Visualizing reaction and diffusion in xanthan gum aerosol particles exposed to ozone

Atmospheric aerosol particles are composed of inorganic and organic compounds. The latter can have 25 a high viscosity that can lead to low molecular diﬀusion in particles and slower chemical reactions than what would be expected if particles were assumed to be in equilibrium with the gas phase following Henry’s Law and reactants were considered to be well-mixed. Heterogeneous chemical reaction rates between gas phase oxidants and condensed phase reactants can be slowed when relative humidity de- creases likely due to the loss of water and of its plasticizing eﬀect on viscous organic matter. Models have predicted spatial concentration gradients in reactant concentration within particles depending on 31 size as a consequence of this phenomena. However, these have never been observed for atmospherically 32 relevant particle diameters. We investigated the reaction between ozone and aerosol particles composed 33 of xanthan gum and FeCl 2 and observed the in situ chemical reaction that oxidized Fe 2+ to Fe 3+ using state of the art X-ray spectromicroscopy. Iron oxidation state of particles as small as 0.2 µ m in diameter 35 were chemically mapped for hours with time resolution on the scale of minutes and spatial scales of tens 36 of nanometers. We found the loss of Fe 2+ accelerated not only when ozone concentration increased from 37 100 to 2000 ppb, but also when relative humidity, RH , increased from 0 to 80% at 20 ◦ C. We calcu- 38 lated the Fe 2+ fraction, α , out of the total iron and developed a unique analytical procedure to derive 39 concentric 2-D column integrated proﬁles with high accuracy. We demonstrated that particle surfaces 40 became oxidized while the core remained completely unreacted at RH = 0 − 20%. At RH = 40 − 80%, 41 gradients in α developed over time, e.g. where α = 0 . 1 and 0.5 at the surface and center, respectively, of 42 a 1 µ m diameter particle. We used the kinetic multi-layer model for aerosol surface and bulk chemistry (KM-SUB) to simulate reaction constrained with our observations and inferred key parameters as a function of RH including Henry’s Law constant for ozone, H O 3 , and diﬀusion coeﬃcients for ozone and iron, D O system. A discussion of other reactive systems of atmospheric importance and why a reacto-diﬀusive framework may be pervasive in aerosol chemistry is presented. Our results have vast implications e.g. for predicting aerosol toxicity changes, loss rate of known tracer compounds to track air mass origin and other aerosol compositional changes important for light scattering and cloud formation. spatio-chemical data allows a unique and exact constraint for modeling aerosol internal chemical proﬁles, i.e. simultaneous reproduction of bulk Fe 2+ depletion and the spatio- temporal evolution of O 3 and Fe 2+ reaction. In the context of our results, we discuss the applicability of the reacto-diﬀusive limiting case and the importance of direct observational constraints on model 160 predictions of atmospheric aerosol chemical aging.


