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Measurements of diffusion coefficients of organic dyes in proxies of atmospheric particles Ullmann, Dagny Anna 2017

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MEASUREMENTS OF DIFFUSION COEFFICIENTS OF ORGANIC DYES IN PROXIES OF ATMOSPHERIC PARTICLES by  Dagny Anna Ullmann  B.Sc., Christian-Albrechts-Universität zu Kiel, 2013  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Chemistry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  June 2017  © Dagny Ullmann, 2017 ii  Abstract Atmospheric particles play a significant role in the atmosphere and climate. To be able to better predict their rate of growth and reactivity, information on diffusion coefficients of organic molecules in these particles is needed. Diffusion coefficients of organic tracer molecules were measured in sucrose water solu-tions, which served as proxies for atmospheric particles. Diffusion coefficients of rhodamine 6G (hydrodynamic radius = 5.89 Å), an organic tracer molecule, ranged from 1.50∙10-14 to 4.73∙10-9 cm2/s as the water activity ranged from 0.38 to 0.8, respectively, in sucrose water so-lutions. The measured diffusion coefficients were compared to diffusion coefficients calculated using the Stokes-Einstein equation, which has often been used in the past to estimate diffusion coefficients in atmospheric particles. A breakdown of the Stokes-Einstein equation was ob-served at a water activity of 0.38 or a viscosity of 3.3∙106 Pa s or Tg/T of 0.94 (Tg being the glass transition temperature and T the temperature of the measurement). In addition, diffusion coefficients of intrinsic fluorophores were measured in brown lim-onene secondary organic material (SOM) which is thought to be important in the atmosphere. The SOM was generated by the oxidation of limonene followed by aging with NH3 vapour. The diffusion coefficients of the intrinsic fluorophores in brown limonene SOM ranged from 3.82∙10-12 to 8.32∙10-9 cm2/s as the water activity ranged from 0.38 to 0.9. From the diffusion coefficients mixing times of large organics in brown limonene SOM were calculated, which ranged from 0.001 to 2.6 s across water activities of 0.9 and 0.38. Hence, mixing times of large iii  organics are short and atmospheric particles consisting of brown limonene SOM are well mixed in the atmosphere when water activities range from 0.38 to 0.9. Furthermore, the hydrodynamic radius of the intrinsic fluorophores within brown limo-nene SOM was determined to be 7.34 ± 1.47 Å. This hydrodynamic radius is consistent with suggested structures for the intrinsic fluorophores.   iv  Lay Summary How will the climate change in the future? Climate researchers have developed models to an-swer that question and predict climate change accurately. The research conducted in this thesis is providing information on atmospheric particles (particles suspended in air) to improve cli-mate models. Atmospheric particles can either cool down climate by scattering sunlight or can heat up climate by absorbing sunlight. The knowledge of growth rates and reactivity of atmos-pheric particles is needed to improve the quality of climate models. Growth rates and reactivity of atmospheric particles depend on the mobility of molecules inside an atmospheric particle, which can be measured in terms of diffusion coefficients. In this thesis, diffusion coefficients of organic molecules within proxies of atmospheric particles were determined. Using the diffusion coefficients, mixing times of large organic molecules and the radius of a diffusing molecule un-known prior to this study was calculated. v  Preface Chapter 2 is part of a co-authored peer-reviewed journal article. The details of my contribution are provided below the citations: Chapter 2 (Second author on a journal article): Chenyakin, Y., Ullmann, D. A., Evoy, E., Ren-baum-Wolff, L., Kamal, S., and Bertram, A. K.: Diffusion coefficients of organic molecules in su-crose–water solutions and comparison with Stokes–Einstein predictions, Atmos. Chem. Phys., 17, 2423-2435, doi:10.5194/acp-17-2423-2017, 2017.  Prepared samples of R6G in sucrose water solutions and performed fluorescence recov-ery after photobleaching experiments on these samples  Conducted data analysis with the help of Dr. Saied Kamal  Writing of the text regarding the experiments on R6G was shared with my supervisor  Contribution of other authors: o Y. Chenyakin and A.K. Bertram identified the research question and developed the experimental setup and wrote the main body of the publication o Y. Chenyakin performed experiments on calcein and fluorescein and conducted data analysis with the help of Dr. Saied Kamal  Chapter 3 and 4 are to be submitted for publication. The details of my contributions to these research chapters are provided below:  Identified research question with help from my supervisor vi   SOM samples were produced by Mallory Hinks from the Department of Chemistry, Uni-versity of California, Irvine, CA, USA  Designed additional experimental setup for the preparation of R6G samples  Prepared samples of SOM at various relative humidities  Performed fluorescence recovery after photobleaching experiments  Conducted data analysis with the help of Dr. Saied Kamal  Prepared all figures for the manuscript  Shared writing of the manuscript with my supervisor  Prof. Allan Bertram and Dr. Saied Kamal derived the correction for fluorescence data of the fluorescent organic molecule in brown limonene SOM  vii  Table of Contents  Abstract ................................................................................................................................ ii Lay Summary .........................................................................................................................iv Preface .................................................................................................................................. v Table of Contents ................................................................................................................. vii List of Tables ........................................................................................................................ xii List of Figures ....................................................................................................................... xv List of Symbols .................................................................................................................. xxiii List of Acronyms ................................................................................................................ xxvi Acknowledgements .......................................................................................................... xxvii Chapter 1: Introduction ......................................................................................................... 1 1.1 Atmospheric Particles ..................................................................................................... 1 1.1.1 Formation, Composition and Sizes ............................................................................. 1 1.1.2 Effects of Atmospheric Particles on Humans and Climate ......................................... 2 1.2 The Importance of Molecular Motion Within Atmospheric Particles ............................ 4 1.3 Theories of Molecular Motion ........................................................................................ 6 1.4 Overview of this Thesis ................................................................................................... 7 Chapter 2: Diffusion Coefficients of Rhodamine 6G in Sucrose Water Solutions, a Proxy for Atmospheric Particles ............................................................................................................ 9 2.1 Introduction .................................................................................................................... 9 viii  2.2 Experimental ................................................................................................................. 12 2.2.1 Sample Preparation .................................................................................................. 12 2.3 Introduction to Fluorescence Recovery After Photobleaching (FRAP)......................... 17 2.3.1 FRAP Measurements ................................................................................................. 18 2.3.2 Analysis of the FRAP Data ......................................................................................... 20 2.3.3 Cylindrical Geometry of the Photobleaching Region................................................ 26 2.3.4 Corrections for Nonlinearity of the Fluorescence Intensity as a Function of Concentration of R6G ........................................................................................................... 27 2.4 Results and Discussion .................................................................................................. 33 2.4.1 Diffusion Coefficients of R6G in Sucrose Water Solutions ....................................... 33 2.4.2 Breakdown of the Stokes-Einstein Equation ............................................................ 33 2.4.3 Comparison with Diffusion Coefficients of Other Molecules in Sucrose Water Solutions................................................................................................................................ 36 2.4.4 Breakdown of the Stokes-Einstein Equation for Molecules of Different Hydrodynamic Radii .............................................................................................................. 37 Chapter 3: Diffusion Coefficients and Mixing Times of Fluorescent Organic Molecules in Brown Limonene Secondary Organic Material ................................................................................. 41 3.1 Introduction .................................................................................................................. 41 3.2 Experimental ................................................................................................................. 44 3.2.1 Generation and Collection of Brown Limonene SOM .............................................. 44 ix  3.2.2 Preparation of Thin Films of Brown Limonene SOM at Water Activities Ranging from 0.38 to 0.9 .................................................................................................................... 45 3.2.3 Measurements of Diffusion Coefficients Using rFRAP ............................................. 46 3.2.4 Analysis of the Images from the rFRAP Recovery Experiments ............................... 48 3.2.5 Effect of Laser Power on Measured Diffusion Coefficients ...................................... 52 3.2.6 Corrections for Non-linearity of the Fluorescence Intensity as a Function of Concentration of the Intrinsic Fluorophores ........................................................................ 52 3.3 Results and Discussion .................................................................................................. 55 3.3.1 Diffusion Coefficients of Intrinsic Fluorophores within Brown Limonene SOM ...... 55 Chapter 4: The Hydrodynamic Radius of Intrinsic Fluorophores in Brown Limonene SOM ..... 59 4.1 Introduction .................................................................................................................. 59 4.2 Experimental ................................................................................................................. 60 4.2.1 Preparation of Brown Limonene SOM Samples at Water Activities of 0.7, 0.8 and 0.9…….. .................................................................................................................................. 60 4.2.2 Introduction of R6G into Brown Limonene SOM Samples ....................................... 61 4.2.3 rFRAP Experiments: Measurements of Diffusion Coefficients of R6G and the Intrinsic Fluorophores in Brown Limonene SOM .................................................................. 63 4.2.4 Analysis of rFRAP Images Recorded for the Samples Containing R6G ..................... 64 4.2.5 Correction for Reversible Photobleaching ................................................................ 66 4.2.6 Corrections for Non-linearity of Fluorescence Intensity as a Function of Concentration of R6G ........................................................................................................... 66 x  4.3 Results and discussion .................................................................................................. 70 4.3.1 Example of Experimental Data.................................................................................. 70 4.3.2 Measured Diffusion Coefficients of the Intrinsic Fluorophores in Brown Limonene SOM….. .................................................................................................................................. 73 4.3.3 Measured Diffusion Coefficients of R6G in Brown Limonene SOM ......................... 74 4.3.4 Calculation of the Hydrodynamic Radius of Intrinsic Fluorophores in Brown Limonene SOM ...................................................................................................................... 75 4.3.5 Comparison with Previous Suggestions of the Molecular Structures and Formulas for the Light Absorbing Compounds and Intrinsic Fluorophores in Brown Limonene SOM 76 Chapter 5: Conclusion and Future Work ............................................................................... 78 5.1 Measurement of Diffusion Coefficients in Proxies of Atmospheric Particles .............. 78 5.2 Average Hydrodynamic Radius of the Intrinsic Fluorophores in Brown Limonene SOM….. ...................................................................................................................................... 79 5.3 Consideration of Future Work ...................................................................................... 79 Bibliography ........................................................................................................................ 81 Appendices ......................................................................................................................... 97 Appendix A ................................................................................................................................ 97 A.1 Parameterization of the viscosity of sucrose in water as a function of water activity… ................................................................................................................................ 98 A.2 Determination of water activities of sucrose solutions ............................................ 99 A.3 Polynomial fit for diffusion coefficients of water from Price et al. .......................... 99 xi  Appendix B .............................................................................................................................. 100 Appendix C .............................................................................................................................. 101  xii  List of Tables  Table 2.1: Information on rhodamine 6G (R6G) including the molecular weight (MW), the chemical structure and the hydrodynamic radius. ....................................................................... 12 Table 2.2: Saturated salt solutions used for conditioning and storing samples at specific water activities in sealed glass jars. ........................................................................................................ 15 Table 2.3: Best fit parameters for concentration vs. normalized fluorescence intensity data in Figure 2.10. c = c0 + A ∙ eB ∙ x, where c is the concentration and x is the normalized fluorescence intensity. The R2 value indicated the quality of the fit. .......................................... 30 Table 2.4: Hydrodynamic radius (RH) and molecular weight (MW) of several molecules considered in this work. ................................................................................................................ 36 Table 2.5: Properties of the molecules shown in Figure 2.15. ..................................................... 39 Table 3.1: Physico-chemical data on limonene including the molecular weight (MW) and the molecular structure. ..................................................................................................................... 42 Table 4.1: Parameterization of the data shown in Figure 4.4. ..................................................... 69 Table 4.2: Average and 95 % confidence intervals of the diffusion coefficients of R6G (D(R6G)) to the diffusion coefficient of the intrinsic fluorophores(D(SOM)) in brown limonene SOM at three different water activities. .................................................................................................... 76 Table 5.1: Diffusion coefficients of R6G in sucrose-water solutions and the intrinsic fluorophores in brown limonene SOM. .............................................................................................................. 78 xiii  Table 5.1: Selected parameters used in rhodamine 6G rFRAP experiments in sucrose water solutions. eq is the characteristic diffusion time of water within sucrose-water droplet (see Eq. 2.1). texp is the time used for conditioning.................................................................................... 97 Table 5.2: Fit parameters of the third order polynomial fit (f(x) =A+ Bx + Cx2 + Dx3) in Figure 5.1........................................................................................................................................................ 