On Quantitative Determination of Volatile Organic Compound

Article pubs.acs.org/est

On Quantitative Determination of Volatile Organic Compound Concentrations Using Proton Transfer Reaction Time-of-Flight Mass Spectrometry Luca Cappellin,†,‡ Thomas Karl,§ Michael Probst,‡ Oksana Ismailova,‡ Paul M. Winkler,§ Christos Soukoulis,† Eugenio Aprea,† Tilmann D. Mar̈ k,‡ Flavia Gasperi,† and Franco Biasioli*,† †

IASMA Research and Innovation Centre, Fondazione Edmund Mach, Food Quality and Nutrition Area, Via E. Mach, 1, 38010, S. Michele a/A, Italy ‡ Institut für Ionenphysik und Angewandte Physik, Leopold Franzens Universität Innsbruck, Technikerstrasse 25, A-6020, Innsbruck, Austria § NCAR Earth System Laboratory, National Center for Atmospheric Research, P.O. Box 3000, Boulder, Colorado 80307, United States S Supporting Information *

ABSTRACT: Proton transfer reaction − mass spectrometry (PTR-MS) has become a reference technique in environmental science allowing for VOC monitoring with low detection limits. The recent introduction of time-of-flight mass analyzer (PTR-ToF-MS) opens new horizons in terms of mass resolution, acquisition time, and mass range. A standard procedure to perform quantitative VOC measurements with PTR-ToF-MS is to calibrate the instrument using a standard gas. However, given the number of compounds that can be simultaneously monitored by PTR-ToF-MS, such a procedure could become impractical, especially when standards are not readily available. In the present work we show that, under particular conditions, VOC concentration determinations based only on theoretical predictions yield good accuracy. We investigate a range of humidity and operating conditions and show that theoretical VOC concentration estimations are accurate when the effect of water cluster ions is negligible. We also show that PTR-ToF-MS can successfully be used to estimate reaction rate coefficients between H3O+ and VOC at PTR-MS working conditions and find good agreement with the corresponding nonthermal theoretical predictions. We provide a tabulation of theoretical rate coefficients for a number of relevant volatile organic compounds at various energetic conditions and test the approach in a laboratory study investigating the oxidation of alpha-pinene.

1. INTRODUCTION Proton transfer reaction − mass spectrometry (PTR-MS) allows for online monitoring of volatile organic compounds (VOC) at ultralow detection limits and fast response times. Thus, PTR-MS is becoming a widely used technique in many fields, in particular in environmental, clinical, and food chemistry. The recent introduction of a time-of-flight mass analyzer (PTR-ToF-MS) opens new horizons in terms of mass resolution, acquisition time, and mass range. Typically in PTRMS applications where quantitative determination of VOC concentrations is required, a calibration procedure employing reference gas mixtures is used. This practice may become timeconsuming when a large number of VOC has to be monitored (PTR-ToF-MS can simultaneously acquire information of hundreds of different mass peaks) or if VOC standards are not readily available. For many compounds it is often difficult to synthesize reliable gas standards. In principle, PTR-MS allows for the absolute quantification of VOC concentrations without calibration if the reaction rate coefficients between VOC and the hydronium ion and the corresponding product © 2012 American Chemical Society

ion branching ratios are known. In fact, as reported by Lindinger and co-workers,1 to a first approximation the VOC concentration can be determined from [VOC ] =

1 [VOC·H+] k τ [H3O+] +

(1)

+

where [VOC·H ] and [H3O ] are ion count rates corresponding to the protonated VOC ions and to the primary ion H3O+; k is the reaction rate coefficient between the VOC and H3O+; and τ is the residence time of the primary ions in the drift tube of the PTR-MS, typically about 100 μs. A better approximation would further consider the presence of H3O+ water clusters [H3O(H2O)n]+ ions. The concentration of these protonated water cluster ions is not negligible especially in the case of Received: Revised: Accepted: Published: 2283

November 9, 2011 January 3, 2012 January 19, 2012 January 19, 2012 dx.doi.org/10.1021/es203985t | Environ. Sci. Technol. 2012, 46, 2283−2290

