Kinetic double-layer model of aerosol surface chemistry and gas-particle interactions ( K 2-SURF ) : Degradation of polycyclic aromatic hydrocarbons exposed to O 3 , NO 2 , H 2 O , OH and NO 3

We present a kinetic double-layer surface model (K2-SURF) that describes the degradation of polycyclic aromatic hydrocarbons (PAHs) on aerosol particles exposed to ozone, nitrogen dioxide, water vapor, hydroxyl and nitrate radicals [1]. The model is based on multiple experimental studies of PAH degradation and on the Pöschl-RudichAmmann (PRA) framework [2] for aerosol and cloud surface chemistry and gas-particle interactions.

The K2-SURF model enables the calculation of ozone uptake coefficients, γ O3 , and of PAH concentrations in the quasi-static particle surface layer.Competitive adsorption and chemical transformation of the surface (aging) lead to a strong non-linear dependence of γ O3 on time and gas phase composition, with different characteristics under dilute atmospheric and concentrated laboratory conditions.Under typical ambient conditions, γ O3 of PAH-coated aerosol particles are expected to be in the range of 10 −6 -10 −5 .
At ambient temperatures, NO 2 alone does not efficiently degrade PAHs, but it was found to accelerate the degradation of PAHs exposed to O 3 .The accelerating effect can be attributed to highly reactive NO 3 radicals formed in the gas phase or on the surface.Estimated second-order rate coefficients for O 3 -NO 2 and PAH-NO 3 surface layer reactions are in the range of 10 −17 -10 −16 cm 2 s −1 and 10 −15 -10 −12 cm 2 s −1 , respectively.
The chemical half-life of PAHs is expected to range from a few minutes on the surface of soot to multiple hours on organic and inorganic solid particles and days on liquid particles.On soot, the degradation of particle-bound PAHs in the atmosphere appears to be dominated by a surface layer reaction with adsorbed ozone.On other substrates, it is likely dominated by gas-surface reactions with OH or NO 3 radicals (Eley-Rideal-type mechanism).
To our knowledge, K2-SURF is the first atmospheric process model describing multiple types of parallel and sequential surface reactions between multiple gaseous and particlebound chemical species.It illustrates how the general equations of the PRA framework can be simplified and adapted for specific reaction systems, and we suggest that it may serve as a basis for the development of a general master mechanism of aerosol and cloud surface chemistry.

Introduction
Aerosols are ubiquitous in the atmosphere and have strong effects on climate and public health.Depending on chemical composition and surface properties, aerosol particles can act as condensation nuclei for cloud droplets and ice crystals, and they can influence trace gas concentrations through heterogeneous chemical reactions (Seinfeld and Pandis, 1998;Pöschl, 2005;Fuzzi et al., 2006;Andreae and Rosenfeld, 2008;Hallquist et al., 2009).Polycyclic aromatic hydrocarbons (PAHs) are one of the most prominent groups of toxic air pollutants.They originate from biomass burning and fossil fuel combustion, and they reside to a large extent in fine air particulate matter that can penetrate deep into human lungs (Finlayson-Pitts and Pitts, 2000;Pöschl, 2002;Schauer et al., 2003).Chemical degradation and transformation (oxidation or nitration) can change the surface properties of aerosol particles and the toxicity of PAH (Pitts, 1983;Atkinson and Arey, 1994;Pöschl, 2002;Schauer et al., 2004;Pöschl et al., 2007).
Moreover, PAH as well as its oxygenated or nitrated derivatives are well defined model substances for the molecular structure of soot, which is the black solid product of incomplete combustion or pyrolysis of organic matter (Homann, 1998;Messerer et al., 2005;Pöschl, 2005;Sadezky et al., 2005).Soot contributes to regional and global climate change because of its role in direct, indirect and semi-direct radiative forcing (Hansen et al., 1997;Ackerman et al., 2000;Jacobson, 2000).Upon emission from combustion sources, fresh soot is initially hydrophobic and mostly externally mixed with non-refractory compounds (Shiraiwa et al., 2007;Schwarz et al., 2008).However, condensation of semi-volatile compounds and chemical processing by ozone and other oxidants can make soot particles hydrophilic (Mikhailov et al., 2006) and influence their ability to act as cloud condensation nuclei (Kuwata et al., 2007).Furthermore, chemical reactions with atmospheric photo-oxidants can lead to substantial degradation, short-term and seasonal variations, and measurement artefacts in the determination of PAHs (Schauer et al., 2003(Schauer et al., , 2004;;Marchand et al., 2004;Liu et al., 2006;Lee and Kim, 2007;Lammel et al., 2009).
As detailed below (Sect.3), several laboratory studies have investigated the heterogeneous reaction of PAHs on various substrates with ozone, nitrogen dioxide, water vapour, hydroxyl and nitrate radicals.So far, however, the experimental results had not yet been compiled in a form that enables efficient modelling of PAH degradation in different types of reaction systems and direct comparison of relevant physicochemical parameters (accommodation, uptake, and reaction rate coefficients; adsorption constants; etc.).
Recently, Springmann et al. (2009) have demonstrated the applicability and usefulness of the PRA framework (Ammann and Pöschl, 2007;Pöschl et al., 2007) for atmospheric modeling of the degradation of benzo[a]pyrene on soot by ozone and nitrogen dioxide.In this study we show that the PRA model approach can be efficiently extended to other PAHs and photo-oxidants.Within the European integrated project on aerosol, cloud, climate and air quality interactions (EUCAARI, Kulmala et al., 2009), we have reviewed and synthesized available literature data to develop a reaction mechanism describing the degradation of PAHs exposed to O 3 , NO 2 , H 2 O, OH and NO 3 radicals in a kinetic doublelayer surface model (K2-SURF).PAH degradation and related ozone uptake are simulated over a wide range of conditions, and the atmospheric implications are discussed.