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Atmospheric aerosol particles are composed of inorganic and organic compounds. The latter can have 25 a high viscosity that can lead to low molecular diffusion in particles and slower chemical reactions than 26 what would be expected if particles were assumed to be in equilibrium with the gas phase following 27 Henry's Law and reactants were considered to be well-mixed. Heterogeneous chemical reaction rates 28 between gas phase oxidants and condensed phase reactants can be slowed when relative humidity de-29 creases likely due to the loss of water and of its plasticizing effect on viscous organic matter. Models 30 have predicted spatial concentration gradients in reactant concentration within particles depending on 31 size as a consequence of this phenomena. However, these have never been observed for atmospherically 32 relevant particle diameters. We investigated the reaction between ozone and aerosol particles composed 33 of xanthan gum and FeCl 2 and observed the in situ chemical reaction that oxidized Fe 2+ to Fe 3+ using 34 state of the art X-ray spectromicroscopy. Iron oxidation state of particles as small as 0.2 µm in diameter 35 were chemically mapped for hours with time resolution on the scale of minutes and spatial scales of tens 36 of nanometers. We found the loss of Fe 2+ accelerated not only when ozone concentration increased from 37 100 to 2000 ppb, but also when relative humidity, RH, increased from 0 to 80% at 20 • C. We calcu-38 lated the Fe 2+ fraction, α, out of the total iron and developed a unique analytical procedure to derive 39 concentric 2-D column integrated profiles with high accuracy. We demonstrated that particle surfaces 40 became oxidized while the core remained completely unreacted at RH = 0 − 20%. At RH = 40 − 80%, 41 gradients in α developed over time, e.g. where α = 0.1 and 0.5 at the surface and center, respectively, of 42 a 1 µm diameter particle. We used the kinetic multi-layer model for aerosol surface and bulk chemistry our understanding of how these small molecules may diffuse through and react within atmospheric  Observations and models mentioned above gave great insight to how molecules react and diffuse in 107 aerosol particles, however direct observation of particle internal concentration gradients of reactants or particles contained detectable iron. We note that iron oxidation state from particle to particle varied 137 and appeared inhomogeneously distributed in this ambient aerosol population 57 . As a polysaccharide 138 and biopolymer, XG is a unique model compound of marine derived organic matter in atmospheric 139 aerosol 66 . The change in XG composition by a few percent in water is enough to result in large changes 140 in solution viscosity, a property that is highly desired for additives used in the food industry 67,68 . XG 141 hygroscopicity is of particular interest as decreasing RH leads to decreasing water content and increasing 142 viscosity 66,69 . We note that XG is a reference compound for quantifying what is known as "transparent 143 exopolymer particles" in oceans 70-72 which has recently been found in ambient air at concentrations of 144 2 µg m −3 in the North Atlantic ocean 73 . For these reasons, the XG/Fe 2+ system is an interesting proxy 145 for understanding molecular diffusion and reaction in atmospheric marine derived aerosol.

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Here, we used iron as a tracer for STXM/NEXAFS to unambiguously identify the spatial location 147 within particles where oxidation reactions took place. These data were used to experimentally derive 2-D 148 projected α profiles within thousands of individual particles in situ yielding the first direct evidence of 149 chemical reaction gradients in viscous particles. We report on how gradients change when particles were 150 dry (RH = 0%) or humidified at RH = 20, 40, 60 and 80%. KM-SUB was used to model diffusion and 151 reaction in spherical shells of aerosol particles and derived 3-D radial profiles of α using known chemical 152 reaction rates. These 3-D α profiles were then used to calculate 2-D column integrated profiles of α for 153 direct comparison with STXM/NEXAFS observations. Model parameters were diffusion coefficients for 154 Fe and O 3 , D Fe and D O 3 , respectively, and were described with a Vignes-type equation as a function 155 of water mole fraction. Henry's Law constant for O 3 in the XG/FeCl 2 matrix, H O 3 , was also derived. 156 We claim our STXM/NEXAFS spatio-chemical data allows a unique and exact constraint for modeling 3 Results and Discussion 162 3.1 NEXAFS spectra 163 Figure 1 shows example NEXAFS spectra of oxidized XG/FeCl 2 particles at dry and humidified con-164 ditions in comparison with the reference material FeCl 2 measured here and FeCl 2 and FeCl 3 from lit-165 erature 57 . Two absorption peaks at 707.8 and 709.6 eV were observed for oxidized XG/FeCl 2 particles 166 and were in agreement with Fe 2+ and Fe 3+ peak absorption energies for FeCl 2 and FeCl 3 , respectively.

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The nearly identical peak positions may indicate that humidity and the organic polysaccharide matrix 168 does not influence Fe electronic excitations. Important to note from Fig. 1   shows that when exposed only to O 2 , no change in α was observed at any RH investigated. Therefore, 180 any reaction taking place between O 2 and Fe 2+ in our particles over t was negligible. have also increased. 201 We acquired high spatial resolution chemical images to quantify α over the particles in two di-202 mensions. To accomplish this, α was averaged over all pixels identified at the perimeter of particles 203 irrespective of particle size. In other words, α was calculated from the particle perimeter to 1 pixel, or 204 35 nm, from the surface. Then, all adjacent concentric pixels toward the particle center (from 1 to 2 205 pixels from the particle surface or 35-70 nm) were identified and their corresponding α values averaged.