Environmental Science & Technology

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using eq 5 tends to underestimate the measured τ since the mobility of water cluster ions is lower than that of H3O+.12 For further details on the estimation of τ we refer to the literature on the subject.5,12 In selected ion flow tube − mass spectrometry (SIFT-MS) measured values of k are used to estimate VOC concentrations with a reported accuracy of better than 10%.14 In PTR-MS it is a common practice to use thermal k, valid for SIFT-MS conditions, or a canonical value of 2•10−9 cm3/s. In order to facilitate the use of the proton transfer reaction − mass spectrometry (PTR-MS), recently, Zhao and Zhang published a list of reaction rate coefficients k together with their polarizabilities and dipole moments15 for more than 100 VOC, including hydrocarbons and oxygenated VOC. The rate coefficients were, however, calculated for thermal conditions at 300 K. While the proposed values are useful in certain applications, e.g. room temperature SIFT-MS experiments,16 their direct application for PTR-MS is at least questionable,17 due to the much higher effective temperature of standard PTRMS operating conditions. In fact, the kinetics of ion molecule reactions in PTR-MS is controlled not only by pressure and temperature in the drift tube but also by the electric field strength inducing far more energetic collisions than those at room-temperature. The effect on k can be negligible for molecules with low dipole moment, such as hydrocarbons, but it must in general be taken into consideration for accurate determination of VOC concentrations, in particular for molecules with larger dipole moments. 18 Experimental determinations of k for PTR-MS working conditions are scarce and are usually affected by large errors, thus theoretical values are to be preferred as stated in Lindinger et al.1 We show here that, under particular working conditions, it is possible to achieve good estimations of VOC concentrations via the first order kinetic description. Inverting this method also allows to determine reaction rate coefficients with PTR-ToF-MS. In summary, this work aims at clarifying and extending the possibility of accurate VOC concentration determinations by PTR-ToF-MS, in particular by - Explaining how VOC concentration can theoretically be calculated from PTR-ToF-MS measurements. - Providing a tabulation of reaction rate coefficients calculated for PTR-MS working conditions (according to Cappellin et al.18) and comparing some of these to the corresponding rates measured with PTR-ToF-MS. - Using the tabulated rate coefficients to predict VOC concentrations in a standard gas cylinder (this is done at the same time as the last point). - Investigating the limitations of the method provoked by sample humidity and by PTR-ToF-MS operating conditions. - Applying the method in a laboratory study investigating the oxidation of alpha-pinene and comparing the results with well-established model predictions.

samples with high humidity or at low collisional energies.2 The historical and most common choice for existing PTR-MS is a quadrupole mass analyzer, which has a different detection efficiency for ions of different masses.3,4 Mass discrimination must be corrected and can be experimentally determined following the procedure proposed in Von Hartungen et al.5 More recently PTR-MS has been coupled to ion trap6,7 and time-of-flight (ToF)8,9 mass spectrometers. The latter is characterized by a duty cycle10 duty cycle(m / z) =

Δl D

m/z m / z max

(2)

that causes a mass discrimination. For a definition of Δl and D see Chernushevich et al.10 In the case of PTR-ToF-MS the measured count rates must be corrected against the effect of the duty cycle, and therefore eq 1 becomes [VOC ] =

+ 1 [VOC·H ]measured k τ [H3O+]measured

(m / z)H O+ 3

(m / z) VOC·H+

(3)

Alternatively to the main parent peak of protonated water at m/z = 19.0178 Th, the isotope of H3O+ at m/z = 21.0221 Th can be used to calculate the concentration of the primary ion H3O+. Depending on the nature of the analyte and the energetic conditions in the drift tube, substantial fragmentation of the protonated VOC may occur. In order to retrieve the correct VOC concentrations, the complete fragmentation pattern must be known, and the contribution from all fragments (denoted as [VOCi·H+]) must be considered [VOC ] =

(m / z)H O+ 1 3 k τ [H3O+]measured

∑ i

[VOCi·H+]measured (m / z)VOC ·H+ i

(4)

