SOA Formation by Biogenic and Carbonyl Compounds: Data

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Environ. Sci. Technol. 2007, 41, 3904-3910

SOA Formation by Biogenic and Carbonyl Compounds: Data Evaluation and Application BARBARA ERVENS* AND SONIA M. KREIDENWEIS Atmospheric Science Department, Colorado State University, Fort Collins, Colorado 80523

The organic fraction of atmospheric aerosols affects the physical and chemical properties of the particles and their role in the climate system. Current models greatly underpredict secondary organic aerosol (SOA) mass. Based on a compilation of literature studies that address SOA formation, we discuss different parameters that affect the SOA formation efficiency of biogenic compounds (Rpinene, isoprene) and aliphatic aldehydes (glyoxal, hexanal, octanal, hexadienal). Applying a simple model, we find that the estimated SOA mass after one week of aerosol processing under typical atmospheric conditions is increased by a few µg m-3 (low NOx conditions). Acid-catalyzed reactions can create >50% more SOA mass than processes under neutral conditions; however, other parameters such as the concentration ratio of organics/NOx, relative humidity, and absorbing mass are more significant. The assumption of irreversible SOA formation not limited by equilibrium in the particle phase or by depletion of the precursor leads to unrealistically high SOA masses for some of the assumptions we made (surface vs volume controlled processes).

Introduction Atmospheric aerosols affect radiation due to direct (absorption/scattering) and indirect (cloud formation) effects. In recent years, many studies have shown that the fine aerosol mass can have significant fractions of organics that play an important role in aerosol forcing (1). A major fraction of this organic aerosol mass is not emitted directly, but is formed by chemical and/or physical processes in the atmosphere (secondary organic aerosol, SOA) (2). Current models underestimate observed SOA mass by up to 90% (3), which may be explained by incorrect emission inventories, missing precursor compounds, or neglected processes of gas-toparticle conversion. Recent laboratory studies have suggested that chemical processes in the particle phase form additional species that shift the physical partitioning equilibrium (absorption, dissolution) toward the particle phase. The occurrence of organic chemical reactions on/in aerosol particles might open pathways for volatile species to contribute to SOA mass by forming low-volatility, higher-molecular-weight compounds (oligomers, humic-like substances (4)). Such compounds have been found in atmospheric particles and can account for up to 35% of the total water-soluble organics (5). Several laboratory studies have shown that higher yields of SOA mass are observed in the presence of acidic seed * Corresponding author phone: 303 497 4396; fax: 303 497 5318; e-mail: [email protected]. 3904

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aerosols than on neutral/basic particles, or even in absence of any seed mass, which might be due to acid-catalyzed reactions such as aldol condensation, or (hemi)acetal formation (6). Different yields for acidic and nonacidic conditions reveal that different chemical processes must be occurring, as the physical partitioning of nonionic species should not be affected by acidity. The magnitude of the SOA mass depends on several parameters such as the reactant, experimental conditions, which also includes preceding oxidation reactions of the precursor compound in the gas phase, and reaction time. As it has been shown in laboratory experiments that the formation of organic mass can continue over several hours (7), it should be evaluated whether kinetic aspects of SOA formation have to be included in atmospheric models. We present a compilation of recent laboratory results for a series of species and experimental conditions and derive a consistent parameter set of equilibrium and kinetic constants for a more complete description of SOA formation. We discuss SOA formation by oxidation products of R-pinene and isoprene, main contributors to global emissions of biogenic compounds, and by aliphatic aldehydes (glyoxal, hexanal, octanal, 2,4-hexadienal) which are polar oxidation products of alkanes and aromatics and partition directly into hygroscopic particles. We focus on these two species classes because they have been investigated in many laboratory experiments for different conditions which might allow the derivation of a robust parameter set. Our procedure of data derivation can also be used to complement SOA parametrizations based on future laboratory studies. Using these parameters, we perform estimates to interpret observed SOA masses in the atmosphere in combination with gas-phase concentrations of these possible precursors. We point out that our exploratory model estimates likely represent upper limits for SOA formation for typical atmospheric conditions and that uncertainties in the applied data set exist due to the difficulty of extrapolating laboratory data to atmospheric conditions.

