Uptake of Pyrene by NaCl, NaNO3, and MgCl2 Aerosol Particles - The

Mar 30, 2012 - Photoelectric charging experiments measure heterogeneous uptake coefficients for pyrene on model marine aerosol particles, including Na...
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Uptake of Pyrene by NaCl, NaNO3, and MgCl2 Aerosol Particles Ephraim Woods III,* Colin Yi, Jacqueline R. Gerson, and Rifat A. Zaman† Department of Chemistry, Colgate University, Hamilton, New York 13346, United States ABSTRACT: Photoelectric charging experiments measure heterogeneous uptake coefficients for pyrene on model marine aerosol particles, including NaCl, NaNO3, and MgCl2. The analysis employs a multilayer kinetic model that contains adsorption and desorption rate constants for the bare aerosol surface and for pyrene-coated surfaces. First coating the aerosol particles with a pyrene layer and following the desorption using both t-DMA and photoelectric charging yields the desorption rate constants. Separate experiments monitor the increase in surface coverage of initially bare aerosol particles after exposure to pyrene vapor in a sliding-injector flow tube. Analyzing these data using the multilayer model constrained by the measured desorption rate constants yields the adsorption rate constants. The calculated initial heterogeneous uptake coefficient, γ0(295 K), is 1.1 × 10−3 for NaCl, 6.6 × 10−4 for NaNO3, and 6.0 × 10−4 for MgCl2. The results suggest that a free energy barrier controls the uptake rate rather than kinematics.

1. INTRODUCTION Polycyclic aromatic hydrocarbons (PAH) constitute an important class of atmospheric pollutants. Formed by incomplete combustion processes in automobile engine exhaust, they are well-known to have carcinogenic and mutagenic properties.1 They are also a component of crude oil with wide ranging vapor pressures, accounting for another source of atmospheric PAH. The gas-particle partitioning of these compounds is important for a number of reasons. First, the lifetime of PAH in the respiratory system is greatly extended when inhaled adsorbed to aerosol particles.2 This increased lifetime may increase the health risk. For example, inorganic aerosols coated with PAH have been shown to induce metabolic activation in human lung epithelial cells and are closely linked to cytotoxicity.3 The heterogeneous chemistry of particle-bound PAH complicates the implications for health. For example, the oxidation of PAH in the atmosphere is also linked to particle adsorption. Benzo[a]pyrene (BaP) is more resistant to photodecomposition when adsorbed to coal fly ash aerosol.4 Similarly, Abbatt and co-workers showed that the heterogeneous reaction of adsorbed BaP with ozone occurs with an organic aerosol substrate, but no reaction occurs with NaCl aerosol as a substrate.5 Because the oxidation products may be even more mutagenic or carcinogenic than the parent compound,6,7 the nature of the substrate is an important factor. Beyond health considerations, adsorbed organic layers can also alter the optical properties and hygroscopicity of aerosol particles, affecting their direct and indirect role in radiation balance. For example, ultrafine carbon particles are active as cloud condensation nuclei at lower supersaturation levels after reaction with O3.8 PAH, in this context, are representative of many semivolatile organic compounds in the atmosphere whose adsorption to particles may contribute to these effects. Some studies9−11 suggest that both composition and particle morphology are important in determining the efficiency of PAH uptake, and our experiments are designed to test this © 2012 American Chemical Society