98 Table 5.3: Parameters from the polynomial fit in Figure 2.14 with f(x)=A+Bx+Cx2+Dx3 based on Price et al.31 ................................................................................................................................... 99 Table 5.4: Selected parameters used in rFRAP experiments with the intrinsic fluorophores in brown limonene SOM. eq is the characteristic diffusion time of water within sucrose-water droplet (see Eq. 2.1). texp is the time used for conditioning. ...................................................... 100 Table 5.5: Values of diffusion coefficients, fluorescence intensities and calculated concentrations in citric acid water solution and sucrose water solution for 90% RH of R6G in brown limonene SOM.eq is the characteristic diffusion time of water within sucrose water droplet (see Eq. 2.1).  texp is the time used for conditioning. ..................................................... 101 Table 5.6: Values of diffusion coefficients, fluorescence intensities and calculated concentrations in citric acid water solution and sucrose water solution for 80% RH of R6G in brown limonene SOM. eq is the characteristic diffusion time of water within sucrose water droplet (see Eq. 2.1). texp is the time used for conditioning. ...................................................... 103 Table 5.7: Values of diffusion coefficients, fluorescence intensities and calculated concentrations in citric acid water solution and sucrose water solution for 70% RH of R6G in xiv  brown limonene SOM. eq is the characteristic diffusion time of water within sucrose-water droplet (see Eq. 2.1).  texp is the time used for conditioning. ..................................................... 104  xv  List of Figures  Figure 1.1: Formation and removal processes and classification of atmospheric particles. ......... 2 Figure 1.2: Schematic of the formation of atmospheric particles and their effects on the climate. Based on Renbaum-Wolff et al. (2013).8 ........................................................................................ 3 Figure 1.3: Radiative forcing of climate forcing species including their uncertainties. Reproduced with permission from Stocker et al. (2013).10 ................................................................................ 4 Figure 1.4: Illustration of the influence of diffusion rates on heterogeneous reactions within atmospheric particles. Reproduced with permission from Lindsay Renbaum-Wolff et al., “Viscosity of α-pinene secondary organic material and implications for particle growth and reactivity”, PNAS, 2013, 110 (20), 8014-8019; doi: 10.1073/pnas.1219548110............................ 5 Figure 2.1: Schematic of the flow cell used to condition samples to the desired water activities........................................................................................................................................................ 14 Figure 2.2: Schematic of the glass jar used to condition samples of water activities below 0.6. 14 Figure 2.3: Schematic of the sample used in the FRAP experiments. Panel a) is a top view and Panel b) is a side view. The sample consists of sucrose, water and trace amounts of the fluorescent tracer dye, rhodamine 6G. ........................................................................................ 16 Figure 2.4: Schematic illustrating the photobleaching and diffusion process of fluorescent molecules. Shown is a side view of the sample cell at various times t during the rFRAP experiment. See text for further details. ...................................................................................... 18 xvi  Figure 2.5: Schematic of a fluorescent film (view from top) and its bleached area. A section of a fluorescent film is scanned in the x- and y-direction. A defined rectangular area (bleached area) of the length lx and the width ly is photobleached. .................................................................... 19 Figure 2.6: A fluorescent film consisting of a sucrose-water solution (aw=0.75) and R6G viewed using a laser scanning microscope. Panel A) shows the fluorescent film prior to photobleaching. Panel B) to F) show the recovery of the fluorescence signal over time t. Panel B) was taken directly after the photobleaching process at time 0s, whereas panel F) shows the fluorescent film after 700s after the photobleaching step. The orange rectangle represents the area that was chosen for photobleaching. ................................................................................................... 24 Figure 2.7: Plots of fluorescent intensity as a function of x-position, integrated over all y-positions of an aw of 0.75. Panel A is an image taken directly after photobleaching and panel B) to D) show the recovery of the fluorescence intensity due to diffusion. The red line is a fit using Equation 2.8. ................................................................................................................................. 25 Figure 2.8: Plot of 𝑤𝐷, 𝑡, 𝑟 as a function of time t for a film of a solution containing R6G, sucrose and water of aw=0.75. Every blue circle represents a value of 𝑤𝐷, 𝑡, 𝑟 obtained from fits to the experimental data, such as shown in from Figure 2.7. The red line is a linear plot to the data. Since 𝑤𝐷, 𝑡, 𝑟 = 𝑟2 + 4𝐷𝑡, the diffusion coefficient could be calculated from the slope of the line. The first 50s have been excluded from the analysis because of reversible photobleaching........................................................................................................................................................ 26 xvii  Figure 2.9: Cross section through a fluorescent film at aw=0.38 after photobleaching. The photobleached areas have a size of 5x5 µm (a) and 20x20 µm (b). The fluorescent films were about 70 µm thick. ........................................................................................................................ 27 Figure 2.10: Fluorescence intensity as a function of the concentration of R6G in sucrose-water solutions, for concentrations in a 50 wt % sucrose-water solution. ............................................ 28 Figure 2.11: Concentration of R6G in mM as a function of fluorescence intensity. The red line is a nonlinear fit to the data using an exponential function. ........................................................... 29 Figure 2.12: Illustration of the choice of droplets used for the experiment on reversible photobleaching. Panel a) shows the droplet which is to be photobleached (red circle) and the reference droplet (blue dashed circle) prior to photobleaching and panel b) shows both droplets after photobleaching. ................................................................................................................... 31 Figure 2.13: The fluorescence intensity-versus-time for two droplets used to test for reversible photobleaching. A sucrose-water droplet containing R6G of aw=0.6 was photobleached over its total area, so that its fluorescence intensity decreased by 18%. While the recovery of the photobleached droplet (blue triangles) was monitored a reference droplet (green crosses) not being photobleached was also monitored. For the analysis of the recovery, the fluorescence intensity was averaged across the complete droplet. .................................................................. 32 Figure 2.14: Shown are the diffusion coefficients of R6G in sucrose water solution in comparison to diffusion coefficient values calculated from viscosities from Quintas et al. (2006; blue triangles)46, Migliori et al. (2007; blue crosses)47, Telis et al. (2007 ; blue circles)48 and Power et al. (2013 ; blue rectangles)15e using the Stokes-Einstein equation and the RH measured by Müller xviii  et al. (2008)24. The error bars for the diffusion coefficients of R6G represent 95% confidence limit, while the red star itself represent the average value of the diffusion coefficients measured. The black solid line represents a 4th order polynomial which was fit to the literature values. The dashed line represents the 95% prediction limit that was fit to the calculated diffusion coefficients. .................................................................................................................... 35 Figure 2.15: Shown are the diffusion coefficients of fluorescein, calcein (data used from Y. Chenyakin32), water (data used from Price et al.31) and R6G in sucrose water solutions. The error bars in x-direction are 95% confidence intervals. ............................................................... 37 Figure 2.16: Dmeasured/Dpredicted as a function of Rdiffusing/Rmatrix. Panel A corresponds to aw=0.6 and Panel B aw=0.38. Dmeasured is the measured diffusion coefficient and Dpredicted is the predicted diffusion coefficient. Rdiffusing is the hydrodynamic radius of the diffusing species and Rmatrix is the hydrodynamic radius of the matrix molecule (sucrose) (Ribeiro et al. (2006)25. The data for calcein and fluorescein was taken from Chenyakin et al. (2016)16b, the data for sucrose was taken from Price et al. (2016)52. In order to calculate Dpredicted using the Stokes-Einstein equation, a parameterization for the viscosity of sucrose water solution was used (see Appendix A). The error bars for all of the data points were calculated conservatively using the largest error possible for Dmeasured as well as Dpredicted  and the total error was determined using a Gaussian error propagation. ......................................................................................................... 40 Figure 3.1: Simplified suggested reaction mechanism for the formation of larger organic molecules, which have the potential to be light absorbing in the UV- and the visible light range, from limonene (Nguyen et al. (2013)).58 ...................................................................................... 42 xix  Figure 3.2: Preparation of the SOM samples from the reaction of limonene with O3. The orange circles represent SOM particles. ................................................................................................... 45 Figure 3.3: Images recorded during an rFRAP experiment with brown limonene SOM at three different water activities: 0.38, 0.6 and 0.9. The orange rectangles depict the area that is to be photobleached. Indicated in the figures are the times (t) after photobleaching. ....................... 48 Figure 3.4: Fluorescence intensities integrated over the bleach width in the y-direction as a function of x-position (in pixels) for selected brown limonene SOM films at aw = 0.38, 0.6 and 0.9. The blue dots represent the intensity measurements and the red line is a fit to the data using Equation 2.8......................................................................................................................... 50 Figure 3.5: Plot of 𝑤𝐷, 𝑡, 𝑟 = 𝑟2 + 4𝐷𝑡as a function of time. The blue circles represent the data which was obtained from figures such as Figure 3.4. The red line is a linear fit to the data. The diffusion coefficients were obtained from the slopes and are D= 0.0007792/4= 0.0001948 µm2/s=1.95∙10-12 cm2/s for aw=0.0.38, D= 0.04189/4= 0.0105 µm2/s=1.05∙10-10 cm2/s for aw=0.6 and D= 3.753/4= 0.938 µm2/s=9.38∙10-9 cm2/s for aw=0.9. .......................................................... 51 Figure 3.6: Diffusion coefficients of intrinsic fluorophores in brown Limonene SOM (black squares). The y-error bars were calculated from the 95% confidence limit. The grey solid line is a linear fit to the data and the grey dotted line the 95% prediction limit of the fit. The blue vertical bar depicts the highest and the lowest limit of calculated diffusion coefficients of brown limonene SOM (reacted with NH3) based on viscosity measurements from Hinks et al. (2016). The secondary y-axis shows the mixing time, which is the time that would be needed for intrinsic fluorophores to mix within a 200 nm brown limonene particle. ................................... 57 xx  Figure 4.1: Schematic illustrating the introduction of R6G into pure brown limonene SOM particles. First, the dye is nebulized onto a glass slide (panel a). Then, the dye is removed from half of the glass slide (panel b). The nebulized glass slide containing R6G is placed on top of a glass slide containing brown limonene SOM droplets and the two glass slides are sandwiched together (panel c). The resulting sample has both SOM films with R6G and without R6G (panel d). .................................................................................................................................................. 62 Figure 4.2: Schematic illustrating the subtraction of fluorescence intensities of images of pure brown limonene SOM from images of brown limonene SOM films containing R6G. Panel a) shows the image of a fluorescent film consisting of R6G in brown limonene SOM at t=0 s, panel b) shows the image of a fluorescent film consisting of pure brown limonene SOM and panel c) shows an image that was produced by subtracting the fluorescent intensity of pure brown limonene SOM from the fluorescence intensity of a brown limonene SOM film containing R6G. Panels e) to g) show the corresponding profiles to the images of panels a) to c). ...................... 65 Figure 4.3: Integrated intensity as a function of the concentration of R6G in various media: citric acid in water (55 wt %), sucrose in water (50 wt %) and pure water. Experiments were carried out with a laser power of 4.08 µW. The open and solid symbols depict measurements performed on two different days to confirm reproducibility of the measurements. For citric acid and sucrose water solutions measurements were performed on two different days and for R6G in water only one measurement was performed. The error bars represent one standard deviation (1σ) obtained from three different measurements. .................................................... 68 xxi  Figure 4.4: Concentration of R6G (mM) as a function of integrated intensity in various media, citric acid in water (55 wt %), sucrose in water (50 wt %) and pure water. The solid lines are plots describing the trend of the data. The open and the solid symbols depict measurements performed on two different days to confirm reproducibility of the measurements. This plot is based on the data from Figure 4.3. .............................................................................................. 69 Figure 4.5: Fluorescence intensities as a function of distance in the x direction (in pixels) for selected films of R6G in brown limonene SOM at aw = 0.7, 0.8 and 0.9. The blue dots represent the intensity data and the red curve is a fit to the data using Eq. 2.8. Before the fit was applied, the fluorescence intensity data was normalized to an image taken prior to photobleaching. ... 71 Figure 4.6: Plot of 𝑤𝐷, 𝑡, 𝑟 = 𝑟2 + 4𝐷𝑡 as a function of time. The blue open circles represent experimental data, which was obtained from figures such as those in Figure 4.5. The red line is a linear fit to the data. The diffusion coefficients were obtained from the slopes and are. The diffusion coefficients are D= 0.0583 µm2/s=5.83∙10-10cm2/s, 0.1182 µm2/s=1.18∙10-9 cm2/s and 0.8292 µm2/s=8.29∙10-9 cm2/s for aw = 0.7, 0.8 and 0.9, respectively. ......................................... 72 Figure 4.7: Comparison of diffusion coefficients of the intrinsic fluorophores in brown limonene SOM measured for this chapter (to determine the hydrodynamic radius of the intrinsic fluorophores (green rectangles)) with diffusion coefficients of the intrinsic fluorophores measured in Chapter 3: (black rectangles). The symbols are average values and the error bars depict the 95% confidence limit. .................................................................................................. 74 Figure 4.8: Comparison of diffusion coefficients of R6G in brown limonene SOM (blue rectangles) with diffusion coefficients of the intrinsic fluorophores in brown limonene SOM xxii  (green rectangles) determined in this chapter for the radius calculations. The symbols are the average values and the error bars give the 95% confidence limit. .............................................. 75 Figure 5.1: Parameterization of the viscosity as a function of water activity for sucrose water solutions using viscosity data from several sources. .................................................................... 