Semiempirical Model for Organic Aerosol Growth by Acid-Catalyzed

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Environ. Sci. Technol. 2005, 39, 164-174

Semiempirical Model for Organic Aerosol Growth by Acid-Catalyzed Heterogeneous Reactions of Organic Carbonyls MYOSEON JANG,* NADINE M. CZOSCHKE, AND AMANDA L. NORTHCROSS Department of Environmental Sciences and Engineering, CB 7431, Rosenau Hall, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, 27599

Aerosol growth by heterogeneous reactions of diverse carbonyls in the presence and absence of acidified seed aerosols was studied in a 4 m long flow reactor (2.5 cm i.d.) and a 2-m3 indoor Teflon film chamber under darkness. The acid catalytic effects on heterogeneous aerosol production were observed for diverse carbonyls in various ranges of humidities and compositions of seed inorganic aerosols. Particle population data measured by a scanning mobility particle sizer were used to calculate organic aerosol growth. To account for the aerosol growth contributed by heterogeneous reactions, the increase in organic aerosol mass was normalized by the organic mass predicted by partitioning or the square of predicted organic mass. The carbonyl heterogeneous reactions were accelerated in the presence of acid catalysts (H2SO4), leading to higher aerosol yields than in their absence. The experimental data from aerosol yields in the flow reactor were semiempirically fitted to the model parameters to predict the organic aerosol growth. The model parameters consist of environmental characteristics and molecular structure information of organic carbonyls. Basicity constants of carbonyls were used to describe the proton affinity of carbonyls for the acid catalysts. Particle environmental factors, such as humidity, temperature, and inorganic seed composition, were expressed by excess acidity and the parameters obtained from an inorganic thermodynamic model. A stepwise regression analysis of the aerosol growth model for the experimental data revealed that either the chemical structure information of carbonyls or characteristic environmental parameters are statistically significant in the prediction of organic aerosol growth. It was concluded that this model approach is applicable to predict secondary organic aerosol formation by heterogeneous reaction.

Introduction Inorganic acids such as sulfuric acid (H2SO4), ammonium bisulfate (NH4HSO4), and nitric acid (HNO3) have been of great interest because these inorganic species are among the important components of atmospheric particulate matter. In particular, sulfuric acid has a long history of haze formation and adverse health effects on the pulmonary system. Many * Corresponding author telephone: (919)966-9010; fax: (919)9667911; e-mail: [email protected]. 164

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studies in toxicology and epidemiology over the past 5 decades suggest that inorganic acids result in adverse health effects associated with complex particulate matter (PM) mixtures (1). The exact mechanism behind both haze formation and adverse health effects associated with inorganic acids such as sulfuric acid is not yet understood (2, 3). Currently, it is believed that the potency of a mixture of environmental chemicals in the particle phase, such as organic/inorganic multicomponents, may be greater than its constitutive parts. The gas-phase reaction of volatile organic compounds (VOCs) associated with atmospheric photochemical oxidant cycles generates large amounts of multifunctional organic carbonyls (4-14), which are potentially toxic (15-18). Carbonyls also serve as an important source of organic peroxy and peroxyacyl nitrates via gas-phase photooxidation in the presence of NOx (4). However, little is understood about the heterogeneous chemistry of carbonyls in the atmospheric aerosol phase and their overall potential for SOA formation. In our previous studies (19-24), it was shown that carbonyl species can be further transformed via heterogeneous acidcatalyzed reactions between the gas phase and atmospheric particulate matter. The net consequence is an increase in SOA mass. The new heterogeneous aerosol reaction products have relatively low vapor pressures and are predominantly present in the particle phase (22). Most studies focusing on inorganic components such as nitrate and sulfate neglect the organic fraction of atmospheric aerosols. In the same way, studies of SOA formation tend to be carried out without considering inorganic components such as atmospheric inorganic acids associated with inorganic salts. Our previous studies show that the acid catalytic effect on aerosol growth is influenced by humidity and the molecular structure of carbonyl species (20-22, 24). For example, the result from a simple aldehyde such as octanal shows a strong linearity between %RH and the logarithm of the aerosol yields normalized with seed aerosol mass at a given composition and experimental conditions (21). This relationship is explained by an acceleration of heterogeneous acid-catalyzed reactions of aldehydes as the particle acidity increases. It was also proposed that multifunctional carbonyls such as conjugated carbonyls and R-oxocarbonyls result in higher organic aerosol yields as compared to saturated aliphatic carbonyls because of their higher basicity and increased stability of the protonated carbonyl (22, 24). In this study, the particle growth by accommodation of different carbonyls onto preexisting inorganic seed aerosols was undertaken at different humidities and inorganic seed aerosol compositions in a 4-m flow reactor and a 2-m3 indoor Teflon film chamber. The objectives of this study were to (i) study acid catalytic effects on aerosol growth at different humidities and seed inorganic aerosol compositions, (ii) describe molecular structural effects of different multifunctional carbonyls on particle growth, and (iii) develop semiempirical model approaches to predict the organic aerosol growth by heterogeneous acid-catalyzed reactions of organic carbonyls by implementing inorganic and organic thermodynamic approaches.