SOA Formation Recent studies have suggested that observed partitioning equilibria include not only physical but also chemical processes and thus, an overall equilibrium constant K* can be defined as

K* )

mp + mchem ∆M ) [m3µg-1] mgmabs mgmabs

(1)

with mp ) physically absorbed mass, mchem ) chemically formed mass, mg ) mass in the gas phase, and mabs ) absorbing mass in the particle (all masses in µg m-3). To differentiate between nonacidic and acidic conditions, we will use K* and K*H+ for the description of partitioning on nonacidic and acidic seed aerosol, respectively. Based only on values of K* and K*H+ that are derived from experimental data, however, the individual contributions of chemical and physical processes cannot be quantified. Under conditions where the newly formed SOA mass ∆M [µg m-3] is large compared to the initial absorbing mass, ∆M increases linearly with the amount of reacted hydrocarbon ∆HC [µg m-3] (8)

∆M ) R ∆HC - (K*)-1

(2)

with R ) stoichiometric yield of the partitioning species. The application of eq 2 is consistent with the suggestion that 10.1021/es061946x CCC: $37.00

 2007 American Chemical Society Published on Web 05/04/2007

TABLE 1. Thermodynamic Equilibrium Kinetic Constants for Biogenic Species (Isoprene and r-pinene), Recommended Values for Different Conditions for Application in the One-Product Parametrization (eq 2 and eq 7) are Marked with an Asterisk

instead of applying a two-product-parametrization to experimental data as done previously (9, 10), it can be assumed, as is done here, that one of the proxy products has a very low volatility and is completely partitioned into the particle phase (8). Thus, the partitioning can be fully described with the two parameters in eq 2. Water-soluble organics are absorbed into hygroscopic particles. For such species, partitioning is usually expressed by means of Henry’s Law constants KH. To account for the total aqueous phase concentration of dissolved species and products of subsequent chemical reactions, we define here an increased Henry’s Law constant KHC.

KHC )

caq[mol L-1] cg[atm]

(3)

with caqorg ) total concentration of dissolved species and additional chemical products, and cg ) equilibrium gas-phase concentration. Our approach here is to reinterpret existing laboratory data using eq 2 or eq 3 to derive values of R and K* for R-pinene and isoprene and KHC for aldehydes.

Parameter Derivation Equilibrium Constants. R-Pinene. SOA formation upon R-pinene ozonolysis has been investigated under various laboratory conditions. Best fit parameters R and K* (eq 2) for both acidic and nonacidic seed aerosols, different R-pinene/NOx ratios, and a range of relative humidities have been obtained by analysis of a systematic series of experiments for a range of ∆HC (Table 1). In Figure 2a, we show ∆M/∆HC data pairs from such experiments (for derivation of these data from the original studies, see the Supporting Information). The different data in Figure 2a can be grouped into various clusters that differ in the slopes R (eq 2). The stoichiometric yield R gives information on the preceding gas-phase chemistry. For some data sets in Figure 2a we did not apply eq 2 in order to derive a reliable R /K* data pair as the experiments were performed for a very narrow range of ∆HC (17, 18). Experiments with OH scavenger compounds (2butanol, cyclohexane) yield slightly smaller ∆M (18). This confirms the minor role of the OH reaction of R-pinene for SOA formation compared to ozonolysis. The addition of NOx to the R-pinene/ozone system leads to smaller yields of condensable species and, thus, smaller

