Environ. Sci. Technol. 2009, 43, 7797–7802
Composition Domains in Monoterpene Secondary Organic Aerosol KATHERINE J. HEATON,† RACHEL L. SLEIGHTER,‡ PATRICK G. HATCHER,‡ WILEY A. HALL IV,† AND M U R R A Y V . J O H N S T O N * ,† Chemistry and Biochemistry Department, University of Delaware, Newark, Delaware 19716, and Department of Chemistry and Biochemistry, Old Dominion University, Norfolk, Virginia 23529
Received April 27, 2009. Revised manuscript received July 28, 2009. Accepted August 25, 2009.
The composition and structure of freshly formed oligomers in R- and β- pinene SOA are studied with high performance mass spectrometry to provide insight into the SOA formation mechanism. Van Krevelen plots (H:C ratio vs O:C ratio) are interpreted in the context of distinct structural domains that correspond to separate oligomer formation routes. The domain containing most of the signal intensity encompasses elemental formulas that correspond to oligomerization reactions of intermediates and/or stable molecule monomers produced by ozonolysis of the precursor. While oligomers involving reactive intermediates from the hydroperoxide channel dominate the product distribution, products are also observed that uniquely map to the stable Criegee intermediate and/ or combinations of stable molecule monomers. A second domain encompasses molecules having lower H:C ratios but similar O:C ratios to the first domain. Many of the products observed in this domain have double bond equivalents greater than the maximum number possible when forming dimers by standard reaction mechanisms and are interpreted in the context of repeated self-reactions of alkoxy/peroxy radicals. A third domain encompasses molecules having very high H:C and O:C ratios consistent with polymerization of formaldehyde and/or acetaldehyde. These domains remain distinguishable from experiment to experiment and among different extraction solvents (50/50 methanol-water, 50/50 acetonitrile-water, 100% water).
Introduction Oligomers are important constituents of laboratory-generated secondary organic aerosol (SOA) and ambient particulate matter (1). Oligomer formation enhances the partitioning of volatile and semivolatile compounds to the particle phase (2) and may modify the optical properties of particles (3). While the polymerization of small molecules such as glyoxal may give a relatively simple product distribution (4), oligomers from larger molecules such as monoterpene oxidation typically give very complex product distributions containing * Corresponding author phone: (302)831-8014; fax: (302)831-6335; e-mail:
[email protected]. † University of Delaware. ‡ Old Dominion University. 10.1021/es901214p CCC: $40.75
Published on Web 09/11/2009
2009 American Chemical Society
hundreds or thousands of individual compounds. This complexity requires advanced mass spectrometry techniques for full characterization (5-8). A particularly useful approach for studying complex natural organic matter is coupling electrospray ionization (9) or another atmospheric ionization method (10) with ultrahigh resolution mass analysis. Individual compounds in the sample are softly ionized, and their atomic formulas are determined through accurate mass measurement. In this study, oligomers produced by monoterpene ozonolysis in a flow tube reactor are characterized. Previous work with this apparatus using low resolution mass analysis has shown that oligomers are produced within the first few seconds of reaction (11, 12). While only partial structural information could be gained, the products were consistent with expected oligomerization reactions between ozonolysis intermediates and either stable end product monomers or other intermediates. The present study extends this work through high resolution mass analysis with ESI coupled to a Fourier transform ion cyclotron resonance (FTICR) mass spectrometer. Over 1000 molecular species are detected, and most are assigned a unique atomic formula. From these complex data sets, van Krevelen diagrams (13) are used to identify composition domains of the product aerosol, and these domains are interpreted to gain insight into the reaction mechanism.