Model description
The K2-SURF model is based on the PRA framework for aerosol and cloud surface chemistry and gas-particle interactions (Pöschl, Rudich and Ammann 2007;Ammann and Pöschl 2007).This framework describes the gas-particle interface by several model compartments and molecular layers in which volatile, semi-volatile and non-volatile species can undergo mass transport and chemical reactions: gas phase, near-surface gas phase, sorption layer, quasi-static surface layer, and (near-surface) bulk of the particle.
As illustrated in Fig. 1, the K2-SURF model does not consider semi-volatile species and processes in the particle bulk, which is just regarded as a substrate that may influence the properties of the quasi-static surface layer.
In describing the degradation of particle-bound polycyclic aromatic hydrocarbons (PAHs) exposed to O 3 , H 2 O, NO 2 , OH, and NO 3 , the focus was on the gas phase diffusion, gas-surface mass transport, surface layer reactions, and gassurface reactions, which are discussed in following sections.We assumed that the effects of surface-bulk mass transport and chemical reactions in the bulk are negligible compared to gas-surface mass transport and chemical reactions at the surface.Nevertheless, the chemical species in the quasistatic surface layer (PAH) can interact with the near-surface particle bulk (substrate), which may influence the effective physicochemical properties of the quasi-static surface layer and related kinetic parameters such as surface accommodation coefficients, desorption lifetimes, and surface reaction rate coefficients (Pöschl et al. 2007).

Gas phase diffusion and gas-surface mass transport
Based on kinetic theory, the gas kinetic flux of X i colliding with the surface J coll,Xi can be expressed as where [X i ] gs is near-surface gas phase concentration of X i and ω Xi is mean thermal velocity given by ω Xi = (8RT/(π M Xi )) 1/2 , where M Xi is the molar mass of X i , R is the gas constant, and T is the absolute temperature.Here we assume that the gas phase concentrations of O 3 , H 2 O, and NO 2 are homogeneous throughout gas phase and near-surface gas phase ([X i ] gs = [X i ] g ).This assumption is well justified when uptake coefficients are below 10 −3 (Ammann and Pöschl, 2007).
On the other hand, uptake of OH and NO 3 by PAH is reported to be high (>0.1)(Bertram et al., 2001;Gross and Bertram, 2008), therefore, the significant net uptake of OH and NO 3 will lead to local depletion of concentration at nearsurface gas phase ([X i ] gs <[X i ] g ) and gas phase diffusion will influence further uptake.In this case near-surface gas phase concentration should be corrected using a gas phase diffusion correction factor C g,Xi .
C g,Xi can be described as follows based on PRA framework (Pöschl et al., 2007).
Kn Xi is Knudsen number which can be approximated by gas phase diffusion coefficient D g,Xi and particle diameter d p .
The flux of adsorption of gas molecules on the quasi-static particle surface can be expressed as where α s,Xi is surface accommodation coefficient and k a,Xi (= α s,Xi ω Xi /4) is a first-order adsorption rate coefficient.In Langmuir adsorption model, α s,Xi is determined by the surface accommodation coefficient on an adsorbate-free surface α s,0,Xi and the sorption layer coverage θ s , which is given by the sum of the fractional surface coverage of all competing adsorbate species (i.e.O 3 , H 2 O, and NO 2 ) θ s,Xp .
θ s,Xp is the ratio between the actual and the maximum surface concentration value of X p : θ s,Xp = [X p ] s /[X p ] s,max = σ s,Xp [X p ] s , where σ s,Xp is the effective molecular cross section of X p .In this study, we assume that the effective molecular cross section is the same for all co-adsorbed species unless mentioned otherwise.Accordingly, the inverse molecular cross section can be regarded as the overall concentration of non-interfering sorption sites on the quasi-static surface layer (Pöschl et al., 2007): [SS] ss = σ −1 s,Xp .The adsorbed molecules can thermally desorb back to the gas phase.Desorption, the inverse of adsorption, can be described by a first-order rate coefficient k d,Xi , which is assumed to be independent on θ s,Xi .The flux of desorption of gas molecules on the quasi-static particle surface can be expressed as The desorption lifetime τ d,Xi is the mean residence time on the surface in the absence of surface reaction and surfacebulk transport.Since molecules are desorbed thermally, k d,Xi depends strongly on temperature.This can be described by an Arrhenius equation as described below.
A pre-exponential factor A is typically ∼10  frequency of a molecule bound to the surface.For physisorbed species, A is typically ∼10 12 s −1 .Adsorption enthalpy of gaseous X i , H ads,Xi can be estimated roughly by assuming A.
The uptake coefficient of gas species X i can be expressed as a ratio between the net fluxes of X i from the gas phase to the condensed phase J net,Xi , and J coll,Xi .