The drift time τ can be estimated both experimentally theoretically via

τ=

l2 μU

11

and

(5)

where l is the drift tube length (typically 9.3−9.8 cm for Ionicon instruments), U is the electric potential applied to the drift tube (typically in the range 400−600 V), and μ is the mobility of the H3O+ ion in the drift tube which depends on the working conditions. Warneke et al.11 provide measurements of the reduced mobility pdrift T 0 μ0 = μ Tdrift p0 (6) for H3O+ in air for a wide range of E/N values, where E is the electric field in the drift tube, and N is the gas number density. pdrift and Tdrift are the pressure and temperature in the drift tube, respectively, while T0 = 273.15 K and p0 = 100 kPa (standard conditions for pressure and temperature). De Gouw et al.12 report good agreement between calculated and measured residence time for E/N values where H 3 O + dominates as primary ion (for their operating conditions over E/N = 100 Td), confirming the findings of Tani et al.13 For low E/N values, where protonated water clusters become the most abundant ions in the drift tube, the residence time calculated

2. MATERIALS AND METHODS 2.1. Instrumental Setup. Measurements were performed with a commercial PTR-ToF-MS 8000 apparatus supplied by Ionicon Analytik GmbH, Innsbruck (Austria) in its standard configuration.8 The ionization conditions in the drift tube were controlled by drift voltage (493 V), drift tube temperature (90 ◦C), and drift pressure (2.28 mbar). The resulting E/N was about 120 Td. 2284

dx.doi.org/10.1021/es203985t | Environ. Sci. Technol. 2012, 46, 2283−2290


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4, with k as unknown variable, to be estimated by fitting the data. Our procedure, and thus the accuracy of the corresponding calculated VOC concentration, is limited by the fact that the kinetics of ion−molecule reactions and the reaction time are not always well-defined. There are regimes for which eq 4 provides a good description. The influence of reactions between the analyte VOC and primary ions other than H3O+, for instance O2+ and NO+, are minimized by tuning the ion source settings. The ion source in commercial PTR-MS instruments can be adjusted to provide a H3O+ signal with a purity of above 99%. Protonated water clusters instead are an important factor to be considered. Especially at high humidity conditions and low E/N values,12 a substantial amount of water cluster ions can be present in the PTR-MS drift tube. These clusters can react with VOC via proton transfer or ligand switching. Not all VOC react with water cluster ions; for example benzene and toluene react with H3O+ but not with water cluster ions,11,29 while monoterpenes react with both H3O+ and H3O·(H2O)+.13 Product ions of the reaction between VOC and water clusters interfere with the signal corresponding to the products of the reaction with H3O+. That is evidently the case when proton transfer from water cluster ions occurs. The products of ligand switching reactions also interfere since product VOC cluster ions are weakly bound and likely dissociate. A further effect is represented by water cluster ions undergoing collision-induced dissociation upon exiting the drift tube region thus interfering with the H3O+ signal.11 Therefore, PTR-MS peaks corresponding to the primary ions and to water cluster ions may not reflect the corresponding ion concentrations in the drift tube. Moreover, the reaction time may not be well-defined.11,14 The presence of water cluster ions in the PTR-MS drift tube is controlled by humidity and by the strength of the applied electric field. Humidity is not just determined by the inlet air but also by water vapor which enters the ion source region and can enter the drift tube region depending on the differential pumping speeds between ion-source and drift regions. Some authors set high levels of water vapor flow from the ion source to achieve an improved sensitivity for some compounds. In this case, the effect of water cluster is very relevant even at very low ambient humidity. Commercial releases of PTR-MS instrument are usually tuned to have a reduced flow of water vapor between the ion source and the drift tube. The electric field applied to the drift region has a major impact on the amount of water cluster ions present in the drift tube. Typically, the working electric field strength is selected as a trade-off between sensitivity, fragmentation, and presence of water clusters. E/N values larger than 120 Td strongly limit the amount of cluster ions to a few percent with respect to the abundance of H3O+ ions even at high relative sample humidities (e.g., 100%).12 However, at lower E/N values, water cluster ions may become the predominant ion if the presence of water vapor is sufficiently high. For the present instrumental setup, the water vapor flowing from the ion source is minimized, and therefore the amount of water cluster ions in the drift tube is mainly controlled by E/N and the humidity of the inlet air. We assessed the effect of water cluster ions on VOC concentration determinations and rate coefficient estimation via eq 4 by comparing calculated and experimental rate coefficients at E/N = 85 Td, 120 Td, and 150 Td and 0%, 50%, and 100% relative humidity of the sample air. Theoretical rate coefficients

