Interactive comment on “ Detailed heterogeneous chemistry in an urban plume box model : reversible co-adsorption of O 3 , NO 2 , and H 2 O on soot coated with benzo [ a ] pyrene ”

The paper could benefit from some more discussion of how the idealized assumptions are likely to effect results, especially the assumption of a Langmuir isotherm for water adsorption and the assumption that no reactions between NO2 and water will occur on the particle surface. The paper would also benefit from performing another model simulation exploring the possibility of using two constant uptake coefficients for each species (one for the first hour and the second for the remaining time in the model simulation).


Introduction
Heterogeneous chemistry describes reactions between gasphase species and condensed matter.In the atmosphere, these heterogeneous reactions can significantly change the composition of aerosol particles and the atmospheric environment.The most prominent example is heterogeneous reactions on polar stratospheric clouds, which are the key processes for the observed strong ozone depletion during polar spring (Crutzen and Arnold, 1986;Molina et al., 1987;Solomon et al., 1992).
Published by Copernicus Publications on behalf of the European Geosciences Union.
An ubiquitous aerosol particle type, particularly in urban environments, is soot.Soot particles originate from the incomplete combustion of hydrocarbons, e.g. in combustion engines (Finlayson-Pitts and Pitts, 2000;Bond et al., 2004), and may be coated with polycyclic aromatic hydrocarbons (PAHs) formed by the same processes (Finlayson-Pitts and Pitts, 2000).
Laboratory studies indicated that gas phase species such as ozone (O 3 ) and nitrogen dioxide (NO 2 ) can react with soot surfaces (Pöschl, 2005;Nienow and Roberts, 2006;Rudich et al., 2007).Ozonolysis experiments on soot showed rapid initial gas uptake followed by a slower uptake regime during which surface reactions occurred (Smith and Chughtai, 1996;Disselkamp et al., 2000;Pöschl et al., 2001).These surface reactions can produce carboxyl groups that stay on the particle surface and/or volatile species such as CO 2 and H 2 O that desorb to the gas phase (Thomas et al., 2001).The same two-step kinetic process, fast initial uptake followed by a slower uptake regime, was found in experiments probing the adsorption and reactivity of NO 2 on soot (Ammann et al., 1998;Kleffmann et al., 1999;Saathoff et al., 2001).Studies also indicated the subsequent formation and desorption of nitrous acid (HONO), which is important for initiating daytime photochemistry by providing a source for the hydroxyl radical (OH) (Ammann et al., 1998;Arens et al., 2001Arens et al., , 2002;;Vogel et al., 2003;Aubin and Abbatt, 2007).Water vapor significantly affects the ozonolysis of soot and the NO 2 adsorption on soot surfaces.It delays the loss of surface species during ozonolysis (Pöschl et al., 2001) and may decrease the NO 2 uptake.
The efficiency of heterogeneous reactions is often expressed employing an uptake coefficient (γ ) which represents the ratio between the net flux of a gas phase species from the gas phase to the condensed phase and the gas kinetic flux of the same gas phase species colliding with the surface (Danckwerts, 1951;Schwartz and Freiberg, 1981;Schwartz, 1986;Pöschl et al., 2007).Modeling studies often assume constant uptake coefficients to describe heterogeneous reactions (Tie et al., 2001;Bey et al., 2001;Aklilu and Michelangeli, 2004), or employ empirical parameterizations of the uptake coefficient in dependence of relative humidity, temperature, and aerosol composition (Evans and Jacob, 2005;Davis et al., 2008).However, the experimental studies on the adsorption of gas-phase species on soot mentioned above indicate that the heterogeneous kinetics depend also on particle surface composition and gas-phase concentrations, in addition to the environmental conditions described by temperature and relative humidity.Consequently, changes in gasphase composition due to reactions within the gas-phase and uptake of gas-phase species by particles can significantly affect the efficiency of the uptake kinetics.For these reasons, the uptake coefficient can not a priori be treated as a constant value.Instead, one would expect that it generally varies over time due to changes in the particle surface composition and gas-phase concentrations.Pöschl et al. (2007) developed a kinetic model framework for aerosol surface chemistry and gas-particle interactions which includes flux-based mass balance and rate equations, and a clear separation of mass transport and chemical reactions.This treatment, also termed the Pöschl-Rudich-Ammann (PRA) framework (Pöschl et al., 2007;Ammann and Pöschl, 2007), allows to consider changes in the rate parameters such as the uptake coefficient as a result of changes in particle surface composition and gas-phase concentrations.For the remainder of this manuscript, we refer to this approach as dynamic uptake coefficient approach emphasizing the potential variability of γ .The PRA framework consists of a double-layer surface model which incorporates gas-surface, surface layer, and surface-bulk reactions and allows the addition of unlimited numbers of chemical species and physicochemical processes (Pöschl et al., 2007).It provides an explicit mechanistic description of concentration and time dependencies of the reactive and non-reactive gas uptake and subsequent changes in particle composition.Using this framework, the two-step kinetic process observed in the ozonolysis and NO 2 adsorption experiments can be described by a Langmuir adsorption-desorption equilibrium followed by Langmuir-Hinshelwood type surface reactions (Pöschl et al., 2001;Rudich, 2003;Rudich et al., 2007;Pöschl et al., 2007).
The focus of this paper is to determine how heterogeneous reactions change the aerosol surface composition and affect the gas-phase concentrations of adsorbing pollutants in an urban plume scenario.To investigate this question, the PRA dynamic uptake coefficient approach is coupled to the Second Generation Regional Acid Deposition Model (RADM2) which is a well-established, nonlinear chemical gas-phase mechanism for modeling atmospheric chemistry on a regional scale (Chang et al., 1987;Stockwell et al., 1990) under consideration of diurnal changes in photolysis frequencies and gas-phase emissions.With this coupled model framework, we are able to assess in yet not achieved detail the effects of heterogeneous reactions on particle and atmospheric gas-phase composition for arbitrary time scales.We apply data from several heterogeneous uptake experiments on soot to model the reversible co-adsorption of O 3 , NO 2 , and water vapor on soot particles coated with the polycyclic aromatic hydrocarbon benzo[a]pyrene (BaP) for an urban plume scenario.These model substances are of high relevance with respect to public health and the environment, as BaP is classified as a "probable human carcinogen" (EPA, 2006a) and the trace gases O 3 and NO 2 are major criteria air pollutants (EPA, 2006b).With these gas-phase species, we define three model scenarios of increasing complexity which are comprised of adsorption and surface reactions of O 3 , of O 3 and NO 2 , and of O 3 , NO 2 , and water vapor.Since each scenario has a different number of co-adsorbing species, we are able to give a detailed account on the influence of coadsorption on heterogeneous chemistry and the gas phase.Instead of applying a prescribed uptake coefficient, we explicitly resolve the fluxes that determine the uptake coefficient.Therefore, the uptake coefficient is a quantity that is diagnosed from our calculations and is dependent on adsorbent specific parameters like molecular cross section, accommodation coefficient, desorption time, and the adsorbents' gas-phase and surface concentrations and reactions.
The new contributions of this study are the coupling of the PRA framework to gas-phase chemistry and the coadsorption of multiple gas-phase species with coupled surface reactions.By including the competing effects of O 3 , NO 2 , and water vapor, the model complexity goes beyond current laboratory experiments, which consider two coadsorbing gas-phase species at most (e.g.Pöschl et al., 2001).It also places the heterogeneous reactions into a more realistic atmospheric context with atmospheric humidity levels, gas-phase and soot emissions, and diurnal photolysis patterns.
The scope of this paper is conceptual and relies on some simplifications.For example, the maximum adsorbents' surface coverage is limited to one monolayer, which means that diffusion processes through multiple surface layers are not considered in our model framework.This allows us to treat the uptake of gas-phase species according to Langmuir adsorption kinetics.To reduce complexity, we neglect changes in particle composition due to coagulation, dilution, and condensation of semi-volatile gas-phase species.We also expect more trace gases than the three considered here to adsorb onto soot particles under atmospheric conditions.However, with limiting the number of adsorbents to three, we are able to specifically assess each adsorbent's influence on the heterogeneous chemistry.Other trace gases, such as OH and NO 3 , are also involved in important heterogeneous reactions (e.g.Bertram et al., 2001;Molina et al., 2004;Hearn and Smith, 2006;Knopf et al., 2006;Gross and Bertram, 2008;Park et al., 2008;Gross and Bertram, 2009), but have not been shown to adhere to Langmuir adsorption kinetics with subsequent surface reactions (Langmuir-Hinshelwood type reactions) and are therefore not the subject of this study.Although we attempt to use realistic values characteristic of an urban plume scenario as input parameters, our purpose is not to make exact atmospheric predictions.
The paper is organized as follows.Section 2 describes the employed model framework consisting of the PRA model framework coupled to the gas-phase solver RADM2.In Sect.3, we outline our model approach by describing the adapted gas-phase chemistry of an urban plume scenario, the representation of soot coated with BaP as a model substance, our model scenarios with the implemented surface reactions, and additional soot emission scenarios.Section 4 presents our results on the temporal evolution of surface composition, the BaP half-life, and the feedback on the gas-phase O 3 quasi-static surface layer Y i (ss) sorption layer X i (s) bulk gas phase X i (g) J ads J des k SLR Fig. 1.The applied surface layer model is shown as a schematic.The gas-particle interface is divide gas-phase (g) with gas-phase species X i (g), a sorption layer (s) with adsorbed gas-phase species X i (s), static surface layer (ss) with non-volatile particle components Y i (ss), and a particle bulk.The adsorp desorption fluxes are indicated as J ads and J des respectively, and the rate coefficient for surface layer r is denoted by k SLR .Adapted from Pöschl et al. (2007).
32 Fig. 1.The applied surface layer model is shown as a schematic.The gas-particle interface is divided into a gas-phase (g) with gasphase species X i (g), a sorption layer (s) with adsorbed gas-phase species X i (s), a quasi-static surface layer (ss) with non-volatile particle components Y i (ss), and a particle bulk.The adsorption and desorption fluxes are indicated as J ads and J des , respectively, and the rate coefficient for surface layer reactions is denoted by k SLR .Adapted from Pöschl et al. (2007).concentration for the dynamic uptake approach and, for comparison, for an approach with constant uptake coefficients.We conclude with summarizing the findings and their atmospheric implications.