Experimental Section Flow Reactor. The experimental flow reactor used in this study has been reported previously (21, 23). Briefly, air streams containing gas and particles were mixed at the inlet of a glass tube flow reactor (4.0 m length × 2.5 cm i.d.) using multi-angular Teflon inlet plates to accomplish rapid gas/ particle mixing. The flow immediately entered the main body 10.1021/es048977h CCC: $30.25

 2005 American Chemical Society Published on Web 12/03/2004

FIGURE 1. Flow reactor setup. of the reactor at flow rates ranging from 4.4 to 6.3 L/min (Reynolds number < 25). The air flow compositions of the flow tube reactor are shown in Figure 1. Sampling ports are placed every 10 cm along the length of the flow reactor. Dry air from a Pure Air Generator (AADCO 737, Rockville, MD) was used as a bath gas and for chemical injections. Seed aerosol was generated using a commercially available largevolume nebulizer (TSI model 3076 Constant Output Atomizer, St. Paul, MN) to aspirate aqueous salt solution into the flow reactor. Different kinds of inorganic seed aerosols were generated by mixing ammonium sulfate [(NH4)2SO4], ammonium bisulfate (NH4HSO4), and sulfuric acid (H2SO4) aqueous solutions. The concentration of each inorganic aqueous seed solution was 1.0 × 10-2 M. Seed aerosols generated from the nebulizer were diluted with dry air (0.40.5 L/min) before being injected into the flow reactor. Carbonyls were introduced into the gas phase of the reactor by blowing dry air through a pure organic saturator at a flow rate of 1.8-3.42 L/min. The air entering the organic saturator was heated to 40 °C. The flow reactor temperature during the course of the experiments was 298-299 K. The relative humidity (%RH) varied from 12 to 60% by controlling the air flow into the water-saturator, organic-saturator, and dry air flows. Table 1 is a summary of the experimental conditions for the heterogeneous reactions of diverse carbonyls in the flow reactor. Teflon Film Indoor Chamber Experiments. The heterogeneous reactions of octanal and 2,4-hexadienal were studied in a 2.0-m3 Teflon film chamber. The organic compound was injected into the gas phase of the indoor Teflon chamber by passing a clean air stream across a T-shaped glass tube and volatilizing the compounds using a heat gun. Prior to the addition of hydrocarbons, inorganic seed aerosol, which was made from an aqueous solution (0.01 M) of ammonium sulfate [(NH4)2SO4], ammonium bisulfate (NH4HSO4), and sulfuric acid (H2SO4), was added to the Teflon chamber. The aerosol was generated using a commercially available largevolume nebulizer (see the Flow Reactor section). The chamber

temperature during the course of the reactions was 294 K, and the relative humidity was 20%. Table 2 is a summary of the organic aerosol yields in the 2.0-m3 Teflon film chamber along with the inorganic seed compositions for the heterogeneous reactions of 2,4-hexadienal and octanal. Materials and Instruments. All of the compounds were purchased from Aldrich (Milwaukee, WI) and are listed in Table 3 along with their calculated vapor pressures (22, 2531). The total particle number and size distribution of the aerosols were monitored with a scanning mobility particle sizer (SMPS 3936 TSI, Shoreview, MN) linked to a condensation nuclei counter (3025A, TSI). The SMPS measured particle size data over a size range of 13.8-697 nm. The aerosol sampling flow was operated in 0.3 L/min with a sheath airflow rate of 3 L/min. The scanning time and the residence time of the aerosol through the internal plumbing column of the SMPS classifier were 180 and 7.4 s, respectively. Temperature and relative humidity measurements were measured with an electronic thermohygrometer (Hanna Instruments, Italy). The chemicals injected to the flow reactor were measured through a series of two impingers (15 mL of acetonitrile) and detected using a Hewlett-Packard 5890 gas chromatograph (30 m, 0.25 mm i.d., J&W DB-5 with 0.25 µm film thickness) interfaced to a 5971 mass selective detector. The temperature program was 70 °C for 1 min, 70-120 °C at 8 °C/min, and 120-290 °C at 25 °C/min.

