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Potentially important nighttime heterogeneous chemistry: NO3 with aldehydes and N2O5 with alcohols Iannone, Richard; Xiao, Song; Bertram, Allan K. 2011

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10214 Phys. Chem. Chem. Phys., 2011, 13, 10214–10223 This journal is c the Owner Societies 2011 Cite this: Phys. Chem. Chem. Phys., 2011, 13, 10214–10223 Potentially important nighttime heterogeneous chemistry: NO3 with aldehydes and N2O5 with alcohols Richard Iannone, Song Xiao and Allan K. Bertram* Received 3rd February 2011, Accepted 22nd March 2011 DOI: 10.1039/c1cp20294d We report the first measurements of the reactive uptake of NO3 with condensed-phase aldehydes. Specifically, we studied NO3 uptake on solid tridecanal and the uptake on liquid binary mixtures containing tridecanal and saturated organic molecules (diethyl sebacate, dioctyl sebacate, and squalane) which we call matrix molecules. Uptake on the solid was shown to be efficient, where g = (1.6  0.8)  102. For liquid binary mixtures the reactivity of aldehyde depended on the matrix molecule. Assuming a bulk reaction, Hmatrix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dmatrixk2;aldehyde p varied by a factor of 2.6, and assuming a surface reaction HSmatrixKSmatrixkS2;aldehyde varied by a factor of 2.9, where Hmatrix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dmatrixk2;aldehyde p and HSmatrixKSmatrixkS2;aldehyde are constants extracted from the data using the resistor model. By assuming either a bulk or surface reaction, the atmospheric lifetimes for aldehydes were estimated to range from 1.9–7.5 h. We also carried out detailed studies of N2O5 uptake kinetics on alcohols. We show that uptake coefficients of N2O5 for five different organics at 293 K varied by more than 2 orders of magnitude, ranging from 3  104 to 1.8  102. We show that the uptake coefficients correlate with ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DalcoholðOH concentrationÞp but more work is needed with other alcohols to completely understand the dependence. Using this kinetic data we show that the atmospheric lifetime of alcohols with respect to N2O5 heterogeneous chemistry can vary from 0.6–130 h, depending on the physical and chemical properties of the organic liquid. 1. Introduction Liquid and solid aerosol particles are abundant in the troposphere and field measurements have shown a broad variety of particulate material, both organic and inorganic. The organic fraction can comprise 10–90% of the total aerosol mass in the troposphere.1–3 This organic material can be in the form of pure organic particles, or alternatively the organic material can be mixed with inorganic material.4–7 The composition of condensed-phase organic material is very diverse, with hundreds to thousands of different organic compounds identified.8–11 Some of the component classes in the organic fraction include alkanes,12,13 alcohols,12,14,15 alkanoic and alkenoic acids,12,15,16 dicarboxylic acids,17–20 polycyclic aromatic hydrocarbons (PAHs),21–23 and aldehydes.24,25 Organic particles or mixed organic–inorganic particles, whilst in the atmosphere, experience reactions with gas-phase species that may lead to the modification of the particle or coating composition. These heterogeneous reactions can have a number of effects. For example, they may lead to toxic or carcinogenic compounds.8,26 These reactions may be a loss pathway of organic compounds in the atmosphere.26–31 Under certain conditions, these reactions may be an important sink for gas-phase species.32 Also, these reactions can lead to volatilisation of organic particulate matter33–36 and are a source of volatile organic compounds (VOCs) in the atmosphere.28,37,38 Hetero- geneous reactions may also have implications for source apportion- ment. Specific organic species often serve as molecular markers for probing sources of organic particles. If heterogeneous reactions change the concentrations of the selected molecular markers they can lead to errors when calculating source strengths.39 Recently heterogeneous reactions between organic particles and OH,27,28,33,40 O3,41–47 and Cl29,48,49 have received signifi- cant attention. In addition, some studies have focused on heterogeneous reactions between organic particles and NO3 32,50–56 and N2O5,52,57–60 important nighttime species. NO3 is formed by the gas-phase reaction of NO2 with ozone.61 Concentrations of this radical range from o10 pptV to 430 pptV.62–67 N2O5 is present in equilibrium with gas-phase NO2 and NO3 and can reach concentrations of up to approxi- mately 15 ppbV.68 Recently, we investigated the reactive uptake of N2O5 on a range of organic substrates including oleic acid, diethyl sebacate, glycerol, and linoleic acid.52 That study showed that the reactive uptake coefficient of N2O5 on liquid glycerol is relatively large with a value of (3.2–8.5)  104, suggesting that N2O5 hetero- geneous reactions with alcohols may be atmospherically relevant. However, the N2O5–alcohol uptake results from Gross et al.52 Department of Chemistry, University of British Columbia, Vancouver, British Columbia, Canada PCCP Dynamic Article Links www.rsc.org/pccp