Coupled PRA model framework
The PRA framework (Pöschl et al., 2007) describes gasphase uptake and surface chemistry by a double-layer surface model with sorption layer and quasi-static layer, and by flux-based rate equations.Figure 1 shows the scenario we adapt on this basis, supported by experiments on the adsorption and subsequent reaction of O 3 on soot (Pöschl et al., 2001) and NO 2 on soot (Ammann et al., 1998): Gas-phase species X i (g) adsorbs onto the sorption layer, quantified by the adsorption flux J ads .Adsorbed species X i (s) can then either desorb, expressed by the desorption flux J des , or react with non-volatile particle components Y i (ss) from the quasistatic surface layer, which is indicated by a second-order rate coefficient k SLR .
The coupling of the PRA model framework to the gasphase mechanism RADM2 is achieved by implementing the PRA framework's net production and loss terms of gas-phase and surface species into the chemical integration routine of RADM2.Section 2.1 describes the gas-phase loss due to the reversible co-adsorption of gas-phase species using a dynamic uptake approach and Sect.2.2 gives an account of the chemical production and loss of adsorbed and surface species due to Langmuir-Hinshelwood type surface reactions.

Dynamic uptake coefficient approach
The presented derivations are relevant to couple the gasphase mechanism RADM2 to the PRA framework (Pöschl et al., 2007;Ammann and Pöschl, 2007).The subsequent equations represent a condensed version of the PRA framework and follow closely its derivations outlined in Pöschl et al. (2007) and Ammann and Pöschl (2007).
The uptake coefficient of gas species X i , γ X i , is defined, in terms of fluxes, as the ratio between the net flux of X i to the condensed phase, J net,X i , and the gas kinetic flux of X i colliding with the surface, J coll,X i : It is important to note that this definition of γ X i does not explicitly include chemical reactions or gas-phase diffusion, as is often assumed when referring to the reactive uptake coefficient.
The collision flux is based on kinetic gas theory and can be expressed as where [X i ] gs is the gas-phase concentration close to the surface and ω X i is the mean thermal velocity of molecule X i given by ω X i = 8 R T /(πM X i ), where R is the universal gas constant, T is the absolute temperature, and M X i is the molar mass of species X i .Significant net uptake of the gas-phase species can lead to its local depletion close to the surface.A gas-phase diffusion correction factor C g,X i can be applied to relate the gasphase concentration close to the surface [X i ] gs to the average gas-phase concentration [X i ] g , such that C g,X i = [X i ] gs [X i ] g .For γ X i -values smaller than one, which is justified for the scenarios considered here, C g,X i can be determined as (Fuchs and Sutugin, 1971) where Kn X i is the Knudsen number given by D g,X i is the gas-phase diffusion coefficient of species X i and d p is the particle diameter.Using the diffusion coefficients for O 3 , NO 2 , and water vapor given by Massman (1998) and a particle diameter of 119 nm for soot (Pöschl et al., 2001) results in Knudsen numbers of about 2.17 for NO 2 and H 2 O and 2.35 for O 3 .Sensitivity runs with and without gas-phase diffusion corrections showed no difference for the case of O 3 and H 2 O uptake, and only a difference within the first 10 s of maximum 2% for NO 2 uptake.For this reason, the gas-phase diffusion correction for the cases considered here can be neglected and the gas-phase concentration close to the surface equals the average gas-phase concentration, [X i ] gs ≈[X i ] g .The net flux to the condensed phase is the difference of the adsorption flux and desorption flux, J net,X i =J ads,X i −J des,X i . (5) The adsorption flux of a gas molecule X i is related to the collision flux via the accommodation coefficient α s,X i representing the molecule's probability of adsorption on the surface: Thus, J ads,X i can be expressed as In case of competitive co-adsorption of several gas-phase species, the accommodation coefficient of the individual species, α s,X i , can be derived using a Langmuir adsorption model in which all adsorbate species compete for a single sorption site on the quasi-static surface, such that where α s,0,X i is the surface accommodation coefficient on an adsorbate-free surface.θ s is the sorption layer surface coverage which is given by the sum of fractional surface coverages of all competing adsorbate species, θ s,X p , i.e. θ s = p θ s,X p .
The fractional surface coverage depends on the surface concentration of the adsorbate species X p , [X p ] s , and its effective molecular cross section, σ s,X p , which corresponds to the inverse of the species' maximum surface concentration in the sorption layer, [X p ] s,max : The desorption flux of species X i can be quantified by the ratio between this species' surface concentration [X i ] s and its desorption lifetime τ d,X i which is the mean residence time of the species on the surface: By combining Eqs. ( 1)-(10) and assuming [X i ] gs =[X i ] g , the uptake coefficient of species X i can be derived as Equation ( 11) shows that the uptake coefficient derived according to Pöschl et al. (2007) depends on the parameters of the adsorbing species such as α s,0,X i , σ s,X p , ω X i , τ d,X i , but also on its surface and gas-phase concentrations [X i ] s and [X i ] g , which can be affected by transport and chemical reactions.Therefore, Eq. ( 11) expresses γ X i as a dynamic uptake coefficient when changes in [X i ] s and [X i ] g are taken into account.The numerator of Eq. ( 11) describes the net flux of X i (g) to the particle and hence the generation of X i (s) in the sorption layer under consideration of the surface coverage of all adsorbing species.Surface reactions need to be taken into account to obtain the total net production of sorption layer species, which we outline in Sect.2.2.It should be noted that the initial adsorbent surface concentration in the sorption layer is zero, thus, the uptake coefficient's initial value is given by the accommodation coefficient, γ X i ,ini =α s,0,X i .The net gas-phase loss of adsorbent X i , i.e. loss L due to uptake onto the particle in the condensed phase minus production P due to desorption back to the gas phase, is calculated by multiplying the adsorbent's collision flux by the corresponding dynamic uptake coefficient and by the particle surface area in air, [PS] g : The next section describes the reaction kinetics between the adsorbed species and surface components according to a Langmuir-Hinshelwood reaction mechanism.