Results and Discussion Aerosol Growth Yields. To explore the model approach for organic aerosol growth resulting from heterogeneous reactions of carbonyls, the organic aerosol mass (OM) experimentally obtained in the glass tube flow reactor was compared to the OM theoretically predicted from fundamental partitioning. The experimental OM is measured from Mmix - MSeed, where Mmix and Mseed are the mass of an aerosol mixture (SOA + inorganic aerosol) and the seed aerosol (mg m-3). The theoretical OM is determined by iKp CiMseed. The Ci is the concentration (mg/m3) of an organic (i) injected to VOL. 39, NO. 1, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. Experimental Conditions for Heterogeneous Reactions of Diverse Carbonyls in the Flow Reactor datea

H2SO4 mol fraction inorg seed

% RH

compounds in data setb

07/01/2003 06/27/2003 06/26/2003 06/25/2003 06/24/2003 09/16/2003 09/17/2003 09/18/2003 09/19/2003 09/22/2003 07/03/2003 02/11/2003 06/16/2003 06/17/2003 06/18/2003 06/12/2003 06/11/2003 07/6/2003

1 0.8 0.6 0.4 0.2 1 1 0.8 0.4 0 1 1 1 0.8 0.6 0.2 0 1

12 12 12 12 12 20 20 20 20 20 25 27 40 40 40 40 40 60

2,4-hexadienal, octanal, 2-hexenal, hexanal, 2-octanone, 2,4-pentanedione, mesityl oxide 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2,4-pentanedione 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2,4-pentanedione 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2,4-pentanedione 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2-octanone, 2,4-pentanedione 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2-octanone, 2,4-pentanedione, mesityl oxide 2,4-hexadienal, octanal, 2-hexenal, 2,4-pentanedione 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2-octanone, 2,4-pentanedione, mesityl oxide 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2-octanone, 2,4-pentanedione, mesityl oxide 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2-octanone, 2,4-pentanedione, mesityl oxide 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2-octanone, 2,4-pentanedione, mesityl oxide 2,4-hexadienal, octanal, 2-hexenal 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2-octanone, 2,4-pentanedione, mesityl oxide 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2-octanone, mesityl oxide 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2-octanone, mesityl oxide 2,4-hexadienal, octanal, 2-hexenal, hexanal, mesityl oxide 2-hexenal, hexanal 2,4-hexadienal, octanal, 2-hexenal, hexanal, 2-octanone, 2,4-pentanedione

a Experimental temperatures were 299 K. b The concentrations of organics depend on the composition of bath air in the flow reactor. The average concentration (mg/m3, the left side number in parenthese) of the gas-phase organics are included here along with its sample standard deviation (mg/m3, the right side number in parentheses): 2,4-hexadienal (3922, 672), octanal (3920, 702), 2-hexenal (7446, 1313), hexanal (18407, 2741), 2-octanaone (6877, 1221), 2,4-pentandione (6963, 1370), and mesityl oxide (20450, 2164).

TABLE 2. Experimental Conditions for Diverse Inorganic Seed Compositions and Aerosol Growth Data in the 2.0-m3 Teflon Film Chamber exp. datea (mm/dd/yy)

chemicals

H2SO4b

NH4HSO4b

(NH4)2SO4b

seed (nm3/cm3)

aerosol (nm3/cm3)

gas concnc (mg/m3)

trioxaned (mg/m3)

Y1 for aldehydee

01/13/04 01/14/04 01/14/04 01/14/04 01/14/04 01/14/04 01/13/04 01/13/04 01/12/04 01/13/04 01/12/04 01/12/04

2,4-hexadienal 2,4-hexadienal 2,4-hexadienal 2,4-hexadienal 2,4-hexadienal 2,4-hexadienal 2,4-hexadienal octanal octanal octanal octanal octanal

1.0 1.0 0.5 0.5 0.2 0 0 1.0 0.5 0.2 0 0

0 0 0.5 0.5 0.8 1.0 0 0 0.5 0.8 1.0 0

0 0 0 0 0 0 1.0 0 0 0 0 1.0

6.59E+10 7.08E+10 7.20E+10 8.24E+10 6.65E+10 6.77E+10 7.79E+10 5.40E+10 8.56E+10 8.82E+10 9.07E+10 6.71E+10

1.13E+11 1.36E+11 1.19E+11 1.24E+11 9.37E+10 9.51E+10 9.31E+10 1.44E+11 2.23E+11 1.99E+11 1.83E+11 1.11E+11

1.31 1.31 1.31 1.31 1.31 1.31 1.23 1.23 1.23 1.23 1.23 1.23

0.0784 0.0196 0.0196 0.0196 0.0196 0.0196 0.0196 0.0062 0.0062 0.0062 0.0062 0.0062

2.66E+06 3.44E+06 2.44E+06 1.90E+06 1.52E+06 1.51E+06 7.26E+05 5.78E+06 5.54E+06 4.35E+06 3.53E+06 2.28E+06

a The experimental temperature was 294 K, and the % RH was 20%. b The mole fraction of each inorganic component c 1.5 µL/m3 of an liquid organic compound was injected into the indoor Teflon chamber. The concentration is calculated from the volume concentration (1.5 µL/m3) and the density of the organic compound: 0.871 g/mL for 2,4-hexadienal and 0.821 g/mL for octanal. d The concentration of 2,4-hexadienal trioxane ) concentration of 2,4-hexadienal × 0.1 (the fraction of trioxane) × 0.15 (correction factor for the injection loss). The concentration of octanal trioxane ) concentration of octanal × 0.1 (the fraction of trioxane) × 0.05 (correction factor for the injection loss). The fraction of trioxane in the liquid aldehyde was determined from the FTIR spectra. e The first order relative aerosol yield (Y1) is calculated by eq 1.

