Article pubs.acs.org/JPCA
“Virtual Injector” Flow Tube Method for Measuring Relative Rates Kinetics of Gas-Phase and Aerosol Species Lindsay Renbaum-Wolff‡ and Geoffrey D. Smith* Department of Chemistry, University of Georgia, Athens, Georgia 30602, United States S Supporting Information *
ABSTRACT: A new method for measuring gas-phase and aerosol reaction kinetics is described in which the gas flow, itself, acts as a ”virtual injector” continuously increasing the contact time in analogy to conventional movable-injector kinetics techniques. In this method a laser is directed down the length of a flow tube, instantly initiating reaction by photodissociation of a precursor species at every point throughout the flow tube. Key tropospheric reactants such as OH, Cl, NO3, and O3 can be generated with nearly uniform concentrations along the length of the flow tube in this manner using 355 nm radiation from the third harmonic of a Nd:YAG laser. As the flow travels down the flow tube, both the gas-phase and particle-phase species react with the photogenerated radicals or O3 for increasingly longer time before exiting and being detected. The advantages of this method are that (1) any wall loss of gas-phase and particle species is automatically accounted for, (2) the reactions are conducted under nearly pseudo-first-order conditions, (3) the progress of the reaction is followed as a continuous function of reaction time instead of reactant concentration, (4) data collection is quick with an entire decay trace being collected in as little as 1 min, (5) relative rates of several species can be measured simultaneously, and (6) bimolecular rate constants at least as small as k = 10−17 (cm3/molecule)/s, or aerosol uptake coefficients at least as small as γ = 10−4, can be measured. Using the virtual injector technique with an aerosol chemical ionization mass spectrometer (CIMS) as a detector, examples of gas-phase relative rates and uptake by oleic acid particles are given for OH, Cl, NO3, and O3 reactions with most agreeing to within 20% of published values, where available.
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INTRODUCTION In measuring the magnitude of gas-phase rate constants it is often convenient to use flow tube techniques in which the reaction is allowed to take place for a variable amount of time. One reactant is introduced into the flow tube through a smaller, movable injector tube while the other reactant enters through a port at the rear of the flow tube. The contact time is then varied by sliding the injector in and out, and the extent of reaction of one of the reactants is monitored as a function of the injector position, which can be converted to contact time with known flow rates and flow conditions (i.e., laminar or turbulent flow). Recently, flow tube techniques have also been used to measure gas−particle uptake kinetics using a movable injector to introduce the particles with a variable contact time with a gas-phase reactant.1−7 Despite the relative simplicity of the movable injector flow tube method, its use imposes several practical design issues when a kinetics experiment is carried out. The method requires that one reactant is in excess and that its concentration is known, which can be limiting especially when a radical or otherwise short-lived species is to be maintained in excess of the other reactant. This constraint is usually not important in measuring gas-phase kinetics because the loss of this short-lived species can be monitored in the presence of an excess of the other gas-phase reactant. However, it is generally not feasible to © 2012 American Chemical Society
generate a large enough concentration of particles to do this with gas−particle reactions. There also must be negligible losses of the reactants to the walls of the flow tube and the injector tube that may be difficult to ensure especially with radicals or particles. Finally, the reactants must be well mixed on a time scale that is short compared to the residence time in the flow tube; otherwise an accurate measurement of the contact time and thus an accurate measure of the rate constant of the reaction will be difficult.8 This manuscript describes an alternate use of a flow tube for measuring gas-phase or gas−particle kinetics in which the gas flow, itself, acts as a “virtual injector” for varying the contact time, overcoming many of the limitations of conventional movable injector techniques. The absence of a physical injector makes it possible to use a light source to photogenerate a reactive species throughout the volume of the flow tube as soon as the light is turned on, and both gas-phase and particle species react with the photogenerated reactive species for increasingly longer time as the flow travels down the flow tube. Measuring the simultaneous loss of a gas-phase reference species with a known rate constant allows the rate constant or uptake Received: April 4, 2012 Revised: May 30, 2012 Published: June 15, 2012 6664
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Figure 1. Schematic of “virtual injector” apparatus. UV (355 nm) radiation from a Nd:YAG laser is used to photolytically generate Cl from Cl2, O3 from NO2, OH from HONO, or NO3 from HONO and HNO3. The light is modulated on and off using a shutter to initiate or stop reaction. The carrier gas flow pushes the gas-phase and particle reactants as they react for an increasingly longer time. The losses of the gas-phase and particle species are monitored using Aerosol CIMS.
Table 1. Reactions Used To Photo-generate Reactive Species, Absorption Cross Sections of Photo-reactive Species at 355 nm, and Maximum Concentrations Generated reactive species
reaction
OH
HCl + NaNO2 → HONO + NaCl
Cl
Cl 2 + hν → 2Cl
cross section of precursor @ 355 nm (cm2/molecule)
max. concn (molecule/cm3)
−19 (10,11)
5 × 108
1.6 × 10−19 (12)
6 × 109
3 × 10
HONO + hν → OH + NO NO3
3 × 10
HNO3 + NaNO2 → HONO + NaNO3
−19 (10,11)
3 × 1011
HONO + hν → OH + NO OH + HNO3 → NO3 + H 2O O3
NO2 + hν → O + NO 5 × 10−19 (13−15)
O + O2 → O3
1 × 1013
atmospheric pressure and temperature and then are detected with the aerosol CIMS. The reactants are created by photolysis of a precursor species using radiation from the third-harmonic (355 nm) of a 10 Hz Nd:YAG laser (Spectra-Physics QuantaRay PRO-250) that is expanded to overfill the 2 in. i.d. of the flow tube using a 6 cm focal length lens. Typically, pulse energies of 25−300 mJ/pulse are used with the power adjusted to achieve the oxidant concentration required. A shutter is removed unblocking the radiation and allowing it to enter the flowtube and initiate reaction. Decay traces of the reactants are built up by monitoring the decreases of the corresponding integrated signals from the CIMS mass spectrum while the laser is fired continuously at 10 Hz. The N2 carrier gas flow is 1.2− 1.8 SLPM (standard liters per minute) resulting in a bulk flow velocity of 1.0−1.5 cm/s and a residence time of 66−100 s (660−1000 laser shots). The flow is laminar with a Reynolds number of 33−50. The photodissociation reactions used to generate the different radicals and O3 are summarized in Table 1. Gases used in the generation of the reactive species are introduced as a mixture with N2 from a lecture bottle (Cl2, NO2) or from a bubbler (H2O, HCl, HNO3) or made in situ (HONO). The HONO that is used for the creation of OH
coefficient to be measured on an absolute basis and wall losses are automatically accounted for. Numerous examples of rate constants and gas−particle uptake coefficients measured using this method demonstrate its utility for measuring the kinetics of the key tropospheric oxidants, O3, NO3, OH, and Cl.