PAPER Downloaded by The University of British Columbia Library on 07 December 201 1 Published on 21 April 2011 on http://pubs.rsc.org | doi:10.1039/C1CP20294 D View Online / Journal Homepage / Table of Contents for this issueThis journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 10214–10223 10215 only examined one alcohol compound, glycerol, thus additional studies with other alcohols are also needed to determine the generality of the results. We have also recently explored the reactive uptake of NO3 on a range of organic substrates with diverse functionalities.51–54,57 One reaction class that has not been studied, however, are those reactions of NO3 with condensed phase aldehydes. This reaction is known to be fast in the gas-phase and so the expectation is that it will also be fast in the condensed phase. We have determined in this investigation the kinetics for N2O5 reactions with alcohols and NO3 reactions with aldehydes. This information is then used to assess the lifetime of alcohols and aldehydes in the condensed phase in the atmosphere. For the N2O5 reactions we studied the uptake on five different liquid alcohols at 263–303 K. For the NO3 reaction we studied the kinetics with the C13 aldehyde tridecanal. The uptake of NO3 on the solid C13 aldehyde was determined at (263  1) K. For the pure aldehyde we were limited to this temperature since the vapour pressure of the aldehyde was high. To explore the reactions of NO3 with aldehydes in the liquid state we studied several binary mixtures of tridecanal with diethyl sebacate (DES), dioctyl sebacate (DOS), and squalane. DES, DOS, and squalane react slowly with NO3 and will be referred to as matrix compounds within this paper. By using binary mixtures where the concentration of the aldehyde is less than approximately 5.5% w/w, the overall partial pressure of the aldehyde in the gas phase was reduced (which is a practical requirement for these flow tube studies). The study of binary mixtures also has the added advantage in that we could assess the importance of the matrix molecules on the NO3–aldehyde kinetics. 2. Experimental 2.1 Rotating-wall flow tube and chemical ionisation mass spectrometer (CIMS) Uptake experiments were conducted in a cylindrical, rotating-wall flow tube reactor coupled to a CIMS. The setup and procedure of the experiments are similar to several recent studies.54,57,69 The flow tube was composed of borosilicate glass. The inside wall of a Pyrex tube (12 cm length, 1.77 cm I.D.) provided a surface for a thin coating of the studied liquid or solid. Total pressures in the flow cell during experiments were 2–4 Torr whereas flow velocities ranged from 480–600 cm s1. Fast flow rates of the carrier gas were chosen to reduce the extent of corrections for axial diffusion. The carrier gas through the cell was a mixture of O2 (B10–15%) in He. NO3 or N2O5 was added through a movable injector whereby the reactive distance, and thus the reaction time, could be quickly changed. The injector position was moved in one centimetre increments every 40–60 s during an experiment to expose an increasing surface area of the organic coating to NO3 or N2O5. For liquid experiments, approximately 0.5–1 mL of liquid was distributed onto the inner wall of the rotating glass cylinder (at a rotation rate of B10 rotations min1). This produced a uniform film approximately 0.5 mm thick. For solid experiments, a liquid was distributed onto the inner wall glass cylinder and then the temperature was decreased to below the freezing point while the inner wall of the glass cylinder was continuously rotated. 2.2 Procedures for NO3 and N2O5 uptake experiments N2O5 was generated by reacting NO2 with an excess amount of O3 in a flow system as described by Schott and Davidson70 and Cosman et al.71 Pure O2 was passed through an ultraviolet light source (Model 600 Ozone Generator, Jelight, Irvine, CA) to generate the O3 necessary for N2O5 production.70,71 N2O5 was trapped and stored as solid white crystals at 197 K. N2O5 was detected as NO3 in the mass spectrometer after chemical ionisation by I, generated by passing a trace amount of CH3I in N2 through a 210Po source (model Po-2031, NRD). The average N2O5 concentration inside the flow tube was estimated at (3.6–8.5)  1011 molecules cm3 based on the rate constant for the gas-phase N2O5 + I reaction.72 The uncertainty of the N2O5 concentration was approximately 40% based on the uncertainty of the ion molecule reaction rate constant. NO3 radicals were obtained by thermal conversion of gaseous N2O5 to NO3 and NO2 at 430 K in a Teflon coated glass oven before entering the movable injector. Approximately 20% of the NO3 thermally dissociates in the Teflon coated glass oven based on well-known gas-phase reaction rates and modelling studies using the Acuchem chemical kinetics simulation program. NO3 was also detected as NO3 in the mass spectro- meter after chemical ionisation by I.53 NO3 concentrations were estimated at (3.5–16)  1010 molecules cm3 through the assumption that all N2O5 is converted to NO3 and NO2. Quantitative conversion of N2O5 to NO3 and NO2 in the oven was confirmed by adding high levels of NO to the exit of the flow tube. This conversion by NO also served as a convenient way to quantify the background signal in the NO3 experi- ments. NO was added in excess which completely titrated NO3 to NO2. Any remaining signal at mass 62 after titration by NO was assigned to the background. The background signal was typically less than 5% of the total signal. Since the residence time for NO3/N2O5 inside the flow tube is very short (B50 ms), no biases are expected due to equilibrium processes between the two species (i.e., the time for NO3 and N2O5 to approach equilibrium is on the order of 1 min). 