the flow reactor, and iKp is an absorptive equilibriumpartitioning coefficient (m3/mg) (32-35). The aerosol growth yields (Y1), called “first-order relative aerosol yield” connected to the simple partitioning theory are defined here as (22)

Y1 ) (Mmix - Mseed)/(iKpCiMseed)

(1)

The Mmix and Mseed are obtained from the particle population data of the volume of aerosol mixture (Volmix) and the seed aerosol (Volseed). The density of aerosol mixture and the seed aerosol are both regarded as one. The relative aerosol yield (Y1) represents the ratio of the experimental organic mass increase to theoretically available particle-phase organic mass in equilibrium partitioning and is unitless. The iKp in eq 1 is given by

Kp ) (7.501RTfom/106 MWomiγ∞om ip°L) (m3/mg)

i

(2)

where R is the gas constant (8.314 J K-1 mol-1), fom is the mass fraction of the absorptive liquid-like material, T is the 166

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ambient temperature (K), ip°L is the vapor pressure (mmHg) of a pure compound (i), MWom is the average molecular weight (g/mol) of the given organic matter (om), and iγ∞om is the activity coefficient of a compound (i) at infinite dilution in a given liquid-like medium. The ip°L of different carbonyls can be calculated by previously known methods: group contribution (25, 26, 28-31) and Antoine regression (27). The iKp was calculated for a water medium. The ip°L values are shown in Table 3 along with iKp at 299 K. The fom used here is 1. Fundamentally, particle acidity is strongly influenced by humidity and inorganic compositions (19-22, 24). Table 1 shows the experimental set used to explore heterogeneous aerosol growth of various carbonyls at different humidity and inorganic seed compositions. In particular, this study focused mostly on acidity greater than NH4HSO4 to envision acid-catalytic effects of sulfuric acid on organic aerosol growth. The experimental inorganic compositions were simply controlled by mole fraction of each inorganic com-

TABLE 3. Molecular Structure and Physical Properties of Carbonyls Used for This Study

a

The vapor pressure (ip°L) was calculated by (28,31): ln p°L )

[ (

∆Svap(Tb)

R

(1.8) 1 -

)

( )]

Tb Tb + (0.8) ln T T

(atm)

(A)

where ∆Svap is the entropy of vaporization, R is a gas constant (8.314 J/K/mol), Tb is a boiling point (K), and T is an ambient temperature (K) for a given organic compound. ∆Svap of an organic compound was calculated using modified Trouton’s method developed by Yalkowsky and coworkers, considering parameters related to molecular geometry and association (26). Boiling points (Tb) of organic compounds were calculated by a group contribution method originally developed by Joback and Reid (30) with a modified equation and modified group contribution parameters (29). b The Antoine type regression equation: log ip°L (mmHg) ) A + B/T + C log T + DT + ET2 where A-E are regression coefficients for a given ∞ compound, and T is a temperature (K) (27). c The activity coefficient is calculated using the Unifac (32, 33). d From eq 2 using the iγwater (Table 3), fom ) 1, and MWom ) 18. The log Kp in the parentheses is estimated based on assumption of partitioning of organics on the thin layer of particle ∞ i e f organic mater (OM): γom ) 1, fom ) 0.01, and MWom ) molecular weight in Table 3. See eq 19. pKBH+ of the trioxane of octanal ) -2.7 (pKBH+ of the formaldehyde trioxane) -0.5 (correction factor for the alkyl group). pKBH+ of the trioxane of 2,4-hexadienal ) -3.2 ((pKBH+ of the octanal trioxane) + 1.6 (conjugated double bond) (48, 49). g,h Organics partition on the thin layer of particle organic mater (OM): iγ∞om ) 1, fom ) 0.01, and MWom ) molecular weight in Table 3. na, not applicable.

FIGURE 2. Organic aerosol yields of 2,4-hexadienal and octanal in the presence of different amounts of acid catalyst and at different humidities. The organic aerosols were generated in the 4-m glass tube flow reactor. The error bars, which were calculated from the SMPS aerosol population data, were determined at a 0.95 confidence level. On average, the error bars show (4.5% of a mean. ponent by mixing H2SO4 and NH4HSO4 solutions. Figure 2 clearly illustrates that strong inorganic acid such as H2SO4 accelerates heterogeneous reactions of carbonyls in the particle phase and leads to significantly higher relative aerosol yields than in the absence of H2SO4. As shown in the previous study (21), organic aerosol yields are strongly related to %RH for a given carbonyl compound at a given temperature. The