Langmuir-Hinshelwood mechanism for surface reactions
The Langmuir-Hinshelwood mechanism describes reactions in which adsorbed gas-phase species react on the particle surface (Pöschl et al., 2007).For the cases considered here, we focus on particle surface reactions between the sorption layer (s) and the quasi-static surface layer (ss) following the derivations by Pöschl et al. (2007) and Ammann and Pöschl (2007).Chemical reactions that proceed between the gas phase and the particle surface, exclusively within the sorption or the quasi-static surface layer, as well as photo-chemical processes on the surface are neglected.We assume the product of the surface reactions to be a surface component residing within the quasi-static surface layer.Applying these assumptions, the net chemical production of quasi-static surface species Y i (ss) from reaction between adsorbed species in the sorption layer, X p (s), and surface components in the quasi-static surface layer, Y q (ss), is determined by where v numbers the rate equation, p and q number the reactants, c SLR are negative or positive stoichiometric coefficients, and k SLR are second-order rate coefficients.
In contrast to quasi-static surface layer components which are produced and lost through surface reactions, adsorbed sorption layer species are only depleted by surface reactions, since we assume the surface reactions considered here to be irreversible.The loss of sorption layer species X i due to the surface reactions is a subset of Eq. ( 13) with the reactant summation index variable p fixed to species X i : The total net chemical production of sorption layer species X i (s) is composed of the loss due to surface reactions and the production and loss due to adsorption and desorption: where the fluxes of adsorption and desorption, J ads,X i and J des,X i , respectively, are described in Sect.2.1.The differential Eqs. ( 12), ( 13), and ( 15) represent the heterogeneous kinetics adapted in our model framework.We implement these differential equations into the chemical integration routine of RADM2 (Chang et al., 1987;Stockwell et al., 1990) to obtain solutions and to account for the temporal evolution of the gas phase.
In the next section, we specify the gas-phase chemistry of RADM2 and give a detailed account of our model approach and implemented heterogeneous chemistry scenarios.

Model approach
We model the reversible co-adsorption and subsequent surface reactions of O 3 , NO 2 , and water vapor on soot coated with BaP in an urban plume scenario.Section 3.1 describes the gas-phase chemistry of this urban plume scenario as implemented into the chemical gas-phase solver RADM2.Section 3.2 gives a representation of soot coated with BaP as a model substance, which is followed by an overview of the implemented surface reactions and corresponding model scenarios in Sect.3.3.Section 3.4 describes two soot emission scenarios to assess the gas-phase feedback from heterogeneous reactions under polluted conditions.

Gas-phase chemistry
The chemical gas-phase solver RADM2 includes 62 chemical species, 21 photolysis reactions, and 140 thermal reactions (Stockwell et al., 1990).A detailed account of the gasphase reactions of RADM2 is given elsewhere (Chang et al., 1987;Stockwell et al., 1990).RADM2 is widely used in atmospheric models to predict concentrations of oxidants and other air pollutants (e.g.Grell et al., 2005;Tie et al., 2007).The main feature that RADM2 provides to this study is the NO x -O 3 chemistry with its diurnal pattern.This results in continuous changes in the O 3 and NO 2 gas-phase concentrations throughout the simulation period.These variations in gas-phase concentrations subsequently affect the magnitude of the individual and combined uptake of O 3 and NO 2 by the soot particles.This investigation of the gas phase-particle surface interrelationship under atmospherically relevant conditions is one of the main foci and and novelty of this study.
We use RADM2 in a tropospheric urban plume scenario (PLUME1) according to Kuhn et al. (1998).This case was designed to represent the chemistry in the polluted boundary layer, which is consistent with an urban plume scenario where emissions of soot occur.This plume scenario includes constant emissions for a variety of trace gases representative for continental European air (Derwent and Jenkin, 1991), such as 0.54 pptv min −1 of SO 2 , 2.68 pptv min −1 of NO, and 5.85 pptv min −1 of CO.Volatile organic compounds (VOCs) are aggregated into 15 classes of reactive organic species with emissions of 0.14 pptv min −1 for formaldehyde (HCHO), 0.037 pptv min −1 for acetaldehyde and higher aldehydes, and 0.46 pptv min −1 for acetone, methyl ethyl ketone and higher ketones.Initial concentrations are set to 50 ppbv for O 3 , 0.5 ppbv for NO 2 , 0.2 ppbv for NO, and 20 000 ppmv for H 2 O which corresponds to 64% relative humidity (RH).Time-dependent photolysis rates are calculated as described in Kuhn et al. (1998).Physical processes such as deposition and dilution of trace gases and soot particles, and particle coagulation are not considered.As suggested by Vogel et al. (2003), the reaction rate for the production of HONO from NO and OH was revised according to Atkinson et al. (2001).
RADM2 is run in a box model version for a modeling period of five days, under atmospheric conditions of 1013.25 hPa pressure and a temperature of 298 K.The simulation starts at 12 noon.The gas-phase chemistry in RADM2 is solved with a variable chemical time step (Chang et al., 1987) ranging from 0.096 s to 3 s.To resolve the rapid adsorption of water vapor in scenario C, a shorter time step is used for the first day of the simulation period, ranging from 0.003 s to 0.006 s.The gas-phase solver RADM2 and the heterogeneous chemistry part outlined in the last section run in a coupled fashion for all model scenarios considered in this paper.

Representation of soot
The chemical surface reactions occur on a population of soot particles coated with BaP.We adopted an initial soot concentration of 10 µg m −3 in air corresponding to concentrations in heavily polluted air (Seinfeld and Pandis, 2006).Since the soot surface is of fractal-like geometry (Van Gulijk et al., 2004), we use the surface area obtained from Brunauer-Emmett-Teller (BET) isotherms as reactive surface area and implement a BET value of 500 m 2 g −1 .This corresponds to values that have been used in laboratory heterogeneous chemistry studies (e.g.Tabor et al., 1994;Choi and Leu, 1998;Disselkamp et al., 2000).Multiplying the BET value by the soot concentration yields a total surface concentration of [PS] g =5×10 −5 cm 2 cm −3 .However, BET values for soot can range from 6 m 2 g −1 for aircraft engine combustor soot (Popovicheva et al., 2008) to approximately 500 m 2 g −1 for the post-treated black carbon Degussa FW2 (Dymarska et al., 2006), which can lead to large differences in [PS] g .Thus, the implemented BET-value of 500 m 2 g −1 may result in an upper limit for the concentration of surface reaction sites.
While the surface concentration remains constant in this model, the passivation of the surface is introduced by the consumption of the BaP coating, which has initially a surface concentration of 1×10 14 cm −2 corresponding to a full monolayer coverage.BaP readily adsorbs onto soot particles and can be regarded as a proxy for the wider class of polycyclic aromatic compounds, but also for soot due to its structural similarities of the surface (Pöschl et al., 2001).Soot can be pictured as agglomerate of graphene layers, while BaP (C 20 H 12 ) represents a single graphene layer consisting of five six-membered aromatic rings (Homann, 1998;Pöschl et al., 2001).Here, BaP provides consumable reactive sites for adsorption processes and surface reactions.