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EXPERIMENTAL DETAILS The virtual injector method requires a flow tube in which the gas-phase or gas−particle reactions occur, a light source for generating the reactive radicals or O3 from a precursor species, and a method for detecting the gas-phase and/or particle species. In this section, the specific components used in the present study are described in detail. A more general discussion of the requirements for using the virtual injector method is presented in the section “Requirements for Virtual Injector Method”. Flow Tube and Generation of Reactive Radicals and Ozone. The virtual injector apparatus used in the present study consists of a 1 m long glass flow tube (2 in. i.d.) coupled to an aerosol chemical ionization mass spectrometer (CIMS) (Figure 1). Both gas-phase and particle species react with photogenerated reactants, OH, Cl, NO3, or O3, in the flow tube at 6665
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radicals is generated by flowing HCl vapor through a trap containing free-flowing NaNO2.9 Chemical Ionization Mass Spectrometer. The gas-phase species and particles exit the flow tube and are analyzed by an aerosol CIMS, which has been described in detail, previously.16 Briefly, these species are sampled into the mass spectrometer through a a flow-limiting orifice (0.5 mm i.d.) held in a heated stainless steel tube (1/4 in. i.d., 10 cm long, 240 °C). The gasphase and vaporized particle species then enter a heated chemical ionization region (140 °C) consisting of a stainless steel tube (1/2 in. o.d., 20 cm long) in which they are ionized through reaction with a reagent ion. Most gas-phase and particle species are ionized through proton-transfer reactions using H+(H2O)n (n = 2, 3) reagent ions generated by flowing N2 through the 210Po ionizer. Some species are ionized using the NO+ reagent ion, generated by flowing a trace amount of NO with N2 through the 210Po ionizer, leading to [M − H]+ and [M + NO]+ ions. The ions resulting from the chemical ionization are then analyzed using a quadrupole mass filter (ABB Extrel). Particle Generation and Characterization. Particles are generated through homogeneous nucleation by flowing 0.9 slpm (standard liters per minute) of N2 through a reservoir containing the liquid sample. The reservoir temperature is typically 130−140 °C. Upon exiting the reservoir the organic vapor cools and spontaneously nucleates. The aerosol is then reheated as it flows through a heated section of glass tubing (1/ 2 in. o.d., 4 in. long) to narrow the distribution of particle sizes to a geometric standard deviation of σg ≤ 1.20 for oleic acid particles and σg ≤ 1.30 for olive oil particles. The temperature of the glass tube is measured using a thermocouple and is typically maintained at 120−130 °C. Chemicals Used. Gas-phase organic species are taken directly from the bottle with no further purification and are introduced either from a lecture bottle containing a mixture in N2 or by placing a small drop on an O-ring at an inlet to the flow tube. Aerosols are generated through homogeneous nucleation of heated vapors. The following chemicals were purchased from Sigma-Aldrich: butanal (99%, CAS #123-72-8), α-pinene (99+%, CAS #7785-70-8), β-pinene (99+%, CAS #18172-67-3), isoprene (99%, CAS #8-79-5), 2-methyl-2butene (≥95%, CAS #513-35-9), 2,4-hexadienal (95%, CAS #142-83-6), 1-octene (98%, CAS #11-66-0), methacrolein (95%, CAS #78-85-3), cyclohexene (99%, CAS #110-83-8), 2,3-dimethyl-2-butene (98%, CAS #563-79-1), acetone (≥99.5%, CAS #67-64-1), acetone-d6 (99.9% atom D, CAS #666-52-4), acetone-2-13C (99 atom % 13C, CAS #3881-06-9), methanol-d3 (99.8 atom % D, CAS #1849-29-2), free-flowing sodium nitrite (99.5%, CAS #7632-00-0), and HNO3 (70%, CAS #7697-37-2). The following chemicals were purchased from Fluka: D-limonene (≥96%, CAS #5989-27-5), oleic acid (>99%, CAS #112-80-1). HCl (36.5−38.0%, CAS #7647-01-0) was purchased from J. T. Baker. (CAS Registry numbers supplied by the authors.) Cl2 gas (high purity) and N2 gas (from a liquid N2 dewar) was purchased from National Specialty Gases. Partially deuterated acetone (acetone-d1 to acetone-d5) was generated through natural H-atom exchange of acetone-d6 vapor with residual water vapor in a stainless steel lecture bottle. The rate of exchange was enhanced by the addition of a drop of HNO3 in the lecture bottle.