Experimental Section The flow tube reactor and experimental conditions are the same as described in our previous work (11, 12). Briefly, SOA was produced by mixing monoterpene vapor (ca. 40 ppm) with ozone (500 ppb) at room temperature under laminar flow conditions. The reactor residence time was 23 s, giving aerosol mass concentrations at the exit on the order of 400 µg/m3 for R-pinene SOA and 200 µg/m3 for β-pinene SOA. Aerosol exiting the reactor was split to a commercial scanning mobility particle sizer (SMPS), a nano aerosol mass spectrometer (NAMS) for online measurement of the O:C elemental ratio of individual particles (14), a microsampling assembly, and waste. The microsampling assembly consisted of an aerodynamic lens (15) and stainless steel collection plate housed inside a vacuum chamber. Particles were focused through the aerodynamic lens into a ca. 1 mm diameter spot on the collection plate. The plate, 3.25 cm in diameter, was positioned 1.8 cm from the exit nozzle of the aerodynamic lens. Because the plate was under vacuum (ca. 10-2 torr) during particle collection, both solvents and volatile/semivolatile compounds were expected to evaporate quickly, minimizing the possibility of on-plate oligomerization reactions. After a collection period of 60 min (typically on the order of 1 µg SOA sampled into the aerodynamic lens), the plate was removed from the chamber, and deposited particles were extracted with two 1 µL aliquots of solvent. Each 1 µL aliquot was applied directly on top of the SOA spot on the collection plate. The amount of sample collected was sufficient to visually locate the spot. The droplet volume was sufficient to wet the entire spot. The collection and extraction process was repeated ten times under the same experimental conditions, and the extracts were combined into a single sample for analysis by electrospray ionization (ESI) coupled to a Fourier transform ion cyclotron resonance mass spectrometer (ESI-FTICR-MS) with a microspray source. Three extraction solvents were studied: 50/50 v/v methanol-water, 50/50 v/v acetonitrile-water, and 100% water. VOL. 43, NO. 20, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. FTICR Analysis of SOA from Monoterpene Ozonolysis no. of no. of no. of NAMS IFM in IFM in IFM in ionization ions ions % of ions % with atomic O:CIM O:C high H:C mid-H:C low H:C FTICR-MS monoterpene extraction solvent mode detected assigned assigned sodium formulasa ratioc ratio domainb domainb domainb 12T 12T 12T 12T 7T 7T 7T 7T
R-pinene R-pinene β-pinene β-pinene R-pinene R-pinene R-pinene R-pinene
50% MeOH 50% MeOH 50% MeOH 50% MeOH 50% MeOH (#1) 50% MeOH (#2) 50% ACN water
+ + + + + +
1458 2042 2446 1046 2293 1819 1501 1449
1143 1118 1426 629 1440 1090 1036 1216
78% 55% 58% 60% 63% 60% 69% 84%
93% N/A 60% N/A 47% 89% 49% 66%
876 784 1185 461 1015 959 774 1104
0.37 N/A 0.34 N/A 0.37 0.34 0.36 0.31
0.38 0.38 0.45 0.45 0.38 0.38 0.38 0.38
a Number of atomic formulas after combining formulas differing only by isotopic substitution, e.g., mass weighted intensity fraction, as calculated from eq 1. c O:CIM is calculated from eq 2.
The organic solvents were LC grade (Fisher Scientific Inc.), and the water was distilled deionized. No differences other than slight experiment-to-experiment variations (see the “Robustness” section below) were observed for samples analyzed immediately after collection vs 1 week after collection. However, we cannot rule out that accretion reactions (16) occurred on the plate during the 60 min collection period. Initially, experiments were performed with 50/50 methanol-water extractions using a 12 T Bruker Daltonics Apex Qe FTICR-MS at Old Dominion University. Subsequent experiments were performed with multiple solvent extractions using a 7T Bruker Daltonics Apex Qe FTICRMS at the University of Delaware. The flow rate of the ESI interface was 1 µL/min for the 12T FTICR-MS and 2 µL/ min for the 7T FTICR-MS. Ions were accumulated in the hexapole for 1 s before being transferred to the ICR cell. The ion transfer efficiency from the ESI source to the ICR cell was optimized for 200-2000 m/z. ICR transients were acquired with either a 4 MWord (12T) or 1 MWord (7T) time domain over a range of 100 to 2000 mass-to-charge (m/z). The summed free induction decay signal was zerofilled once and Sine-Bell apodized prior to fast Fourier transformation and magnitude calculation using the Bruker Daltonics Data Analysis Software. Mass spectra were externally calibrated with a polyethylene glycol standard and internally calibrated by homologous series that were identified by Kendrick mass defect analysis. Accurate m/z ratios of individual peaks were assigned molecular formulas with the Molecular Formula Calculator v1.0 (National High Magnetic Field Laboratory 1998, Tallahassee, FL). Only peaks with a signal greater than 0.5% of the total ion signal were analyzed. Assigned formulas were required to be within 2.5 ppm of the measured mass and contained only oxygen, carbon, hydrogen, and, for positive ion spectra, up to one sodium. For peaks assigned a unique atomic formula, the average error between the measured and expected masses was less than 0.4 ppm. In the discussion below, only the assigned formulas having an O:C ratio between 0.1 and 1.0 and an H:C ratio less than 2.25 are considered, as these ions represented almost all of the ESI signal intensity.