2.3 Determination of reactive uptake coefficients (c) From the collected CIMS traces, plots were generated for the natural logarithm of the depletion of the NO3 or N2O5 signal as a function of reaction time. The slopes of the linear fits were used to determine the observed first-order loss rate coefficients, kobs. Corrections for both radial and axial diffusion were applied to all kobs values using the formulations described by Brown73 and Howard,74 respectively. Reactive uptake coefficients (denoted by g) were calculated from the corrected rate constants, kcorr, using a procedure described by Knopf et al.75 Diffusion coefficients used within these calculations were taken from Rudich et al.76 and Knopf et al.69 The two main sources of uncertainty for the uptake coefficient measurements were the gas-phase diffusion coefficients of NO3 and N2O5 and the measurement of kobs. We calculated the error from gas phase diffusion by assuming a 20% uncertainty of these diffusion coefficients. This uncertainty determined Downloaded by The University of British Columbia Library on 07 December 201 1 Published on 21 April 2011 on http://pubs.rsc.org | doi:10.1039/C1CP20294 D View Online10216 Phys. Chem. Chem. Phys., 2011, 13, 10214–10223 This journal is c the Owner Societies 2011 for the NO3 uptake experiments is based on the those reported by Rudich et al.,77 where the uncertainties of the gas-phase diffusion coefficients for NO3 in helium is B8% and that for NO3 in O2 is B20%. In our study, the carrier gas is a mixture of He and O2. We used the larger uncertainty (20%) as the uncertainty for the NO3 gas phase diffusion coefficient in the He-O2 mixture. The uncertainty for N2O5 uptake experiments is also assumed to be 20% (see Knopf et al.69 and references therein). For the uncertainty of kobs, we used the standard deviation (1s) of the measurements. Reported errors include both uncertainties. 2.4 Chemicals and gases Tridecanal, (Z 95%), squalane (99%), diethyl sebacate (98%), bis(2-ethylhexyl) sebacate (or dioctyl sebacate) (Z 97.0%), poly(ethylene glycol) (PEG-300 and PEG-400), (+)-diethyl- L-tartrate (>99%), and 1,2,6-trihydroxyhexane (96%) were obtained from Sigma-Aldrich. All chemicals were used as delivered. NO2 (99.5%) was acquired from Matheson while N2 (99.999%), O2 (99.993%), and He (99.999%) gases were procured from Praxair. Fig. 1 provides molecular structures for all organic compounds studied. 3. Results and discussion 3.1 Kinetics of the NO3 reaction with solid tridecanal and liquid binary mixtures of tridecanal and matrix molecules For the uptake of NO3 on pure solid tridecanal at (263  1) K, seven reactive uptake coefficients were measured. The mean g value was determined as (1.6  0.8)  102, where the uncertainty represents the 95% confidence interval. Table 1 provides a comparison of our measured uptake coefficients with those uptake coefficients of NO3 measured on other single component solid surfaces. Table 1 illustrates that indeed the reaction of NO3 with aldehydes is an efficient heterogeneous reaction compared with other heterogeneous substrates. For the classes of organics studied, the following trend is observed: PAHs > alkenoic acids > aldehydes > alcohols > alkanoates. Assuming that the alkenoic acid reaction is due to the carbon- carbon double bond, this trend is roughly consistent with that of measured gas-phase rate constants of NO3 reactions at 298 K: 1010–1013 for PAHs and alkenes, 1014–1015 for aldehydes, 1015–1016 alcohols, and 1016–1018 for alkanoates (all in units of cm3 molecule1 s1).78 Fig. 2 provides results for the uptake coefficient of NO3 on binary liquid mixtures containing the aldehyde. The uptake coefficients with 0 wt% tridecanal represent the reactions of NO3 with pure matrix molecules (DES, DOS, and squalane). For all the matrix compounds studied, the addition of small amounts of tridecanal (o6 wt%) increased g. Also, the increase depends on the type of matrix. For example, at approximately 4.5 wt% tridecanal, the reactive uptake coefficient in DES increased by a factor of 3 but in squalane the g value only increased by a factor of 1.4. To check whether the uptake is a reversible or irreversible, at the end of every experiment the injector was moved to a position where the coated organic mixture was no longer exposed to the NO3 flow. The absence of any release of NO3 indicated that the uptake was irreversible. This irreversibility in uptake also applies to all the N2O5 experiments in section 3.3. 