Article
VIRTUAL INJECTOR METHOD
Principle of Operation. Upon introduction of the laser radiation, the reactive species is generated instantaneously throughout the length of the flow tube. Consequently, reactions between those species and other gas and/or particle species are initiated instantaneously at every point in the flow tube. The gas flow itself acts as a “virtual injector” by pushing the gas and particles down the flow tube toward the mass spectrometer, changing the reaction time continuously in analogy to a conventional movable injector in which the reaction time is varied by moving the point of introduction of one of the reactants. Although it is not plug flow, it is useful to think of individual plugs of gas flowing down the length of the flow tube and being characterized by the aerosol CIMS sequentially with no mixing along the axial dimension. In reality the flow is better described as Poiseuille flow displaying a parabolic velocity profile along the radial dimension with a corresponding gradient of reaction times. However, as we demonstrate later, the mass spectrometer samples the entire flow with an average reaction time that is determined by the bulk flow velocity. In conventional flow tube kinetics techniques, fast mixing through diffusion or turbulent flow is required to ensure that the reactants are well mixed with minimal radial concentration gradients. In the virtual injector method described here, diffusion at atmospheric pressure is too slow to mix completely in the radial dimension; for example, OH radicals would take approximately 23 s to diffuse the 1 in. radius of the flow tube with a diffusion constant of 0.22 cm2/s17 if generated only in the center of the flow tube. Also, because the flow is laminar, there is no mixing from turbulence. However, because the reactive gas precursor is well mixed with the gas-phase reference and gas or particle-phase reactant(s) before entering the flow tube and because the reactive species are regenerated every 100 ms. by the laser throughout the flow tube in both the radial and axial dimensions, there are minimal concentration gradients established for these species. Any variation in reactant concentration that may exist in the flow tube is therefore accounted for by monitoring the reactive loss of the gas-phase reference species enabling relative rates measurements. This relative rates approach also accounts for any temporal inhomogeneities in concentrations of the photogenerated reactant species arising from the pulsed light source. A large concentration of the oxidant may be generated initially followed by a decay between pulses (100 ms) due to reactions with itself or other species. However, in the generation of both Cl and OH radicals, it is estimated that even with the largest precursor concentrations ([Cl2] = 1014 molecules/cm3, [HONO] = 1012 molecules/cm3) and the largest laser pulse energies (300 mJ/ pulse), the radical concentration decreases by no more than 4% between laser shots due to reactions with itself or precursor species. Reaction with a gas-phase reference species could deplete the radical, though. For example, it is estimated that 3− 99% of the Cl radical would be removed by reaction with the reference species during the 100 ms between laser shots depending on which reference was used (acetone or isoprene). However, even a large depletion of the reactive species will not affect the relative rates measurement because the rates of reaction of both the reference and the species to be measured will be affected equally. Requirements for Virtual Injector Method. The virtual injector method as demonstrated here uses a pulsed laser to initiate reaction and a chemical ionization mass spectrometer to 6666
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Detector. An analytical instrument or set of instruments capable of detecting relative changes in concentrations of the gas-phase reference species and the gas-phase or particle reactant(s) is required. Because relative rates are measured, it is not necessary to be able to detect absolute concentrations of these species. In the present experiments, one instrument, a chemical ionization mass spectrometer, is used to detect simultaneously all relevant gas-phase and particle species. However, it may be advantageous to use a set of instruments in conjunction with one another to separately optimize detection of the various gas-phase and particle species; for example, FTIR (Fourier transform infrared) spectroscopy could be used to detect gas-phase species and an aerosol mass spectrometer could be used to detect particle species. However, the use of more than one instrument requires synchronization on the time scale of the slowest sampling rate of the instruments used. Furthermore, this slower sampling rate will determine the minimum flow tube residence time that is required, as discussed above. The use of a FTIR spectrometer, for example, might necessitate a 30 s sampling time which would require a flow tube residence time of at least 600 s. Minimal Depletion. It is also necessary for the concentration of the reactive species generated by the radiation source to be nearly uniform along the length of the flow tube. This condition ensures that the kinetics are measured as a function of the continuously changing reaction time instead of as a function of the changing concentration of the reactive species. This uniformity requires that neither the precursor concentration nor the radiation source intensity are depleted significantly along the length of the flow tube. As a rule of thumb, the precursor concentration should be low enough that the radiation intensity is reduced by no more than 10% at the exit of the flow tube. For the 1 m long flow tube used in the present experiments, a simple Beer’s Law calculation indicates that the product of the precursor concentration and its absorption cross section must be no more than ≈1 × 10−3 cm−1; for example, in the generation of O3 from NO2 photolysis, the NO2 absorption cross section at 355 nm is σ = 5 × 10−19 cm2/molecule,13−15 so no more than ≈2 × 1015 molecules/cm3 of NO2 should be used. Conversely, if the radiation intensity is too large the precursor concentration could be diminished. To deplete no more than ≈10% of the precursor, the photolysis frequency, j, which is the product of the radiation fluence, precursor absorption cross section and photodissociation quantum yield, should be kept below ≈j = 1 × 10−3 s.−1 In the generation of O3 from NO2 photolysis, this requirement means that the laser fluence should be kept below ≈2 × 1015 (photons/cm2)/s. However, NO2 is continually regenerated through the reactions of NO with O3 and O, so laser fluences higher than this can be and are used. Significant depletion of either the precursor or the radiation intensity can be observed experimentally as deviations from an exponential form in plots of the reactant signals vs reaction time. Additional Requirements. Use of the virtual injector method also has the same requirements that other relative rates methods do. Namely, the reactants and precursors must be well mixed. Also, the gas-phase reference compound must react with the reactive species at nearly the same rate as the species being studied. As a rule of thumb, these rates should be within a factor of 3 of one another. Furthermore, the rate constant for the reaction of the gas-phase reference species must be well established so that the relative rate measured can be put on an absolute scale.