dependence. In this work, we focus on models for sea spray. Marine aerosol particles represent an important component of tropospheric aerosol, accounting for as much as 1012 or 1013 kg of the aerosol mass.12 These particles influence climate through light scattering and cloud condensation, and they affect the composition of the atmosphere through heterogeneous chemistry. Each aspect depends strongly on the physical and chemical characteristics of the particle surfaces, which are generally complex in both their composition and their morphology. While there are some previous observations of PAH uptake on NaCl particles,11,13 they do not report any kinetic data. In seawater, Na+ and Cl− are the two most prominent ionic species, prompting the choice of NaCl in this study. Mg2+, although the second most abundant cation in seawater, is a relatively minor component of sea spray (Mg:Na ≈ 0.11). Experiments show that the surface environment of model marine aerosols is enriched in Mg2+ salts relative to the bulk value.14−16 This enrichment arises from the tendency of these salts to remain in solution to relatively low values of relative humidity (RH).17−19 The structure of these aerosols at very low RH may be viewed as a course-grained core−shell structure, with primarily NaCl in the interior and Mg salts clustered on the exterior.16 It is, therefore, important to consider these salts in our study as well. The composition of sea spray aerosol is altered by reaction with NOx, generating NO3− in place of Cl−.20 To represent NOx-aged aerosol, we include NaNO3 in our experiments. There are several examples of experiments that examine the uptake by either NaCl or sea salt models of oxidizing atmospheric gases, such as HO2,21,22 HNO3,23−25 and N2O5.26,27 The experiments all involve the reactive uptake of these gases. The adsorption of PAH onto model sea salt particles provides a system that can probe the adsorption of Received: February 12, 2012 Revised: March 28, 2012 Published: March 30, 2012 4137

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A separate 2.00-slpm flow passes through a pyrene pickup cell before entering the rear of the flow tube. The pickup cell is a jacketed flask, and dimethyl silicone fluid circulates through the jacket to control the cell temperature. For the uptake experiments, the temperature of the pyrene bed in the pickup cell is 318 K to ensure that 295 K air flow is saturated with pyrene. The pyrene-saturated air is a few degrees warmer than the aerosol carrier gas when it enters the sliding injector flow tube, but the slow linear velocity in the flow tube (approximately 1 cm/s) allows ample time for equilibration. The following section provides more details about our treatment of the pyrene vapor pressure in the flow tube. The aerosol flow and pyrene flow combine in the sliding injector flow tube. The sliding injector is 0.25-in. stainless steel tubing, and the tube itself has a 2.375-in. inner diameter. The aerosol exits through small holes drilled through the side of the injector tubing rather than through the end, which is plugged. This modification results in a short region of turbulence where the pyrene and aerosol flows first mix. The combined flow is laminar for the majority of the interaction time, however. The temperature inside the flow tube is that of the laboratory, which is 295 ± 1 K. The RH of the combined flow in the flow tube is less than 3%, the result of mixing the particle flow with dry air in the DMA and diluting it with dry air from the pickup cell. We measure the pyrene gas−particle interaction times directly by switching the control voltage on the DMA and timing the arrival of particles using an aerosol electrometer (TSI 3068A) as the detector. In the absence of a control voltage on the DMA, there are a negligible number of particles that enter the flow tube, and the aerosol electrometer produces a zero signal. Applying the control voltage injects size-selected and singly charged particles into the flow. These particles produce a signal at the aerosol electrometer. The flow time from the DMA inlet to the sliding injector on the flow tube is a constant and may be subtracted from the total flow time to yield the interaction time. The arrival of particles is dispersed in time, as much as 15% for flow times near 60 s. In these cases, we use the midpoint in time between the arrival of the first particles and the steady-state concentration. The values measured this way are within a few seconds of values calculated using the volume flow rate. After interacting with pyrene vapor in the flow tube, the particles enter the ionization cell where a 355 nm laser beam, the third harmonic of a Nd:YAG laser, multiphoton ionizes surface adsorbed pyrene. The laser is unfocused and operates at 2.0 mJ/pulse. At this point, any further adsorption or desorption of pyrene is irrelevant as it does not affect the aerosol charge state. The ratio of the electrometer signal after ionization to that with the laser blocked (which reflects only the number density of singly charged aerosol particles exiting the DMA) is proportional to the number of pyrene molecules adsorbed to each particle. We refer to this number as the photoelectric charging efficiency (ϕ). These experiments generally focus on regimes where the final average coverage is less than one monolayer. To make kinetic measurements, it is necessary to calibrate accurately this photoelectric charging signal. Our approach is to coat the particles with a sufficiently thick layer of pyrene that the growth may be detected by tandem differential mobility analysis (t-DMA) and correlating the growth with charging efficiency. We use the density of neat pyrene to calculate the number of pyrene molecules in the shell.

