J. Phys. Chem. A 2006, 110, 10435-10443
10435
On the Reactive Uptake of Gaseous Compounds by Organic-Coated Aqueous Aerosols: Theoretical Analysis and Application to the Heterogeneous Hydrolysis of N2O5 Tatu Anttila,† Astrid Kiendler-Scharr, Ralf Tillmann, and Thomas F. Mentel* ICG-II: Tropospha¨re, Forschungszentrum Ju¨lich, 52425 Ju¨lich, Germany ReceiVed: April 19, 2006; In Final Form: July 3, 2006
The presence of organic coatings on aerosols may have important consequences to the atmospheric chemistry, in particular to the N2O5 heterogeneous hydrolysis. This is demonstrated by recent experiments which show that the uptake of N2O5 by aqueous aerosols is slowed considerably when an organic coating consisting of monoterpene oxidation products is added on the particles. To treat the mechanisms behind the suppression, an extension of the resistor model, which has been widely applied in investigation of the heterogeneous uptake by aerosols, was derived. The extension accounts for dissolution, diffusion, and chemical reactions in a multilayered organic coating, and it provides a parametrization for the heterogeneous uptake by organiccoated aerosols that can be applied in large-scale models. Moreover, the framework was applied to interpret the findings regarding the decreased uptake of N2O5 by the organic-coated aerosols. Performed calculations suggested that the reaction rate constant of N2O5 in the coating is decreased by 3-5 orders of magnitude, in addition to which the product of the solubility of N2O5 and its diffusion coefficient in the coating is reduced more than an order of magnitude compared to the corresponding value for the aqueous phase. The results suggest also that the accommodation coefficient of N2O5 to such coatings is no more than a factor of 2 smaller than that to pure water surfaces. Finally, the relevance of the results to the atmospheric N2O5 heterogeneous hydrolysis is discussed and implications to planning further laboratory studies focusing on secondary organic aerosol formation are pointed out.
1. Introduction One of the main sources of uncertainty in the current predictions concerning climate change arises from our inability to predict reliably the microphysical structure of atmospheric clouds, in particular the number and size of cloud droplets.1,2 Since atmospheric aerosol particles act as nuclei onto which cloud droplets are formed, the cloud microphysical properties are sensitive to the number, size, and chemical composition of atmospheric aerosols.2,3 The last property is probably most poorly characterized despite numerous studies dedicated to identification and classification of aerosol phase compounds. What makes the topic challenging is the large diversity of organic compounds present in the atmosphere, and consequently the net effect of organics on the climatically relevant properties of atmospheric aerosols is still unclear.4,5 One open question related to atmospheric organic compounds is their distribution in mixed inorganic/organic aerosols. The question arises because some atmospheric organics exhibit surface activity, i.e., they tend to partition into an air/water interface, and are thus able to concentrate on the aerosol surfaces. As mounting evidence shows, this may lead to a formation of organic coatings. It has been proposed, for example, that freshly formed marine aerosols contain a hydrophobic monolayer (a so-called inverted micelle) that is formed by amphiphilic fatty acid molecules residing on the ocean surfaces.6 The hypothesis is supported by observations of Tervahattu and co-workers,7,8 Mochida et al.9, and Russell et al.10 Long-chain fatty acids have also been observed on the surfaces of continental † Current address: Finnish Meteorological Institute, Research and Development, Climate and Global Change, P.O. Box 503, 00101 Helsinki, Finland.