98  xxiii  List of Symbols 𝑎𝑤   water activity 𝑐  concentration [µM, mM] 𝑐1  concentration prior to photobleaching 𝑐2  concentration after photobleaching 𝑐𝑁  normalized concentration 𝐷𝑝  particle diameter [Å] 𝐷  diffusion coefficient [cm2/s] 𝐷𝑤𝑎𝑡𝑒𝑟  diffusion coefficient of water [cm2/s] 𝐷𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 measured diffusion coefficients [cm2/s] 𝐷𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 diffusion coefficients predicted using the Stokes-Einstein equation [cm2/s] 𝐷(𝑅6𝐺) diffusion coefficient of Rhodamine 6G [cm2/s] 𝐷(𝑆𝑂𝑀) diffusion coefficient of the fluorescent organic molecule in brown limonene SOM [cm2/s] 𝜖  extinction coefficient 𝜂  dynamic viscosity [Pa s] erf(𝑥)  error function   𝐹  fluorescence intensity 𝐹0  fluorescence intensity prior to photobleaching 𝐹𝜆  fluorescence intensity of a material at a certain excitation wavelength 𝐹𝑁  fluorescence intensity normalized to 𝐹0 xxiv  𝐼0  intensity of incoming light 𝐼  intensity of outgoing light 𝐽  flux of particles 𝐾0  effective bleach depth 𝑘′  rate constant 𝑘𝐵  Boltzmann-constant 𝑙𝑥, 𝑙𝑦  length of the region of interest in x and y direction MW  molecular weight [g/mol] 𝑁𝐴  numerical aperture 𝑝𝐻2𝑂  water vapour pressure in the atmosphere 𝑝𝐻2𝑂,𝑠𝑎𝑡 saturated water vapour pressure   𝜇  velocity of a spherical particle (as part of the Stokes law) 𝑟  lateral resolution 𝑅𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑛𝑔 hydrodynamic radius of the diffusing molecules [Å] 𝑅𝑚𝑎𝑡𝑟𝑖𝑥 hydrodynamic radius of the matrix molecules [Å] 𝑅𝐻  hydrodynamic radius [Å] 𝑅𝐻  relative humidity [%] sccm  standard cubic centimetres per minute 𝑇  temperature [K or °C] 𝑇𝑔  glass temperature [K or °C] 𝑇𝜃  reference temperature of 298.15 K xxv  t  time [s, ms] Υ  transmittance prior to photobleaching 𝑤  concentration of sucrose in water 𝑤(𝐷, 𝑡, 𝑟)  replaces the function 𝑟2 + 4𝐷𝑡 wt %  weight percent of sucrose in water 𝑧  distance in z-direction xxvi  List of Acronyms BC   black carbon BrC   brown carbon CCN   cloud condensation nuclei CLSM   confocal laser scanning microscope CW   continuous wavelength FPR fluorescence photobleaching recovery FRAP   fluorescence recovery after photobleaching IN   Ice nuclei IR   infrared light range LSM   laser scanning microscope R6G   rhodamine 6G rFRAP   rectangular fluorescence recovery after photobleaching SOA   secondary organic aerosol SOM   secondary organic material UV   ultraviolet light range VOC   volatile organic material xxvii  Acknowledgements To complete this Master’s thesis successfully would not have been possible without the great support of my supervisor, my family, my friends and my lab mates! I would like to thank, first and foremost, my supervisor, Professor Dr. Allan Bertram. Thank you for your guidance through this complex project and for your advice whenever I did not see a solution to the plentiful challenges that this research project was offering. Yes, Ryan is right; the level of dedication, kindness and understanding that you show all of us is deeply appreciated and helps us grow as scientists.  A big thank you also goes to Dr. Saied Kamal, whose vast mathematical knowledge, his conta-gious enthusiasm for science and his support during scientific challenges have helped this pro-ject to move on. Thank you, Saied! I would also like to thank the past and current Bertram group members who provided a friendly supportive and encouraging atmosphere. Thank you, Ryan M., James, Vickie, Meng, Erin, Adri-an, Yuri, Allie, Cédric, Stephen, Mijung, Kaitlin, Ryan A., Jingwei, Michael, Pit, Christina, Ugo and Yuan! In particular, I would like to thank Ryan M. for his open ear and his suggestions whenever I got stuck, James for teaching me the very finicky bead mobility technique, Vickie for the help-ful conversations and Yuri for introducing me into his project and teaching me the basics of the FRAP method. Thank you, Erin, Adrian and Meng for being brave and persistent hiking and lab companions and for being thorough proof-readers. xxviii  Also important for the progress of this thesis was Mallory Hinks’ work who was preparing the brown limonene SOM samples in her lab in UC Irvine, Los Angeles, California, USA. Thank you, Mallory, for the fast preparation! I will not forget to thank the members of the Mechanical shop who were unbelievably quick in finishing my requests and I would like to thank Pat from Chemistry Requisition and John from Chemistry Acquisition for their organizational skills.  I am especially grateful for my family and my friends, who have supported me during the past two years during dark (in the laser lab) and successful hours of research. Thank you for the spe-cial hiking, biking, climbing adventures, Rob, Sam, Gordon, Rike, Matthias, Jean-Simon, Clem-ens, Jonas, Livia and Nadia – the joy and laughter with you helped every day! Thank you every-one from the UBC Salsa Rueda group and the UBC gymnastics group, dancing and tumbling with you was a lot of fun! Thank you, Imke, for always having an open ear when needed!  Mama and Papa, thank you for setting a great example and for giving me the love, support, encourage-ment and advice to achieve my goals! Kaja and Aina, thank you for all the good moments and for supporting your big sister with the dream to live in Canada. Last, I wish to acknowledge that the research and work presented in this thesis was carried out in the UBC chemistry department which is located on the traditional, ancestral, and unceded territory of the Musqueam people.   xxix           To my parents, Bettina and Siegfried, and to my sisters, Aina and Kaja  1  Chapter 1: Introduction 1.1 Atmospheric Particles 1.1.1 Formation, Composition and Sizes Atmospheric aerosols are particles that are suspended in the Earth’s atmosphere. These particles can either be emitted directly to the atmosphere (primary particles) or can be formed in the atmosphere by gas-to-particle conversion (secondary particles) (Figure 1.1).1 The sources of atmospheric particles can be either natural or anthropogenic. Anthropo-genic sources include combustion of fossil fuels and industrial processes, while natural sources include volcanoes, plants, deserts and the ocean.2 Due to their different sources atmospheric particles can consist of a range of components including organics, metal oxides and inorganic species such as sulfates, nitrates, and ammonium.2-3 Atmospheric particles can be divided based on their size into fine particles (≤1 µm in di-ameter) and coarse particles (1-10 µm).2 Coarse particles are mostly formed by mechanical im-pact of wind on the Earth’s surface which causes dust, sea spray and vegetation debris to be emitted into the atmosphere. Fine particles, on the other hand, are formed by condensation of gases (Figure 1.1).2 2   Figure 1.1: Formation and removal processes and classification of atmospheric particles.  1.1.2 Effects of Atmospheric Particles on Humans and Climate Atmospheric particles have two major effects on this planet. First, they can affect public health. For example, atmospheric particles produced by fossil fuel combustion have been shown to increase chances of inflammation or even cancer.4 As another example, during har-vesting season, when the concentrations of fungal spores and biologic particles are increased, farm workers reported coughing and breathlessness.5 Also, a negative effect on the lung func-tion of children during an increase in fine particles, especially the organic fraction, was ob-served.6 Furthermore, studies with cells exposed to secondary organic aerosols (SOA) suggest that SOA can cause premature cell death. 7 Fine Mode(<10 nm-1 µm)EmissionPrecursor gases(H2SO4, organics etc.)NucleationCondensation orCoagulationCoarse mode (1 µm-10 µm)EmissionDry removal &RainoutPrimary particlesSecondary particles3  Second, atmospheric particles can affect climate (Figure 1.2). Atmospheric particles can directly affect climate by scattering and absorbing sunlight. An indirect effect is also possible, where atmospheric particles act as cloud condensation nuclei (CCN) or as ice nuclei (IN). If the atmospheric particles act as CCN or IN, they can induce cloud formation, and the clouds can then scatter light.2  Figure 1.2: Schematic of the formation of atmospheric particles and their effects on the climate. Based on Ren-baum-Wolff et al. (2013).8 There are many factors particles influencing the climate, including the concentrations of gases and atmospheric particles. To quantify the influence of atmospheric components (e.g. greenhouse gases and atmospheric particles) on the climate, a parameter called “radiative forc-Particle growthCloud activation Direct effectIndirect effectAtmospheric particles Grown particles4  ing” has been introduced by the Intergovernmental Panel on Climate Change (IPCC, 1990).9 Ra-diative forcing is a measure of the effect that a factor (such as atmospheric particles) has on the radiative energy budget of the Earth-atmospheric system. Radiative forcing is normally report-ed at the top of the troposphere in units of W/m2. The values that are calculated can be posi-tive or negative: positive values indicate a warming effect and negative values indicate a cooling effect of the contributing component.  The radiative forcing of greenhouse gases is known with very high confidence, while the radiative forcing of atmospheric aerosols has a high uncertainty (see Figure 1.3).10 The uncer-tainties in the radiative forcing of aerosols from aerosol-radiation (i.e. direct effect) and aero-sol-cloud interactions (i.e. indirect effect) are as high as 100%. To be able to assess the impact of atmospheric aerosols on the climate with a higher level of confidence, more research is needed.  Figure 1.3: Radiative forcing of climate forcing species including their uncertainties. Reproduced with permission from Stocker et al. (2013).10 1.2 The Importance of Molecular Motion Within Atmospheric Particles In the atmosphere, particles can undergo heterogeneous reactions with atmospheric gas-phase oxidants, such as ozone (O3). The timescale of these reactions depends on the mobili-5  ty of molecules within the atmospheric particles (Figure 1.4). Fast diffusion and low viscosity promote reactions throughout the entire volume of the particles. Slow diffusion and high vis-cosities favour reactions confined to the surface of the particles (Figure 1.4).8  Figure 1.4: Illustration of the influence of diffusion rates on heterogeneous reactions within atmospheric parti-cles. Reproduced with permission from Lindsay Renbaum-Wolff et al., “Viscosity of α-pinene secondary organic material and implications for particle growth and reactivity”, PNAS, 2013, 110 (20), 8014-8019; doi: 10.1073/pnas.1219548110. Molecular motion within atmospheric particles also influences the growth rate of these particles. Fast diffusion and low viscosities lead to fast growth rates of atmospheric particles, while slow diffusion and high viscosities lead to slow growth rates. Hence, predictions of size O3 OzoneOrganic or inorganic material6  and mass of atmospheric particles in atmospheric models are sensitive to molecular motion within atmospheric particles, with important implications for climate and air quality.  1.3 Theories of Molecular Motion The heat induced, random movement of molecules is also known as Brownian motion. Brownian motion was first discovered in 1827 by the Scottish botanist Robert Brown.11  Almost 80 years later in 1905, Einstein derived a mathematic expression to describe Brownian mo-tion: 2, 12 < 𝑥2 > = 2 ∙ 𝐷 ∙ 𝑡, 1.1 where D is the diffusion coefficient and < 𝑥2 > is the mean squared displacement, which is the distance, that a molecule moves on average within a certain time interval t. The Stokes-Einstein equation relates the diffusion coefficient, 𝐷, to the viscosity of the medium, 𝜂, and to the hy-drodynamic radius of the diffusing molecule, 𝑅𝐻,: 𝐷 =𝑘𝐵𝑇6𝜋𝜂𝑅𝐻, 1.2 where 𝑘𝐵 is the Boltzmann constant and 𝑇 is the temperature. The Stokes-Einstein equation has been derived for laminar flow conditions, a spherical shape of the diffusion species12 and for the case where the  diffusing species is significantly larger than the molecules of the medi-um that the species is diffusing through. The latter condition guarantees that the diffusing spe-cies cannot slip between the molecules of the medium.13 7  1.4 Overview of this Thesis As discussed above, molecular diffusion of molecules within atmospheric particles can influence their growth rate and reactivity with important implications for predicting the radia-tive forcing of atmospheric particles and air quality.14 Nevertheless, the scientific understanding of molecular diffusion within atmospheric particles remains poor. In the past, diffusion coefficients of organic molecules within atmospheric particles have been estimated using viscosity measurements and the Stokes-Einstein equation.8, 15However, the Stokes-Einstein equation is based on assumptions (section 1.3) which may not be applicable to atmospheric particles. 16 In Chapter 2:, the validity of the Stokes-Einstein equation was tested by directly measur-ing diffusion coefficients of organic molecules in simple proxies of atmospheric particles with known viscosities (consisting of binary mixtures of sucrose and water) and by comparing the measured diffusion coefficients with Stokes-Einstein calculated diffusion coefficients. Diffusion coefficients were measured between 38% and 80% relative humidity (RH), since the relative humidity can change in the atmosphere.17 Measuring diffusion coefficients as a function of relative humidity is important because 1) as the RH changes in the atmosphere the water content of atmospheric particles changes to maintain equilibrium with the gas phase water vapour, and 2) diffusion coefficients within at-mospheric particles are expected to be sensitive to water content. Relative humidity is defined by the following equation: 8   RH =𝑝𝐻2𝑂𝑝𝐻2𝑂,𝑠𝑎𝑡∙ 100,  1.3 where 𝑝𝐻2𝑂 is water vapour pressure in the atmosphere and 𝑝𝐻2𝑂,𝑠𝑎𝑡 is the saturation water vapour pressure at a certain temperature.2 In the atmosphere, the relative humidity var-ies between 20 to 100 %.17 Many literature studies reported diffusion coefficients as a function of relative humidity or as a function of water activity, aw, where RH = 100∙aw.  In Chapter 3:, diffusion coefficients of fluorescent organic molecules in brown limonene secondary organic material (SOM) were measured over a range of relative humidities from 38% to 90%. Brown limonene SOM is an important type of atmospheric particles,18 and there have only been a few measurements of diffusion coefficients in limited types of SOM15d and none in brown limonene SOM. Up to now, it has been assumed in climate models that diffusion coeffi-cients of organic molecules in SOM are large (similar to the diffusion coefficients of organic molecules in water), which may not be true under certain conditions such as low RH.15a, 19  In Chapter 4:, the average hydrodynamic radius of fluorescent organic molecules in brown limonene SOM was determined. The chemical structure and size of these organic mole-cules were not known prior to this study.   9  Chapter 2: Diffusion Coefficients of Rhodamine 6G in Sucrose Water Solutions, a Proxy for Atmospheric Particles 2.1 Introduction Secondary organic material (SOM) originates from volatile organic compounds (VOCs) which are emitted by anthropogenic sources (e.g. cars) or natural sources (e.g. trees). VOCs, such as limonene, α-pinene and toluene, amongst other hydrocarbons, are oxidized in the at-mosphere by a complex series of reactions to form SOM.15a, 20 A fraction of this SOM can then condense to form SOM particles. SOM makes up 30-70% of the mass concentrations of atmos-pheric particles depending on the region of the atmosphere.  SOM particles can influence cli-mate either directly by absorbing or scattering sunlight or indirectly by acting as CCN or IN. Air quality and health can also be influenced by atmospheric particles.7, 21 See Section 1.1.2 for fur-ther details. As discussed in Section 1.2, diffusion rates of organic molecules in atmospheric particles, such as SOM particles, influence particle growth rates and reactions rates. As a result, diffusion rates of organics in SOM have become an active area of research.22 In the past, researchers assumed that the diffusion coefficients of organic molecules in SOM are large (similar to the diffusion coefficients of organic molecules in pure water). More recently, diffusion coefficients of organic molecules in SOM have been estimated by measuring viscosities in SOM particles and then calculating diffusion coefficients using the Stokes-Einstein and the measured viscosities.15a For example, Song et al. (2015) used this approach to estimate diffusion coefficients of organic molecules in SOM derived from the ozonolysis of α-pinene.15d 10  Hinks et al. (2016) also used this approach to determine diffusion coefficients of organic mole-cules in SOM produced from the ozonolysis of limonene.23 However, the Stokes-Einstein equa-tion is based on assumptions that might not be appropriate for atmospheric particles (section 1.4).  