Surface layer reactions (Langmuir-Hinshelwoodtype mechanism)
The surface layer reactions (SLRs) occur within the surface double layer and involve only adsorbed species or components of the quasi-static layer.In this study the PAH-O 3 system is considered to follow a Langmuir-Hinshelwood-type mechanism, in which ozone first adsorbs to the surface and then reacts with PAH in a quasi-static surface layer (Pöschl et al., 2001;Ammann et al., 2003;Ammann and Pöschl, 2007;Pöschl et al., 2007).Note, however, that traditionally the term "Langmuir-Hinshelwood mechanism" is used for surface catalytic reactions between adsorbed gas species and not to describe reactions that transform the surface (Masel, 1996;IUPAC, 1997).Here we consider three SLRs: The products of SLR1 and SLR3, O1-PAH and O2-PAH, are oxidized non-volatile PAHs.The surface reaction of O 3 and NO 2 produces the highly reactive NO 3 radical, which can react with PAH immediately.The degradation rate of PAH (L SLR,PAH ) can be described using the second-order rate coefficients k SLR,PAH,O3 and k SLR,PAH,NO3 , where k s,PAH (= k SLR,PAH,O3 [O 3 ] s + k SLR,PAH,NO3 [NO 3 ] s ) is an apparent first-order PAH decay rate coefficient.
The production rate of NO 3 on the surface, P SLR,NO3 , can be described as

Gas-surface reaction (Eley-Rideal-type mechanism)
The gas-surface reaction is a single kinetic step of collision and reaction between gaseous species and surface molecules, which can be regarded as an Eley-Rideal-type mechanism (Ammann and Pöschl, 2007;Pöschl et al., 2007).Note that traditionally the term "Eley-Rideal mechanism" (also named Rideal-Eley or Langmuir-Rideal mechanism) is used for surface catalytic reaction between adsorbed gas species rather than for reactions that transform the surface (Masel, 1996;IUPAC, 1997).Here we consider two GSRs.
Here γ GSR,Xi,PAH is defined as the elementary surface reaction probability that X i (OH or NO 3 ) undergoes gassurface reaction when colliding with PAH on the surface.θ ss,PAH is the surface coverage of PAH.

Steady-state conditions
The surface mass balance and rate equations can be described as below in summary (Pöschl et al., 2007).
Steady-state conditions are characterized by d[X i ] s /dt=0 (X i =O 3 , H 2 O, and NO 2 ).The effective Langmuir adsorption equilibrium constant K ads,Xi can be described as below should be follows.
If surface reactions are much slower than desorption (k d,Xi k s,Xi ), then K ads,Xi is equal to a Langmuir adsorption equilibrium constant K ads,Xi (=σ s,Xi k a,0,Xi /k d,Xi ).Under these conditions the desorption lifetime τ d,Xi and firstorder rate coefficient k d,Xi are given by The surface concentration of X i can be expressed as An apparent first order rate coefficient k s,PAH can be described as where k s,PAH,max is a maximum pseudo-first order rate coefficient of PAH.
The uptake coefficient of ozone (γ O3 ) can be calculated as The initial concentration of PAH is considered to be the inverse of the effective molecular cross section σ PAH and is estimated assuming one aromatic ring has 0.2 nm 2 .For example, σ BaP is assumed to be 1 nm 2 because BaP consists of five aromatic rings (Pöschl et al., 2001).