Surface reactions
We define three model scenarios with an increasing level of complexity.These scenarios represent the adsorption and surface reactions of O 3 in scenario A, of O 3 and NO 2 in scenario B, and of O 3 , NO 2 , and water vapor in scenario C. As starting point for the dynamic uptake coefficient approach described in Sect.2.1, we implemented experimentally determined initial uptake coefficients as accommodation coefficients in accord to Ammann and Pöschl (2007).This approach is justified, since initially γ X i =α s,0,X i , as can be seen from Eq. ( 11).In the following, we discuss each scenario with regards to the implemented surface reactions and adapted input parameters with reference to Table 1.
Scenario A represents the adsorption of O 3 and subsequent surface reactions of O 3 with BaP and its derivatives.After O 3 is adsorbed to the sorption layer (s), it participates in three surface reactions with the quasi-static surface layer (ss), (R1) to (R3), as given in Table 1.These reactions convert BaP into chemical derivatives Y2, Y3, and Y4, whose chemical form is not exactly known, but can be pictured as BaP derivatives with an increasing number of oxygenated functional groups and decreasing reactivity towards photooxidants such as BaP-quinones, hydroxy-ketones, acid anhydrides, lactones, etc. (Letzel et al., 1999a(Letzel et al., ,b, 2001;;Pöschl, 2002).This scenario corresponds to Model System Solid 1 (Ammann and Pöschl, 2007), except that it includes the atmospheric context by the coupling to RADM2.The reaction rate k SLR1 and the O 3 -specific parameters α s,0,O 3 , σ O 3 , τ d,O 3 are adapted from results of aerosol flow tube experiments at ambient temperature and pressure (Pöschl et al., 2001).The reaction rate coefficients for reactions (R2) and (R3), k SLR2 and k SLR3 , were chosen according to Ammann and Pöschl (2007) to account for the decreasing reactivity of the BaP derivatives.
Scenario B represents the co-adsorption and subsequent surface reactions of O 3 and NO 2 .In addition to surface reactions (R1) to (R3), adsorbed NO 2 also reacts with BaP derivatives according to surface reactions (R4) and (R5) as listed in Table 1.Based on Model System Solid 2 (Ammann and Pöschl, 2007), the products consist of another surface component (with increased oxygenated functional group) and a volatile component which desorbs to the gasphase.Input parameters are based on experimental data for the reaction and adsorption of NO 2 at the surface of soot particles in Knudsen cell experiments (Gerecke et al., 1998), aerosol flow reactor experiments (Ammann et al., 1998), and filter deposition experiments (Ammann et al., 1997).The reaction rate coefficient for surface reaction (R4), k SLR4 , was adjusted by Ammann and Pöschl (2007) to fit the experimental data.In surface reaction (R5), we identify the volatile component with nitrous acid (HONO) and apply a reaction rate of 3.7×10 −3 s −1 according to Ammann et al. (1998), which yields 7.5×10 −21 cm 2 s −1 .
Scenario C involves the co-adsorption of O 3 , NO 2 , and water vapor, with subsequent surface reactions of O 3 and NO 2 according to surface reactions (R1) to (R5) as listed in Table 1.For this scenario, we assume that water vapor adsorbs to the surface without being involved in subsequent surface reactions.This is supported by Pöschl et al. (2001), who observed a slower decay of BaP and smaller gas-phase O 3 loss under humid conditions indicating the inhibition of O 3 adsorption by competitive adsorption of water vapor at the aerosol surface.Since freshly emitted discharge soot particles are known to be hydrophobic, physisorption of water vapor on soot was suggested as mechanism for adsorption, supported by the water vapor's small desorption lifetime (Pöschl et al., 2001).The H 2 O specific parameters α s,0,H 2 O and τ d,H 2 O are adapted from Rogaski et al. (1997) and Pöschl et al. (2001), and σ H 2 O is taken from Nishino (2001).
In our first set of simulations we start with an initial soot concentration and do not include any emissions of fresh soot over the course of the simulation.While the surface concentration [PS] g remains constant, the uptake coefficient γ X i does change with time, according to the available surface reaction sites and gas concentrations, which is explicitly predicted from Eq. ( 11).In the second set of simulations, we also keep the surface concentration constant, but include the effect of soot emissions by replenishing the reactive surface sites, which we describe in the next section.

Soot emissions
In polluted areas, soot is emitted continuously by a variety of sources, such as car traffic (Finlayson-Pitts and Pitts, 2000;Bond et al., 2004).Once emitted, the surface of soot particles is expected to become passivated as surface sites are taken up by adsorbents.Therefore, at any given point in time, soot particles of different ages with different surface reactivities co-exist, ranging from freshly emitted particles with large numbers of reactive surface sites to aged particles where most of the surface sites are depleted.In such an environment, the continuous emission of fresh soot particles could be important when estimating the gas-phase feedback from heterogeneous reactions on soot.In our box model framework, individual soot particles that are introduced at different times due to continuous emissions cannot be tracked.Nevertheless, to estimate the effect of freshly emitted soot particles on the gas phase in our box-model framework, we adopt the following approach as a sensitivity study.
The emission of fresh soot in our box model is approximated by resetting the soot surface to its initial condition with a BaP surface concentration of [BaP]=1×10 14 cm −2 and no secondary surface components.At this point in the simulation, the existing population of soot with the residual BaP concentration and higher order surface components is discarded.While the number of reactive surface sites changes to account for the effect of soot emissions on chemical reactions, we assume the overall soot production and loss to be in equilibrium and therefore keep the soot surface concentration [PS] g constant.We neglect physical processes, such as coagulation, deposition, and dilution of the soot particles.The BaP surface concentration on soot is replenished according to the two following scenarios.In the low emission scenario, the reactive surface is replenished every six hours, and in the high emission scenario, it is replenished every hour.The error from neglecting gas-phase uptake on discarded populations for these replenishing times will be assessed in the next section.
The replenishing times are related to hourly emission rates, R emission , by where [PS] g =5×10 −5 cm 2 cm −3 is the particle surface concentration, BET=500 m 2 g −1 , t r is the replenishing time, and h box is the box height which we choose as 1 km corresponding to the depth of the tropospheric boundary layer.This yields hourly emission rates of 1.67 kg km −2 h −1 for the low emission scenario with t r =6 h, and 10 kg km −2 h −1 for the high emission scenario with t r =1 h.These emission rates are comparable in magnitude to the soot emission rates of 0.72 kg km −2 h −1 and 7.2 kg km −2 h −1 chosen in a previous study by Aklilu and Michelangeli (2004) to model typical atmospheric background conditions with the lower rate and locations close to urban combustion sources with the higher rate.This completes our set of model scenarios consisting of the co-adsorption scenarios A, B, and C, and the two classes of emission scenarios which are labeled by the number of replenishments per day as A 4x , B 4x , C 4x , and A 24x , B 24x , C 24x .For matters of comparison, we define additional scenarios at Table 1.Adsorbents, surface reactions, reaction rates, and parameters -accommodation coefficient (α), effective molecular cross section (σ ), desorption time (τ ) -applied in model scenarios A, B, C.

Scenario adsorbents Surface reactions
Reaction rates [cm 2 s  following the surface reactions defined in Table 1 is plotted on a logarithmic timescale for day one (left panels) and on a linear timescale for the four following days (right panels).
various places in this paper.We briefly discuss these scenarios when defined, since they involve only minor changes of the scenarios described above.

Results and discussion
In this section, we present and discuss the results of the different model scenarios.Section 4.1 focuses on the soot surface chemistry and composition, followed by an account on the characteristic lifetime of the coating substance BaP in Sect.4.2.In Sect.4.3, we assess the influence of heterogeneous reactions on the gas-phase O 3 concentration for emission and non-emission scenarios.These results are then compared with the gas-phase O 3 feedback obtained by applying constant uptake coefficients in Sect.4.4.