There have only been a few previous studies that have tested the validity of the Stokes-Einstein equation for predicting diffusion coefficients of organics in matrices consisting of or-ganics and water (Note, both organics and water are important for SOM, since SOM is hygro-scopic and will take up water in the atmosphere as relative humidity changes). Champion et al. (1997) found that the Stokes-Einstein equation underpredicts diffusion coefficients of the or-ganic dye fluorescein in sucrose water solutions at viscosities above 7.9 x 104 Pa s (Tg/T ≥ 0.9, where Tg is the glass transition temperature of the binary mixture of sucrose and water and T is the measured temperature).16c Corti et al. (2008) found that the Stokes-Einstein equation gives valid results up to viscosities of 1.2 Pa s (Tg/T ≥ 0.7) for the diffusion of fluorescein in sucrose water solutions, but shows a break down at higher viscosity values.16d Longinotti and Corti (2007) found a breakdown of the Stokes-Einstein equation for the diffusion of ferrocene-methanol in sucrose water solutions at viscosities higher than 47.4 Pa s (Tg/T ≥ 0.8).16e To add to the limited number of studies testing the Stokes-Einstein equation for predict-ing diffusion of organics in organic and water mixtures, the diffusion coefficients of the organic tracer molecule rhodamine 6G (Table 2.1) were measured at various atmospherically relevant RHs in mixtures of sucrose and water. The aim of the current study is to determine, if the Stokes-Einstein equation gives accurate results at atmospherically relevant RHs. Rhoda-11  mine 6G (R6G) was chosen as a fluorophore for this study, since the hydrodynamic radius of R6G (5.89 Å)24 is similar to the radius of the matrix molecules (the radius of sucrose is 4.7Å).25 In addition, R6G can be studied using the microscope system available in the department of chem-istry at the University of British Columbia (Zeiss Axio Observer LSM 5 10 MP laser scanning mi-croscope with a 543 nm laser). Sucrose-water mixtures have been chosen as matrix molecules, because  1) sucrose has an oxygen-to-carbon (O:C) ratio of 0.92, which is similar to the O:C ratio of SOM found in atmospheric particles26,  2) viscosities of sucrose-water mixtures, information that is needed to test the Stokes-Einstein relation, are known over a wide range of water activi-ties and 3) sucrose-water mixtures show similar viscosities to some types of SOM at room tem-perature (compare viscosity values of sucrose-water mixtures measured by Power et al. (2013) with the viscosities of toluene SOA measured by Song et al. (2016) and α-pinene viscosities measured by Grayson et al. (2016)).15e, 27 This work is part of a manuscript that investigated the diffusion coefficients of fluoresce-in, R6G and calcein in sucrose-water mixtures: Chenyakin, Y., Ullmann, D. A., Evoy, E., Renbaum-Wolff, L., Kamal, S., and Bertram, A. K.: Diffusion coefficients of organic molecules in sucrose–water solutions and comparison with Stokes–Einstein predictions, Atmos. Chem. Phys., 17, 2423-2435, doi:10.5194/acp-17-2423-2017, 2017.   12  Table 2.1: Information on rhodamine 6G (R6G) including the molecular weight (MW), the chemical structure and the hydrodynamic radius. Name MW (g/mol) Chemical Structure Hydrodynamic Radius RH (Å) rhodamine 6G 479.01   5.89 (Müller et al., 2008)24  2.2 Experimental Diffusion coefficients of R6G in mixtures of sucrose and water were determined using a tech-nique called rectangular area fluorescence recovery after photobleaching (rFRAP). Below, the method of producing samples of sucrose, water and trace amounts of R6G needed for the rFRAP experiments is described (section 2.2.1). Then, the procedure of the rFRAP experiments is described in detail (section 2.3).  2.2.1 Sample Preparation For the rFRAP experiments thin films (45-100 µm thick) containing homogeneous mix-tures of sucrose (Sigma Aldrich, ≥99.5 %), water and trace amounts of R6G (Acros Organics, 99 %) were needed. The concentration of R6G in thin films was 0.51 mM. This concentration was chosen, so that the concentrations did not influence the viscosity of the sucrose-water mix-ture and the fluorescence signal was large enough to detect in the experiments. The water ac-13  tivities (aw) in the thin films ranged from 0.8 to 0.38; at these water activities, the sucrose-water solutions were supersaturated with respect to sucrose. The method of preparing supersaturated solutions with respect to sucrose is as follows: first, a solution of 60 wt % sucrose in water with a concentration of 0.51 mM R6G was prepared gravimetrically and filtered using a 0.45 µm filter (Merck Millipore) followed by a 0.02 µm filter (WhatmanTM) to reduce dust particles in the solution which could enhance nucleation of crys-talline sucrose. 28 Next, a droplet of the solution was pipetted onto a hydrophobic glass slide (Hampton Research), and in order to condition the droplets to a certain water activity, the glass slide containing the droplet was placed in a flow cell or in a glass jar with controlled relative humidity and hence water activity. The flow cell was used to achieve water activities from 0.6 to 0.8 and the glass jar was used to achieve water activities from 0.38 to 0.6. The flow cell used for conditioning droplets is shown in Figure 2.1 and the glass jar used for conditioning droplets is shown in Figure 2.2. The aw in the flow cell was controlled by using nitrogen gas (Ultrapure, Praxair) that was humidified by directing the gas through a bubbler within a temperature-controlled water bath. Subsequently, the humidified nitrogen gas was directed across the sample with a constant flow of 2500 sccm. To monitor the aw of the humidified nitrogen gas, a dew point hygrometer com-bined with a chilled mirror sensor (General Eastern Model D2) and a handheld hygrometer (Omega RH85) were used. During the conditioning experiments the temperature of the sample was measured directly in the flow cell using a thermocouple thermometer (HH200A Omega). 14   Figure 2.1: Schematic of the flow cell used to condition samples to the desired water activities. Prior to performing experiments, the hygrometer in combination with the chilled mirror sensor was calibrated. For this, the deliquescence relative humidity of ammonium sulphate par-ticles was determined and the experimental value was compared to the literature. The uncer-tainty of the aw was 0.025 at aw=0.803 after calibration.   Figure 2.2: Schematic of the glass jar used to condition samples of water activities below 0.6. Humidified gas flowDew point hygrometer18.6 CResealable opening Sample N2WaterFridge18.6 CFlow cellGlove bag20.0 CThermometerSaturated salt solutionSampleGlass jarTeflon tube spacersAir of desired aw15  In cases where sealed glass jars were used to condition the droplets to a known aw, the aw in the jars were controlled using a saturated inorganic salt solution of a certain aw (see Table 2.2).29 The sample droplet was placed on a glass slide and the glass slide was then placed above the inorganic salt solution by using spacers made of Teflon tubes which were placed in the inor-ganic salt solution and were long enough to keep the sample above the salt solution (Figure 2.2). Table 2.2: Saturated salt solutions used for conditioning and storing samples at specific water activities in sealed glass jars. Water activity (+/- 0.025) at 20°C Salt Reference 0.80 ammonium sulfate Greenspan 29 0.70 potassium iodide Greenspan 29 0.60 sodium bromide Greenspan 29 0.50 calcium nitrate tetrahydrate (at 25°C) Winston and Bates 30 0.38 sodium iodide Greenspan 29  The time needed for the droplets to condition to the water activity in the flow cell was estimated based on the following equation15f: 𝜏𝑒𝑞 =𝑟2𝐷𝑤𝑎𝑡𝑒𝑟 ∙ 𝜋2,  2.1  Where 𝜏𝑒𝑞is the characteristic diffusion time of water within sucrose-water droplet, 𝑟 is the radius of the sucrose-water droplet and 𝐷𝑤𝑎𝑡𝑒𝑟 is the diffusion coefficient of water in su-crose-water solutions. 𝐷𝑤𝑎𝑡𝑒𝑟 was obtained from Price et al. (2014)31: 16  log 𝐷𝑤𝑎𝑡𝑒𝑟 = 𝑎 + 𝑏𝑎𝑤 + 𝑐𝑎𝑤2 + 𝑑𝑎𝑤3, 2.2 where 𝑎𝑤 is the water activity, 𝐷𝑤𝑎𝑡𝑒𝑟 is the diffusion coefficient of water, 𝑎, 𝑏, 𝑐 and 𝑑 are constants with the following values: 𝑎 = −20.89, 𝑏 = 25.92, 𝑐 = −26.97 and 𝑑 = 13.25. A minimum time of 3 ∙ 𝜏𝑒𝑞 was used to condition the droplets, which has been shown to be a sufficient time period for the samples to equilibrate. 32 Once the droplet of sample was conditioned to a certain aw, a second hydrophobic glass slide was placed on top and the droplet was sandwiched between the two slides to make a thin film with thickness 45-120 µm where the thickness was controlled using aluminum spacers (Figure 2.3). Whether samples were conditioned in glass jars over saturated salt solutions or within a flow cell, the sandwiching process was done within a Glove BagTM where the air had the same aw as was used to condition the sample. To ensure that the water activity of the sam-ples did not change over time, the glass slides were sealed with vacuum grease and were stored over an inorganic salt solution of the corresponding water activity.  Figure 2.3: Schematic of the sample used in the FRAP experiments. Panel a) is a top view and Panel b) is a side view. The sample consists of sucrose, water and trace amounts of the fluorescent tracer dye, rhodamine 6G.  Vacuum greaseGlass slideAl spacerSample droplet13421 2aaa22 mmb) Side viewa) Top viewa43bb45-120µm17  2.3 Introduction to Fluorescence Recovery After Photobleaching (FRAP) Fluorescence recovery after photobleaching (FRAP) has been used for nearly forty years33 to analyze the mobility of molecules in various components such as cytoplasm of cells34, cell nuclei35 and biopolymers36. The FRAP method is based on its predecessor, fluorescence photobleaching recovery (FPR)37, and has undergone improvements because of the develop-ment of confocal microscopes and new types of lasers.38 In this work, we use a variation of the FRAP technique called rectangular area fluores-cence recovery after photobleaching (rFRAP).37, 39 The rFRAP measurement technique is based upon the diffusion of fluorescent organic tracer molecules through a medium, which is illustrat-ed in Figure 2.4 showing a side view of the sample cell. The green circles depict fluorescent tracer molecules, the black circles depict tracer molecules that have been photobleached (i.e. irreversibly lost their ability to fluoresce) and the orange rectangle represents the area that has been chosen for photobleaching. Panel A) shows a homogeneously fluorescent film prior to photobleaching. Panel B) shows the same film just after photobleaching with a high intensity laser beam. Panel C) to F) show the recovery of the fluorescence within the photobleached rec-tangle over time t after photobleaching. Diffusion coefficients can be determined from the time dependence of this fluorescence recovery (see section 2.3.2 for further details).  18   Figure 2.4: Schematic illustrating the photobleaching and diffusion process of fluorescent molecules. Shown is a side view of the sample cell at various times t during the rFRAP experiment. See text for further details.   2.3.1 FRAP Measurements The FRAP measurements were conducted on a Zeiss Axio Observer LSM 5 10 MP laser scanning microscope with the low numerical aperture 10x 0.3 NA objective (Zeiss EC-Plan Neofluar 10x/0.3) to ensure near uniform photobleaching in the z-direction. One-dimensional scanning of a speed of 8 was performed, which translates to a pixel dwell of 2.56 µs and an im-age scan time of 1.57 s. The images were acquired with 512x512 pixels with a pinhole set to 80 µm. For scanning and photobleaching, a Helium-Neon laser (543 nm) with a maximum pow-er of 1.2 mW was used. For photobleaching a laser power of 330 µW was used and for scanning a laser power of 4.08 µW was used. The experiments were performed using the Zen 2008 soft-ware and photobleaching was performed in the “Zoom-In” bleach mode. For photobleaching, a time was chosen such that the fluorescence intensity within the bleached area was decreased by between 10 and 32 %. Previous work has shown that bleach depths smaller than 50 % give accurate diffusion values.40 A) Prior to photobleaching B) t=0s C) t=50sD) t=100s E) t=300s F) t=700s19  The geometry chosen for photobleaching in the experiments was a rectangle with length (lx) and width (ly) (Figure 2.5). The sizes of the rectangles chosen depended on the diffu-sion times with smaller areas for longer diffusion times. The image sizes in relation to the bleach size were chosen such that the entire bleach profile could be imaged even for long re-covery times. For samples at aw=0.75 and 0.8, bleached areas of 36 µm by 36 µm and image sizes of 199.61 µm by 199.61 µm were chosen. For samples at aw=0.6, bleached areas of 10 by 10 µm and image sizes of 99.8 µm by 99.8 µm were used and for aw=0.52 and 0.38, bleached areas of 5 by 5 µm and image sizes of 59.88 µm by 59.88 µm were used.  A minimum of three samples was prepared for each aw and three measurements per sample were obtained.   Figure 2.5: Schematic of a fluorescent film (view from top) and its bleached area. A section of a fluorescent film is scanned in the x- and y-direction. A defined rectangular area (bleached area) of the length 𝐥𝐱 and the width 𝐥𝐲 is photobleached. lxlyxyfluorescent filmBleached area20  2.3.2 Analysis of the FRAP Data Fick’s first law of diffusion describes the relationship between the net flux J⃗ of particles that occurs due to a change in concentration with a change in distance (𝜕𝑐𝜕𝑧): J⃗  = −D ∙𝜕𝑐𝜕𝑧, 2.3 where D is the diffusion constant or diffusion coefficient.41 Fick’s second law of diffusion de-scribes the relationship between the change in concentration with a change in time to the sec-ond derivative of the concentration with respect to distance: 𝜕𝑐𝜕𝑡= D ∙𝜕2𝑐𝜕𝑧2, 2.4 where D is location-independent.42 Fick’s second law describes how the concentration profile changes as the particles start diffusing from higher towards lower concentrations in order to balance concentration differences. To describe diffusion of fluorescent molecules in an rFRAP experiment, Deschout et al.40 devel-oped a mathematical model based on Fick’s first and second laws.  Deschout et al.40 made assumptions which were partially based on Axelrod et al.37: a. The bleaching process is a first-order reaction and irreversible. 37, 40 b. The time that is chosen for photobleaching is short, such that, no diffusion of fluo-rescent molecules in or out of the bleached area takes place during photobleach-ing. 37, 40 c. The photobleached area is rectangular.37, 40 21  d. Photobleaching should be limited to a maximum of 50% of the fluorophores in the samples.40 e. A two dimensional diffusion is assumed with molecules diffusing only in the x- and y-plane and the sample being photobleached uniformly in z-direction which is a rea-sonable assumption for 45-120 µm thick films and using a regular CLSM with a low numerical aperture lens.40 Using all of the assumptions above Deschout et al. derived a mathematic expression for two dimensional single photon rFRAP based on Fick’s second law of diffusion (see section 1.3): F(x, y, t)F0= 1 −K04[erf (x +lx2√r2 + 4Dt) − erf (x −lx2√r2 + 4Dt)]× [erf (y +ly2√r2 + 4Dt) − erf (y −ly2√r2 + 4Dt)], 2.5 where F is the fluorescence intensity at coordinate (x,y) and time t. F is normalized to the fluo-rescence intensity prior to photobleaching, F0(x, y). K0 is the effective bleach depth, which describes the decrease of the fluorescence intensity within the photobleached area. lx and ly are the lengths of the photobleached area. r is the lateral resolution of the microscope and D is the diffusion coefficient. The error function is defined as: erf(𝑧) =2√𝜋∙ ∫ 𝑒−𝑥2𝑧0𝑑𝑥.  2.6  In this work, a one-dimensional model for the analysis of the recovery of the fluores-cence intensity was used. For samples of aw of 0.80 to 0.52, the fluorescence images recorded 22  after photobleaching were integrated over the entire width of image in the y-direction. For this case, Eq. 2.5 was simplified by integrating the intensities over all y positions: F(x, t)F0= 1 −K04[erf (x +lx2√r2 + 4Dt) − erf (x −lx2√r2 + 4Dt)]× (∫ [erf (y +ly2√r2 + 4Dt) − erf (y −ly2√r2 + 4Dt)]+∞−∞dy),  2.7  which resulted in the following expression: F(x, t)F0= 1 −K04[erf (x +lx2√r2 + 4Dt) − erf (x −lx2√r2 + 4Dt)] × 2ly,  2.8  For samples of aw=0.38, the fluorescence images recorded after photobleaching were integrat-ed only over the width of the bleach area (−ly2 to +ly2) in order to increase the signal-to-noise ratio, which resulted in the following equation: F(x, t)F0= 1 −K04[erf (x +lx2√r2 + 4Dt) − erf (x −lx2√r2 + 4Dt)]× (∫ [erf (y +ly2√r2 + 4Dt) − erf (y −ly2√r2 + 4Dt)]+ly2−ly2dy),  2.9  Equations 2.8 and 2.9 were implemented into a Matlab script which was used to analyze the images of the recovery process. In the following sections, the expression r2 + 4Dt will be re-placed by 𝑤(𝐷, 𝑡, 𝑟).  23  Shown in Figure 2.6 is an example of images recorded during a typical rFRAP experiment for the diffusion of R6G in a sucrose-water mixture. Steps involved analyzing these types of images are listed below: a. The images after photobleaching were normalized to an image recorded prior to photo-bleaching or a region in the image not affected by photobleaching using the open source programme ImageJ43. Images of films with 0.52≤aw≤0.8 were normalized to a prebleach image. Images of films at aw=0.38 were normalized using a region in the image outside of the photobleaching region and not affected by diffusion. The latter method of nor-malization was used for films at aw=0.38, since gradual photobleaching of the entire im-age occurred during these measurement due to long experimental time. b. In a subsequent step, the images were downsized from 512x512 pixels to 128x128 pixels by averaging in order to reduce noise. Then, the data was reduced from two dimensions to one dimension by integrating the intensities over all y-positions for the case of sam-ples aw≥0.52 or integrating the intensities for y-positions ranging from −ly2 to +ly2 for the case of aw=0.38. See Figure 2.7 as an example. c. The normalized data in 1-dimensional form was fit to Eq.2.8 or 2.9 using a Matlab script (The Mathworks, Natick, MA, USA) with  𝐾0 as well as the background left as free pa-rameters for the analysis. Examples of fits are shown in Figure 2.7. From this step 𝑤(𝐷, 𝑡, 𝑟) was determined for each time at which an image was recorded.  24  d. 𝑤(𝐷, 𝑡, 𝑟) was plotted as a function of 𝑡 and a straight line was fit to the data (Figure 2.8). Since 𝑤(𝐷, 𝑡, 𝑟) = (𝑟2 + 4𝐷𝑡), the diffusion coefficient, 𝐷, could be calculated from the slope of the line.  Figure 2.6: A fluorescent film consisting of a sucrose-water solution (aw=0.75) and R6G viewed using a laser scanning microscope. Panel A) shows the fluorescent film prior to photobleaching. Panel B) to F) show the re-covery of the fluorescence signal over time t. Panel B) was taken directly after the photobleaching process at time 0s, whereas panel F) shows the fluorescent film after 700s after the photobleaching step. The orange rec-tangle represents the area that was chosen for photobleaching.  