This dissertation is available at Iowa Research Online:

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1 University of Iowa Iowa Research Online Theses and Dissertations Summer 2015 Optical properties of mineral dust aerosol including analysis of particle size, composition, and shape effects, and the impact of physical and chemical processing Jennifer Mary Alexander University of Iowa Copyright 2015 Jennifer Mary Alexander This dissertation is available at Iowa Research Online: Recommended Citation Alexander, Jennifer Mary. "Optical properties of mineral dust aerosol including analysis of particle size, composition, and shape effects, and the impact of physical and chemical processing." PhD (Doctor of Philosophy) thesis, University of Iowa, Follow this and additional works at: Part of the Physics Commons

2 OPTICAL PROPERTIES OF MINERAL DUST AEROSOL INCLUDING ANALYSIS OF PARTICLE SIZE, COMPOSITION, AND SHAPE EFFECTS, AND THE IMPACT OF PHYSICAL AND CHEMICAL PROCESSING by Jennifer Mary Alexander A thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Physics in the Graduate College of The University of Iowa August 2015 Thesis Supervisor: Professor Paul D. Kleiber

3 Copyright by JENNIFER MARY ALEXANDER 2015 All Rights Reserved

4 Graduate College The University of Iowa Iowa City, Iowa CERTIFICATE OF APPROVAL PH.D. THESIS This is to certify that the Ph.D. thesis of Jennifer Mary Alexander has been approved by the Examining Committee for the thesis requirement for the Doctor of Philosophy degree in Physics at the August 2015 graduation. Thesis Committee: Paul D. Kleiber, Thesis Supervisor Vicki H. Grassian Thomas F. Boggess Wayne N. Polyzou Markus Wohlgenannt

5 ACKNOWLEDGMENTS First off, I would like to thank my thesis advisor, Dr. Paul Kleiber. Thank you for all of your help and encouragement throughout the years, as well as your unwavering patience with me while I learn. Whether it was the many, many revisions of manuscripts or the frustrating days in the lab when everything seemed to be broken, your motivation has made this thesis possible. There are many other professors that have helped me throughout my academic career. Thank you to Dr. Mark Young for all your help with the YAG laser and Dr. Vicki Grassian for your helpful suggestions with manuscripts as well as your support with the PNNL project. I would also like to thank the rest of my thesis committee, Dr. Boggess, Dr. Wohlgenannt, and Dr. Polyzou for taking time out of your busy schedules. Thank you to my physics and math professors at St. Ben s and St. John s University, especially Dr. Dean Langley, my undergraduate thesis advisor for introducing me to optics and Dr. Tom Kirkman. I would like to thank Brian Meland for teaching me the ropes in the lab. Your encouragement and reassurance has been invaluable. Even your notes in the lab book expressing your true frustration with the laser has helped me with my own frustrations, and reminded me that I am not the only one who feels that way. In addition, your Matlab codes were perfect examples that helped me learn to write my own codes. I would also like to thank Olga Laskina for answering all of my many, many dumb chemistry questions as well as helping me make processed samples and take SEMs. I would like to thank Alla Zelenyuk, Dave Bell, and Arun Devaraj at the Pacific Northwest Nation Laboratory for allowing me to come to your lab for three weeks and working on this projects with me. I would like to acknowledge the sources of funding I have received throughout my time as a graduate student. I first received the Dean s Fellowship through the University of Iowa which allowed me to focus on classes my first year as well as get a jump start on research. In addition, I ii

6 would like to thank the National Science Foundation and NASA for their funding, without which this research would not be possible. Lastly, and probably most importantly, I would like to thank my family and friends. You have truly kept me sane for the past 5 years. Thanks to my family and friends back home for understanding why I ve had to cut visits short or miss holidays altogether. Thanks to all my great at the University of Iowa, happy hours have been a great way to de-stress after all the many long weeks. iii

7 ABSTRACT Atmospheric mineral dust has a large impact on the earth s radiation balance and climate. The radiative effects of mineral dust depend on factors including, particle size, shape, and composition which can all be extremely complex. Mineral dust particles are typically irregular in shape and can include sharp edges, voids, and fine scale surface roughness. Particle shape can also depend on the type of mineral and can vary as a function of particle size. In addition, atmospheric mineral dust is a complex mixture of different minerals as well as other, possibly organic, components that have been mixed in while these particles are suspended in the atmosphere. Aerosol optical properties are investigated in this work, including studies of the effect of particle size, shape, and composition on the infrared (IR) extinction and visible scattering properties in order to achieve more accurate modeling methods. Studies of particle shape effects on dust optical properties for single component mineral samples of silicate clay and diatomaceous earth are carried out here first. Experimental measurements are modeled using T-matrix theory in a uniform spheroid approximation. Previous efforts to simulate the measured optical properties of silicate clay, using models that assumed particle shape was independent of particle size, have achieved only limited success. However, a model which accounts for a correlation between particle size and shape for the silicate clays offers a large improvement over earlier modeling approaches. Diatomaceous earth is also studied as an example of a single component mineral dust aerosol with extreme particle shapes. A particle shape distribution, determined by fitting the experimental IR extinction data, used as a basis for modeling the visible light scattering properties. While the visible simulations show only modestly good agreement with the scattering data, the fits are generally better than those obtained using more commonly invoked particle shape distributions. The next goal of this work is to investigate if modeling methods developed in the studies of single mineral components can be generalized to predict the optical properties of more iv

8 authentic aerosol samples which are complex mixtures of different minerals. Samples of Saharan sand, Iowa loess, and Arizona road dust are used here as test cases. T-matrix based simulations of the authentic samples, using measured particle size distributions, empirical mineralogies, and a priori particle shape models for each mineral component are directly compared with the measured IR extinction spectra and visible scattering profiles. This modeling approach offers a significant improvement over more commonly applied models that ignore variations in particle shape with size or mineralogy and include only a moderate range of shape parameters. Mineral dust samples processed with organic acids and humic material are also studied in order to explore how the optical properties of dust can change after being aged in the atmosphere. Processed samples include quartz mixed with humic material, and calcite reacted with acetic and oxalic acid. Clear differences in the light scattering properties are observed for all three processed mineral dust samples when compared to the unprocessed mineral dust or organic salt products. These interactions result in both internal and external mixtures depending on the sample. In addition, the presence of these organic materials can alter the mineral dust particle shape. Overall, however, these results demonstrate the need to account for the effects of atmospheric aging of mineral dust on aerosol optical properties. Particle shape can also affect the aerodynamic properties of mineral dust aerosol. In order to account for these effects, the dynamic shape factor is used to give a measure of particle asphericity. Dynamic shape factors of quartz are measured by mass and mobility selecting particles and measuring their vacuum aerodynamic diameter. From this, dynamic shape factors in both the transition and vacuum regime can be derived. The measured dynamic shape factors of quartz agree quite well with the spheroidal shape distributions derived through studies of the optical properties. v

9 PUBLIC ABSTRACT Mineral dust that is blown into the atmosphere has an impact on the earth s climate by absorbing and scattering the incoming sun light and outgoing infrared radiation from the earth. Different kinds of mineral dust can absorb and scatter radiation differently depending on the particle s size, shape, and composition, all of which can be very complex. Atmospheric mineral dust can have very irregular shapes as well as be composed of many different kinds of minerals and other atmospheric components. In this work, measurements of the visible scattering properties are measured and compared to model simulations. Different models are needed for different types of mineral dust which will have different compositions and particle shapes. Single component mineral samples are studied first. It is found that in order to simultaneously simulate the infrared extinction and visible scattering properties of illite and kaolinite, two silicate clay minerals, a model that allows particle shape to vary with particle size is required. Diatomaceous earth is also investigated because of its extreme particle shape. Authentic mineral dust samples are studied next because of the added complexity of having a mixture of different minerals which can each have different shape characteristics. Mineral dust samples are also processed with organic acids and humic material in order to better understand how the visible light scattering properties of mineral dust can change when it is atmospherically aged. Lastly, dynamic shape factors are explored and correlated to the spheroidal shape distributions derived in studies of the optical properties. vi

10 TABLE OF CONTENTS LIST OF TABLES... x LIST OF FIGURES... xii LIST OF SYMBOLS... xix Introduction Mineral Dust in the Atmosphere Laboratory Measurements of Mineral Dust Light Scattering Properties Modeling the Radiative Effects T-Matrix Theory Current Project... 8 Experimental Methods Optical Properties Apparatus Visible Scattering Apparatus Infrared Extinction Apparatus Aerosol Flow and Particle Size Distribution Measurements Light Scattering Theory Mie Theory T-Matrix Theory Application of the T-Matrix Method Background Studies Size Dependent Shape Distributions of Silicate Clay Aerosol Introduction Experimental Methods and Results Single Mode Modeling Analysis Bimodal Modeling Analysis Conclusions IR Based Shape Distributions of Diatomaceous Earth Aerosol vii

11 6.1 Introduction Experimental Methods and Results Modeling Analysis Modeling Results IR Extinction Results Visible Scattering Results Variations in Refractive Indices Conclusions Complex Authentic Dust Samples Introduction Experimental Methods and Results Modeling Analysis Particle Size Distributions Mineral Optical Constants Particle Shape Distributions Sample Mineralogy Empirical Mineral Compositions Revised Empirical Mineral Compositions Cumulative Optical Properties for Mixed Samples Model Results and Discussion Simulation Results using the Empirical Mineralogy Discussion of the IR Extinction Results Discussion of the Visible Scattering Results Simulation Results using the Revised Empirical Mineralogy Simulation Results Including Hematite Simulation Results with Varied Densities Conclusions viii

12 Mineral Dust Processed with Organic Acids and Humic Material Introduction Experimental Methods and Results Sample Preparation Experimental Results Experimental Discussion Modeling Analysis Unprocessed Mineral Dust Organic Salts Processed Mineral Dust Quartz Processed with Humic Acid Sodium Salt Calcite Processed with Acetic Acid Calcite Processed with Oxalic Acid Conclusions Dynamic Shape Factors of Quartz Aerosol Introduction Theoretical Background Experimental Methods Experimental Results Mobility Selected Particles Mass Selected Particles ADS Selected Particles Conclusions Future Work Larger Mineral Dust Aerosol Particles Brown Carbon Studies REFERENCES ix

13 LIST OF TABLES Table 2.1 Sources of aerosol samples used in this work Table 5.1 Table of log normal size distribution parameters that best fit the measured (volume equivalent) particle size distributions for illite and kaolinite in the IR extinction and visible light scattering experiments.* Table 5.2 Comparison of chi square values for the simulations of the optical properties of a) illite and b) kaolinite, as shown in Figures 5.1 and 5.2. Values listed in the table have been scaled by a factor of Table 6.1 Table of log normal size distribution parameters that best fit the measured (volume equivalent) particle size distributions for diatomaceous earth (DE) in the IR extinction and visible light scattering experiments. r m is the mode radius of the particle number size distribution, σ is the width parameter, and MWMD is the mass weighted mean particle diameter. In the visible scattering experiments, the measured size distribution showed a bimodal character and was modeled by a linear combination of two log normal functions with the fitting parameters as given Table 6.2 Comparison of chi square values for simulations of the visible scattering properties of diatomaceous earth. Values listed in the table have been scaled by a factor of Table 6.3 Visible refractive indices used in simulations of the light scattering properties of diatomaceous earth Table 7.1 Table of log normal size distribution parameters that best fit the measured (volume equivalent) particle size distributions for, Saharan sand, Iowa loess, and Arizona road dust (ARD) in the IR extinction and visible light scattering experiments. r m is the mode radius of the particle number size distribution, σ is the width parameter, and MWMD is the mass weighted mean particle diameter. In the visible light scattering experiments, the measured size distribution for Arizona road dust showed a bimodal character and was modeled by a linear combination of two log normal functions with the fitting parameters as given Table 7.2 References for the optical constants of the mineral components considered in this study a Table 7.3 Shape distributions used for each of the potential mineral components of Saharan sand, Iowa loess, and Arizona road dust * Table 7.4 Mineral compositions (in percentage of particle number density) for the authentic samples of Saharan sand, Iowa loess, and Arizona road dust Table 7.5 Elemental composition (in atomic %) of complex dust samples determined from the empirical mineralogy of Lakina et al. [2012] and revised model of Alexander et al. [2013b], and energy dispersive X-ray analysis (EDX) x

14 Table 7.6 Comparison between T-matrix simulations and experiment Table 7.7 Comparison of the scattering asymmetry parameter of T-matrix simulations and experiment Table 8.1 Comparison between experimental measurements of the visible scattering a) phase function and b) linear polarization profiles for unprocessed and processed samples at selected angels Table 8.2 Table of log normal size distribution parameters that best fit the measured volume equivalent particle size distribution. r m is the mode radius of the particle number size distribution and σ is the width parameter. All samples except calcium acetate were fit with a linear combination of two log normal distributions (bimodal) Table 8.3 Optical constants of mineral and organic compounds considered in this study. All of the values are measured or interpolated at λ=532 nm except calcium oxalate where the wavelength for the reported value was unspecified Table 9.1 Information regarding the lasers used in SPLAT II Table 9.2 Experimental results for mass selected particles. Corresponding graphs are shown in Figures Table 9.3 Experimental results for ADS selected particles Table 9.4 Dynamic shape factors for spheroidal particles in the vacuum and continuum regime. Values for χ v were taken from Davies [1979], and values for χ c were calculated from the dimensionless drag coefficients in Dahneke [1973] xi

15 LIST OF FIGURES Figure 2.1 Visible light scattering experimental apparatus, adapted from Meland [2011]. Diagram is not to scale Figure 2.2 Detailed view of the optical experimental set up as described in Section Diagram is not to scale Figure 2.3 CCD image and corresponding integrated scattered light intensity from quartz at 532nm for a) parallel and b) perpendicular polarized incident light. Background and direct scattered light have been subtracted Figure 2.4 Experimental phase function of diatomaceous earth at a wavelength of 550nm. Experimental data in the forward direction (θ < 6 ) has been spliced with simulations using Mie theory (blue solid line) and T-matrix theory (red dashed line) and normalized according to Equation 2.3. Note the very small difference in the normalization Figure 2.5 CCD image and corresponding integrated scattered light intensity from PSL 799nm diameter at 532nm for a) parallel and b) perpendicular polarized incident light. Background and direct scattered light have been subtracted Figure 2.6 Experimental phase function and linear polarization profile of PSL 779nm diameter at 532nm after being mapped from pixel position to scattering angle (green line). Note, the correction for the system response function has not been applied yet. Mie theory is also included for comparison (blue line) Figure 2.7 a) Calibration curve for 799nm diameter PSL (green line) and the corresponding fit (black dashed line). b) The scattering intensity of PSL 799nm at 532nm after the calibration has been applied (green line) compared to Mie theory (black line) Figure 2.8 Comparison of the a) phase function and b) linear polarization profile of PSL 799nm diameter at a wavelength of 532nm (green lines) after the calibration function has been applied and Mie theory (black lines). In addition, theoretical Mie data has been spliced to the phase function for angles < 6 and a linear extrapolation has been used for angles > 172 ; this is shown green points Figure 2.9 Comparison of the measured phase function of PSL 799nm at a wavelength of 532nm before being smoothed (green line solid) and after being smoothed (blue dashed line) Figure 2.10 Comparison of calibrated phase function and linear polarization profile for a) PSL 994nm diameter and b) PSL 600nm diameter (green lines) with Mie theory (black lines). Experimental data has been calibrated using the calibration curve generated from PSL 799nm (shown in Figure 2.6). In addition, theoretical Mie data has been spliced to the phase function for angles < 6 and a linear extrapolation has been used for angles > 172 ; this is shown green points xii

16 Figure 2.11 Diagram of the IR extinction apparatus Figure 5.1 Comparison of single mode simulations with experimental data for illite. Simulations use an extreme oblate shape parameter (green lines), a prolate shape parameter (blue lines), a moderate uniform shape distribution with shape parameters in the range ξ 1.4 (red lines), and a more eccentric uniform shape distribution with shape parameters in the range -3 ξ +5 (cyan lines) Figure 5.2 Comparison of single mode simulations with experimental data for kaolinite. Simulations use extreme oblate shape parameters (green lines), a prolate shape parameter (blue lines), a moderate uniform shape distribution with shape parameters in the range ξ 1.4 (red lines), and a more eccentric uniform shape distribution with shape parameters in the range -3 ξ +5 (cyan lines) Figure 5.3 Comparison of a bimodal simulation with experimental data for illite Figure 5.4 Comparison of a bimodal simulation with experiment for kaolinite Figure 6.1 A scanning electron microscope image of a sample of diatomaceous earth dust Figure 6.2 A scanning electron microscope image of a sample of quartz dust for comparison to the extreme particle shapes of diatomaceous earth, shown in Figure Figure 6.3 Experimental particle size distributions (blue points) measured simultaneous with the a) IR extinction and b) visible scattering experiments compared with log fits (pink lines) as listed in Table Figure 6.4 Comparison of the experimental IR extinction spectrum and visible scattering phase function and polarization profiles for diatomaceous earth (points) with model simulations using different shape distributions. The T- matrix simulation results use the IR based shape distribution (red line) and the quartz shape distribution studied by Meland et al. [2010] (green line). Mie theory simulations are also shown for comparison (blue line) Figure 6.5 Shape distributions used in the simulations shown in Figure 6.2 including the IR based shape distribution (red bars), the quartz shape distribution (green bars) and Mie theory (blue bar) Figure 6.6 Comparison of the experimental visible scattering phase function and polarization profiles for diatomaceous earth (points) with model simulations using different refractive indices. All T-matrix simulation results use the IR based shape distribution shown as red bars in Figure 6.3. Lines shown in red use optical constants reported by Khashan & Nassif [2000], green lines use the optical constants reported by Egan [1985], and blue lines use optical constants reported by Longtin et al. [1988] Figure 6.7 IR based shape distributions derived using different sets of IR optical xiii

17 constants. Red bars represent the IR based shape distribution resulting from simulations using optical constants for glassy quartz as reported by Zolotarev [2009] and blue bars represent the IR based shape distribution resulting from simulations using the optical constants for crystal quartz as reported by Longtin et al. [1988] Figure 6.8 Comparison of the experimental IR extinction spectrum and visible scattering phase function and polarization profiles for diatomaceous earth (points) with model simulations using different sets of refractive indices. The T-matrix simulation results use the IR based shape distributions that have been optimized for each set of refractive indices. Simulations using optical constants for glassy quartz are shown in red and crystal quartz is shown in blue Figure 7.1 Comparison of the experimental data (points) with model simulations for Saharan sand: (a) the IR spectral extinction (b) the scattering phase function and (c) the linear polarization profiles at λ=550nm. The T-matrix simulation results for the optimized particle shape distributions given in Table 3 are shown in red; T-matrix simulation results assuming an equiprobable (flattop) shape distribution for all the mineral components (-1.4 ξ +1.4) are shown in green; Mie theory results are shown in blue Figure 7.2 Figure 7.3 Comparison of the experimental data (points) with model simulations for Iowa loess. The labeling is as in Figure Comparison of the experimental data (points) with model simulations for Arizona road dust. The labeling is as in Figure Figure 7.4 Experimental particle size distributions (blue dots) measured simultaneous with the visible scattering experiments compared with log fits (pink lines) for a) Saharan sand, b) Iowa loess, and c) Arizona road dust Figure 7.5 Comparison of T-matrix simulations for the calcite component of Saharan sand. Simulations shown in pink have been calculated using an average of the birefringent optical constants. Simulations shown as dashed cyan lines have been calculated by spectrally averaging the birefringent scattering properties Figure 7.6 Particle shape distribution models for the components of the external mixtures as described in Section 5.1.3, a) non-clay mineral components and b) clay components Figure 7.7 Comparison of simulations of the visible scattering a) phase function and b) linear polarization of Arizona road dust. Simulations shown in blue use a moderate shape distribution (-1.4 ξ +1.4) for the calcite component of the mixed sample, and simulations shown in green use a broad distribution of spheroids (-3 ξ +5) for the calcite component. Both simulations use the optimized shape distributions for the other mineral components (Table 7.3) and the revised mineral composition (Table 7.4) for Arizona road dust Figure 7.8 Comparison of the experimental IR extinction spectra of albite (points) with xiv

18 a T-matrix simulation using a cubic power law shape distribution as shown in Figure 7.6 as red bars Figure 7.9 Comparison of the experimental data (points) with model simulations for potential mineral components of Saharan sand including a) the relative IR extinction, b) the scattering phase function, and c) the linear polarization profiles at λ=550nm Figure 7.10 Comparison of experimental IR extinction data (points) with the empirical fits of a) Saharan sand and b) Arizona road dust. The red lines use the mineralogy derived using the methods of Laskina et al. [2012] and the blue lines use the revised mineral compositions as discussed in Section Figure 7.11 Comparison of the experimental data (points) with T-matrix model simulations for Saharan sand: (a) the IR spectral extinction (b) the scattering phase function and (c) the linear polarization profiles at λ=550nm. The T- matrix simulations use the particle shape distributions given in Table 3. Red lines use the empirical mineralogy derived by Laskina et al. [2012] (Section ) and the blue lines use the revised mineralogy of Alexander et al. [2013b] (Section ) Figure 7.12 Comparison of the experimental data (points) with T-matrix model simulations for Iowa loess. The labeling is as in Figure Figure 7.13 Comparison of the experimental data (points) with T-matrix model simulations for Arizona road dust. The labeling is as in Figure Figure 7.14 Comparison of the experimental data (points) with T-matrix model simulations (lines) for Iowa loess. Blue dashed lines use the revised mineral compositions and green lines use the revised mineral compositions with an additional 7% hematite component. All simulations use the optimized shape distributions Figure 7.15 Comparison of the experimental data (points) with T-matrix model simulations (lines) using different densities for Saharan sand. Blue dashed lines use a density of 2.7 and green lines use a density of 2.3. All simulations use the revised mineral compositions and optimized shape distributions Figure 8.1 Conceptual illustration from an optical scattering perspective of the different types of mixtures that could potentially result from mineral dust interacting with organic acids and humic material. These interactions can form: a) internal mixtures including, homogeneously mixed particles, coatings, or more physically segregated heterogeneous particles, b) external mixtures where each particle is either mineral dust or organic salt, or c) a combined internal/external mixture Figure 8.2 Experimental visible scattering phase functions and linear polarization profiles for a) quartz processed with humic acid sodium salt (QHA Mix), b) calcite processed with acetic acid (CAA Mix), and c) calcite processed with oxalic acid (COA Mix), shown in red. Also shown are visible scattering xv

19 properties of the corresponding unprocessed mineral components (quartz or calcite) in blue and commercial samples of the expected organic species (humic acid sodium salt/naha, calcium acetate, or calcium oxalate) in green. Shaded regions represent the standard deviation from measurements taken over several days Figure 8.3 Experimentally measured size distributions for a) quartz processed with humic acid sodium salt (QHA Mix), b) calcite processed with acetic acid (CAA Mix), and c) calcite processed with oxalic acid (COA Mix), shown in red. Also shown measured size distributions of the corresponding mineral components (quartz or calcite) in blue and organic species (humic acid sodium salt/naha, calcium acetate, or calcium oxalate) in green. It should be noted that the relative peak heights are not meaningful due to differences in sample concentrations Figure 8.4 Comparison of experimentally measured visible scattering phase function and polarization profiles (points) for quartz with model simulations (blue lines) using the optimized shape distribution as shown in the bar graphs Figure 8.5 Comparison of experimentally measured visible scattering phase function and polarization profiles (points) for quartz with model simulations (blue lines) using the optimized shape distribution as shown in the bar graphs Figure 8.6 SEM images of a) humic acid sodium salt, b) calcium acetate and c) calcium oxalate particles collected from the aerosol flow Figure 8.7 Comparison of experimentally measured visible scattering phase functions and linear polarization profiles (points) for a) humic acid sodium salt and b) calcium acetate with Mie theory simulations (green lines) using optimized optical constants as shown Figure 8.8 Comparison of experimental visible scattering phase function and polarization profiles for calcium oxalate (points) with model simulations (green lines) using the optimized shape distribution as shown in the bar graph Figure 8.9 Comparison of experimental visible scattering properties (points) with internal mixture model simulations of quartz processed with humic acid sodium salt. Simulations use the quartz shape distribution (blue lines) or an optimized shape distribution (red lines). Corresponding shape distributions used in the simulations are shown in c). See Section for details Figure 8.10 Differences between the experimental data for quartz processed with NaHA and the model simulations shown in Figure Figure 8.11 Comparison of experimental visible scattering properties (points) with combined internal/external mixture model simulations of quartz processed with humic acid sodium salt. Simulations use the quartz shape distribution (blue lines) or an optimized shape distribution (red lines). Corresponding shape distributions used in the simulations are shown in c). See Section for details xvi

20 Figure 8.12 Differences between the experimental data for quartz processed with NaHA and the model simulations shown in Figure Figure 8.13 Comparison of experimental visible scattering properties (points) for calcite procesed with acetic acid with model simulations. Simulations using an external mixing assumption are shown in blue and simulations for the combined mixture model that includes an internally mixed fraction of particles along with externally mixed particles are shown in red. See Section for details Figure 8.14 Differences between the experimental data for calcite processed with acetic acid and the model simulations shown in Figure Figure 8.15 Comparison of experimental visible scattering properties (points) for calcite procesed with oxalic acid with model simulations using different shape distributions as shown in c). Simulations using calcite s shape distribution (Section 4.1) are shown in blue, simulations using calcium oxalate s shape distribution (Section 4.2) are shown in green, and simulations using the shape distribution optimized to fit the experiment (Section 4.3.3) are shown in red. See Section for details Figure 8.16 Differences between the experimental data for calcite processed with oxalic acid and the model simulations shown in Figure Figure 9.1 Conceptual illustration of methods to consider the dynamic shape factor and particle density for particles with internal voids Figure 9.2 Diagram of the ADS instrument Figure 9.3 Diagram of the SPLAT instrument Figure 9.4 Measured mobility size distributions for quartz aerosol (points). The data has been smoothed in order to guide the eye (line) Figure 9.5 Measured vacuum aerodynamic size distribution for quartz aerosol (points). The data has been smoothed in order to guide the eye (line) Figure 9.6 Measured vacuum aerodynamic diameter size distributions of mobility selected particles. Note, doubly charged particles have been removed from the 100nm graph; doubly charge particles have not been removed from the other graphs Figure 9.7 Figure 9.8 Relationship between vacuum aerodynamic diameters and mobility diameters for mobility selected particles (magenta) and mass selected particles (cyan) Effective density of mobility selected particles. The bulk cryastal density of quartz is shown as a dashed black line. Vertical bars represent the width in the measured d va values, and not experimental errors Figure 9.9 Measured a) mobility diameter and b) vacuum aerodynamic size xvii

21 distributions of mass selected particles. Note that the smaller peak located at smaller d m values is due to doubly charge particles and is marked with + +. Doubly charged particles have been removed in b) Figure 9.10 Measured mobility diameters in the transition regime (red points) and vacuum aerodynamic diameters in the free molecular regime (blue point) as a function of mass for mass selected particles. Fitted lines are shown to guide the eye Figure 9.11 Measured mobility diameters in the transition regime (red points) and vacuum aerodynamic diameters in the free molecular regime (blue points) as a function of volume equivalent diameter for mass selected particles. Fitted lines are shown to guide the eye Figure 9.12 Calculated dynamic shape factors as a function of mass for mass selected particles in the transition regime (red points) and free molecular regime (blue points). Fitted lines are shown to guide the eye Figure 9.13 Calculated dynamic shape factors as a function of volume equivalent diameter for mass selected particles in the transition regime (red points) and free molecular regime (blue points). Fitted lines are shown to guide the eye Figure 9.14 Calculated dynamic shape factors (points) of mass selected particles in a) the transition regime as a function of measured mobility diameters and b) the free molecular regime as a function of measured vacuum aerodynamic diameters. Fitted lines are shown to guide the eye Figure 9.15 Vacuum dynamic shape factors (points) as a function of transition dynamic shape factors for mass selected particles. Fitted lines are shown to guide the eye Figure 9.16 Mobility diameters chosen for ADS measurements. The peak, as well as each side of the distribution was used in order to measure the range of shape factors of the particles Figure 9.17 Calculated dynamic shape factors as a function of selected mass for ADS selected particles in the transition regime (red) and free molecular regime (blue). Vertical bars show the range in measured shape factors, not experimental errors Figure 9.18 Calculated dynamic shape factors as a function of selected mobility diameter for ADS selected particles in a) the transition regime and b) the free molecular regime. The three points for each mass is from the three selected mobility diameters shown in Figure xviii