effect on Y1 in the presence of acid inorganic aerosol appears to be greater at low %RH. Figure 2 also illustrates that the Y1 is influenced by the molecular structure of the carbonyl species. For example, higher Y1 were obtained in a 2,4hexadienal system than octanal at a given experimental condition as shown in Figure 2. When only simple partitioning theory [log(iKpCiMseed)] is implemented to predict observed organic aerosol mass [log(Mmix - Mseed)], no predictivity power was achieved, as shown in Table 4 (R 2 ) 0.0069 for 101 data points). This result indicates that a new conceptual model approach is essential to predict heterogeneous organic aerosol growth in the presence of acid catalyst. Kinetics for Heterogeneous Acid-Catalyzed Reaction of Carbonyls. Possible acid-catalyzed reaction mechanisms of carbonyls are shown in Scheme 1. When the reaction system includes only an aldehyde, the major possible reactions in the condensed medium (e.g., aerosol phase) include hydration, cyclotrimerization (trioxane formation), polymerization, and aldol condensation (36). Equilibrium between an aldehyde and its hydrate is quickly established (37). Aldehydes also further react with the hydrate form of an aldehyde, resulting in higher molecular weight dimers, trimers, and polymers (38-40). Cyclotrimerization of aldehydes in the presence of a Lewis acid catalyst has common industrial applications (41) as stabilizers in color photography, flavoring materials, and carriers for scents, repellents, deodorants, and insecticides. Trioxanes produced from an aldehyde, exist mainly as an equatorial conformer (42). Aldol condensation VOL. 39, NO. 1, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 4. Correlation Coefficients of Predictive Semiempirical Model Equations for the Relative Organic Aerosol Yields in the Presence of an Acid Catalyst model

compounds

obs.

variables

eq 1 eq 16 eq 18 eq 19 eq 17 eq 17 eq 17 eq 17 eq 1 eq 18 eq 17 eq 17 eq 17 eq 19′ a

all carbonyls all carbonyls all carbonyls all carbonyls 2,4-hexadienal octanal 2-hexenal hexanal all aldehydes all aldehydes 2-octanone 2,4-pentandione Mesityl oxide all carbonyls

101 101 101 101 18 17 17 16 68 68 11 12 10 101

log(Mmix - Mseed) vs log(iKp Ci Mseed) X, Z, log(KBH+), log(Khyd) X, Z, log(KBH+) X, Z, log(KBH+), I X, Z X, Z X, Z X, Z log(Mmix - Mseed) vs log(iKp Ci Mseed) X, Z, log(KBH+) X, Z X, Z X, Z X, Z, log(KBH+), I

x

z

r

s

0.65 0.32 0.65 0.88 0.98 0.58 0.61

1.85 0.53 1.91 1.94 2.27 0.83 1.38

0.36 0.12 0.21

1.01

0.75 0.93 0.40 0.60 0.77

1.54 3.23 1.24 1.97 1.51

0.22

0.36

i

2.13

0.88

c 13.08 9.64 9.66 10.82 10.56 9.34 9.48 11.96 10.27 7.54 9.85 10.41

R2 0.0069 0.799 0.039 0.786 0.906 0.833 0.827 0.806 0.376 0.667 0.585 0.352 0.645 0.699

The log Kp is estimated based on assumption of partitioning of organics on the thin layer of particle organic mater (OM): iγ∞om ) 1, fom ) 0.01, and MWom ) molecular weight of an individual compound in Table 3. a

SCHEME 1. Acid-Catalyzed Reaction Mechanisms of Carbonyls

reactions may occur slowly via carbonyl acid-catalyzed heterogeneous reactions (Scheme 1). Some evidence of Aldol condensation reactions was reported for volatile compounds (acetone and acetaldehyde) on mineral oxide particles (43) and stratospheric sulfuric acid particles (44). In recent studies, the oligomeric structures from aerosol produced by the reaction of R-pinene and ozone in the presence of inorganic acidic substrates have been characterized using various mass 168

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spectroscopic techniques such as electrospray ionization (ESI)/MS, matrix-assisted laser desorption ionization (MALDI) (38, 45), and ion chromatography (IC)/ESI/MS (46). The characterization of heterogeneous reaction products evinces that the reaction products are complicated and include multiple reaction mechanisms as shown in Scheme 1. Several factors contribute toward driving the reaction toward high molecular weight products. (i) Atmospheric

SCHEME 2. Reaction Mechanisms for Rate-Determining Steps

particle reactions progress in an open system, which allows volatile species to partition on the particle surface. For example, the products of aldol reactions often undergo a subsequent elimination of water, forming unsaturated carbonyls which are thermodynamically stable, as shown in the Scheme 1. (ii) Some heterogeneous products such as trioxanes are thermodynamically favored and can be present in the particle phase as a stable form, giving significant yields. (iii) The solubility of polymeric structures changes as the polymerization reactions progress. With conversion to the polymeric products, the medium becomes a poor solvent due to the size of polymer molecules. The protonation equilibrium constant (KBH+) of a carbonyl is commonly given by (47-52)