The sampling time per channel in the ToF was set to 0.1 ns, amounting to 349000 channels for a mass spectrum up to about 400 Th. PTR-ToF-MS spectra were acquired for different known mixing ratios at a frequency of 0.1 Hz. Every spectrum is the sum of 285800 acquisitions lasting for about 35 μs each. A flux of dry synthetic air (80% nitrogen, 20% oxygen) was continuously mixed with a standard gas mixture, which was gravimetrically prepared and provided by NOAA according to protocols published by Montzka et al.19 Gas standard 1 contained methanol (1.89 ppmv), acetonitrile (2.00 ppmv), acetaldehyde (3.53 ppmv), acetone (1.99 ppmv), methylvinylketone (1.1 ppmv), limonene (2.1 ppmv), 2-methyl-3-buten-2ol (2.2 ppmv), pyrrole (2.1 ppmv), benzene (1.49 ppmv), toluene (2.3 ppmv), and methylethylketone (2.2 ppmv) with an uncertainty of ±5%. Gas standard 2 was purchased from ScottMarrin (Riverside, CA, USA) and contained a mixture of acetaldehyde (5.84 ppmv, ±3%), acetone (5.66 ppmv, ±3%), acetonitrile (5.44 ppmv, ±10%), methanol (4.6 ppmv, ±3%), and toluene (5.74 ppmv, ±3%). A dynamic dilution system similar to refs 20 and 21 was set up, where a calibrated dilution flow of dry air was directed through two mass flow controllers (Tylan/Millipore, FC-280 - SAV, 2 slm), one leading to a water reservoir containing distilled water. Both flows were mixed with a third small flow controlled by a mass flow controller (MKS Instruments, 1259-CC, 0−50 sccm) carrying the ppmv level VOC mixture. Variations of humid and dry flow were achieved by setting different flow rate ratios for the main two dilution flow controllers (1 slm each), thus getting different humidities in the range of 0−100%. Different E/N values (by varying the drift voltage) and humidity conditions were tested. Separate experiments were carried out in order to assess the influence of protonated water clusters for VOC concentration estimations. Flowtube setup: A 1.4 m long glass flow tube (inner diameter: 0.1 m) was purged with zero air at a flow rate of 25 slpm supplied by a Pure Air Generator (Aadco Model 737). An alpha-pinene concentration of 85 ppbv was generated using a dynamic dilution system at the flow tube entrance. The flow rate of this stream was controlled using a rotometer and checked prior to each experiment using a bubble flow meter (Gilibrator, Gilian In-strument Corp.). Ozone was generated using an ultraviolet ozonizer whose intensity could be adjusted to control the concentration of ozone entering the flow tube. Typical ozone concentrations achieved with this setup were 3.7 ppmv. Residence times (15, 30, 45, and 60 s) in the flow tube were adjusted by varying the flow rate through the flow tube. 2.2. PTR-ToF-MS Data Analysis. Spectra preprocessing included correction of count losses due to the detector dead time effect22 and calibration of the m/z domain.23 Noise reduction24 and peak extraction followed the methodology described in Cappellin et al.,25 employing a modified Gaussian peak shape.9 This methodology allows for extraction of the measured signal with a high accuracy. We employed eq 4 to calculate VOC concentrations from the measured PTR-ToF-MS signals for different mixing ratios at E/ N = 121 Td and a drift tube temperature of T = 90 °C. For each compound, particular care has been devoted to consider the full fragmentation pattern,26−28 including peaks corresponding to the most abundant isotopologues. The difference between the parent ion and its isotopes in their reaction rate coefficients with H3O+ was neglected. For each compound, we also determined an experimental reaction rate coefficient via eq 2285