3.2 Analysis of the reactive uptake coefficient data using the resistor model To analyse the uptake results presented in Fig. 2, the resistor model of gas-substrate interactions was used.79 If the reaction occurs in the bulk and the reactive uptake coefficient is not limited by the mass accommodation coefficient (i.e., a c g, where a is the mass accommodation coefficient), then the following equation applies for the binary liquid mixtures (see Appendix): g2mixture  g 2 matrix ¼ ð4HmatrixRTÞ2Dmatrixk2;aldehyde c2NO3 Maldehyde; ð1Þ where gmixture is the reactive uptake coefficient of NO3 in the two-component mixture, gmatrix is the reactive uptake coefficient of NO3 with the pure matrix molecules, Hmatrix is the Henry’s law solubility constant of NO3 in the matrix (mol L1 atm1), R is the gas constant (L atm mol1 K1), T is the temperature (K), Dmatrix is the diffusion coefficient for NO3 in pure matrix molecules (cm2 s1), k21,aldehyde is the bulk second-order rate Fig. 1 Molecular structures for all studied organic compounds. The n value in poly(ethylene glycol) (PEG) depends on the molecular weight (e.g., PEG-300 represents PEG with an average MW of 300 g mol1). Downloaded by The University of British Columbia Library on 07 December 201 1 Published on 21 April 2011 on http://pubs.rsc.org | doi:10.1039/C1CP20294 D View OnlineThis journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 10214–10223 10217 constant for NO3 reaction with the aldehyde (mol L1 s1), cNO3 is the mean molecular velocity of NO3 (cm s1), and Maldehyde is the molarity of the aldehyde in each matrix (mol L1). According to eqn (1), a plot of g2mixture  g2matrix against Maldehyde is expected to yield a straight line. In contrast to eqn (1), if the reaction occurs on the surface and assuming the reactive uptake coefficient is not limited by the adsorption coefficient, the following equation applies for the binary liquid mixtures (see Appendix): gmixture  gmatrix ¼ 4HSmatrixRTKSmatrixkS2;aldehyde cNO3 Maldehyde; ð2Þ where HSmatrix is the surface analogue for the Henry’s law equilibrium for the bulk, KSmatrix is an equilibrium constant linking the surface concentration to the bulk concentration Table 1 Comparison of reactive uptake coefficients for heterogeneous reactions involving solid organic substrates and NO3 radicalsa Class Chemical T, K Reactive uptake coefficient (g) Polycyclic Aromatic Hydrocarbons Benz[a]anthracene 273–297 1.0–66  102b Pyrene 273–297 >8.0  102b,c Fluoranthene 273–297 >2.0  102b Alkenoic Acid Conjugated linoleic Acid 263 (8.0  3.0)  102d Oleic Acid 268–283 (5.3  1.1)  102d Aldehyde Tridecanal 263 (1.6  0.8)  102e Alcohol Glycerol 268–293 (0.8–1.7)  103d Alkanoate Diethyl sebacate (DES) 263–272 (2.3–4.1)  104d a Only g results from this laboratory group have been included and they have been ordered by decreasing g values. The only other report of g values for NO3 uptake on pure organics is found in Moise et al.32 and our results are generally similar to their g values except in the case of alkanoic acids (this is discussed in further detail in Gross et al.52). b Taken from Gross and Bertram.57 c Taken from Mak et al.54 d Taken from Gross et al.52 e This study. Fig. 2 Measured uptake coefficients of the NO3 reaction with tridecanal in DES, DOS, and squalane matrices at 275 K. Fig. 3 Plots of g2mixture  g2matrix (panels a–c) and gmixture  gmatrix (panels d–f) as a function of Maldehyde. Panels a and d correspond to the reaction of NO3 + tridecanal in DES, panels b and e correspond to the reaction of NO3+tridecanal in DOS, panels c and f correspond to the reaction of NO3+tridecanal in squalane. Downloaded by The University of British Columbia Library on 07 December 201 1 Published on 21 April 2011 on http://pubs.rsc.org | doi:10.1039/C1CP20294 D View Online10218 Phys. Chem. Chem. Phys., 2011, 13, 10214–10223 This journal is c the Owner Societies 2011 of the organic liquid, kS2;aldehyde is the second-order rate constant for NO3 reaction with the reactant at the surface, and Maldehyde is the molarity of aldehyde in each matrix. If the reaction occurs at the surface and the assumptions outlined above are valid, then a plot of gmixture gmatrix against Maldehyde is expected to yield a straight line. In Fig. 3, panels a–c, we have plotted g2mixture  g2matrix against Maldehyde and in panels d–f, we have plotted gmixture  gmatrix against Maldehyde. To evaluate the goodness-of-fit for the two different models (bulk and surface) we calculated the R2 values, the results of which are included in Fig. 3. Based on the R2 values, kinetics for DOS and squalane mixtures are explained well by both the bulk and surface model. For DES, the kinetic data fit better to the surface model than the bulk model. Conservatively, below we use results from both models when estimating the lifetime of aldehydes in the atmosphere as well as making conclusions about the effect of the matrix on the NO3–aldehyde organic reactions. As it happens similar conclusions are reached regardless of the model used for the interpretation of the results. Table 2 summarises values of Hmatrix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dmatrixk2;aldehyde p and HSmatrixKSmatrixkS2;aldehyde that were extracted from the kinetic measurements of NO3 with tridecanal in the different matrices. It is interesting to note that the trend in