KBH+ )

aSaH+ aSH+

(3)

where aS, aSH+, and aH+ are the activity of a carbonyl, a protonated carbonyl, and a proton. The hydration of the carbonyl is described by the equilibrium constant (Khyd):

Khyd )

ahydrate aS aW

(4)

where the ahydrate, aS, and aW are the activities of the hydrate, a carbonyl, and water. Kinetic studies of the formation of polymers initiated by a Lewis acid typically reveal a second-order dependence of rate on the monomer (aldehyde) concentration. The rate of polymerization is generalized by initiation (Ri), propagation (Rp), and termination (Rt) rates (48) at a given T, %RH, and acidity. In general, the derivation of the rate expression for polymerization (Rp) under steady-state conditions is given by (53)

dCS/dt ) Rp ) kappCS2

formation and imitates the rate of dimerization, as shown in Scheme 2, the Rp can be given by

Rp ) kp′ahydrateaSH+/f *

(6)

where f * is the activity coefficient of the transition state (54). When the equilibrium constant for hydration is favorable, polyacetal formation of an aldehyde can be considerable. From the KBH+ and the Khyd of a carbonyl, the Rp is rewitten by

Rp ) kp′(KhydaSaW)(aSaH+/KBH+)/f *

(7)

From eqs 5 and 7, the observed apparent rate constant (kapp) is given by

kappCS2 ) kp′(KhydaSaW)(aSaH+/KBH+)/f *

(8)

The activity (a) can be substituted by the product of the activity coefficient and the concentration of a carbonyl and a proton. Equation 8 is then given by

kappCS2 ) kp′CS2CH+aW(Khyd/KBH+)fS(fSfH+/f *)

(9)

It is assumed that the activity coefficient term ( fSfH+/f *) is a linear function of the protonation of carbonyl (54):

log( fS fH+/f *) ) m′ log( fSfH+/fSH+)

(10)

The log( fSfH+/fSH+) term in eq 10 is linearly dependent on the excess acidity, X (55). X is the difference between the observed acidity and the acidity for the ideal system and indicates the ability of the acid medium to donate a proton to a base such as a carbonyl. Equation 10 then becomes

m′ log( fSfH+/fSH+) ) m′m*X

(11)

(5)

where the CS is the concentration of a carbonyl, t is the reaction time (s), and kapp is the apparent or pseudo rate constant for polymerization. Equation 5 is analogous to the expression for the observed second-order reaction rate. If we assume that polymerization progresses by polyacetal

The term m* depends on the reaction mechanism and type of compounds. If the variation of fs with acidity is small, eq 11 is rewritten as

log kapp - log CH+ - log aw ) log(kp′Khyd/KBH+) + m′m*X (12) VOL. 39, NO. 1, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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log(kapp/kp′) ) log(Khyd/KBH+) + m′m*X + (log CH+ + log aw) (13) The best assumption is that the overall reaction for the heterogeneous reactions of carbonyls is a linear function of eq 13. Then, we have

log kapp′ ) log(Khyd/KBH+) + coefficient 1 X + coefficient 2 (log CH+ + log aw) + constant (14) where kapp′ is the observed apparent rate constant normalized by iKp and Mseed. Equation 14 shows that the rate constant of polymerization can have the form of a linear relationship. Semiempirical Model Approaches. When the reaction is at steady state and has a small value for iKpMseed (much less than 1), the aerosol mass increases (OM) normalized with Mseed are proportional to the consumption of a monomer or the polymerization rate. To apply eq 14 to the organic aerosol yield, the OM/(MseedMWi) is divided with CS2 (eq 5), which is calculated by iKpCi/MWi. Thus, another aerosol yield (Y2) associated with the second-order reaction of a carbonyl defined as

Y2 )

103MWi(OM) Mseed(iKpCi)2

(15)

The Y2, called “second-order relative organic aerosol yield”, is proportional to kapp′ at a given temperature and given reaction time. Under this assumption, the logarithm of the Y2 is semiempirically expressed by

log Y2 ) x1X + z1Z + r1 log(KBH+) + s1 log(Khyd) + c1 (16) The X is the excess acidity (eq 11) and the Z is accounted for by log(CH+aw). The X can be obtained as a function of the %RH (21, 24) from the relationships of the H2SO4-water composition versus X (55) and the relationships of the H2SO4-water composition versus %RH (56). The concentration of proton (CH+) and water activity (aw) are calculated from an inorganic aerosol thermodynamic model (25, 57, 58). Coefficients x1 and z1 depend on the particle environment in a given class of compounds and reactions, while coefficients r1 and s1 correspond to chemical properties of target organic carbonyls. All variables in eq 16 are statistically significant. A statistical analysis was also employed for the stepwise forward regressions. The partial F statistic associated with each remaining variable based on regression equations containing that variable and variables selected in a prestepwise regression were calculated and tested (at level R ) 0.05). The order of the significance of the variables is Khyd > KBH+ > X > Z. When the organic aerosol growth is limited to only the one compound, the equation can be simplified to

log Y2 ) x2X + z2Z + c2

(17)