detect gas-phase and particle species. However, other radiation sources and methods of detection could be used. In general, the requirements for using the virtual injector method are (1) a radiation source for generating reactive species along the length of the flow tube with minimal temporal variability in the radiation flux, (2) a residence time in the flow tube that is much longer than the sampling time of the detector, (3) a detector (or detectors) that is able to measure relative changes in the concentrations of gas-phase reference and other reactant species, and (4) the precursor gas and the radiation intensity not being depleted significantly along the length of the flow tube. Each of these requirements is discussed in more detail, below. Radiation Source. A radiation source is required because it is necessary that the reactive species be generated throughout the entire flow tube rapidly on a time scale much shorter than the residence time in the flow tube. This source can be either a pulsed or continuous wave laser or a lamp, and it can be directed coaxially with or alongside the flow tube. In the present work the third-harmonic of a 10 Hz pulsed Nd:YAG laser (355 nm) is directed coaxially with, and expanded to fill, the flow tube. The important consideration is that the radiation is able to fill the volume of the flow tube so that the reactive species can be generated throughout with minimal concentration gradients. Some sort of shutter is needed to allow the light to be introduced to or blocked from the flow tube, and the source fluence must be stable over the course of the experiment (i.e., the residence time in the flow tube) to minimize temporal variability in the reactive species concentration. The fluence of 355 nm light from the Nd:YAG laser used here has a shot-toshot variability of no more than 10%. Finally, the source must have sufficient intensity at the wavelength(s) used to photodissociate the precursor efficiently. The exact intensity required will depend on the specific details of the experiment, including the precursor concentration and cross section, residence time, and magnitude of the rate constant to be measured. Residence Time. It is recommended that the residence time in the flow tube be much longer than the sampling time required by the detector. The ratio of the residence time to the sampling time will determine how many different contact times (i.e., injector positions in analogy to the movable injector method) can be obtained in a kinetic decay. Though it is still possible to measure the rate of a reaction if the residence time is much shorter than the sampling time, it would be based on a kinetic “decay” consisting of a single reaction time. Thus, as a rule of thumb, a minimum of 20 different decay times is recommended; in the experiments described here, the sampling time to collect a complete mass spectrum is 0.5 s, so a residence time of at least 10 s is needed. In practice, much longer times are used (66−100 s), providing many more data points (132− 200) from which to construct the decays. The maximum residence time that can be used is determined by the minimum total flow through the flow tube, which is limited by the sampling flow required by the detector. In these experiments, the smallest sampling flow rate is 0.6 SLPM corresponding to a maximum residence time of 200 s for the 2 L flow tube. The residence time can be increased by increasing the flow tube volume, reducing the sampling flow rate while maintaining the sampling flow of the detector, or reducing the flow rate inside the flow tube to below the sampling rate while introducing a dilution before the sampling inlet sampling (though this will reduce detection sensitivity). 6667
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The use of the gas flow as a virtual injector also makes it possible to follow the progress of the reaction as a function of reaction time instead of reactant concentration, as is often done, especially in studying gas−particle kinetics. This distinction can be important because the rates of a reaction derived in these two ways may not be comparable. For example, the rate of a reaction may be a function of radical or O3 concentration if mass transport in the particles is limiting or if secondary chemistry involving transient species contributes to the loss of one or more particle species. The virtual injector method also makes it possible to study reactions of all four major oxidants of organic species in the troposphere, O3, NO3, OH, and Cl, using photolysis of suitable precursors. Similar studies with a movable injector would be possible, though it would be more difficult to introduce high concentrations and ensure good mixing of some of the reactive species. Furthermore, it is possible to generate these species with the virtual injector method using a single wavelength (e.g., 355 nm), which makes it easier to study the kinetics of the different reactants with a single light source. Another advantage of the virtual injector method is that the experiments can be carried out in a relatively short amount of time as determined by the residence time of the flow in the flow tube. In the experiments presented here, this time is as short as 1 min, and when the laser is blocked, the recovery of the signal can also be used to derive kinetic data. Thus, two reactive decays can be collected in as little as 2 min. A similar approach using a Teflon bag or an environmental chamber would require much longer times proportional to their volumes, though it would be possible to use lower concentrations of reactants in that case. Finally, the measurement of relative rates makes it possible to monitor the loss of multiple species simultaneously, which can be especially useful when the reactions of complex, multicomponent aerosol particles are studied, as demonstrated with the reactions of olive oil particles (see “Reactive Uptake by Mixed Particles: Olive Oil”). Conversely, absolute methods in which the loss of the radical or O3 species is monitored can only be used to measure the rate constant of a single reaction in the absence of other reactive species. The measurement of relative rates also eliminates complications arising from competitive cross reactions between radical species because both the gas-phase reference reaction and the reaction to be measured are affected equally. Potential Limitations of Virtual Injector Method. Despite the many advantages of the virtual injector method, its use is limited in several respects as well. First of all, though it is possible to use it to measure absolute rates of reaction, doing so would require measuring the absolute concentration of the reactive species and assuming that this concentration was uniform throughout the flow tube. In practice, it is much more convenient to use the virtual injector method to measure rates relative to a reference reaction. Consequently, the accuracy of a measured rate constant or uptake coefficient is limited by the accuracy of the reference rate constant, and in many cases this can be the limiting source of accuracy. It can also prove to be difficult to find an appropriate gas-phase species to use as a reference because it must meet several criteria; it must (1) react with the radical or O3 at a similar rate as the species to be measured, (2) not absorb strongly the light that is being used to initiate the reaction (355 nm in the present experiments), (3) not react with the precursor species used to photogenerate the radical or O3, and (4) be able to be detected at the same time