organic constituents in the atmosphere without the complication of diffusion and reaction in the particle phase. It provides the opportunity to assess the factors that control the initial uptake dynamics separately from subsequent reaction dynamics. Further, these sea salt aerosols produce very little background signal in our experiment, which uses a photoionization detection scheme. As a result, we can easily detect submonolayer coverages of PAH, which is readily photoionized. For this study, we have chosen pyrene as the representative PAH. Among its desirable qualities are its relatively low ionization potential (7.4 eV in the gas phase),28 which makes it suitable for our detection scheme, and its vapor pressure. For this work, we require that the PAH vapor pressure is low enough to partition appreciably to the particle phase, yet high enough to produce enough gas−particles collisions to appreciably coat surfaces on the time scale of our experiment (∼1 min). The primary goal is to characterize the interaction of pyrene with bare salt surfaces; however, including adsorption and desorption processes for multilayer coatings in our analysis is necessary, because the experiments access coverage regimes that are too high to ignore them.

2. EXPERIMENTAL SECTION Figure 1 shows a schematic of the experimental apparatus. The experiment makes use of a laser-based, ambient-pressure,

Figure 1. Schematic diagram of the experiment. The dashed box labeled SMPS is the scanning mobility particle sizer, and it comprises a differential mobility analyzer and condensation particle counter.

photoelectric charging scheme that is conceptually similar to other designs used to measure particle-bound PAH.11,29,30 There are three configurations for the experiment: ionization signal calibration, desorption, and uptake. The design of our apparatus is optimized for measuring uptake kinetics rather than desorption kinetics. Here, we describe the uptake configuration in detail, then describe the necessary modifications for the other two experiments. The source of the aerosol flow is an atomizer (TSI model 3076), which produces 2.00 standard liters per minute (slpm) atmospheric pressure flow of aerosol. A 0.50 slpm portion of this flow passes through a diffusion dryer, where the RH falls below 15% RH, and a Po-210 static elimination device, which brings the flow into charge equilibrium. A differential mobility analyzer (DMA) running with a 3.00 slpm sheath flow size selects the aerosol flow, and the monodisperse output of the DMA enters the sliding injector inlet of a cylindrical flow tube. 4138

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where k+1 is the bare-surface adsorption rate constant, k−1 is the desorption rate constant for pyrene adsorbed directly to the surface, and C is the gas-phase concentration of pyrene molecules. The measured diffusion constant for pyrene in air at 298 K of 6.68 × 10−2 cm2/s32 implies a limiting uptake coefficient on order unity for the particle size (200 nm diameter) in our experiment, while our measured uptake coefficients are on order 10−3. As a result, this approach assumes that gas-phase diffusion is rapid such that there is no gas-phase concentration gradient in the vicinity of the particle surface. The rate of change of the fraction covered by only one layer of pyrene has four contributions. It may increase by desorption from x2 and adsorption by x0. It may also decrease by adsorption and desorption processes involving x1. In total, the rate of change for x1 is

To produce the thin coatings, we raise the temperature of the pyrene pickup cell such that the carrier flow is near 345 K as it enters the flow tube. As shown in Figure 1, some of the particles that exit the flow tube divert into an SMPS system (TSI), which measures the size distribution of the aerosol. An empty volume placed immediately before the ionization cell ensures that the flow time trough the SMPS system matches that of the ionization portion. As a result, the amount of pyrene on the particles in the two paths is consistent even though some desorption takes on the time scale of the measurement. We vary the size of the particles by changing the injector position in the flow tube. In our analysis, we assume that the sensitivity of the photoionization is similar for submonolayer and multilayer coatings. Accordingly, we limit the range of the calibration to ∼2 nm of growth, which is roughly 10 times greater than the deviation in the average size from consecutive scans of the same distribution. The desorption of pyrene on the time scale of the experiment must be taken into account in the uptake experiment as well as the calibration experiment. The kinetic model we use for the analysis allows for distinct desorption rate constants from the base salt surface and pyrene-coated surface. To estimate these desorption rate constants, we vary the desorption times of the coated aerosol particles in a volume where the pyrene pressure is negligible and monitor the calibrated charging efficiency. This volume comprises a variable number of flasks coated with activated carbon to ensure that the pyrene vapor pressure, and, thus, adsorption rate, is negligible. We allow the coated particles to cool to the laboratory temperature of 295 K before recording the first (nominally t = 0 s) data point. Monitoring desorption for a sufficiently long time scale (a few minutes) ensures that we span both multilayer and monolayer desorption regimes.