22 LIST OF SYMBOLS εε Axial ratio for oblate spheroids (εε 1) and its inverse for prolate spheroids (εε < 1) θ λ ξ ξ n ξ RMS π n Dielectric constant Scattering angle Wavelength Spheriodal particle shape parameter Riccati-Bessel function Root mean square shape factor Angular functions ρ o Standard density (1 g/cm 3 ) ρ p ρ bulk σ τ n χ 2 χ χ c χ t χ v ψ n dω a n A i a mn b n B i Particle density Density of the bulk material Width parameter Angular functions Chi-square value Dynamic shape factor in any regime Dynamic shape factor in the continuum regime Dynamic shape factor in the transition regime Dynamic shape factor in the free molecular regime Riccati-Bessel function Differential solid angle Mie expansion coefficients Variable parameters in the fitting of the response function Expansion coefficients for the incident electric field Mie expansion coefficients Variable parameters in the fitting of the response function xix

23 b mn c mn c C(θ) C c C ext(ξ) C ext(ξ) d a d c d m d mn d d p d ta d va d ve D F D i E inc E scat Expansion coefficients for the incident electric field Expansion coefficients for the internal electric field Matrix form of the expansion coefficients for the internal electric field Calibration function Cunningham slip correction factor Cross sectional extinction coefficient Cross sectional scattering coefficient Aerodynamic diameter in any regime Cut off diameter Mobility diameter in the transition regime Expansion coefficients for the internal electric field Matrix form of the expansion coefficients for the internal electric field Particle diameter Aerodynamic diameter in the transition regime Aerodynamic diameter in the free molecular regime Volume equivalent diameter Particle face diameters Variable parameters in the fitting of the response function Incident electric field vector Scattered electric field vector inc E Parallel (to the scattering plane) component of the incident electric field inc E Perpendicular (to the scattering plane) component of the incident electric field scat E Parallel (to the scattering plane) component of the scattered electric field scat E Perpendicular (to the scattering plane) component of the scattered electric field f i Volume fraction of the inclusions xx

24 F αβ(θ) F(θ) g I I inc Normalized scattering matrix elements Phase function Scattering asymmetry parameter Stokes parameter Incident light intensity scat I Scattered light intensity from parallel polarized incident light scat I Scattered light intensity from perpendicular polarized incident light ( θ ) I Scattered light intensity from parallel polarized incident light ( θ ) I Scattered light intensity from perpendicular polarized incident light k m M mn n N mn N(ξ) p mn p 1 P n P(θ) q mn q Q Q ij Q r Imaginary part of the complex refractive index or wavenumber Complex refractive index Spherical harmonic functions Real part of the complex refractive index Spherical harmonic functions Relative number of particles Expansion coefficients for the scattered electric field Matrix form of the expansion coefficients for the scattered electric field Legendre function of the first kind of degree n Linear polarization profile Expansion coefficients for the scattered electric field Matrix form of the expansion coefficients for the scattered electric field Stokes parameter Elements of the Q-matrix Q-matrix Distance from the scatterer to the observation point xxi

25 r m S ij S i T ij Mode radius Elements of the amplitude scattering matrix Elements of the Mueller matrix Submatrices of the T-matrix ij T mnm n Elements of the T-matrix T U V x T-matrix Stokes parameter Stokes parameter Size paramete xxii

26 Introduction Atmospheric aerosols, defined as solid or liquid particles suspended in a gas, can have a large impact on the climate [Forster et al., 2007], chemical [Seinfeld and Pandis, 2006] and biogeochemical cycles [Meskhidze et al., 2005; Hand et al., 2004], and human health [Anderson et al., 2012; Brook et al., 2010]. Much of the aerosol in the atmosphere is naturally occurring, such as windblown dust, volcanic ash, smoke from forest fires, sea salt, and water droplets [Hinds, 1999]. However there are also anthropogenic sources such as fossil fuel and biomass burning [Kondratyev et al., 2006]. Aerosol particles are typically in the range from nanometers to 10 s of μm and can stay suspended in the troposphere for a few minutes to a couple of weeks [Hinds, 1999; Williams et al., 2002]. Throughout this time, the particles can be transported long distances and undergo complex chemical and physical aging processes [Badarinath et al., 2010; Ben-Ami et al., 2010; Cwiertny et al., 2008]. These atmospheric aerosols also have a large effect on the earth s radiation balance. The focus of this work is on the optical properties of mineral dust aerosol, one of the important components of the total atmospheric dust load. 1.1 Mineral Dust in the Atmosphere It is estimated that every year, on the order of Tg of mineral dust is blown into the atmosphere by wind action [Zender et al., 2004]. North Africa, the Middle East, Central Asia, and the Indian subcontinent are the largest contributors to the global mineral dust load [Prospero et al., 2002]. The most significant source of the total atmospheric dust load is North Africa, including the Saharan desert, which is estimated to contribute 62-73% of the global atmospheric dust load [Tanaka and Chiba, 2006; Luo et al., 2003]. One extreme example is the Bodélé Depression, located in northern Chad, which has been referred to as the dustiest place on Earth [Giles, 2005; Bristow et al., 2009]. While being only 0.2% of the size of the Saharan desert, the Bodélé Depression is estimated to be the single biggest source of atmospheric mineral dust on Earth [Koren et al., 2006; Prospero et al., 2002; Washington et al., 2003]. 1

27 Dust storms can clearly have a local impact on the atmospheric dust load but the aerosols can also be transported long distances and have a global impact. For example, dust from the Saharan desert can be transported to Northern Europe [Ansmann et al., 2003], the Mediterranean [Moulin et al., 1998], the Middle East [Ganor, 1994], and across the Atlantic to Barbados [Chiapello et al., 2005], South America [Prospero et al., 1981; Swap et al., 1992], and the eastern United States [Perry et al., 1997; Prospero, 1999; Yin et al., 2005]. Recent studies have even estimated that half of the dust deposited annually in the Amazon forest originates from over 3,000 miles away in the Bodélé Depression [Koren et al., 2006]. This mineral dust supplies the Amazon, as well as the Atlantic ocean, with vital nutrients [Bristow et al., 2010] and is responsible for over 40% of the dust optical depth over the Amazon in the winter [Koren et al., 2006; Tegen et al., 2006]. Mineral dust that is suspended in the atmosphere, possibly being transported long distances, can also age as it comes into contact with other atmospheric constituents. Many field studies have found that atmospheric mineral dust can often be mixed with other inorganic material such as nitrate, sulfate, and chloride. These mixtures have most likely resulted from chemical reactions between dust particles and trace acidic gases including NO y, SO 2, and HCl [Li and Shao, 2009; Sullivan et al., 2007; Kojima et al., 2006; Lee et al., 2002]. For example, Li and Shao [2009] collected aerosol during brown haze episodes in Beijing China and found that 90% of mineral particles collected had visible coatings formed by atmospheric heterogeneous reactions with acidic gases. Along with inorganic components, mineral dust is also often found mixed with organic acids [Takahama et al., 2010; Falkovich et al., 2004; Maria et al., 2004; Russell et al., 2002]. For example, another field study found that 95% of mineral dust particles collected in Atlanta contained water-soluble organic acids [Lee et al., 2002]. The interaction of mineral dust and atmospheric acids can have many consequences including changes in the aerosol s chemical composition and physical properties [Matsuki et al., 2

28 2005; Laskin et al., 2005; Gibson et al., 2006]. For instance, reactive mineral dust can come into contact with trace acidic gases in the atmosphere and react to form mixtures of the mineral dust and new reaction products, thereby clearly changing the chemical composition. In addition, the processed particle could appear as an agglomeration of the mineral dust and reaction product components, possibly making the particle more irregular. On the other hand, the reaction product could form a coating around the mineral dust core creating a larger, more spherical processed particle. Regardless of the morphology of the aged particles, the chemical and physical changes caused by interactions with other atmospheric components will affect the optical properties of the aerosol. The aerosol optical properties need to be well understood because while suspended in the atmosphere, aerosols, including mineral dust, can scatter and absorb both incoming solar radiation as well as outgoing terrestrial radiation and therefore directly affect the Earth s radiation balance and climate [Boucher et al., 2013]. While there is still a lot of uncertainty about the direct radiative forcing effect of mineral dust, the Intergovernmental Panel on Climate Change (IPCC) estimates that direct radiative forcing effect of mineral dust lies in the range between W/m 2 and has changed by ± 0.11 W/m 2 from [Boucher et al., 2013; Mahowald et al., 2010]. In addition, these aerosols also have indirect effects, including the ability to act as cloud condensation and ice nuclei which greatly affects the Earth s albedo, as well as provide surfaces for heterogeneous chemistry that can alter atmospheric concentrations of important trace gases such as SO x and NO x species [Lohmann and Feichter, 2005; Bauer et al., 2004; Dentener et al., 1996]. In order to correctly model both the direct and indirect effects of atmospheric dust, it is important to have accurate estimates of dust concentrations, composition, and size distributions [Zhao et al., 2013; Claquin et al., 1998]. This data can be determined from field measurements using satellites, ground-based telescopes, or LIDAR methods [Dubovik et al., 2011; Li et al., 3

29 2013], however, accurate modeling of the dust optical properties is needed in order to correctly interpret the data which can be used in climate modeling. Therefore studies of dust optical properties are important not only for modeling the direct radiation effect, but also for minimizing errors in climate modeling. 1.2 Laboratory Measurements of Mineral Dust Light Scattering Properties In order to better understand the radiative effects of mineral dust aerosol, many groups have developed different laboratory methods to measure the light scattering properties of aerosols. For example, Hunt and Huffman [1973] have developed a scattering apparatus where incident light, which has been passed through a polarization modulator, is scattered by aerosol and the scattered light intensity is detected by a photomultiplier tube that is attached to a rotating arm. In addition, filters and polarizers can be placed in front of the detector in order to measure different elements of the scattering matrix. Several other groups have used similar techniques and made improvements to the apparatus including Jaggard et al. [1981], Volten et al. [2001], and Muñoz et al. [2010, 2011]. While this method does allow for measurements of all the elements of the scattering matrix, there are some limitations. First, this method takes a lot of time as the detector must be moved around to take data at individual angles. Therefore, since it is unable to measure the full range of angles simultaneously, any changes in the aerosol concentration and size distribution will affect the scattering results. Another limitation with this setup involves measurements of the size distribution. For example, Jaggard et al. [1981], analyzes electron micrographs of the sample collected on Nuclepore filters which takes time and can lead to errors from only providing information about two dimensions of the particles. Muñoz et al. [2011] and Volten et al. [2001] use laser particle sizers which fit the optical properties data and thus require accurate information about the refractive index and particle shape which is typically unknown for complex samples. 4

30 Another technique used to measure the light scattering properties of aerosol was developed by West et al. [1997]. This apparatus uses filtered light from a tungsten lamp that has been polarized as incident light on the aerosol sample. The scattered light is then detected by a linear array of silicon photodiodes spaced around the circular scattering housing. This allows for measurements of the angular dependence of the phase function and linear polarization profile at every 2 and allows for better time resolution than the setup described above because the full angle spectrum can be measured simultaneously. In addition, this method forms the basis for our improved design that uses a CCD array. As will be discussed in greater detail in Chapter 2, our experimental apparatus uses an elliptical mirror to reflect the light scattered from an aerosol sample towards a CCD camera [Curtis et al., 2007]. A tunable-wavelength pulsed laser as well a continuous wave diode laser have both been used for sources of incident light. More recently, this elliptical mirror technique has been applied to a portable high-resolution polar nephelometer [McCrowey et al., 2013]. Unlike the apparatus developed by Hunt and Huffman [1973], our experimental setup is capable of simultaneously measuring all angles in the range from ~ In addition, our experimental apparatus includes aerosol particle sizing instruments which allow for measurements of the full particle size distributions in real time. Our group, also has a separate experimental apparatus which can measure the IR extinction spectra in order to better characterize the aerosol samples and study the effects of particle non-sphericity as well as mineralogy across the spectrum from the IR to the visible. Regardless of the type of experimental setup used, many groups have found that the non-spherical shapes of mineral dust have a large impact on the measured light scattering properties. 1.3 Modeling the Radiative Effects In order to accurately model dust radiative transfer effects and understand the effect on Earth s radiation balance, information regarding aerosol concentration, composition, and particle 5

31 size and shape distributions is needed. Remote sensing data, either from satellite or ground-based instruments, can be used to retrieve much of this data and characterize atmospheric mineral dust if the aerosol optical properties are known [Ackerman, 1997; Sokolik, 2002; Thomas and Gautier, 2009]. These dust retrieval algorithms rely on accurate a priori estimates of the aerosol optical properties [Mishchenko et al., 2003; Kalashnikova et al., 2005; Koven and Fung, 2006]. Unfortunately, modeling the absorption and scattering properties of dust is complicated because atmospheric dust aerosol is typically composed of complex internal and external mixtures of different minerals [Claquin et al., 1999; Durant et al., 2009; Sokolik and Toon, 1999]. Modeling the optical properties of mineral dust is further complicated because the particles are often irregular in shape [Okada et al., 2001; Kalashnikova and Sokolik, 2004]. In the past, Mie theory, which simply assumes that the particles are spherical in shape, has been applied to both dust retrieval algorithms and climate forcing calculations [Nakajima et al., 1996; Kaufman et al., 1997; Tanré et al., 1997; Torres et al., 1998]. However, if dust particle shape effects are not properly accounted for, large errors can occur in climate forcing calculations or remote sensing retrieval algorithms from space or ground based platforms [Kalashnikova and Sokolik, 2002, 2004; Mishchenko et al., 2003; Kahnert et al., 2005; Kahnert and Kylling, 2004; Veihelmann et al., 2004; Dubovik et al., 2006; Klüser et al., 2012; Haapanala et al., 2012]. Although many different theoretical approaches have been developed to simulate the optical properties of irregularly shaped particles, significant challenges remain in applying these methods to atmospheric mineral dust. For example, both discrete dipole approximation (DDA) [Lindqvist et al., 2011; Nousiainen et al., 2009; Veihelmann et al., 2006] and finite difference time domain (FDTD) [Yang et al., 2000; Ishimoto et al., 2010] methods have been used to model the scattering properties of non-spherical, inhomogeneous particles, including the effects of fine scale surface features. However, these methods require significant computational resources, thus limiting their application to relatively small particles. Another approach, useful for simulating the 6

32 light scattering of larger non-spherical particles, is based on a geometric ray optics approximation. This method has been used to model light scattering from dust by approximating irregularly shaped particles as a distribution of Gaussian random shapes, triaxial ellipsoids, or nonsymmetric hexahedral prisms [Volten et al., 2001; Nousiainen et al., 2003, 2011a; Muñoz et al., 2007; Bi et al., 2009, 2010; Meng et al., 2010;]. 1.4 T-Matrix Theory T-matrix theory based techniques, often coupled with the uniform spheroid approximation, have also been widely used to simulate atmospheric dust optical properties. While not essential to the theory, the spheroid approximation is often applied in T-matrix simulations because the orientational averaging is simplified, making the method computationally efficient. Although the spheroid approximation may seem unrealistic, given the highly irregular shapes that often characterize natural mineral dust particles, it has been shown that spheroids can provide more flexibility in simulating the scattering properties than polyhedral prisms, and it also performs well compared to many other modeling approaches in fitting light scattering data [Nousiainen et al., 2006]. Therefore T-matrix methods, under the spheroid approximation, are being applied in both dust retrieval algorithms and climate forcing calculations [Dubovik et al., 2006; Mishchenko et al., 2004; Sinyuk et al., 2007]. While T-matrix methods can provide important tools for modeling aerosol radiative transfer effects, determining sample mineralogy and appropriate distributions of particle shapes as inputs to these models still remains a significant challenge. It is also not clear if the shape distributions that best fit the aerosol optical properties are correlated with the actual physical shapes of the particles as determined, for example, from electron microscopy. Indeed, there is good reason to doubt such a correlation [Nousiainen et al., 2011b; Meland et al., 2010]. Certainly electron microscope images of individual dust particles rarely look like smooth spheroids. However, many studies have investigated different spheroidal particle shape distributions 7

33 in order to determine which can reliably simulate the visible light scattering and/or the infrared (IR) extinction spectra of single component minerals [Kahnert et al., 2005; Merikallio et al., 2011; Nousiainen and Vermeulen, 2003; Kleiber et al., 2009; Meland et al., 2010, 2011, 2012; Meland, 2011]. For example, in studies of quartz aerosol, Meland et al. [2010] showed that spheroidal particle shape distributions based on analysis of electron microscope images of dust particles can result in very poor simulations of the optical properties data, and that accurate modeling of dust optical properties often requires including more extreme particle shapes in the distribution. This work also showed that particle shape distributions inferred from fitting the IR extinction spectra were able to give good model fits to the measured visible scattering data. Because the approach used by Meland et al. [2010] forms the basis for much of the work of this thesis, it is described more fully in Section Current Project The main goal of this work is better understand aerosol optical properties throughout the infrared and visible and to achieve more accurate modeling methods by investigating correlations in aerosol particle size, shape, and composition. In Chapter 5, the work of Meland et al. [2010] is extended to investigate particle shape distributions that can accurately simulate the observed extinction and scattering properties of illite and kaolinite, two important silicate clay minerals [Meland et al., 2012]. Simulations using a shape distribution model that is constant with respect to particle size, as used in the work of Meland et al. [2010], are unable to accurately simulate the full range of measured optical properties data. Therefore, the correlation between particle size and shape is explored for the silicate clays, illite and kaolinite (Chapter 5). Mineralogical studies have shown that small, fundamental clay particles are very thin sheets, having a flake like character, however larger particles are formed from these flakes stacking and bonding face-to-face, resulting in a much more moderate shaped particle. Because of this variation in particle shape as a function of size, typical modeling 8

34 methods fail to reproduce the measured optical properties. Therefore a bimodal model that treats small particles as highly eccentric oblate spheroids and larger particles as a distribution of more moderate spheroids is explored. Including the effect of these size-shape correlations in the modeling significantly improves the accuracy of the simulations over single mode approaches where such correlations are ignored. The correlation between composition and particle shape is explored next for diatomaceous earth, the main component of dust from the Bodélé Depression (Chapter 6) [Alexander et al., 2013a]. This is an interesting test case because it has a similar composition to quartz (silica), but is known for having extreme particle shapes. Meland et al. [2010] was able to achieve good model fits for quartz by using an IR based particle shape distribution that had been derived by fitting the measured IR extinction spectra and then applying the derived shape distribution to visible scattering simulations. Therefore the methods used by Meland et al. [2010] for modeling the optical properties of quartz is tested here to attempt to find an appropriate particle shape distribution for diatomaceous earth. To further complicate the modeling process, mineral composition and mixing state must be considered when simulating the optical properties of mixed, authentic samples. For example, a study by Mishra and Tripathi [2008] used T-matrix methods to model the optical properties of dust over the Indian desert and found that the single scattering albedo is actually more sensitive to the hematite content than particle nonsphericity. The mineral composition of dust can also vary greatly depending on what part of the world it originated from [Sokolik and Toon, 1999; Claquin et al., 1999; Krueger et al., 2004] and Saharan sand s composition can even vary within the desert itself [Avila et al., 1997; Caquineau et al., 2002; Thomas and Gautier, 2009; Formenti et al., 2011]. To further complicate the matter even more, dust aerosol composition has also been found to vary with particle size [Glaccum and Prospero, 1980; Eltayeb et al., 2001; Kim et al., 2003]. 9

35 The next goal of this work is to investigate if modeling methods determined in the studies of single mineral components can be generalized to predict the optical properties of more authentic samples, assuming the mineral composition is known (Chapter 7). Authentic field samples of Saharan sand, Iowa loess, and Arizona road dust are used here as test cases. Empirical mineral compositions, as well as slightly revised mineral compositions, found by Laskina et al. [2012] and Alexander et al. [2013b] are assumed and applied to T-matrix simulations for comparison to experimental measurements of the IR extinction and visible scattering phase function and linear polarization profiles. Along with having complex shapes and being composed of mixtures of different minerals, atmospheric dust aerosol particles can also undergo physical and chemical processing while suspended in the atmosphere. Therefore, a third goal of this project is to model changes in visible light scattering properties of mineral dust caused physical and chemical reactions with organic acids and humic material (Chapter 8) [Alexander et al., 2015]. More specifically, quartz is processed with humic acid sodium salt and calcite is processed with acetic and oxalic acid. Clear differences are seen in the visible scattering properties of all three of these processed samples when compared to the unprocessed mineral dust and organic components. When simulating these changes, many factors must be accounted for including the mixing state and possible changes in the particle s chemical composition and shape. Initial assumptions of the mixing state of these processed samples are based off of a study by Laskina et al. [2013], however adjustments are made to these models based off of the current experimental data. In addition to particle shape affecting the optical properties of aerosols, it also affects the aerodynamic properties. In order to account for these effects, the dynamic shape factor is used to give a measure of particle asphericity. Therefore, a fourth goal of this work is to explore the correlation between measured dynamic shape factors and the shape distribution derived by fitting the optical properties of quartz aerosol. Experimental measurements were carried out at the 10

36 Pacific Northwest National Laboratory using a combined, aerosol particle mass analyzer, differential mobility analyzer, and a single particle mass spectrometer. Dynamic shape factors of quartz are measured by mass and mobility selecting particles and measuring their vacuum aerodynamic diameter. From this, dynamic shape factors in both the transition and vacuum regime can be derived. 11

37 Experimental Methods 2.1 Optical Properties Apparatus A diagram of the visible scattering apparatus and aerosol flow, adapted from Meland [2011], is given in Figure 2.1 and discussed in the following sections Visible Scattering Apparatus Diagrams of the experimental scattering apparatus are given in Figure Figure 2.2. For visible scattering measurements, light is generated by a tunable Nd:YAG laser (Continuum Precision II) pumped optical parametric oscillator (OPO, Continuum Sunlight EX) or, alternatively, a 532nm laser diode (Thor Labs). The Nd:YAG pump is operated at 10Hz with an average output power of ~2.5W at 355nm. This is used to pump the OPO which can be tuned to wavelengths between 450nm-1.7µm, but all of the work in this thesis (using the Nd:YAG light source) has been carried out at a wavelength of 550nm, where the average output power is ~450mW. The output of the OPO also has a pulse width of ~7ns, bandwidth of ~0.08cm -1, and is linearly polarized (99%). In addition, the output is attenuated by a factor of 100 using a series of neutral density filters in order to bring the average power down to ~ 4.5mW. The output of the laser diode has an average power of ~4.5mW and is then linearly polarized using a prism polarizer. For either light source, the laser light is then sent through a Keplarian telescope with a spatial filter to ensure a Gaussian beam profile and to reduce the beam size to ~1.5mm. Next, a double Fresnel rhomb is used to rotate the polarization to be either parallel or perpendicular to the scattering plane (the optics table). The beam is then focused (60cm focal lens) and directed into the scattering chamber where it will cross paths with the aerosol (see Section 2.2) at the scattering region. This scattering region (~1 mm 3 ) is located at the first focal length of an elliptical mirror (Opti-Forms, Inc., major diameter 60cm and minor diameter 35cm). Because the scattering region 12

38 is a finite volume, and not a point, the angular resolution of our setup is limited [Meland, 2011]. The light scattered by the particles is reflected by the elliptical mirror and focused at the second focal point of the mirror and detected using a CCD camera (Santa Barbara Instrument Group). Examples of light scattering images captured by the CCD camera are shown in Figure 2.3. This allows for measurements of the relative intensity as a function of pixel position for parallel and perpendicular polarized incident light. In order to subtract out background light, mostly caused by scattering off of the edges of the mirror, images are also taken when no dust is present in the scattering region. In addition, light that has been directly scattered towards the camera (not reflected by the mirror) and passes through the pinhole must also be subtracted out and therefore the mirror is blocked and images are taken with and without the dust being present. All images are taken for incident light polarized both parallel and perpendicular to the scattering plane (same plane as the optics table). Once the background and direct scattered light has been subtracted, the light intensity is integrated along the z-axis of the scattering band. This results in the scattered light intensity as a function of pixel position along the y axis for parallel and perpendicular polarized incident light. More details of this procedure are given in Meland [2011]. Examples of CCD images, after having the background and direct scattered light subtracted, as well as the corresponding integrated light intensity are shown in Figure 2.3. From the integrated light intensity data, the differential cross section, ( F ( θ )) and the degree of linear polarization ( ( θ )) using the following equations, where ( θ ) ( ) I ( θ ) I ( θ ) F + P θ ( θ ) P can be calculated (2.1) I = I ( θ ) I ( θ ) ( θ ) + I ( θ ) I is the scattering intensity for perpendicular (to the scattering plane) polarized (2.2) 13

39 incident light and ( θ ) I is the scattering intensity for parallel (to the scattering plane) polarized incident light. The phase function is also normalized according Bohren & Huffman [1998], 1 2 π = 0 sin( θ ) ( θ ) dθ 1 F (2.3) Due to the physical geometry of the apparatus, scattering measurements are limited to an angle range of θ 6º - 172º; however for normalization purposes, this range is fully expanded by splicing on theoretical simulations. Potential normalization errors associated with this process are very small as seen by Figure 2.4 which compares diatomaceous earth aerosol measurements that have been spliced with Mie theory or with a T-matrix simulation and normalized according to Equation 2.3. Monodisperse polystyrene latex spheres (PSL), with well-known light scattering properties (Mie theory) are used to calibrate the detection system. Examples of CCD images and corresponding integrated light intensity for PSL 799nm diameter is shown in Figure 2.5. The first step in the calibration is to generate a mapping from Y pixel position to scattering angle. This is done by optimizing the fit between the experimental polarization of PSL and the polarization calculated from Mie theory. The polarization is used to generate the angle mapping because it will not be affected by the angular variation in the detection system response as those variations will cancel out when taking the polarization ratio (see Equation 2.2), and the pronounced interference structure apparent in the peaks and valleys of Figure 2.6 allow a unique solution. Figure 2.6 shows the optimized fit of the polarization as well as the phase function after the angle mapping has been applied. At this point, adjustments to the position of the mirror and nozzle are made on a day to day basis in order to optimize the raw fit to Mie theory. It should be noted that the experimental data for PSL is not able to exactly reproduce the theory at the peaks and valleys due to the limited angular resolution caused by finite scattering volume effects. However, because mineral dust samples are polydisperse, they do not show these pronounced peaks and valleys. 14