In measuring gas−particle heterogeneous uptake coefficients it can be even more difficult to find a suitable gas-phase reference because the finite particle size reduces the efficiency of the reaction compared to a similar gas-phase reaction. For example, the reaction of Cl with a 100 nm spherical oleic acid particle (with a density of 0.9 g/cm3 and a molecular weight of 282 g/mol) might have an uptake coefficient as high as 1.0 (i.e., every Cl−particle collision results in reaction), but the corresponding effective second-order rate constant is only 3.3 × 10−12 (cm3/molecule)/s. The rate constant for reaction between Cl and a normal alkane, such as n-decane, is 5.5 × 10−10 (cm3/molecule)/s,18 i.e., at the gas-kinetic collision rate and approximately 167 times larger than the Cl−particle reaction. Thus, even though the molecules are similar structurally, the gas-phase alkane reacts too fast to be a useful reference species. Instead, a slower reaction must be used, and for this reason acetone [k = 2.07 × 10−12 (cm3/molecule)/s]19 was used as the gas-phase reference for the oleic acid + Cl uptake measurement in the present work. If the uptake coefficient is much lower than 1.0, a reference reaction with an even lower rate constant is required. For many hydrogenabstraction reactions, deuteration provides a way to systematically slow the rate of reaction, and for this reason we have measured the rate constant for Cl plus fully and partially deuterated acetone (see “Gas-Phase Relative Rates Measurements”). The rate constants span a range from k = 3.93 × 10−13 (cm3/molecule)/s for Cl + acetone-d6 to k = 1.83 × 10−12 (cm3/molecule)/s for Cl + acetone-d1, a range in which few other Cl reactions fall. Advantages of Virtual Injector Method. There are several advantages to using the virtual injector method for measuring kinetics, especially gas−particle uptake kinetics. First of all, any losses of the reactants to the walls of the flow tube are accounted for because they are not coupled to the reactions taking place. The reactants always flow down the entire length of the flow tube regardless of how long they react with the radicals or O3, so the fractional loss to the walls is independent of the extent of reaction. In a movable injector experiment, on the other hand, the loss to the walls changes when the extent of reaction is varied by moving the injector. Consequently, the rates of loss to the walls of each species must be measured. Similarly, kinetics measured in an environmental chamber must be corrected for wall loss. Not only do the wall losses not have to be measured when the virtual injector method is used, but it also is not even necessary to assume that the wall loss rates are constant along the length of the flow tube or that they are the same for each species. Thus, it is possible to measure the relative rates of reaction of species with very different volatilities without explicitly measuring the wall losses. This advantage is also beneficial in measuring the rates of reaction of particles which can have appreciable losses to the walls of the flow tube. A derivation of the relative rate equation including wall loss is presented in the Supporting Information, and from this derivation it can be seen that as long as the rate of wall loss is not coupled to the extent of reaction and it does not change over the course of the experiment (i.e., a few minutes), the wall loss cancels out and can be ignored. Another advantage of this method is that the reactions can be carried out under nearly pseudo-first-order conditions because the reactants are continually regenerated down the entire length of the flow tube. This ability makes it possible to study reactions even when the radical or O3 concentrations are smaller than those of the other gas-phase or particle reactants. 6668
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that the other reactant(s) is (are) detected. Another limitation of the virtual injector method is that the radical or O3 must be generated from photodissociation of a precursor species. Although it has proven possible to accomplish this for O3, NO3, OH, and Cl, there are other reactive species that may prove more difficult, if not impossible, to generate in this way. For example, it would be difficult to study reactions of N2O5 using a photolysis source because there would also be significant amounts of NO3 radicals present. Thus, it is not possible to study reactions if more than one reactive species is present.
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EXAMPLES USING THE VIRTUAL INJECTOR METHOD Measurement of Relative Rates of Reaction. In a typical experiment the fractional reactive losses of a gas-phase reference species and one or more gas-phase or particle species are monitored from the corresponding peak areas in the mass spectra. An example of one experiment is shown in Figure 2a in which isoprene (m/z = 98 amu) and α-pinene (m/z = 166 amu) react with OH generated when the 355 nm radiation is introduced. The behaviors of the two corresponding signals illustrate several important aspects of the virtual injector method. First of all, the fact that the signals decrease as soon as the radiation is introduced confirms that the gases near the exit of the flow tube are reacting with OH. If OH were not created there, for example, if the radiation was attenuated significantly by the HONO precursor, then a delay would be observed. Second of all, the signals decay for the entire 66 s residence time as calculated from the bulk linear flow velocity (1.5 cm/s in this experiment). Thus, the gases at the entrance of the flow tube are reacting, too. Third, the decays are nearly exponential, indicating that the reactions are almost pseudo-first-order with a nearly uniform OH concentration throughout the entire length of the flow tube. An OH concentration gradient could result for several reasons including attenuation of the 355 nm radiation, depletion of the HONO precursor or wall losses of any of the species, but it would manifest itself as a nonexponential decay. Fourth, the recovery of the signals when the radiation is removed also provides useful kinetic data because it represents the reverse experiment in which the reaction time is continuously decreased. Gas-Phase Relative Rates Measurements. From the simultaneous decays of the gas-phase reactive and reference species, it is possible to measure bimolecular rate constants through the well-established relative rates method: ⎛ [X] ⎞ ⎛ [R] ⎞ k −ln⎜ ⎟ = − X ln⎜ ⎟ kR ⎝ [R]0 ⎠ ⎝ [X]0 ⎠
Figure 2. (a) CIMS signals of isoprene and α-pinene demonstrating decays when the reaction with OH radicals is initiated by introducing the laser into the flow tube. (b) ln−ln plot of the α-pinene and isoprene signals from the decays in (a) yields a slope of 0.53 which is the ratio of the rate constants.
