduced to a complex number with coefficients as shown by equations E.14 and E.15, where j represents the imaginary number.

−1 퐼퐴 퐼퐵 푉퐴푉퐵 푍푝 = ( − ) = (E.13) 푉퐴 푉퐵 푉퐵퐼퐴−푉퐴퐼퐵

푉퐵퐼퐴 = 푎 + 푏푗 (E.14)

푉퐴퐼퐵 = 푐 + 푑푗 (E.15)

Using the presented coefficient simplification, equation E.13 can be expanded to equation E.14 where the real component of the plasma impedance, namely plasma resistance, is used to calculate the electron density from the plasma-fluid model, equation E.7.

푉 푉 ((푎−푐)−(푏−푑)푗) 푍 = 퐴 퐵 (E.16) 푝 (푎−푐)2+(푏−푑)2

289

2. Approach for the calculation of Particle Charge Fraction

Figure E-4. Comparison of the different methods for calculation of charge fraction

Method 1

The neutral particles coming out of CPR 1 were passed through the plasma followed by an SMPS to obtain the total size distribution. Then, CPR 2 was employed before the neutralizer to capture all the charged particles exiting the plasma. The uncharged particles exiting the CPR 2 were then passed through the SMPS to measure the neutral particle size distribution. The particle concentration with the CPR 2 turned ON was compared to the concentration without the CPR 2

290

before the SMPS. This ratio gives the fraction of neutral particles fraction as the function of particle diameter.

This method of measuring neutral particle fraction has a major drawback as some of the particles charged passing through plasma are lost electrophoretically in the quartz tube. The total concentration measured by the SMPS is lower than the actual value as electrophoretic losses are not accounted for. Hence, the neutral fraction calculated by this method is higher than the actual neutral fraction.

Method 2

The size of magnesium sulfate particles is not affected by the plasma because of the high melting point of this salt. The difference in the size distribution of magnesium sulfate particles measured with the plasma turned OFF as compared to the size distribution with the plasma turned ON, is due to the electrophoretic losses of charged particles in the quartz tube when the plasma is turned

ON. This reasoning is used to overcome the drawback of Method 1.

In Method 2, the neutral particles coming out of CPR 1 were passed through the quartz tube with plasma turned off followed by an SMPS to obtain the total size distribution. Since the particles passing through the quartz tube are neutral, there are no electrophoretic losses. Then, the plasma was turned on and CPR 2 was employed before the neutralizer to capture all the charged particles exiting the plasma. The uncharged particles exiting the CPR 2 were then passed through the SMPS to measure the neutral size distribution. The particle concentration with the plasma and CPR 2

291

turned ON was compared to the total concentration. This ratio gives the fraction of neutral particles fraction as the function of particle diameter.

3. Effect of mean electron temperature on particle charging

Mean Characteristic Time Electron Temperature RF AC 0.5 eV 4.92 ns 11.3 µs 1.0 eV 9.84 ns 22.7 µs 1.5 eV 14.8 ns 34.0 µs 2.0 eV 19.7 ns 45.4 µs Table E-1. Effect of different mean electron temperatures on the characteristic times for particle charging in RF and AC plasmas.

The effect of different mean electron temperatures on the characteristic time for particle charging is summarized in Table E.1. A range of different values 0.5-2 eV were considered based on literature [4-6]. The characteristic time was found to increase with electron temperature, but the difference between a RF plasma (~nanoseconds) and an AC plasma (microseconds) was general and more significant. The effect of different mean electron temperatures on particle charging is shown in Fig. E.4. The average particle charge is more sensitive to the particle size than electron temperature. Therefore, we assumed 1.0 eV for our analysis as a representative value for the mean electron temperature.

292

Figure E-5. Average particle charge as a function of particle diameter for RF and AC plasmas calculated assuming different mean electron temperatures (0.5 – 2 eV).

293

4. Flux balance and evolution of charge on particles inside plasma

Figure E-6. Evolution of electron and ion flux to the particle surface inside the plasma for dp = 90 nm

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Figure E-7. Evolution of particle charge inside the plasma for dp = 90 nm

The charging of particle inside plasma is due to flux of ions and electrons to the particle surface, thermoionization and photoionization. Usually, in a plasma, the emission processes are relatively less significant as compared to the flux of electrons and ions to the particle surface. Figure E5 shows the evolution of the electron and ion flux to the particle surface, with time inside plasma region (both RF and AC plasma). Figure E.6 shows the evolution of particle charge with time. The particle charge and the fluxes are evaluated using equation E.3- E.5. The parameters used for these calculations are listed in Table E.2.