Results and Discussion The positive and negative 12T ESI-FTICR mass spectra for methanol-water extracted R- and β-pinene SOA are given in the Supporting Information (Figures S1 and S2). Qualitatively, these spectra are similar to both low and high resolving power ESI mass spectra reported previously for SOA from bag and smog chamber experiments (6, 7, 17). Ions are observed almost continuously from about 350 to >1000 m/z, multiple peaks are detected at most nominal m/z values, and all peaks are singly charged. The only 7798
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5% N/A 4% N/A 21% 6% 14% 5% 12
C vs
80% N/A 80% N/A 50% 54% 46% 42% 13
C.
b
15% N/A 16% N/A 29% 40% 40% 53%
IFM is the
substantial difference is that hardly any monomer signal is detected in the current experiments. The lack of monomer signal is not surprising - most of these compounds are semivolatile and would be expected to evaporate since aerosol collection was performed under vacuum. It is also possible that parameters used for acquiring FTICR mass spectra discriminated against monomer detection and/or that experimental conditions used for SOA generation in the flow tube strongly favored oligomer formation. Additional experiments are needed to distinguish these possibilities. Table 1 gives summary statistics for the 12T spectra and others obtained in this study. For example, 1458 peaks were detected in the R-pinene positive spectrum. Of these, 78% were assigned an elemental formula, and 93% of the assigned formulas contained one sodium atom. After formulas that differed only by an isotopic substitution e.g., 12C vs 13C were removed, the assigned peaks represented 876 unique elemental combinations. The high percentage of positive ions assigned to formulas containing a sodium atom is consistent with previous studies (6-8). The negative ion spectra with the 12T instrument were dominated by a small set of peaks at nominal m/z values of 297, 311, 325, and 339, whose accurate masses corresponded to a homologous series separated by CH2 units (C12H25O8, C13H27O8, C14H29O8, and C15H31O8) that are background related since they are observed in the solvent blanks and are not observed with the 7T instrument. The high intensities of these peaks suppressed the signal of other ions in the spectra. Therefore, spectra in the negative ion mode were obtained by isolating the ions around 400, 500, and 600 m/z so that lower intensity peaks could be detected. Isolation occurred in the quadrupole before transfer to the ICR cell. Both the absolute number and fraction of total peaks assigned an atomic formula were lower for the negative ion spectrum than the positive ion spectrum. Composition Domains. Compositional diversity among the assigned formulas from a complex sample can be assessed in several ways (10). In this study, composition domains were identified through the use of van Krevelen diagrams, where the H:C ratio is plotted against the O:C ratio for individual assigned atomic formulas (13). Van Krevelen diagrams for assigned formulas from R-pinene and β-pinene SOA are shown in Figures 1 and 2, respectively, for both the positive and negative spectra. Three distinct domains are evident. The first domain encompasses a range of H:C from about 1.4 to 1.8 and O:C from about 0.2 to 0.6. This domain contains by far the greatest number of peaks and the greatest overlap between the positive and negative ion spectra. Overlap is defined as two ions having the same elemental formula “M” where the ion detected in the positive spectrum is (M+Na)+ and the ion detected in the negative ion spectrum is (M-H)-. The second domain encompasses H:C from about 0.8 to 1.4 and O:C from about 0.1 to 0.5. Assigned peaks from both
FIGURE 1. van Krevelen diagram for r-pinene SOA extracted with methanol-water. Blue - positive ions; red - negative ions; green - common elemental formulas “M” for ions (M+Na)+ and (M-H)-. Composition domain ovals are drawn as an aid to the eye.