dx1 = k−x 2 + k1+Cx0 − k+Cx1 − k1−x1 dt

where k+ and k− are the adsorption and desorption rate constants for multilayer pyrene, respectively. The remaining fractions have the same four contributions to their rate of change, giving: dxi = k−x i + 1 + k+Cx i − 1 − k+Cx i − k−x i dt

∑ i·xi·NML i

⎛ t − tf − t ⎞ ⎟ C = C0 exp⎜ int ⎝ ⎠ τ

(5)

In this expression, C0 represents the vapor pressure of pyrene as it enters the back of the flowtube adjusted for the small dilution by the aerosol flow, tint is the interaction time corresponding to a particular injector position, tf is the interaction time at its maximum, τ is the first-order time constant for wall losses, and t is the real time integration variable. Because the adsorption by particles accounts for very little loss of gas-phase pyrene (98% of the surface. To be conservative, however, our model includes fractions through x6. Accordingly, the differential rate law for x6 is missing the terms describing the formation of the seventh layer (−k+Cx6) and the desorption from the seventh layer (−k+x7). To account for first-order losses of pyrene onto the wall of the flowtube, we replace C with an interaction-time-dependent term:

3. MULTILAYER KINETIC MODEL The multilayer kinetic model follows the treatment of Vinokurov and Kankare,31 who provided analytic solutions for the full system of differential equations for an arbitrary number of layers with Langmuir-type uptake rules. Because of the adsorption of pyrene vapor onto the walls of our flow tube prevents our using their result directly, we restrict our model to a fixed number of layers and numerically integrate the resulting equations. Let xi represent the fraction of the aerosol particle surface covered by only i layers of adsorbed pyrene. Using this definition, the bare salt surface would have x0 = 1 and the remaining fractions would be zero. A surface with a uniform monolayer of pyrene would have x1 = 1 with the other fractions zero. The total number of adsorbed pyrene molecules per aerosol particle is N=

(3)

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flow rates and collection times, extracting the pyrene in cyclohexane, and determining the pyrene concentration using fluorescence spectroscopy calibrated against standard solutions. By comparing the amounts collected on filters placed on the inlet and outlet of the flow tube, we can estimate the loss rate. The value of τ calculated this way is 25 ± 5 s for the flow conditions in our experiment. A second method is to make it an adjustable parameter in our model fits. In most cases, the parameters τ and k+ are too strongly coupled to determine them uniquely. For fits where the value of k+ is relatively unimportant (very low coverages), we can constrain it. In those cases, we find good agreement with the experimental value. For all of the analyses presented here, we fix the value of τ to be 25 s. Estimating the footprint of a pyrene molecule lying flat as 1.0 nm2 provides a crude estimate for NML of 1.3 × 105, assuming a lower limit of surface area provided by a sphere of diameter 200 nm, the size used in our experiments. The crystal structure of pyrene,35 characterized by stacks of two pyrene molecules that alternate in orientation of the molecular plane (represented roughly by //=//, where each line represents the plane of the molecule), provides another estimate of NML. The footprint of the pyrene unit cell oriented this way is approximately 1.3 nm2, and the cell contains four pyrene molecules. Assuming that only 3 pyrene molecules in a cell account for the first layer, we can estimate that one monolayer of coverage corresponds to a surface number density of 2.3 nm−2. This value is likely an upper limit. Again assuming a spherical geometry for the particles, the surface area of a 200 nm particle is 1.3 × 105 nm2, and the value of NML is 2.9 × 105 for a 200 nm particle. Our fits use an intermediate value between these limiting estimates of 2.0 × 105. The error in this value maps approximately linearly onto errors in k+1 , but, fortunately, the initial uptake coefficient, γ0, is insensitive to this value over quite a large range of NML. This insensitivity results from the low average coverages accessed in our experiments.