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It can be seen from Figure E.5 that initially, electron flux to the particle surface is very high as compared to the ion flux. This is due to the higher mobility of electrons as compared to ions.

Therefore, particle attains a negative charge with time (Figure E.6). Due to higher electron flux, the negative charge on particle will increase with time and the electrons will start to experience repulsive forces from the particles while the ions will start to experience the attractive forces. As the result, electron flux will decrease while the ionic flux will start increasing with time due to

Coulombic forces. Eventually, both ion and electron flux become equal and particle attains equilibrium charge inside the plasma as can be seen from Figure E.5 and Figure E.6. The time for particles to achieve equilibrium charge for electron temperature of 1 eV in the plasma is very low,

9.8 ns for RF plasma; and 22.7 µs for AC plasma as compared to the residence time (3.8 ms).

Therefore, increasing the flowrate of the gas should not affect the charge that particle attains within the plasma.

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Figure E-8. Average particle charge as a function of particle diameter for RF/AC plasma Effect for different electron temperatures (0.5 – 2 eV)

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References

Y. P. Raizer, Gas Discharge Physics, 2nd ed. Springer, 1997. V. N. Ochkin, Spectroscopy of Low Temperature Plasma. Wiley-VCH, 2009. A. V. Pipa and R. Brandenburg, Atoms, 7 (1) 2019. Balcon N et al 2007 Plasma Sources Sci. T. 16(2) 217 Zhu X et al 2009 J. Phys. D. 42(14) 142003 Zhu X et al 2009 J. Phys. D. 43(1) 015204

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Curriculum Vitae Girish Sharma Email: [email protected]

ACADEMIC BACKGROUND 2020 Ph.D., Energy, Environment and Chemical Engineering., Washington University in St. Louis. Advisor: Prof. Pratim Biswas and Rajan Chakrabarty 2020 M.S., Energy, Environment and Chemical Engineering., Washington University in St. Louis 2019 CEFRC Combustion Summer School, Princeton University, USA 2013 B.Tech., Chemical Engineering, Indian Institute of Technology, Bombay

RESEARCH EXPERIENCE 2015- Graduate research assistant, Washington University in St. Louis present Ph.D. Thesis: “Particle-Particle and Particle-Ion Interactions in Aerosol Reactors”

2014-2015 Junior research fellow, IIT Bombay, Mumbai, India Developed control strategy for the “Simulated moving bed Chromatography”

PROFESSIONAL EXPERIENCE 2013-2014 Graduate Engineer Trainee, Reliance Industries. Jamnagar, Gujarat Worked to understand the basic operations and processes of coker plant in world’s largest grassroot refinery

2012 Summer Intern, Dupont, India Based on mass balance calculations, Suggested and implemented changes in breather relief valves set points, thereby reducing N2 consumption by 60% and preventing the solvent vapor loss completely

HONORS AND AWARDS 2015-2020 McDonnell International Scholars Academy Scholarship for PhD program 2015-2020 Corning Corporate Fellow; Invited talk at Corning Headquarters, NY 2019-2020 Emeritus Chancellor Wrighton Leader Fellowship to study air pollution in India 2019 1st and 2nd Prize for Particle Art Competition at 37th American Association for Aerosol Research Annual Conference, Portland, OR 2017 Student Travel Award, 36th American Association for Aerosol Research Annual Conference, Rayleigh, NC 2017 Best poster award, 36nd American Association for Aerosol Research Annual Conference, Portland, OR 2016 Graduate Student Teaching Assistant Award, Department of Energy Environmental and Chemical Engineering, Washington University in St. Louis

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PUBLICATIONS AND PRESENTATIONS Journal Publications