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Table 1. Comparison between Experimental (Determined Using PTR-TOF-MS) and Theoretical Reaction Rate Coefficient between the H3O+ Ion and Various Compoundsa compound methanol acetonitrile acetaldehyde acetone methyl vinyl ketone (MVK) pyrrole benzene limonene 2-methyl-3-buten-2-ol (MBO) toluene methyl ethyl ketone (MEK)

kexp [10−9cm3/s] 2.15 3.92 3.00 3.59 3.20 2.64 1.95 2.28 2.31 2.05 3.03

± ± ± ± ± ± ± ± ± ± ±

15% 15% 15% 15% 15% 15% 15% 15% 15% 15% 15%

ktheory [10−9cm3/s]

ktheory/kexp

± ± ± ± ± ± ± ± ± ± ±

1.03 1.02 1.04 0.92 1.05 0.93 0.99 1.07 1.05 1.02 1.08

2.22 3.99 3.12 3.32 3.39 2.46 1.93 2.44 2.42 2.08 3.28

10% 10% 10% 10% 10% 10% 10% 10% 10% 10% 10%

kthermal [10−9cm3/s]

kthermal/kexp

± ± ± ± ± ± ± ± ± ± ±

1.17 1.39 1.32 1.16 1.29 1.09 0.99 1.12 1.24 1.02 1.30

2.52 5.44 3.97 4.16 4.14 2.87 1.93 2.55 2.87 2.08 3.95

15% 15% 15% 15% 15% 15% 15% 15% 15% 15% 15%

Experimental conditions: E/N = 120 Td, drift tube temperature T = 90 °C. Notice that, given our experimental procedure, ktheory/kexp is equal to [VOC]cylinder/[VOC]PTR‑ToF‑MS, where [VOC]PTR‑ToF‑MS is the theoretically predicted VOC concentration estimated from PTR-ToF-MS measurements and [VOC]cylinder is the VOC concentration in the standard gas. a

at the considered E/N values were calculated according to Cappellin et al.18

corresponding experimental estimations (Table 1). The uncertainty increases to 15% when polarizability and dipole moment values are taken from Zhao and Zhang.15 The obtained rate coefficients are listed in Table S1 reported in the Supporting Information (SI). The comparison between the rate coefficients in Table S1 and the corresponding values15 calculated at thermal conditions indicates the latter are in general systematically higher (a small part of this is due to the effects of the different values for polarizability and dipole moment used), and the discrepancy increases for larger E/N. The difference is almost negligible for most hydrocarbons because of their low dipole moment value; it increases substantially for compounds having large dipole moment, especially when high E/N operating conditions are considered. In section 3.2 we will provide a comparison between thermal rate coefficients and corresponding data measured at PTR-MS working conditions. It is worth mentioning that the main difference between our presently calculated values and the corresponding thermal values does not arise from a difference in the estimation of k by using either the average dipole orientation (ADO) theory or other methods proposed by Su.30,39,40 In general, these provide comparable results. In our present calculations we consider real experimental conditions under which the ion molecule collisions occur, which explains most of the observed differences: that is, we take into account that reactions are not taking place at room temperature but at much higher effective temperatures due to the applied electric field. We use Su’s method because of its advantages, i.e. it allows to directly include the effect of the collision energy. In principle, ADO theory could also be used, for example by including the effect of collision energy in the temperature parameter, i.e. by employing an effective temperature. However, this would require an estimation of the average-dipoleorientation coefficient at the resulting effective temperature since no such values are, to the best of our knowledge, available in the literature. 3.2. Quantitative VOC Concentration Estimations and Experimental Reaction Rate Coefficients. Equation 4 was used to calculate VOC concentrations (at E/N = 121 Td and a drift tube temperature T = 90 °C) based on measured PTRToF-MS signals for different mixing ratios obtained from the dynamic dilution system. We used reaction rate coefficients calculated according to the preceding section for given operating conditions. Figure 1A depicts the results for 2-