25   Figure 2.7: Plots of fluorescent intensity as a function of x-position, integrated over all y-positions of an aw of 0.75. Panel A is an image taken directly after photobleaching and panel B) to D) show the recovery of the fluo-rescence intensity due to diffusion. The red line is a fit using Equation 2.8. A) t=50s B) t=100sC) t=300s D) t=700s26   Figure 2.8: Plot of 𝒘(𝑫, 𝒕, 𝒓) as a function of time t for a film of a solution containing R6G, sucrose and water of aw=0.75. Every blue circle represents a value of 𝒘(𝑫, 𝒕, 𝒓) obtained from fits to the experimental data, such as shown in from Figure 2.7. The red line is a linear plot to the data. Since 𝒘(𝑫, 𝒕, 𝒓) = (𝒓𝟐 + 𝟒𝑫𝒕), the diffusion coefficient could be calculated from the slope of the line. The first 50s have been excluded from the analysis because of reversible photobleaching.  2.3.3 Cylindrical Geometry of the Photobleaching Region Prior to determining diffusion coefficients with the rFRAP technique, the geometry of the photobleached region in z-direction was determined. The films chosen had a thickness be-tween 45 and 120 µm and were prepared at an aw=0.38 to ensure that the photobleached area does not recover significantly while taking a stack of images in z-direction (z-stack). Photo-27  bleaching areas of 5 by 5, 10 by 10 and 20 by 20 µm were used. The photobleaching was near cylindrically shaped in z-direction for all the film thicknesses tested as expected (Figure 2.9).  Figure 2.9: Cross section through a fluorescent film at aw=0.38 after photobleaching. The photobleached areas have a size of 5x5 µm (a) and 20x20 µm (b). The fluorescent films were about 70 µm thick.  2.3.4 Corrections for Nonlinearity of the Fluorescence Intensity as a Function of Concentra-tion of R6G In FRAP experiments, the relationship between the fluorescence intensity and the con-centration of R6G needs to be known. To determine this relationship, samples consisting of 50 wt % sucrose-water solution and different concentrations of R6G were prepared and the relationship between fluorescence intensity and concentration of R6G was determined. Shown in Figure 2.10 are the results from these measurements. Each data point consists of an average of three values obtained by measuring the fluorescence intensity of three droplets of the same concentration. Error bars represent the standard deviation (1σ) of the fluorescence intensities. a) b)28   Figure 2.10: Fluorescence intensity as a function of the concentration of R6G in sucrose-water solutions, for concentrations in a 50 wt % sucrose-water solution. As mentioned above, the concentration of R6G used in the rFRAP experiments was 0.51 mM. Since the fluorescence intensity does not show a linear relationship to the concentra-tion above 0.1 mM, the non-linearity of the fluorescence intensity with the concentration needs to be accounted for in the analysis of the FRAP data.  0.0 0.5 1.0 1.5 2.0020406080100120140160 Set 1 - April 21 Set 2 -May 06Fluorescence intensity (a.u.)Concentration of  R6G (mM)29   Figure 2.11: Concentration of R6G in mM as a function of fluorescence intensity. The red line is a nonlinear fit to the data using an exponential function.  An exponential function was fit to the data in Figure 2.11 (red line). The obtained rela-tionship (shown in Table 2.3) was used to convert fluorescence intensity into concentration in the rFRAP analysis. The difference between diffusion coefficients calculated assuming a linear relation between concentration and fluorescence intensity compared to using an exponential function (Table 2.3) was relatively small (within the uncertainty of the measurements). Never-theless, the exponential function was used to convert fluorescence intensity to concentration for completeness in the data reported here. 0.0 0.2 0.4 0.6 0.8 1.00.00.20.40.60.81.0Conc. (mM)Normalized fluorescence intensity (a.u.)30  Table 2.3: Best fit parameters for concentration vs. normalized fluorescence intensity data in Figure 2.11. 𝒄 = 𝒄𝟎 + 𝑨 ∙ 𝒆(𝑩∙𝒙), where c is the concentration and x is the normalized fluorescence intensity. The R2 value indicated the quality of the fit. Variable 𝑐0 𝐴 𝐵 𝑅2 Value -0.0398 0.0748 2.8974 0.9955  2.3.5 Corrections for Reversible Photobleaching It has been observed in former studies that some types of photobleached organic dyes can recover within the first few seconds (referred to as “reversible photobleaching”). This re-versible photobleaching can be due to photoswitching or recovery of the triplet state.44 Addi-tional experiments were performed to test, if reversible photobleaching occurs with R6G as a tracer dye.  To test for reversible photobleaching, small droplets (10-50 µm radius) of the 10 wt % sucrose-water solution containing R6G were nebulized onto a glass slide and were conditioned at a water activity of aw=0.6. For the experiments, two droplets were chosen of a similar size: one droplet was photobleached across the entire area of the droplet and the second droplet was used as a reference droplet to ensure that the droplets were not photobleached while monitoring (Figure 2.12). For photobleaching, bleaching depths of 16%, 30% and 55% were used. Since the complete droplet had been photobleached uniformly, a recovery of fluores-cence intensity due to diffusion of fluorescent molecules could be excluded. Also, the reference droplet helped to determine, if changes to the image happened (i.e. change in distance or 31  change in illumination) so that a change in fluorescence due to illumination was not attributed to fluorescence recovery.   Figure 2.12: Illustration of the choice of droplets used for the experiment on reversible photobleaching. Panel a) shows the droplet which is to be photobleached (red circle) and the reference droplet (blue dashed circle) prior to photobleaching and panel b) shows both droplets after photobleaching.  An example of results from one of these tests is shown in Figure 2.13. The results show that reversible photobleaching occurs within the first 50s after photobleaching. However, no dependence on the bleaching depth was observed. To account for the reversible photobleach-ing in the data analysis, data recorded during the first 50s after photobleaching were excluded from the data analysis. Prior to photobleaching After photobleaching a) b) 32   Figure 2.13: The fluorescence intensity-versus-time for two droplets used to test for reversible photobleaching. A sucrose-water droplet containing R6G of aw=0.6 was photobleached over its total area, so that its fluorescence intensity decreased by 18%. While the recovery of the photobleached droplet (blue triangles) was monitored a reference droplet (green crosses) not being photobleached was also monitored. For the analysis of the recovery, the fluorescence intensity was averaged across the complete droplet.  0 50 100 150 200 250 3000.820.840.860.880.900.920.940.960.981.00 photobleached droplet reference dropletFluorescence intensity (a.u.)time (s)≈ 18 % bleach depth50s Recovery33  2.4 Results and Discussion 2.4.1 Diffusion Coefficients of R6G in Sucrose Water Solutions The diffusion coefficients in this work were measured across a wide range of water ac-tivities from 0.38 to 0.80. As expected, the diffusion coefficients decrease with decreasing aw, since the viscosity of sucrose water solutions increase as the water activity increases.15e For the water activities from 0.38 to 0.8, the diffusion coefficients ranged from 1.50∙10-14 to 4.73∙10-9 cm2/s. Since the time needed for recovery of the fluorescence signal for aw<0.38 was on the order of months, diffusion coefficients were not measured at aw<0.38.  2.4.2 Breakdown of the Stokes-Einstein Equation In Figure 2.14, the measured diffusion coefficients of R6G are displayed as a function of water activity. A secondary and tertiary x-axis have been included in Figure 2.14 is the mass fraction of sucrose and Tg/T, where Tg is the glass transition temperature and T is the tempera-ture of the matrix (which is sucrose and water in this case). This information has been included in Figure 2.14, since literature studies conducted in the past report diffusion coefficient values as a function of mass fraction of sucrose or as a function of Tg/T. The glass transition tempera-ture was calculated using Champion et al. (1997) and the relationship between the water activi-ty and the mass fraction of sucrose was determined using Zobrist et al. (2011).45 In Figure 2.14, the measured diffusion coefficients of R6G were compared to diffusion coefficients calculated using the Stokes-Einstein equation, the hydrodynamic radius (RH) of 5.89 Å measured by Müller et al. (2008)24 and various viscosity values. Also included are a 4th 34  order polynomial fit and 95% confidence limit to the calculated diffusion coefficient values. The measured diffusion coefficients of R6G in sucrose water solutions show good agreement with the values calculated with the Stokes-Einstein equation for values above aw of 0.5. However, at an aw of 0.38 the diffusion coefficient of R6G deviates from the calculated value by a factor of between 2 and 50.  An aw of 0.38 would correspond to a Tg/T value of 0.94 (Figure 2.14). In the past, a breakdown of the Stokes-Einstein equation has been observed for fluorescein at Tg/T of 0.86 and 0.65 in sucrose water solutions by Champion et al. (1997)16c and Corti et al. (2008)16d, re-spectively. The measurements in this work are in agreement with the Tg/T value measured by Champion et al. (1997) but deviate from Corti et al. (2008).    35   Figure 2.14: Shown are the diffusion coefficients of R6G in sucrose water solution in comparison to diffusion coefficient values calculated from viscosities from Quintas et al. (2006; blue triangles)46, Migliori et al. (2007; blue crosses)47, Telis et al. (2007 ; blue circles)48 and Power et al. (2013 ; blue rectangles)15e using the Stokes-Einstein equation and the RH measured by Müller et al. (2008)24. The error bars for the diffusion coefficients of R6G represent 95% confidence limit, while the red star itself represent the average value of the diffusion coeffi-cients measured. The black solid line represents a 4th order polynomial which was fit to the literature values. The dashed line represents the 95% prediction limit that was fit to the calculated diffusion coefficients.  0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.01.06 0.99 0.93 0.87 0.81 0.75 0.68 0.59 0.49Tg /T  Diffusion coefficients of R6G measured          in this work Quintas et al. 2006 Migliori et al. 2007 Telis et al. 2007 Power et al. 2013Diffusion coefficient (m2/s)aw. 60.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.96 0.94 0.92 0.90 0.84 0.78 0.71 0.58 0.181E-181E-171E-161E-151E-141E-131E-121E-111E-101E-91E-81E-71E-61E-51E-4Mass fraction sucrose Diffusion coefficient of rhodamine 6G           measured in this work 4th order polynomial 95% prediction limits for          calculated diffusion coefficients Power et al. 2013 Telis et al. 2007 Migliori et al. 2007 Quintas et al. 2006Diffusion coefficient (cm2/s)aW036  2.4.3 Comparison with Diffusion Coefficients of Other Molecules in Sucrose Water Solu-tions In Figure 2.15, diffusion coefficients of R6G in sucrose water solutions are compared with diffusion coefficients of other molecules in the same solution. The data for the diffusion coefficients of fluorescein and calcein was taken from Y. Chenyakin32. The diffusion coefficients of water were calculated using a polynomial fit from Price et al. (2014) (Appendix A.3). Since calcein is larger and fluorescein is smaller than R6G (Table 2.4), one would expect the diffusion coefficient of R6G to be in between the diffusion coefficients of calcein and fluo-rescein at a given aw. However, the uncertainties in the measurements of this work are too large to conclude this. Water has the smallest hydrodynamic radius of all molecules analyzed and shows significantly larger values for diffusion coefficients compared to the other molecules analyzed. Table 2.4: Hydrodynamic radius (RH) and molecular weight (MW) of several molecules considered in this work. Diffusing molecule RH (Å) MW (g/mol) fluorescein 5.02 (Mustafa et al. (1993)49) 376 rhodamine 6G 5.89 (Müller et al. (2008)24) 479 calcein 7.4 (Tamba et al. (2010)50) 622 water 1.41 (Pang (2014)51)a 18                                                       a The reported radius is the Van-der-Waals radius instead of the hydrodynamic radius. 37   Figure 2.15: Shown are the diffusion coefficients of fluorescein, calcein (data used from Y. Chenyakin32), water (data used from Price et al.31) and R6G in sucrose water solutions. The error bars in x-direction are 95% confi-dence intervals.  2.4.4 Breakdown of the Stokes-Einstein Equation for Molecules of Different Hydrodynamic Radii As illustrated in Figure 2.16, diffusion coefficients have been measured for other large dyes and water in sucrose water solutions (Table 2.5). In addition, diffusion coefficients have 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.96 0.94 0.92 0.90 0.84 0.78 0.71 0.58 0.1810-1510-1410-1310-1210-1110-1010-910-810-710-610-5Mass fraction sucrose rhodamine 6G fluorescein calcein waterDiffusion coefficient (cm2/s)aw4600.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.01.06 0.99 0.93 0.87 0.81 0.75 0.68 0.59 0.491E-81E-71E-61E-51E-41E-30.010.1110100Tg/T fluorescein rhodamine 6G calcein FITC-Dextran 150Diffusion coefficient (m2/s)aw0.4638  been measured for sucrose in sucrose water solutions. In this work, the measured diffusion coefficients were used to generate Figure 2.16. Shown in Figure 2.16, is the ratio of the meas-ured diffusion coefficients, Dmeasured, to the Stokes-Einstein predicted diffusion coefficients, Dpre-dicted, as a function of the ratio of the radius of the diffusing molecule, Rdiffusing, (i.e. calcein etc.) to the radius of the matrix, Rmatrix, (hydrodynamic radius of sucrose = 4.7 Å25). The results for fluorescein and calcein in Figure 2.16 are based on measured diffusion values by Chenyakin et al.16b. The results for water and sucrose are based on Price et al. (2014)31 and Price et al. (2016)52, respectively.  In Figure 2.16, a Dmeasured/Dpredicted-value that equals 1, indicates agreement between the Stokes-Einstein equation and measured diffusion coefficient values. Values below and above 1 indicate an over- and an underprediction.  For larger molecules with Rdiffusing/Rmatrix-values of 1.00 to 1.57, such as sucrose, fluores-cein, rhodamine 6G and calcein, the Stokes-Einstein equation holds at aw=0.6. However, for molecules as small as water and a Rdiffusing/Rmatrix-value of 0.3, the Stokes-Einstein equation breaks down at aw=0.6 and underpredicts the diffusion coefficient by up to 2.5 orders of magni-tude.  At aw=0.38, the Stokes-Einstein equation breaks down for larger molecules as well as for water. For calcein, the Stokes-Einstein equation underpredicts the diffusion coefficients in su-crose water solutions by a factor of 7 to a factor of 150. For R6G, the values are underpredicted by a factor of 2 to a factor of 50 and for fluorescein the diffusion coefficients are underpredict-39  ed by a factor of 8 to a factor of 500. Sucrose shows an underprediction of a factor of 20 to a factor of 90. Water shows an underprediction of up to 4.5 orders of magnitude. Table 2.5: Properties of the molecules shown in Figure 2.16. Molecule RH (Å) MW (g/mol) Rdiffusing/Rmatrix water 1.41 (Pang (2014)51) 18 0.30 sucrose 4.7 (Ribeiro et al. (2006)25) 342 1.00 fluorescein 5.02 (Mustafa et al. (1993)49) 376 1.07 rhodamine 6G 5.89 (Müller et al.(2008)24) 479 1.25 calcein 7.4 (Tamba et al. (2010)50) 622 1.57  40   Figure 2.16: Dmeasured/Dpredicted as a function of Rdiffusing/Rmatrix. Panel A corresponds to aw=0.6 and Panel B aw=0.38. Dmeasured is the measured diffusion coefficient and Dpredicted is the predicted diffusion coefficient. Rdiffusing is the hydrodynamic radius of the diffusing species and Rmatrix is the hydrodynamic radius of the matrix molecule (su-crose) (Ribeiro et al. (2006)25. The data for calcein and fluorescein was taken from Chenyakin et al. (2016)16b, the data for sucrose was taken from Price et al. (2016)52. In order to calculate Dpredicted using the Stokes-Einstein equation, a parameterization for the viscosity of sucrose water solution was used (see Appendix A). The error bars for all of the data points were calculated conservatively using the largest error possible for Dmeasured as well as Dpredicted  and the total error was determined using a Gaussian error propagation. 0.0 0.5 1.0 1.5 2.010-1100101102103104105 water sucrose fluorescein rhodamine 6G calceinDmeasured /DpredictedRdiffusing /RmatrixB) aw=0.380.0 0.5 1.0 1.5 2.010-1100101102 water sucrose fluorescein rhodamine 6G calceinDmeasured /DpredictedRdiffusing /RmatrixA) aw=0.641  Chapter 3: Diffusion Coefficients and Mixing Times of Fluorescent Organic Mole-cules in Brown Limonene Secondary Organic Material 3.1 Introduction Brown carbon in atmospheric particles, referred to as BrC, is yellow to brown coloured  and absorbs in the near ultra violet (300-400 nm) and the visible range.18 BrC is divided into primary and secondary BrC depending on its mechanism of formation in the atmosphere. Pri-mary BrC is directly emitted to the atmosphere during combustion processes, such as forest fires and biomass burning 53, or it can be directly emitted to the atmosphere from soils, fungi or plants 18, 54. Secondary BrC, on the other hand, is produced by a complex series of gas-phase reactions followed by condensation of reaction products in the atmosphere.  