slopes (14). The studies that yield the highest slopes in Figure 2a have been performed without any NOx in the reaction chamber (8, 11-13). Other studies used high R-pinene/NOx ratios (14, 15) and the results exhibited significantly smaller R (about a factor of 1.5-2 smaller) because more volatile products (e.g., hydroperoxides) were formed. Note that we define HC/NOx [ppb C/ ppb NOx] ) 8 as a limit between high and low ratios as this is approximately the value between NOx and HC limited scenarios in the atmosphere (19). The smallest yields are derived based on the data which were obtained at very low R-pinene/NOx ratios (15). In addition, results are shown from a comparison of SOA formation on dry vs wet seed aerosol which reveals higher yields on wet particles (16). We also distinguish between results which were performed on nonacidic (or no) and acidic seed aerosol. It is evident that the influence of gas-phase chemistry (i.e., presence/absence of NOx) and relative humidity (dry vs aqueous aerosols) is greater than the chemical influence by acid-catalysis. In summary, the extreme values depicted in Figure 2a might represent conditions which are unlikely to be encountered in the atmosphere: first, there will always be some NOx present, and second, it is likely that aerosols exist in their metastable and, thus, liquid state (20). Isoprene. The derivation of partitioning parameters from isoprene oxidation can be treated in a similar way as for R-pinene since its SOA mass does not show any dependence on the initial hygroscopic seed mass (21). Unlike SOA formation during oxidation of species with only one double bond (e.g., R-pinene), the photooxidation of isoprene occurs in multiple steps (11). Its major first-generation products, methyl vinyl ketone (MVK) and methacrolein (MACR), are volatile and only their oxidation products contribute to SOA formation to a significant extent. In such systems, the final SOA yield, i.e., upon complete consumption of the initial hydrocarbon and after no further increase in SOA mass is observed, should be considered to derive information on the SOA formation efficiency (11). Time-dependent growth curves, however, shed light on the rate-limiting effects by first- vs second-generation products. Such ∆M/∆HC plots usually exhibit two ranges: a linear increase of ∆M with ∆HC marks the SOA formation by first generation products; after all hydrocarbon has been consumed, the further oxidation of first-generation products forms additional mass and ∆M increases without further change in ∆HC. VOL. 41, NO. 11, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Change in newly formed SOA mass ∆M as a function of consumed hydrocarbon ∆HC. (a) r-Pinene (filled symbols: acidic seed, open symbols, neutral seed); (b) isoprene.

FIGURE 2. Predicted SOA masses ∆M [µg m-3] after one week processing time using equilibrium constants from the (a) ozonolysis of r-pinene, (b) OH reaction of isoprene, and (c) partitioning of aldehydes and the conditions in Table 2. In Figure 2b, we show ∆M values upon photooxidation of isoprene as a function of ∆HC. We do not include timedependent growth experiments as we focus on the data interpretation following eq 2. Experiments have been performed for quite different ranges of ∆HC and experimental conditions. In general, data obtained for NOx free conditions exhibit the highest slopes. The effects of HC/NOx ratio and RH cannot be clearly separated from this figure as only experiments for low HC/NOx ratios, in combination with low RH (21, 22), and vice versa (23) have been performed. The addition of SO2 also influences SOA yields; only two data points are available but it seems that, in absence of SO2, less SOA mass is formed (this SOA mass was close to the detection limit in the experiment and, thus, uncertain (24). Experiments in which no photooxidation was performed show results which are not necessarily comparable to the others in Figure 1b (25). In Table 1, we summarize the R and K* values we obtained from the data in Figure 2b and using eq 2 together with a two-product-parametrization that has been recently suggested for the description of SOA formation from isoprene (26). Glyoxal. It has been found that the measured partitioning of glyoxal KHC (eq 3) on even slightly acidic seed aerosols exceeds the physical solubility (KH) by about 2 orders of magnitude at RH ) 55% (Table 2) (27). We also expressed the final results from another set of studies (28, 29) on the reactive uptake of glyoxal as equilibrium constants. These data show a slight increase with time (see the Supporting 3906

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Information) which might point to the fact that the system has not reached equilibrium yet; in Table 2 we only show the data as calculated at the end of the experiments. These constants are higher by a factor of ∼4 than those of the other study, with an increasing difference with increasing RH. Experiments on a shorter time scale (40 min (6) compared to several hours (28, 29) yield a comparable KHC at the same RH. This finding suggests that the chemical SOA mass formation occurs on a relatively short time scale. The increase of KHC with decreasing RH might be explained by a “saltingin” effect that causes higher solubility at high ionic strength. Another possibility might be the formation of additional organic products that incorporate initial seed mass, such as organic sulfates (28). Monoaldehydes. Experiments with a series of monofunctional aldehydes have been performed (6, 30). In many experiments, decanol has been added to the reaction chamber to enhance the rate of the aldehyde-reaction with alcohol (aldol condensation). We only consider experiments without this additional reactant since its presence might bias the interpretation of the results with regards to the parametrization for individual aldehydes. The two equilibrium constants for hexanal differ by more than 1 order of magnitude (Table 2). The experiments that lead to the higher constants have been performed in systems with very high reactant concentrations which might cause additional chemical reactions in the particle. Quantum chemical calculations of the equilibrium constant for either hydration