Figure 2. The top panel shows the size distribution of pyrene-coated aerosol particles in the calibration experiment. The solid line corresponds to a relatively small coverage, while the dotted line represents a coating corresponding to an increase of a few nanometers in mobility diameter. The bottom panel shows the photoelectric charging efficiency plotted versus the average number of pyrene molecules per particle (N). The value of N comes from the increase in mobility diameter implied by the measured distributions. The circled points correspond to the distributions shown in the top panel.

4. RESULTS AND ANALYSIS Calibration of Photoelectric Charging Signal. The top panel of Figure 2 shows the SMPS distributions for two different injector positions in a calibration experiment. The bottom panel shows the photoelectric charging efficiency as a function of the number of adsorbed pyrene molecules. Using the density of bulk pyrene, we calculate the number of adsorbed pyrene molecules using the change in volume implied by the increase in diameter, assuming a spherical geometry for the particles. NaCl aerosols in this size range have shape correction factors of approximately 1.05,36 producing an approximately 10% mistake in the calculated volumes. These correction factors can depend on a number of factors including the drying rate of the particles.37 NaNO3 aerosol particles are quite spherical even at low values of RH,38 and MgCl2 particles, which retain water to very low values of RH,39 are likely to be as well. In any case, ignoring the shape correction factors produces a small error as compared to the uncertainty in the pyrene pressure inside the flow tube. As the figure shows, the photoelectric charging efficiency grows linearly with increasing numbers of pyrene molecules. The slope of the line yields a sensitivity of 4.7 × 10−5 molecule−1. The sensitivity for NaNO3 is similar, and, for MgCl2, it is approximately twice as large. This difference in sensitivity may be correlated to the higher interfacial polarity observed on the surface Mg salts as compared to Na salts.40

Desorption Kinetics. Figure 3 shows the number of pyrene molecules adsorbed to a NaCl aerosol particle as a function of desorption time. In this experiment, the particles become coated with pyrene as in the calibration experiment, but then enter a volume that has no source of pyrene vapor pressure and is lined with activated carbon. The activated carbon removes the pyrene vapor already in the flow, as well as the vapor that arises from desorption. Adjusting the residence time in this volume enables the observation of desorption kinetics in an environment where the adsorption rate is negligible. Fitting the data in Figure 3 with a biexponential decay function of the form N(t) = Ae−t/τ1 + Be−t/τ2 yields the decay constants of 6.8 and 49.7 s. The figure also shows the result of fitting the data with a single exponential (dashed line), and this fit is clearly less satisfactory. Because we expect desorption to be a first-order process, the results suggest that there are processes occurring on two different time scales. We attribute the faster process to desorption from pyrene-covered surface and the slower process to desorption from the bare salt surface. 4140

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Figure 3. Desorption of pyrene from NaCl aerosol particles. The solid represents the fit to a biexponential decay function that yields the desorption rate constants, k−1 = 0.0216 s−1 and k− = 0.146 s−1. The dashed line represents a fit using a single exponential, which is less satisfactory.

Figure 4. The uptake of pyrene by NaCl aerosol particle surfaces. The plot shows the average number of pyrene molecules per aerosol particle (N) as a function of the interaction time. The squares represent the experimental data, and the solid line represents the fit of these data to the multilayer kinetics model described in the text. The rate constants determined for NaCl are k+1 = 3.0 × 10−14 cm3/s and k+ = 4.3 × 10−13 cm3/s.

The desorption rate constants, which we estimate as the reciprocal of the folding constants, are k−1 = 0.020 s−1 and k− = 0.15 s−1 respectively. We note that the amplitude of the slower exponential, which should roughly correspond to NML in this treatment, is approximately 1.8 × 10−5. This value is close to our earlier approximation for NML of 2.0 × 105. Retrieving the desorption rate constants from the multilayer kinetic model (with adsorption processes removed) is problematic, because the initial set of xi is unknown; however, we can use the model to reproduce the experimental data using the above rate constants for realistic (although not unique) initial conditions. Table 1 shows these results and the results from repeating this experiment with NaNO3 and MgCl2. The variation in k+ is smaller than the uncertainty in the measurement, and we fix it at the value of 0.146 s−1 in our model. One would expect the desorption rate of pyrene from pyrene-coated surfaces to be nearly independent of the substrate, which lies several layers below. The values for k−1 vary only by a factor of approximately 2 and are similar to that reported for desorption of pyrene from soot particles.41 Uptake Experiments. Figure 4 shows uptake data for pyrene interacting with NaCl aerosol particles. In these experiments, the initially bare aerosol particles interact with pyrene vapor in the flow tube, and interaction time is a function of the position of the sliding injector. The average number of adsorbed pyrene molecules per particle increases as the interaction time increases, because adsorption is dominant under these conditions. The pressure of pyrene in the flow tube here is much smaller than in the calibration experiment, and the coverage corresponds to less than one monolayer even at the largest interaction time.