Hmatrix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dmatrixk2;aldehyde p is in the order of DES > DOS > squalane. This trend is the same as that of Dmatrix. The diffusion coefficients can be estimated using the Stokes– Einstein equation Dmatrix = kbT(6pZr)1, where kb is the Boltzmann constant, T is the temperature, Z is the viscosity of pure matrix molecules, and r is the radius of the diffusing species (i.e., NO3 radicals). The Dmatrix values for DES, DOS, and squalane were calculated as 1.8  106, 4.3  107, and 3.0  107 cm2 s1, respectively, at 293 K. As mentioned above Hmatrix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dmatrixk2 ;aldehyde p and HSmatrixKSmatrixkS2;aldehyde values are directly proportional to the slopes in Fig. 3. Hence the trends in Hmatrix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dmatrixk2 ;aldehyde p and HSmatrixKSmatrixkS2;aldehyde values are the same as the trends in the slopes in Fig. 3. 3.3 Reactive uptake of N2O5 with alcohols Our previous study52 showed that the reactive uptake coefficients of N2O5 on liquid glycerol ranged from (3.2–8.5)  104 between 268–303 K and thus the heterogeneous reaction between N2O5 and alcohols may be potentially important in the atmosphere. In this study, we investigated the hetero- geneous N2O5 reaction with four other organic reactants which all contain hydroxyl groups. Fig. 4 provides the measured uptake coefficients for the N2O5 reaction as well as the glycerol results for comparison. The N2O5 reactive uptake coefficient on PEG-300 was the largest, (1.5–1.9)  102, while the smallest was on 1,2,6-tri- hydroxyhexane which was (0.8–1.5)  104. The overall trend in the reactive uptake coefficients was PEG-300 > PEG-400 > glycerol > (+)-diethyl-L-tartrate > 1,2,6-trihydroxyhexane. For PEG-400, above 278 K the film was liquid and below this temperature the film was solid. A sharp decrease in the g value for the experiment below the freezing point of PEG-400 suggests that the net liquid-phase reaction may be a combination of both a surface reaction and a bulk reaction, since the freezing process is expected to greatly decrease the importance of any bulk reactions in our experiments. Alternatively, the reactive uptake for both the liquid- and solid-phase experiments might only be due to surface reac- tions, where the liquid surface is much more favourable for uptake and reactivity. 3.4 Trend of N2O5 reactivity The uptake coefficients of N2O5 for single-component experi- ments varied by more than 2 orders of magnitude, which was surprisingly large. To try to rationalise these findings, we again used the resistor model of gas-liquid interactions. If the reaction occurs in the bulk and the reactive uptake coefficient is not limited by the mass accommodation coefficient (i.e., a c g, where a is the mass accommodation coefficient), the reactive uptake coefficient for a single-component alcohol can be explained with the following equation: g ¼ 4RTHalcohol ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dalcoholk1;alcohol p cN2O5 ; ð3Þ where g is the reactive uptake coefficient of N2O5 with the reactant, Halcohol is the Henry’s law solubility constant of N2O5 in the alcohol, R is the gas constant, T is the temperature, Dalcohol is the diffusion coefficient for N2O5 in the alcohol, k11,alcohol is the bulk first-order rate constant for reaction between N2O5 and the alcohol, and cN2O5 is the mean molecular velocity of N2O5. According to eqn (3) the reactive uptake coefficient should be proportional to Halcohol ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dalcoholk1 ;alcohol p . Here we assume that the reaction rate constant k11,alcohol is proportional to the concentration of hydroxyl functional groups in the liquid that could potentially react with N2O5. To represent the concentration of hydroxyl groups in the liquid we use ‘‘OH concentration,’’ or [–OH], with units of –OH groups L1 of the organic component. Table 3 summarises the viscosity (Z), diffusion coefficient (Dalcohol), OH concentration, the product of Dalcohol and OH concentration, and the corresponding uptake coefficients at 293 K for reactions of N2O5 with alcohols. Table 2 Calculated values for Hmatrix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dmatrixk2 ;aldehyde p and HSmatrixKSmatrixkS2 ;aldehyde for the reactions of NO3 with tridecanal in different matrices at 275 K Matrix: Hmatrix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dmatrixk2 ;aldehyde p , cm M0.5 atm1 s1a HSmatrixKSmatrixkS2 ;aldehyde, L cm2 atm1 s1a DES 9.44  2.47 14.43  0.42 DOS 6.93  2.29 12.43  1.04 Squalane 3.65  0.50 4.91  0.64 a Error estimates obtained from 1s standard deviations of each corresponding slope in Fig. 3. Downloaded by The University of British Columbia Library on 07 December 201 1 Published on 21 April 2011 on http://pubs.rsc.org | doi:10.1039/C1CP20294 D View OnlineThis journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 10214–10223 10219 According to eqn (3), if we assume all the alcohols have similar Halcohol values, the reactive uptake coefficient g should be proportional to ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dalcoholk1 ;alcohol p . Then plotting values of g against ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dalcohol  ½OH p is expected to yield a straight line fit to the data. In contrast to a bulk reaction, if the reaction occurs at the surface and the reactive uptake coefficient is not limited by the adsorption coefficient (i.e., S c g, where S is the adsorption coefficient), the reactive uptake coefficient can be explained with the following equation: g ¼ 4RTHSalcoholKSalcoholkS1;alcohol cN2O5 ; ð4Þ where HSalcohol is the surface Henry’s law constant, analogous to a Henry’s law equilibrium for the bulk condensed phase, KSalcohol is an equilibrium constant linking the surface concen- tration to the bulk concentration of the organic liquid, and kS1;alcohol is the first-order rate constant for the N2O5 reaction with alcohol at the surface. At a fixed temperature (i.e., at 293 K), eqn (4) shows that the reactive uptake coefficient is propor- tional to HSalcoholKSalcoholkS1;alcohol. We assumed that all the reactants here have similar HSalcoholKSalcohol values and also that kS1 ;alcohol was proportional to the ‘‘OH concentration.’’ Then, for a surface reaction, plotting values of g against [–OH] is expected to yield a straight-line fit to the data. In Fig. 5, we plot the reactive uptake coefficient as a functions of (Dalcohol  [–OH])0.5 (Panel a) and [–OH] (Panel b). Panel b shows that the surface model with the assumptions listed above cannot explain the data (R2 = 0.336). In contrast, Panel a shows that the reactive uptake coefficient is correlated well with (Dalcohol  [–OH])0.5 (R2 = 0.792). However the bulk model does not completely capture the trend in the data. This could be because the bulk model is not appropriate for some or all the alcohols studied and/or the assumptions discussed above (such as a single Henry’s law solubility for all the alcohols) are not appropriate. Regarding the former, it is interesting to note that for both glycerol and 1,2,6-trihydroxy- hexane, the self-diffusion coefficient is on the order of 1010 cm2 s1. This is in the range where calculations suggest that the transport of the condensed phase reactant can start to limit the overall uptake coefficient.80 This process is not included in the bulk model discussed above and may be, in part, why the bulk model does not accurately represent all the data. For the purpose of comparison, we have also plotted the reactive uptake coefficient as functions of solely the diffusion coefficient of N2O5 in the alcohol and the square root of Dalcohol (graphs not shown). In these cases the R2 values for plots against Dalcohol and Dalcohol0.5 were 0.732 and 0.763, respectively. Because those values are lower than the 0.792 R2 value presented in Table 3, it is demonstrated that the inclusion of OH concentration [–OH] leads to a better description of the observed trends in reactive uptake. We conclude that g does correlate with (Dalcohol  [–OH])0.5 but more work is needed with other alcohols to completely understand the dependence. It is likely that properties such as the Henry’s low solubility of the different alcohols, steric effects on the OH reaction rate constant, and transport of the alcohol within the matrix need to be considered. Fig. 4 Measured reactive uptake coefficients for reactions of N2O5 with liquid and solid polyalcohols as a function of temperature. Solid lines are meant to guide one’s eye and they do not represent fits to the data. Dashed lines are used to show phase changes for the organics. The uptake coefficients for glycerol were obtained from Gross et al.52 Table 3 Information pertaining to the discussion of the trend of N2O5 uptake coefficients Compound Z, cP Dalcohol, cm2 s1a OH concentration, (mol –OH) L1 Dalcohol  [–OH], cm2 mol L1 s1 g at 293 K PEG-300 70 8.0  108 7.5 5.8  107 1.80  102 PEG-400 90 6.0  108 5.6 3.4  107 9.20  103 Glycerol 1500 3.6  109 40.7 1.5  107 6.45  103 (+)-Diethyl-L-Tartrate N/A N/A 11.7 N/A 5.17  104 1,2,6-Trihydroxyhexane 2630 2.0  109 24.8 5.0  108 3  104 b a The diffusion coefficient of a species in a liquid is related to the viscosity through the Stokes–Einstein equation D = kbT(6pZr)1, where D is the diffusion coefficient, kb is the Boltzmann constant, T is the temperature, Z is the viscosity of the liquid, and r is the radius of the diffusing species. Here we have calculated the diffusion coefficient of N2O5 in the alcohols based on their viscosity at 293 K. The radius of the N2O5 particles was estimated as twice of the radius for O3. The radius of O3 was obtained based on a recent modelling study.45 b This value was estimated from the g value of 1,2,6-trihydroxyhexane at 278 K according to the general trend of uptake coefficients at different temperatures. Downloaded by The University of British Columbia Library on 07 December 201 1 Published on 21 April 2011 on http://pubs.rsc.org | doi:10.1039/C1CP20294 D View Online10220 Phys. Chem. Chem. Phys., 2011, 13, 10214–10223 This journal is c the Owner Societies 2011 In the next section, we use both the surface model and the bulk model to obtain an order of magnitude estimate of the atmospheric lifetime of the alcohols. The conclusions regarding the lifetime do not depend strongly on the model used. 4. Atmospheric implications 4.1 Lifetime