FIGURE 2. van Krevelen diagram for β-pinene SOA extracted with methanol-water. Blue - positive ions; red - negative ions; green - common elemental formulas “M” for ions (M+Na)+ and (M-H)-. Composition domain ovals are drawn as an aid to the eye. positive and negative ion spectra are found in this domain, but there is little overlap between the two. The third domain encompasses H:C from about 1.8 to 2.2 and O:C from about 0.6 to 0.9. This domain is dominated by positive ions. Similar domains are readily apparent in the van Krevelen diagrams of SOA produced from R-pinene and β-pinene. In Table 1 and the discussion below, the three regions of these van Krevelen diagrams are referred to as low, medium, and high H:C domains. Because of space limitations, only R-pinene SOA is discussed in detail. The medium H:C domain contained the highest number of assigned formulas and mass weighted intensity fraction in the positive ion spectra. The mass weighted intensity fraction of an individual assigned formula (IFM,i) is given by IFM,i )
(m/z)iIi
∑ (m/z) I
(1)
i i
i
where Ii is the absolute intensity of an assigned formula and (m/z)i is the nominal mass. Summing IFM among all the assigned peaks within the medium H:C domain for R-pinene SOA gives a value of 80%; in other words 80% of the total mass weighted intensity is encompassed within this domain. IFM was not calculated for the negative ion spectrum because the manner in which it was acquired, by isolating ions in increasing m/z groups, distorted the ion signal intensities. The similarity between positive and negative ion spectra in this domain suggests that each molecular structure contains
FIGURE 3. Modified van Krevelen diagram for expected dimers from r-pinene ozonolysis. Point sizes are scaled to relative intensities in the 12T positive ion spectrum; the smallest points indicate expected combinations that are not detected. Blue intermediate+intermediate; red - intermediate+monomer; green - monomer+monomer; violet - formulas common to at least two types of combinations.
multiple functional groups, both carboxylic acids which preferentially form (M-H)- ions and carbonyls/alcohols which preferentially form (M+Na)+ ions (8). Oligomerization reactions were proposed by Jang et al. (18) involving the coupling of known, stable monomer products of monoterpene ozonolysis through processes such as Aldol condensation. Expected products of this type were subsequently found to be consistent with low and high resolution mass spectra of SOA produced in bag and environmental chamber reactors (6, 7, 17). More recently, our group has studied SOA produced in a flow tube reactor under conditions similar to this work (11, 12). Neither the bulk SOA composition (e.g., O:C atomic ratio) nor the ion distributions in the mass spectra were consistent with oligomerization of stable monomers alone. Instead, the oligomerization process was viewed as reactions between intermediates of monoterpene ozonolysis with other intermediates or stable molecular end products. For example, the stabilized Criegee intermediate (SCI) or a hydroperoxide molecule could react with another intermediate or stable molecule end product. Reaction of the SCI or hydroperoxide with a molecule containing a carbonyl would form a secondary ozonide or a peroxy hemiacetal, respectively. Reaction of either type of intermediate with a molecule containing a carboxylic acid would form a peroxide ester. The oligomer composition is known to evolve over time (19, 20), and it appears that the short time scale of the flow tube experiment (e23 s) leads to a different product distribution than longer time scale reactions in bags and chambers. Tables S1, S2, and S3 in the Supporting Information show the various combinations possible by the reaction of an intermediate with a stable monomer, an intermediate with another intermediate, and a stable monomer with another stable monomer, respectively. Almost all dimers from intermediates are observed. Of the 254 possible products involving at least one intermediate, 251 have elemental formulas equivalent to assigned formulas in the positive and/ or negative ion spectra after accounting for charge, i.e., (M+Na)+ and (M-H)-. Many dimers from stable molecule monomers are also observed. Of the 378 possible products involving the reaction of two stable monomers, 214 have elemental formulas equivalent to assigned formulas in the mass spectra. A modified van Krevelen diagram for these products is shown in Figure 3 where the size of each elemental formula in the plot corresponds to its intensity in the positive ion mass spectrum. Several conclusions can be drawn. First, the great majority of dimers from Tables S1-S3 that are VOL. 43, NO. 20, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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detected in the mass spectra fall within the medium H:C domain; a few monomer combinations fall within the low H:C domain. Conversely, most (>80%) of the assigned formulas in the medium H:C domain having m/z values in the range of dimers can be explained by the reaction products in Tables S1-S3. Together, these observations link the medium H:C domain and hence the majority of the total ion current to oligomerization reactions that have been postulated previously. Second, dimers from all three processes (Tables S1-S3) are required to explain the entire