Basic physicochemical parameters
As illustrated in Fig. 3, the pseudo-first order PAH decay rate coefficients (k s,PAH ) typically exhibit a nonlinear dependence on gas phase ozone concentration, which is consistent with a Langmuir-Hinshelwood-type mechanism.In contrast, an Eley-Rideal-type mechanism would lead to a linear dependence of k s,PAH on gas phase ozone concentration.In the PAH-O 3 -H 2 O system Eq.( 23) can be simplified to The parameters of k s,PAH,max and K' ads,O3 were obtained by a non-linear least-squares fit of Eq. ( 25 (IGOR software).The experimental data were taken from the referenced studies, and the fit results are summarized in Table 1.Pöschl et al. (2001) also measured the surface concentration of ozone, [O 3 ] s , as a function of gas phase ozone concentration, which can be described by the following equation: A non-linear least squares fit yielded σ s,O3 =0.17 nm 2 ([SS] ss =5.8×10 14 cm −2 ).We assumed this value for the other studies as well, because Pöschl et al. (2001) is the only study that reported [O 3 ] s .Second-order rate coefficients (k SLR,PAH,O3 ) were calculated using the relation k s,PAH,max =k SLR,PAH,O3 σ −1 s,O3 .Ozone desorption lifetimes (τ d,O3 ) and the corresponding desorption rate coefficients (k d,O3 ) were estimated using Eq. ( 21), assuming a surface accommodation coefficient of α s,0,O3 =1.0×10 −3 (Rogaski et al., 1997) for the adsorbate-free surface.
The obtained τ d,O3 values are in the range of 10 ms-10 s depending on the substrate (Table 1).The relatively long desorption lifetimes suggest chemisorption of O − 3 possibly in the form of O atoms.Thus, the τ d,O3 values should be regarded as apparent desorption lifetimes that may effectively include the dissociation of ozone or other intermediate steps of chemical interaction at the surface as will be discussed below.
From k d,O3 = τ −1 d,O3 approximate adsorption enthalpies H ads,O3 were estimated using Eq. ( 8) and assuming a preexponential factor of A = 10 14 s −1 (Pöschl et al., 2001).Test calculations with A = 10 12 -10 15 s −1 gave an uncertainty range of ± 6 kJ mol −1 in H ads,O3 .K' ads,O3 is approximated to K ads,O3 , as k d,O3 is one to three orders of magnitude larger than k s,O3 .The K ads,O3 values are one to three orders of magnitude larger for solid substrates compared to liquid substrates.This corresponds to longer desorption lifetimes and larger negative adsorption enthalpy values for solid substrates ( H ads,O3 ≈ −(70-90) kJ mol −1 ).Additionally, k s,PAH,max and k SLR,PAH,O3 are by an order of magnitude larger on solid substrates.Self-assembled monolayers of alkenes show similar adsorption and reaction rate coefficients as PAHs on solid substrates, whereas the parameters for cypermethrin are similar to PAHs on liquid substrates.
Most studies were performed under dry conditions (RH ≈ 0%), but Pöschl et al. (2001) and Kwamena et al. (2004) also reported results for humid conditions.The K ads,H2O values obtained from these data are of the order of 10 −17 cm −3 (Table 2), i.e., 2-4 orders of magnitude smaller than K ads,O3 .Assuming α s,0,H2O = 6.0 × 10 −4  (Rogaski et al., 1997) we obtained H 2 O desorption lifetimes of the order of 0.1 ms, indicating physisorption of H 2 O.The adsorption enthalpy H ads,H2O was estimated to be −36( ± 9) kJ mol −1 assuming a pre-exponential factor in the range of 10 8 -10 12 s −1 (Pöschl et al., 2001).Kwamena et al. (2007) pointed out that the substrate influences the partitioning of ozone to the surface irrespective of the PAH adsorbed to it.They also suggested that different experimental approaches can yield different results.In particular, they found that PAHs may dissolve into the substrate of thin film experiments, thereby affecting the reaction kinetics and partitioning of O 3 as will be discussed below.
According to molecular dynamics (MD) simulations the desorption lifetime of ozone on at the interface of pure water and air should be only 36 ps (Vieceli et al., 2005) which is much shorter than the values listed in Table 1.Possible explanations for the differences are: (1) The surfaces considered in our study are covered by PAH molecules and thus likely to interact differently with ozone.(2) The desorption lifetimes calculated from measurement-derived adsorption constants depend inversely on the assumed surface accommodation coefficients (α s,0 ) and might thus be up to three orders of magnitude shorter if α s,0 were close to unity.(3) The chemical species actually residing at the surface might be O atoms rather than ozone molecules, and thus additional processes such as a dissociation reaction or other intermediate steps of chemical interactions at the surface might have to be considered for full mechanistic understanding.(4) Surface-bulk exchange as well as mass transport and chemical reactions might also play a role for liquid substrates.Further investigations will be needed to resolve these issues, and we are planning to pursue such investigations using K2-SURF as well as kinetic double-and multi-layer models that resolves also diffusion and reaction in the bulk of the particle or substrate, respectively (K2-SUB, Pfrang et al., 2009;KM-SUB, Shiraiwa et al., 2009).
Systems on a solid substrate such as soot, glass and solid organic substrate are well described by the red lines in Fig. 4, covering over five orders of magnitude in both γ O3 and [O 3 ] gs .Most experimental data were obtained at high [O 3 ] gs , but along the model lines γ O3 can be extrapolated to atmospheric conditions ([O 3 ] gs <150 ppb).There γ O3 is estimated to be ∼10 −5 for PAHs on a soot surface and ∼10 −6 on a solid organic surface.
On liquid substrates γ O3 is substantially lower (≈ 10 −8 ).A possible explanation is that some PAH may be dissolved in the liquid substrate (Kwamena et al., 2007), leading to a reduction of the actual PAH concentration on the surface and to a decrease of γ O3 according to Eq. ( 24).Transport of PAH from the quasi-static layer to the bulk can be modelled by surface-bulk exchange fluxes (J ss,b , J b,ss ) which goes beyond the present study.Still, these data are well fitted by the black solid line suggesting γ O3 values of the order of 10 −8 under atmospheric conditions.