Figure 3A shows the plot of experimental log OM versus predicted log OM by a thermodynamic theory for individual carbonyls used in this study. The regression lines for most aldehydes showed poor correlation with some scatter (R 2 ) 0.55-0.79). However, the inclusion of variables X, Z in eq 17 considerably improved the predictability of the increase of organic aerosol mass (OM) and Y2 as shown in Figure 3B (R 2 ) 0.94-0.96) and Table 4 (R 2 ) 0.81-0.91). For example, the R 2 of the predicted OM for 2,4-hexadienal was improved from 0.55 (Figure 3B) to 0.96 and the R 2 of the predicted OM for 2-hexenal, 0.71-0.94. 170

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TABLE 5. Correlation Matrix between Variables Used for the Semiempirical Prediction (eqs 16 and 19) of OM Generated by Heterogeneous Acid-Catalyzed Reactions of Carbonyls log(Khyd) log(KBH+) X Z I

log(Khyd)

log(KBH+)

X

Z

I

1 -0.319 -0.015 -0.049 0.970

1 -0.0203 -0.0212 -0.122

1 -0.805 -0.0166

1 -0.0626

1

When the reaction of a carbonyl species is acid-catalyzed, variables X, Z, and log(KBH+) are essential for the semiempirical model approaches, and the model equation can be simplified by

log Y2 ) x3X + z3Z + r3 log(KBH+) + c3

(18)

The R 2 from a simple partitioning model for all aldehydes was 0.376 as shown in Table 4. The semiempirical correlation between experimental data (69 data points) for all aldehydes used here and the model approach using eq 18 is shown in Table 4 and improved to a R 2 of 0.667. Figure 4 demonstrates the predictability of log(Y2) for diverse carbonyl species (101 data points) using the semiempirical model approach by eq 16. The R 2 was significantly improved to 0.799 (Figure 4) as compared to 0.00069 (partitioning theory) in Table 4. While coefficients x, z, and r are universal for the acid-catalyzed reactions or carbonyl species, the s is specific for the reaction type such as hydration of aldehyde, aldol condensation, or rearrangement of a molecular structure. In particular, eq 16 is derived based on the assumption of the reaction of an aldehyde hydrate and its polymerization. However, the actual reaction mechanisms that lead the high molecular weight products are much more complicated. In general, aldehydes are much more reactive than ketones and eventually result in higher aerosol growth. Possible explanations for the high aerosol yields in the aldehyde system as compared to the ketone system are the higher reactivity of aldehydes and the favorable equilibrium constants for the hydrate form and enolization (59). An indicator variable, of a finite number of values, is introduced into the regression model to include the variability of reaction types as related to different molecular structures. With the indicator variable (I) the semiempirical model for logarithm of the aerosol yield is expressed by

log Y2 ) x4X + z4Z + r4 log(KBH+) + i4I + c4

(19)

The indicator variables used here were 1 for the aldehydes and 0 for ketones. This indicator variable provided statistically significant improvement for the model prediction power (R 2 ) 0.79) of the given data set as compared to model eq 18 (R 2 ) 0.039 in Table 4). Table 5 gives the correlation matrix for the variables shown in eqs 16 and 19. These results suggest that semiempirical approaches can vastly improve our ability to predict the organic aerosol growth of a variety of different carbonyls in the presence of inorganic acid. For equilibrium conditions in the atmosphere this approach can be applied directly. As such, this work is an additional step in developing the ability to predict aerosol formation and ultimately the fate of carbonyls in the atmosphere under various conditions. Although more data points are desirable to strengthen the statistical power of the regression analysis used herein, the discussion above shows that the correlation coefficients are consistent with the observations from the data and lends credence to this overall approach. It is also important to emphasize at this point that the correlation coefficients and their equations are not only a function of the particle

FIGURE 3. Experimentally observed organic matter (OM) for individual carbonyls was plotted vs the OM predicted from the partitioning theory (A). The experimentally observed organic matter (OM) for individual carbonyls was plotted vs the OM predicted from eq 17 (B).