Surface composition
The surface chemistry of scenario A is shown in Fig. 2, panel A. During the first 0.1 min, O 3 adsorbs onto an essentially adsorbate free surface with θ s ≈0.This causes the initial plateau of the O 3 uptake coefficient γ O 3 where its value is dominated by the adsorption flux, so that γ O 3 ≈0.001=αs,0,O 3 .When reaching a O 3 surface concentration of [O 3 ] s ≈1.5×10 14 cm −2 , the surface becomes saturated leading to the first decrease in γ O 3 until around 1 min.The subsequent plateau in γ O 3 is due to the chemical reaction of O 3 in the sorption layer with BaP in the quasi-static surface layer.As a result, the BaP surface concentration decreases, the reactions product concentration [Y2] ss increases, and O 3 uptake remains constant to sustain the reaction.Further depletion of BaP causes the second decrease of γ O 3 at 10 min, followed again by a plateau due to the reaction of O 3 with Y2 that increases the surface concentration of Y3.The same temporal pattern applies for the production of Y4 from the reaction of O 3 with Y3.After the first day, the gasphase O 3 concentration increases due to the photochemical production from the reactions of the O 3 precursors NO x and VOCs.This is shown in Fig. 2, panel G, which presents the gas-phase concentrations and diurnal cycles of O 3 , NO 2 , NO, and HONO corresponding to scenario A. Since the effect of the surface chemistry on the gas phase is negligible in scenario A, B, and C, the temporal evolution of the gas-phase concentrations in scenarios A, B, and C are identical.An increase in gas-phase O 3 concentration results in a larger O 3 uptake according to Eq. ( 11).However, with γ O 3 <1×10 −7 , its magnitude stays below first-day values due to increased surface saturation and the consumption of reactive primary surface components.Within the first day, BaP is decreased by almost 100%, essentially turning off surface reaction (R1) which subsequently slows down or inhibits reactions (R2) to (R5) due to the decrease of educt production.During nighttime, the O 3 adsorption flux decreases due to O 3 -depleting reactions and the absence of gas-phase O 3 sources.On the other hand, high surface saturation leads to an increase in the desorption flux of surface O 3 , so that the desorption flux can temporarily exceed the adsorption flux.This results in negative γ O 3 -values which represent the direct response to the diurnal cycle of gas-phase O 3 as depicted in Fig. 2, panel G, and are indicated by the discontinuations along the abscissa in Fig. 2, panel A. The value of γ O 3 decreases by more than five orders of magnitude and then becomes negative.
The surface chemistry of scenario B is shown in Fig. 2, panel B. In this scenario, two gas-phase species, O 3 and NO 2 , adsorb onto the soot surface.Initial adsorption of gas-phase species, chemical consumption of BaP and surface components, and chemical production of surface components proceed similar to scenario A. Although NO 2 gasphase concentrations are lower, the initial NO 2 uptake exceeds that of O 3 due to a larger accommodation coefficient for NO 2 of α s,0,NO 2 =0.14 compared to α s,0,O 3 =0.001for O 3 .In comparison to scenario A, the O 3 surface concentration is reduced in scenario B due to the co-adsorption of NO 2 .Also concentrations of the other surface components are different compared to the ones in scenario A. The lifetime of Y2 decreases by almost two days due the added Y5-producing reaction with NO 2 .The Y3 concentration is reduced by almost half in comparison to scenario A, since not all Y2 are converted into Y3 anymore.As given in Table 1, the reaction rates for the reactions of NO 2 with Y2 and Y3 are faster than the reaction rates for the reactions of O 3 with Y2 and Y3.Therefore, NO 2 converts Y2 into Y5 and Y3 into HONO faster than O 3 converts Y2 to Y3 and further to Y4.This delays Y4 production by over two days.The proportionality between adsorption flux and gas-phase concentration in Eq. ( 7) relates the adsorbents' uptake coefficients and surface concentrations to their gas-phase concentrations.This becomes evident after the initial surface saturation at around one minute of simulation time and, more pronounced, after six hours.Since the NO 2 adsorption flux initially exceeds that of O 3 , more NO 2 molecules than O 3 molecules are occupying surface sites.Therefore the NO 2 surface concentration exhibits the same temporal evolution as the NO 2 gas-phase concentration, which can be seen by comparing panels B and G in Fig. 2. The O 3 surface concentration increases when surface sites become available from a decrease in the NO 2 surface concentration due to a decrease in the NO 2 gas-phase concentration.The resulting alternating evolution of O 3 and NO 2 surface concentrations also induces an alternating evolution of O 3 and NO 2 uptake coefficients, with maxima ranging from 1×10 −5 to 1×10 −4 for γ NO 2 , and from 5×10 −8 to 3×10 −7 for γ O 3 on days two to five.However, these values are three orders of magnitude smaller than the initial uptake coefficients.This indicates that 99.9% of the uptake occurs within the first six hours.
The surface chemistry of scenario C is shown in Fig. 2, panel C.In this scenario, also water vapor, in addition to NO 2 and O 3 , co-adsorbs onto the soot surface, but it does not take part in chemical surface reactions.Table 1.34 Fig. 3.The temporal evolution of the soot surface coverage θ in scenario C is shown for the first 2 min (a), and for the entire simulation period of five days (b).The total surface coverage is indicated by θ total , and the fractional surface coverages of O 3 , NO 2 , and H 2 O by θ O 3 , θ NO 2 , and θ H 2 O , respectively.Input parameters and surface reactions for scenario C are given in Table 1.concentration of about 20 000 ppmv.This corresponds to 64% RH and is six and eight orders of magnitude larger than the gas-phase concentrations of O 3 and NO 2 , respectively.Due to its high partial pressure, H 2 O adsorbs rapidly onto the soot surface.Figure 3a shows that the H 2 O surface coverage is initially over 90%, but decreases to below 82% within the first 2 min of simulation time.Figure 3b indicates that H 2 O constantly occupies about 75% of the total surface for the course of the simulation.This reduces the adsorption fluxes of O 3 and NO 2 and results in a decrease in the surface concentrations and uptake coefficients of O 3 and NO 2 by almost one order of magnitude and half an order of magnitude, respectively, as can be seen by comparison with Fig. 2, panel B. Since O 3 and NO 2 adsorption have little influence on the total surface coverage, their gas-phase uptakes and surface concentrations are not as interdependent as in scenario B. Consequently, both the O 3 and the NO 2 surface concentrations mimic closely their respective gas-phase concentrations, which are depicted in Fig. 2, panel G. Lower surface concentrations of O 3 and NO 2 also result in slower surface reactions, thereby delaying the production of higher order surface components by over half an order of magnitude.For this reason, the uptake coefficients exhibit only two plateaus on the first day, one due to the initial uptake and one governed by the reactions of O 3 with BaP and NO 2 with Y2.On days two to five, the evolution of O 3 and NO 2 uptake coefficients is similar to the one in scenario B, but in comparison to scenario B, maximum γ -values are reduced by up to one order of magnitude.
We investigated the effect of high NO-emissions on the gas phase and particle surface composition of scenario B by increasing the NO emission 10-fold, from 2.68 pptv min −1 to 26.8 pptv min −1 .The simulation results are shown in Fig. 4. Figure 4, panel G, shows the temporal evolution of the gas-phase concentrations of O 3 , NO 2 , NO, and HONO for this model scenario.While the NO gas-phase concentration increases from 0.2 ppbv to 97 ppbv during the five days simulation period, more NO can react with O 3 to produce NO 2 and O leading to a strong nighttime titration of O 3 from the second to the fifth day. Figure 4, panel B * , presents the soot particle's surface concentrations.As can be seen in Fig. 4, panel B * , the O 3 gas-phase depletion is accompanied by a decrease in the O 3 surface concentration.During periods of O 3 depletion, γ O 3 becomes negative, since surface desorption exceeds the reduced adsorption from the gas phase.The overall decrease in the O 3 surface concentration delays the production of the surface component Y4 until the fifth day of the simulation period.The decrease in the O 3 surface coverage yields increases in the NO 2 surface concentration resulting in NO 2 saturation with a maximum surface concentration of 1/σ NO 2 =3×10 14 cm −2 .Although only the NO emission rate was changed compared to scenario B, the particle surface compositions of this scenario and of scenario B are significantly different.While in scenario B (see Fig. 2, panel B) the O 3 surface concentration is almost double the amount of the NO 2 surface concentration at the end of the five day simulation period, the sorption layer surface in the high NO emission scenario is almost entirely filled with NO 2 molecules (see Fig. 4, panel B * ).This clearly demonstrates that temporal changes in the gas-phase composition can lead to large differences in the particle surface composition.
The variations in the adsorbents' surface concentrations and uptake coefficients after the first day of the simulation period exemplify the differences to uptake scenarios that do not account for a dynamic gas-phase chemistry, such as the Models Systems Solid 1 and 2 discussed in Ammann and Pöschl (2007).However, as shown in Fig. 2, variations in the adsorbents' gas-phase concentrations have a direct effect on the adsorbents' surface concentrations and, consequently, on their uptake coefficients.By accounting for variable gas-phase concentrations in our coupled PRA framework, we can resolve variations in the uptake coefficient over atmospherically relevant time scales and study the effect of different gas-phase scenarios on the particle surface chemistry.