TABLE 2. Thermodynamic Equilibrium Constants for Carbonyl Compounds for Different Conditions, Recommended Values for Different Conditions are Marked with an Asterisk

a Average of K C at RH ) 55% and RH ) 50%, respectively. b Based on quantum chemical calculations for hydration in the aqueous phase. H Based on quantum chemical calculations for aldol condensation in the aqueous phase. d Kprot ) 106 M-1 and Kenol )10-4 (dimensionless), based on ref 41. c

or aldol condensation of hexanal in the particle phase show that neither of these processes can explain the observed partitioning (31). The derived equilibrium constants for octanal differ by several orders of magnitude (Table 2). However, even the smallest value in acidic solution (32) is about 15 times higher than the physical solubility in water (KH) (33). The high initial octanal concentrations in the experiments (∼ppm) for which the highest KHC values have been determined (6, 30, 34) exceed typical atmospheric concentrations by some orders of magnitude. Thus, the value obtained based on more moderate aldehyde concentrations, KHC ∼3187 mol L-1 atm-1 (32), is more appropriate. The values of KHC for 2,4-hexadienal in Table 2 have been derived from experiments with different gas-phase concentrations (∼330 ppb (34); 0.3 ppb (32)) and at different RH. As for glyoxal, KHC for 2,4-hexadienal increases by about an order of magnitude with increasing RH. Kinetic Parameters. To evaluate if significant amounts of SOA mass can be formed within the lifetime of an atmospheric aerosol particle (∼ one week), kinetic approaches should be tested in models. The time constant of the reaction of hydrogen peroxide with isoprene (or its oxidation products) in the particle phase has been estimated as τ ∼ 1 h (35). Assuming that the H2O2 concentration in the particle phase is much higher than that of isoprene, a (pseudo)first-order rate constant for a volume reaction can be calculated as

kisoprene )

ln 2 ∼ 2 × 10-4 s-1 3600s

(4)

This value agrees well with the rate constant of k ∼ 10-4 s-1 that has been suggested for SOA formation upon ozonolysis of limonene (36). The good agreement between the two rate constants gives confidence that the reactivity of the compounds is comparable and controlled by the number of double bonds. For R-pinene (one double bond) no kinetic data are available; the application of the value from eq 4 might represent an overestimate. The upper limits of the reactive uptake of MVK and MACR have been determined in sulfuric acid solutions as kMVK < 3 × 10-4 s-1 and kMACR ∼ 10 s-1 (37). However, MVK does not lead to SOA formation (22);

the value for MACR seems very high, but MACR represents only one oxidation product and the SOA efficiency of additional (higher-generation) products is not included in this single value. For glyoxal, reactive uptake coefficients, γ, are reported which have been obtained based on the observed growth rates of individual particles and eq 5 (28, 29)

jc k ) γ A [s-1] 4

(5)

with jc ) mean molecular speed ()[8 RT/(π M)]0.5 (R ) 8.314 J (K mol)-1, T ) temperature [K], M ) molecular weight [kg mol-1]), and A ) surface area of particles [m2 m-3]. The application of γ implies a surface reaction that adds mass in proportion to the surface area of an aerosol population. Since the experiments did not reveal if the formation occurs on a particle surface or in the particle volume, we give an alternative parametrization by converting observed growth rates into rates (R) as a function of available absorbing (water) mass that allows a more general application to atmospheric data. The values are in the range 10-5 to 10-4 [µgSOA µgwater-1 s-1], being higher on acidic particles (Table 2, and Supporting Information). Experiments with much higher seed masses (∼10 000 µg m-3 (38) vs ∼10 µg m-3) lead to rate constants which are 104 times smaller. Such high aerosol masses are not encountered in the atmosphere and formation rates as given by the R values are more applicable for glyoxal under atmospheric conditions. Aldol condensation has been suggested to be one of the most important reactions of aldehydes in acidic solution. The second-order rate constants for aldol condensation, kaldol [L mol-1 s-1], vary with acidity x [%] and depend on the protonation constant Kprot and on the enolization constant Kenol of the aldehyde. It can be parametrized as follows for various species (39, 40)

log10(k aldol) ∼ 0.065x + 7.5 + log10(Kenol/Kprot)

(6)

Glyoxal is mostly present in its diol form and its aldol reaction is unlikely; for hexadienal, Kenol is not available. Thus, we only investigate the possible importance of aldol condensaVOL. 41, NO. 11, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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tion for hexanal and octanal. In Table 2, we summarize their constants and show kaldol for x ) 50% (as an upper limit for tropospheric aerosols). In addition to the rate constants k derived here, in Table 2 we have listed all (reactive) uptake coefficients γ for glyoxal and hexadienal that have been reported in the literature from fits to growth kinetics according to eq 5 (28, 29, 32).