of aldehyde due to NO3 oxidation Next we use the kinetic parameters measured above for the mixtures, to estimate the lifetime of an aldehyde in the tropo- sphere. If the reaction occurs in the bulk then the following equation81–83 can be used together with parameters shown in Table 2 to estimate the lifetime: ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½aldehydep ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½aldehyde0 q  3PNO3Hmatrix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dmatrixk2 ;aldehyde p 2rparticle t; ð5Þ where [aldehyde] is the concentration of an aldehyde at time t, [aldehyde]0 is the initial concentration of the aldehyde in the particle, PNO3 is the NO3 partial pressure in the atmosphere, t is the time that the particle was exposed to NO3, and rparticle is the radius of the particle in the atmosphere. If the reaction occurs at the surface then the following equation together with parameters in Table 2 can be used to estimate the lifetime of an aldehyde in the atmosphere: ln ½aldehyde½aldehyde0   ¼  3PNO3HSmatrixKSalcoholkS2 ;aldehyde rparticle t: ð6Þ Table 4 shows the estimated lifetime of an aldehyde calculated using kinetic parameters determined with aldehyde in different matrices at 275 K and using an NO3 volume mixing ratio of 25 pptV (24 h average) which is representative of moderately polluted levels.84 Several conclusions can be drawn from the data available in Table 4. A comparison of the calculated bulk and surface cases reveals that the lifetimes differ by only a factor of 2. This is a reasonably small effect upon consideration of the uncertainties that arise when extrapolating laboratory data to the atmosphere (e.g., particle composition). When making the comparison between the different matrices studied, the lifetimes differ by a factor of 2–3. This is also reasonably small. Finally, regardless of the matrix or the assumption of liquid vs. bulk dominance, all calculated lifetimes are short (i.e., all o8 h). One can thus conclude that the lifetime of aldehydes similar to tridecanal is likely short in the atmosphere if the NO3 concentra- tions are >25 pptV, the particle matrix is in the liquid state, and the diffusion coefficient of the aldehyde in the matrix is greater than 1010 to 1015 cm2 s1.80,85 At smaller diffusion coefficients the reactive uptake can be limited by the diffusion of the aldehyde in the particle. As a result, different equations other than eqn (5) and (6) would be used to calculate the lifetime of the particle.80,83,85 4.2 Lifetime of alcohols due to N2O5 oxidation Here we assume the reaction of N2O5 with alcohols should follow either a bulk mechanism or a surface mechanism. Equations analogous to eqn (1), (2), (5), and (6) were used to calculate Hmatrix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dmatrixk2 ;aldehyde p values, HSmatrixKSmatrixkS2;aldehyde values, and atmospheric lifetimes for alcohols. Table 5 summarises the calculated Hmatrix ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dmatrixk2;aldehyde p and HSmatrixKSmatrixkS2 ;aldehyde values and the estimated atmospheric lifetimes of different pure alcohol particles due to N2O5 oxidation. An N2O5 concentration of 1 ppbV was used in these calculations, roughly corresponding to moderately polluted levels.84 Several conclusions can be drawn from Table 5. First, comparing the calculations assuming bulk with the calcula- tions assuming surface, the lifetimes only differ by a factor of 1.3 which is a small effect. Second, the lifetime of alcohols with respect to N2O5 can be very short, consistent with initial work based on glycerol.52 Third, the lifetime of alcohols with respect to N2O5 can also be long, depending on the physical and chemical properties of the organic liquid. As a result, one should be careful when applying the uptake results of one molecule to a whole class of compounds. Details such as steric effects, Henry’s law solubilities, and transport of the reactant in the liquid all need to be considered. With this in mind, one should also be cautious when applying our tridecanal results liberally to all aldehydes. Studies with other aldehydes are also needed, as well as studies in other matrices such as solids or glasses.86 The N2O5 studies with alcohols give some indications that diffusion of the condensed phase reactant could be important. Limitations of the overall uptake by diffusion of the condensed phase species is an important area for future research, especially Fig. 5 Plots of the reactive uptake coefficient as a function of (Dalcohol  [–OH])0.5 for the bulk assumption (panel a), and as a function of [–OH] for the surface assumption (panel b). In both assumptions, the fit line is forced through 0. Downloaded by The University of British Columbia Library on 07 December 201 1 Published on 21 April 2011 on http://pubs.rsc.org | doi:10.1039/C1CP20294 D View OnlineThis journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 10214–10223 10221 considering that recent work suggests that organic particles in the atmosphere can often be in a glass state, where the self diffusion coefficient of the condensed phase is small.86 4.3 Possible condensed-phase reaction products from N2O5 and