BaP lifetime
The consumption of the soot's BaP coating can be regarded as an initial surface oxidation process due to the reaction with O 3 and NO 2 .The efficiency of the heterogeneous kinetics of this oxidation processes can be quantified by the BaP half-life.Figure 5 shows the temporal evolution of the BaP concentration for scenarios A, B, C, and scenario C * with the BaP half-lives highlighted by the intersection with the horizontal dotted black line.Scenario C * represents the co-adsorption of O 3 and H 2 O following the surface reactions (R1) to (R3) as given in Table 1.It is meant to serve as an additional comparison to scenario A to identify the influence of the co-adsorption of H 2 O. Figure 5 indicates that the half-life of BaP surface molecules in scenario A is about 4 min.The addition of the co-adsorbing species NO 2 in scenario B extends the half-life by 54% to 6.2 min.Taking into account H 2 O physisorption and atmospheric relative humidity of 64% in scenario C increases the half-life of BaP to 32.5 min as indicated in Fig. 5. Without the NO 2 co-adsorption in scenario C * , the BaP half-life is 30 min, 10% less than in scenario C.This indicates that the H 2 O coadsorption is responsible for over 90% of the increase in BaP half-life between scenarios A and C. The reason for this is the rapid adsorption of H 2 O on the surface where it occupies a large portion of the available surface sites resulting in a high fractional surface coverage of H 2 O, as illustrated in Fig. 3.The reactive surface sites occupied by H 2 O are not available anymore for the adsorption of O 3 and subsequent BaP consumption via surface reaction (R1).Compared to scenarios A and B, the co-adsorption of water vapor leads to a more than five-fold increase in BaP half-life between scenarios C and B, and more than a seven-fold increase between scenarios C * and A.
The sensitivity of the BaP half-life on the adsorption of H 2 O is influenced by the H 2 O concentration and therefore by RH. Figure 6 shows that the BaP half-life increases linearly with RH.An increase from 0% RH to 25% RH results in an almost threefold increase in the BaP half-life from 6 min to 17 min for scenario C. Also shown in Fig. 6 are the half-lives of scenarios P and P * .Scenario P * represents BaP half-lives as a function of RH derived from experimental data from the ozonolysis of soot coated with BaP (Pöschl et al., 2001).Scenario P represents our modeling results using the experimental conditions of Pöschl et al. (2001) as input parameters.These are a 30 ppbv constant gas-phase O 3 concentration, an initial BaP surface concentration of 1.8×10 13 cm −2 , a temperature of 296 K, and O 3 and H 2 O as adsorbing species.Other input parameters are identical to the ones listed in Table 1. Figure 6 shows that the simulated BaP half-lives in scenario P are slightly longer than the ones inferred from laboratory measurements (Pöschl et al., 2001) given by scenario P * .The simulated BaP half-lives in scenario P are 5.8 min for 0% RH, 22.5 min for 25% RH, and 56 min for 75% RH.The BaP half-lives in scenario P * as derived by Pöschl et al. (2001) are 5 min for 0% RH, 18 min for 25%, and 45 min for 75% RH.Reasons for the longer simulated lifetimes in scenario P could be parameter sensitivity or physio-chemical processes that were not accounted for in our model approach.Regarding the former, a 20% reduction in the value for the effective molecular cross section of H 2 O would result in half-lives in agreement with the measurements of Pöschl et al. (2001).
Regarding the latter, physiochemical processes that are not captured in our model framework are, e.g. the diffusion of adsorbents through surface H 2 O which could lead to surface oxidation and a reduction in the BaP half-life even though most reactive sites are occupied by H 2 O. Also, changes in the soot particle's hydrophilicity could result in changes of the residence time of surface H 2 O, subsequently affecting particle oxidation.A variation of the H 2 O desorption time, τ H 2 O , of about ±10% due to possible changes in particle hydrophilicity changes the BaP lifetime by about ±5 min.

Feedback on the gas-phase O 3 concentration with differing uptake and emission scenarios
In this section, we assess the gas-phase O 3 feedback from scenarios A, B, C, and from the emission scenarios A 4x , B 4x , C 4x , and A 24x , B 24x , C 24x .Figure 7 shows the temporal evolution of the gas-phase O 3 concentrations in these scenarios and a base scenario which does not include any heterogeneous reactions on soot.The diurnal cycle of gas-phase O 3 and the potential decreases in the gas-phase O 3 concentration due to the heterogeneous reactions implemented in our model scenarios can be clearly identified.represents the co-adsorption of O3, NO2 and H2O following the surface reactions given in Table 1 initial gas-phase O3 concentration of 50 ppbv, an initial BaP surface concentration of 1 × 10 14 cm −2 temperature of 298.15 K. Scenario P represents the co-adsorption of O3 and H2O following surface react to (3) from Table 1 with a constant gas-phase O3 concentration of 30 ppbv, an initial BaP surface conce of 1.8 × 10 13 cm −2 , and a temperature of 296 K corresponding to the boundary conditions of an aero tube experiment conducted by Pöschl et al. (2001).Scenario P * represents the experimentally deriv half-lives from the aerosol flow tube experiment (Pöschl et al., 2001) with the same boundary condi used in scenario P. 37 Fig. 6.The BaP half-life is plotted as a function of relative humidity for scenarios C, P, and P * .Scenario C represents the co-adsorption of O 3 , NO 2 , and H 2 O following the surface reactions given in Table 1 with an initial gas-phase O 3 concentration of 50 ppbv, an initial BaP surface concentration of 1×10 14 cm −2 , and a temperature of 298.15 K. Scenario P represents the co-adsorption of O 3 and H 2 O following surface Reactions (R1) to (R3) from Table 1 with a constant gas-phase O 3 concentration of 30 ppbv, an initial BaP surface concentration of 1.8×10 13 cm −2 , and a temperature of 296 K corresponding to the boundary conditions of an aerosol flow tube experiment conducted by Pöschl et al. (2001).Scenario P * represents the experimentally derived BaP half-lives from the aerosol flow tube experiment (Pöschl et al., 2001) with the same boundary conditions as used in scenario P.
The gas-phase uptake in scenarios A, B, and C cause no significant decrease in the gas-phase O 3 concentration with respect to the base scenario.Detail 1 in Fig. 7 resolves the differences among scenarios A, B, C. The strongest O 3 depletion among these scenarios is 0.33 ppb in scenario B which is less than 2‰ in comparison to the base scenario after the five days modeling period.The difference to the weakest O 3 depleting scenario C is less than 1‰.This insignificance of the gas-phase O 3 feedback from the non-emission scenarios is in agreement with previous studies (Kamm et al., 1999;Disselkamp et al., 2000;Nienow and Roberts, 2006) which considered O 3 depletion on soot surfaces as probably negligible under conditions relevant to the upper troposphere and lower stratosphere.
Figure 7 shows a larger gas-phase O 3 reduction for the low emission scenarios A 4x , B 4x , and C 4x in comparison to the non-emission scenarios A, B, C and the base scenario.Detail 2 in Fig. 7 indicates the strongest O 3 reduction for scenario B 4x , in which the O 3 concentration is 7.88 ppbv or 4.8% less than in the base scenario after the five days modeling period.The difference in O 3 concentration between scenarios B 4x and A 4x is less than 1%.In scenario C 4x , the O 3 concentration is decreased by 2.6% with respect to the base scenario, which is almost half the decrease of scenario B 4x .Table 1.38 Fig. 7.The temporal evolution of the gas-phase O 3 concentration is shown for a base scenario with no heterogeneous chemistry, for the model scenarios A, B, C, and the corresponding low and high emission scenarios A 4x , B 4x , C 4x and A 24x , B 24x , C 24x , respectively.Detail 1 shows an enlarged view of the results of the base scenario and model scenarios A, B, and C. Detail 2 shows an enlarged view of the results for the low emissions scenarios A 4x , B 4x , C 4x .Input parameters for the A, B, and C-scenarios are given in Table 1.
The high emission scenarios A 24x , B 24x , and C 24x exhibit the largest O 3 reductions.Figure 7 shows the lowest O 3 concentration for scenario B 24x , which is 41.6 ppbv or 25.6% less than the O 3 concentration for the base scenario after the five days modeling period.The scenarios A 24x and C 24x exhibit a decrease in O 3 concentration with respect to the base scenario of 33.8 ppbv and 19.2 ppbv, respectively.These reductions in the tropospheric O 3 concentration indicate that these heterogeneous reactions may have an impact on urban O 3 concentrations.
Figure 7 also shows clear differences in O 3 concentrations between the specific co-adsorption scenarios.The scenarios C, C 4x , and C 24x are associated with the least O 3 depletion in comparison to the A and B-scenarios.This is due to the co-adsorption of water vapor which hinders direct O 3 uptake by constantly occupying over 75% of the total reactive surface as discussed in Sect.4.1.In terms of gas-phase O 3 reduction, the A-scenarios, in which only O 3 is taken up, do not deplete gas-phase O 3 concentrations as much as the B-scenarios, in which less O 3 is taken up by the soot surface directly.However, the additional NO 2 uptake in the B-scenarios affects the gas-phase NO x -O 3 production cycle leading to a lower O 3 concentration than in cases with no NO 2 uptake.Consequently, no clear relationship between the number of adsorbing species and the resulting O 3 depletion can be established.As can also be seen from Fig. 7, the relative difference in gas-phase O 3 concentrations between the A, B, and C-scenarios increases disproportionately from the non-emission and low emission scenarios to the high emission scenarios.This highlights the non-linear behavior of the gas-phase O 3 depletion due to the co-adsorption of the interdependent species O 3 and NO 2 , and the rapid coadsorption of H 2 O.
Since there is a wide range of measured uptake coefficients for NO 2 on soot, ranging from smaller than 4×10 −8 to 0.12 (Aubin and Abbatt, 2007), we simulated the B-scenarios with accommodation coefficients of α NO 2 =10 −6 (Kleffmann et al., 1999) and α NO 2 =10 −3 (Kirchner et al., 2000).These lower initial uptake coefficients yield, within 1 ppbv, the same gas-phase feedback as the A-scenarios, which have no NO 2 co-adsorption implemented.Thus, the gas-phase feedback from the co-adsorption of NO 2 obeying an accommodation coefficient smaller than 10 −3 is negligible.
It should be noted that the feedback on the gas-phase O 3 concentration from the desorption of HONO in surface reaction (R5) given in Table 1 was found to be negligible for all model scenarios due to the small production rate in relation to gas-phase production.The HONO production rate from desorption is 0.22 ppmv −1 min −1 which is five orders of magnitude smaller than the gas-phase production rate of NO with OH.In the mornings, the gas-phase HONO production temporarily decreases due to low OH concentrations, but surface desorption is still one order of magnitude smaller than the gas-phase production and thus does not exert a significant influence.
The error in both emission scenarios from neglecting gasphase uptake on disregarded surface sites can be estimated with reference to Sect.4.1 and Fig. 2. Figure 2 shows that, for each adsorption scenario, the uptake coefficients decrease by more than three orders of magnitude or 99.9% within the first six hours of simulation time.Therefore, the error in the low emission scenarios from neglecting gas-phase uptake on soot he temporal evolution of the gas-phase O3 concentration is shown for a base scenario with no heterochemistry and for the constant uptake scenarios Aconst, Bconst, Cconst.Scenarios Aconst, Bconst, se constant uptake coefficients of γO 3 = 1 × 10 −3 (Stephens et al., 1986;Pöschl et al., 2001), 0.14 (Gerecke et al., 1998;Ammann and Pöschl, 2007), and γH 2 O = 0.4 × 10 −3 (Rogaski et al., schl et al., 2001) but are otherwise equivalent to scenarios A, B, and C as defined in Table 1.
surfaces that are older than six hours is not significant.After one hour of simulation time, the uptake coefficients fall by one to two orders of magnitude, depending on the scenario.Thus, up to 10% of gas-phase uptake is neglected in the high emission scenarios due to an hourly replenishing time, which results in a small underestimate of the total gas-phase uptake.
In the next section, we compare the gas-phase feedback from heterogeneous chemistry obtained in this section for the dynamic uptake coefficient approach with the gas-phase feedback obtained from the use of constant uptake coefficients.