PAH-O
The oxidation of the PAH benzo[a]pyrene upon interaction with O 3 , H 2 O and NO 2 was investigated using data from Schauer (2004).As illustrated in Fig. 5, the pseudo-first order PAH decay rate coefficients (k s,PAH ) exhibit a nonlinear dependence on gas phase ozone concentration, which is consistent with a Langmuir-Hinshelwood-type reaction mechanism and can be described by the following equations.
Table 4 shows the basic physicochemical parameters of O 3 in this system.The apparent overall concentration of sorption sites [SS] ss decreases systematically as the NO 2 concentration increases, which implies that the effective molecular cross section of adsorbed ozone is smaller than that of NO 2 .This finding suggests that ozone may indeed be adsorbed in the form of O atoms, because molecular O 3 is not expected to be smaller than NO 2 .Alternatively or in addition, other intermediates might also be involved in the coadsorption of O 3 and NO 2 (e.g., NO 3 or N 2 O 5 formed by reaction of NO 2 with O 3 or O).Further investigations will be needed to elucidate the actual mechanism of interaction between different co-adsorbed species, and additional processes could be flexibly included in K2-SURF.Nevertheless, the simple Langmuir-Hinshelwood-type formalisms applied in this study appear to sufficient for efficient description of multi-component systems as illustrated in Figs. 4 and 5.
Apparent second-order surface reaction rate coefficients k SLR,PAH,O3 were derived assuming k SLR,O3,NO2 = 0, because no PAH degradation was observed upon exposure to NO 2 without O 3 (Pöschl, 2002;Schauer, 2004;Schauer et al., 2004).Interestingly, however, the measured and derived rate coefficients k s,PAH,max and k SLR,PAH,O3 exhibit a systematic increase with increasing NO 2 concentration.For example, k SLR,PAH,O3 increases by a factor of ∼2 from 2.66 × 10 −17 cm 2 s −1 in the absence of NO 2 to Atmos.Chem. Phys., 9, 9571-9586, 2009 www.atmos-chem-phys.net/9/9571/2009/5.70 × 10 −17 cm 2 s −1 at 500 ppb NO 2 .The accelerating effect of NO 2 can be attributed to the formation of highly reactive NO 3 radicals in the gas phase or on the surface.Other reactive nitrogen species like N 2 O 5 or HNO 3 are unlikely to play a major role because the uptake coefficients reported for them are <10 −5 (Gross and Bertram, 2008).

Numerical modeling of transient conditions
Here we simulate the temporal evolution of surface composition and uptake coefficients of ozone over timescales from microseconds to days under standard conditions (298 K, 1013 hPa).The model calculations were performed by solving the rate equations (Eq.14-18) numerically with Matlab software (ode23s solver).No steady-state assumptions were applied in the numerical simulations.The initial PAH surface concentration is set to 1 × 10 14 cm −2 , and the initial surface concentration of gas species (X i = O 3 , H 2 O, NO 2 , and NO 3 ) is set to zero.In the exemplary simulations, we consider soot and solid organic surfaces.The required basic physicochemical parameters are listed in Table 5.The α s,0 values were taken from earlier studies (Tabor et al., 1994;Rogaski et al., 1997).The τ d and k SLR,PAH,O3 values were taken from Sect. 3. The gas phase ozone concentration is set to 100 ppb, which is typical for polluted air masses.The chemical half-life of the PAH (t 1/2 ) is defined as the time when the PAH concentration reaches half of the initial concentration.