40 Once the system is aligned, a system response function, defined as the ratio of the theoretically calculated phase function to the experimentally measured phase function, is generated. As seen in Figure 2.7a, the response function contains noise, which will vary for different samples. However the response function also contains an overall structure which is independent of particle sample. This slow variation in the response function is due to the system geometry, including the effects of finite scattering volume and the transformation Jacobian for the elliptical mirror geometry. Meland [2011] contains a detailed analysis and discussion of these effects. Therefore, a calibration function is determined by fitting the slow variation in the response function with a simple form, C B ( θ D1 ) B2 ( θ D2 ) B3 ( θ D3 ) ( ) = A e + A e + A e θ 1 + A (2.4) in order to correct for the nonlinear response associated with the geometry of the set up. In addition, a sinusoidal function is fit to the forward scattering and added to the calibration function in order to remove the effects of the light diffraction around the edge of the elliptical mirror. An example of this fit is compared to the response function in Figure 2.7a and the corresponding phase function, after calibration, is shown in Figure 2.7b. The final calibrated and normalized PSL 799nm phase function and linear polarization profiles are shown in Figure 2.8. It should be noted, that the fine scale wiggles seen in the response function of Figure 2.7 at larger angles (>160 ) result from flaws in the mirror surface which has degraded over time from damage associated with the floods of For most of the data in this thesis (Chapters 4-7) the effects of these flaws was negligible. However, degradation worsened over time and for the data presented in Chapter 8 the flaws became more problematic. In order to eliminate the damage related fine scale wiggles apparent in these later experimental measurements (data presented in Chapter 8), a smoothing function has been applied to the phase functions. Figure 2.9 compares the measured phase function of PSL 799nm before and after the smoothing function has been applied. 15

41 To verify the alignment and calibration of the system, the angle mapping and calibration generated from one size of PSL is applied to experimental light scattering measurements from other sizes of PSL. As an example, the angle mapping and calibration generated from PSL 799nm (Figure 2.7) is applied to the measured light scattering properties from PSL 600nm and PSL 994nm and compared to Mie theory in Figure Additional tests are carried out by comparing data sets for standard samples that have been previously measured by our group to ensure reproducibility Infrared Extinction Apparatus Fourier transform infrared (FTIR) spectroscopy of the aerosol samples has been carried out by Olga Laskina and Paula Hudson of the Grassian research group at the University of Iowa and was published in Hudson et al. [2008a], Laskina et al. [2012], and Alexander et al. [2013b]. In those studies, the aerosol flow was directed through a long path extinction cell where an FTIR spectrometer (Thermo Nicolet, Nexus Model 670) was used to measure the spectra from cm -1, because that spectral range includes the characteristic vibrational resonance features observed from mineral dust. A diagram of the IR extinction apparatus is shown in Figure A full description of the IR extinction apparatus is given in Hudson et al. [2007]. 2.2 Aerosol Flow and Particle Size Distribution Measurements Aerosol samples used in this work were obtained commercially or from the field as specified in Table 2.1. Samples are prepared by suspending dust in HPLC grade water (Optima, Fischer Scientific and an aerosol flow is generated from the dust sample using a constant output atomizer (TSI, Model 3076). Excess water vapor is removed using a series of drying tubes in the aerosol flow. The relative humidity in the flow varied with time as the samples are run but typical RH values lie in the range of 5-25%. After passing through the scattering region, the mineral dust aerosol flow is collected and then directly passed to sizing instruments to measure particle size distributions simultaneous with the optical properties. An aerodynamic particle sizer (TSI, APS 16

42 Model 3321) is used in parallel with a scanning mobility particle sizer (TSI, APS Model 3034) in order to measure the full particle size distribution from 20 nm to 20 μm, however the particle size in the flow is restricted by the atomizer to particle diameters less than ~2.5 μm, corresponding to the accumulation mode size range (~ μm). In this size range, particles can stay suspended in the atmosphere for long periods of time and be transported over long distances [Williams et al., 2002; Prospero, 1999]. Because the APS and SMPS measure different size related physical properties and cover different ranges, the measured size distributions are combined and converted to a volume equivalent diameter as described by Meland [2011]. Briefly, the SMPS measures the mobility diameter (d m) of particles in the range ~ µm and the APS measures the transition aerodynamic diameter (d ta) in the range ~0.5 20µm. However a full, volume equivalent, size distribution is needed for the modeling analysis. The mobility diameter and aerodynamic diameter can converted to a volume equivalent diameter using the following equations [DeCarlo et al., 2004], d ve Cc ( dve ) 1 = d (2.5) m Cc ( dm ) χt d ve ρ C ( da ) ( d ) 0 c = da χt (2.6) ρ Cc ve assuming the dynamic shape factor, χ t, is known. In the previous equations, C c is the Cunningham slip correction factor, ρ p is the particle density, and ρ 0 is the standard density. The dynamic shape factor can be obtained by splicing the together the APS and SMPS data as described by Hudson et al. [2008a, 2008b], however using the current apparatus, there is no overlap in the measured size distributions. Therefore, the SMPS data is fit with a log normal function in order to extend the distribution. The dynamic shape factor can then be derived by overlapping the APS data with the fit to the SMPS data. However, it should be noted that this method assumes a single χ t for the entire shape distribution. While several studies have found that χ t changes as a function of particle size [Beranek et al., 2012; Zelenyuk et al., 2014], the current apparatus and analysis is unable to 17

43 account for the dependence. 18

44 Table 2.1 Sources of aerosol samples used in this work. Aerosol Sample Illite 1 Kaolinite Diatomaceous Earth Saharan Sand 2 Iowa Loess Arizona Road Dust Quartz 1 Calcite Humic Acid Sodium Salt Calcium Acetate Monohydrate Source Source Clay Repository IMt-1 Source Clay Repository KGa-1b, low defect Alfa Aesar Item #89381 CAS# Field Sample South Central Sahara Field Sample Loess Hills Powder Technology Inc. ISO , A2 Fine Test Dust Strem Chemicals Item # CAS# OMYACARB Sigma Aldrich SKU H16752 CAS# Sigma Aldrich SKU CAS# Calcium Oxalate Monohydrate Alfa Aesar Stock #13007 CAS# Ground with a mortar and pestle prior to aerosolization. 2 Filtered using a 100µm sieve prior to aerosolization in order to remove extremely large particles. 19

45 Figure 2.1 Visible light scattering experimental apparatus, adapted from Meland [2011]. Diagram is not to scale. Dry Air Diffusion Dryer Dry Air Conditioning Tube Spatial Filter Laser Atomizer Aperture Polarization Rotator Elliptical Mirror CCD Camera Computer Aerodynamic Particle Sizer Scanning Mobility Particle Sizer Vacuum Pump 20

46 Figure 2.2 Detailed view of the optical experimental set up as described in Section Diagram is not to scale. Laser Output Lens Pin Hole Lens Turning Prism Turning Prism 65 cm Polarization Rotator Lens Scattering Box Elliptical Mirror 60 cm 35 cm Pin Hole Scattering Region CCD 60 cm 21

47 Figure 2.3 CCD image and corresponding integrated scattered light intensity from quartz at 532nm for a) parallel and b) perpendicular polarized incident light. Background and direct scattered light have been subtracted. 22

48 Figure 2.4 Experimental phase function of diatomaceous earth at a wavelength of 550nm. Experimental data in the forward direction (θ < 6 ) has been spliced with simulations using Mie theory (blue solid line) and T-matrix theory (red dashed line) and normalized according to Equation 2.3. Note the very small difference in the normalization. Diatomaceous Earth Phase Function 10 1 Spliced With Mie Theory Spliced with T-Matrix Theory Scattering Angle 23

49 Figure 2.5 CCD image and corresponding integrated scattered light intensity from PSL 799nm diameter at 532nm for a) parallel and b) perpendicular polarized incident light. Background and direct scattered light have been subtracted. 24

50 Figure 2.6 Experimental phase function and linear polarization profile of PSL 779nm diameter at 532nm after being mapped from pixel position to scattering angle (green line). Note, the correction for the system response function has not been applied yet. Mie theory is also included for comparison (blue line). a) Scattering Intensity 10 7 PSL 799nm Experimental Mie Theory 10 3 b) Scattering Angle Linear Polarization Experimental Mie Theory Scattering Angle 25

51 Figure 2.7 a) Calibration curve for 799nm diameter PSL (green line) and the corresponding fit (black dashed line). b) The scattering intensity of PSL 799nm at 532nm after the calibration has been applied (green line) compared to Mie theory (black line). a) F(θ) Theory \F(θ) Measured PSL 799nm Response Function Fit to Response Function b) Scattering Angle 10 7 Scattering Intensity Experimental Mie Theory Scattering Angle 26

52 Figure 2.8 Comparison of the a) phase function and b) linear polarization profile of PSL 799nm diameter at a wavelength of 532nm (green lines) after the calibration function has been applied and Mie theory (black lines). In addition, theoretical Mie data has been spliced to the phase function for angles < 6 and a linear extrapolation has been used for angles > 172 ; this is shown green points. a) 100 PSL 799nm Experimental Mie Theory Phase Function b) Linear Polarization Scattering Angle Scattering Angle Experimental Mie Theory 27

53 Figure 2.9 Comparison of the measured phase function of PSL 799nm at a wavelength of 532nm before being smoothed (green line solid) and after being smoothed (blue dashed line). Phase Function PSL 799nm Before Smoothing After Smoothing Scattering Angle 28

54 Figure 2.10 Comparison of calibrated phase function and linear polarization profile for a) PSL 994nm diameter and b) PSL 600nm diameter (green lines) with Mie theory (black lines). Experimental data has been calibrated using the calibration curve generated from PSL 799nm (shown in Figure 2.6). In addition, theoretical Mie data has been spliced to the phase function for angles < 6 and a linear extrapolation has been used for angles > 172 ; this is shown green points. 100 a) PSL 994nm 100 b) PSL 600nm Phase Function 10 1 Experimental Mie Theory Phase Function 10 1 Experimental Mie Theory Linear Polarization Scattering Angle Scattering Angle Experimental Mie Theory Linear Polarization Scattering Angle Scattering Angle Experimental Mie Theory 29

55 IR Extinction Figure 2.11 Diagram of the IR extinction apparatus. Dry Air Diffusion Dryer FTIR Reaction/Hydration Chamber Atomizer IR Observation Tube MCT Detector Computer Aerodynamic Particle Sizer Scanning Mobility Particle Sizer CCN Counter 30

56 Light Scattering Theory When light is incident on an object, such as a particle, the light can be transmitted, absorbed, or scattered, depending on the physical properties of the particle (size, shape, orientation, and composition) and also the properties of the incident light (wavelength and polarization state). While an in depth discussion on the theory of light scattering is beyond the scope of this work, a brief overview is given here based on the discussion by Bohren & Huffman [1998]. Assume a plane electromagnetic wave, with wavenumber k, is incident on a particle at the origin of a spherical coordinate system, a distance, r, from the observation point. The scattered scat scat electric fields ( E and E ) can be related to the incident electric fields ( using the Mueller matrix as follows, inc E and inc E ) scat ik ( r z ) inc E S S e 2 3 E = scat inc (3.1) E ikr S4 S1 E Similarly, the scattered and incident Stokes parameters can also be related using a scattering matrix, I Q U V scat scat scat scat 1 = 2 k r 2 S S S S S S S S S S S S S S S S I Q U V inc inc inc inc (3.2) where the electric fields and Stokes parameters are related using the following equations, * * E + E I = E E (3.3) 31

57 * * E E Q = E E (3.4) * * E + E E U = E (3.5) V * * E E E = i E (3.6) Thus, elements of the scattering matrix in Equation 3.2 can directly be calculated from the Mueller matrix elements in Equation 3.1. These equations can be found in Bohren & Huffman [1998] and a selected few are shown below ( S1 + S2 + S3 4 ) ( S 2 S1 + S 4 3 ) S = + (3.7) S 1 11 S 2 = (3.8) 1 12 S 2 * * [ S S S ] S + = (3.9) 33 Re 1 2 3S4 * * [ S S S ] S + = (3.10) 34 Im 2 1 4S3 While there are no exact methods to calculate the exact scattering matrix for a particle with an arbitrary shape and size, there are several methods that use reasonable approximations to calculate the scattering matrix depending on the particle s size parameter, x, π n d p x = (3.11) λ where n is the index of refraction of the external medium, d p is the diameter of the particle, and λ is the wavelength of the incident light. For particles that are small compared to the wavelength of light (x << 1), Rayleigh theory can be used to approximate the scattering properties. In this regime, the incident electromagnetic field is treated as being uniform over the particle which then becomes a dipole oscillating with the same frequency as the light and the scattered light intensity becomes proportional to λ -4 [Hinds, 1999]. For particles that are large compared to the wavelength of light (x >> 1), geometric scattering approximations can be used. In this regime, incident light can be thought of as a collection of separate rays that are reflected, refracted, and diffracted by the large particle [van de Hulst, 1981]. One of the most widely used methods to 32

58 calculate light scattering properties is Mie theory which will be discussed in the following section. 3.1 Mie Theory Mie theory, developed by Gustav Mie in 1908, describes the scattering of an electromagnetic plane wave by a homogeneous sphere of arbitrary radius and refractive index [Mie, 1908]. While an in depth discussion on the theory of light scattering is beyond the scope of this work, a brief overview is given here based on the discussion by Bohren & Huffman [1998]. When considering the scattering for a sphere, Equations simplify to E ik ( r z ) e S2 = ikr 0 0 E S 1 E scat inc E scat inc (3.12) I Q U V scat scat scat scat 1 = 2 k r 2 S S S S S 33 S 34 0 I 0 Q S 34 U S 33 V inc inc inc inc (3.13) where the scattering matrix elements are also simplified to, 2 2 ( S1 2 ) 2 2 ( S 2 1 ) S = + (3.14) S 1 11 S 2 = (3.15) 1 12 S 2 * * ( S S S ) S = + (3.16) S S1 * * ( S S S ) = (3.17) S1 The scattering elements S 1 and S 2 can then be calculated as a summation of Mie coefficients (a n and b n), representing the weighting factors for each of the normal scattering modes. 2n + 1 S = + (3.18) 1 n n ( ) ( a ) n π n bnτ n n + 1 2n + 1 S = + (3.19) 2 n n ( ) ( a ) n τ n bnπ n n

59 where π n 1 Pn = (3.20) sin ( θ ) And 1 dp τ n n = (3.21) dθ 1 P n is the associated Legendre function of the first kind of degree n. These Mie coefficients can be calculated from Riccati-Bessel functions ( ψ n and ξ n ), a b n n mψ n ( mx) ψ n ( x) ψ n ( x) ψ n ( mx) = (3.22) mψ ( mx) ξ ( x) ξ ( x) ψ ( mx) n n n n ψ n ( mx) ψ n ( x) mψ n ( x) ψ n ( mx) = (3.23) ψ ( mx) ξ ( x) mξ ( x) ψ ( mx) n n n n where x is the size parameter and m is the complex index of refraction. Note that as m approaches 1 and the particle disappears, a n and b n approach zero and there is no scattered light. From these abstract mathematical equations, physical properties of the light scattering can be calculated. For example, the scattering intensity for parallel and perpendicularly (respectively) polarized incident light is, Note, scat I and I inc 2 inc ( S + S ) I S I scat = scat = (3.24) inc 2 inc ( S S ) I S I 2 I = = 1 (3.25) scat I are the properties that are experimentally measured as described in Section In addition, the phase function and linear polarization can be calculated using the following equations, inc scat scat ( ) S I = I I F = 11 + θ (3.26) scat scat S I I 12 P( θ ) = = (3.27) scat scat S I + I 11 While, not directly measured by the current experimental set up, the extinction and scattering 34

60 cross sections are both important properties which will be needed for modeling analysis. The scattering cross section is defined as the ratio of the rate of scattered energy over the total incident light intensity (units of length 2 ). Similarly, the extinction cross section is the ratio of the rate of scattered and absorbed energy over the total incident light intensity. These cross sections can be calculated from the Mie coefficients using, C C ext scat 2π = Re 2 k 2π = k n= 1 ( 2n + 1) [ a + b ] 1 2 n= ( 2n + )( an + bn ) n n (3.28) (3.29) While in the past Mie theory has been used to calculate the light scattering properties of atmospheric mineral dust as well as aerosol retrieval algorithms and climate forcing calculations, significant errors can occur when particle shape effects are ignored [Curtis et al., 2008; Meland et al., 2010; Dubovik et al., 2006; Kahnert et al., 2005; Haapanala et al., 2012]. Therefore, T- matrix theory, which can account for particle asphericity has become more widelyapplied recently. 3.2 T-Matrix Theory T-matrix theory uses boundary value conditions to numerically solve Maxwell s equations for the scattering from a non-spherical object, although it exactly reduces down to Mie theory when applied to spheres. Waterman [1965, 1971] first used this approach to calculate the scattering properties of homogenous, arbitrarily shaped objects. A brief overview of T-matrix theory, based off of the discussion by Mishchenko et al. [2002], is provided below. Assume there is a particle scattering the light from a plane electromagnetic wave. The ( ) electric field of the incident wave E inc ( r) (M mn and N mn), can be written as,, expanded as a series of vector spherical harmonics 35

61 inc n ( r) = [ amn RgM mn ( kr) + bmn RgN mn ( kr) ] E (3.30) n= 1 m= n where aa mmmm and bb mmmm are the expansion coefficients for the incident wave and the Rg denotes the ( ) ( ) regular solution. Similarly, the scattered E scat ( r) and internal E int ( r) fields can be written as, scat n ( r) = [ pmnrgm mn( kr) + qmnrgn mn( kr) ] E (3.31) int n= 1 m= n n ( r) = [ cmnrgm mn( mkr) + dmnrgn mn( mkr) ] E (3.32) n= 1 m= n where p mnand q mn are the expansion coefficients for the scattered wave and c mn and d mn are the expansion coefficients for the internal wave and m is refractive index of the object relative to the surrounding medium. Because Maxwell s equations are linear, then the relationship between the incident and scattered wave expansion coefficients must also be linear and can therefore be related by a transition or T-matrix (T) as follows, p a T = T = q b T T T a b (3.33) Similarly, the internal wave expansion coefficients are linearly related by the matrix, Q, through the following equations, a c Q = Q = b d Q Q Q c d (3.34) p c RgQ RgQ c = Rg Q = (3.35) q d RgQ RgQ d The elements of the Q matrix are two dimensional integrals over the objects surface which depend on object s size relative to wavelength, shape, orientation, and refractive index. It should 36

62 be noted that different approximations about the particle shape are typically applied in order to simplify the calculations due to orientational averaging and vastly improve the computational efficiency. The T-matrix can then be calculated from the Q matrix using the following equation, 1 T = Rg Q Q (3.36) The T-matrix is only dependent on the properties of the scatterer (size relative to wavelength, shape, orientation, and refractive index) and not the incident or scattered waves. Therefore, a T-matrix for an object can be used to calculate the scattering properties for any polarization and orientation of incident light. For randomly oriented, non-spherical objects, the extinction and scattering cross sections can be directly calculated from the T-matrix using the following equations, C ext n 2π = Re [ T + ] 2 mnmn Tmnmn k n= 1 m= n (3.37) C scat 2π = 2 k n n' n= 1 m= n n' = 1 m' = n' T 11 mnm' n' 2 + T 12 mnm' n' 2 + T 21 mnm' n' 2 + T 22 mnm' n' 2 (3.38) The full scattering matrix can also be calculated from the T-matrix using equations of Mishchenko et al. [2002]. 3.3 Application of the T-Matrix Method Model IR extinction and visible light scattering phase function and polarization profiles are generated using NASA s publically available T-matrix code [Mishchenko and Travis, 1998]. Required inputs to the code include parameters specifying the size distribution, refractive index data (optical constants), and particle shape. Particle size distributions, measured simultaneous to optical properties measurements, are fit with a log normal form for use in the code. Refractive indices were found in literature or derived in this work (Section 8.3.2). Particle shape effects are treated using the uniform spheroid approximation. In this approach particle shape is specified by 37

63 a shape parameter, ξ, defined for oblate and prolate spheroids as, ε 1 ε 1 (oblate) ξ = (3.39) 1 1 ε ε 1 (prolate) where ε is the ratio of major-to-minor axis lengths for oblate spheroids (ε 1) and its inverse for prolate spheroids (ε < 1). Particle shape parameters included in this work are limited to the range -3 ξ +5 due to well documented convergence problems in the T-matrix code for larger particles and particles with more eccentric shapes [Mishchenko and Travis, 1998]. It should be noted that the spheroid assumption represents a crude approximation to the actual shapes of mineral dust aerosol particles which can be highly irregular and may contain voids, sharp edges, and fine scale surface structure [Muñoz et al., 2007, 2011; Volten et al., 2001], however and the spheroid approximation has performed well compared to many other modeling approaches in fitting light scattering data [Nousiainen and Vermeulen, 2003; Nousiainen et al., 2006; Meland et al., 2010]. It should be noted that the validity of the smooth spheroid approximation is still an open question, which is further explored in this work. For a given distribution of particle shapes, T-matrix calculations of single particle shape parameters can be averaged to simulate the optical properties for a distribution of particle shapes using the following equations: C ext = N( ξ ) Cext ( ξ ) (3.40) ξ ( ) N ξ ( ξ ) C ( ξ ) F ( ξ ) Fαβ θ = (3.41) N ξ scat ( ξ ) C ( ξ ) scat αβ where N(ξ) is the relative number of particles, C(ξ) is the average extinction and scattering cross sections per particle and F αβ(ξ) is the normalized scattering matrix elements for particles with the 38

64 shape parameter ξ [Meland et al., 2012]. A major goal of this work, as well as previous studies, is to investigate the shape distributions that are most appropriate for simulating the optical properties of mineral dust aerosol and will be discussed in more detail in the following section. 39

65 Background Studies The work in this project has been, in part, based off of the work of several previous studies by Hudson et al. [2008a, 2008b], Kleiber et al. [2009], and Meland et al. [2010]. In the work done by Hudson et al. [2008a, 2008b], the measured IR extinction of several single component mineral dust aerosol samples were modeled using a simple Rayleigh-based analytic theory and compared to Mie theory simulations. They found that improvements over Mie theory were achieved by using the Rayleigh method and a continuous distribution of ellipsoids as the particle shape model for non-clay samples (quartz, calcite, and dolomite). A similar study was done for several clay components of mineral dust including illite, kaolinite, and montmorillonite. In that study, Hudson et al. [2008a] also achieved better model fits by using Rayleigh theory compared to Mie theory, however with the clays, a disk-shaped model resulted in the best fits to the experimental data. These results clearly suggested that optical properties depend on particle shape, and that particle shape is correlated with mineralogy. It also suggests that the use of fairly simple generic shape models for different mineral components could improve the quality of theoretical light scattering calculations of the optical properties of atmospheric mineral dust compared to Mie theory. This work was furthered by Kleiber et al. [2009] who used T-matrix theory, including the spheroidal particle shape approximation, to model the IR extinction of quartz, calcite, illite, kaolinite, and montmorillonite. T-matrix theory allows for much more flexibility in the particle shape distributions used in the simulations. Again, Kleiber et al. [2009] found that the clay samples required vastly different shape distribution models when compared to the non-clay sample, quartz. Similarly to Hudson et al. [2008b], the IR extinction spectra of quartz was best fit by a broad distribution of spheroids including both extreme oblate and prolate shapes. Calcite was found to be best fit by a model that only includes a moderate distribution of particle shapes. Conversely, the silicate clays studied all required extreme oblate (disk-like) spheroidal shape 40

66 models to achieve accurate fits to the experimental IR spectra. This again not only agrees with the results of Hudson et al. [2008a], but also with the known sheet-like character of silicate clay particles. Meland et al. [2010] then took this concept and extended it to experimental measurements of the visible scattering properties of quartz. Their goal was to simultaneously simulate the IR extinction and visible scattering phase function and linear polarization profile with a single particle shape model. Particle shape distributions were first determined through analysis of electron microscope images, resulting in a shape distribution that only includes moderately shaped spheroids (AR< 2.6) and strongly peaks at nearly-spherical spheroids (mean AR ~ 1.4). However, simulations using the SEM based shape distribution failed to accurately simulate either the IR extinction or the visible scattering profiles at different wavelengths. This could be due to the fact that SEM images only provide information about two dimensions of a three dimensional particle. In addition, fine scale surface roughness that may not be readily apparent in SEM images, might have a significant effect on the measured optical properties. It is also possible that a spheroidal shape distribution that optimally fits the particle s optical properties may have no obvious correlation to the gross physical shapes of the particles. Therefore, based on the previous studies already discussed, Meland et al. [2010] determined a spheroidal shape distribution by fitting the measured IR extinction spectra and then applied that distribution to model the visible scattering properties. In agreement with Kleiber et al. [2009], this spheroidal shape distribution was found to consist of a broad distribution of spheroids ranging from extremely prolate to extremely oblate shape parameters. Simulations using this IR based shape distribution not only resulted in excellent fits to the IR spectra, but also all of the light scattering properties at three different scattering wavelengths in the visible. This has motivated the work in the following chapters where it is tested for other samples of mineral dust and further applied to complex mixtures of different minerals. 41

67 Size Dependent Shape Distributions of Silicate Clay Aerosol 5.1 Introduction As previously discussed, Meland et al. [2010] were able to simultaneously simulate both the IR extinction spectra and visible scattering properties of quartz aerosol using the same particle shape distribution model. The goal of this chapter is to extend that approach to model the optical properties of the silicate clays, a major component of wind-blown dust. Fundamental silicate clay particles are known be very thin flakes, having a sheet-like character [Nadeau, 1985, 1987], corresponding to very large positive (oblate) shape factors. However, larger clay particles are formed when the small, flake like particles bond face-to-face, creating a thicker layered particle that is more moderately shaped. These characteristic shape effects could cause several difficulties when modeling the optical properties of clay particles. First, the extreme eccentricity of small clay flakes can cause convergence problem in many numerical simulation methods. Second, variations in the particle shape as a function of particle size will affect the observed optical properties and most commonly used simulation methods do not account for these variations. Therefore the first goal of this chapter is to explore if the variation in particle shape with particle size for silicate clay minerals has a significant effect on the measured optical properties and must be accounted for in the modeling, or if the effects can be safely ignored. In addition, a second goal is to see if there is, in fact, any correlation between the actual physical shapes of the particles (as determined from the mineralogical studies) and the shape distribution models that best fit the optical properties. 5.2 Experimental Methods and Results Experimental IR extinction spectra and visible phase function and linear polarization profiles at a wavelength of 550nm are shown in Figure 5.1 for illite and Figure 5.2 for kaolinite. IR extinction measurements for both illite and kaolinite were measured by Paula Hudson and 42

68 published in Hudson et al. [2008a]. Light scattering properties for kaolinite were experimentally measured by Brian Meland and published in Meland et al. [2012]. Log normal fits to the measured size distributions are listed in Table Single Mode Modeling Analysis As a first step, a spheroidal shape distribution is derived by fitting the IR extinction spectra, similar to the methods of Meland et al. [2010]. Using a single shape parameter, the IR based shape distribution for illite is found to be the most eccentric oblate spheroid allowed in the fitting routine (due to convergence issues), ξ = +7, and ξ = +4 for kaolinite. The fit to the IR extinction spectra are shown in Figure 5.1 as green lines and are quite good. However, when these extreme oblate shape distributions are applied to the corresponding visible scattering properties, the quality of the fits are much worse. Both of the simulated phase functions under predict the backward scattering and the peak polarization profiles are too high when compared to measurements. It appears that the visible scattering properties require a much more moderate shape distribution in order to accurately reproduce the measured data. However, more moderate shape distribution in turn result in poor fits to the IR extinction spectra. Therefore, each of the individual optical properties can be fit well by a single mode shape distribution but with correspondingly poor fits to the other two optical properties. All attempts to simultaneously fit the whole range of measured optical properties using a single mode model have failed to achieve acceptable results. As an example, several shape distribution models are also shown in Figures 5.1 and 5.2 including a prolate shape factor (ξ = -2), a moderate shape distribution ( ξ 1.4), and the broad shape distribution that was derived for quartz in Meland et al. [2010] (-3 ξ +5). 5.4 Bimodal Modeling Analysis While attempts to fit the full range of measured optical properties for illite and kaolinite, 43