Gas-phase O 3 feedback for constant uptake parameterizations
To study the gas-phase feedback from a heterogeneous modeling approach employing constant uptake coefficients, we implement the experimentally determined constant uptake coefficients of γ O 3 =1×10 −3 for O 3 uptake (Pöschl et al., 2001), γ NO 2 =0.14 for NO 2 uptake (Gerecke et al., 1998), and γ H 2 O =0.4×10 −3 for the uptake of water vapor (Rogaski et al., 1997) into the non-emission scenarios A, B, and C.These γ X i -values represent initial uptake coefficients that were previously implemented in our model as accommodation coefficients.The gas-phase loss is computed according to Eq. ( 12) with the same input parameters, particle surface concentration and gas-phase concentrations that were previously used in scenarios A, B, and C. We denote these constant uptake coefficient scenarios by A const , B const , C const .
The application of constant uptake coefficients reduced the computation time by a factor of about 18 compared to a dynamic uptake approach and needed roughly the same time as a simulation without any heterogeneous reactions implemented.
Figure 8 shows the temporal evolution of the gas-phase O 3 concentration for scenarios A const , B const , C const and for a base scenario without heterogeneous chemistry.After two hours of modeling time, the gas-phase O 3 concentration in the constant uptake coefficient scenarios A const , B const , and C const falls by more than one order of magnitude and is approaching zero.This fast depletion of O 3 is due to the fact that the gas-phase uptake is not limited by surface saturation, which otherwise would reduce the uptake coefficients.The uptake is now solely determined by the adsorbents' constant uptake coefficients, their molecular velocities, and their gas-phase concentrations via Eq.( 12).This results also in a different ordering of scenarios in terms of their O 3 depletion efficiency when compared to the dynamic uptake scenarios.Scenario A const shows the least gas-phase O 3 depletion, since it employs the lowest uptake coefficient.Scenarios B const and C const show the same O 3 depletion, since in this constant uptake coefficient approach, the co-adsorption of water vapor in scenario C const does not reduce the gas-phase uptake of O 3 and NO 2 which therefore is the same as in scenario B const .
Clearly, these constant uptake coefficient scenarios do not represent the underlying physical and chemical processes and result in an unrealistically high gas-phase O 3 depletion which may not describe typical urban plume conditions.
In addition to using the initial uptake coefficients as constant uptake values, we also attempted to parameterize the uptake process by several time-specific uptake values modeled after the temporal evolution of the uptake coefficients as shown in Fig. 2. Neither a 3-step uptake parametrization, nor a 2-step one using an initial uptake value from laboratory measurements and subsequent values from our model was successful in capturing the O 3 depleting effect.Application of a single constant uptake value for each adsorbent yielded acceptable agreement with the gas-phase O 3 concentration of the respective model scenarios if an uptake value was chosen significantly different from the laboratory measurements and model results.However, this approach is only successful for a certain time frame and certain boundary conditions, such as initial gas-phase concentrations.Furthermore, the adsorbentspecific uptake values determined in such a way, could not be used to capture the combined effect on the O 3 concentration of two or more adsorbents.Thus, the uptake values obtained in this manner are heavily scenario dependent and therefore of little use in general atmospheric models.These difficulties in obtaining a simplified and thus computationally more efficient description of the uptake process clearly indicate the underlying complexity of the involved physicalchemical mechanisms, emphasizing the need for a detailed modeling framework to accurately resolve the uptake process.