sulfate particles.11 Moreover, aqueous particles may acquire a coating in the atmosphere through condensation of low-volatile vapors with a biogenic origin.12,13 Such coatings are probably hydrophobic, and their thickness is not limited to that of a monolayer but is controlled by the availability of condensing vapors. The presence of organic coatings on atmospheric aerosols is suggested to have implications regarding atmospheric chemistry and cloud microphysics.5,12,14,15,17 One particular mechanism underlying these effects is an inhibition of mass transfer between the gas phase and particles. The retardation might be caused by a reduced mass accommodation of molecules to the organic surface, a decreased solubility into the organic phase, and/or mass transfer limitations caused by diffusion through the coating. In this regard, nonreactive and reactive compounds should be distinguished, since even though an organic coating may not influence mass transfer of nonreactive compounds (e.g., water), it may inhibit the uptake of reactive compounds. This is because molecules consumed in fast particle phase reactions need to be rapidly replenished in order to maintain the overall reaction rate, and therefore even a small decrease in the flux of gaseous precursors may slow the reactive uptake. Influence of organic coatings on mass transfer of nonreactive compounds, including water, has been investigated theoretically and via model simulations5,14,16 but a similar study considering reactive compounds is to our best knowledge lacking. The reactive uptake of gaseous compounds by aerosols can be treated using a so-called resistor model, here termed as a traditional resistor model, which has been widely applied in analyzing data from laboratory experiments and in reactive uptake parametrizations for large-scale models.18-22 Since the
10.1021/jp062403c CCC: $33.50 © 2006 American Chemical Society Published on Web 08/17/2006
10436 J. Phys. Chem. A, Vol. 110, No. 35, 2006
Anttila et al.
traditional resistor model assumes that aerosols contain a single bulk phase, we extend the formalism to cover aerosols with an organic coating. We focus on coatings that are thick enough to be considered as bulk absorbing phases, in contrast to monolayers or submonolayers of which effects have been investigated experimentally by Thornton and Abbatt23 and McNeill et al.24 While the extended model lacks the generality of that presented by Po¨schl et al.,25 it explicitly accounts for the above-mentioned retardation mechanisms and can be applied directly to organiccoated aerosols. The paper is organized as follows. We first present the background of the approach and then derive the formalism following closely the derivation of the traditional resistor model (sections 2.1 and 2.2). In section 2.3, we explore the conditions under which dissolution and diffusion in the organic coating becomes the rate-limiting step in the reactive uptake. We also apply the developed model to explain our recent experimental findings regarding decreased uptake of N2O5 by aqueous sulfate aerosols coated with monoterpene oxidation products (section 3), and discuss the implications of the experimental results and their interpretation (section 4). Finally, conclusions and summary are given in section 5. 2. Theory The uptake coefficient γ of a gas-phase reactive compound can be defined in terms of the molar flux, Jgas, of the reactant into a particle:20
γ Jgas ) ApCgas〈c〉 4
(
1 d 2 dC rD - kC ) 0 dr r2 dr
(
(1)
where Ap (m2) is the particle surface area, Cgas (mol/m3) is the reactant gas-phase concentration, and 〈c〉 (m/s) is the average velocity of the reactant in the gas phase. The quantity Jgas can also be expressed as the following:20
Jgas ) Vpkmt Cgas -
in the reactions are constant, which may not hold for large, viscous particles and for large reactant gas-phase concentrations.26,27 To assess quantitatively under which conditions the assumption is valid, a numerical solution of the diffusionreaction equations is required.27 This is beyond the scope of this study; here, our focus is to provide an analytical expression for the uptake coefficient. Furthermore, we suppose that the system is in a steady-state, e.g., the time derivate of the reactant concentration is set equal to zero. Finally, the Kelvin effect is neglected since it has importance only for extremely small particles with diameters 1/Γaq or when
l>
HorgDorg HaqxDaqkaq
(12)