69 using the approach of Meland et al. [2010], have yielded poor results, it should be noted that IR extinction and visible scattering properties scale differently with particle size. This suggests that a particle shape distribution that varies with size could result in better overall fits to the experimental data. A particle size dependent shape distribution is also in agreement with studies of the physical shapes of clay particles. For example, studies by Nadeau [1985, 1987] found that fundamental (small) clay particles are very thin and flake-like in character while the larger clay particles, formed by face-to-face bonding of the small particles, can have thicker layered structures that are much more moderately shaped than the small particles. Therefore to account for the expected correlation between particle size and shape, a simple bimodal shape distribution was proposed where the small particles are modeled as highly eccentric oblate spheroids, and the larger particles are modeled as a distribution of moderate spheroids. More specifically, the clay particle size-shape distribution is separated by an empirically determined cutoff diameter, d c, (with 450 nm < d c < 700 nm) into small-particle (d ve < d c) and large-particle modes (d ve > d c), which are then allowed to have different shape distributions. The small particles (mode 1, ξ 1) are modeled with a single, highly eccentric oblate shape factor and the large particles (mode 2, ξ 2) are modeled with a moderate shape distribution. Similarly to Equations 3.40 and 3.41, the simulation results of the two modes can be combined using the following equations, C ext ( ) ( 1 ( ) ) ( 2 ( ) ) ( 2 ( N ξ C ξ N ( ξ ) C ) ( ξ )) 1 = + (5.1) ξ ext ext ( θ ) ξ ( 1 ) ( 1) ( 1 ( ) ( ) ) ( 2 ( ) ) ( 2 ( ) ) ( 1 ( N ξ C ( ) ) scat ξ Fαβ θ + N ξ Cscat ξ Fαβ ( θ )) ( 1 ) ( 1) ( 2 ( ) ( ) ) ( ( N ξ C + ( ) ) scat ξ N ξ Cscat ( ξ ) ) Fαβ = 2 (5.2) ξ subject to the normalization condition 44

70 (1) (2) ( ( ξ ) + N ( ξ )) N = 1 (5.3) ξ where the variables are as in Equations 3.40 and 3.41 and the superscript (1) and (2) denote the small and large particle size modes 1 and 2, respectively. The specific values for d c (d c = 600 nm) and ξ 1 (ξ 1 = +7 for illite and +4 for kaolinite) were empirically determined to give the best overall fit to the full range of measured IR and visible optical properties for the individual clays, illite and kaolinite [Alexander et al., 2013b]. In addition, a cubic power law form for the large particle mode and the range of ξ 2 values (0 ξ ) was also empirically chosen to use in this model. The oblate character of the large particle mode is also physically reasonable to assume because as the fundamental sheets stack by bonding face-to-face, the particle is likely to retain an oblate shape as opposed to becoming more pointy and prolate. It should be noted that it is difficult to define the best simultaneous fit to all three optical properties because it depends on the relative weights assigned to the chi-squares of the three optical properties. Simulation results using the bimodal shape distribution just described are compared to experimental data in Figures 5.3 and 5.4 for illite and kaolinite. Clearly, this bimodal shape distribution results in a large improvement compared to any of the single mode shape distributions in Figures 5.1 and 5.2. This can also be seen in the chi square values listed in Table 5.2. Good fits to the experimental data can also be achieved using a range of modeling parameters and will depend on the values of the chosen refractive indices. The modeling analysis in this chapter is based on the refractive indices reported by Friedrich et al. [2008] (n illite = 1.587, n kaolinite = 1.564), however, they are quite different from the refractive indices reported by Egan & Hilgeman [1979] (n illite = 1.413, n kaolinite = 1.493). A similar analysis was done using the Egan & Hilgeman [1979] refractive indices and the bimodal model also improved on the model fits 45

71 compared to any single mode model, the exact model parameters were slightly different. For example, the cut off diameter was d c = 600 nm (as opposed to d c = 650 nm), small particle mode shape factor for illite was increased to ξ 2 = +11, and the large particle mode included a uniform distribution of moderate prolate and oblate spheroids. While these differences in the shape distribution may seem large, the basic characteristics of the bimodal model (extremely oblate small particles and more moderately shaped larger particles) improve the model fits when compared to any single mode model, regardless of the refractive indices chosen. In fact, this bimodal shape distribution agrees quite well with studies of the physical shapes of silicate clay particles. Studies by Nadeau [1985, 1987] found that illite and kaolinite fundamental clay flakes have average face diameters of D F ~ nm, and an average face diameter-to-thickness ratio of ~ 4-8 for kaolinite and ~40-80 for illite. This agrees well with the bimodal model parameters found from the optical properties fitting. It is possible that even better fits to the experimental measurements could be achieved by adding more adjustable parameters to the model. For example, adding an intermediate size mode that includes shape parameters in the range between the extreme and moderate factors used for the small and large modes could potentially improve the fits. Including this intermediate size mode would also be justified by the physical shapes of the stacked flakes. However, adding more adjustable parameters would further complicate the model and make it less practical for applications to climate models and remote sensing algorithms. In addition, the simple bimodal described here, with few adjustable parameters, has made an improvement over single mode models and could prove useful in simulating the optical properties of authentic mineral dust with a large clay fraction. 5.5 Conclusions The correlation between particle size and shape of silicate clay minerals have been found to have a significant effect on the optical properties of silicate clay minerals. In addition, 46

72 commonly used single mode models fail to simulate the full range of measured optical properties and the size-shape correlation must be accounted for in modeling methods. Therefore a simple bimodal model that allows particle shape to vary with particle size is explored for two silicate clay minerals, illite and kaolinite. In this model, small particles are treated as highly eccentric oblate spheroids while the larger particles are modeled using a range of more moderate oblate spheroids. This simple bimodal model is a large improvement over single mode models which are unable to fit all three optical properties simultaneously. The bimodal model is shown to give good agreement to the full range of measured optical properties including the IR extinction and visible scattering phase function and linear polarization profiles. In addition, the variation in particle shape with particle size that is provided by this bimodal model is also supported by the known correlation between particle size and shape for silicate clays. In fact, our model shape distributions are roughly consistent with mineralogical studies of the physical shapes of silicate clay particles [Nadeau, 1985, 1987], suggesting that there is physical significance to the particle shape factors, and that they are not simply mathematical modeling parameters without physical meaning. 47

73 Table 5.1 Table of log normal size distribution parameters that best fit the measured (volume equivalent) particle size distributions for illite and kaolinite in the IR extinction and visible light scattering experiments.* IR Visible (550 nm) r m (nm) σ r m (nm) σ Illite Kaolinite * Here r m is the mode radius of the particle number size distribution and σ is the width parameter of the size distribution. Table 5.2 Comparison of chi square values for the simulations of the optical properties of a) illite and b) kaolinite, as shown in Figures 5.1 and 5.2. Values listed in the table have been scaled by a factor of a) Illite χχ 2 IR Extinction Phase Function Polarization Bimodal Model ξ = ξ = Moderate Model Quartz Distribution b) Kaolinite χχ 2 IR Extinction Phase Function Polarization Bimodal Model ξ = ξ = Moderate Model Quartz Distribution

74 Figure 5.1 Comparison of single mode simulations with experimental data for illite. Simulations use an extreme oblate shape parameter (green lines), a prolate shape parameter (blue lines), a moderate uniform shape distribution with shape parameters in the range ξ 1.4 (red lines), and a more eccentric uniform shape distribution with shape parameters in the range -3 ξ +5 (cyan lines). a) Extinction Experiment ξ= +7 ξ= - 2 Moderate Dist. Quartz Dist. Illite b) Phase Function Wavenumber Experiment ξ= +7 ξ= - 2 Moderate Dist. Quartz Dist. 0.1 c) Scattering Angle Linear Polarization Experiment -0.5 ξ= +7 ξ= - 2 Moderate Dist. Quartz Dist Scattering Angle 49

75 Figure 5.2 Comparison of single mode simulations with experimental data for kaolinite. Simulations use extreme oblate shape parameters (green lines), a prolate shape parameter (blue lines), a moderate uniform shape distribution with shape parameters in the range ξ 1.4 (red lines), and a more eccentric uniform shape distribution with shape parameters in the range -3 ξ +5 (cyan lines). a) Extinction Experiment ξ= +4 ξ= - 2 Moderate Dist. Quartz Dist. Kaolinite 0.05 b) Phase Function Wavenumber Experiment ξ= +4 ξ= - 2 Moderate Dist. Quartz Dist Scattering Angle c) 1.0 Linear Polarization Experiment -0.5 ξ= +4 ξ= - 2 Moderate Dist. Quartz Dist Scattering Angle 50

76 Figure 5.3 Comparison of a bimodal simulation with experimental data for illite. a) Relative Extinction Illite Experiment Bimodal Model b) Wavenumber Phase Function 10 1 Experiment Bimodal Model Scattering Angle c) 1.0 Linear Polarization Experiment Bimodal Model Scattering Angle 51

77 Figure 5.4 Comparison of a bimodal simulation with experiment for kaolinite. a) Relative Extinction Kaolinite Experiment Bimodal Model Wavenumber b) Phase Function 10 1 Experiment Bimodal Model 0.1 c) Scattering Angle Linear Polarization Experiment Bimodal Model Scattering Angle 52

78 IR Based Shape Distributions of Diatomaceous Earth Aerosol 6.1 Introduction Diatomaceous earth is a major component of dust from the Bodélé Depression in northern Chad, As discussed in the Introduction sections, the Bodélé Depression represents a major source of atmospheric dust and consists of the skeletal remains (frustules) of diatoms, microscopic one celled organisms that can live in both fresh water and salt water [Klein et al., 1999; Calvert, 1930]. These particles can have intricate structures with very complex shapes ranging from thin plates to sharp rods. Some of the plate-like particles also have obvious regular hole patterns. Other particles show clear evidence for fine scale surface roughness. Some of these extreme particle shape characteristics can be seen in the SEM image shown in Figure 6.1. As already mentioned, particle shape can have a large effect on dust optical properties. Previous studies of mineral dust aerosol have determined particle shape distributions though spectral fitting of experimental IR extinction profiles [Kleiber et al., 2009; Meland et al., 2010]. As already discussed, a study of quartz aerosol by Meland et al. [2010] found that the particle shape distributions derived from analysis of the measured IR extinction spectra were able to give excellent fits to the measured phase function and linear polarization profiles. This method is applied here to a sample of diatomaceous earth in order to investigate if particle shape distributions derived from IR extinction spectra can give good fits to the measured visible scattering properties for this sample as well. Diatomaceous earth is an interesting test case for this method because it is compositionally similar to quartz since they are both composed of silica, however diatomaceous earth has much more eccentrically shaped particles. The extreme shape of the diatomaceous earth particles are especially obvious when compared to the shapes of typical quartz particles, seen in Figure 6.2. In addition, diatomaceous earth is a good test case to investigate the possible limitation of the spheroid approximation when applied to irregularly shaped mineral dust particles. While previous studies on quartz and silicate clay have suggested 53

79 that the spheroid approximation can work well, provided appropriate shape distributions are used, diatomaceous earth could provide a much more difficult test for the approximation. 6.2 Experimental Methods and Results Diatomaceous earth, which reflects the general characteristics of diatomaceous earth field samples from the Bodélé Depression of North Africa, was purchased commercially from Alfa Aesar (Item 89381). Results from a bimodal lognormal fit to the measured size distributions for the diatomaceous earth sample are shown in Table 6.1 and Figure 6.3. The experimental IR extinction spectrum and visible light scattering data at a wavelength of 550nm for diatomaceous earth are shown as points in Figure 6.4. The linear polarization data is particularly noteworthy; the peak polarization signal is extremely high, measure 0.7 at a scattering angle around 90. High linear polarization can be indicative of extreme particle shape factors as might be expected from the SEM images. The experimental IR spectrum has been corrected to eliminate a sloping baseline associated with falling IR lamp intensity toward the low energy end of the spectrum, as discussed by Laskina et al. [2012]. Results from different theoretical simulations are shown in the figures by solid lines and will be described in the following sections. 6.3 Modeling Analysis Since diatomaceous earth consists of hydrated amorphous silica [Calvert, 1930], optical constants for glassy quartz were used in the T-matrix simulations. Optical constants for glassy quartz were used as oppose to crystal quartz since it is unlikely that the silica in diatomaceous earth has a crystalized structure like quartz, however this is also explored. IR and visible optical constants were taken from literature by Zolotarev [2009] and Khashan & Nassif [2000], respectively. The T-matrix simulations also use the measured particle size distributions for each of the corresponding visible and IR optical properties (Table 6.1). The IR based shape distribution is determined by adjusting the weights of the simulations 54

80 that use different shape parameters in order to optimize the fit to the experimental IR extinction spectral line profile. A least squares fitting routine, constrained to include only non-negative weights, was written to optimize the fit. The particle shape parameters included in the fit were limited to the range -3 ξ +5 because of convergence problems in the code for more extreme particle shape factors in the visible simulations; the T-matrix calculations are converged over the full particle size distributions for this range of shape factors. The shape distribution that best fits the IR extinction spectra was found to consist predominantly of the most eccentric oblate and prolate spheroid shape factors in the range studied ( 3 and +5) and is shown as red bars in Figure 6.5. More specifically, the best fit shape distribution was found to include ξ = -3 (44%), +1 (6%), and +5 (49%). While the fitting routine allowed shape factors to vary over the range -3 ξ +5 (with a step size Δ ξ = 1), all other shape factors were found to have < 0.2% weight. 6.4 Modeling Results Simulation results for the IR extinction spectra and visible scattering properties of diatomaceous earth are shown as solid red lines in Figure 6.4 and are compared to experimental measurements (points). Also shown as green lines for comparison are simulations that use the shape distribution for quartz particles found by Meland et al. [2010] (uniform, -3 ξ +5), blue line which use a moderate shape distribution (uniform,, and orange lines which use Mie theory (ξξ = 0). It should be noted that IR simulations using the quartz particle shape distribution, the moderate shape distribution, and Mie theory have been normalized to 1 so that only the line shape is relevant for comparison and not the relative normalization IR Extinction Results Clearly, since the IR based shape distribution was derived by optimizing the fit to the experimental IR spectra of diatomaceous earth, the IR based simulation results give much better 55

81 fits than the simulations using either the quartz or spherical shape distributions. The IR based simulation does fit the shape of the experimental IR spectra reasonably well but the peak position is slightly blue shifted by ~11 cm -1. Perhaps the fit could be improved if more eccentric particles were included (and not limited by convergence issues), or if a different set of IR optical constants were used. Note, however, that including more moderate particle shapes in the distribution increases the error in the simulated peak position; the quartz shape distribution results in a blue shift ~16 cm -1 while the moderate shape distribution results in an even larger blue shift ~31 cm -1. The IR based shape distribution offers a clear improvement over the more moderate shape distributions, and further supports the conclusion that extreme particle shape factors are often needed in order to accurately model mineral dust optical properties Visible Scattering Results The visible simulation results using the IR based particle shape distribution, shown in Figure 6.4b and Figure 6.4c as red lines, give reasonably good fits to the experimental scattering data compared to other simulations, however the simulated phase function is too low in the backward scattering direction, and the peak polarization is also quite low. Increasing the fraction of the moderate particle shapes in the model (as in the quartz model) significantly improves the phase function fit but leads to a clear degradation in the fit to the polarization profile. Simply restricting the shape distribution to include only moderate spheroids (blue line) or simply spheres (orange line) results in very poor fits to both the experimental phase function and polarization profiles. The fits are qualitatively compared using chi square values shown in Table 6.2. In order to fit the very high values of the linear polarization at scattering angles near 90, the simulations would most likely require even more extreme particle shape factors, although this might further degrade the fit to the phase function data. In any case, the convergence limitations of the T-matrix code preclude carrying out visible simulations with more extreme shape factors. It appears possible that no single particle shape distribution can simultaneously improve 56

82 the simulation fits to both the phase function and polarization data. It is possible that a more sophisticated model which allows particle shape to vary with particle size might provide enough flexibility to improve the fits to the data [Meland et al., 2012], but our attempts along these lines have been thus far unproductive. As previously mentioned, the relatively poor fit to the visible scattering data could also be due to a breakdown in the validity of the smooth spheroid approximation to model the very extreme particle shapes apparent in Figure 6.1. In addition, the effect of surface roughness might play an important role in the scattering process [Kahnert et al., 2011; Nousiainen and Muinonen, 2007; Li et al., 2004]. 6.5 Variations in Refractive Indices Since the fit to the IR extinction is quite good, simulations of the visible scattering properties are run for a range of visible optical constants. In addition to the optical constants for glassy quartz (n = 1.507) reported by Khashan & Nassif [2000], simulations are also calculated using optical constants for diatomaceous earth (n = 1.45), as reported by Egan [1985], and crystal quartz (n = 1.55), as reported by Longtin et al. [1988]. The optical constants used in this section are listed in Table 6.3. Simulations of the visible scattering properties using this range of optical constants and the IR based shape distribution derived with glassy quartz IR optical constants (Section 6.4) are shown in Figure 6.6 As seen in the figure, decreasing the real part of the refractive index (Egan OC) improves the fit to the experimental polarization but the quality of the phase function fits was made worse. Oppositely, increasing the real part of the refractive index (Longtin et al. OC) improves the fit the experimental phase function, but degrade the fit to the polarization. It should be noted that the simulation results are insensitive to the imaginary part of the index of refraction for values < Therefore it appears that simply adjusting the visible refractive indices does not result in better overall fits to the full range of measured optical properties. However, perhaps a change in the IR optical constants, and thus a change in the IR based 57

83 shape distribution, could improve the overall fit to the full range of measured optical properties. Therefore, the analysis described in Section 6.3 was repeated using the IR and visible optical constants for crystal quartz as reported by Longtin et al. [1988] (IR refractive indices for diatomaceous earth were not found in literature). The corresponding IR based shape distribution was found to be very similar to that derived using optical constants for glassy quartz, containing mostly extreme prolate and oblate shape factors and are shown graphically in Figure 6.7. This IR based shape distribution is applied to T-matrix simulations and compared to experimental measurements as well as the simulations using the optical constants for glassy quartz in Figure 6.8. The fit to the IR extinction is reasonable, especially considering Longtin et al. [1988] only report refractive indices at 15 different IR wavenumbers in the range studied here while Zolotarev [2009] reported values at 55 wavenumbers. When these IR based shape distributions are applied to simulations of the visible scattering properties, the fit to the phase function is slightly improved, however the quality of the fit to the polarization was made worse. Again, it appears that no single particle shape distribution can simultaneously model the full range of optical properties for diatomaceous earth. However, the improvement in the fits to the experimental data when using IR based shape distributions, that include extremely eccentric shapes, compared to other commonly used methods much be reemphasized. 6.6 Conclusions An IR based particle shape distribution for diatomaceous earth was derived by fitting the experimental IR spectra with T-matrix simulations. This method, as studied by Meland et al. [2010] for a sample of quartz dust, was then tested by applying the derived shape distribution to visible scattering simulations and compared to measurements. Despite the somewhat limited agreement between the simulations and the visible scattering data, the overall agreement with the full range of experimental IR and visible optical properties data for diatomaceous earth has been improved by using the IR based particle shape distribution which emphasizes extreme particle 58

84 shape factors. However, the limited agreement may indicate the limitations of applying the smooth spheroid approximation to particles with such extreme shapes. 59

85 Table 6.1 Table of log normal size distribution parameters that best fit the measured (volume equivalent) particle size distributions for diatomaceous earth (DE) in the IR extinction and visible light scattering experiments. r m is the mode radius of the particle number size distribution, σ is the width parameter, and MWMD is the mass weighted mean particle diameter. In the visible scattering experiments, the measured size distribution showed a bimodal character and was modeled by a linear combination of two log normal functions with the fitting parameters as given. DE (peak1) (peak2) IR Visible (550 nm) r m (nm) σ MWMD (nm) r m (nm) σ MWMD (nm) Table 6.2 Comparison of chi square values for simulations of the visible scattering properties of diatomaceous earth. Values listed in the table have been scaled by a factor of χχ 2 Phase Function Polarization IR Based Model Quartz Model Moderate Model Mie Theory Table 6.3 Visible refractive indices used in simulations of the light scattering properties of diatomaceous earth. n k Reference Glassy Quartz E-8 Khashan & Nassif [2000] Diatomaceous Earth E-4 Egan [1985] Crystal Quartz E-4 Longtin et al. [1988] 60

86 Figure 6.1 A scanning electron microscope image of a sample of diatomaceous earth dust. 61

87 Figure 6.2 A scanning electron microscope image of a sample of quartz dust for comparison to the extreme particle shapes of diatomaceous earth, shown in Figure 6.1. Figure 6.3 Experimental particle size distributions (blue points) measured simultaneous with the a) IR extinction and b) visible scattering experiments compared with log fits (pink lines) as listed in Table a) IR Size Distribution 3.5 b) Visible Size Distribution dn/dlogd (10 5 #/cm 3 ) Experiment Log Fit dn/dlogd (10 5 #/cm 3 ) Experiment Log Fit Diameter (nm) Diameter (nm) 62

88 Figure 6.4 Comparison of the experimental IR extinction spectrum and visible scattering phase function and polarization profiles for diatomaceous earth (points) with model simulations using different shape distributions. The T-matrix simulation results use the IR based shape distribution (red line) and the quartz shape distribution studied by Meland et al. [2010] (green line). Mie theory simulations are also shown for comparison (blue line). a) Extinction Diatomaceous Earth Experiment IR Based Model Quartz Model Mie Theory 0.2 b) Wavenumber Phase Function 10 1 Experiment IR Based Model Quartz Model Mie Theory 0.1 c) Scattering Angle Linear Polarization Experiment IR Based Model Quartz Model Mie Theory Scattering Angle 63

89 Figure 6.5 Shape distributions used in the simulations shown in Figure 6.2 including the IR based shape distribution (red bars), the quartz shape distribution (green bars) and Mie theory (blue bar). Particle Shape Distributions 0.4 IR Based Model Quartz Model Mie Theory Relative Weight Shape Parameter (ξ) 64

90 Figure 6.6 Comparison of the experimental visible scattering phase function and polarization profiles for diatomaceous earth (points) with model simulations using different refractive indices. All T-matrix simulation results use the IR based shape distribution shown as red bars in Figure 6.3. Lines shown in red use optical constants reported by Khashan & Nassif [2000], green lines use the optical constants reported by Egan [1985], and blue lines use optical constants reported by Longtin et al. [1988]. a) Phase Function 10 1 Diatomaceous Earth Experiment Khashan & Nassif OC Egan OC Longtin et al. OC 0.1 b) Scattering Angle 1.0 Linear Polarization Experiment Khashan & Nassif OC Egan OC Longtin et al. OC Scattering Angle 65

91 Figure 6.7 IR based shape distributions derived using different sets of IR optical constants. Red bars represent the IR based shape distribution resulting from simulations using optical constants for glassy quartz as reported by Zolotarev [2009] and blue bars represent the IR based shape distribution resulting from simulations using the optical constants for crystal quartz as reported by Longtin et al. [1988]. Particle Shape Distributions Zolotarev OC Longtin et al. OC Relative Weight Shape Parameter (ξ) 66

92 Figure 6.8 Comparison of the experimental IR extinction spectrum and visible scattering phase function and polarization profiles for diatomaceous earth (points) with model simulations using different sets of refractive indices. The T-matrix simulation results use the IR based shape distributions that have been optimized for each set of refractive indices. Simulations using optical constants for glassy quartz are shown in red and crystal quartz is shown in blue. a) Extinction Diatomaceous Earth Experiment Zolotarev OC Longtin et al. OC 0.2 b) Phase Function Wavenumber 10 1 Experiment Khashan & Nassif OC Longtin et al. OC 0.1 c) Scattering Angle Linear Polarization Experiment Khashan & Nassif OC Longtin et al. OC Scattering Angle 67

93 Complex Authentic Dust Samples 7.1 Introduction Modeling the optical properties of atmospheric mineral dust is complicated because these aerosols typically include complex internal and external mixtures of different minerals that are often irregular in shape [Claquin et al., 1999; Okada et al., 2001; Durant et al., 2009; Nousiainen, 2009]. For example, previous mineralogical investigations have found that windblown Saharan sand consists mostly of silicate clays (montmorillonite, illite, and kaolinite) and quartz, with smaller amounts of other minerals, including chlorite, feldspar, and calcite [Avila et al., 1997; Sokolik and Toon, 1999; Schütz and Sebert, 1987; Thomas and Gautier, 2009; Kandler et al., 2009; Glaccum and Prospero, 1980; Caquineau et al., 2002; Linke et al., 2006]. Similarly, studies of field samples of Iowa loess, in the fine particle mode ( μm), have found that the samples consist mostly of silicate clays with minor concentrations of other minerals such as quartz and calcite [Cuthbert, 1940; Davidson and Handy, 1953]. The goal of this chapter is to test if a priori shape distributions, determined through previous work on single components minerals, can be successfully applied to simulations of the optical properties of complex authentic mineral dust samples. Saharan sand, Iowa loess, and Arizona road dust are modeled here as external mixtures of silicate clays with possible amounts of quartz, amorphous silica, feldspars, calcite, and dolomite. In an external mixture, individual particles consist of only one mineral but particles of different minerals are mixed together. In an internal mixture, individual particles are composed of a mixture of different minerals. An external mixing assumption was chosen for this work in order to investigate if the modeling methods determined in the studies of single mineral components can be generalized to predict the optical properties of more authentic samples. In addition, several studies have found that external mixing assumptions work well for complex mixed dust [Koven and Fung, 2006; McConnell et al., 2010; Köhler et al., 2011]. 68

94 7.2 Experimental Methods and Results Authentic mineral dust samples of Saharan sand and Iowa loess were collected by colleagues on field missions and used in this work. The Saharan sand sample was collected from the south central Sahara and the Iowa loess sample was obtained from the Loess Hills of western Iowa. A sample of Arizona road dust, often used as a simulant for complex authentic dust mixtures was purchased commercially from Powder Technology Inc. (Burnsville, MN) for this study. While samples of Iowa loess and Arizona road dust were used as received, most of the Saharan sand sample consisted of particles too large to pass through the flow system, and therefore a 100 μm sieve was used to filter out the extremely large particles from the sample prior to aerosolization (where the atomizer further limits the particle size to < ~2.5 μm). Results from lognormal fits to the measured size distributions for each sample are shown in Table 7.1. Because the size distributions are measured simultaneously with each optical properties data set, the size distributions vary somewhat between the IR and visible measurements, but the differences are not large. The size distributions for Arizona road dust, measured during the visible scattering experiments, had a bimodal character and were thus fit by a linear combination of two lognormal functions with the parameters given in Table 7.1. Experimental IR extinction spectra and visible light scattering data for samples of Saharan sand, Iowa loess, and Arizona road dust are shown as points in Figure 7.1- Figure 7.3, respectively. Experimental IR spectra have been corrected to eliminate a sloping baseline associated with falling IR lamp intensity toward the low energy end of the spectrum, as discussed by Laskina et al. [2012]. Experimental error bars for the visible measurements include both random errors in day to day fluctuations and possible systematic errors due to uncertainties in the calibration function. The random errors are obtained from the standard deviation of the mean for data collected over several days. The systematic uncertainties are estimated from applying calibration functions generated on various days to the scattering properties. Results from different 69