+ isoprene rate constant determined in previous studies (kR = 1.00 × 10−10 (cm3/molecule)/s),20 the rate constant for OH + α-pinene is measured to be 5.38 (±0.30) × 10−11 (m3/ molecule)/s. This value is in good agreement with previous measurements of 5.45 × 10−11 (cm3/molecule)/s21 and the value of 5.3 × 10−11 (m3/molecule)/s recommended by the IUPAC Subcommittee on Gas Kinetic Data Evaluation at 298 K.20 As a validation of this method, rate constants for several gasphase organic species reacting with O3, NO3, OH, and Cl were measured using various reference species (see Supporting Information Table S1). The measured rate constants are shown in Figure 3 plotted vs values taken from the literature and demonstrate very good agreement for most species spanning a range of more than 5 orders of magnitude. As with any relative rates measurement, the uncertainty in the measured rate constant is limited by the accuracy of the published rate constants of the reference species. The notable exceptions to
(1)
where [X]/[X0] is the fraction remaining of the gas-phase reactive species being measured after a given amount of reaction time, [R]/[R0] is the fraction of the gas-phase reference species remaining, and kX and kR are the rate constants for the corresponding reactions with the photogenerated radical or O3. Thus, from the slope of a ln−ln plot of the relative concentrations the ratio of rate constants can be obtained, and from a knowledge of the gas-phase reference rate constant, kR, the value of kX can be calculated. An example of this type of plot is shown in Figure 2b for the reaction of OH with α-pinene and the gas-phase reference isoprene. From the slope of the linear fit (=kXkR = 0.53) and knowledge of the OH 6669
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Figure 3. Comparison of measured rate constants with those from the literature for gas-phase reactions of a variety of species with O3, NO3, Cl, and OH. The high level of agreement is demonstrated by the proximity of the data points to the 1:1 line.
Figure 4. Rate constants for the reactions of deuterated isotopologues of acetone with Cl measured relative to that of undeuterated acetone as measured by Zhao and co-workers.19 The measured kinetic isotope effect is 5.4 as determined from the linear fit to the data.
to H-abstraction. There are no values for these rate constants in the literature to which to compare, but Wine and co-workers measured the rate constant for the Cl + acetone-d6 reaction to be 3.94 (±0.25) × 10−13 (cm3/molecule)/s using an absolute method (resonance fluorescence detection of Cl radicals),23 in very good agreement with the value measured in this work, k = 3.93 (±0.71) × 10−13 (cm3/molecule)/s. The measured kinetic isotope effect (kH/kD = 5.4) is also similar to values reported for the OH + acetone/acetone-d6 reaction (5.33,24 5.15,25 5.926 and 6.027 at 298 K). The fact that these rate constants span the range from 4 − 20 × 10−13 (cm3/molecule)/s could make the acetone isotopologues useful as reference species for measuring the kinetics of slower Cl reactions including those with aerosol particles for which effective rate constants are generally 3 × 10−12 (cm3/molecule)/s and smaller (for a particle diameter of 100 nm). Aerosol Reactive Uptake Measurements. Reactive Uptake by Single-Component Particles: Oleic Acid. It is also possible to measure the rate of reaction of a particle species relative to a gas-phase reference reaction with the virtual injector method. However, because the effective rate constant, kX, obtained from the observed loss of the particle species depends on many factors, including particle shape and size, it is often more useful to express the efficiency of a reaction in terms of a reactive uptake coefficient, γ. This uptake coefficient is unitless and represents the fraction of gas−particle collisions that results in reactive loss. The uptake coefficient can be calculated from the measured fractional rate of loss of the particle species, X:
the good agreement are the rate constants for the reactions of OH with methacrolein and 1-octene, which are 28% and 31% lower than the literature values, respectively. Each of these experiments was performed using α-pinene as the gas-phase reference, so it is possible that the discrepancy could be attributed to the rate constant used for that reaction, kR = 5.45 × 10−11 (cm3/molecule)/s.21 However, the reaction of OH + α-pinene has been studied extensively by many researchers using a variety of techniques (see evaluation of Atkinson et al.20 and references therein), and it seems unlikely that it could be in error by as much as 30%. Furthermore, the measurement of 2methyl-2-butene + OH was also made using α-pinene as the gas-phase reference species, and the rate constant was found to be in very good agreement with the literature value (within 5%). Thus, the reason for the discrepancies in these two rate constants remains unresolved, but given the good agreement in all of the other measurements they do not appear to invalidate the virtual injector method. Because the reactions are carried out under nearly pseudofirst-order conditions with respect to the radicals or O3, the kinetics are measured by following the losses of the other gasphase reactants. Consequently, it is possible to measure simultaneously the rates of reaction of multiple species with the same radical or O3. As a demonstration of the usefulness of this aspect of the method, the rates of reaction of Cl radicals with a mixture of acetone and the various deuterated isotopologues of acetone, acetone-d1 to acetone-d6, were measured simultaneously (see Figure 4 and Supporting Information Table S1). The Cl + acetone reaction was used as the reference reaction because it has been studied by several researchers (see evaluation of Atkinson et al.20 and references therein as well as the recent work of Romanias et al.22) and its rate constant is well-known (k = 2.07 (±0.31) × 10−12 (cm3/ molecule)/s19). The rate constant for the acetone-d2 + Cl reaction could not be measured because a product ion appeared at the same m/z as acetone-d2, likely from reaction of Cl with the flow tube walls, which is difficult to account for quantitatively. The rate constants exhibit a decrease with increasing deuterium substitution consistent with the larger zero-point corrected energy barrier to D-abstraction compared