1. Sharma G., Vignesh S., Hariprasad K., Bhartiya S. Control-relevant multiple linear modeling of simulated moving bed chromatography. IFAC-PapersOnLine 48.8, 2015: 477-482 2. Sharma G.*, Wang Y.*, Koh C., Kumar V., Chakrabarty R, Biswas P. Influence of flame- generated ions on the simultaneous charging and coagulation of nanoparticles during combustion. Aerosol Science and Technology, 2017, 51(7), 833 * Equal Contribution 3. Zhang Q., Sharma G, Wong J., Davis A., Black M., Biswas P., Weber R.. Investigating particle emissions and aerosol dynamics from a consumer fused deposition modeling 3D printer with a lognormal moment aerosol model. Aerosol Sci. Tech., 2018, 52(10) 4. Sharma G. Dhawan S., Chakrabarty R., Biswas P. Collisional growth rate and correction factor for TiO2 nanoparticles at high temperatures in free molecular regime. Journal of Aerosol Science, 2018, 127, 27-37 5. Sharma G., Wang Y., Chakrabarty R, Biswas P. Modeling simultaneous coagulation and charging of nanoparticles at high temperatures using the method of moments. Journal of Aerosol Science, 2019, 132, 70-82 6. Sharma G.*, Zhang H.*, Wang Y., Li S., Biswas P. Numerical modeling of the performance of high flow DMAs to classify sub 2-nm particles, Aerosol Science and Technology, 2019, 53(1), 106-118 * Equal Contribution 7. Zhang H., Sharma G., Dhawan S., Dhanraj D., Li Z., Biswas P. Comparison of different aerosol dynamics models based on accuracy and computational time, In Press, Aerosol Science and Technology 8. Sharma G.*, Abuyazid N.*, Dhawan S.*, Sankaran M., Biswas P. Charge Characterization of Nanoparticles Exiting Non-Thermal Atmospheric Pressure Plasmas, Accepted, Journal of Physics D

9. Sharma G., Dhawan S., Mishra R., Biswas P. Collisional growth rate for TiO2 nanoparticles through molecular dynamics trajectory calculations. In writing for Journal of Nanoparticle Research 10. Sharma G.*, Zhang H.*, Li S., Biswas P. Transfer function, and penetration of high flow DMA using Brownian dynamics simulations: comparison with experimental observations, In writing for Journal of Aerosol Science 11. Sharma G., Wang M., You X., Biswas P. Charge characteristics of 1-10 nm particles during the flame synthesis of TiO2 in a premixed flame stabilized by a stagnation plane, In writing for Combustion and Flame 12. Wang M., Sharma G., You X., Biswas P. Investigation of the early stages of soot particles nucleation, and growth (1-10 nm) in ethylene flame stabilized by stagnation plane, Submitted to Fuel 13. Sharma G., Zhang M., Attoui M., You X., Biswas P. Measurement of sub 3nm flame-generated particles using TSI boosted butanol CPC, In writing for Aeroosl Science and Technology

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14. Kavadiya S., Strzalka J., Sharma G., Wheelus, R., Biswas, P. et al. Understanding the formation and degradation mechanism of perovskite thin film fabricated by electrospray technique, In writing 15. Dhawan S., Vidhwans A., Sharma G., Abuyazid N., Sankaran M., Biswas P. Improving Capture Efficiency of Nanoparticles using Atmospheric Pressure, Flow through RF Plasma with Downstream DC Bias, In writing for EST letters

Selected Conference Presentations Invited Talk 1. Sharma G. Collisional growth, charging, and measurement of molecular clusters to sub-10 nm particles. Corning Headquarters, NY, June, 2019. 2. Sharma G. Particle-Particle and Particle-Ion Interactions in Aerosol Reactors. Mechanical Engineering Department, MIT, February, 2019

Platform Presentation (Presenting author marked by #) 1. Sharma G.#, Wang Y., Chakrabarty R., Biswas P. Investigating the coagulation coefficient and sticking probability of nanoparticles at high temperatures. Platform Talk, American Association of Aerosol Research, 36th Annual Conference, 2017 2. Wang Y.#, Sharma G., Attoui M., Biswas P. Particle formation in combustion environments: importance of charge distributions on evolution of aerosol size distributions. Platform Presentation, 10th International Aerosol Conference, 2018 3. Zhang H.#, Sharma G., Wang Y., Li S., Biswas P.. A numerical model to predict the performance of high flow DMAs to classify sub-nm aerosols. Platform Presentation, 10th International Aerosol Conference, 2018 4. Sharma G., Zhang H.#, Biswas P.. Investigation of collisional growth rate of titania nanoparticles at high flame temperatures through molecular dynamics simulations. Platform Presentation, 10th International Aerosol Conference, 2018 5. Zhang H.#, Sharma, G. Biswas P. Brownian dynamics simulation to investigate the performance of half mini DMA to classify sub-2 nm particles. Platform Presentation, American Association of Aerosol Research, 37th Annual Conference, 2019 6. Sharma G., Wang M., Zhang H., You X., Biswas P. Role played by charge in the early stages of particle formation and growth of titania and soot nanoparticles in high temperature flame environment. Platform Presentation, American Association of Aerosol Research, 37th Annual Conference, 2019