95 theoretical simulations are shown in the figures by solid lines and will be described in the following sections. 7.3 Modeling Analysis Particle Size Distributions The experimental size distributions were fit to a lognormal form for the analysis. The parameters specifying the lognormal size distributions for Saharan sand, Iowa loess, and Arizona road dust were determined from least squares fits to the experimentally measured size distributions and are found in Table 7.1 Fits to the size distribution data taken simultaneous to the visible scattering measurements are shown in Figure 7.4. In the analysis that follows, it is assumed that the individual mineral components all have the same size distribution, namely that of the sample as a whole. In fact, studies of some mineral dust samples have actually found that to be untrue. For example, Glaccum and Prospero [1980] found that in the Saharan sand samples of their study, illite had the smallest particle size fraction (0.1-4µm) while quartz particles were found to exceed 50 µm. However, we have no means to determine the size distributions for each mineral component in the complex samples Mineral Optical Constants In an external mixing model, refractive index data for the individual mineral components are needed. The index of refraction data used in this analysis was taken from the literature and is summarized in Table 7.2. For amorphous silica, the optical constants for glassy quartz are used. The plagioclase feldspars albite and oligoclase are treated together using the optical constants for albite, as IR refractive index data for oligoclase is not available. For the birefringent minerals (such as calcite, dolomite, and quartz), a weighted average of the optical constants was used, i.e. the o-ray and e-ray optical constants have been combined with a 2/3 : 1/3 weighting because there are 2 ordinary and 1 extraordinary optical axes [Hudson et al., 2008b]. This approximation 70

96 greatly simplifies the analysis and shortens the calculation time. Hudson et al. [2008b] has shown that this approach gives good agreement with experimental IR extinction spectra for the birefringent mineral considered here. This approach was also tested for the visible scattering properties and found that simulations using averaged optical constants results in nearly identical results to simulations that have been averaged after the scattering properties have been separately calculated for the o-ray and e-ray component, also known as spectrally averaged. An example of this is shown for the calcite component of Saharan sand in Figure Particle Shape Distributions Previous work by our group has shown that there are clear differences in the particle shape distributions needed to best fit aerosol optical properties depending on dust mineralogy [Hudson et al., 2008a, 2008b; Kleiber et al., 2009; Meland et al. 2010, 2012]. Therefore, optimized spheroidal particle shape distributions have been derived in other work to best fit the visible light scattering properties and/or the IR extinction spectra of several key mineral components of atmospheric dust [Kleiber et al., 2009; Nousiainen et al., 2006; Meland et al., 2010, 2011]. The particle shape distributions determined from those earlier studies of single component mineral samples are used here as a basis for modeling the effects of particle shape in Saharan sand, Iowa loess, and Arizona road dust. Particle shape distributions used in this analysis are summarized in Table 7.3, shown graphically in Figure 7.6, and further discussed below. It should be reiterated, the particle shape distributions used in this analysis are based on previous studies of the IR spectral extinction and visible light scattering properties of individual single mineral samples. The results, however, are not extremely sensitive to the specific details of the shape models. For example, Meland et al. [2010] showed that very similar fits to the IR and visible optical properties data for quartz could be obtained with slightly different particle shape models (e.g., an equiprobable model distribution as used here, or a Gaussian shape distribution model), provided the models all included a similarly broad range of extreme shape parameters. 71

97 Similarly, Meland et al. [2012] showed that simulations using a range of bimodal size-shape distribution parameters could result in fits of similar quality for the optical data for illite and kaolinite, provided the general properties of the bimodal distribution were maintained (i.e. extremely oblate small particles and a more moderate distribution of shape factors for larger particles). Thus, these particle shape distribution models are not unique, but place reasonable limits on the range of shape parameters necessary to adequately describe the IR extinction and visible light scattering data for these mineral dust components. For the quartz mineral component of the external mixtures, a very broad, flattop shape distribution of spheroids with shape parameters in the range -3 ξ +5 is used and shown graphically in Figure 7.6a as blue bars. As already discussed in Chapter 4, a study of quartz aerosol by Meland et al. [2010] found that this distribution gave good fits to both the IR and visible optical properties. The experimental IR Si-O vibrational stretch resonance line profile for amorphous silica is similar to that found for quartz in position and shape although somewhat broader. Therefore, in the modeling of the complex samples, it is assumed that quartz and amorphous silica (glassy quartz) can be modeled using the same broad distribution of shape parameters. A flattop distribution of spheroids with more moderate shape parameters, as described by Kleiber et al. [2009], is used for calcite and is shown graphically in Figure 7.6a as green bars. This distribution was shown to give good fits to the calcite IR extinction data, however fits to the visible scattering measurements were less accurate. This could introduce some error into the fitting of the visible scattering properties of the mixed samples, however, the carbonate fraction in these samples is quite small and therefore the errors are small as well. To explore this, Figure 7.7 shows model simulations for Arizona road dust using both a moderate shape distribution (-1.4 ξ +1.4) and a broad shape distribution (-3 ξ +5) for the 5% of the calcite component in the revised mineral compositions (see Section ). As seen in the figure, the large change in the 72

98 shape distribution causes a nearly indistinguishable difference in the final scattering results. The simulations for dolomite use the same shape parameters as calcite because they are both carbonates with similar mineralogical structures, except that dolomite has alternating layers of calcium and magnesium [Klein et al., 1999]. For the feldspar mineral component of the external mixtures, a cubic power law shape distribution, f ( ) ξ 3 ξ, with shape parameters in the range -1.6 ξ +1.6 is used and is shown graphically in Figure 7.6a as red bars. Nousiainen et al. [2006] investigated the particle shape effects on the scattering properties of one sample of small feldspar particles using T-matrix methods with the spheroid approximation and found that this shape distribution was able to accurately fit the visible scattering properties. This distribution was further investigated here to check if it may also be used to model the IR spectral extinction of feldspars. T-matrix simulations, using this cubic power law shape distribution, is compared to experimental measurements in Figure 7.8. While the simulated IR extinction spectra is not able to reproduce the detailed fine structure of the measured spectra (probably due to limitations in the published index of refraction data), this simple particle shape model does give a reasonably good fit to the overall peak position and width of the spectral line. As previously discussed in Chapter 5, a bimodal shape distribution that allows for the particle shape to vary as a function of size is able to simultaneously simulate the IR extinction and visible scattering properties for silicate clay aerosols. Therefore, this bimodal shape distribution will be used to model the illite and kaolinite mineral components of the complex authentic dust samples. The specific model parameters used in this chapter are listed in Table 7.3. The montmorillonite optical properties are simulated using the same bimodal size-shape distribution parameters as for illite because both are micaceous clays with similar structures [Grim, 1939]. 73

99 7.3.4 Sample Mineralogy In order to compute the optical properties of mixed dust samples such as our samples of Saharan sand, Iowa loess, and Arizona road dust, the mineral composition must be specified. The analysis in this chapter uses two sets of mineral compositions to simulate the IR extinction and visible scattering phase function and polarization profiles of these mixed mineral dust samples. In previous work, Laskina et al. [2012] determined empirical mineral compositions based off of IR extinction spectra for the same samples of Saharan sand and Iowa loess as used here, and this same empirical method is applied here to the sample of Arizona road dust. However, it appears that the empirical mineralogy over predicts the amount of dolomite in the Saharan sand and Arizona road dust samples. Therefore, a set of revised mineral compositions, excluding dolomite, is derived here as well. This second set of mineral compositions will also be used to simulate the optical properties of the mixed samples. It should be noted that it is extremely difficult to determine the exact mineral composition of any authentic mineral dust sample. These mineral compositions were derived solely through IR spectra analysis which has some drawbacks. For example, some very important minerals do not show a characteristic absorption resonance in the spectral range covered in our FTIR measurements, cm -1. Hematite, a common iron oxide, can have a significant impact on the visible absorption, but does not have a characteristic absorption resonance in the measured spectral range. As a result, the IR analysis of the mineralogy is insensitive to the presence of hematite in the samples. The effect of potential fractions of hematite in the visible scattering simulations is discussed in Section It is also important to note that it is very difficult to distinguish between individual clay types on the basis of IR spectroscopy alone because there is significant overlap in the resonance absorption bands for the different clays. Similarly, IR spectra of the carbonate minerals, calcite and dolomite, also overlap in the resonance absorption bands and can be difficult to distinguish 74

100 solely through IR spectra analysis. While other mineralogical analysis techniques, such as X-ray diffraction (XRD), could perhaps be used to determine the mineralogy, they require more grams of sample than can be collected from the flow. In addition, aerosol particles in the flow tend to be small, <1µm, and XRD is very difficult to apply quantitatively to powder samples of very small particles. Other characterization methods can be used to give elemental compositions but relating elemental composition to mineral composition is difficult and highly uncertain. Figure 7.9 shows, for illustration purposes, simulations of the optical properties of individual mineral components of Saharan sand in comparison with experimental data. This figure shows how differences in the sample mineralogy may influence the simulations results. As seen in Figure 7.9a, there is significant IR spectral overlap of the extinction of for the individual clay mineral components near 1050 cm -1 ; this makes it very difficult to distinguish between different clay minerals based solely on IR measurements. The same problem is true for the calcite and dolomite resonance peaks near ~1480 cm -1 and the quartz and amorphous silica peaks near ~1110cm -1. However, it should be noted that there is relatively good separation between the groups of minerals (clays, quartz, and carbonates). The mineral compositions derived by Laskina et al. [2012] and in Section generally agree with other studies of similar samples as well as elemental analysis of the same samples. These two sets of mineral compositions will be further discussed, including some potential concerns, in the following subsections. Again, for the analysis in this chapter, the mineral compositions derived by Laskina et al. [2012] and here are assumed in order to test whether the a priori shape distributions of single component minerals can be used as a basis for modeling the optical properties of complex, authentic dust samples Empirical Mineral Compositions Laskina et al. [2012] previously reported mineral compositions for our samples of Saharan sand and Iowa loess, assuming an external mixture. In that study, IR spectral 75

101 measurements of individual mineral components were fit to the IR extinction spectra of the mixed sample by adjusting the relative weights of the minerals until the best fit was achieved. This empirical analysis was repeated for the sample of Arizona road dust and shown in blue in Figure 7.10b. The resulting empirical mineral compositions for Saharan sand, Iowa loess, and Arizona road dust are given in Table 7.4. While all three samples are found to consist primarily of silicate clays (illite, kaolinite, and montmorillonite), there are some concerns about the empirical mineralogy derived for Saharan sand. First, the relatively high montmorillonite weight as a fraction of the total silicate clay is somewhat unusual for Saharan sand [Avila et al., 1997; Caquineau et al., 2002; Turner, 2008; Kandler et al., 2009]. However, it appears to be consistent with other samples taken from the southern Sahara [Schütz and Sebert, 1987; Linke et al., 2006] and it is important to understand that it is very difficult to distinguish between individual clay types on the basis of IR spectroscopy alone because there is significant overlap in the resonance absorption bands for the different clays. This generally does not lead to a significant error in modeling since the different silicate clays tend to show similar visible scattering properties as well [Curtis et al., 2008] as seen in Figure 7.9. The low measured value for the quartz fraction may also seem surprising since many other studies have found quartz to be a major component of Saharan sand [Glaccum and Prospero, 1980; Caquineau et al., 2002; Avila et al., 1997; Schütz and Sebert, 1987; Sokolik and Toon, 1999; Thomas and Gautier, 2009]. This finding is, however, consistent with a recent field study by Turner [2008], who also failed to find a significant amount of quartz in the mineral analysis of dust aerosol collected over the Sahel region of North Africa. It should be noted that since the quartz Si-O resonance absorption band is spectrally well separated from the silicate bands of the clays, it is unlikely that the IR spectral fitting routine has swapped clay for quartz. There is some spectral overlap between quartz and the feldspars however, and this could affect 76

102 the mineralogical analysis. It is also important to point out that bulk sand properties often differ markedly from the properties of dust aerosol. In fact, a strong quartz signature is observed in electron diffraction measurements of the bulk (not aerosolized) Saharan sand sample used in this work. Elemental analysis of the bulk sample which has been sieved to exclude particles > 40 µm shows a Si:Al ratio of ~4.6 [Krueger et al., 2004]; this is consistent with the presence of quartz at a level in excess of ~ 40%. However, the aerosol used in this study includes only the fine fraction of particles that are aerosolized and can pass through our flow system (diameters < ~ 2.5 µm). Because quartz particles tend to be much larger than clay particles, it is not surprising that the mineralogy of the aerosolized sample here differs appreciably from that found in the bulk, or in other studies that may include a wider range of particle sizes. Elemental compositions of the major crustal elements (Si, Al, Mg, Ca, Na, Fe, K) in Saharan sand, Iowa loess, and Arizona road dust, were deduced from the empirical mineral compositions in order to further investigate their reliability. A comparison between the derived elemental compositions using the empirical mineralogy of Laskina et al. [2012] with those directly measured using EDX is given in Table 7.5. The comparison shows reasonably good agreement for all three aerosol samples; however some discrepancies are worth noting. The empirical mineral compositions tend to underestimate the amount of Fe and overestimate the amounts of Ca and Mg. The Ca and Mg fraction is closely related to the presence of dolomite in the sample so this suggests that the amount of dolomite could be overestimated. This point will be further discussed below. The Fe content is commonly associated with Fe-rich clays or with iron oxides such as hematite. As noted, the IR analysis of the mineralogy is insensitive to the presence of hematite in the samples and will be discussed in Section In comparing the elemental compositions it is also important to recognize that the clay designations illite and montmorillonite refer to classes of clays with wide compositional 77

103 variability in the trace metals [Grim et al., 1937]. Similarly there is a wide compositional variation in different forms of feldspars. As a result, some differences in the concentrations of the trace elements are not surprising Revised Empirical Mineral Compositions As was discussed in the previous section and will be shown in simulation results in Section 7.4, it seems likely that the empirical mineralogy of Laskina et al. [2012] over predicts the dolomite fraction in the mineral compositions for both Saharan sand and Arizona road dust. To further explore this point, revised empirical mineral compositions were derived by repeating the IR spectral analysis used by Laskina et al. [2012], but with dolomite excluded from the model. The revised mineral compositions for all three mixed samples are shown in Table 7.4. In addition, the revised empirical fits are compared to experimental IR extinction spectra along with the initial empirical fits in Figure 7.10 (Iowa loess was excluded from the figure because the revised and initial compositions were the same). As seen in the figure, excluding dolomite from the analysis results in empirical extinction spectra for both Saharan sand and Arizona road dust that are nearly indistinguishable from the empirical IR fits of Laskina et al. [2012]. This furthers the idea that it is difficult to distinguish between calcite and dolomite based solely on IR analysis. Note that the empirical mineralogy for Iowa loess did not find any dolomite in the sample and therefore the revised mineralogy is unchanged. Elemental compositions deduced from the revised mineral compositions are shown in Table 7.5. Note also the improved agreement between the measured elemental concentrations and those derived from the revised mineralogies compared to the empirical mineralogies, particularly for Mg and Ca Cumulative Optical Properties for Mixed Samples For a given mineral composition, a forward simulation of the IR spectral extinction and visible light scattering data can be run for each mineral species in the sample. The IR extinction 78

104 coefficient C ext and scattering matrix elements, F ( θ ) αβ, for each mineral component can then be combined through a weighted average to determine the cumulative properties of the externally mixed sample using the following equations: C ext = i N ( i ) C ( i ) ext (7.1) ( θ ) N ( θ ) i Fαβ = (7.2) ( i ) ( i ) N C i ( i ) C ( i ) ext F ( i ) αβ ext subject to i ( i ) N = 1 (7.3) where the summations are over the different mineral components, N (i) is the fractional number of particles, and (i) C ( ) (i) scat C is the average scattering (extinction) cross section per particle for the i th mineral component [Meland et al., 2012]. ext 7.4 Model Results and Discussion Simulation Results using the Empirical Mineralogy T-matrix spectral simulation results for Saharan sand, Iowa loess, and Arizona road dust, based on a priori shape distributions (Table 7.3) and mineral compositions (Table 7.4) as discussed above, are shown in red and compared with the experimental IR extinction spectra and visible light scattering data in Figure Figure 7.3. The simulated T-matrix and measured IR extinction spectra in these figures are each normalized to one at the peak. Due to variations in the baseline for the experimental IR spectra as noted above, all the extinction spectra have been baseline corrected. The visible light scattering simulations are absolute comparisons with the measured phase function and polarization data, with no adjustable parameters. Also shown in 79

105 Figure Figure 7.3 are model simulations based on Mie theory (blue lines) and based on the use of an equiprobable distribution of moderately shaped spheroids (green lines) for all the mineral components of the complex samples. This equiprobable distribution of moderate spheroids, with 1.4 ξ +1.4, is based on analysis of electron microscope images of dust field samples, and is commonly used to model the radiative transfer effects of atmospheric mineral dust [Mishchenko et al., 1997]. T-matrix simulations using the particle shape distributions that are optimized for each mineral component (Table 7.3), are in reasonably good overall agreement with the full range of experimental IR extinction and visible light scattering data. For most of the data, these simulations fall within or near the limit of the experimental uncertainties. This approach also offers a very significant improvement over both Mie theory and T-matrix simulations using a simpler equiprobable distribution of moderately shaped spheroids. These results suggest that this T-matrix approach, based on a priori particle shape distributions, determined from studies of the individual mineral components, can be used to more accurately simulate the optical properties of complex authentic dust mixtures, across a broad spectral range from the IR to the visible. Closer inspection, however, reveals some noteworthy differences between the optimized T-matrix simulations and the experimental data Discussion of the IR Extinction Results In all three samples, the simulated IR extinction spectra, obtained using the optimized particle shape distributions, show significant improvement over the simulations using the equiprobable shape distribution or Mie theory (Figure 7.1 -Figure 7.3). These two commonly used shape distributions result in IR silicate resonance absorption lines that are strongly blueshifted from the experimental line positions by ~ cm -1. However, using the optimized shape distributions leads to much smaller errors of ~ cm -1 in the silicate resonance line positions. 80

106 It should be noted that the measured IR resonance peak positions for illite and kaolinite are fit very well using the optimized T-matrix simulations (Figure 5.2). Because the empirical modeling approach of Laskina et al. [2012] finds a significant montmorillonite fraction in all three samples, it is possible that the assumed particle shape distribution for montmorillonite is not optimal. It was assumed, for simplicity, that montmorillonite could be described by the same particle shape distribution as illite. However, montmorillonite also presents other difficulties in the analysis as well; it is a swellable clay meaning that it absorbs and retains water between the layers in the silicate framework. This might change the particle shape or refractive index depending on the degree of water uptake. Shifts of ~ 10 cm -1 in the montmorillonite spectral line position have been reported at higher relative humidity levels by Frinak et al. [2005]. Since the aerosol samples used in this study are atomized from a slurry of mineral dust in water, it is likely that there is an associated water shift in the montmorillonite peak position. Therefore, errors on the order of cm -1 in the simulated silicate resonance absorption peak position for montmorillonite-rich samples are probably not unreasonable. However, it must be emphasized that by including the effects of thin clay flakes (modeled as highly eccentric oblate spheroids), the optimized shape distributions lead to a significant improvement in modeling fits over the results for Mie theory and the moderate equiprobable shape distribution. As shown in Figure 7.1 -Figure 7.3, the simulations that ignore the shape effects associated with highly oblate clay particles show significant errors in the IR resonance peak position for these clay-rich authentic dust samples. The Arizona road dust sample, which shows the most varied mineralogy, also shows the most significant differences in the IR spectral fitting for the silicate resonance region (Figure 7.3a). This could be related to a breakdown in the external mixing assumption. Furthermore, the empirical IR spectral fitting approach finds significant amounts of feldspar and amorphous silica in the composition. It should be noted that the simulations for the feldspar components use IR 81

107 optical constants for albite, only one member of the plagioclase feldspar family. As discussed by Alexander et al. [2013b], T-matrix simulations based on these optical constants do not accurately simulate the observed fine structure in the absorption spectra for different feldspars. In addition, the same particle shape distributions are used for both quartz and amorphous silica which could lead to some error in the simulation. There are also significant differences between the simulated and experimental absorption line strengths for the carbonate peak near 1480 cm -1, associated with dolomite, in the Saharan sand and Arizona road dust results shown in Figure 7.1a and Figure 7.3a, respectively. A similar discrepancy was found in the analytic model results for Saharan sand of Laskina et al. [2012]. It is possible that there is an error in the magnitude of the dolomite optical constants that affects the absorption line strength. In this regard it is also evident from the elemental analysis results shown in Table 7.5 that the mineralogy of Laskina et al. [2012] significantly overestimates the Ca and Mg elemental fraction in the Saharan sand and Arizona road dust samples. Since Mg and Ca are characteristic of dolomite this could indicate that the empirical mineralogy of Laskina et al. [2012] has somewhat overestimated the dolomite fraction in the analysis. This point has already been noted above and will be discussed in more detail in Section Despite these shortcomings, the IR simulations based on a priori particle shape distributions, found in previous work on single component minerals, show a significant improvement over both Mie theory and a commonly used moderate spheroidal-particle shape distribution, particularly for the predominantly clay Saharan sand and Iowa loess samples Discussion of the Visible Scattering Results The simulation results for both the phase function and polarization profiles for Iowa loess at a visible wavelength of 550nm are in excellent agreement with experimental measurements (Figure 7.2). Note that Iowa loess is the most homogeneous of the three samples (in terms of its mineralogy) and has the highest clay fraction (88%). The scattering properties of Iowa loess are 82

108 well modeled by simulations based on the bimodal size-shape distribution model proposed for the silicate clays. For Saharan sand, the phase function results are excellent, but the simulated polarization peak is clearly too low compared to experimental measurements (Figure 7.1). This low polarization could be related in part to an overestimate of the non-clay fraction of the mineral composition, since the non-clay minerals (particularly dolomite) have lower polarization signals. Lowering the dolomite fraction and increasing the clay fraction in the Saharan sand sample mineralogy would improve the polarization fit, the IR extinction fit in the region near 1480 cm -1, and the fit to the measured elemental compositions in Table 7.5, as will be considered in Section The Arizona road dust simulation shows a reasonably good fit to the measured phase function and the polarization fit is very good (Figure 7.3). As with the Saharan sand sample, it is possible that fine-tuning the mineralogy might improve the overall quality of the fits (vide infra). Furthermore, as already suggested, these discrepancies might also result from a breakdown of the external mixing assumption for this more complex sample. Despite these differences it is apparent that the visible simulations, based on a priori particle shape distributions suggested by previous work on single component minerals, show a significant improvement over both Mie theory and a more commonly used moderate spheroid shape distribution. This improvement is also shown in the comparison of chi-square values listed in Table 7.6. The differences in phase functions can also be quantified using the asymmetry parameter, g, which is a measure of the degree of scattering anisotropy into the forward or backward directions and is defined as, 1 g = F ( θ ) cos( θ ) dω (7.4) π where F 11 is the scattering phase function [Bohren and Huffman, 1998]. The asymmetry 83

109 parameter is very important for modeling radiative transfer effects because small errors in this parameter can lead to significant differences in the estimated radiative forcing effect [Andrews et al., 2006]. Comparison of the asymmetry parameters for the experimental data and the T-matrix simulations is shown in Table 7.7. Mie theory clearly underestimates the asymmetry parameters for all three authentic samples where the relative error using the optimized shape distribution is <1% for Saharan sand and Iowa loess and <4% for Arizona road dust. One additional point is worth reiterating here. There are no adjustable parameters in the comparison between experiment and the model simulations shown here for the visible scattering data. The sample mineralogies were determined independently in previous work by Laskina et al. [2012] and Alexander et al. [2013b], the particle size distributions were experimentally measured, and the particle shape distributions were fixed by previous studies of single component mineral dust. Given the limited number of adjustable parameters and the range of experimental IR extinction and visible light scattering data, the overall agreement is remarkably good. It may be possible to improve the quality of the fits further by fine-tuning the sample mineralogy (see Section 7.4.2), or by considering the possible effects of internal mixing Simulation Results using the Revised Empirical Mineralogy T-matrix simulations based on the revised mineralogies from Alexander et al. [2013b] are shown as blue dashed lines and are compared to measured optical property data for Saharan sand, Iowa loess, and Arizona road dust in Figure 7.11 Figure Also shown in red for comparison are the simulation results using the empirical mineral compositions as previously discussed and shown in Figure Figure 7.3. Note that in Figure 7.12, there is no change in the simulations for Iowa loess because the original empirical compositions did not find any dolomite in the sample. However, there is significant improvement in the fits to the carbonate IR resonance absorption bands near 1480 cm -1 for both Saharan sand and Arizona road dust. The visible polarization fit for Saharan sand is only slightly improved and the predicted 84

110 polarization at mid-range angles is still too low. As discussed above, it is possible that the particle shape distribution used for the montmorillonite component in the sample may not be optimal, or the visible index of refraction values for montmorillonite may be in error or may be altered by water loading. Because scattered light polarization is highly sensitive to both particle size and shape distributions, these errors could also indicate that there is some variation in mineralogy with particle size in the distribution (contrary to our assumption that all the mineral components in the sample have the same size distribution). In addition, we cannot rule out the possibility that the particle shape distributions for the mineral components in this field sample might differ from the a priori distributions of single mineral components, perhaps due to weathering processes. It is also possible that the underlying spheroid approximation may not be wholly adequate to describe the shape distributions of the Saharan sand dust sample. However including these factors into the modeling approach would greatly complicate the analysis, making it less practical to apply to a wide range of authentic samples. Despite these differences, it is clear that the use of a priori particle shape models for the individual mineral components of these authentic samples, which account for variations in particle shape with mineralogy and include highly eccentric spheroid shape parameters, offers a very significant improvement over commonly used particle shape models that cover a more limited shape parameter range Simulation Results Including Hematite As previously noted, the possible presence of hematite must also be considered. Elemental analysis places an upper limit of ~5% hematite in the mineral composition of the Saharan sand sample, ~7% for Iowa loess, and ~3% for Arizona road dust. A previous study measured a low polarization profile in the scattered light signal from hematite aerosol at visible wavelengths [Meland et al., 2011]. In the authentic dust samples considered here, adding even a small amount of hematite to the simulated external mixture (up to ~5%), noticeably depresses the 85

111 calculated polarizations and flattens out the phase functions. To explore this, a 7% fraction of hematite has been added to the visible scattering simulation results for Iowa loess in Figure As seen, the hematite contribution has made the simulated phase function less step and also lowered the peak polarization. Therefore adding hematite fractions to the revised mineral compositions will decrease the accuracy of the simulation fits. This suggests that the Fe content observed in the elemental analysis is probably primarily associated with Fe-rich clays rather than in the form of iron-oxides Simulation Results with Varied Densities In addition to variations in the mineral compositions, particle size distributions, which are dependent on the density, also has a large effect on the optical properties. To further explore if the density could be the potential discrepancy in the Saharan sand models, simulations using a size distribution that has been analyzed using a density of 2.7 (instead of 2.3 as in the previous sections) have been calculated. A density of 2.7 was chosen here because it is closer to the typical density values reported for the silicate clays, which Saharan sand is primarily composed of, and is reported in literature. In addition, a higher density will result in a volume equivalent size distribution with smaller particles, which correspond to higher peak polarization profiles. Therefore, simulations using a size distribution that has been analyzed using a density of 2.7 compared to measurements in Figure As seen in the figure, the IR extinction is much less sensitive to small changes in the size distribution compared to the visible scattering. Using the higher density value of 2.7 leads to a noticeable improvement in the fits to the visible polarization data in Figure Conclusions Visible scattering phase functions and linear polarization profiles for complex authentic mineral dust samples were measured at a wavelength of 550nm. Authentic samples investigated 86