A few terpenes, such as limonene (Table 3.1), can form secondary BrC and 16 % of the global emissions of monoterpenes consist of limonene.20, 55 Once in the atmosphere, limonene can react with OH, NO3 and ozone to form secondary organic material (SOM), a fraction of which can condense to form particles. 56  After the limonene SOM particles are formed, they can react with ammonia, to form brown limonene SOM particles, which show enhanced fluorescence and absorption.57 Once formed, brown limonene SOM particles may play a role in climate and visibility by directly ab-sorbing solar radiation.  At this point, the identity of the compounds that cause the enhanced fluorescence and absorption in both BrC and brown limonene SOM are uncertain.55 Even though the molecular structures of the fluorescent and absorbing substances in BrC and brown limonene SOM are 42  uncertain, some molecular structures for the formation of possible UV- and visible light absorb-ing molecules have been suggested by Nguyen et al. (Figure 3.1).58  Figure 3.1: Simplified suggested reaction mechanism for the formation of larger organic molecules, which have the potential to be light absorbing in the UV- and the visible light range, from limonene (Nguyen et al. (2013)).58 Table 3.1: Physico-chemical data on limonene including the molecular weight (MW) and the molecular structure. Compound Molecular formula Molecular structure MW (g/mol) Limonene C10H16  136.24   When predicting the formation and evaporation of SOM, including brown limonene SOM particles, it is often assumed that diffusion rates of organics are fast (i.e. similar to the diffusion rates of organics within water).8, 15a, 19a-c However, measurements have shown recently that diffusion rates of organics within SOM particles may be much slower than initially thought under certain conditions (such as low relative humidities).22a, 59 If these diffusion rates are sig-nificantly slower than originally thought, then past predictions of SOM particles and their at-mospheric implications may be inaccurate and chemical transport models will need to be modi-fied.   43  To determine diffusion rates of organics in SOM, researchers have previously measured viscosities of SOM particles and then calculated diffusion rates of organics within the SOM using the viscosities and the Stokes-Einstein equation.8, 15d, 23 However, as shown in Chapter 2, this approach can underpredict diffusion rates due to the breakdown of the Stokes-Einstein equa-tion at high viscosities.  There have only been a few direct measurements of diffusion rates within SOM, and most of these studies have been limited to dry conditions. 59a, 60 Within the atmosphere, how-ever, RH varies typically from 20 to 100% (and hence aw varies from 0.2 to 1). This variability of RH and water activity can change diffusion rates of organics significantly, since water acts as a plasticizer and as the water activity in SOM increases, the diffusion rates of organics should also increase. 15e In the current study, diffusion coefficients of organic fluorescent molecules within brown limonene SOM are measured over a wide range of water activities using rFRAP. Brown limonene SOM was chosen as a matrix for this study, since it is thought to be an important type of SOM particle in the atmosphere (because of its high abundance and its ability to absorb light) and since it already contains fluorescent organic molecules (i.e. intrinsic organic fluorophores) that can be used in the rFRAP experiments. This avoids the need to add a fluorescent organic tracer molecule for the rFRAP measurements. From the diffusion rates, mixing times of organic molecules within SOM particles due to molecular diffusion are calculated and the implications are discussed. 44  3.2 Experimental 3.2.1 Generation and Collection of Brown Limonene SOM Particles containing limonene secondary organic material were generated in a 20 L flow tube by dark ozonolysis of limonene by M. Hinks at UC Irvine, California, USA. Pure liquid limo-nene (Sigma-Aldrich, 97%) was injected and volatilized under a flow of dry air resulting in a typ-ical mixing ratio of 70 ppm in the flow tube. Ozone was produced externally by photolysis of O2 (Airgas, Ultra High Purity) and then added to the flow tube resulting in a mixing ratio of 10 ppm of ozone. Within the flow tube, the reaction of gas-phase limonene with ozone led to a concen-tration of 1,000 µg/m3 of limonene SOM particles in the air. Upon exiting the flow tube, the SOM particles then passed through a charcoal denuder to eliminate excess ozone and gas-phase organics. The SOM particles were collected on a hydrophobic slide (Hampton Research) continuously for 45 min using a Sioutas impactor equipped with a single stage (stage D -0.25 μm cut point at 9 SLM collection flow rate) (Figure 3.2). Brown limonene SOM particles were generated by placing the hydrophobic slide con-taining the limonene SOM particles  within a small, glass petri dish, which was inserted within a larger covered petri dish containing a solution of 0.1 M ammonium sulfate (EMD, >99 %). Over a period of three days, ammonia vapour from the solution (300 ppb NH3estimated using the Extended AIM Aerosol Thermodynamics Model II)61 reacted with the fresh limonene SOM form-ing a visible brown colour. 45   Figure 3.2: Preparation of the SOM samples from the reaction of limonene with O3. The or-ange circles represent SOM particles. 3.2.2 Preparation of Thin Films of Brown Limonene SOM at Water Activities Ranging from 0.38 to 0.9  The brown limonene SOM samples were received on hydrophobic glass slides (Hampton Research, Canada) from UC Irvine, California, USA. Three to six small droplets (radius of 100 µm to 225 µm) of the sample were transferred from the sample to a second hydrophobic glass slide using the tip of a needle (BD Precision GlideTM Needle, 0.9 mm x 40 mm). The brown limonene SOM droplets were conditioned at the desired water activity using the setup described in sec-Dry AirO3LimoneneCharcoal DenuderGlass SlideImpactor46  tion 2.2.1. To calculate the conditioning times of the brown limonene droplets with the sur-rounding water vapour, it was assumed that the diffusion rate of water within brown limonene SOM was equal to the diffusion rate of water in sucrose-water mixtures at the same water ac-tivity. This assumption most likely overestimates the time needed for conditioning, since the viscosity of sucrose-water mixtures is higher than the viscosity of brown limonene SOM at the same water activity.8 For each aw, a minimum of three glass slides containing four to six drop-lets of brown limonene SOM were prepared. Once the droplets were conditioned to a known water activity, a second glass slide was placed on top of the droplet, and the droplet was sand-wiched between the two slides as discussed in section 2.2.1, forming a thin film (thickness = 30-90 µm) of the brown limonene SOM. The diffusion coefficients were measured three times per glass slide for each thin film prepared.  3.2.3 Measurements of Diffusion Coefficients Using rFRAP Diffusion coefficients of the intrinsic fluorophores within the brown limonene SOM were measured with rFRAP. The same microscope, Zeiss Axio Observer LSM 5 10 MP laser scanning microscope, and similar scanning settings as described in section 2.3 were used. The scanning laser power was varied between 21.3 to 42.6 µW depending on the fluorescence of the sample. In order to achieve a bleach depth of about 30%, the laser power for photobleaching was varied between 93 and 297 µW depending on the sample. For the experiments, a rectangular geometry was chosen with the sizes of the rectangle depending on the diffusion times with smaller areas for longer diffusion times. The image sizes 47  were chosen in relation to the bleach size such that the diffusing front in the experiments re-mained within the image even for long recovery times. For samples at aw≥0.8 photobleaching areas of 20 µm by 20 µm and image sizes of 199.61 µm by 199.61 µm were chosen. For samples conditioned to 0.5≤aw≤0.7, photobleaching areas of 10 by 10 µm and image sizes of 99.8 µm by 99.8 µm were used, and for aw=0.38 photobleaching areas of 10 by 10 µm and image sizes of 99.8 µm by 99.8 or 59.88 by 59.88 µm were used.  Shown in Figure 3.3 are examples of images recorded during a FRAP experiment with brown limonene SOM films with water activities of 0.38, 0.6 and 0.9. At a low water activity of 0.38, the recovery times are on the order of hours, while at high water activities of 0.9 the re-coveries are on the time scale of seconds. 48   Figure 3.3: Images recorded during an rFRAP experiment with brown limonene SOM at three different water activities: 0.38, 0.6 and 0.9. The orange rectangles depict the area that is to be photobleached. Indicated in the figures are the times (t) after photobleaching.  3.2.4 Analysis of the Images from the rFRAP Recovery Experiments The analysis of images from the rFRAP experiments with brown limonene SOM films was conducted as described in section 2.3. When analyzing the images as a function of time after photobleaching, the images were normalized to the image recorded prior to photobleaching. Images were not analyzed using a region within the image itself, as described in section 2.3, since in some cases there were no large regions within the images unaffected by diffusion. Figure 3.4 shows examples of fluorescence intensities integrated over the width of the bleach area according to Eq. 2.9 as a function of distance along the x-dimension in the image. aw=0.38aw=0.6aw=0.9prephotobleach t=5s t=43s t=108st=24minprephotobleach t=30s t=2minprephotobleach t=5min t=2.6h t=12.8h49  Also included are fits to the data using Eq. 2.9. Figure 3.5 shows plots of w(D,t,r) as a function of time extracted from plots such as Figure 3.4 for the brown limonene experiments. In Figure 3.5, the first five seconds were excluded from the data analysis, since experiments similar to section 2.3.5 showed that reversible photobleaching was occurring during the first five seconds after photobleaching. Note, that in these plots the maximum intensity even far away from the pho-tobleached region decreases with time after photobleaching. This is, because the scanning laser used to monitor the fluorescence with time after photobleaching is also causing some minor photobleaching. However, this does not affect the calculations of the diffusion coefficients, since the diffusion coefficient is only dependent on the bleach width, which is not affected by this gradual photobleaching.  50   Figure 3.4: Fluorescence intensities integrated over the bleach width in the y-direction as a function of x-position (in pixels) for selected brown limonene SOM films at aw = 0.38, 0.6 and 0.9. The blue dots represent the intensity measurements and the red line is a fit to the data using Equation 2.8.aw=0.38aw=0.6aw=0.9t=10 min t=2.6h t=12.8ht=24mint=30s t=2mint=5s t=43s t=108s51   Figure 3.5: Plot of 𝒘(𝑫, 𝒕, 𝒓) = 𝒓𝟐 + 𝟒𝑫𝒕as a function of time. The blue circles represent the data which was obtained from figures such as Figure 3.4. The red line is a linear fit to the data. The diffusion coefficients were obtained from the slopes and are D= 0.0007792/4= 0.0001948 µm2/s=1.95∙10-12 cm2/s for aw=0.0.38, D= 0.04189/4= 0.0105 µm2/s=1.05∙10-10 cm2/s for aw=0.6 and D= 3.753/4= 0.938 µm2/s=9.38∙10-9 cm2/s for aw=0.9.  aw=0.9aw=0.6aw=0.3852  3.2.5 Effect of Laser Power on Measured Diffusion Coefficients In order to see if the laser intensities used for photobleaching influenced the measured diffusion coefficients, experimental diffusion coefficients were determined using two different laser intensities for photobleaching: a laser power of 139.9 µW was used for 20% bleach depth and a laser power of 330 µW for 50% bleach depth. The tests were performed on the same sample. The sample was conditioned to aw =0.9 and for each photobleaching test, a new area was chosen.  The tests at the different bleach depths gave diffusion coefficients which agree within the error margin. Using a laser power of 139.9 µW, a diffusion coefficient of (2.5±0.5)∙10-9 cm2/s was obtained and using a laser power of 330 µW a diffusion coefficient of (2.8±0.1)∙10-9 cm2/s was obtained (uncertainties correspond to confidence intervals). From these observations it was concluded that the laser power used during photobleaching does not significantly influence the measured diffusion coefficients in brown limonene SOM.  3.2.6 Corrections for Non-linearity of the Fluorescence Intensity as a Function of Concen-tration of the Intrinsic Fluorophores As discussed in Section 2.3.4, in rFRAP experiments the relationship between the fluo-rescence intensity and the concentration of fluorophore needs to be known. In the previous chapter, this relationship was determined by measuring the fluorescence intensity as a function of fluorophore concentration in the films. However, this was not possible for the case of the intrinsic fluorophores in brown limonene SOM, because the concentration of the intrinsic fluor-53  ophores could not be changed in the film and the concentration of the intrinsic fluorophores could not be measured. To overcome this limitation, a relationship between the normalized fluorescence signal and the normalized concentration was derived from first principles that could be used together with knowledge of the transmittance of the light through the brown limonene SOM samples to convert normalized fluorescence signal to normalized concentrations (details are below). The fluorescence intensity 𝐹 of a material depends on the intensity of the incoming light, 𝐼0, the intensity of the outgoing light, 𝐼,  and the rate constant, 𝑘′, that takes the ability of a molecule to fluoresce into account:62 𝐹 = 𝑘′(𝐼0 − 𝐼). 3.1 In addition, the absorbance of a material with respect to the concentration of fluorescing mole-cules can be described by the Beer-Lambert law:  𝐴 = 𝜖𝑐𝑙 = log (𝐼0𝐼),  3.2  where 𝜖 is the extinction coefficient, 𝑙 is the distance the light has to travel through the fluores-cent medium (which is the thickness of the thin film in this case) and 𝑐 is the concentration. Eq. 3.1 and Eq. 3.2 can be combined to give the following: 𝐹 = 𝑘′𝐼0(1 − 10−𝜖𝑙𝑐). 3.3 In the experiments, 𝜖, 𝑙, 𝑘′ as well as 𝐼0 are constant, but the photobleaching process changes the concentration 𝑐 of the intrinsic fluorophores and hence the fluorescence intensity 𝐹 chang-54  es. The fluorescence intensity before photobleaching (prephotobleaching) can be described by the following expression: 𝐹1 = 𝑘′𝐼0(1 − 10−𝜖𝑙𝑐1), 3.4 where the subscript 1 represents pre-photobleaching conditions. The fluorescence intensity after photobleaching can be described by the following expression: 𝐹2 = 𝑘′𝐼0(1 − 10−𝜖𝑙𝑐2), 3.5 where the subscript 2 represents post-photobleaching conditions. A normalized fluorescence intensity, 𝐹𝑁, can be introduced with respect to the fluorescence intensity prior to photobleach-ing, 𝐹1: 𝐹𝑁 =𝐹2𝐹1=𝑘′𝐼0(1 − 10−𝜖𝑙𝑐2)𝑘′𝐼0(1 − 10−𝜖𝑙𝑐1)=1 − 10−𝜖𝑙𝑐21 − 10−𝜖𝑙𝑐1. 3.6 The transmittance 𝑇1 prior to the photobleaching process is: 𝑇1 = 10−𝜖𝑙𝑐1 , 3.7 which can be measured with the same confocal laser scanning microscope that is used for the rFRAP experiments. Eq. 3.7 can be substituted into Eq. 3.6 to give the following:  𝐹𝑁 =1 − 10−𝜖𝑙𝑐21 − 𝑇1. 3.8 Equation 3.8 can be solved for 𝑐2, which gives: 𝑐2 = −1𝜖𝑙∙ [log(1 − 𝐹𝑁(1 − 𝑇1))]. 3.9 Since the factor 𝜖𝑙 is not a measured quantity and stays constant, it can be expressed in terms of the pre-bleached concentration, 𝑐1, using Eq.3.7: 𝜖𝑙 = −𝑐1log(𝑇1), 3.10 55  Substituting Eq. 3.10 into Eq. 3.9 gives the following equation, where 𝑐𝑁 =𝑐2𝑐1 is the concentra-tion after photobleaching normalized to the pre-photobleaching concentration: 𝑐𝑁 =log[1 − (1 − 𝑇1) ∙ 𝐹𝑁]log(𝑇1). 3.11 𝑇1 was measured using the same confocal microscope used for the rFRAP experiments and then the fluorescence intensity profile in the rFRAP experiments was transformed to nor-malized concentrations using Eq. 3.11 and the measured 𝑇1. The normalized concentrations were then used when calculating diffusion coefficients. Similar to the diffusion coefficients of R6G in sucrose water solutions, the corrected and uncor-rected diffusion coefficients of the fluorescent organic molecule in brown limonene SOM do not show significant differences (the difference was within the uncertainties of the measurements). Nevertheless, for completeness the corrected values were used in the following sections.  3.3 Results and Discussion 3.3.1 Diffusion Coefficients of Intrinsic Fluorophores within Brown Limonene SOM Error! Reference source not found. shows the diffusion coefficients of intrinsic fluorophores in brown limonene SOM as a function of water activity. The diffusion coefficients ranged from 8.32∙10-9 cm2/s to 3.82 x 10-12 cm2/s as the water ac-tivity decreased from 0.9 to 0.38. The decrease in diffusion coefficients (3.5 orders of magni-tude) as the water activity decreased was expected, since brown limonene SOM is hygroscopic and water is a plasticizer. 63 56  Also included in Error! Reference source not found. are estimates of diffusion coeffi-cients based on measured viscosities of brown limonene SOM 23, the Stokes-Einstein relation and an assumed hydrodynamic radius of 7.34 Å for the intrinsic fluorophores (see next chap-ter). Although the two datasets do not overlap in terms of water activity, if diffusion coeffi-cients are extrapolated to aw=0.3 using a linear fit, good agreement is observed between the two data sets at this water activity. This suggests that the Stokes-Einstein predicted diffusion coefficients are consistent with the measured diffusion coefficients at values of 1.50∙10-14 cm2/s, which is consistent with the results in the previous chapter.  