One feature of these data is that there is some curvature to the uptake curves due to pyrene losses to the wall of the flow tube. In our design, short interactions times correspond to injector positions where the particles only sample the region near the exit of the flow tube. On the other hand, long interaction times include the region of the flowtube where the pyrene first enters and wall losses are minimal. As a result, the uptake at long interaction times reflects a higher average pressure of pyrene, and, thus, greater rate, than does the uptake at short times. The curvature does not arise from any depletion of the pyrene concentration due to adsorption by particles, which is on the order of about 1% of the total. We analyze the uptake data using the built in nonlinear fit functions in Mathematica 8.42 The software numerically integrates the system of differential equations described in eqs 2−4 to find for each interaction time, tint, the set of xi. Equation 1 then yields the number of pyrene molecules per particle, N, for each tint. The rate constants, k+1 and k+, are adjustable parameters produced by fitting this calculated N versus tint to the experimental data. The remaining constants are constrained as described above. Fitting the data in Figure 4 with the constraints k−1 = 0.146 s−1, k− = 0.0216 s−1, and τ = 25 s yields k+1 = (3.0 ± 1.5) × 10−14 s−1 and k+ = (4.3 ± 1.5) × 10−13 s−1. Table 1 shows the results of this and other similar fits with the other salts. NaCl has the largest value of k+1 , followed by NaNO3 and MgCl2, which are similar. The fitted value of k+ is similar in each salt. We expect this consistency, because k+ is

Table 1. Summary of Rate Constants and the Calculated Initial Uptake Coefficient NaCl NaNO3 MgCl2

k−1 /10−3 s−1

k−1 /s−1

k+1 /10−14 cm3/s

k+/10−14 cm3/s

γ0/103

20 ± 2 26 ± 2 5.2 ± 0.6

0.15 ± 0.01 0.15 ± 0.01 0.15 ± 0.01

3.0 ± 1.1 1.9 ± 0.5 1.6 ± 0.5

43 ± 10 52 ± 10 41 ± 10

1.1 ± 0.4 0.7 ± 0.2 0.6 ± 0.2

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coefficient for NaCl as compared to the other two salts. Aerosol particles created from aqueous solutions of MgCl2 and NaNO3 retain appreciable amounts of water to very low values of RH. Interfacial water may be responsible for suppressing the uptake coefficient of these particles. Future experiments may test more directly the sensitivity of the uptake coefficient to the amount of interfacial water by adjusting the RH to more typical ambient values. Another pertinent result is that the multilayer adsorption rate constant (k+) is greater than the rate constant for the formation of the first layer (k+1 ). This disparity leads to a nonuniform distribution of pyrene on the surface of aerosol particles. For example, at the longest interaction time in Figure 4, the coverage fractions are x0 = 0.82, x1 = 0.11, x2 = 0.04, and x3 = 0.02. If we use the model to calculate the coverage at times long enough to reach steady state (approximately 300 s with the pressure of pyrene set to vapor pressure at 298 K), the average coverage corresponds to 0.3 monolayers, while 76% of the surface is bare. In this scenario, 16% of the surface is covered by 1 pyrene, and the remaining 8% is covered by at least 2 pyrene molecules. Increasing the vapor pressure to the equilibrium pressure at 305 K (without changing the rate constants, i.e., exposure to a supersaturated environment) produces an average coverage of 1.5 monolayers in steady state with roughly 50% of the surface left uncovered. Similarly, increasing the temperature to 310 K results in continuous growth that saturates our sixlayer model. These experiments show that PAH can partition to the particle phase under conditions where homogeneous nucleation rates are vanishingly small. Given the added health risks associated with particle-phase carcinogens, this propensity may have important health consequences. The consequences will be even greater for larger PAH. Because the free energy barrier, rather than kinematics, controls the uptake rate, other PAH may have very similar uptake rates. Larger PAH, which have smaller desorption rates, could build up significant surface concentrations on particles exposed to air samples near combustion sources, where gas-phase PAH concentrations may be high.