112 in this study include Saharan sand, Iowa loess, and Arizona road dust. Measurement of the infrared extinction spectra for these samples are taken from Laskina et al. [2012] and also used for comparison to model simulations. The principle goal of the work in this chapter has been to determine if a priori spheroidal particle shape distribution models (determined in previous studies) of single-component mineral dust samples can be used as a basis to accurately model the IR extinction and visible scattering properties of complex, authentic samples of mineral dust. T-matrix simulations of Saharan sand, Iowa loess, and Arizona road dust were carried out based on an external mixing assumption. The simulations rely on very few adjustable parameters. Particle size distributions were measured, optical constants were taken from literature, and a priori mineral component shape distributions and empirical mineral compositions were used. The T-matrix simulations based off of the shape distributions from previous studies of single mineral components show significant improvement over simulations using more commonly used shape distributions that do not account for variations in particle shape with mineralogy. The good overall agreement between laboratory measurements and T-matrix simulations for the full range of data support the conclusion that these particle shape distributions can provide a useful basis for modeling more complex authentic dust samples. While the use of a priori spheroidal particle shape distributions result in significant improvements in the model fits of the measured optical properties, there are some discrepancies between the simulations and measurements that must be noted. In the IR extinction spectra of Iowa loess and Saharan sand, there is a ~10-20cm -1 shift in the simulated Si-O vibrational resonance peak located near 1050cm -1 compared to experimental measurements. This could be due to errors in the relative amounts of the different clays, especially illite and montmorillonite. Furthermore, the assumed particle shape distribution for montmorillonite might not be optimal however further improvements in the montmorillonite shape distribution are complicated by the possible line shifts caused by water uptake in the clay. As for the IR extinction of Arizona road 87

113 dust, the discrepancies between the optimized model and measurements are larger than the other two samples, most likely due to the more varied mineralogy and the possibility of internally mixed particles. Simulations for the visible scattering properties of these three complex samples are an excellent fits to the measurements at 550nm. Both the phase function and linear polarization profiles for Iowa loess and Arizona road dust are in excellent agreement with experimental data for the entire range of scattering angles. While the simulated phase function for Saharan sand is also a good fit to measurements, there is a large discrepancy, well outside the experimental uncertainties, in the peak polarization. While most of the discrepancies in the IR spectra were associated with possible uncertainties in the mineral compositions, the differences in the Saharan sand polarization are not. Instead, it is possible that these discrepancies are due to errors in the assumed shape distributions, especially montmorillonite, or refractive indices. As previously discussed, it is likely that the mineralogy of the Saharan sand sample could change as a function of particle size which could also be adding to errors in simulated polarization profile. While finetuning the mineralogy and optimized particle shape distributions, including the possibility variations in mineralogy as a function of particle size, could improve the model fits, these investigations are beyond the scope of this project. However, it is important to reemphasize that the use of a priori shape distributions that account for differenced in particle shape with mineralogy and include a broader range of more eccentric spheroid shape parameter lead to significant improvements in the model simulations compared to other commonly used models that ignore variations in the particle shape with size and mineralogy, and include only a moderate range of shape parameters. 88

114 Table 7.1 Table of log normal size distribution parameters that best fit the measured (volume equivalent) particle size distributions for, Saharan sand, Iowa loess, and Arizona road dust (ARD) in the IR extinction and visible light scattering experiments. r m is the mode radius of the particle number size distribution, σ is the width parameter, and MWMD is the mass weighted mean particle diameter. In the visible light scattering experiments, the measured size distribution for Arizona road dust showed a bimodal character and was modeled by a linear combination of two log normal functions with the fitting parameters as given. IR Visible (550 nm) r m (nm) σ MWMD (nm) r m (nm) σ MWMD (nm) Saharan Sand Iowa Loess ARD (peak1) (peak2) Table 7.2 References for the optical constants of the mineral components considered in this study a. IR Illite Querry, 1987 Kaolinite Querry, 1987 Montmorillonite Querry, 1987 Calcite Lane, 1999 Dolomite Posch et al., 2007 Amorphous Silica Zolotarev, 2009 Quartz Longtin et al., 1988 Visible (m = n + i k ) (interpolated at 550nm) i 7.7E 4; b Friedrich et al., i 4.8E 5; b Friedrich et al., i 3.8E 5; Egan & Hilgeman, i 1.0E 4 Ivlev & Popova, i 1.0E 4 Klein et al., i 8.0E-8 Khashan & Nassif, i 1.0E 4 Longtin et al., i 1.0E 4 Plagioclase (Albite) Mutschke et al., 1998 Klein et al., 1999 a For the birefringent materials (calcite, dolomite, and quartz), the optical constants were obtained by combining the e-ray and o-ray index values with a 1/3 : 2/3 weighting. It should be noted that the optical constants for glassy quartz were used for amorphous silica. b Friedrich et al [2008] do not report imaginary index (k) values for visible wavelengths. We use imaginary index values interpolated from data in Egan and Hilgeman [1979], but note that the visible results are quite insensitive to the k- values for k <

115 Table 7.3 Shape distributions used for each of the potential mineral components of Saharan sand, Iowa loess, and Arizona road dust *. d c ξ 1 ξ 2 Illite 600nm +7 Kaolinite 600nm +4 Montmorillonite 600nm +7 Calcite - Equiprobable: -1.4 ξ +1.4 Dolomite - Equiprobable: -1.4 ξ +1.4 Amorphous Silica - Equiprobable: -3 ξ +5 Quartz - Equiprobable: -3 ξ +5 Power Law: f(ξ) ~ ξ 3 0 ξ Power Law: f(ξ) ~ ξ 3 0 ξ Power Law: f(ξ) ~ ξ 3 0 ξ Plagioclase Feldspar - Power Law: f(ξ) ~ ξ ξ +1.6 * A bimodal size-shape distribution was used for the clay components (illite, kaolinite, montmorillonite) and a single mode shape distribution was used for calcite, dolomite, amorphous silica, quartz, and feldspar. d c is the assumed cutoff diameter that separates the small and large particle modes in the bimodal clay size distributions. See Section 5.4 for details. Table 7.4 Mineral compositions (in percentage of particle number density) for the authentic samples of Saharan sand, Iowa loess, and Arizona road dust. Saharan Sand Iowa Loess Arizona Road Dust Empirical Mineralogy Revised Mineralogy Empirical Mineralogy Revised Mineralogy Empirical Mineralogy Revised Mineralogy Illite Kaolinite Montmorillonite Calcite Dolomite 9 NA 0 NA 11 NA Quartz Amorphous Silica Plagioclase Feldspar* *Includes the amounts of albite and oligoclase, which are both plagioclase feldspars 90

116 Table 7.5 Elemental composition (in atomic %) of complex dust samples determined from the empirical mineralogy of Lakina et al. [2012] and revised model of Alexander et al. [2013b], and energy dispersive X-ray analysis (EDX). Element Empirical Model Saharan Sand Iowa Loess Arizona Road Dust Revised Model EDX Analysis Empirical Model Revised Model EDX Analysis Empirical Model Revised Model EDX Analysis Si Al Na Mg Fe K Ca Ti, Ni, Cu

117 Table 7.6 Comparison between T-matrix simulations and experiment. Saharan Sand Iowa Loess Arizona Road Dust χχ Optimized Equiprob Mie Optimized Equiprob Mie Optimized Equiprob Mie IR Phase Function Linear Polarization Table 7.7 Comparison of the scattering asymmetry parameter of T-matrix simulations and experiment. g Saharan Sand Iowa Loess Arizona Road Dust Experiment Optimized Equiprobable Mie

118 Figure 7.1 Comparison of the experimental data (points) with model simulations for Saharan sand: (a) the IR spectral extinction (b) the scattering phase function and (c) the linear polarization profiles at λ=550nm. The T-matrix simulation results for the optimized particle shape distributions given in Table 3 are shown in red; T-matrix simulation results assuming an equiprobable (flattop) shape distribution for all the mineral components (-1.4 ξ +1.4) are shown in green; Mie theory results are shown in blue. a) 1.2 Saharan Sand Relative Extinction Experiment Optimized Equiprobable Mie 0.2 b) Wavenumber Phase Function 10 1 Experiment Optimized Equiprobable Mie c) Scattering Angle 1.0 Linear Polarization Experiment Optimized Equiprobable Mie Scattering Angle 93

119 Figure 7.2 Comparison of the experimental data (points) with model simulations for Iowa loess. The labeling is as in Figure 7.1. a) Relative Extinction Iowa Loess Experiment Optimized Equiprobable Mie b) Wavenumber Phase Function 10 1 Experiment Optimized Equiprobable Mie c) Scattering Angle 1.0 Linear Polarization Experiment Optimized Equiprobable Mie Scattering Angle 94

120 Figure 7.3 Comparison of the experimental data (points) with model simulations for Arizona road dust. The labeling is as in Figure 7.1. a) 1.2 Arizona Road Dust Relative Extinction Experiment Optimized Equiprobable Mie 0.2 b) Wavenumber Phase Function 10 1 Experiment Optimized Equiprobable Mie c) Scattering Angle 1.0 Linear Polarization Experiment Optimized Equiprobable Mie Scattering Angle 95

121 Figure 7.4 Experimental particle size distributions (blue dots) measured simultaneous with the visible scattering experiments compared with log fits (pink lines) for a) Saharan sand, b) Iowa loess, and c) Arizona road dust. 4.5 a) Saharan Sand 2.5 b) Iowa Loess 3.5 c) Arizona Road Dust dn/dlogd (10 5 #/cm 3 ) Experiment Log Fit dn/dlogd (10 5 #/cm 3 ) Experiment Log Fit dn/dlogd (10 5 #/cm 3 ) Experiment Log Fit Diamter (nm) Diamter (nm) Diameter (nm) 96

122 Figure 7.5 Comparison of T-matrix simulations for the calcite component of Saharan sand. Simulations shown in pink have been calculated using an average of the birefringent optical constants. Simulations shown as dashed cyan lines have been calculated by spectrally averaging the birefringent scattering properties. a) Phase Function 10 1 Model Calcite Component of Saharan Sand Optical Constant Average Spectral Average b) Scattering Angle 1.0 Linear Polarization Optical Constant Average Spectral Average Scattering Angle 97

123 Figure 7.6 Particle shape distribution models for the components of the external mixtures as described in Section 5.1.3, a) non-clay mineral components and b) clay components. Relative Weight a) Non-Clay Particle Shape Distributions Calcite and Dolomite Plagioclase Feldspar Quartz and Amorphous Silica Shape Parameter (ξ) b) Clay Particle Shape Distributions Relative Weight Illite and Montmorillonite Mode 1 Kaolinite Mode 1 Clays Mode Shape Parameter (ξ) 98

124 Figure 7.7 Comparison of simulations of the visible scattering a) phase function and b) linear polarization of Arizona road dust. Simulations shown in blue use a moderate shape distribution (-1.4 ξ +1.4) for the calcite component of the mixed sample, and simulations shown in green use a broad distribution of spheroids (-3 ξ +5) for the calcite component. Both simulations use the optimized shape distributions for the other mineral components (Table 7.3) and the revised mineral composition (Table 7.4) for Arizona road dust. a) Arizona Road Dust Phase Function 10 1 Calcite Shape Dist: -1.4 < ξ < +1.4 Calcite Shape Dist: -3 < ξ < +5 b) Scattering Angle 1.0 Linear Polarization Calcite Shape Dist: -1.4 < ξ < +1.4 Calcite Shape Dist: -3 < ξ < Scattering Angle 99

125 Figure 7.8 Comparison of the experimental IR extinction spectra of albite (points) with a T-matrix simulation using a cubic power law shape distribution as shown in Figure 7.6 as red bars. Albite IR Extinction Relative Extinction Experiment Simulation Wavenumber 100

126 Figure 7.9 Comparison of the experimental data (points) with model simulations for potential mineral components of Saharan sand including a) the relative IR extinction, b) the scattering phase function, and c) the linear polarization profiles at λ=550nm. Saharan Sand Relative Extinction Experiment Albite Amorphous Silica Calcite Dolomite Illite Kaolinite Montmor. Quartz Wavenumber Phase Function 10 1 Experiment Albite Amorphous Silica Calcite Dolomite Illite Kaolinite Montmorillonite Quartz Scattering Angle 1.0 Linear Polarization Experiment -0.5 Albite Illite Amorphous Silica Kaolinite Calcite Montmorillonite Dolomite Quartz Scattering Angle 101

127 Figure 7.10 Comparison of experimental IR extinction data (points) with the empirical fits of a) Saharan sand and b) Arizona road dust. The red lines use the mineralogy derived using the methods of Laskina et al. [2012] and the blue lines use the revised mineral compositions as discussed in Section Relative Extinction a) Saharan Sand Experiment Laskina et al. [2012] Revised Empirical Fit Wavenumber Relative Extinction b) Arizona Road Dust Experiment Laskina et al. [2012] Method Revised Empirical Fit Wavenumber 102

128 Figure 7.11 Comparison of the experimental data (points) with T-matrix model simulations for Saharan sand: (a) the IR spectral extinction (b) the scattering phase function and (c) the linear polarization profiles at λ=550nm. The T-matrix simulations use the particle shape distributions given in Table 3. Red lines use the empirical mineralogy derived by Laskina et al. [2012] (Section ) and the blue lines use the revised mineralogy of Alexander et al. [2013b] (Section ). a) 1.2 Saharan Sand Relative Extinction Experiment Empirical Mineralogy Revised Mineralogy 0.2 b) Wavenumber Phase Function 10 1 Experiment Empirical Mineralogy Revised Mineralogy c) Scattering Angle 1.0 Linear Polarization Experiment Empirical Mineralogy Revised Mineralogy Scattering Angle 103

129 Figure 7.12 Comparison of the experimental data (points) with T-matrix model simulations for Iowa loess. The labeling is as in Figure 7.5. a) 1.2 Iowa Loess Relative Extinction Experiment Empirical Mineralogy Revised Mineralogy 0.2 b) Wavenumber Phase Function 10 1 Experiment Empirical Mineralogy Revised Mineralogy c) Scattering Angle 1.0 Linear Polarization Experiment Empirical Mineralogy Revised Mineralogy Scattering Angle 104

130 Figure 7.13 Comparison of the experimental data (points) with T-matrix model simulations for Arizona road dust. The labeling is as in Figure 7.5. a) Relative Extinction Arizona Road Dust Experiment Empirical Mineralogy Revised Mineralogy 0.2 b) Wavenumber Phase Function 10 1 Experiment Empirical Mineralogy Revised Mineralogy c) Scattering Angle 1.0 Linear Polarization Experiment Empirical Mineralogy Revised Mineralogy Scattering Angle 105

131 Figure 7.14 Comparison of the experimental data (points) with T-matrix model simulations (lines) for Iowa loess. Blue dashed lines use the revised mineral compositions and green lines use the revised mineral compositions with an additional 7% hematite component. All simulations use the optimized shape distributions. a) Iowa Loess Phase Function 10 1 Experiment Revised Mineralogy 7% Hematite Included b) Scattering Angle 1.0 Linear Polarization Experiment Revised Mineralogy 7% Hematite Included Scattering Angle 106

132 Figure 7.15 Comparison of the experimental data (points) with T-matrix model simulations (lines) using different densities for Saharan sand. Blue dashed lines use a density of 2.7 and green lines use a density of 2.3. All simulations use the revised mineral compositions and optimized shape distributions. a) 1.2 Saharan Sand Relative Extinction Experiment Density = 2.3 Density = b) Wavenumber Phase Function 10 1 Experiment Density = 2.3 Density = 2.7 c) Scattering Angle 1.0 Linear Polarization Experiment Density = 2.3 Density = Scattering Angle 107

133 Mineral Dust Processed with Organic Acids and Humic Material 8.1 Introduction While suspended in the atmosphere, mineral dust aerosol can encounter reactive trace gases such as ozone, nitrogen oxides, sulfur oxides, and organic compounds causing heterogeneous chemical reactions and the production of externally mixed or coated particles [Cwiertny et al., 2008]. This atmospheric aging of mineral dust can have a large impact on the chemical, physical, and optical properties of the aerosol [Matsuki et al., 2005; Laskin et al., 2005; Krueger et al., 2006]. These changes can not only affect the direct radiative forcing properties of aerosols, but also the indirect atmospheric properties, including the cloud condensation and ice nucleation activity [Gibson et al., 2006; Möhler et al., 2008; Sullivan et al., 2009]. For instance, when mineral dust comes into contact with organic acids, it can possibly chemically react to form an organic salt. This reaction could result in a heterogeneous internal mixture of reagents and products [Laskina et al., 2013] that can consist of particles with a coating of organic salt over the mineral dust core (possibly making the resultant particles more spherical in shape) or the components could also be more physically segregated within the particle, forming larger, more eccentrically shaped agglomerates (Figure 8.1a). Conversely, the processing could instead form an external mixture where the components (such as mineral dust and organic salt product) exist as individual particles (Figure 8.1b). However, in general, these processes will form mixtures that will most likely contain both distinct (externally mixed) mineral or organic salt particles as well as internally mixed particles, which will be referred to here as a combined internal/external mixture in this work (Figure 8.1c). Regardless of the resulting mixing state, these processes can affect both the particle size and shape distributions as well as the composition of the aerosol which could be different from the original mineral dust emitted into the atmosphere. 108

134 The work in this chapter focuses on understanding changes in the visible light scattering properties of mineral dust (quartz and calcite) that has been processed with organic acids (acetic and oxalic) and humic material. Calcite (CaCO 3 ) is used here an example of a highly reactive mineral dust component [Krueger et al., 2004] and is processed with solutions of acetic acid (CH 3 COOH) and oxalic acid (H 2 C 2 O 4 ) which are both relatively abundant carboxylic acids in the atmosphere [Wang et al., 2007; Limón-Sánchez et al., 2002; Andreae et al., 1988]. For example, a studies of Asian mineral dust have found that ~10% of mineral dust particles contained oxalic acid/oxalate [Sullivan and Prather, 2007; Yang et al., 2009]. It has been shown that calcite will chemically react with acetic acid to form the organic salt, calcium acetate (Ca(CH 3COO) 2) [Prince et al., 2008] through the following process, + 2CH3COOH Ca( CH3COO) + H 2O (8.1) 2 CaCO 3 + CO 2 Similarly, in the presence of oxalic acid, calcite will chemically react to form calcium oxalate salt (CaC 2O 4) [Gierlus et al., 2012] through, CaCO + + (8.2) 3 H 2C2O4 CaC2O4 + H 2O CO2 In addition to calcite, quartz is studied here as an example of a less reactive mineral dust component [Krueger et al., 2004] and is mixed with solutions of humic acid sodium salt (NaHA) in order to explore the effect of humic material coatings on mineral dust [Hatch et al., 2008]. NaHA is used here as a proxy for complex humic materials that may be found in the atmosphere. These same processed samples have been found to contain a fraction of internally mixed particles in a study by Laskina et al. [2013]. More specifically, the study used micro-raman spectroscopy combined with functional group mapping of single particles to investigate the spatial distribution of components within internally mixed particles and to explore variation in the spatial distribution depending on the nature of the interaction. For example, in the processed quartz sample, internally mixed particles were found to have a coating of humic material over the 109

135 entire quartz core, but the internally mixed particles in the processed calcite samples had more physically segregated mineral dust and organic salt components within the particles. However, it should be noted that the study by Laskina et al. [2013] was specifically focused on identifying and mapping internally mixed particles; no attempt was made to determine the overall fraction of internally mixed versus externally mixed aerosol in the sample. Furthermore, single particle Raman mapping of inhomogeneous particles can only be carried out on larger particles (greater than ~ 3µm diameter) and the vast majority of particles in the processed samples were too small to be analyzed by Raman mapping. The results reported in this chapter suggest that there is also a large fraction of externally mixed components in some of the samples. Therefore this analysis considers both internally and externally mixed fractions of mineral dust and organic salt products in combined internal/external mixtures. The overall goal of this chapter is to investigate changes in the visible scattering properties of the internally mixed mineral dust particles that result from physicochemical processing in order to better understand how the optical properties of mineral dust aerosol may change in the atmosphere. 8.2 Experimental Methods and Results Sample Preparation Quartz, calcite, humic acid sodium salt, calcium acetate monohydrate, and calcium oxalate monohydrate were all purchased commercially (Table 2.1) for scattering measurements. In addition, glacial acetic acid was purchased from Alfa Aesar and oxalic acid was purchased from Sigma Aldrich to mix with calcite. Processed samples were initially prepared as described in Laskina et al. [2013]; 1 gram of mineral dust was mixed with a 1.5 wt% solution of the acid or salt in 20 ml of Optima water. The samples were then sonicated for 90 minutes (as described by Laskina et al., [2013]). 110

136 The aerosol flow from the quartz-naha sample contained a high concentration of residual humic acid sodium salt particles, which dominated the visible scattering from the mixture. Therefore, after the initial processing was carried out as described in Laskina et al. [2013], the sample was allowed to settle overnight and then the liquid portion (containing mostly dissolved NaHA) was siphoned off and replaced with Optima water. This was found to be an effective way to lower the externally mixed NaHA aerosol concentration in the flow which allowed for better analysis of the scattering from the processed quartz mineral dust sample. Since an unknown amount of material was removed from the mixture, the initial bulk concentrations could not be used to determine the relative concentrations of quartz and NaHA in the sample. Instead, aerosol was collected from the flow for energy-dispersive X-ray spectroscopy (EDX) analysis. The measured ratio of Si:Na was 32.2:0.260 (by weight %). Using the elemental composition of Aldrich humic acid sodium salt reported by Ramos-Tejada et al. [2003] and the known densities of quartz and NaHA, the ratio of Si:Na can be used to calculate the volume fraction of quartz and NaHA in the aerosolized mixture. This resulted in a mixing fraction of 93% quartz and 7% NaHA (by volume) which will be used for simulations in this chapter. It is also important to note that the simulation results in this chapter are relatively insensitive to variations in this mixing ratio. The processed calcite samples resulted in particle densities in the aerosol flow that were too high for visible light scattering experiments. Therefore, to reduce the total aerosol concentration in the flow, the calcite sample processed with acetic acid was diluted by a factor of twenty and the calcite processed with oxalic acid sample was diluted by a factor of ten. Based off of the known reaction stoichiometry for the calcite reactions (Equations 8.1 and 8.2), it is assumed that all of the organic acid will react to form the corresponding salt with an excess amount of unreacted calcite in the processed sample. Predicted bulk concentrations were converted to volume concentrations using known molar masses and bulk solid densities (from 111

137 literature). This resulted in a predicted bulk concentration of 59% calcium acetate and 41% unreacted calcite (by volume) for the sample of calcite processed with acetic acid. Similarly, the predicted bulk concentration is 56% calcium oxalate and 44% unreacted calcite (by volume) for the sample of calcite processed with oxalic acid. Of course, these are the expected bulk reaction concentrations; the mineral and organic salt concentrations in the aerosol flow may be different due to differences in the aerosolization efficiencies. It should also be noted that if the aerosol components have the same size distribution, the volume concentrations are equal to the concentrations by particle number density Experimental Results Experimental results for the scattering phase function and linear polarization profiles at a wavelength of 532nm for quartz processed with humic acid sodium salt (QHA Mix), calcite processed with acetic acid (CAA Mix), and calcite processed with oxalic acid (COA Mix) are shown in red in Figure 8.2. The corresponding scattering profiles from the unprocessed mineral dust samples (quartz or calcite) are shown in blue. In addition, the scattering profiles obtained from aerosolized samples of the expected products in each case (NaHA, calcium acetate, and calcium oxalate) are shown in green in Figure 8.2 for comparison. The standard deviation of these measurements taken over a period of several days is represented by the shaded region for each sample. Comparison between experimental measurements of the visible scattering phase function and linear polarization profiles for unprocessed samples and processed samples at selected angles are shown in Table 8.1. Corresponding measured particle size distributions are shown in Figure 8.3 and log normal fits to these measured size distributions are shown in Table 8.2. As seen in Figure 8.2, there are clear differences in the phase functions for all three processed mineral dust samples when compared to both the unprocessed original mineral dust and the organic salts. The differences in phase functions can be quantified using the asymmetry parameter (Equation 7.4). The measured asymmetry parameters for the quartz-naha (g = 0.685) 112

138 and calcite-acetic acid (g = 0.586) mixtures lie in between those of the unprocessed mineral dust (g quartz = 0.702, g calcite = 0.665) and organic salt (g NaHA = 0.522, g CalAcetate = 0.491) components. However the scattered light from calcite processed with oxalic acid (g = 0.717) is more forward directed than either calcite (g calcite = 0.665) or calcium oxalate (g CalOxalate = 0.695). There are also obvious changes in the linear polarization profiles for quartz processed with NaHA and calcite processed with acetic acid. While less obvious, although apparent on closer inspection, there is a change in the polarization profile for the calcite processed with oxalic acid sample as well. Therefore, it is clear that the mineral dust samples are being physically and/or chemically altered by the interaction with the organic acids or humic material, and the dust optical properties are changing as a result Experimental Discussion The processing of mineral dust with organic acid/salts can lead to significant changes in the characteristics of the aerosol sample, including the composition, size, and shapes of the particles. Changes in the composition can occur if the mineral dust is reactive or if the mineral dust particles become agglomerated or coated with the organic salt which can also have an effect on the size and shape of the particles. In general, the processed samples will be complex mixtures including internally mixed particles that have multiple components within the same particle as well as homogeneous particles that are externally mixed in the sample (combined internal/external mixture as described previously in Section 8.1). This complexity makes it difficult to quantitatively model changes in the visible scattering properties without any additional measurements. Nevertheless, reasonable assumptions can still be made about the nature of these interactions from the observed changes in the visible scattering properties. It can also provide insights into how the optical properties of mineral dust in the atmosphere might evolve as it ages. Although quartz and NaHA do not chemically react to form any new products, the visible scattering measurements for quartz processed with NaHA suggest that the interaction does lead to 113

139 physical changes in the quartz particles. The processed sample has a lower peak polarization than either the unprocessed mineral dust or NaHA component. This implies that the mixture has not simply formed an external mixture of unprocessed quartz and NaHA particles but instead has formed some kind of internal mixture. This also agrees with other studies that have found that NaHA can form coatings over mineral dust particles [Hatch et al., 2008; Laskina et al., 2013]. These coatings will not only affect the chemical composition of the particles, but it is also likely to change the physical shapes of the quartz particles, both of which could account for the observed changes in the visible scattering properties. In fact, particles that are less eccentrically shaped tend to show a lower peak polarization, as observed in the experimental data. However, the size distribution data in Figure 8.3 shows the presence of an additional fraction of small particles in the processed sample that is not seen in the unprocessed quartz sample. This suggests that along with internally mixed particles, there is also a fraction of externally mixed NaHA particles in the aerosol flow, thus forming a combined internal/external mixture. The experimental data for calcite processed with acetic acid appear consistent with the expected light scattering properties of a purely external mixture of calcite and calcium acetate because the scattering properties of the processed sample appear to be a simple average of the scattering profiles of the mineral dust and organic salt components. An external mixture is also expected because calcium acetate is highly soluble (logk sp = -0.77) [Fredd and Fogler, 1998]. Therefore, once the acetic acid reacts with calcite, it is likely that the reaction product (calcium acetate) will dissolve into solution and form distinct calcium acetate particles in the aerosol flow. However, internally mixed particles can also form if the calcium acetate agglomerates onto a calcite particle in the aerosol flow during the drying processes. Indeed, Laskina et al. [2013] did find that the processed sample contained some large particles that were internally mixed. These internally mixed particles even appeared to have an agglomerated form as appose to a uniform coating found for the quartz-naha sample. Thus, it seems likely that the calcite-acetic acid 114