PAH-O 3 -H 2 O system
Here we simulate PAH degradation upon interaction with O 3 and H 2 O. Fig. 6 shows the surface concentrations of all involved chemical species and the uptake coefficient of O 3 (γ O3 ). Figure 6a displays the model results for a soot surface at 25% RH.The initial plateau of γ O3 is equal to α s,0,O3 (=10 −3 ) up to 1 s, which can be explained by adsorption of O 3 onto a nearly adsorbate-free surface.The second plateau of γ O3 at ∼10 −5 is due to chemical reaction of O 3 with PAH.Under dry conditions the model results are similar (not shown in figure), but due to the absence of competitively adsorbing H 2 O the surface coverage of O 3 increases and the PAH chemical half-life decreases 188 s (25% RH) to 168 s (dry).
www.atmos-chem-phys.net/9/9571/2009/Atmos.Chem.Phys., 9, 9571-9586, 2009  Fig. 6b displays the model results for a solid organic surface at 25% RH.Under these conditions the dominant species on the surface is H 2 O, and the O 3 surface concentration is much lower than on soot.Consequently, the PAH degradation proceeds slower and the second plateau of γ O3 is longer (∼10 4 s) and lower (γ O3 = ×10 −7 ).
The differences of PAH degradation on soot and on the solid organic surface are mainly caused by the different desorption lifetimes of ozone as derived and discussed in Sect. 3 (∼10 s vs. ∼0.1 s).We speculate that the longer apparent desorption lifetime on soot may reflect stronger electron donor-acceptor interactions between the graphene layers (aromatic rings) and the adsorbed ozone molecules or oxygen atoms, respectively.

PAH-O 3 -H 2 O-OH system
Here we simulate PAH degradation by O 3 , H 2 O, and OH radicals for which we assume an elementary surface reaction probability of γ GSR,OH,PAH = 0.32 (Bertram et al., 2001).The two dotted lines in Fig. 6a and 6b correspond to different OH concentration levels: an estimated global average value of [OH] g = 10 6 cm −3 ) (Prinn et al., 1992) and an approximate upper limit value of [OH] g = 10 7 cm −3 .The near-surface gas phase concentration [OH] gs was calculated from Eqs. ( 2) and (3) assuming a particle diameter of 200 nm (C g,OH = 0.87).
Figure 6a indicates that OH does not significantly affect PAH degradation on soot, where ozone is strongly adsorbed and plays a dominant role.On the solid organic surface, however, where ozone is less efficiently adsorbed, OH strongly accelerates PAH degradation as shown in Fig. 6b.Consequently, the PAH decay proceeds faster and the length of the second plateau of γ O3 decreases with increasing OH concentration.

PAH chemical half-life on the surface and atmospheric implications
Here we simulate the chemical half-life of PAH (t 1/2 ) on soot, organic and liquid surfaces, when exposed to ambient concentrations of O 3 and OH at 25% RH.   Figure 7 displays the results of calculations.The black line is the t 1/2 of PAH on a soot surface, which showed t 1/2 of ∼10 min at typical atmospheric O 3 concentration of 30 ppb.We calculated t 1/2 under dry conditions as well, which resulted in a t 1/2 value of ∼5 min at 30 ppb O 3 .Therefore, the competitive adsorption of O 3 and H 2 O leads to a significant increase in t 1/2 .However, the t 1/2 values showed only a slight change with increasing [OH] g .This is because PAH degradation on soot is dominated by the surface layer reaction of PAH with O 3 .
The t 1/2 values on a solid organic surface (red and blue line) are estimated to 2-15 h at 30 ppb O 3 when [OH] g is 0. The t 1/2 value on a liquid surface like octanol and water (green line) is estimated to a few days.As shown in Fig. 7, τ d,O3 is a critical factor in estimating the chemical half-life of PAH on the surface.OH plays a critical role in these cases.It accelerates the PAH degradation by one to two orders of magnitude depending on OH concentration.
In summary, the PAH chemical half-life on the surface (t 1/2 ) ranges from ∼10 min on soot, to 1-5 h on solid organics and 6 h on liquid particles under typical ambient conditions (30 ppb O 3 , 25% RH, 10 6 cm −3 OH).Therefore, the relative importance of PAH degradation by O 3 and OH depends on the substrate of PAH.Fig. 7.Chemical half-life of PAHs on different substrates (soot, solid organic, liquid) as a function of gas phase ozone concentration at 25% RH assuming OH concentrations of 0 (solid lines), 1.0×10 6 cm −3 (dashed lines), and 1.0×10 7 cm −3 (dotted lines).