3. RESULTS AND DISCUSSION 3.1. Nonthermal Reaction Rate Coefficients. We already described 18 how nonthermal working conditions of a commercial PTR-MS can be accounted for by using Su’s parametrization of trajectory collision rate coefficients.30 The resulting correction improves the calculation of rate coefficients in the case of VOC with larger dipole moments, and therefore it is particularly suitable for oxygenated VOC. Here we apply this approach and recalculate the k coefficients provided by Zhao and Zhang15 for different E/N values and a drift tube temperature of 363 K. For completeness, we added calculated values for several other compounds. For most compounds, we use polarizabilities and dipole moments obtained from the results of quantum chemical calculations provided by NIST.31 Most of them were obtained from density functional calculations with the Becke−Lee−Yang−Parr three-parameter functional (B3LYP).32,33 As basis sets aug-cc-pVQZ, augccpVTZ, or aug-cc-pvDZ34−36 were used. Hybrid density functionals like B3LYP generally provide good estimations37 of these properties, contrary to Hartree−Fock or standard Kohn− Sham calculations in the local density approximation. In case only other calculations were published in NIST, we selected, if available, the best available density functional. For several compounds, no suitable calculated values could be found when searching the NIST database. For these we calculated polarizabilities and dipole moments based on the B3LYP/ aug-cc-pVTZ level parametrization. The corresponding procedure is described elsewhere.18 As pointed out,18 the results of quantum chemical calculations on the B3LYP/aug-cc-pVTZ or B3LYP/aug-cc-pVQZ levels are affected by a typical uncertainty of about 4%. The smaller aug-cc-pvDZ basis set results in a slightly larger uncertainty, of typically up to 10%.38 Similar errors are encountered for B3PW91/aug-cc-pVDZ, B1B95/ aug-cc-pVDZ, and B3LYP/cc-pVTZ, which have been used for the NIST database. For some compounds, we employed the values reported by Zhao and Zhang.15 Given a 5% uncertainty30 in Su’s parametrization of trajectory collision rate coefficients and the above-mentioned uncertainty in the polarizability and dipole moment values, a 10% overall uncertainty for the present determination of the rate coefficients is estimated. This is also supported by the comparison (within 8%) with the 2286



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compounds and always smaller than 8%. This agreement supports the conclusion, which has already been motivated by theoretical arguments,18,41 that theoretical rate coefficients calculated at room temperature (referred to as “thermal rate coefficients”) are not suitable for the energetic conditions in the PTR-MS drift tube. Table 1 also reports rate coefficients calculated at thermal conditions via parametrized trajectory calculations.39,40 Apart from the case of compounds having negligible dipole moment such as benzene or toluene, the discrepancy with measured values is evident. Estimations of rate coefficients at thermal conditions using ADO theory can be found in Zhao and Zhang.15 Upon comparison with the measured values reported in Table 1, a systematic overestimation (of up to 21%) is found. Our experimental rate coefficients are, however, affected by some factors of uncertainty: the real concentration of the calibration gas ( 100 Td). Overall, an error of 15% can be assigned to the measured kexp. Note that all the results reported in Table 1 agree within 8% with their corresponding theoretical estimation. Literature values for reaction rate coefficient at the considered energetic conditions are scarcely available for comparison. For all data listed in Table 1 we have neglected any interference of protonated water clusters since we worked with dry air and an E/N of 120 Td. At such conditions, the effect of protonated water clusters is not critical.12 Moreover, the influence of O2+ and NO+ ions is also negligible, as stated above. For measuring real atmospheric samples, when dry conditions are only exceptional, relative humidities in the range of 0% to 100% have to be considered. It is therefore of interest to investigate the impact of the sample relative humidity on the calculations of VOC concentrations. As already discussed, the effects of water cluster ions represent the main caveat of the present procedure. Figure 1B and Figure 2 depict a comparison between calculated and experimental rate coefficients for all considered compounds at different E/N values and humidity conditions. Obviously, this also tests the extent to which eq 4 is suitable for calculating VOC concentrations. At 0% relative humidity of the sample air, the agreement is within 10% for all compounds with the exception of acetone (12% at E/N = 85 Td) and pyrrole (12% at E/N = 150 Td). In fact, the presence of protonated water clusters in the drift tube is limited. The total ToF signal of water cluster ions related to the flow of water vapor from the ion source into the drift tube was about 13%, 2%, and 2% of the H3O+ signal for E/N = 85 Td, 120 Td, and 150 Td, respectively. The close correspondence between theoretical and experimental reaction rates for the selected E/N values further confirms that nonthermal rate coefficients are suitable for PTR-MS. At 50% relative humidity and E/N = 120 Td the agreement is still good. Increasing the humidity to 100% worsens the results, leading to errors up to 15% for all compounds but pyrrole (23%) and MBO (20%). At E/N = 150 Td good agreement is always found. Under such high electric field strength, cluster ions are strongly suppressed, and no relevant effect of humidity is found. On the other hand, the results are extremely sensitive to humidity conditions at an electric field strength of E/N = 85 Td; here we find a dramatic