γ=
d([X][X 0]) 1 4RT V [X 0] dt [Y] c ̅ SA
(2)
where [Y] is the concentration of the gas-phase reactive species, R is the gas constant, T is the temperature, c ̅ is the mean speed of the gas-phase reactant, and V/SA is the volume-to-surfacearea ratio.6 Note that this formulation will differ from the reactive uptake coefficient calculated from the rate of loss of the gas-phase species if there are other reactions that involve the particle species. This has been demonstrated explicitly for the O3 + oleic acid particle reaction28,29 as reviewed by Zahardis 6670
dx.doi.org/10.1021/jp303221w | J. Phys. Chem. A 2012, 116, 6664−6674
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the loss of oleic acid in a manual injector flow tube. Similarly, the reaction of OH with oleic acid particles is found to occur at nearly the OH−particle collision rate with γ = 0.40 (±0.03), and this value agrees relatively well with the value of γ = 0.24 (±0.10) from the only other study to have measured it39 (from OH scattering off of an oleic acid film). Such large values have also been found in previous studies of OH reaction with other organic aerosols, including uptake to erythritol (γ = 0.75),40 levoglucosan (γ = 0.9140), and squalane (γ = 0.28,41 γ = 0.30,32,39 γ = 0.5142). Likewise, the large uptake coefficient measured here for reaction of Cl with oleic acid particles, γ = 1.23 (±0.16), is consistent with the value measured previously for Cl reaction with dioctyl sebacate particles (γ = 1.7 ± 0.3).43 Note that the values greater than 1 may be indicative of secondary loss processes for the particle species after the initial reaction with the radicals. For example, secondary chemistry involving the reaction of Cl2 with particle-phase radical species has been observed in the Cl radical initiated oxidation of 2octyldodecanoic acid, leading to reactive uptake coefficients greater than unity at high [Cl2].41 The reaction of oleic acid with O3 has been studied extensively, and the uptake coefficient measured here, γ = 8.1 (±0.9) × 10−4, is in fairly good agreement with values from previous studies, γ ∼ 1.4 × 10−3 5,28,44 and γ = 6.1 × 10−4,45 in which the rates were also measured from oleic acid loss. Other studies in which O3 loss to oleic acid surfaces was measured have yielded values of γ = 8 × 10−4,4,46,47 and the difference between these measurements and the widely accepted value of the reactive uptake measured by oleic acid loss (γ ∼ 1.4 × 10−3) has been attributed to secondary chemistry, which enhances the rate of loss of oleic acid compared to the rate of loss of O3. Perhaps, then, the lower value obtained in the present study reflects the true rate of ozonolysis with minimal interference from the secondary chemistry, possibly because of the longer reaction times and lower O3 concentrations used. Alternatively, the adsorption of the gas-phase reference compound (bicyclo(2,2,1)-2-heptene), the OH scavenger (cyclohexane), or the O3 precursor (NO2) to the particle surface could slow the rate of reaction in the particle. In fact, recent work from this lab has demonstrated that oxidant precursors (such as O3 in the photogeneration of OH) can inhibit the rate of reaction with liquid organic particles by up to a factor of 2.41 It is not unlikely, therefore, that other species may effectively hinder O3 reactions at the particle surface. It is also possible that the measured uptake coefficient is lower than the widely accepted value measured by oleic acid loss because the rate constant for the gas-phase reference (bicyclo(2,2,1)-2-heptene) reacting with O3 is low, though it was measured in the present work and agrees well with the previously published value.18 Finally, the measured uptake coefficient could be low if OH radicals produced from ozonolysis are not scavenged completely by the cyclohexane scavenger; these OH radicals would react with the gas-phase reference, bicyclo(2,2,1)-2-heptene, at a rate approximately 100 times faster than with the oleic acid particles. Consequently, even a small concentration of OH could enhance the rate of loss of the gas-phase reference and cause the observed rate of loss of the oleic acid to appear too slow. Reactive Uptake by Mixed Particles: Olive Oil. Because the gas−particle reactive uptake kinetics are derived from the observed loss of the particle species, it is also possible to measure the rates of reaction of several different particle species simultaneously. Such a method makes it straightforward to
and Petrucci,30 for example, where reactions subsequent to ozonolysis contribute to the depletion of oleic acid. To use eq 2, the fractional rate of loss of X needs to be measured, which requires an explicit knowledge of [X]/[X0] as a function of time. Furthermore, the absolute concentration of the gas-phase reactant, Y (O3, NO3, OH, or Cl in the present experiments), needs to be known because the collision rate of Y with the particle is proportional to this concentration. However, in making mixed-phase relative rates measurements, as is done in the present work, it is not necessary to know the reaction time or the concentration of the gas-phase species explicitly because the observed rate of loss of the gas-phase reference species, R, serves as an in situ measure of both of these factors.2,31 An effective bimolecular rate constant for the gas− particle reaction, kX, can be measured from the slope of a ln−ln plot of the relative concentrations of the particle species, X, and the gas-phase reference, R, using eq 1. From kX a reactive uptake coefficient can be calculated:32
γ=
4kXρ0 NA S
c ̅ VA MX
(3)
Here, ρ0 is the initial density of the particle, NA is Avogadro’s number, c ̅ is the mean speed of the reactive radical or O3, SA/V is the surface area-to-volume ratio of the particle, and MX is the molar mass of X. If the particle is spherical, the SA/V ratio is 6/ d, where d is the diameter of the particle. When a log-normal distribution of spherical particles is used, this ratio is 6/dsurf, where dsurf is the surface-area-weighted mean diameter.32 It should be noted that eq 3 is only valid for the reaction of onecomponent particles because the initial concentration of species X is required (in the form of ρ0 and MX). If reactive uptake coefficients of multicomponent particles are to be measured, then the concentrations of individual species in the particles need to be known. To demonstrate the feasibility of measuring reactive uptake coefficients with the virtual injector method, the reactions of oleic acid particles with OH, Cl, NO3, and O3 were studied (Table 2). Oleic acid is a good species with which to validate Table 2. Measured Reactive Uptake Coefficients of the Four Reactive Species with Oleic Acid Particles reactive species