Initialization. In the following, we apply the equilibrium and kinetic data and compare different effects on SOA formation we have discussed in the previous sections (HC/ NOx ratio, acidity, RH). We assume typical atmospheric mixing ratios for the six organic precursor gases (isoprene ) 1.5 ppb, R-pinene ) 0.15 ppb, glyoxal ) 0.2 ppb, hexanal, octanal, and 2,4-hexadienal ) 0.001 ppb (each)). These mixing ratios are held constant over the simulation time (one week), unlike in laboratory experiments that are performed for closed systems, i.e., with a limited supply of reacting hydrocarbon. In our calculation, ∆HC is calculated as a function of time (∆HC(t)) from the rate of ozonolysis of R-pinene and from the OH- and O3-reactions of isoprene (Supporting Information), assuming a constant ozone mixing ratio of 40 ppb and constant [OH] of 5 × 105 molecules cm-3 derived from estimates of typical emission fluxes. The assumption of steady-state for the gas phase is likely an overprediction, since diurnal variations in these SOA precursor concentrations are typically observed, and if the air mass is transported away from emissions regions, the gas phase cannot be replenished. We note that the results represent upper limits for possible effects on SOA formation and we seek to find the order of magnitude of several effects and to identify key parameters and species that are crucial in future experiments. For this study, we assume a total initial aerosol mass of ∼40 µg m-3. Surface area and volume distribution are determined by the shape of the aerosol distribution. For these comparisons, we assume a lognormally distributed aerosol particle population, composed of (NH4)2SO4 (median radius rg ) 0.06 µm, geometric standard deviation σ ) 1.6, and number concentration N ) 500 cm-3). The aerosol mass is exposed to two different relative humidities (RH ) 60%; RH ) 90%) which is the basis for the calculation of the water mass (mH2O ) 20 µg m -3 (RH ) 60%) and mH2O ) 120 µg m-3 (RH ) 90%)) that determines the SOA mass partitioning from aldehydes. For biogenic compounds we assume different initial absorbing aerosol masses mabs(0) (0.05 µg m-3; 0.5 µg m-3, 5 µg m-3). Equilibrium Calculations. While in laboratory experiments with R-pinene and isoprene, usually no initial absorbing mass is present (i.e., the seed aerosol, if any, is hygroscopic), this simplification does not hold for the atmosphere. Due to mixing and/or aging processes, an organic phase likely exists in many atmospheric particles. To predict SOA formation under atmospheric conditions, the simplified assumption which has been included in eq 2 might not be valid. Therefore, in model applications for atmospheric conditions, the yield expression for for nonzero initial absorbing mass mabs(0) should be used (8).