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This continued toward the center of particles and generated a 2-D concentric profile of α, which is also 207 a column integrated profile. conditions than for more humid conditions. Prior to exposure, initial values of α were not equivalent to 215 1, implying that the short time (∼ 30 minutes) spent in contact in ambient laboratory air was enough to under more humid conditions. We argue that faster diffusion of Fe 2+ out of the particle core and faster 243 diffusion of O 3 into the particle from the surface brings them together more readily allowing reactions 244 to proceed at a faster rate.  Table 1.

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A rate coefficient for O 3 and FeCl 2 was derived from previous studies 52-56 following, and 263 FeO The rate coefficient, k, for reaction R1 has been reported 52-56 in a range k R1 = (1.7 − 8.2) × 10 5 M −1 s −1 . reaction R2 is very fast. Therefore, we suggest the net reaction where k R3 = k R1 . We use k R3 = 3.7 × 10 5 M −1 s −1 (which is the geometric mean of reported k R1 values) 278 equivalent to 6.2 × 10 −16 cm 3 s −1 indicated in Table 1 which are shown in Fig. S7 of the ESI † . Water uptake of XG as a function of RH has been previously 290 quantified using a hygroscopicity factor, κ = 0.08 66 . We calculated the water concentration in particles 291 assuming XG contributes primarily to the water uptake and insignificantly from FeCl 2 . respectively, in agreement with our observations. Consistently, Fe is predicted to remain more reduced 296 in particle cores than at particle surfaces. Although not explicitly fit, the modeled α averaged over the  Table 1 and where x w is the mole fraction of water and D O 3 (RH = 0%), D Fe (RH = 0%), H O 3 (RH = 0%), C and D 306 are fitting parameters given in Table 2. Other parameters given in Table 2  "salting-in" effect. This is characterized by an increase in the product of ionic strength and activity 328 coefficients of the solution (i.e. decreasing water content) and thus causes an increase in gas solubility.

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We note that a similar result is found for O 2 solubility, which is generally higher in organic liquids than 330 in water 88,89 . The degree to which activity of XG/FeCl 2 solutions changes as a function of RH is not 331 known. Therefore, we use again a Vignes-type equation as a function of water mole fraction (eqn (7)) to 332 parameterize the RH dependence of H O 3 shown in Fig. 4. A mixing rule was also derived for comparison where wt w is the weight fraction of water in the particles. Equation (9) is also shown in Fig. 4 Fig. 3 (solid lines). Gradients in α at RH = 0% (Fig.   364 5a) spanned a few nanometers. A reduction in gradients to roughly a uniform profile over hundreds on nanometers was determined as RH increased to 80% as seen in Fig. 5i. Despite the extent of gradients 366 in α, O 3 was found only in the first picometer to 2.7 nm at RH = 0 to 80%, respectively. We note that 367 a length of 1 pm is much smaller than molecular scale and the Fe 2+ ionic diameter of 0.7Å. However,

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constraining layer thickness to 0.3nm as previously done 47 could not resolve O 3 gradients in our case. 369 We therefore can only define layer thickness to satisfy continuum condition, meaning that we allowed 370 layer thickness without a lower limit. We argue that this has no consequence, however, because bulk  Our observations allowed us to test the most basic of assumptions for predicting α, that our particles 376 were well-mixed for both Fe 2+ and Fe 3+ and also for O 2 and O 3 in equilibrium with Henry's Law.