Here we have used the assumption that Rp . l or Rc ≈ Rp. Provided that the values of the relevant parameters can be determined or estimated, eq 12 provides a simple tool to investigate under which conditions dissolution and diffusion in a coating may limit the reactive uptake. Moreover, the coating thickness l needed in order to make 1/Γcoat the largest term in eq 11 is seen to be inversely proportional to the square root of kaq, which illustrates the point that rapid aqueous phase reactions are most susceptible to the presence of organic coatings on particles. 2.3. Comparison of Various Expressions for the Uptake Coefficient. Mass transfer resistance caused by the presence of an organic coating on an aqueous aerosol has three potential sources: a reactant molecule must first accommodate into the particle surface, then dissolve into the coating, and finally diffuse to the aqueous phase. Through performing a large set of calculations we addressed the following questions: (1) under which conditions is the reactive uptake limited due to dissolution and diffusion in the coating and (2) what is the valid range of eq 11? This was done by comparing the uptake coefficients predicted by eqs 9 and 11 and by the traditional resistor model with each other. We denote these quantities as γfull, γmod, and γtrad, respectively. The parameter γtrad was calculated assuming that the organic coating has identical properties with the aqueous phase, i.e., influence of organic coatings on the reactive uptake is neglected. The molecular weight of the gaseous reactant was assumed to be 108 g/mol, and T, Dgas, and Daq were set equal to 298 K, 10-5, and 10-9 m2/s, respectively. The choice of the molecular weight is motivated by the N2O5 heterogeneous hydrolysis on which we focus in the next section. The following results are not sensitive to the value of this parameter, however. The values of the remaining parameters (Rp, l, Dorg, Haq, Horg, kaq, korg, and R) were varied independently of each other so that the parameter space was covered with approximately 25 000 calculations. The explored parameter range is shown in Table 1. The Kelvin effect is not accounted for in the comparison,
Figure 2. Maximum deviation of γtrad from γfull (top) and the mean relative difference between γtrad and γfull (bottom) as a function of the relative coating thickness l/Rp. The relative difference between γtrad and γfull is here |(γtrad - γfull)/γfull)|, and the mean and maximum relative differences are obtained by dividing the results into groups according to the value of l/Rp and calculating these quantities for each group.
since the performed sensitivity calculations showed that it has negligible influence on the results. Figure 2 shows that γtrad predicts consistently higher uptake rates compared to those predicted by γfull. This is expected since chemical reactions were assumed to proceed at equal or lower rate in the coating than in the aqueous phase. Furthermore, the magnitude of the overprediction is strongly dependent on the relative thickness of the coating, i.e., on l/Rp. The parameter γtrad gives a good approximation for γfull if the coating is relatively thin and Horg/Haq as well as Dorg/Daq are close to unity. On the other hand, if Horg and/or Dorg are decreased by an order of magnitude or more, even nanometer-sized films may inhibit the reactive uptake, and consequently large errors are induced to the uptake rates predicted by the traditional resistor formalism. The key assumption behind expression 11 (γmod) is that qorg is small compared to unity, and therefore we examined how the ratio γfull/γmod behaves as a function of qorg (Figure 3). For qorg < 10-4, both the mean relative difference between γfull and γmod and the maximum deviations of γfull from γmod are seen to be extremely small, i.e., an excellent agreement between γmod and γfull is reached when qorg < 10-4. This shows that γmod gives a good approximation to γfull when chemical reactions taking place in the coating are slow enough. To be more precise, it was found that γfull and γmod agree within 15% when korg < 0.1 s-1 (not illustrated by a figure). The deviations increase, however, with increasing value of qorg such that the mean difference between γmod and γfull exceeds 1% and 10% when qorg is larger than 10-3 and unity, respectively. Moreover,
Heterogeneous Hydrolysis of N2O5
J. Phys. Chem. A, Vol. 110, No. 35, 2006 10439
Figure 3. Mean relative difference between γmod and γfull (MRD) (gray line) as well as the minimum and maximum values of γmod/γfull, MIN(γmod/γfull), and MAX(γmod/γfull) (black lines), respectively, for the performed calculations as a function of qorg. The relative difference between γmod and γfull is defined as |(γmod - γfull)/γfull)|, and the mean relative difference is obtained by dividing the calculations into groups based on the value of qorg and calculating the average for each group. The parameters MIN(γmod/γfull) and MAX(γmod/γfull) are obtained in a similar fashion.
excluding some calculations in the range 10 < qorg