Often it is assumed in chemical transport models when predicting the formation of SOM particles that the mixing time of organics by molecular diffusion within SOM particles is <1 hour. To determine the validity of this assumption, mixing times of organic molecules by molecular diffusion within SOM particles were calculated in Error! Reference source not found. using the measured diffusion coefficients and the following equation:15f  𝜏𝑚𝑖𝑥𝑖𝑛𝑔 =𝐷𝑝24𝜋2𝐷,   3.12  where 𝐷𝑝is the diameter of the atmospheric particle and 𝐷 the measured diffusion coefficient. For the calculation of the mixing time, a diameter of the atmospheric particle of 200 nm was assumed. The mixing time is the time, after which the concentration of the diffusing molecule in the atmospheric particle deviates by 1/e from the equilibrium concentration.8 57   Figure 3.6: Diffusion coefficients of intrinsic fluorophores in brown Limonene SOM (black squares). The y-error bars were calculated from the 95% confidence limit. The grey solid line is a linear fit to the data and the grey dotted line the 95% prediction limit of the fit. The blue vertical bar depicts the highest and the lowest limit of calculated diffusion coefficients of brown limonene SOM (reacted with NH3) based on viscosity measurements from Hinks et al. (2016). The secondary y-axis shows the mixing time, which is the time that would be needed for intrinsic fluorophores to mix within a 200 nm brown limonene particle.  Shown in Error! Reference source not found. are mixing times (secondary y-axis) calcu-lated using Eq. 3.12. Mixing times ranged from 0.001 to 2.6s across water activities of 0.9 and 0.38. These small values illustrate that mixing times of large organics within brown limonene SOM are short (<<1hr) for most of the relative humidities found in the atmosphere. Hence the assumption of well mixed SOM particles in chemical transport models within 1 hr seems appro-priate for brown limonene SOM. The results in this study apply to large organic molecules, since the fluorescent organic molecules studied here likely have molecular weights in the range of 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.010-1310-1210-1110-1010-910-810-7 Measured diffusion coefficients of brown limonene Linear fit to data 95% prediction limit Calculated diffusion coefficients of brown         limonene SOM based on Hinks et al. (2016)Diffusion coefficient (cm2/s)aW0 20 40 60 80 100-3-210-110010110210-310-210-1100101102mixing , 200 nm (s) Mixing timeMixing timeRH58  285 up to 777 g/mol based on the mass spectrometry results and the mechanism proposed by Nguyen et al. (2013) for intrinsic fluorophores in brown limonene SOM particles. 58 For compar-ison some of the most abundant molecules identified in limonene SOM particles are limonon-aldehyde and ketolimononaldehyde, which have molecular weights of 168.23 and 170.20 g/mol, respectively.64    59  Chapter 4: The Hydrodynamic Radius of Intrinsic Fluorophores in Brown Limo-nene SOM 4.1 Introduction Brown limonene SOM is formed from the reaction of limonene with ozone followed by aging with ammonia gas. Brown limonene SOM absorbs in the near UV (300-400 nm) and the visible range and emits fluorescence over the range of 400 to 550 nm.65 Nguyen et al. (2013) studied ketolimononaldehyde, which is a second-generation ozo-nolysis product of limonene.58 The group reacted ketolimononaldehyde with ammonia and looked at the absorbance at wavelengths between 300 and 600 nm as well as performed an ESI/HRMS on the obtained products. The majority of products, that were detected, were mon-omers (C9), dimers (C18), trimers (C27) and tetramers (C36) of ketolimononaldehyde. The prod-ucts shown in Figure 3.1 were chosen as examples for potentially light absorbing compounds and possible intrinsic fluorophores in brown limonene SOM because of their high double bond equivalencies (DBE; C18H20O3 = DBE 9, C18H20N2O2 = DBE 10, C18H23NO3 = DBE 8).58 Another study on composition of light absorbing compounds and intrinsic fluorophores in brown limonene SOM was performed by Bones et al. (2010).55 This study found that the ab-sorbing species in SOM are minor components of SOM which show a maximum mass-to-charge ratio of 800. However, the definite structures of the light absorbing compounds and intrinsic fluorophores in brown limonene SOM have not been solved to date. The goal of the current chapter is to determine the average radius of the intrinsic fluor-ophores in brown limonene SOM. This information provides additional constraints on the 60  mechanism for forming these molecules, which is needed for predicting the formation of brown limonene SOM in the atmosphere. To determine the average radius of the intrinsic fluoro-phores the diffusion rates of R6G in brown limonene SOM were measured and compared to the diffusion rates of the intrinsic fluorophores within brown limonene SOM. Since the radius of R6G is known, the radius of the intrinsic fluorophores can be calculated using the relative diffu-sion rates and the Stokes-Einstein equation. Experiments were carried out at water activities of 0.7, 0.8 and 0.9. At these water activities, diffusion rates are fast and since the fluorescent or-ganic molecules studied in this work are large, the Stokes-Einstein equation should be applica-ble.  4.2 Experimental 4.2.1 Preparation of Brown Limonene SOM Samples at Water Activities of 0.7, 0.8 and 0.9 Brown limonene SOM was generated in a 20L flow tube by dark ozonolysis of limonene by M. Hinks at UC Irvine, California, USA according to section 3.2.1. Brown limonene SOM was received on a glass slide (Hampton Research) from which droplets were transferred to a second glass slide using the tip of a needle (BD Precision GlideTM Needle, 0.9 mm x 40 mm). The brown limonene SOM droplets were conditioned at the desired water activity using the setup de-scribed in section 2.2.1. To calculate conditioning times, it was again assumed that the diffusion rate of water within brown limonene SOM was equal to the diffusion rate of water in sucrose-water mixtures at the same water activity as explained in section 3.2.2. 61  4.2.2 Introduction of R6G into Brown Limonene SOM Samples For the introduction of the R6G dye into brown limonene SOM droplets, the following procedure was used:  First, R6G was dissolved in acetone to give a saturated solution (0.022 g R6G in 50 mL acetone). The solution was then nebulized onto a glass slide (Hampton Research) (Figure 4.1, panel a). In order to ensure an even distribution of R6G, the glass slide was moved in a circular motion through the stream of nebulized acetone/R6G. In the next step, R6G was removed using acetone from half of the glass slide (Figure 4.1, panel b). For the introduction of R6G, the glass slide with the R6G was placed carefully on top of the glass slide with the six brown limonene SOM droplets (Figure 4.1, panel c) and the two slides were sandwiched together forming six thin films of brown limonene SOM, three films with R6G introduced and three films without R6G (Figure 4.1, panel D). The three films without R6G were used to subtract the fluorescence intensity of the intrinsic fluorophores from fluorescence intensity of the samples containing R6G as well as to measure the diffusion coefficients of the intrinsic fluorophores. See below for further details.  62   Figure 4.1: Schematic illustrating the introduction of R6G into pure brown limonene SOM particles. First, the dye is nebulized onto a glass slide (panel a). Then, the dye is removed from half of the glass slide (panel b). The nebulized glass slide containing R6G is placed on top of a glass slide containing brown limonene SOM droplets and the two glass slides are sandwiched together (panel c). The resulting sample has both SOM films with R6G and without R6G (panel d).  caN2R6G in AcetoneGlass slideNebulizerdSOM dropletSOM without R6GSOM with R6GAluminum spacerVacuum greaseGlass slideR6G sprayed on glass slidebRemove with Acetone63  4.2.3 rFRAP Experiments: Measurements of Diffusion Coefficients of R6G and the Intrinsic Fluorophores in Brown Limonene SOM Diffusion coefficients of R6G and the intrinsic fluorophores in brown limonene SOM were determined using rFRAP. The three films without R6G added were used to determine the diffusion coefficients of the intrinsic fluorophores. The three films with R6G added were used to determine the diffusion coefficients of R6G. Although the diffusion coefficients of the intrinsic fluorophores were determined in the previous chapter, they were measured again here to en-sure consistent preparation between the two types of films to eliminate uncertainties when determining the hydrodynamic radius of the intrinsic fluorophores. For photobleaching all the thin films containing R6G, a laser power of 330 µW was used and for scanning 4.08 µW or 6.29 µW were used. For photobleaching the thin films containing only the intrinsic fluorophores, a laser power of 170.5 µW was used and for scanning a laser power of 21.3 µW was used. The geometry chosen for the experiments was a rectangle with varying length (x) and width (y). The sizes of the rectangles were chosen depending on the dif-fusion times with smaller areas for longer diffusion times. The image sizes in relation to the bleach size were chosen such that the diffusing front remained within the monitored area. For samples at aw=0.9 areas of 36 µm by 36 µm and 20 by 20 µm and image sizes of 199.61 µm by 199.61 µm were chosen. For samples conditioned to aw=0.8, areas of 20 by 20 µm and 10x10 µm and image sizes of 99.8 µm by 99.8 µm were used and for aw=0.7 bleach areas of 10x10 µm and image sizes of 99.8 µm by 99.8 µm were used.  64  A minimum of three samples was prepared for each aw and three measurements per sample were obtained. The three values of the diffusion coefficients for R6G, which were ex-tracted for one sample, were averaged.  4.2.4 Analysis of rFRAP Images Recorded for the Samples Containing R6G The brown limonene SOM samples containing R6G contained two types of fluorophores (R6G and the intrinsic fluorophores). To determine only the diffusion coefficient of the R6G, the rFRAP methodology had to be modified from previous chapters. As illustrated in Figure 4.2, images corresponding to films containing only the intrinsic fluorophores were subtracted from images corresponding to films containing R6G and the in-trinsic fluorophores prior to extracting diffusion coefficients for R6G. The subtraction was per-formed for all images prior to normalizing and downsizing. At a laser power of 4.08 µW the flu-orescence intensity of the intrinsic fluorophores was relatively low (Figure 4.2, panel b). Hence, the subtraction process did not strongly affect the intensity profile as shown panel c in Figure 4.2. After the subtraction the new intensity profile was analyzed according to section 2.3.2.  65   Figure 4.2: Schematic illustrating the subtraction of fluorescence intensities of images of pure brown limonene SOM from images of brown limonene SOM films containing R6G. Panel a) shows the image of a fluorescent film consisting of R6G in brown limonene SOM at t=0 s, panel b) shows the image of a fluorescent film consisting of pure brown limonene SOM and panel c) shows an image that was produced by subtracting the fluorescent in-tensity of pure brown limonene SOM from the fluorescence intensity of a brown limonene SOM film containing R6G. Panels e) to g) show the corresponding profiles to the images of panels a) to c).  In order to determine if the subtraction had a large effect on the calculated diffusion coefficients, diffusion coefficients were calculated using images that have been subtracted and ones that have not been subtracted. The difference in diffusion coefficients between the two cases ranged from 2 to 57%, which is within the uncertainty of our measurements. Neverthe-less, for completeness, in the results section only the results from images that had the fluores-cence from the intrinsic fluorophores subtracted were reported.  0 50 100 150 200405060708090100110Integrated Intensity (a.u.)Distance (m)0 50 100 150 200405060708090100110Integrated Intensity (a.u.)Distance (m)0 50 100 150 2002.02.53.03.54.04.5Integrated Intensity (a.u.)Distance (m)- =- =a) b) c) e) f) g) 66  4.2.5 Correction for Reversible Photobleaching In Chapter 2.3.5, it was shown that reversible photobleaching occurs for R6G in sucrose within the first 50s after photobleaching. For the brown limonene SOM experiments, diffusion coefficients were determined using two methods: using all data collected after photobleaching and using only data recorded 50s after photobleaching. The difference in diffusion coefficients determined using both techniques ranged from 1 to 11%, which is within the uncertainty of the measurements. In the results section, we only include data recorded 50s after photobleaching to ensure reversible photobleaching was not an issue in our experiments.  4.2.6 Corrections for Non-linearity of Fluorescence Intensity as a Function of Concentration of R6G The concentration of R6G in brown limonene SOM was estimated from the fluorescence intensity of those films. Since brown limonene SOM are a complex mixture of various chemical compounds, the fluorescence intensity behaviour of R6G in three different media, which might be used to approximate the fluorescence behaviour of R6G in SOM, was studied. The media chosen were water, sucrose water solution (50 wt %) and citric acid water solution (55 wt %). Figure 4.3 shows a plot of the integrated fluorescence intensity as a function of concen-tration for these three different media. The fluorescence intensity varies significantly with the type of media. R6G shows the highest fluorescence intensity in citric acid water solution proba-bly related to the pH. Using the 4th order polynomial fits depicted in Figure 4.4 and the fluores-cence intensities of R6G in brown limonene SOM films, the concentrations of R6G in brown 67  limonene SOM were estimated. The concentrations varied between a minimum of 0.084 mM, using a calculation based on the values for citric acid, or 0.080 mM, when calculated for su-crose, up to 0.543 mM, calculated for citric acid, or 1.165 mM, when calculated for sucrose (Appendix C  ). However, most concentrations were between 0.1 and 0.3 mM, which is within the linear region for the fluorescence intensity. Thus, it was possible to use the fluorescence intensity data without any further corrections.  68   Figure 4.3: Integrated intensity as a function of the concentration of R6G in various media: citric acid in water (55 wt %), sucrose in water (50 wt %) and pure water. Experiments were carried out with a laser power of 4.08 µW. The open and solid symbols depict measurements performed on two different days to confirm repro-ducibility of the measurements. For citric acid and sucrose water solutions measurements were performed on two different days and for R6G in water only one measurement was performed. The error bars represent one standard deviation (1σ) obtained from three different measurements.  0.0 0.5 1.0 1.5 2.0050100150200250300 /  R6G in citric acid water solution/  R6G in sucrose water solution          R6G in waterIntegrated Intensity (a.u.)Conc. (mM)69   Figure 4.4: Concentration of R6G (mM) as a function of integrated intensity in various media, citric acid in water (55 wt %), sucrose in water (50 wt %) and pure water. The solid lines are plots describing the trend of the data. The open and the solid symbols depict measurements performed on two different days to confirm reproducibil-ity of the measurements. This plot is based on the data from Figure 4.3. Table 4.1: Parameterization of the data shown in Figure 4.4. Medium Function Citric acid in water (Green circles) 𝑓(𝑥) = (4.52 ∙ 10−2) − (3.65 ∙ 10−4) ∙ 𝑥 + (8.24 ∙ 10−5) ∙ 𝑥2− (−5.61 ∙ 10−7) ∙ 𝑥3 + (1.31 ∙ 10−9) ∙ 𝑥4 Sucrose in water  (blue triangles) 𝑓(𝑥) = (2.13 ∙ 10−2) + (2.60 ∙ 10−2) ∙ 𝑥 + (1.06 ∙ 10−4) ∙ 𝑥2− (2.10 ∙ 10−6) ∙ 𝑥3 + (1.31 ∙ 10−8) ∙ 𝑥4 Water (black rectangles) 𝑓(𝑥) = exp (−2.17 + (1.17 ∙ 10−2) ∙ 𝑥 + 9.66 ∙ 𝑥2) 0 50 100 150 200 250 3000.00.51.01.52.02.5/  R6G in citric acid water solution/  R6G in sucrose water solution          R6G in waterConc. (mM)Integrated Intensity (a.u.)70  4.3 Results and discussion 4.3.1 Example of Experimental Data In Figure 4.5, fluorescence intensity (integrated over the bleach width in the y-direction) as a function of x-position is shown for water activities of 0.7, 0.8 and 0.9. The red line repre-sents a fit to the data using Eq. 2.8. Figure 4.5 illustrates that Eq. 2.8 fits well to the experi-mental data. Figure 4.8 shows examples of plots of w(D,t,r) as a function of time, which are ex-tracted from plots such as Figure 4.5. Figure 4.6 illustrates that plots of w(D,t,r) as a function of t, are described well by a linear function, as expected. 71   Figure 4.5: Fluorescence intensities as a function of distance in the x direction (in pixels) for selected films of R6G in brown limonene SOM at aw = 0.7, 0.8 and 0.9. The blue dots represent the intensity data and the red curve is a fit to the data using Eq. 2.8. Before the fit was applied, the fluorescence intensity data was normalized to an image taken prior to photobleaching.  