product distribution - the participation of both intermediates and stable molecule monomers in oligomer formation are clearly established. Third, products of intermediates from both the SCI and hydroperoxide reaction pathways are unambiguously observed. In Tables S1 and S2, 11 elemental formulas correspond uniquely to products of the SCI, and of these 6 are observed in the mass spectra. Similarly, 87 elemental formulas correspond uniquely to products of the hydroperoxide channel and of these 62 are observed in the mass spectra. While products of the hydroperoxide channel appear to dominate the high signal intensity products as would be expected from the work of Docherty et al. (21), both reaction pathways are needed to explain the entire product distribution. Finally, it should be noted that higher order oligomers are also observed in the middle H:C domain, but detailed analysis of elemental formulas with respect to specific combinations of monomers and/or intermediates is difficult because of many overlapping possibilities. Consistent with the work of Reinhardt et al. (7), the O:C atomic ratio generally decreases as the m/z increases from the dimer to multimer region. This difference is apparent upon inspection of Figures 1 and 3 - the dimers in Figure 3 tend to fall in the higher O:C range of the middle H:C domain in Figure 1. The low H:C domain shows a divergence between the assigned formulas to the positive and negative ions, that is only a few elemental formulas are observed in both spectra. This region has the second highest mass-weighted intensity fraction, 14%. The difference between elemental formulas assigned in the positive and negative spectra suggest that individual molecules contain fewer functional groups or preferentially functional groups of a single kind. Most elemental formulas have similar O:C ratios to those in the middle H:C domain but much lower H:C ratios. The question arises whether or not dimer formation reactions postulated for the middle H:C domain can be the source of products in the low H:C domain. Double bond equivalents (DBE) for experimentally observed dimers in the low H:C domain, defined here as elemental formulas having 20 or fewer carbon atoms, range from 8-12. For many elemental formulas, the DBE is too large to be explained by simple transformation of the products in Tables S1-S3. To illustrate this problem, we define the maximum DBE from ozonolysis, DBEmax ) N+2 where N ) number of oxygen atoms. When ozone attacks the CdC bond in R-pinene, two of the three DBEs in the molecule are removed - the CdC bond and one ring. If all of the oxygen atoms in the subsequent dimer product are eventually transformed into carbonyls, the DBE will be N+2 where N represents the carbonyls and “2” represents the cyclobutane ring in each monomer that was untouched by ozone attack. Of the 86 dimer elemental formulas observed in the low H:C domain, 25 have DBE > DBEmax indicating that additional CdC bonds and/or rings must exist in the molecule. The actual number of dimers having additional CdC bonds and/or rings is likely to be larger since it is unreasonable to assume that other functionalities such as carboxylic acids do not exist in any of the remaining molecules. The formation of CdC bonds and/or rings cannot be explained by traditional ozonolysis reaction sequences. Walser et al. (8) have postulated that under NOx free conditions, an initial alkyl peroxy radical produced by 7800
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ozonolysis can undergo repeated self-reactions where the peroxy radical is converted to an alkoxy radical, which subsequently isomerizes and reacts with oxygen to produce a new peroxy radical. A cascade of reactions of this type could lead to the production of many alcohol functionalities in the molecule that subsequently dehydrate to produce CdC bonds. These bonds could remain stable on the time scale of the reaction since ozone is the limiting reactant, and its concentration is substantially reduced near the end of the flow tube reactor. In preliminary experiments with SOA formation in a 500 L bag reactor (ca. 30 min reaction time), we find that low H:C domain products are formed with similar relative signal intensities. Therefore, their formation is not linked specifically to the experimental conditions of the flow tube reactor. The high H:C domain encompasses the smallest massweighted intensity fraction, 5%. These compounds are almost fully saturated (DBE ) 0 or 1 in the dimer m/z region, increasing to 1-2 in the multimer region) and therefore must consist mostly of poly ether and/or alcohol functionalities. These functionalities are consistent with nearly exclusive detection in the positive ion spectra, where sodium cationization is the preferred route for ion formation. Byproducts of R- and β-pinene ozonolysis include formaldehyde, formic acid, acetaldehyde, and acetic acid, among others (22). The simultaneously high H:C and O:C ratios of compounds in this domain may arise from polymerization of small molecules, particularly formaldehyde as it is produced in the highest molar yield. All of the elemental formulas observed in this domain can be assigned to polymers containing various combinations of formaldehyde and acetaldehyde with either alcohol or carbonyl/acid end groups. A relatively small number of the assigned formulas, 35 out of 113 total, can