Figure 1. A. Comparison between MBO concentrations in the sample air and the respective calculated values from PTR-ToF-MS data. The axis bisector represents a line of perfect agreement. B. Effect of E/N (in Td units) and relative humidity. Dashed lines are plotted at ratio values of 0.9 and 1.1.

methyl-3-buten-2-ol (MBO), where a close agreement is found. It is important to notice that MBO undergoes substantial fragmentation at E/N = 121 Td; the relevant fragments are m/z = 41.0386 Th, 69.0699 Th, and 87.0804 Th. A method to judge the deviation from the line of perfect agreement is by comparing the theoretical rate coefficient with the experimental rate coefficient estimated via eq 4, using k as unknown variable. Theoretical rate coefficient refers to the rate coefficient calculated at the (nonthermal) working condition of the PTR-MS drift tube, according to Section 3.1. The results for the experimentally determined reaction rate coefficients for the presently investigated compounds are listed in Table 1. Good agreement is found upon comparison with the respective theoretical estimations. This suggests that the concentration estimation for selected compounds based on eq 4 using the theoretical rate coefficient are in close agreement with the actual concentration values. Our results also highlight that PTR-MS coupled to a ToF mass spectrometer may be successfully employed to measure reaction rate coefficients at suitable PTR-MS working conditions. To the best of our knowledge, the only example of using PTR-MS to experimentally determine reaction rate coefficients is the work published by Tani et al.13 Tani and coworkers employed a PTR-MS coupled with a quadrupole mass analyzer (PTR-Quad-MS); they based their results on a relative estimation with respect to the reaction rate of toluene.13 They estimated the reaction rate coefficients at E/N = 120 Td for several monoterpenes, including limonene, for which they found k = 2.3·10−9 cm3 s−1. Here we find close agreement with an experimental value of kexp = 2.28·10−9 cm3 s−1 (see Table 1). PTR-ToF-MS, contrary to PTR-Quad-MS, allows for a more quantitative and absolute determination of rate coefficients (k), because an accurate theoretical description of the mass discrimination of the detector is possible. Table 1 reports the discrepancy between experimental and theoretical rate coefficients. The difference is a few percent for most 2287



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Figure 2. Effect of E/N (in Td units) and relative humidity. Dashed lines are plotted at ratio values of 0.9 and 1.1.

established.42 Figure 3 shows a comparison between predicted concentration changes based on calculated values obtained by PTR-ToF-MS using procedures described in section 2 and rate coefficients from Table S1 (squares) and modeled concentrations of alpha-pinene and pinonaldehyde using the Leeds master mechanism (solid lines).43 Overall good agreement within 10% is reached. The result suggests that a quantitative description of oxidation chemistry is possible using PTR-ToFMS as long as instrument specific details of operation are considered.

deviation from the theoretical values. The explanation relates to the amount of water clusters that are present in the drift tube at such conditions. These results illustrate some of the main differences between PTR-MS and SIFT or similar atmospheric pressure ionization techniques. For an independent evaluation we quantitatively compare the predicted and measured decrease of alpha-pinene concentrations in the flowtube along with the production of the dominant first order generation product pinonaldehyde upon exposure to ozone. We chose alpha-pinene, because the reaction rate coefficients with respect to the main oxidizing agents OH, O3, and NO3 and yields for pinonaldehyde are well 2288



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Figure 3. Oxidation of alpha-pinene. Measured (squares) and modeled (solid lines) mixing ratios for alpha-pinene (blue) and pinonaldehyde (red).

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ASSOCIATED CONTENT

S Supporting Information *

Table S1 reports reaction rate coefficients between the hydronium ion (H3O+) and selected VOC for different E/N values. Polarizability and dipole moment values are also reported. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +39 0461 615187. Fax: +39 0461 650956. E-mail: [email protected].

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ACKNOWLEDGMENTS L.C. acknowledges Armin Wisthaler for fruitful discussions. M.P. acknowledges support from the Austrian Ministry of Science via an infrastructure grant to the LFU scientific computing platform and from the RFBR-FWF projects 09-0391001a and I200-N19. The National Center for Atmospheric Research is supported by the National Science Foundation.

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REFERENCES

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