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Oxidation of Fe 2+ due to O 2 exposure follows the reaction where γ is the reactive uptake coefficient and ω is the mean thermal velocity of O 3 . It is important 406 to note that eqn (10) is the net flux that results in a loss of gas phase O 3 because γ is defined as the 407 probability that a molecular collision on an aerosol particle surface results in an irreversible loss from 408 the gas phase. The first order loss rate of O 3 from the gas phase is then where N p is the number of particles per volume of air and S p is the surface area of a single particle such 410 that the product N p S p is the total surface area of aerosol particles per volume of air. Implicit to eqn 411 (10) and (11) is that net O 3 loss in the gas phase equals to the Fe 2+ loss or where [Fe 2+ ] g is exactly the number of Fe 2+ atoms in the particle phase per unit volume of air. Typically,

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[Fe 2+ ] g is not considered and so a conversion to the more familiar particle phase concentration is as 414 follows, where [Fe 2+ ] is previously defined as the number of Fe 2+ atoms in the particle phase per unit volume of 416 particle phase and V p is the volume of a single particle such that the product N p V p is the total volume 417 of aerosol particles per volume of air. Substituting eqn (12) and (13) into eqn (11) yields Notice in Fig. 5 where R is the universal gas constant. When substituting in eqn (15) into (14), the square-root depen-423 dence on the depletion of Fe 2+ in a particle can be written as is the equation for the reacto-diffusive rate constant 36 . We note that S p /V p of half spheres on a flat plate is 6/d p . Solving eqn (16) and substituting in eqn (17) and α from eqn (1) yields, Rearranging eqn (18) and again recognizing that The left hand side of eqn (19) is entirely dependent on measurable and available quantities while the 429 right hand side is in terms of the fitted parameters used in KM-SUB. Therefore, this provides a point of 430 comparison to evaluate the suitability of the reacto-diffusive framework to predict Fe oxidation reaction.

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Equation (19) is applied to each individual particle probed. Figure 6 shows a box plot of experimentally unrealistic. However, we choose to include these in Fig. S9 as they contribute to the scatter in our data.

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If a data point falls outside of three times the average deviation from the median, it is considered an 439 outlier and shown as a symbol with a cross in Fig. S9.

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Direct comparison of data and model (eqn (19)) validate the use of the reacto-diffusive framework.

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An important feature of eqns (16) and (17) is that D Fe is not required, which inherently means that the 442 reacto-diffusive framework assumes uniform gradients in α. Despite observed reaction gradients (Fig. 3), 443 the assumption that Fe 2+ was well-mixed is "good enough" due to agreement in Fig. 6 without any input from KM-SUB. Figure 2 shows the result as a shading using the geometric mean of 446 d p respective to each experiment. There is good agreement between data and predictions considering all 447 uncertainties. The vast number of particles and the high time resolution used in our observation ensures 448 enough data is available to effectively conclude that approximation in the reacto-diffusive framework is 449 acceptable to describe O 3 oxidation. 450 We previously noted that model predicted 3-D profiles in α were much sharper than those in 2-D,  This degree of homo-or inhomogeneity was never observed, and instead was always in between this 460 extreme case and uniformity. We note that a spatial inversion of our data was not performed, i.e. from  and humidity and for materials such as secondary organic aerosol and their proxies 13 . Doing so would 507 allow further evaluation of when the reacto-diffusive framework is a valid approximation to describe the 508 loss of condensed phase reactants. We suggest that the reacto-diffusive framework may be pervasive 509 to gas-to-particle kinetics which would certainly simplify representation of atmospheric heterogeneous particle perimeters, i.e. the outer most pixels of all particles, α was consistently lower than concentric 520 pixels toward the particle center. Therefore, we conclude that O 3 oxidized particle surfaces more than exponentially as a function of RH and could also be described using a Vignes-type equation. A volume 532 mixing rule over-predicted H O 3 and is advised not to be used for this system. Our findings may apply 533 for ozone in marine derived organic aerosol due to XG being a proxy of polysaccharide and exopolymer 534 particles found to be aerosolized from oceans. 535 We have used a limiting case in heterogeneous aerosol chemistry referred to as a reacto-diffusive 536 limitation to describe our results following a square root dependent loss rate of α. This corresponding 537 framework assumes that a reactant is uniformly distributed (or well-mixed) and oxidation takes place in water partial pressure and T p was used to determine the RH the particles were exposed to using the OD images over the same FOV taken over a range of X-ray energies were aligned and processed using 583 publicly available software 110 . We primarily investigated the X-ray energy range 700-735 eV, which is 584 the Fe L-edge absorption. When present in particles, peak absorption due to Fe 2+ and Fe 3+ occur at 585 slightly different X-ray energies, allowing to differentiate between the two 111,112 . The X-ray energy at 586 Fe 2+ peak absorption for FeCl 2 measured here was compared with previous literature 57 and an energy 587 offset was obtained as a calibration. Peak absorptions for ferrous and ferric chloride are at 707.8 and 588 709.5 eV, respectively 57 as seen in Fig. 1.