PAH-O
Here we simulate PAH degradation on soot upon interactions with O 3 , H 2 O, NO 2 , and NO 3 .As shown in Table 4, NO 2 could accelerate PAH degradation.For example, the apparent k SLR,PAH,O3 is increased from 2.7×10 −17 cm 2 s −1 to 5.7×10 −17 cm 2 s −1 under 500 ppb NO 2 , leading to a reduction of t 1/2 from 188 s to 170 s at 100 ppb O 3 and 25% RH.Here we consider two possible explanations for the acceleration of PAH degradation by NO 2 : (1) surface reaction of O 3 with NO 2 (Langmuir-Hinshelwood-type mechanism) and (2) gas-surface reaction between PAH and gas phase NO 3 radical (Eley-Rideal-type mechanism).
Figure 8a shows the exemplary simulation of this system using τ d,NO3 =10 s, k SLR,O3,NO2 =10 −17 cm 2 s −1 , and k SLR,PAH,NO3 =10 −14 cm 2 s −1 .Temporal evolution is similar to Fig. 6a, but the PAH degradation was accelerated by formation of NO 3 radical, whose concentration reaches ∼10 12 cm −2 .The uptake coefficient of O 3 (γ O3 ) stayed 10 −5 because of continuous surface reaction of O 3 with NO 2 .γ NO2 was also calculated and it was 0.064 initially up to 10 −2 s, which is equal to α s,0,NO2 .As it is shown by [NO 2 ] s which reached steady-state condition quickly, γ NO2 decreased away after 0.1 s.

Gas-surface reaction with NO 3
Gas-surface reaction between gas phase NO 3 radicals and PAH is another possible explanation for the acceleration of PAH degradation.This system corresponds to a possible nighttime chemistry of PAH degradation, as NO 3 is the dominant oxidant at nighttime.
Here we simulate PAH degradation by O 3 , H 2 O, NO 2 , and gas phase NO 3 radicals for which we assume an elementary surface reaction probability of γ GSR,OH,PAH =0.13 (Rudich et al., 1996).Note that the surface reaction of O 3 with NO 2 is not considered in this simulation.The near-surface gas phase concentration [NO 3 ] gs was calculated from Eqs.
(2) and (3) assuming a particle diameter of 200 nm (C g,NO3 =0.94).The NO 2 concentration at 25% RH is set to 500 ppb.Four NO 3 concentrations that cover the range of ambient concentrations (1, 10, 20, and 100 ppt) are assumed (Finlayson- Pitts and Pitts, 2000).Figure 8b indicates that the presence of NO 3 does not impact the degradation of PAHs significantly when [NO 3 ] g =1 ppt,, but rather ozone plays a dominant role in PAH degradation.The NO 3 radicals compensate the competitive adsorption of NO 2 when [NO 3 ] g =10 ppt with t 1/2 of 186 s.The t 1/2 is 144 s when [NO 3 ] g =20 ppt.And for [NO 3 ] g =100 ppt, the t 1/2 is calculated to 38 s, indicating PAH degradation is dominated by the NO 3 radical at this condition.

PAH chemical half-life on the surface and atmospheric implications
Here we simulate the chemical half-life of PAH (t 1/2 ) on soot, organic and liquid surfaces, when exposed to O 3 , H 2 O, NO 2 , and NO 3 at typical ambient concentration level at night time (<150 ppb O 3 , 60% RH, 100 ppb NO 2 , 1-10 ppt NO 3 ).Note that at higher RH water vapor may undergo multilayer adsorption and its effect may thus not be well described by a Langmuir adsorption isotherm (Thomas et al., 1999;Mikhailov et al., 2009).Figure 9 displays the results of calculations.Neither the surface reaction of O 3 with NO 2 nor gas-surface reaction of NO 3 was considered for the thick solid line.NO 3 accelerates the PAH degradation by one to three orders of magnitude depending on NO 3 concentration (dotted and dashed line).The surface reaction of O 3 and NO 2 decreases the t 1/2 by ca.40% on every surface (solid line).In summary, under typical ambient conditions at night time (i.e. 30 ppb O 3 , 100 ppb NO 2 , 60% RH, 1 ppt NO 3 ), t 1/2 ranges from ∼10 min on soot, to 30-60 min on solid organics and liquid particles.