γpart (±2σ)
gas-phase reference
O3 NO3 OH Cl
8.1 (±0.9) × 10−4 0.14 (±0.03) 0.40 (±0.03) 1.23 (±0.16)
bicyclo(2,2,1)-2-heptene8,33 isoprene8,34 3-hexanone35 methanol8,20
this method for measuring heterogeneous kinetics because it forms spherical liquid particles (with a well-defined surfacearea-to-volume ratio), has a low vapor pressure such that the particles do not evaporate, and its reactions with O3, NO3, and OH have been studied previously. The reaction of NO3 with oleic acid particles is found to be very efficient with an uptake coefficient of γ = 0.14 (±0.03). This value is in good agreement with other studies that have reported the reactive uptake of NO3 on oleic acid particles. For ⎛+0.82 ⎞ ⎟ by measuring example, Gross et al.36 report γ = 0.18 ⎜ ⎝−0.11 ⎠ NO3 loss. Unpublished data by Paul Ziemann also suggests that the reactive uptake of NO3 by oleic acid particles is fast with γ = 0.13 ± 0.02.37 Zhao et al.38 have measured γ = 0.27 (±0.06) by 6671
dx.doi.org/10.1021/jp303221w | J. Phys. Chem. A 2012, 116, 6664−6674
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From the initial slopes of the decays during the first 25% of reaction, effective second-order rate constants, kX, are derived on the basis of previous measurements of the respective gasphase reference rate constant. Reactive uptake coefficients for each of the species cannot be calculated from the values of kX using eq 3 because their concentrations in the olive oil particles are unknown. However, the effective rate constants can be used to compare the reactivity of the different components with all four of the reactive species, O3, NO3, OH, and Cl, and are listed in Table 3. Because the effective rate constants measured in this way are functions of the particle surface-area-to-volume ratio, and therefore of particle size, the rate constants in Table 3 have been normalized to a particle size of 100 nm for intercomparison. From these rate constants it can be concluded that oleic acid and squalene react at similar rates for all of the reactant species with squalene reacting approximately 3−5 times faster. This is not surprising in the case of the O3 reaction where a double bond is required for reaction to occur because squalene is a polyunsaturated molecule with six double bonds whereas oleic acid contains only one. Although reaction of OH, Cl, and NO3 may occur with species lacking double bonds, the presence of a double bond, in most cases, leads to a faster reaction.8 What is more surprising is that the relative reactivity of these two species in the olive oil particles cannot be predicted from the pure oleic acid and squalene kinetics. For example, squalene particles react with OH radicals 13 times faster than oleic acid particles do; however, when mixed together in olive oil particles, squalene only reacts 3 times faster than oleic acid. It is not clear why these species react at different relative rates when mixed, but it may be related to the mixing state of the particles, for example, if oleic acid resides preferentially at the surface of the mixed particles compared to squalene. Alternatively, it may be that the rate of loss of oleic acid is enhanced in the presence of the other constituents in the olive oil particles, perhaps through a radical-chain mechanism involving alkoxy or alkyperoxy radicals derived from the oxidation of the other organic species. Evidence supporting such an enhancement can be seen in the effective rate constants measured for oleic acid reacting with OH: in pure particles, kX = 1.9 × 10−12 (cm3/molecule)/s (derived from an uptake coefficient of γ = 0.40 for a 100 nm diameter particle), whereas in olive oil particles, kX = 3.5 × 10−11 (cm3/molecule)/s (normalized to 100 nm particle diameter) representing an increase of more than a factor of 18. Smaller enhancements are also observed for the reactions of NO3 radicals (3×) and Cl radicals (6×) with oleic acid in olive oil particles compared to
compare the relative rates of reaction of individual species in homogeneously mixed particles and to measure the kinetics of key species such as molecular markers in complex particles that resemble ambient aerosols. Alternative approaches in which the loss of the reactive gas-phase species to particles or a bulk surface is measured cannot be used for this purpose because only the aggregate rate of loss of the radical or O3 can be measured. As a demonstration of the usefulness of the virtual injector method for measuring uptake kinetics of mixed particles, reactions of olive oil aerosol with O3, NO3, OH, and Cl were carried out. Olive oil was chosen because it is a liquid at room temperature forming spherical particles, and though it is chemically complex it is known to contain large amounts of oleic acid and squalene,48 which appear in the proton-transfer mass spectrum at m/z = 283 and m/z = 411, respectively (Figure 5). The rates of loss of these species as well
Figure 5. Aerosol CIMS mass spectrum of olive oil particles. Peaks at m/z = 287 and m/z = 411 represent oleic acid and squalene, major constituents of olive oil. The identity of the component represented by the peak at m/z = 397 is undetermined. The loss of all three of these peaks was followed upon reaction with O3, NO3, Cl, and OH from which effective second-order rate constants were determined.
as of an unknown component represented by peaks at m/z = 397 (with proton-transfer ionization) and m/z = 426 (with NO+-adduct ionization) were measured with all four reactive species.
Table 3. Effective Rate Constants of Olive Oil Constituents with the Four Gas-Phase Reactive Species: O3, NO3, OH, and Cl Normalized to a Particle Diameter of 100 nma reactive species O3 NO3 OH Cl
keff(oleic acid) [(cm3/molecule)/s] −15
2.1 × 10 2.3 × 10−15 1.1 × 10−12 3.5 × 10−13 3.5 × 10−11 1.9 × 10−12 2.6 × 10−11 4.1 × 10−12
keff(squalene) [(cm3/molecule)/s]
keff(m/z = 397 or 426) [(cm3/molecule)/s]
gas-phase reference
−15