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The KM-SUB model was used to simulate chemical reaction and molecular diffusion inside of our    Figure 1: Near edge X-ray absorption fine structure (NEXAFS) spectra of oxidized XG/FeCl 2 particles at RH = 0 and 60% shown as the red and orange lines, respectively, along with measured FeCl 2 spectra as the blue line. Chemical standards for ferrous and ferric chloride are shown as the blue and green shading, respectively 57 . Spectra have been scaled and shifted vertically for clarity. Dashed lines indicate typical peak absorption for Fe 2+ and Fe 3+ at X-ray energies of 707.9 and 709.6 eV. The error bars are either ±0.07 or the propagated error from photon counting statistics, whichever is greater. Solid lines are calculations from the KM-SUB model using parameters given in Table 1. Shadings in panel a) are predictions applying the reacto-diffusive framework described in more detail in the text.  Table 1.  (e-f), 60% (g-h) and 80% (i-j). The color scale from 0 − 1 is the same for both α shown in the left panels (a, c, e, g and i) and [O 3 ] norm shown in the right panels (b, d, f, h and j). The distance from the particle surface is the ordinate. Note that the scales for all panels can be different.  Table 1. : Damage assessment of X-ray exposed particles of xanthan gum (XG) mixed with FeCl 2 . Blue, green, orange and red colors were acquired one after another and indicate increasing damage. a) A full near edge X-ray absorption fine structure (NEXAFS) spectra over the same particle is shown where each pixel was irradiated with approximately 1700 photons at 50 energy points. b) A map (4 energy points) of particles where each pixel was irradiated with approximately 250 photons. c) A map of particles where each pixel was irradiated with approximately 800 photons.

OD OD OD
OD m OD OD m Figure S2: Average optical density derived at the Fe pre-edge, OD pre , as a function of the sum of optical density at the Fe 2+ and Fe 3+ peak at 707.8 and 709.5 eV, respectively, or OD Fe 2+ + OD Fe 3+ . Each symbol is the average over an individual particle. The dashed line is a fit to the linear equation indicated in the figure.  Figure S4: Measured Fe 2+ fraction, α, as a function of particle diameter, d p , during O 2 exposure for a) RH = 0, b) 22, c) 43, d) 60 and e) 80%. Each data point is an average over a single particle where the number of pixels per particle is given in the top abscissa. The data here was also used to determine averages in Fig. S3. Error bars indicate the error on the average value propagated from X-ray photon counting statistics. The standard deviation of α for individual particles is not shown here, but included in Fig. S3. x y z Figure S6: Geometric representation of a 2-D projection on a grid box of a finite volume from a spherical shell outlined in green inside of an spherical aerosol particle. The particle radius is r and outlined in blue. The shell outside and inside diameter is r i and r i−1 , respectively, and outlined in red. Black solid lines are the axis and black dashed lines indicate the grid box. , as a function of particle surface to volume ratio, S p /V p , at a relative humidity RH of a) 0%, b) 22%, c) 43%, d) 60% and e) 80%. Each data point is an individual particle. Values which deviate more than 3x the average deviation of the median are indicated with an "x". The dotted line is derived from fitted parameters and its value indicated in each panel.  Technol., 2018, 52, 7680-7688.