Poster Presentation (Presenting author marked by #)

1. Zhang Q.#, Sharma G., Wong J., Davis A., Black M., Biswas P., Weber R. Investigating particle emissions from a consumer fused deposition modeling 3D printer with a lognormal moment aerosol dynamic model. Poster Presentation, American Association of Aerosol Research, 36th Annual Conference, 2017

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2. Sharma G.#, Wang Y., Chakrabarty R., Biswas P. Modeling simultaneous coagulation and charging of nanoparticles at high temperatures using moment lognormal size distribution. Poster Presentation, 10th International Aerosol Conference, 2018 3. Sharma G.#, Dhawan S., Li Z., Dhanraj D., Biswas P. Comparison of different aerosol dynamics models based on accuracy and computational time. Poster Presentation, 10th International Aerosol Conference, 2018 4. Dhawan S.#, Sharma G., Biswas P. Investigation of the role of charging on the particle growth during combustion in spray flame aerosol reactor. Poster Presentation, 10th International Aerosol Conference, 2018 5. Sharma G.#, Biswas P. Collisional growth, charging and measurement of molecular clusters to sub-10 nm particles in high temperature flame environment. Poster Presentation, Non- Equilibrium Multiphase Systems (NEMS) Symposium, 2018 6. Sharma G.#, Wang M., Attoui M., Biswas P. Measurement of Sub 3 nm flame-generated particles using boosted butanol CPC 3776 and DEG CPC. Poster Presentation, American Association of Aerosol Research, 37th Annual Conference, 2019 7. Sharma G.#, Chakrabarty R., Biswas P. Collisional Growth, charging and measurement of molecular clusters to sub-10 nm particles in high temperature flame environment. Poster Presentation, American Association of Aerosol Research, 37th Annual Conference, 2019 8. Sharma G.#, Abuyazid N., Dhawan S., Sankaran M., Biswas P. Charge characterization of nanoparticles exiting nonthermal atmospheric pressure plasmas. Poster Presentation, American Association of Aerosol Research, 37th Annual Conference, 2019

PEDAGOGICAL EXPERIENCE Assistant to the instructor for three graduate level courses 1. Aerosol Science and Technology (2016, Fall) 2. Advanced Topics in Aerosol Science and Technology (2017, Spring) 3. Transport Phenomena in EECE (2017, Fall)

COMMUNITY ENGAGEMENT 1. Served as a Reviewer for the Journal of Aerosol Science, reviewed more than 15 manuscripts 2. Served as chair (2019), and co-chair (2018) for conducting presentation sessions at aerosol conferences

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COURSE WORK SUMMARY Semester Course Code Course Title Credit Grade FL2015 E44 501 Transport Phenomena in Energy, 3.0 A+ Environmental and Chemical Engineering FL2015 E44 503 Mathematical Methods in Engineering 3.0 A+ FL2015 E44 504 Aerosol Science and Technology 3.0 A+ SP2016 E44 507 Kinetics and Reaction Engineering 3.0 A+ Principles SP2016 E44 510 Advanced Topics in Aerosol Science 3.0 A+ & Technology FL2016 L31 503 Advanced Math Methods for 3.0 A- Physicist & Engineers I SP2017 L31 504 Advanced Math Methods for 3.0 A- Physicist & Engineers I SP2018 E37 5612 Atomistic Modeling of Materials 3.0 A SP2018 L07 550 Mass Spectrometry 3.0 B+ FL2018 E44 512 Combustion Phenomenon 3.0 A E63 600 Doctoral Research 30.0 A Cumulative GPA 3.93

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