140 sample could also include a fraction of internally mixed particles, and therefore consist of a combined internal/external mixture. However, the measured light scattering profiles and the solubility considerations suggest that the processed sample may be dominated by an external mixture of calcite and calcium acetate. While calcite processed with acetic acid appears to be predominantly an external mixture, the calcite sample processed with oxalic acid does not. The processed sample has a steeper phase function and slightly higher polarization than either the mineral or organic salt components. Furthermore, calcium oxalate is very insoluble (logk sp = -8.70) [Nancollas and Gardner, 1974] and, therefore, it is reasonable to assume that the calcium oxalate formed by the reaction will remain on the surface of the calcite particle instead of dissolving into solution. Laskina et al. [2013] also found internally mixed particles in the samples of calcite processed with oxalic acid. Similarly to the internally mixed calcite-calcium acetate particles, Raman mapping showed that the calcium oxalate component of the internally mixed particles was segregated from the calcite component. Thus, it seems reasonable to assume that the processing of calcite with oxalic acid primarily forms an internal mixture of calcite and calcium oxalate, altering the size, shape, and composition of the particles. Regardless of the type of mixture that results from processing, in all samples clear differences between the unprocessed and processed samples are observed in the measured scattering properties and particle size distributions. 8.3 Modeling Analysis Size distributions, needed as input to the T-matrix codes, were measured using the particle sizing instruments and are shown in Figure 8.3. However, there is some uncertainty in the size distributions of the processed mineral dust samples due to uncertainty in the particle density (see Section 8.3.3). Refractive indices for the mineral dust samples and organic salts were taken from the literature when available and others are derived in Section and can be found in 115

141 Table 7.2. Simulations for internally mixed particles use effective refractive indices that have been approximated using the Bruggeman effective medium theory (Section 8.3.3). As previously mentioned, mineral dust particle shapes could be affected due to interactions with the organic acids and humic material used in this work. Therefore in order to investigate these changes, models of the light scattering of the unproccesed mineral dust and organic salts are explored first Unprocessed Mineral Dust To begin, the visible scattering properties of the unprocessed mineral dust samples (quartz and calcite) are modeled using measured volume equivalent diameter size distributions and published refractive indices shown in Table 7.2. Effective particle shape distributions were derived by finding the best simultaneous fit to both the phase function and linear polarization profiles using a nonlinear, least squares fitting algorithm. Simulations using the resulting optimized shape distribution are compared to experimentally measured phase function and linear polarization profiles for quartz in Figure 8.4. The measured optical properties are fit extremely well by a broad shape distribution that includes the most oblate and prolate shape parameters allowed in the fitting routine (ξ = +5: 35%, ξ = +1: 25% ξ = -1: 17%, and ξ = -3: 24%). This shape distribution is in good agreement with the earlier results of a study by Meland et al. [2010] and discussed in Chapter 4 which found that the visible scattering as well as the infrared extinction of quartz aerosol could be fit well by a broad uniform shape distribution that included highly prolate and oblate particles. Simulations using the resulting optimized shape distribution for calcite are compared to experimentally measured phase function and linear polarization profiles in Figure 8.5. Calcite s visible scattering properties are best fit by a spheroidal particle shape distribution that includes the most oblate shape parameter (ξ = +5: 31%) and moderately prolate shape parameters (ξ = -1: 62% and ξ = -2: 7%). The models of the visible scattering profiles of quartz and calcite that use the derived optimized shape distributions are both able to accurately simulate the experimental 116

142 visible scattering data Organic Salts In order to understand how mineral dust changes in the presence of organic acids/salts and model the light scattering properties of the processed dust samples, the organic salt component of the mixed samples (humic acid sodium salt, calcium acetate, and calcium oxalate) must also be investigated. Refractive indices for humic acid sodium salt were not found in literature and are determined here. While optical constants for calcium acetate were found in the literature, the reported values greatly varied depending on the source; Weast et al. [1975] reported n = 1.55 while Hampton Research (unpublished data, available from measured the refractive index as n = Because of this discrepancy, refractive indices for calcium acetate are also determined here. SEM images of humic acid sodium salt and calcium acetate particles collected directly from the aerosol flow are shown in Figure 8.6. The particles appear quite spherical, and are assumed to be so in order to derive their refractive indices using Mie theory. T-matrix simulations of the scattering profiles of spherical particles (ξ = 0, equivalent to Mie theory) were calculated over a grid of both real and imaginary refractive indices. Initial attempts to fit the refractive indices for both NaHA and calcium acetate were based on simulating the measured total scattering phase function and linear polarization profiles. However, these results did not converge. Therefore, the measured scattered light intensities from incident light polarized parallel and perpendicular to the scattering plane were used for the fitting instead [Barkey et al., 2007]. The simulations were quantitatively compared to the experimental data using the sum of squared residuals (SSR). The SSR for the parallel and perpendicular scattering intensities were added together (total SSR) for each point of the grid of optical constants and the best simultaneous fit was determined from the grid point with the minimum total SSR. Simulations of the parallel and perpendicular scattering profiles were calculated over a 117

143 grid of refractive indices ranging from n = and k = for humic acid sodium salt, and n = and k = for calcium acetate. The best simultaneous fit to the scattering properties was achieved using n = 1.51 ± 0.01 and k < 1E-4 (k=0 is used here) for humic acid sodium salt and n = 1.44 ± 0.01 and k < 1E-4 (k = 0 is used here) for calcium acetate. Note that the results for calcium acetate lie in the middle of the range of indices of refraction previously reported in the literature. Scattering simulations using the best fit index of refraction are compared to experimental measurements in Figure 8.7. Values for the refractive indices of calcium oxalate were found in a book by Anthony et al. [2003] and are used here. Calcium oxalate particles are clearly not spherical as seen in SEM images (Figure 8.6), and therefore an optimized spheroidal particle shape distribution must be determined in order to model the light scattering properties. Using the same methods as described above for calcite and quartz, the optimized shape distribution was found to consist mostly of moderately shaped prolate spheroids (ξ = -1: 86%) and some eccentric oblate spheroids (ξ = +5: 14%). Model results using this optimized shape distribution fit the experimentla data quite well and are shown in Figure Processed Mineral Dust The processed samples are likely to be complex mixtures which contain both internally mixed particles as well as homogeneous particles that are externally mixed in the sample. Therefore, the mixing ratio of internally mixed to externally mixed particles must be known or approximated. For samples that are primarily external mixtures, the visible scattering properties are simulated by first calculating the optical properties of each of the components separately and then averaging them together using Equation 7.2). In the external mixing case, it would also be ideal to use different size distributions and different densities for the simulations of each of the components in the mixture, however, there is no easy way to measure the individual size distribution of each component. This will be further discussed in the following sections. 118

144 For models assuming an internal mixture, the distribution of the mineral and organic salt components within the particles must be known. For example, the different components could be physically segregated, forming agglomerates of the components, within the particle. On the other hand, shell like (uniform) coatings could form over a mineral core and core-shell Mie theory could potentially be used, although particle shape effects would then be ignored. Therefore, all forms of internally mixed particles are approximated here as having a homogeneous composition (the two components are well-mixed). Using this approximation, effective medium theories are used to calculate average refractive indices for use in simulations of the visible scattering profiles. For example, an internally mixed particle consisting of a medium with dielectric constant m 2 2 ( nm km ) + 2inmkm = (8.3) and inclusions with dielectric constant i 2 2 ( ni ki ) + 2iniki = (8.4) will have an effective medium dielectric constant, εε aaaaaa, which can be calculated by solving the Bruggeman formula, i avg m avg ( ) ( )( ) 0 f (8.5) i f + 2 = i avg i m avg where ff ii is the volume fraction of the inclusions [Bohren and Huffman, 1998]. From the effective medium dielectric constant, the complex refractive indices (m = n + ik) can be calculated using the following equations, eff + Re( eff ) n = (8.6) 2 eff Re( eff ) k = (8.7) 2 119

145 In this chapter, simulations assuming an internal mixture use effective medium refractive indices that have been calculated using the Bruggeman formula. Regardless of the type of mixture formed when these mineral dust samples are processed with organic acids and humic material, it is possible that the interactions can affect the particle shapes. This change in the particle shape distribution can be quantified by defining a root-mean square (RMS) shape factor, ξ RMS = ξ = ξ N ξ ( ξ ) (8.8) where N ( ξ ) is the relative weighting for a given shape factor. The ξ RMS gives an average deviation from sphericity (the larger ξ RMS is, the more eccentric the particles are). All three processed samples have resulted in different changes to the scattering properties and measured size distributions when compared to the unprocessed mineral dust and organic salt samples and therefore a range of modeling approaches have been applied to the different processed samples as discussed in detail below Quartz Processed with Humic Acid Sodium Salt Based on the measured scattering results for quartz processed with humic acid sodium salt, it appears that the sample is dominated by internally mixed particles because the measurements do not appear to be an average of the results from the mineral and organic salt components; the measured polarization profile for the processed sample is lower than either the unprocessed quartz or NaHA samples. An internal mixing assumption also agrees with the results of previous studies by Hatch et al. [2008] and Laskina et al. [2013], which have shown that humic acid sodium salt can coat mineral dust particles rather than form an external mixture. Therefore an internal mixing model assuming a homogeneous sample of only internally mixed NaHA-quartz particles is explored first. 120

146 For the internal mixture model, effective medium refractive indices are calculated using the Bruggeman formula as shown in Equation 8.5. Using the 93% quartz and 7% humic acid sodium salt mixing proportion as described above, the effective medium complex refractive index is m = i However, it should be noted that because the refractive index values for quartz and NaHA are so similar (n quartz = 1.55, n NaHA = 1.5), the resulting effective refractive indices are quite insensitive to the assumed mineral and organic salt concentrations. As seen in Figure 8.2, the measured peak polarization of the processed sample is clearly lower than that of the mineral and organic salt components. This suggests that there has been a change in the particle shape distribution. In order to further explore this possibility, the measured scattering profiles for the quartz processed with NaHA have been simulated using different particle shape distributions. Simulations using the particle shape distribution previously determined for unprocessed quartz are shown as blue lines in Figure 8.9. In addition, figures of the differences between experimental data and simulation results of the phase function and linear polarization are shown in Figure As predicted, this shape distribution is unable to accurately simulate the experimental data and results in a polarization profile that is too high. This suggests that the coated particles have become less eccentric in shape because particles that are more spherical in shape tend to show a lower peak polarization. To explore this, an optimized shape distribution for the internally mixed NaHA-quartz particles was derived using the same methods as described in Section The optimized shape distribution includes shape factor weightings ξ = -1: 71%, ξ = 0: 9%, and ξ = +5: 20% Note that this optimized shape distribution is more moderately shaped than the unprocessed quartz particle s broad shape distribution as seen visually in Figure 8.9c. The resulting scattering simulations that use the optimized shape distribution are shown as green lines in Figure 8.9 (differences are shown in Figure 8.10). These modeling results suggest that the NaHA coating could make the particles more 121

147 spherical. The unprocessed quartz sample described in Section has a root mean square shape factor ξ RMS = 3.4, and the shape distribution for the processed quartz sample has a ξ RMS = 2.4, a significant decrease in the average particle eccentricity. However, it is possible that the decrease in eccentricity could simply reflect a smoothing out of the surface roughness of the quartz particles due to the coating. For example, in the spheroid approximation, it could be possible that the fine-scale surface roughness is best modeled by including more eccentric shape factors into the particle shape distribution and therefore a smoothing of the surface structure and roughness (from a thin coating) could result in a more moderate spheroidal shape distribution. In a combined internal/external mixture model, the light scattering properties of the internally mixed (coated quartz) component and the externally mixed component are simulated separately and then averaged together using Equation 8.5. For this model the components are averaged together using particle number density concentrations based on the assumed 93:7, coated quartz:naha volume mixing ratio. The externally mixed NaHA component of the processed sample is simulated assuming spherical particles with the size distribution and refractive index of unprocessed NaHA aerosol. The coated quartz component in the mixture is simulated using the size distribution of unprocessed quartz but the effective index of refraction for internally mixed quartz-naha particles (m = i ). As for the particle shape distribution of the coated quartz component, if it is assumed to have the same shape distribution as unprocessed quartz, the simulations using the combined model will again predict a phase function that is too steep and a linear polarization profile that is too high in comparison to the experimental data. This can be seen in Figure 8.11 which compares experimental data and simulations that assume a combined internal/external mixture. In addition, figures of the differences between experimental data and simulation results of the phase function and linear polarization are shown in Figure Therefore, an optimized shape distribution that allows the coated quartz component to be 122

148 less eccentric (closer to spherical) is derived in order to achieve better fits to the measured scattering properties. The optimized shape distribution contains mostly moderate spheroids (ξ = - 1: 63%) and and some spheres (ξ = 0: 2%), with a smaller fraction of the most eccentric spheroids (ξ = +5: 14%; ξ = -3: 21%). The RMS shape factor for this shape distribution is ξ RMS = 2.6, compared to ξ RMS = 2.4 for the pure internal mixture model and ξ RMS = 3.4 for unprocessed quartz. Simulations using this combined internal/external mixture model and the optimized shape distribution are shown in red in Figure 8.11 (differences are also shown in Figure 8.12) and fit the measured visible scattering peroperties reasonably well. This modeling analysis, again, suggests that the quartz particles must become more moderately shaped (closer to spherical) when processed with NaHA in order to make the phase function less steep and lower the simulated polarization to match the experimentally measured scattering properties. It should be noted that both the purely internal and the combined internal/external models use simple approximations in order to simulate the visible scattering properties of the processed quartz-naha sample. An approximation used in the internal mixture model is that all of the particles are assumed to be homogeneously mixed while it is much more likely that the internally mixed particles have more of a core-shell form. It is also likely that there is an additional fraction of externally mixed particles in the sample, which is ignored in the first model. While this is accounted for in the combined internal/external model, there are also other approximations that are made. For example, it is assumed that the components have the same size distributions as those of the unprocessed samples. It should also be noted that there are also uncertainties in the assumed 93:7 mixing ratio of quartz and NaHA. However, the results are fairly insensitive the ratio of quartz to NaHA used in the simulations. In fact, repeating the analysis using a 66:34, quartz:naha ratio (based on the initial volume concentrations before removing excess NaHA) results in a comparable overall decrease in the RMS shape factor for the processed sample. Nevertheless, even with these crude 123

149 approximations and uncertainties, both models support the same conclusion: the coated quartz particles in the processed sample have likely become more moderate in shape than the unprocessed quartz particles Calcite Processed with Acetic Acid The visible light scattering properties of calcite processed with acetic acid are first simulated as an external mixture of calcite and calcium acetate (the reaction product) because the experimental data for the processed sample appears to be an average of the mineral and organic salt components. In an external mixture, it is unlikely that the calcite and calcium acetate components have the same size distribution (that of the processed sample as a whole) and therefore the measured size distribution of the processed sample should be considered a sum of two distinct distributions. Therefore, as discussed in Section for the combined coated quartz-naha model, the measured size distributions of the unprocessed calcite and calcium acetate can be used to approximate the particle size distributions of the mineral and organic salt components in the external mixture. While this may not be rigorously correct (i.e. the calcite particles may change size as a result of the chemical reaction with acetic acid), it is a simple way to approximate the size distributions of the individual components. As discussed above for external mixtures, simulations of the individual components are calculated separately and then averaged together using Equation 7.2 and the appropriate mineral and organic salt component weights. Therefore, the calcite component of processed sample will be simulated using the measured size distribution, refractive indices, and shape distribution of the unprocessed calcite sample (see Section 8.3.1). Similarly, the calcium acetate component of the processed sample will be simulated using the same measured size distribution, derived refractive indices, and spherical particle shape as unprocessed calcium acetate (see Section 8.3.2). These simulations are then averaged together using concentrations by particle number density based on the predicted bulk concentrations (41% calcite and 59% calcium acetate, by volume). 124

150 Simulations of the visible scattering properties calcite processed with calcium acetate assuming an external mixture are shown as blue lines and compared to experimental measurements in Figure In addition, differences between experimental data and simulations is shown in Figure This model results in reasonably good fits to the measured optical properties. The good agreement between models and measurements supports the assumption that the processed sample has formed an external mixture. It also appears that there is no need to assume that the acetic acid has significantly altered the shape of the calcite particles. However, this consistency does not prove that the processed sample is strictly externally mixed or that the calcite particles have not changed shape. It is possible that while most of the calcium acetate dissolved in the solution will form distinct particles, some of the calcium acetate could also remain agglomerated on the calcite particles, thus resulting in a combined internal/external mixture. Therefore, a combined internal/external model is investigated here as well. In this model, the internally mixed calcite and calcium acetate component will be simulated using the measured size distribution and derived shape distribution of unprocessed calcite, however effective medium refractive indices will be used (m = i based off of the predicted bulk concentrations). It should be noted that the internally mixed component may not have the same size distribution as unprocessed calcite, it is used here for simplicity. The externally mixed calcium acetate component is simulated using the same parameters as in the external mixture model (measured size distribution, derived refractive indices, and spherical particle shape as unprocessed calcium acetate). The internally mixed component and externally mixed calcium acetate component are then averaged together using the predicted bulk concentration mixing ratio, 41:59 calcite:calcium acetate. Simulations using this combined internal/external model are shown as red lines in Figure 8.13 (differences are also shown in Figure 8.14). While there is no significant improvement in the fit to the measured phase function, the 125

151 fit to the measured polarization is extremely good. However, it should be noted that there are various modeling conditions that could achieve similar or better agreement between simulations and experimental measurements. For example, there is an inherent uncertainty in the concentrations of calcite and calcium acetate and adjusting the mixing fraction could improve the model fits. It is also possible that the chemical reaction could alter the particle shape distribution of the residual calcite component or internally mixed component and therefore fitting the scattering properties by adjusting the shape distribution, as needed for the quartz-naha sample, would improve the simulations as well. While it is clear that the presence of acetic acid affects the optical properties of calcite, it remains difficult to draw firm conclusions about the details of these changes or the form of the processed sample. This is, in part, due to the fact that the light scattering properties of this processed sample are not strongly affected by particle shape or internal structure because the sample is dominated by very small particles. However, these results do show that reasonable fits to the measured visible scattering properties of calcite processed with acetic acid can be achieved without requiring any significant change in the particle shape or size distributions of either calcite or calcium acetate Calcite Processed with Oxalic Acid The visible scattering properties for calcite processed with oxalic acid is simulated assuming an internal mixture of calcite and calcium oxalate (the reaction product). An internal mixing assumption was chosen because the measured scattering properties of the processed sample does not appear as an average of the two components; the phase function of the mixture is much steeper than either unprocessed calcite or calcium oxalate and the polarization is also slightly higher. In contrast to calcium acetate, calcium oxalate is actually very insoluble and therefore it is likely that as the oxalic acid reacts with a calcite particle, the calcium oxalate formed will remain on the calcite particle instead of dissolving into solution, thus supporting an internal mixing assumption. 126

152 Given an internal mixing assumption, the measured size distribution of the processed sample (with the weighted averaged density) and effective medium refractive indices are used in the simulations. Using Equations and the predicted bulk concentrations (44% calcite and 56% calcium oxalate), the effective medium refractive indices are m = i10-4. As a first attempt, simulations use the shape distribution of unprocessed calcite which could physically be the result if the calcium oxalate forms a very thin coating over the calcite core and the particle retains the same calcite particle shape as before the reaction. Therefore simulations using the shape distribution of unprocessed calcite (Section 8.3.1), shown in blue, are compared to measurements in Figure In addition, differences between experimental data and simulations are shown Figure While the fit to the polarization is reasonable, the simulated phase function is not steep enough compared to the experimental data. On the other hand, it is possible that the oxalic acid could consume most of the calcite particle and change the shape of the particle to more closely resemble calcium oxalate s shape. Therefore simulations using calcium oxalate s shape distribution (Section 8.3.2) are shown as green lines in Figure 8.15 (differences are shown in Figure 8.16). This again results in a phase function that is not steep enough compared to the measured data but also a linear polarization that is also too low. Therefore, an optimized shape distribution is derived in an attempt to improve the model fit. Using the methods described in Section 8.3.1, the optimized shape distribution is found to consist of shape factors including ξ = -1: 60%, ξ = +2: 13% and ξ = +5: 27%. Shown graphically as red bars in Figure 8.15c, the optimized shape distribution appears to be an average of the unprocessed calcite and calcium oxalate shape distribution, perhaps suggesting that some of the particles have retained the shape of the original calcite particle while others have transformed in shape to more closely resemble calcium oxalate. The RMS shape factor for the processed sample has slightly decreased to ξ RMS = 2.8 from a value of ξ RMS = 2.9 for unprocessed calcite. Simulations of the visible scattering properties using this optimized shape factor are shown in 127

153 Figure 8.15 in red (differences are shown in Figure 8.16). The simulated phase function is still unable to reproduce the steepness of the measured data most likely because it is relatively insensitive to the shape distribution (due to the small average particle size). This suggests that processing calcite particles with oxalic acid results in internally mixed particles with a shape distribution that may be closer to that of the calcium oxalate product. However, the relatively poor fit to the measured phase function is still a concern. The relatively steep phase function measured for calcite processed with oxalic acid appears more consistent with a size distribution that has a larger average particle size than that used in these simulations. As discussed, there is some uncertainty in the effective particle density and thus also the size distributions of the processed samples. These simulations use a size distribution determined from a weighted average density (ρ =2.43) based on the predicted bulk concentrations. If a much lower average particle density is assumed, the size distribution shifts to larger particles and the model fits can be improved. This however, does not seem plausible unless the calcium oxalate formed during this reaction has a much more diffuse or porous structure and/or contains more voids than the commercial calcium oxalate sample used here. The poorer fit to the experimental data could also be due to a breakdown in the validity of the spheroid approximation. It is possible that the reaction has formed particles with sharp edges and/or fine surface roughness which cannot be readily approximated by smooth spheroids. While the reasons for the poor modeling fits are unclear for this sample, overall, the observed differences between the unprocessed and processed mineral dust samples in the visible scattering properties and measured particle size distributions are clear. 8.4 Conclusions Visible scattering phase function and linear polarization profiles for mineral dust processed with organic acids and humic material were measured and compared to unprocessed mineral dust and organic salt samples. Processed samples studied here include quartz mixed with 128

154 humic acid sodium salt, calcite reacted with acetic acid, and calcite reacted with oxalic acid. The visible scattering properties of all three processed samples show clear changes compared to both the unprocessed mineral dust and the associated organic salt (humic acid sodium salt, calcium acetate, or calcium oxalate). This supports the conclusion that the presence of trace organic acids and humic material must be considered when analyzing the visible scattering properties of atmospherically aged mineral dust. T-matrix simulations are compared to the experimentally measured scattering properties in order to investigate the physical and chemical changes caused by the processing of mineral dust with organic acids. The measured light scattering properties of quartz processed with humic acid sodium salt (NaHA) suggest that the interaction forms internally mixed NaHA-quartz particles because the polarization profile of the processed sample is lower than either the unprocessed quartz or NaHA samples. However, the measured particle size distribution suggests that the processed sample also contains a fraction of externally mixed NaHA particles, thus resulting in a combined internal/external mixture. Regardless of the assumptions made about the type of mixing, simulations of the visible scattering properties of quartz processed with NaHA suggest that the processed quartz particles have become less eccentric in shape, perhaps due to a coating of humic material forming over the mineral core. The visible scattering measurements of calcite processed with acetic acid are consistent with the expected light scattering properties of an external mixture of calcite and calcium acetate (the reaction product of calcite and acetic acid) because the measured phase function and polarization profiles of the processed sample appear to be an average of the scattering properties of the two components. Furthermore, simulations of the light scattering properties of the calciteacetic acid system are able to accurately model experimental data without requiring any significant change to the calcite particle shape distribution, however these results cannot rule out the possibility of such physical changes. 129

155 The measured scattering properties of calcite processed with oxalic acid suggests that the processed sample has formed an internal mixture because the phase function is much steeper than either unprocessed calcite or calcium oxalate (the reaction product of calcite and oxalic acid). However, we have not been able to achieve good, simultaneous fits to both the phase function and linear polarization data and the reasons for the poorer fit are somewhat unclear. It could be caused by uncertainty in the assumed effective particle density or the inability of the uniform spheroid approximation to adequately treat the complex processed particles. While the reasons for the poor modeling fits to the measurements are not fully understood, the experimental data alone shows that there are clear changes to the visible scattering properties of calcite when oxalic acid is present. All three processed mineral dust samples show clear changes in the visible scattering phase function and linear polarization profiles when compared to the scattering properties of unprocessed dust. The observed changes in the scattering properties of processed mineral dust can have atmospheric implications, potentially affecting the impact of dust on the Earth s radiation balance and the accuracy of remote sensing retrieval algorithms. For example, the asymmetry parameter is an important measurement for modeling the radiative transfer effect of atmospheric dust. In all three cases, the processing of mineral dust with organic acids and humic material had a significant effect on scattering asymmetry parameter compared to the unprocessed samples. Therefore the presence of these substances in the atmosphere must be considered when simulating the optical properties of aged mineral dust for climate forcing calculations or remote sensing retrieval algorithms. The observed differences in the scattering properties are likely the result of changes in the chemical and/or physical properties (including particle density, size, and shape) of the aerosols. These underlying changes to the chemical and physical properties of the aged mineral dust particles can also indirectly affect the atmosphere by altering their hygroscopicity, cloud condensation nuclei activity, and ice nucleation activity as well as affecting 130

156 the concentrations of trace organic acids in the atmosphere. The aerosol properties that may be affected by the processing of mineral dust with organic acids and humic material will need further study in order to gain a better understanding of the full impact on the atmosphere and global climate change. 131

157 Table 8.1 Comparison between experimental measurements of the visible scattering a) phase function and b) linear polarization profiles for unprocessed and processed samples at selected angels. a) Phase Function Scattering Angle QHA Mix Quartz NaHA CAA Mix Calcite Calcium Acetate COA Mix Calcite Calcium Oxalate b) Linear Polarization Scattering Angle QHA Mix Quartz NaHA CAA Mix Calcite Calcium Acetate COA Mix Calcite Calcium Oxalate

158 Table 8.2 Table of log normal size distribution parameters that best fit the measured volume equivalent particle size distribution. r m is the mode radius of the particle number size distribution and σ is the width parameter. All samples except calcium acetate were fit with a linear combination of two log normal distributions (bimodal). Sample rm (nm) σ Quartz Peak 1 Peak Calcite Peak 1 Peak NaHA Peak 1 Peak Calcium Acetate Calcium Oxalate Peak 1 Peak QHA Mix Peak 1 Peak CAA Mix Peak 1 Peak COA Mix Peak 1 Peak Table 8.3 Optical constants of mineral and organic compounds considered in this study. All of the values are measured or interpolated at λ=532 nm except calcium oxalate where the wavelength for the reported value was unspecified. Sample Refractive Index (m = n + i k ) Reference Calcite i 1E-4 Ivlev and Popva, 1973 Quartz i 1E-4 Longtin et al., 1988 Calcium Acetate i 0 This work Calcium Oxalate i 1E-4 Anthony et al., 2003 Humic Acid Sodium Salt i 0 This work 133

159 Figure 8.1 Conceptual illustration from an optical scattering perspective of the different types of mixtures that could potentially result from mineral dust interacting with organic acids and humic material. These interactions can form: a) internal mixtures including, homogeneously mixed particles, coatings, or more physically segregated heterogeneous particles, b) external mixtures where each particle is either mineral dust or organic salt, or c) a combined internal/external mixture. 134

160 Figure 8.2 Experimental visible scattering phase functions and linear polarization profiles for a) quartz processed with humic acid sodium salt (QHA Mix), b) calcite processed with acetic acid (CAA Mix), and c) calcite processed with oxalic acid (COA Mix), shown in red. Also shown are visible scattering properties of the corresponding unprocessed mineral components (quartz or calcite) in blue and commercial samples of the expected organic species (humic acid sodium salt/naha, calcium acetate, or calcium oxalate) in green. Shaded regions represent the standard deviation from measurements taken over several days. 135