be explained by polymerization of several formaldehyde and/ or acetaldehyde molecules with an intermediate or stable molecule monomer. While the participation of monomers in the production of high H:C domain compounds cannot be ruled out, neither can it fully explain the range of compounds produced. Formaldehyde polymerization can be initiated by either basic and acidic species, giving a product that is both highly saturated and oxygenated (23). Recently, it has been suggested that glyoxal (C2H2O2), another product of R-pinene ozonolysis (24), contributes to oligomer formation in SOA (25). While this process may occur, it is not the main contributor to the high H:C domain because its polymerization product has too low an H:C ratio. Robustness of the Composition Domain Approach. Since compositional bias is inherent to the extraction and analysis steps (10), complete experiments (SOA generation, collection, extraction, analysis) were repeated to assess robustness. First, the R-pinene experiment was repeated two additional times using methanol-water extraction and subsequent analysis with the 7T FTICR-MS at the University of Delaware. Figure 4 compares van Krevelen diagrams constructed from the 12T experiment and one of the 7T experiments (#1 in Table 1). A comparison of the two 7T experiments is similar. Although the list of assigned elemental formulas shows some variation, the essential features of the van Krevelen diagram in Figure 1 are reproduced in Figure 4. In particular, the three composition domains are observed in similar massweighted intensity ratios, and the majority of assigned formulas for all three experiments match (Table 1). The one notable exception is the high H:C region, where the range of O:C ratios appears to change from experiment to experiment. This may arise from small run to run variations in the reactant concentrations that influence the production of small molecule precursors and/or polymerization catalysts. While the range of O:C ratios do change in this region from run to run, the range of H:C ratios and molecular size distribution do not. In preliminary work with a 500 L bag
FIGURE 4. van Krevelen diagram (positive ions only) for two separate experiments using methanol-water extraction. Blue data from 12T experiment; red - data from 7T experiment; green - common elemental formulas among the two data sets. reactor, we find that the high H:C domain products are sometimes missing from the corresponding van Krevelen plot. These observations highlight the extreme sensitivity of this domain to the experimental conditions. The other two domains, however, are relatively unaffected from experiment to experiment, despite minor variations of the assigned formulas. Second, the R-pinene experiment was repeated using 50/ 50 v/v acetonitrile/water as the extraction solvent. Recently, it has been suggested that extractions with methanol may cause additional reactions such as esterification or hemiacetal formation (26). It is also possible that different solvents will preferentially extract different chemical species. In Figure S3 and Table 1, the van Krevelen plots of methanol and acetonitrile extracted samples are compared. The results are similar in character to those described for the experiment in Figure 4. Most of the signal intensity and common formulas reside in the first two domains; differences are most pronounced in the third domain. While differences are also found among the specific elemental formulas assigned in the first two domains, it is unclear how much is caused by experiment-to-experiment variation vs solvent artifact. While a solvent artifact cannot be ruled out, it does not lead to a different interpretation of the plot with respect to the three composition domains. Third, the R-pinene experiment was repeated using 100% water as the extraction solvent to characterize the watersoluble organic carbon (WSOC) fraction. After extraction, the sample was diluted with an equivalent volume of methanol prior to ESI-FTICR-MS analysis. In Figure S4, the van Krevelen plots of the water and methanol-water extracted samples are compared. Again, the three composition domains are apparent, and there is a high degree of overlap particularly in the first two domains. An independent check of how representative the extraction and analysis procedure is of the true SOA composition was performed for the 12T FTICR-MS experiments by simultaneously measuring the O:C elemental ratio of individual particles with the nano aerosol mass spectrometer (NAMS). The results were measured for over 500 particles to give an average O:C ratio for the aerosol. Accurate mass data from the positive ion spectra were compared to the NAMS data by calculating an intensity weighted average of the O:C ratios of individual assigned formulas
∑ (O I ) i i
O:CIM )
i
∑ (C I )
(2)
i i
i
where O:CIM is the weighted average, Oi is the number of oxygen atoms in the elemental formula of species i, Ci is
the number of carbon atoms in the elemental formula of species i, and Ii is the absolute intensity of species i. Equation 2 is also essentially mass weighted since the total number of atoms in the elemental formula are used. This equation is based on the premise that all species in the positive ion spectrum have the same response factor. In practice, we find that inclusion/exclusion of intensity weighting has little effect (