without NOx. In the presence of NOx, ∆M can be decreased by up to a factor 5 with decreasing differences with increasing mabs(0). The acidity effect seems high compared to recent estimates based on field measurements that predicted an overall increase in SOA mass of 5 ( 8% due to inorganic acidity (42). However, the K* and K*H+ values we applied here were from laboratory measurements over the time range of a few hours. Processing over several days might overcome any kinetic-only effects and lead to the same equilibrium SOA mass for both acidic and nonacidic aerosols. In Figure 2b, we show SOA masses from isoprene as a function of HC/NOx ratios and RH. Again, the highest ∆M are obtained based on the parameter set derived from NOxfree experiments. The other two sets of results suggest that both increasing RH and increasing NOx levels might counteract each other but a clear statement about the absolute effects is not possible. However, the results from Figure 2a and b suggest that in anthropogenically influenced regions where both high NOx levels and high concentrations of acidic trace gases (e.g., SO2) are present effects on SOA formation might (partially) cancel each other. These complex feedbacks of preceding gas-phase chemistry, partitioning of species onto particles depending on ambient relative humidity, and particles’ acidity suggest that it does not seem reasonable to use a constant factor to all species to simulate increased partitioning under specific conditions as applied in a recent modeling study (43). The predicted partitioning of aldehydes shown in Figure 2c suggests that glyoxal, one of the main oxidation products of aromatic compounds which are thought to be important contributors to SOA in anthropogenically influenced regions, has the highest importance for SOA formation (∼3 µg m-3) among the compared aldehydes, mainly because its atmospheric concentration exceeds those of the other aldehydes. The other aldehydes might only contribute to SOA at high RH, i.e., if plenty of water on particles is available (we only display ∆M g 1 ng m-3 in Figure 2c, more data are summarized in the Supporting Information). Kinetic Calculations. Reactive uptake coefficients γ rate constants k or formation rates R in Tables 1 and 2 do not include any upper limit for SOA formation in the particle phase and imply irreversible accumulation of the reaction products. In a closed system, such as in reaction chambers used in laboratory experiments, SOA formation will stop if all hydrocarbons are consumed. However, the extrapolation of γ and/or R values to the atmosphere suggests continuous SOA formation if the precursor species are assumed to be at steady-state. After one week of exposure to organic gases, glyoxal might add 0.7-1.3 µg m-3 SOA mass by surface reactions (6.4‚10-8 < γ < 4.6‚10-3, 60% < RH < 90%) but several hundred µg m-3 by volume reactions to an existing aerosol population. The contribution of isoprene using the k in Table 1 leads to a mass increase of ∼1 ng m-3. For monoaldehydes, we investigate if aldol condensation might contribute to SOA formation by aldehydes. We assume that the time limiting step in the aldol condensation is the particle phase (p) reaction between the carbonyl compound RC(O) and the enol RCOH (37). If [RCOH] is substituted by [RC(O)]/Kenol (41), the rate can be calculated as

∆M R K* ∆M ) mabs(0) + ∆HC(t) 1 + K*(mabs(0) + ∆M)

kaldol d[RC(O)]p )[RC(O)]p2 dt Kenol

Data Application and Discussion

(7)

In Figure 2a, we compare the SOA masses from R-pinene predicted for the different sets of equilibrium constants K* (Table 1). The application of K*H+ leads to the highest ∆M values. (Note that in Figure 2 we present average values ( standard deviation if more than one data set is available for specific conditions; see, also, the Supporting Information). However, these values were derived based on experiments 3908

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(8)

If every reacted carbonyl molecule produces SOA mass (which is probably an overestimate) the SOA formation rate is equivalent to, but opposite in sign of, the carbonyl reaction rate. To relate eq 8 to gas-phase concentrations, we assume thermodynamic equilibrium between the particle and gas (g) phase and apply Henry’s Law constant KH. The SOA formation rate as a function of a

gas-phase concentration is then

d[SOA]p kaldol ‚(KH[RC(O)]g)2 ) dt Kenol

(9)

Assuming a particle mass of mH2O ) 120 µg m-3, eq 9 yields a SOA mass formation rate of 3.6 × 10-13 µg m-3 s-1 for a constant ambient aldehyde concentration. Based on this rate, aldol condensation of aliphatic aldehydes (hexanal and octanal) can be excluded as an efficient process for SOA formation, in agreement with thermodynamic calculations (31, 44), as in about t ∼ 1010 s (∼ years), only 1 ng SOA m-3 is formed. The mass distribution due to surface and volume processes differs, which is of importance for hygroscopic or optical properties of individual particles (composition, size). Our results reveal that an equilibrium state might be reached which defines an upper limit for SOA formation and that transport and/or limitations due to emission/source fluxes in the gas phase should be included in model estimates. Kinetic data (and product studies) from laboratory studies will lead to a better understanding of chemical SOA formation and might allow an improved parametrization of SOA formation.

Acknowledgments This work was supported by the NOAA Climate Program Office (Atmospheric Composition and Climate). We thank Ryan Hamerly for calculations of various constants and Graham Feingold for useful discussions.

Supporting Information Available Data derivation for R-pinene, isoprene, glyoxal, monoaldehydes; estimates of SOA formation. This material is available free of charge via the Internet at http://pubs.acs.org.

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Received for review August 13, 2006. Revised manuscript received November 23, 2006. Accepted March 28, 2007. ES061946X