161 Figure 8.3 Experimentally measured size distributions for a) quartz processed with humic acid sodium salt (QHA Mix), b) calcite processed with acetic acid (CAA Mix), and c) calcite processed with oxalic acid (COA Mix), shown in red. Also shown measured size distributions of the corresponding mineral components (quartz or calcite) in blue and organic species (humic acid sodium salt/naha, calcium acetate, or calcium oxalate) in green. It should be noted that the relative peak heights are not meaningful due to differences in sample concentrations. dn/dlogd (10 4 #/cm 3 ) a) Quartz Processed with NaHA Diameter (nm) Quartz NaHA QHA Mix dn/dlogd (10 4 #/cm 3 ) b) Calcite Processed with Acetic Acid Calcite Calcium Acetate CAA Mix Diameter (nm) dn/dlogd (10 4 #/cm 3 ) c) Calcite Processed with Oxalic Acid Diameter (nm) Calcite Calcium Oxalate COA Mix 136

162 Figure 8.4 Comparison of experimentally measured visible scattering phase function and polarization profiles (points) for quartz with model simulations (blue lines) using the optimized shape distribution as shown in the bar graphs. Quartz 10 Experiment Quartz Model Phase Function Scattering Angle Linear Polarization Experiment Quartz Model Scattering Angle Relative Weight Quartz Optimized Shape Distribution Shape Parameter (ξ) 137

163 Figure 8.5 Comparison of experimentally measured visible scattering phase function and polarization profiles (points) for quartz with model simulations (blue lines) using the optimized shape distribution as shown in the bar graphs. Calcite 10 Experiment Calcite Model Phase Function Scattering Angle 1.0 Linear Polarization Experiment Calcite Model Scattering Angle 60 Calcite Optimized Shape Distribtuion Relative Weight Shape Parameter (ξ) 138

164 Figure 8.6 SEM images of a) humic acid sodium salt, b) calcium acetate and c) calcium oxalate particles collected from the aerosol flow. 139

165 Figure 8.7 Comparison of experimentally measured visible scattering phase functions and linear polarization profiles (points) for a) humic acid sodium salt and b) calcium acetate with Mie theory simulations (green lines) using optimized optical constants as shown. a) Humic Acid Sodium Salt b) Calcium Acetate 10 Experiment n = 1.51 k = 0 10 Experiment n = 1.44 k = 0 Parallel Intensity 1 Parallel Intensity Scattering Angle Scattering Angle 10 Perpendicular Intesity 1 Experiment n = 1.51 k = 0 Perpendicular Intesity 1 Experiment n = 1.44 k = Scattering Angle Scattering Angle 140

166 Figure 8.8 Comparison of experimental visible scattering phase function and polarization profiles for calcium oxalate (points) with model simulations (green lines) using the optimized shape distribution as shown in the bar graph. Calcium Oxalate Phase Function 10 1 Experiment Calcium Oxalate Model Scattering Angle 1.0 Linear Polarization Experiment Calcium Oxalate Model Scattering Angle Relative Weight Calcium Oxalate Optimized Shape Distribution Shape Parameter (ξ) 141

167 Figure 8.9 Comparison of experimental visible scattering properties (points) with internal mixture model simulations of quartz processed with humic acid sodium salt. Simulations use the quartz shape distribution (blue lines) or an optimized shape distribution (red lines). Corresponding shape distributions used in the simulations are shown in c). See Section for details. a) Phase Function 10 1 Quartz Processed with NaHA - Internal Mix Models Experiment Internal Mixture - Quartz Shape Dist. Model Internal Mixture - Optimized Shape Dist. Model b) Scattering Angle Linear Polarization Experiment Internal Mixture - Quartz Shape Dist. Model Internal Mixture - Optimized Shape Dist. Model Scattering Angle c) Relative Weight Quartz Shape Distribution Internal Mixture - Optimized Shape Distribution Shape Parameter (ξ) 142

168 Figure 8.10 Differences between the experimental data for quartz processed with NaHA and the model simulations shown in Figure 8.8. a) Phase Function Difference Quartz Processed with NaHA - Internal Mix Models Internal Mixture - Quartz Shape Dist. Model Internal Mixture - Optimized Shape Dist. Model b) Polarization Difference Scattering Angle Internal Mixture - Quartz Shape Dist. Model Internal Mixture - Optimized Shape Dist. Model Scattering Angle 143

169 Figure 8.11 Comparison of experimental visible scattering properties (points) with combined internal/external mixture model simulations of quartz processed with humic acid sodium salt. Simulations use the quartz shape distribution (blue lines) or an optimized shape distribution (red lines). Corresponding shape distributions used in the simulations are shown in c). See Section for details. a) Phase Function 10 1 Quartz Processed with NaHA - Combined Mix Models Experiment Combined Internal/External Mixture - Quartz Shape Dist. Model Combined Internal/External Mixture - Optimized Shape Dist. Model Scattering Angle b) 1.0 Linear Polarization Experiment -0.5 Combined Internal/External Mixture - Quartz Shape Dist. Model Combined Internal/External Mixture - Optimized Shape Dist. Model Scattering Angle c) Relative Weight Quartz Shape Distribution Combined Internal/External Mixture - Optimized Shape Distribution Shape Parameter (ξ) 144

170 Figure 8.12 Differences between the experimental data for quartz processed with NaHA and the model simulations shown in Figure a) Quartz Processed with NaHA - Combined Mix Models 6 Phase Function Difference Combined Internal/External Mixture - Quartz Shape Dist. Model Combined Internal/External Mixture - Optimized Shape Dist. Model b) Polarization Difference Scattering Angle Combined Internal/External Mixture - Quartz Shape Dist. Model Combined Internal/External Mixture - Optimized Shape Dist. Model Scattering Angle 145

171 Figure 8.13 Comparison of experimental visible scattering properties (points) for calcite procesed with acetic acid with model simulations. Simulations using an external mixing assumption are shown in blue and simulations for the combined mixture model that includes an internally mixed fraction of particles along with externally mixed particles are shown in red. See Section for details. a) Phase Function 10 1 Calcite Processed with Acetic Acid Experiment External Mixture Model Combined Internal/External Mixture Model b) Scattering Angle 1.0 Linear Polarization Experiment External Mixture Model Combined Internal/External Mixture Model Scattering Angle 146

172 Figure 8.14 Differences between the experimental data for calcite processed with acetic acid and the model simulations shown in Figure a) 0.2 Calcite Processed with Acetic Acid Phase Function Difference External Mixture Model Combined Internal/External Mixture Model b) Scattering Angle 0.2 Polarization Difference External Mixture Model Combined Internal/External Mixture Model Scattering Angle 147

173 Figure 8.15 Comparison of experimental visible scattering properties (points) for calcite procesed with oxalic acid with model simulations using different shape distributions as shown in c). Simulations using calcite s shape distribution (Section 4.1) are shown in blue, simulations using calcium oxalate s shape distribution (Section 4.2) are shown in green, and simulations using the shape distribution optimized to fit the experiment (Section 4.3.3) are shown in red. See Section for details. a) Phase Function 10 1 Calcite Processed with Oxalic Acid Experiment Calcite Shape Distribution Calcium Oxalate Shape Distribution Optimized Shape Distribution Scattering Angle b) 1.0 Linear Polarization c) Relative Weight Experiment Calcite Shape Distribution Calcium Oxalate Shape Distribution Optimized Shape Distribution Scattering Angle Shape Parameter (ξ) Calcite Shape Distribution Calcium Oxalate Shape Distribution Optimized Shape Distribution 148

174 Figure 8.16 Differences between the experimental data for calcite processed with oxalic acid and the model simulations shown in Figure a) Phase Function Difference Calcite Processed with Oxalic Acid Calcite Shape Distribution Calcium Oxalate Shape Distribution Optimized Shape Distribution b) Scattering Angle 0.2 Polarization Difference Calcite Shape Distribution Calcium Oxalate Shape Distribution Optimized Shape Distribution Scattering Angle 149

175 Dynamic Shape Factors of Quartz Aerosol 9.1 Introduction As shown in this work, particle shape can clearly affect the optical properties of aerosol but it can also affect the aerodynamic properties of dust because of drag. In order to account for this shape effect, the dynamic shape factor, χ, is used to give a measure of particle asphericity. The dynamic shape factor is defined as, drag p F χ = (9.1) F drag ve or the ratio of the actual force on an aspherical particle over the force on a volume equivalent sphere, both moving at the same velocity [Hinds, 1999]. The dynamic shape factor is not an intrinsic characteristic of a particle but instead is a correction factor for Stokes s law for non-spherical particles and is typically used to convert different measurements of particle size. For example, many particle sizing instruments (including the APS used in the above experiments) use time of flight to measure an aerodynamic diameter, d a. The aerodynamic diameter is defined as the diameter of a sphere with standard density, ρ o, that settles at the same terminal velocity as the non-spherical particle. Therefore the aerodynamic diameter will clearly depend on the drag force and therefore the dynamic shape factor. However, other sizing instruments (including the SMPS used in the above experiments) measures a mobility diameter, d m, by balancing the force of an electric field on a charged particle with the drag force exerted on the particle. The mobility diameter is defined as the diameter of a sphere with the same migration velocity in a constant electric field as the non-spherical particle. In addition, in order to be able to convert both the aerodynamic diameter and the mobility diameter to the volume equivalent diameter, the dynamic shape factor is needed. Since the dynamic shape factor is a measure of particle behavior, it will depend on the 150

176 pressure, flow regime, particle size and density, and orientation in the flow field. In the continuum flow regime (Kn<<1) the aerosol particles are large compared to the mean free path of the suspending gas and therefore the gas acts like a continuous fluid flowing around the particle [DeCarlo et al., 2004]. In the free molecular regime (Kn>>1), particles are small compared to the mean free path of the gas particles and therefore interact with the particles through a series of ballistic collisions [DeCarlo et al., 2004]. In between the continuum and free molecular regimes is the transition regime (Kn~1). All of the size measurements in the above experiments were done in the transition or continuum regimes, however, other particle sizing instruments also operate in the free-molecular regime. Due to lack of data, dynamic shape factors in different regimes are often assumed to be the same [DeCarlo et al., 2004; Zelenyuk et al., 2006]. However, a few studies have measured dynamic shape factors in different regimes to test this assumption and found that it is not generally valid [Beranek et al., 2012; Zelenyuk et al., 2014]. 9.2 Theoretical Background A theoretical background of the dynamic shape factor is given in this section and follows the discussion in Hinds [1999] and DeCarlo et al. [2004]. As previously mentioned, the dynamic shape factor is needed to convert from different measures of particle size. The mobility diameter, d m, can be related to the volume equivalent diameter, d m, using the following equation, d m C c ( d m ) = dve χ (9.2) t C ( d ) c ve where χ t is the dynamic shape factor in the transition regime (the regime which d m is typically measured), and C c is the Cunningham slip correction factor. Therefore, for a particle with a given d ve, the more aspherical the particle is (larger χ t), the larger the measured d m will be. The aerodynamic diameter, d a, can be related to the volume equivalent diameter by, 151

177 d 1 χ ρ C ( dve ) ( d ) p c a = dve (9.3) ρo Cc a where χ is the dynamic shape factor in any regime and ρ p is the density of the particle. However, in the free molecular regime, ( d ) ( dve ) dva ( dva ) dve C 1 (9.4) c C c = d C c This simplifies Equation 9.3 and yields the relationship between the vacuum aerodynamic diameter (the aerodynamic diameter in the free molecular regime), d va, and the volume equivalent diameter, 1 ρ p d va = d ve (9.5) χ ρ v o where χ v is the dynamic shape factor in the free molecular regime. Therefore, for a particle with a given d ve, the more aspherical the particle is (larger χ v), the smaller the measured d va will be. Because it can be difficult to separate the effects of particle shape and particle density, these are often combined into a single effective density, ρ eff using the ratio of Equations 9.2 and 9.5, d d va m ρ p = ρ 0 1 Cc χ χ C v t χvρo ( dva ) c eff ( d ) m ρ p ρ (9.6) There are also different ways to consider the effect of porosity or the presence of internal voids in a particle. Suppose there is a spherical particle made out of material with a bulk density ρ bulk, but the particle has a void in it, as suggested in Figure 9.1. One way to consider this is that the particle density is equal to the bulk material density (ρ p = ρ bulk) but the particle s dynamic shape factor is not spherical (χ 1). A second way to consider this situation is that the particle shape is spherical (χ = 1), but the density of the particle is not equal to the bulk material density of the 152

178 material (ρ p ρ bulk). Except as otherwise noted, the second interpretation will generally be used in this study. That is, the presence of internal voids will be assumed to affect a particle s density but not directly affect its dynamic shape factor. 9.3 Experimental Methods The experimental data presented in this section was collected using the ADS instrument at the Pacific Northwest National Laboratory. A diagram of the ADS apparatus is shown in Figure 9.2. A full description of the experimental apparatus is given in Beranek et al. [2012] and a brief description will be provided here. First, an aerosol flow is generated using a constant output atomizer (TSI, Model 3076) and dried using two diffusion driers (TSI Inc., Model 3062). Particles with different characteristics are then either selected or measured using the instrumentation described below. An aerosol particle mass analyzer (APM, Kanomax Inc.) can be used to select particles with a narrow distribution of masses (m). These mass selected particles will also have a narrow distribution of volume equivalent diameters because, d ve 6 m = π ρ p 1/3 (9.7) where ρ p is the particle density. It should be noted that since the APM classifies particles based on their mass-to-charge ratio, it will also select multiply charged particles whose mass is larger than the mass of the particles of interest. A differential mobility analyzer (DMA, TSI Inc., Model 3081) can be used to select particles with a narrow distribution of mobility diameters (d m), or when connected with a condensation particle counter to form a scanning mobility particle sizer (SMPS, TSI Inc., Model 3936) can measure the distribution of mobility diameters in the flow. The DMA has a similar problem as the APM, since the DMA classifies particles based on their mobility diameter-to- 153

179 charge ratio, it also selects multiply charged particles whose mobility diameter is larger than that of the particles of interest. [Hinds, 1999]. Lastly, a single particle mass spectrometer (SPLAT II, referred to as SPLAT) can be used to measure the distribution of vacuum aerodynamic diameters (d va) and characterize the chemical composition of the particles [Zelenyuk et al., 2009]. A more detailed diagram of SPLAT is shown in Figure 9.3. An aerodynamic lens inlet is first used to transport particles from ambient pressure to a vacuum and form a low-divergence particle beam where the particle velocity is directly dependent on the d va. Therefore, the d va of a particle can be determined by measuring the time it takes to travel between two points (particle time of flight). This is done by orienting two diode pumped Nd:YAG lasers (see Table 9.1) perpendicular to the particle path and focused at the first focal point of elliptical reflectors. The light scattered by the particles as they cross the laser beam, is then collected by the elliptical reflectors and refocused at the second focus of the ellipse where PMTs are located in order to detect the signal. The time difference between when the two PMTs detect the particle (time of flight) can then be used to calculate the velocity of the particle and thus the d va. This time of flight measurement is also used to generate triggers to fire lasers needed for the single particle mass spectrometer. A UV excimer laser (see Table 9.1) is used to ablate the particles generate ions. An angular reflectron time of flight mass spectrometer (modified from R.M. Jordan Inc., Model D-850) is then used to analyze the masses of the generated ions. The combination of these instruments can lead to detailed information about particle size and shape. For example, the use of the DMA and SPLAT provides information about the effective density as well as a relationship between d m and d va. If the APM and SMPS are used in series, the relationship between mass (and thus d ve) and d m can be measured as well as dynamic shape factors in the transition regime. Similarly, the APM and SPLAT can be used in series in order to measure the relationship between mass (and thus d ve) and d va as well as dynamic shape 154

180 factors in the free molecular regime. The use of the APM, DMA, and SPLAT is referred to here as the ADS and can yield more detailed information about shape factors for size and mass selected particles. 9.4 Experimental Results Size distributions for the aerosolized quartz sample are shown in Figure 9.4 and Figure 9.5 in terms of the measured mobility diameter and the vacuum aerodynamic diameter, respectively Mobility Selected Particles In this section, the aerosol particle flow is first directed to the DMA to select the mobility diameter and then sent to SPLAT for measurements of the vacuum aerodynamic diameter. An example of the measured distribution of vacuum aerodynamic diameters from a flow of mobility selected particles is shown in Figure 9.6. As mentioned in the previous section, multiply charged particles are also selected by the DMA which can be seen as the second peak at larger d va values. It should be noted that doubly charged particles are still present in the distributions with d m > 313nm, however, this contribution is small compared to the number of singly charged particles at those larger selected mobility diameters. It is also clear in Figure 9.6 that the relative widths (measured FWHM/d va) of the d va distributions (for the singly charged particles) increase with selected mobility diameter. A broader d va distribution of selected particles can indicate several things. First, it can indicate that the particles have a wider range of dynamic shape factors. It can also indicate that the particles, as a whole, are more aspheric because the time-of-flight will vary depending on the orientation of the non-spherical particle in the inlet. Lastly, a broad d va distribution of selected particles can also be indicative of the particles having a distribution of densities, possibly due to varying porosity. The relationship between mobility and vacuum aerodynamic diameter for mobility 155

181 selected particles is derived using data from Figure 9.6 and shown in Figure 9.7 in magenta. Note that the non-linearity of this relationship suggests that the rate of increase in d va with d m significantly decreases with increasing particle size. Because the selected mobility diameter is in the transition regime and the vacuum aerodynamic diameter is in the free molecular regime, and the volume equivalent diameter is unknown, the dynamic shape factors cannot be determined from these measurements alone. However, the d m vs. d va data can be used to calculate the effective density of the particle, ρ eff, using Equation 9.6. A plot of the effective density for mobility selected particles is shown in Figure 9.8. As seen in the figure, the effective density has an negative linear relationship to mobility diameter, decreasing from ρ eff(d m ~ 151nm) ~2 to ρ eff(d m ~ 600nm) ~1. These values are significantly different from the bulk density of quartz, ρ bulk = 2.65g/cm 3, even at small mobility diameters. This suggests that the shape factors are significantly different from 1 (spheres). In addition, the decrease in the effective density also suggests that either the shape factors increases (more aspherical particles) or the particle density decreases as the mobility diameter increases (voids). It should be noted that the vertical bars shown in Figure 9.8 represent the width of the measured d va values and not experimental errors. Again, the relative width of the d va distributions, and height of the bars shown in Figure 9.8, can indicate that the particles are more aspheric, have a larger range of particle shapes, or that the particles contain internal voids Mass Selected Particles In this section, an APM is used to select particles with narrow distribution of masses (and thus d ve); then the flow is directed to either an SMPS for measurements of the mobility diameter or SPLAT for measurements of the vacuum aerodynamic diameter. An example of the measured distribution of mobility diameters and vacuum aerodynamic diameters from a flow of mass selected particles is shown in Figure 9.9a and b, respectively. As previously mentioned, multiply 156

182 charged particles are also selected by the APM. These multiply charged particles will have smaller mobility diameters and can be seen as the smaller peaks in Figure 9.9a. Distributions shown in Figure 9.9b also contain multiply charged particles but the multiply charged peaks are less distinct than in the d m distributions. The measured mode mobility and vacuum aerodynamic diameters from these distributions are listed in Table 9.2 and plotted as a function of selected mass in Figure 9.10, which shows the non-linearity in this relationship. In addition, since the masses are known (selected), the volume equivalent diameter, d ve can be calculated using Equation 9.6, assuming the particle density, ρ p, is known or can be approximated by the density of the bulk material (as is done here). The relationships between the volume equivalent diameter and the measured vacuum aerodynamic and mobility diameters are shown in Figure The data in Table 9.2 also provides information about the relationship between mobility and vacuum aerodynamic diameter for mass selected particles. This relationship between d m and d va for mass selected particles (cyan) is compared to the same relationship for mobility selected particles (magenta) in Figure 9.7. The difference between the two sets of data is that the magenta points are measurements from particles with a narrow distribution of d m while the cyan points are measurements from particles with a narrow distribution of masses. This difference is very small for smaller particles, but begins to diverge as the particles become larger. Furthermore, since d ve is known (mass is selected), χ t and χ v can be calculated using Equations 9.2 and 9.5 and are listed in Table 9.2. The calculated dynamic shape factors are plotted as a function of selected mass and volume equivalent diameter in Figure and lie in the range χ t = and χ v = Figure 9.12 shows that the dynamic shape factors in the vacuum regime are larger than in the transition regime for all particle masses in this study. In addition, the dynamic shape factors in both regimes increase with particle mass. However, the exact relationships are quite different in the different regimes. In the free molecular 157

183 regime, the dynamic shape factor appears to increase nearly linearly with mass while the relationship between χ t and mass in the transition regime is non-linear. However, if the mass is converted to volume equivalent diameter, the relationship between vacuum dynamic shape factor and diameter becomes linear as seen in Figure While the volume equivalent diameter is an intrinsic characteristic of the particle, independent of flow regime, it does depend on assumptions about the particle density. Therefore the shape factors are also compared to the corresponding diameter measurements in Figure Regardless of how the shape factors are plotted, Figure all show very clearly that the dynamic shape factors, in both regimes, increase with increasing particle size/mass. This again indicates that larger particles are more aspherical. However, it is important to note that this conclusion rests on the assumption that particle density or void fraction is constant, independent of particle size. In addition, Figure also show that not only do the dynamic shape factors not equal each other in the different flow regimes, but they also vary differently as a function of particle size. Therefore the relationship between the dynamic shape factors in the transition and free molecular regime is further explored in Figure ADS Selected Particles In this section, particles were first mass selected using the APM, then mobility selected using the DMA, and then directed to SPLAT for measurements of the vacuum aerodynamic diameter. By selecting particles with a narrow distribution of masses (and thus d ve) and mobility diameters (referred to as ADS selected) the particle flow after the DMA will contain particles with a narrow distribution of masses and shape factors in the transition regime (assuming all particles have a uniform density). Then, the measurements of the aerodynamic diameter will yield information on the dynamic shape factors of mass and mobility selected particles in two flow 158

184 regimes. It should be noted that while mass selected particles have a narrow distribution of volume equivalent diameters, they can have a wide distribution of particle shapes that results in large relative widths of the mobility and vacuum aerodynamic diameters (Figure 9.9). However, by also selecting the particles by mobility diameter, the particles will have a narrow distribution of volume equivalent diameters and shape factors in the transition regime. At each selected mass (20, 40, 80 and 120fg), the peak and each side of the distribution of mobility diameters were selected as shown in Figure 9.16 and listed in Table 9.3. This allows for information regarding the range of particle shapes included in the ADS aerosol flow. Experimental results for mass and mobility selected particles for quartz aerosol are shown in Table 9.3. Calculated dynamic shape factors, as a function of selected mass are shown in Figure It should be noted that the vertical bars represent the breadth of measured dynamic shape factors and not the experimental error. These dynamic shape factors are also shown as a function of selected mobility diameter in Figure Again the three points for each selected mass shows the breadth of shapes that are present in the aerosol flow for mass selected particles. This data clearly shows that quartz particles with a narrow distribution of masses can have a wide range of particle shapes. 9.5 Conclusions The results for quartz dust clearly shows that dynamic shape factors, and thus particle asphericity increases with particle mass and size. Measured dynamic shape factors for mass selected particles range from as the mass increases from fg in the transition regime and from as the mass increases from 2.5fg to 120fg in the free molecular regime. Similar results were observed by selecting particles both by the mass and mobility diameters. It is also clear that the measured dynamic shape factors depend on flow regime, and assuming χ t = χ v is not a good approximation for quartz aerosol. In addition, the data shows that quartz particles have a wide distribution of dynamic shape factors, even for particles with a 159

185 narrow distribution of masses. The data presented in this chapter yield information on the dynamic shape factors of quartz particles. While the magnitude of dynamic shape factors gives a measure of particle asphericity, it does not directly give information about the 3D particle shape. Instead, the dynamic shape factors reflect the particle behavior in different flow regimes. However, the following conclusions are given in an attempt to compare the measurements in this chapter with three dimensional shapes, specifically spheroids as used in the optical properties measurements in Chapters 5-8. In order to compare these measured dynamic shape factors to the spheroidal shape distributions found by fitting the optical properties of quartz dust in Section and from the work by Meland et al. [2010], dynamic shape factors in both the continuum regime [Fuchs, 1964; Davies, 1979] and free molecular regime [Dahneke, 1973; DeCarlo et al., 2004] are listed in Table 9.4. As seen in the table, the measured dynamic shape factors in the free molecular regime (χ v ) correspond to ξ (oblate spheroids with AR 6-11) and ξ (prolate spheroids with AR 6 16). These spheroidal shape factors are quite a bit larger than those included in the modeling analysis of Section and Meland et al. [2010]. It should be noted that larger shape factors were not included in the optical modeling because of convergence limitations of the T-matrix code at visible wavelengths. It is possible that including larger shape factors in the optical properties modeling could give better agreement with experimental data. In the transition regime, if one assumes that χ t lies between χ v and χ c, then the measured dynamic shape factors in the transition regime (χ t ) can be compared to spheroidal shape factors by interpolating Table 9.4. This interpolation leads to a corresponding range of spheroid shape parameters ξ (oblate spheroids with AR 3 8) and ξ -2-6 (prolate spheroids with AR 3 7). These values are much closer to the spheroidal shapes found 160

186 in the modeling analysis of Section and Meland et al. [2010], both of which are in the transition and continuum regime (depending on the size of the particle). Other studies have also measured the dynamic shape factors of quartz particles. For example, χ c = 1.36 was measured for particles less than 10µm in the continuum regime by measuring the rate of particles falling in liquid [Cartwright, 1962; Davies, 1979]. This corresponds to spheroids with ξ -5 and +6 or AR 6 (prolate) and 7 (oblate). Another study found that χ = (regime not specified) for particles ~ 1µm, which is much closer to the size range of particles used in this study [Davies, 1979]. Regardless of the flow regime, it seems that the spheroidal AR corresponding to both the dynamic shape factors (measured here, as well as other sources) and optical properties fittings are quite different from the particle shapes inferred from SEM images and micrographs. For example, Meland et al. [2010] analyzed SEM images of quartz aerosol and found that AR were limited to values less than 3. Indeed, the quartz particles shown in the micrographs in Davies [1979] from Kotrappa [1971] and Cartwright [1962] appear to consistently show AR 3. As suggested for the optical shape factors, it is possible that surface roughness and angular edges could also affect the aerodynamic properties of particles which are aerodynamically equivalent to a spheroid with a much larger AR than physically observed. 161

187 Table 9.1 Information regarding the lasers used in SPLAT II. Laser Source Wavelength Pulse Width Power Nd:YAG Excimer CrystaLaser, Model GCL-300 GAM Lasers Inc., Model EX5 532nm CW 300mW 193nm 15ns 1-10mJ/pulse Table 9.2 Experimental results for mass selected particles. Corresponding graphs are shown in Figures Selected Mass (fg) dve (nm) Measured dm (nm)* χt Measured dva (nm)* χv *Mode diameters of the measured distributions 162

188 Table 9.3 Experimental results for ADS selected particles. Selected Mass (fg) dve (nm) Selected dm (nm) χt Measured dva (nm)* χv *Mode diameters of the measured distributions

189 Table 9.4 Dynamic shape factors for spheroidal particles in the vacuum and continuum regime. Values for χ v were taken from Davies [1979], and values for χ c were calculated from the dimensionless drag coefficients in Dahneke [1973]. Dpolar/Dequitorial Axial Ratio ξ χv χc

190 Figure 9.1 Conceptual illustration of methods to consider the dynamic shape factor and particle density for particles with internal voids. Figure 9.2 Diagram of the ADS instrument. Dry Air Atomizer Diffusion Dryer Aerosol Particle Mass Analyzer (APM) Single Particle Mass Spectrometer (SPLAT II) Differential Mobility Analyzer (DMA) 165

191 Figure 9.3 Diagram of the SPLAT II instrument. Composition Measurement Mass Spectrometer Aerodynamic Diameter Measurement PMT 2 PMT 1 Aerodynamic Lens Inlet UV Excimer Laser Visible Nd:YAG Lasers 166