Conclusions
We have developed and applied a kinetic double-layer surface model (K2-SURF) and chemical reaction mechanism to describe the degradation of polycyclic aromatic hydrocarbons (PAHs) on aerosol particles interacting with ozone, nitrogen dioxide, water vapor, hydroxyl and nitrate radicals.Basic physicochemical parameters have been derived from experimental data and used to simulate PAH degradation and ozone uptake by aerosol particles under a wide range of conditions.The main conclusions are: (1) The heterogeneous reaction between particle-bound PAHs and ozone can be well described by Langmuir-Hinshelwood-type mechanism and rate equations with effective Langmuir adsorption constants and surface first-order desorption rate coefficient of X i k SLRv,Xp,Xq , second-order rate coefficients for surface k SLRv,Xp,Yq layer reactions of X p with X q , X p with Y q , respectively K ads,Xi adsorption equilibrium constant of X i K ads,Xi effective adsorption equilibrium constant of X i α s,0,Xi surface accommodation coefficient of X i on an adsorbate-free surface t 1/2 chemical half-life of PAHs on the surface reaction rate coefficients depending on the substrate material.Note, however, that the exact reaction mechanisms, rate limiting steps and possible intermediates still remain to be resolved (e.g., surface diffusion and formation of O atoms or O − 3 ions at the surface).
(2) Competitive and reversible adsorption and chemical transformation of the surface (aging) lead to a strong non-linear dependence of the ozone uptake coefficients on time and gas phase composition with different characteristic features under dilute atmospheric and concentrated laboratory conditions.Under typical ambient conditions the ozone uptake coefficients of PAH-coated aerosol particles are likely in the range of 10 −6 -10 −5 .
(3) Nitrogen dioxide undergoes competitive co-adsorption with ozone.At ambient temperatures NO 2 alone does not efficiently degrade PAHs, but it can accelerate PAH degradation by ozone.The accelerating effect of NO 2 can be explained by the formation of highly reactive NO 3 radicals in the gas phase and on the surface.
(4) The chemical half-life of PAH is expected to range from a few minutes on the surface of soot, to multiple hours on solid organics and days on liquid particles.On soot, PAH degradation appears to be dominated by a surface layer reaction with adsorbed O 3 (Langmuir-Hinshelwood-type mechanism).On other substrates, it seems to be dominated by gas-surface reaction with OH and NO 3 radicals (Eley-Rideal-type mechanism).
www.atmos-chem-phys.net/9/9571/2009/Atmos.Chem.Phys., 9, 9571-9586, 2009 (5) To our knowledge, K2-SURF is the first atmospheric process model describing multiple types of parallel and sequential surface reactions between multiple gaseous and particle-bound chemical species.We propose that K2-SURF may be used to design, analyze, and interpret experiments for better understanding of heterogeneous reaction systems.For example, systematic sensitivity studies can help to determine the range of experimental conditions (reactant concentrations, reaction time, etc.) that are likely to provide most information and direct insight into possible reaction mechanisms and the underlying physicochemical parameters (e.g., Langmuir-Hinselwood-type vs. Eley-Rideal-type mechanisms, physisorption vs. chemisorption, adsorption/desorption vs. chemical reaction rate coefficients, etc.).Moreover, we suggest that K2-SURF may serve as a basis for the development of a general master mechanism of aerosol and cloud surface chemistry.

Fig. 6 .
Fig.6.Temporal evolution of the surface concentration of the volatile species (O 3 and H 2 O), of PAH in the quasi-static surface layer, and of the ozone uptake coefficient (γ O3 ) at 100 ppb O 3 and 25% RH assuming OH concentration of 0 (solid line), 1.0 × 10 6 cm −3 (dotted line) and 1.0 × 10 6 cm −3 (dashed line).PAHs are either (a) on soot or (b) on a solid organic surface. 49 Figure 7. 21

Table 1 .
) to the experimental data pairs of k s,PAH and [O 3 ] gs for each PAH and substrate Basic physicochemical parameters of O 3 in the PAH-O 3 -H 2 O system with different PAHs and substrates.The upper part is kinetics data of PAHs on solid substrates, the middle part is that of PAHs on liquid substrates, and the bottom part is that of non-PAH.

Table 2 .
Basic physicochemical parameters of H 2 O in the BaP-O 3 -NO 2 -H 2 O system on soot and azelaic acid.
Ozone uptake coefficients (γ O3 ) for different PAHs and substrates.Symbols represent literature data (Table
* Values in italic are interpolated.

Table 5 .
Basic physicochemical parameters of O 3 , H 2 O, and NO 2 used in the numerical simulations of transient conditions.
[SS] ss sorption site surface concentration[X i ] g gas phase concentration of X i [X i ] gs near-surface gas phase concentration of X i [X i ] s surface concentration of X i (sorption layer) [Y j ]ss surface concentration of Y j (quasi-static layer)