FIGURE 4. Experimentally observed relative second-order aerosol yield (Y2) for all the carbonyls (101 data points) was plotted vs the semiempirically predicted Y2 using eq 16. VOL. 39, NO. 1, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 5. (A) First-order relative aerosol yield (Y1) obtained from the 2-m3 indoor Teflon film chamber for the heterogeneous reactions of 2,4,-hexadienal and octanal in the preexisting inorganic acid catalyst. The experiments were conducted with different inorganic seed compositions (see Table 2). The Y1 is calculated at the maximum organic yield using eq 1. The error bars, which were calculated from the SMPS aerosol population data, were determined at a 0.95 confidence level. On average, the error bars show (8% of a mean. (B) Second-order relative aerosol yields (Y2) predicted by eq 19′ for trioxane of 2,4-hexadienal and octanal. The semiempirical model equation is obtained from the results (101 data points) of the flow reactor (see Table 4). The Y2 are corrected for the different time scale: the ratio of the indoor Teflon chamber to flow tube reactor is 36. environment, which is operated by humidity and inorganic compositions, but also a function of organic molecular structure and chemistry. Flow Tube Reactor versus Indoor Chamber. Table 2 shows the aerosol yields of octanal and 2,4-hexadienal obtained from different inorganic compositions using a 2-m3 indoor Teflon chamber. The Y1 in Table 3 was calculated at the maximum aerosol yields. The Y1 in Table 2 from the indoor chamber is much higher (up to 3 orders of magnitude) than the Y1 in the flow reactor (Figure 2), when the Y1 is calculated from an aldehyde. This high Y1 in the indoor chamber can be explained by the presence of high molecular weight structures, such as 2,4,6-trialkyl-trioxane and tetramers, in the liquid aldehydes. It is known that aldehydes can be cyclotrimerized over silica gel (e.g., the glass surface of an injection tube) at ambient temperature with the exclusion of water (60). Even for a small injection of aldehydes (∼2 µL), a higher heating temperature and a longer injection time were required than that of other chemical species (e.g., C9C12 alkanes) with vapor pressure similar to the aldehydes. Figure 5A illustrates the estimated Y1 with the assumption of 10% of trioxane impurities in the gas phase. The impurity level (e.g., trioxane) varies from 5 to 25% in FTIR spectra 172

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according to the condition of the aldehyde storage. Figure 5B showed that the log Y2 of trioxanes can be properly predicted by semiempirical model approach using eq 19′ (Table 4). The log Y2 of trioxane was corrected for the time scale of the indoor Teflon chamber. The vapor pressures estimated using the group contribution and the pKBH+ of cyclotrioxanes are shown in Table 3. The semiempirical model approach was developed using the experimental results from the flow reactor in order to eliminate the chemical changes associated with the current injection method of heating small amounts of aldehyde in a glass tube. The results from the indoor Teflon chamber (≈12 min at the maximum aerosol yield) can also be used to support the results from the flow reactor (≈20 s at the maximum aerosol yield) (21). The results obtained from the indoor chamber can be exploited to show the tendency for aerosol growth at a longer time scale. Figure 6 shows that the aerosol yields of 2,4-hexadienal reached a maximum at a longer reaction time than octanal and decayed slower after aerosol yields were maximized. This tendency indicates that the heterogeneous reactions of a conjugated aldehyde such as 2,4-hexadienal are more extensive compared to an aliphatic aldehyde such as octanal.

FIGURE 6. Organic aerosol yield time profile for the heterogeneous reaction of 2,4-hexadienal (A) and octanal (B) in the 2-m3 indoor Teflon film chamber. The organic aerosol yields were generated in different inorganic seed compositions and calculated by (Volmix - Volseed)/ Volseed. The error bars, which were calculated from the SMPS aerosol population data, were determined at a 0.95 confidence level. On average, the error bars show (8% of a mean.

Possible Uncertainties in a Flow Reactor Experiment. Some possible uncertainties in applying the experimental data from the flow reactor include artifacts for aerosol population data and the time scale of the reaction. The major uncertainty in particle population as described in the previous work (21) is particle off-gassing by dilution with sheath air in the SMPS. At typical aerosol flow rates (aerosol sampling + sheath air rates) through the SMPS (3.3 L/min), the aerosol spends 7.4 s between the flow reactor and the measurement. In this work, detailed study of the particle off-gassing was not carried out. When the organic species are less reactive toward the heterogeneous reactions and either the particle acidity or the acid concentration drops, the particle offgassing may be more significant. Likewise, the bias in the heterogeneous aerosol production yields in the short time scale of the flow reactor will be more considerable for reactive species and an acidic particle environment. Another consideration for future study of heterogeneous aerosol production is the reaction in a non-steady-state. Unlike the reaction in the solvent system, the aerosol phase reactions occur at very high concentrations of carbonyls. The conversion of total carbonyls (Ci in eq 1) to high molecular weight products may deviate from a steady state and be slower than reaction in the solution. The viscosity of reaction media becomes high as the heterogeneous reaction progresses and

decreases further conversion of carbonyls to high molecular mass products.

Acknowledgments This work was supported by a grant from National Science Foundation (ATM-0314128) and a STAR grant from the U.S. EPA to the University of North Carolina at Chapel Hill.

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Received for review July 4, 2004. Revised manuscript received September 9, 2004. Accepted October 7, 2004. ES048977H