Conclusions
The PRA framework (Pöschl et al., 2007), which allows a dynamic uptake coefficient treatment, was coupled to a box model version of the gas-phase solver RADM2 (Stockwell et al., 1990) to model heterogeneous reactions of O 3 , NO 2 , and water vapor on soot coated with benzo[a]pyrene for a period of five days.Gas-phase reactions and emissions were based on an urban plume scenario (Kuhn et al., 1998).This allowed us to study, in detail, the heterogeneous kinetics and its dependency on diurnal changes in gas-phase composition due to photochemical processes.
A detailed analysis of surface chemistry showed that the O 3 and NO 2 uptake coefficients vary by more than five orders of magnitude due to competition for reactive surface sites and changes in gas-phase composition.Within the first six hours of simulation time, the uptake coefficients decrease by more than three orders of magnitude or 99.9%.From day two to five, periodic peaks of the uptake coefficient follow the diurnal cycle of the adsorbents' gas-phase concentrations.
The half-life of BaP was found to increase with the number of co-adsorbing species.Physisorption of water vapor increased the BaP half-life by a factor of five to seven by permanently occupying about 75% of the surface and thereby delaying the surface reactions of O 3 and NO 2 .The BaP halflife increases linearly with RH and the linearity is preserved under changes in O 3 and BaP concentrations, temperature, and number of adsorbing species.Our results show that even at low RH, the adsorption of water vapor can play a major role in the soot surface chemistry.An increase from 0% RH to 25% RH increases the BaP half-life by a factor of three.
This study indicates the importance of the co-adsorption of water vapor for heterogeneous chemistry also for aerosol particles other than soot coated with BaP.Since BaP belongs to the group of polycyclic aromatic hydrocarbons which are known to be hydrophobic (Rogge et al., 1993), an even greater impact of water vapor co-adsorption on surface chemistry can be expected for more hydrophilic surfaces.While our model does not capture changes in hydrophilicity, it assesses surface oxidation which is thought to influence the activation of tropospheric aerosols as cloud condensation nuclei (CCN) (Rudich, 2003;Rudich et al., 2007;Kanakidou et al., 2005;Petters et al., 2006;Shilling et al., 2007).Our modeling approach is able to estimate surface oxidation times, such as the BaP half-life, in an atmospheric context and may therefore be used in part to derive CCN activation times.
We also assessed the feedback of heterogeneous uptake on the gas-phase O 3 concentration.The different co-adsorption scenarios with no soot emissions implemented showed no significant feedback on the gas-phase composition.However, two emission scenarios in which reactive surface sites are replenished every six hours and every hour induced significant changes in the gas-phase O 3 concentration.The largest O 3 depletions were observed for the hourly high emission scenario with a reduction in O 3 concentration of up to 41.6 ppbv or 25% for the co-adsorption of O 3 and NO 2 .It also resulted in a reduction of 33.8 ppbv or 21% for the scenario with the adsorption of O 3 , and of 19.2 ppbv or 11.8% for the scenario with the co-adsorption of O 3 , NO 2 , and water vapor.In comparison, the low emission scenarios replenishing reactive sites every six hours showed a decrease in gasphase O 3 concentration of maximum 7.8 ppbv or 5%.Hence, our conceptual study employing soot particles in an urban environment indicates that heterogeneous chemistry has the potential to significantly alter the gas-phase composition.
Our model results indicated that the uptake is sensitive to the co-adsorbing species and their interactions with each other.The scenario with the most O 3 uptake from the exclusive adsorption of O 3 is surpassed in overall gas-phase O 3 reduction by the scenario in which O 3 and NO 2 co-adsorb.This is due to the additional O 3 reduction induced by the gasphase reactions between O 3 and NO 2 .This exemplifies the non-linear feedbacks obtained from a co-adsorption scheme.
Although heterogeneous reactions can be an important source for nitrous acid (HONO) (Stemmler et al., 2006), the desorption of HONO from surface reactions of NO 2 on soot particles was found to be negligible for the gas-phase O 3 concentration.
We compared the dynamic uptake coefficient approach with a constant uptake coefficients approach.The use of experimentally determined reactive uptake coefficients which were kept constant in these model scenarios led to an almost complete gas-phase O 3 depletion after two hours of modeling time which is highly unrealistic for an urban plume scenario.Since surface conditions and reactions were not related to the uptake dynamics in these constant uptake coefficient scenarios, the co-adsorption of water vapor had no impact on the efficiency of gas-phase O 3 depletion which ignores the underlying physical and chemical picture and is in contrast to the results from the dynamic uptake coefficient approach.
It should be noted that modeling studies used constant uptake coefficients, but employed consumable reactive sites on the soot surface to account for surface passivation (Aklilu and Michelangeli, 2004).This approach yields a more physical picture of the gas-phase uptake, but it still lacks the accurate description of the heterogeneous kinetics involving the interdependence of gas-phase and adsorbed surface species.Our study showed that the superposition of fixed reactive uptake coefficients, despite being experimentally determined, can result in erroneous results for the overall uptake efficiency and thus gas-phase composition.
Other modeling studies used empirical parameterizations of the uptake coefficient as a function of relative humidity, temperature, and aerosol type (Evans and Jacob, 2005;Davis et al., 2008).As such, the parametrization of N 2 O 5 hydrolysis yields gas-phase concentrations in good agreement with climatological observations (Evans and Jacob, 2005).This may be due to the fact that the N 2 O 5 hydrolysis in aqueous aerosol particles follows an absorption type reaction www.atmos-chem-phys.net/9/7461/2009/Atmos.Chem.Phys., 9, 7461-7479, 2009 mechanism (Hanson and Ravishankara, 1991;Knopf et al., 2007;Cosman et al., 2008), i.e. the uptake can be dominated by dissolution of the gas-phase species into the particle governed by Henry's law constant and by subsequent reaction in the bulk (Finlayson-Pitts and Pitts, 2000).In such heterogeneous processes, gas-phase species do not compete for reactive surface sites, which therefore have no effect on the subsequent uptake.In contrast, heterogeneous reactions following adsorption kinetics may predominantly occur at the surface of solid or crystalline particles (Rudich, 2003) and aqueous surfaces coated by an organic surfactant (Donaldson and Vaida, 2006).This limits the available number of reactive surface sites in comparison to the bulk liquid.Therefore, higher order reactive uptake processes such as Langmuir-Hinshelwood surface reactions will not be correctly represented by the application of constant reactive uptake coefficients.
This study clearly emphasizes the need for laboratory data of physical and chemical parameters for atmospherically relevant adsorbents and aerosols to predict, in detail, the effects of heterogeneous chemistry on the gas-phase and aerosol composition.

Fig. 2 .
Fig.2.The temporal evolution of gas-phase component concentrations (G), surface component concentrations, and uptake coefficients for the adsorption and surface reaction of O3 (A), the co-adsorption of O3 and NO2 (B), and the co-adsorption of O3, NO2 and H2O (C) following the surface reactions defined in Table1is plotted on a logarithmic timescale for day one (left panels) and on a linear timescale for the four following days (right panels).

Fig. 2 .
Fig. 2.The temporal evolution of gas-phase component concentrations (G), surface component concentrations, and uptake coefficients for the adsorption and surface reaction of O 3 (A), the co-adsorption of O 3 and NO 2 (B), and the co-adsorption of O 3 , NO 2 , and H 2 O (C) following the surface reactions defined in Table1is plotted on a logarithmic timescale for day one (left panels) and on a linear timescale for the four following days (right panels).

Fig. 3 .
Fig. 3.The temporal evolution of the soot surface coverage θ in scenario C is shown for the first 2 min (a), and for the entire simulation period of five days (b).The total surface coverage is indicated by θ total , and the fractional surface coverages of O 3 , NO 2 , and H 2 O by θ O 3 , θ NO 2 , and θ H 2 O , respectively.Input parameters and surface reactions for scenario C are given inTable 1.

Fig. 4 .Fig. 4 .
Fig. 4. The temporal evolution of gas-phase component concentrations (G), surface component concentrations, and uptake coefficients for scenario B * are shown and plotted on a logarithmic timescale for day one (left panels)and on a linear timescale for the four following days (right panels).Scenario B * corresponds to scenario B with a 10-fold increase of the NO emission rates.

Fig. 6 .
Fig.6.The BaP half-life is plotted as a function of relative humidity for scenarios C, P, and P * .Sce

Fig. 7 .
Fig. 7.The temporal evolution of the gas-phase O3 concentration is shown for a base scenario with no heterogeneous chemistry, for the model scenarios A, B, C, and the corresponding low and high emission scenarios A4x, B4x, C4x and A24x, B24x, C24x, respectively.Detail 1 shows an enlarged view of the results of the base scenario and model scenarios A, B, and C. Detail 2 shows an enlarged view of the results for the low emissions scenarios A4x, B4x, C4x.Input parameters for the A, B, and C-scenarios are given inTable 1.
he temporal evolution of the ratio of actual BaP surface concentration to initial BaP concentration is r scenarios A, B, C, and C * .Scenario A represents the adsorption of O3, scenario B the co-adsorption d NO2, scenario C the co-adsorption of O3, NO2 and H2O, and scenario C * the co-adsorption of O3 .Scenarios A, B, and C follow the surface reactions given inTable 1; scenario C * follows the surface (1) to (3) given in Table 1.The horizontal dotted lines indicate BaP half-life (dotted black line) and ime (dotted grey line).The temporal evolution of the ratio of actual BaP surface concentration to initial BaP concentration is shown for scenarios A, B, C, and C * .Scenario A represents the adsorption of O 3 , scenario B the co-adsorption of O 3 and NO 2 , scenario C the co-adsorption of O 3 , NO 2 , and H 2 O, and scenario C * the coadsorption of O 3 and H 2 O. Scenarios A, B, and C follow the surface reactions given in Table 1; scenario C * follows the surface reactions (R1) to (R3) given in Table 1.The intersection with the horizontal dotted lines indicate BaP half-life (dotted black line) and BaP lifetime (dotted grey line).