governed by pyrene−pyrene interactions rather than pyrene− surface interactions. We can calculate the uptake coefficient in the limit of zero pyrene coverage (γ0) using the relationship: NML ·

σCu ̅ γ0 dx1(t = 0) = k1+C = dt 4

(6)

where σ is the particle surface area, and u̅ is the average speed of pyrene gas molecules. The uncertainties for the adsorption rate constants in Table 1 are estimates that come from determining the model sensitivity to the uncertainty in the wall loss time constant, τ, the vapor pressure of pyrene, C0, and the desorption rate constants, k−1 and k−. We do not include the uncertainty in the NML parameter, because it results in little uncertainty in the calculated uptake coefficients. The value of τ is the largest source of error in the fitted constants, but it is a systematic error. The uncertainties implied by the deviation in successive uptake experiments are much lower, approximately 15% in k+1 and γ0. Although the uptake rates for all three salts are of the same order of magnitude, we can conclude that the initial uptake rate for NaCl is higher by about a factor of 2 than it is for MgCl2 and NaNO3.

5. DISCUSSION The uptake rates for these three salts are perhaps more notable for their similarity than their difference. The washboard model43 provides a simple means of estimating the trapping fraction for gas−surface collisions. The model is an extension of a simple “cube” model44 that accounts for the effects of surface corrugation. This type of model, where conservation of energy and normal momentum determine the change in the component of gas momentum normal to the surface, would predict a much higher initial uptake coefficient, or sticking probability, than reported here. For example, we can construct a crude washboard model by estimating the surface corrugation parameter, α, to be 5°, the adsorption well depth, W, to be ΔH0vap for pyrene, and the effective surface mass to be 58 amu (the mass of one NaCl formula unit). In this case, the sticking probability is unity for a collision energy on the order of kBT. One would have to increase the effective mass of the surface to approximately 10 000·MNaCl to reproduce the experimental uptake coefficient for NaCl. This result suggests that purely kinematic considerations are insufficient to understand the result; there must be a significant free energy barrier to adsorption. Similarly, the desorption rate constants for first layer provide insight into the free energy of adsorption. A simple transition state prediction for the desorption rate constant is given by: k1− =

kBT −ΔG⧧ / kBT e h

6. CONCLUSION We investigated the interaction of pyrene gas with three salts, NaCl, MgCl2, and NaNO3, that model components of sea spray and aged sea spray. The initial uptake coefficient is similar for all three salts, ranging from 6.0 × 10−4 for MgCl2 to 1.1 × 10−3 for NaCl. The small uptake rates suggest that adsorption is an activated process. The steady-state surface concentrations derived from these kinetic data are modest for pyrene, but could be much larger for PAH with smaller vapor pressures.

(7)

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⧧

where ΔG is the activation free energy for evaporation. If there were no barrier in excess of the free energy of evaporation, we can estimate ΔG⧧ as 55 kJ/mol at 298 K,34 which yields an upper limit for k−1 as 1.4 × 103 s−1. The measured value of k−1 = 0.0261 s−1 for NaCl is much smaller and implies a ΔG⧧ of 82.4 kJ/mol, and, thus, a barrier to adsorption of 27.4 kJ/mol. Donaldson and co-workers10 reported the initial uptake coefficient for pyrene onto the surface of water as 1 × 10−5, which is also small and suggestive of an activated process. The lower uptake coefficient for the pure water surface perhaps gives a clue to the small, but measurably higher uptake

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address †

Dartmouth Medical School, Hanover, New Hampshire 03755, United States. Notes

The authors declare no competing financial interest. 4142

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ACKNOWLEDGMENTS This work was funded by the National Science Foundation through grant number CHE-1012224. R.A.Z. thanks the Petroleum Research Fund for summer support.

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