t=50s t=100saw=0.9t=50s t=200saw=0.8aw=0.7t=50s t=300s72   Figure 4.6: Plot of 𝒘(𝑫, 𝒕, 𝒓) = 𝒓𝟐 + 𝟒𝑫𝒕 as a function of time. The blue open circles represent experimental data, which was obtained from figures such as those in Figure 4.5. The red line is a linear fit to the data. The diffusion coefficients were obtained from the slopes and are. The diffusion coefficients are D= 0.0583 µm2/s=5.83∙10-10cm2/s, 0.1182 µm2/s=1.18∙10-9 cm2/s and 0.8292 µm2/s=8.29∙10-9 cm2/s for aw = 0.7, 0.8 and 0.9, respectively. aw=0.9aw=0.8aw=0.773  4.3.2 Measured Diffusion Coefficients of the Intrinsic Fluorophores in Brown Limonene SOM Shown in Figure 4.7 are the diffusion coefficients of the intrinsic fluorophores in brown limonene SOM determined from work related to this chapter and compared with the diffusion coefficients of the intrinsic fluorophores measure independently in chapter 3. At water activi-ties of 0.7 and 0.8, the measurements agree within the uncertainties of the measurements. At a water activity of 0.9, the measurements determined in this chapter are on average a factor of 3 higher than the values determined in the previous chapter. The difference between the two measurements may be related to the uncertainties in the water activities (±0.025) as well as small differences in the composition of the SOM from batch to batch, although the latter seems unlikely since good agreement is observed at water activities of 0.7 and 0.8. 74   Figure 4.7: Comparison of diffusion coefficients of the intrinsic fluorophores in brown limonene SOM measured for this chapter (to determine the hydrodynamic radius of the intrinsic fluorophores (green rectangles)) with diffusion coefficients of the intrinsic fluorophores measured in Chapter 3: (black rectangles). The symbols are average values and the error bars depict the 95% confidence limit. 4.3.3 Measured Diffusion Coefficients of R6G in Brown Limonene SOM Figure 4.8 shows the diffusion coefficients of R6G in brown limonene SOM in compari-son to the diffusion coefficients of the intrinsic fluorophores in brown limonene SOM measured at identical water activities and in an identical same matrix. The diffusion coefficients of R6G in brown limonene SOM are on average smaller than the diffusion coefficients of the intrinsic fluorophores. This leads to the conclusion that the average radius of the intrinsic fluorophores must be larger than the hydrodynamic radius of R6G.  0.65 0.70 0.75 0.80 0.85 0.90 0.9510-1010-910-8Diffusion coefficients of the intrinsic        fluorophores in brown limonene SOM        for radius calculationDiffusion coefficients of the intrinsic        fluorophores in brown limonene SOM        from chapter 3Diffusion coefficients (cm2/s)aw75   Figure 4.8: Comparison of diffusion coefficients of R6G in brown limonene SOM (blue rectangles) with diffusion coefficients of the intrinsic fluorophores in brown limonene SOM (green rectangles) determined in this chapter for the radius calculations. The symbols are the average values and the error bars give the 95% confidence limit. 4.3.4 Calculation of the Hydrodynamic Radius of Intrinsic Fluorophores in Brown Limonene SOM For the calculation of the hydrodynamic radius of the intrinsic fluorophores in brown limonene SOM, the ratio of the diffusion coefficient of R6G in brown limonene SOM (D(R6G)) to the diffusion coefficient of intrinsic fluorophores in brown limonene (D(SOM)) was calculated for each activity. Table 4.2 shows the average ratio as well as the 95% confidence interval at the three different water activities. The ratio at each water activity agrees within the uncertainty of 0.65 0.70 0.75 0.80 0.85 0.90 0.9510-1010-910-8Diffusion coefficients of R6G in brown limonene SOMDiffusion coefficients of the intrinsic fluorophores in         brown limonene SOM for radius calculationDiffusion coefficients (cm2/s)aw76  the measurements (95% confidence interval), indicating that the ratio is not a strong function of the water activity. Using the average value of the ratio for all water activities of 1.25 and a hydrodynamic radius of R6G of 5.89 Å (Müller et al.24), the average hydrodynamic radius of the intrinsic fluor-ophores diffusing in brown limonene SOM equals (7.34 ±1.47) Å. The uncertainty in the number was calculated using 95% confidence limit of the average value for all water activities (Table 4.2). Table 4.2: Average and 95 % confidence intervals of the diffusion coefficients of R6G (D(R6G)) to the diffusion coefficient of the intrinsic fluorophores(D(SOM)) in brown limonene SOM at three different water activities. aw Average D(R6G)/D(SOM) 95 % confidence in-terval 0.9 1.37 ±0.13 0.8 1.09 ±0.30 0.7 1.28 ±0.32 Average 1.25 ±0.25   4.3.5 Comparison with Previous Suggestions of the Molecular Structures and Formulas for the Light Absorbing Compounds and Intrinsic Fluorophores in Brown Limonene SOM As discussed in the introduction of this chapter, Nguyen et al. (2013) suggested the following molecular formulas for the light absorbing compounds and intrinsic fluorophores in brown lim-onene SOM: C18H20O3, C18H20N2O2, and C18H23NO3.58 Here, the focus lies on the dimers suggest-ed by Nguyen et al. (2013), since the structures of these molecules were provided by Nguyen et al. (2013).The structures of these molecules are shown in Figure 3.1. To calculate a lower limit 77  to the hydrodynamic radii of these molecules, a spherical geometry was assumed and a density of 1.3 g/cm3.66 With these assumptions hydrodynamic radii of 4.51 Å, 4.48 Å and 4.42 Å, respec-tively, were calculated. To calculate an upper limit of the hydrodynamic radii for these mole-cules, the Van-der-Waals radii (using the molecular structures together with the bond angles and bond lengths) were calculated and it was assumed that the molecules diffused perpendicu-lar to the plane containing the carbon backbone of the molecule. With these assumptions hy-drodynamic radii of 6.3 Å, 7.6 Å and 5.5 Å, respectively, were obtained. These upper limits are consistent with the measured hydrodynamic radius. Hence, the molecules suggested by Nguyen et al. (2013) are consistent with the measured hydrodynamic radii of the intrinsic fluorophores studied here.58 78  Chapter 5: Conclusion and Future Work 5.1 Measurement of Diffusion Coefficients in Proxies of Atmospheric Particles In chapter 2 diffusion coefficients of R6G in sucrose water solutions were measured at water activities ranging from 0.38 to 0.8 using rFRAP. In chapter 3, diffusion coefficients of in-trinsic fluorophores in brown limonene SOM were measured at water activities ranging from 0.38 to 0.9 using rFRAP. The range of diffusion coefficients measured is listed in Table 5.1.  For R6G in sucrose water solutions, a breakdown of the Stokes-Einstein equation was observed at water activities of 0.38 (3.3 × 106 Pa s and a Tg/T of 0.94) with a deviation from the measured diffusion coefficients by a factor of 2 to 50. In chapter 3, diffusion coefficients of the intrinsic fluorophores in brown limonene SOM were measured for the first time. A dependence of diffusion coefficients on water activity was observed and mixing times were calculated based on the measured diffusion coefficients. Since the mixing times even at water activities as low as 0.38 did not exceed 2.6s, rapid mixing within brown limonene SOM can be assumed in atmospheric models. These research findings will lead to improved models of air quality and climate. Table 5.1: Diffusion coefficients of R6G in sucrose-water solutions and the intrinsic fluorophores in brown limo-nene SOM. Fluorescent dye Tested medium Diffusion coefficient, aw,high (cm2/s) Diffusion coefficient, aw,low (cm2/s) Rhodamine 6G (R6G) Sucrose-Water 4.75∙10-9 at aw=0.8 1.5∙10-14 at aw=0.38 Intrinsic fluorophores in brown limonene SOM brown limonene SOM 8.32∙10-9 at aw=0.9 3.82∙10-12 at aw=0.38  79  5.2 Average Hydrodynamic Radius of the Intrinsic Fluorophores in Brown Limonene SOM Chapter 4 focuses on the calculation of the average hydrodynamic radius of intrinsic fluorophores in brown limonene SOM. This was achieved by measuring the diffusion coeffi-cients of R6G within brown limonene SOM and measuring the diffusion coefficients of the in-trinsic fluorophores within brown limonene SOM at three different water activities, 0.7, 0.8 and 0.9. Assuming the Stokes-Einstein equation is valid under these conditions (high water activities and low viscosities) the hydrodynamic radius could be calculated using the known hydrodynam-ic radius of R6G. The average hydrodynamic radius of the intrinsic fluorophores was found to be7.34±1.47 Å.   5.3 Consideration of Future Work In order to be able to calculate diffusion coefficients accurately from viscosities, even outside the validity range of the Stokes-Einstein equation more data would be needed at lower water activities (aw<0.38). Corrections factors could be calculated for water activities where the Stokes-Einstein equation breaks down.   Since the ratio of the radius of the diffusing molecule in comparison to the matrix mole-cules is an important factor that determines when the Stokes-Einstein equation breaks down, measurements of diffusing molecules of sizes between 1.4 Å < RH< 5.02 Å (a ratio of Rdiffus-ing/Rmatrix between 1 <Rdiffusing/Rmatrix< 3.6) and sizes between 7.4 Å < RH< 83.1 Å (a ratio of Rdiffus-ing/Rmatrix between 5.2 <Rdiffusing/Rmatrix< 60) in sucrose-water solutions should be studied. This would cover size ranges that have not been studied in this work and would give a better picture 80  of the breakdown of the Stokes-Einstein equation. In this work, diffusing molecules of smaller radii have not been studied because of limitations in excitation wavelengths available for the study. Another factor, important in the atmosphere other than the water activity, is the tem-perature. Temperatures found in the troposphere go down as low as -56°C (217 K).2 The study presented in this work was performed at room temperature; however, a study of the change of the diffusion coefficients as a function of temperature at varying water activities would give insight into the temperature dependence of mixing times and reaction rates within and reac-tion rates of atmospheric particles. These studies could be done for sucrose water solutions and brown limonene SOM particles. 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Atmospheric Chemistry and Physics 2008, 8 (17), 5221-5244.  97  Appendices Appendix A   Table 5.1: Selected parameters used in rhodamine 6G rFRAP experiments in sucrose water solutions. eq is the characteristic diffusion time of water within sucrose-water droplet (see Eq. 2.1). texp is the time used for condi-tioning.  aw Slide # Dropletradius (µm) eq  texp Measured D value (µm2/s) 0.80 1 350 11 min 1 h 0.492 2 350 11 min 1 h 0.492 3 350 11 min 1 h 0.441 0.75 1 350 17 min 1 h 0.0840 2 350 17 min 1 h 0.0918 3 350 17 min 2 hrs 0.0783 0.60 1 140 0.85 hrs 3 hrs 0.00194 2 125 0.67 hrs 3 hrs 0.00545 3 90 0.35 hrs 3 hrs 0.00259 0.52 1 190 11 hrs 6 d 15 hrs 0.000125 2 150 7 hrs 6 d 15 hrs 0.000155 3 200 12 hrs 6 d 15 hrs 0.000143 0.38 1 75 1 d 6 d 3.98E-06 2 60 17 hrs 12 d 2.29E-06 3 100 2 d 93 d 9.56E-07 4 75 1 d 93 d 6.44E-07      98  A.1 Parameterization of the viscosity of sucrose in water as a function of water activity  Figure 5.1: Parameterization of the viscosity as a function of water activity for sucrose water solutions using viscosity data from several sources.  Table 5.2: Fit parameters of the third order polynomial fit (f(x) =A+ Bx + Cx2 + Dx3) in Figure 5.1.  A B C D R2 Fit parameters 20.97 -0.5641 0.0057 -2.4365 x 10-5 0.9948   0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.020 30 40 50 60 70 80 90 10010-410-310-210-11001011021031041051061071081091010RH (%) Power et al. 2013 Telis et al. 2007 Quintas et al. 2006 Migliori et al. 2007 Handbook of chemistry,        Lide 2001 Green and Perry 1991 Swindells et al. 1958 Polynominal fitViscosity (Pa s)aw99  A.2 Determination of water activities of sucrose solutions The amount of sucrose which was needed to obtain a certain water activity was calcu-lated using a parameterization from Zobrist et al. (2011)67:  𝒂𝒘(𝑻, 𝒘) =(𝟏 + 𝑨𝒘)(𝟏 + 𝑩𝒘 + 𝑪𝒘𝟐)+ (𝑻 − 𝑻𝜽)(𝑫𝒘 + 𝑬𝒘𝟐 + 𝑭𝒘𝟑 + 𝑮𝒘𝟒).  5.1  In this parameterization, the water activity, 𝑎𝑤, is  calculated as a function of the tem-perature 𝑇 and the concentration of sucrose in water 𝑤 : 𝑤 = 𝑤𝑒𝑖𝑔ℎ𝑡 𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑜𝑓𝑠𝑢𝑐𝑟𝑜𝑠𝑒(𝑤𝑡 %)/100,   5.2 𝑇𝜃 is a reference temperature of 298.15 K and 𝐴 to 𝐺 are fit parameters (𝐴 = −1, 𝐵 =−0.99721, 𝐶 = 0.13599, 𝐷 = 0.001688, 𝐸 = −0.005151, 𝐹 = 0.009607, 𝐺 = −0.006142). The experiments were performed at room temperature (19.9 °C to 22.4 °C) and because minor changes of the temperature only results in minor changes of the 𝑎𝑤, calculations regarding the 𝑎𝑤 were performed using a temperature of 𝑇 = 20°C.  A.3 Polynomial fit for diffusion coefficients of water from Price et al. Table 5.3: Parameters from the polynomial fit in Figure 2.15 with f(x)=A+Bx+Cx2+Dx3 based on Price et al.31 Molecule A B C D Water -20.89 25.92 -26.97 13.25    100  Appendix B   Table 5.4: Selected parameters used in rFRAP experiments with the intrinsic fluorophores in brown limonene SOM. eq is the characteristic diffusion time of water within sucrose-water droplet (see Eq. 2.1). texp is the time used for conditioning. aw Slide # Dropletradius (µm) cd  texp Measured D value (µm2/s) 0.90 1 200 23 s 17 min 0.60 2 175 17 s 17 min 1.01 3 160 15 s 22 min 0.82 4 200 23 s 22 min 0.91 0.80 1 175 2.2 min 22 min 0.064 2 175 2.2 min 18 min 0.073 3 175 2.2 min 18 min 0.030 0.70 1 160 11.3 min 1.5 h 0.012 2 160 11.3 min 3 h 0.017 3 125 7 min 3 h 0.018 0.60 1 190 1.5 h 8 h 0.0092 2 225 2.2 h 8 h 0.0086 3 175 1.3 h 7 h 0.0094 0.52 1 150 6.6 h 38 d 0.0024 2 185 10 h 38 d 0.0024 3 150 6.6 h 38 d 0.0025 0.38 1 200 7.6 d 47 d 5.68E-4 2 100 2 d 47 d 3.68E-4 3 200 7.6 d 35 d 2.10E-4 101  Appendix C   The values for the concentration of R6G in citric acid and sucrose and water were calculated by subtracting the value of “Fluores-cence without R6G” from “Fluorescence with R6G” and using the parameterization to calculate the concentration value. Table 5.5: Values of diffusion coefficients, fluorescence intensities and calculated concentrations in citric acid water solution and sucrose water solution for 90% RH of R6G in brown limonene SOM.eq is the characteristic diffusion time of water within sucrose water droplet (see Eq. 2.1).  texp is the time used for conditioning. aw Slide Number of Bleach Spot cd  texp Droplet radius (µm) Fluorescence without R6G (a.u.) Fluorescence with R6G (a.u.) Conc. In citric acid Conc. In sucrose water Diffusion coefficient (µm) 0.9 1 1 90 s 18 min 400 7.8 72 0.273 0.290 0.203 2 7.8 69 0.259 0.279 0.207 3 7.8 89 0.354 0.373 0.1972 4 1 60 s 20 min 320 12 57 0.203 0.215 0.3529 2 12 64 0.236 0.243 0.3529 3 12 55 0.194 0.206 0.403 8 1 55 s 21 min 310 5 31 0.098 0.130 0.1961 2 5 34 0.108 0.144 0.17001 3 5 34 0.108 0.144 0.1716 4 5 32 0.102 0.134 0.1736 9 1 98 s 21 min 415 5.6 30 0.091 0.122 0.1962 2 5.6 33.5 0.099 0.139 0.2131 3 5.6 34 0.100 0.141 0.2399 102  aw Slide Number of Bleach Spot cd  texp Droplet radius (µm) Fluorescence without R6G (a.u.) Fluorescence with R6G (a.u.) Conc. In cit-ric acid Conc. In sucrose water Diffusion coefficient (µm) 0.9 12 1 62 s 24 min 330 4 78 0.302 0.334 0.3920 2 4 79 0.307 0.338 0.4110 3 4 76 0.292 0.324 0.3785 14 1 100 s 59 min 420 4.6 132 0.543 1.165 0.2013 2 4.6 100 0.405 0.490 0.2294 3 4.6 104 0.423 0.537 0.2412 20 1 62 s 80 min 330 9 32 0.102 0.115 0.6659 2 9 32 0.102 0.115 0.7906 3 9 39 0.127 0.148 0.8147 22 1 82 s 70 min 380 9 32.5 0.103 0.118 0.8821 23 1 62 s 70 min 330 9 30 0.095 0.106 0.6977 2 9 26.5 0.084 0.089 0.4799 3 9 27 0.086 0.092 0.3058    103  Table 5.6: Values of diffusion coefficients, fluorescence intensities and calculated concentrations in citric acid water solution and sucrose water solution for 80% RH of R6G in brown limonene SOM. eq is the characteristic diffusion time of water within sucrose water droplet (see Eq. 2.1). texp is the time used for conditioning. aw Slide Number of Bleach Spot cd  texp Droplet radius (µm) Fluorescence without R6G (a.u.) Fluorescence with R6G (a.u.) Conc. In citric acid Conc. In sucrose water Diffusion coefficient (µm) 0.8 3a 1 6.5 min 45 min 300 7 64 0.236 0.262 0.02073 2 7 66 0.245 0.270 0.02591 3 7 76 0.292 0.310 0.06527 5 1 6.5 min 67 min 300 14 36.5 0.117 0.113 0.009281 2 14 30 0.095 0.082 0.01489 7 1 6.5 min 36 min 300 11.5 35 0.112 0.118 0.05436 11 1 4.16 min 49 min 240 7.2 65 0.240 0.265 0.1336 2 7.2 61.5 0.224 0.252 0.09991 3 7.2 58 0.208 0.238 0.1033 14 1 4.9 min 49 min 260 2 75 0.288 0.329 0.01435 2 4.9 min 260 2 84 0.330 0.378 0.01722   104  Table 5.7: Values of diffusion coefficients, fluorescence intensities and calculated concentrations in citric acid water solution and sucrose water solution for 70% RH of R6G in brown limonene SOM. eq is the characteristic diffusion time of water within sucrose-water droplet (see Eq. 2.1).  texp is the time used for conditioning. aw Slide Number of Bleach Spot cd  texp Droplet radius (µm) Fluorescence without R6G (a.u.) Fluorescence with R6G (a.u.) Conc. In citric acid Conc. In sucrose water Diffusion coefficient (µm) 0.7 3 1 35 min 45 min 280 11 42 0.139 0.153 0.05486 2 11 42 0.139 0.153 0.04915 3 11 41 0.135 0.148 0.04454 5 1 40 min 119 min 300 8 56 0.199 0.227 0.01782 2 8 48 0.163 0.194 0.01023 3 8 50 0.172 0.202 0.02011 6 1 48 min 119 min 330 11 28 0.089 0.087 0.01395 2 11 26.5 0.084 0.080 0.01199 9 1 18 min 120 min 200 10.5 68 0.254 0.264 0.005821 2 10.5 72 0.273 0.280 0.004813 3 10.5 86 0.340 0.341 0.00228  

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