NO3 oxidation We can speculate on the products of the reactions discussed above based on previous gas-phase or condensed phase chemistry. For N2O5, reactions with condensed phase saturated alcohols are known to produce organonitrates.87 The mechanism has been suggested to occur via a six-membered ring, leading to an organic nitrate and HNO3.88 For NO3, reactions with gas-phase saturated aldehydes are known to produce peroxyacyl nitrates and aldehydes smaller than the starting material.89 We hypothesise that similar chemistry may occur in the condensed phase. However, additional studies are needed to verify such chemistry. Appendix Derivation of eqn (1) According to the resistor model, if the reaction occurs in the bulk, and if NO3 can react with both tridecanal and the matrix molecules, and if the reactive uptake coefficient is not limited by the mass accommodation coefficient (i.e., a c g, where a is the mass accommodation coefficient) then the following equation applies for our binary liquid mixtures:76,79,90 gmixture ¼ 4HmixtureRT ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dmixtureðk2;matrixMmatrix þ k2;aldehydeMaldehydeÞp cNO3 ; ðA1Þ where Hmixture corresponds to the Henry’s law solubility constant of NO3 in the mixture, Dmixture corresponds to the diffusion coefficient for NO3 in the mixture, k21,matrix is the second-order rate constant for the NO3 reaction with matrix molecules, and Mmatrix is the molarity of the matrix molecules in the mixture. In this study, the amount of the reactant (tridecanal) was always very small (wt% o6%) in the mixture. As the Henry’s law solubility constant and the diffusion coefficient of NO3 in the mixture is approximately the same as the Henry’s law solubility constant and the diffusion coefficient of NO3 in pure matrix molecules (i.e., Hmixture E Hmatrix and Dmixture E Dmatrix where Hmatrix is the Henry’s law solubility constant of NO3 in the pure liquid of matrix molecules, and Dmatrix is the diffusion coefficient of NO3 in the pure liquid of matrix molecules). Substituting these approximations into eqn (A1) results in the following: g2mixture ¼ ð4HmatrixRTÞ2Dmatrix c2NO3 k2;matrixMmatrix þ ð4HmatrixRTÞ2Dmatrix c2NO3 k2;aldehydeMaldehyde: ðA2Þ For our study g2mixture varies at least by a factor of 1.4, but Mmatrix only varies by 3%. Hence we assume that the first term in eqn (A2) is constant and equal to g2 for a pure liquid of matrix molecules. We refer to this as g2matrix. After making this assumption and substitution we obtain the following: g2mixture  g 2 matrix ¼ ð4HmatrixRTÞ2Dmatrixk2 ;aldehyde c2NO3 Maldehyde: ðA3Þ Table 5 Estimated Halcohol ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DN2O5k2 ;alcohol p and HSalcoholKSkS2 ;alcohol values and the oxidation lifetimes (t)a of pure polyalcohol particles exposed to N2O5 radicals Compound Halcohol ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DN2O5k2 ;alcohol p , cm M0.5 atm1 s1 t, hb HSalcoholKSkS2 ;alcohol, L cm2 atm1 s1 t, hc PEG-300 2.18 0.65 1.13 0.82 PEG-400 1.29 0.95 0.75 1.24 Glycerol 0.41 6.50 0.11 8.34 (+)-Diethyl-L- Tartrate 0.05 35.2 0.02 44.1 1,2,6- Trihydroxyhexane 0.02 104.7 0.007 130.4 a Calculations of atmospheric lifetimes were performed under the assumptions of pure alcohol particles with a diameter of 200 nm. b Lifetime estimates where reactions dominated by the bulk mechanism are assumed. c Lifetime estimates where reactions dominated by the surface mechanism are assumed. Table 4 Estimates of the atmospheric lifetimes of Aldehyde-containing organics aerosol particles, taldehyde, using parameters determined from uptake experiments with tridecanal in different matrices (DES, DOS, and squalane) System used for determining kinetic parameters taldehyde, ha Assuming a bulk mechanism Assuming a surface mechanism Tridecanal in DES 1.90 2.56 Tridecanal in DOS 1.98 2.96 Tridecanal in squalane 3.60 7.54 a When calculating the atmospheric lifetime it was assumed that the mole fraction of the aldehydes in the particle was 0.1 and that the particle diameter was 200 nm. Downloaded by The University of British Columbia Library on 07 December 201 1 Published on 21 April 2011 on http://pubs.rsc.org | doi:10.1039/C1CP20294 D View Online10222 Phys. Chem. Chem. Phys., 2011, 13, 10214–10223 This journal is c the Owner Societies 2011 Eqn (A3) is equivalent to eqn (1) in the main text. A similar equation to that of eqn (A1) was used in the literature to describe the uptake coefficient of NO3 on an aqueous solution that had two parallel bulk reactions: a reaction with water and a reaction with ions.76,90 Derivation of eqn (2) According to the resistor model, if NO3 can react with both tridecanal and the matrix molecules at the surface and the reactive uptake coefficient is not limited by the adsorption coefficient (i.e., S c g, where S is the adsorption coefficient) then the following equation applies for our binary liquid mixtures:79,83,91 gmixture ¼ 4RTHSmixtureKSmixturekS2;matrixMmatrix cNO3 þ 4RTHSmixtureKSmixturekS2 ;aldehydeMaldehyde cNO3 : ðA4Þ Employing approximations similar to the ones used to derive eqn (A2) above, we derive eqn (A5) below: gmixture ¼ 4RTHSmatrixKSmatrixkS2;matrixMmatrix cNO3 þ 4RTHSmatrixKSmatrixkS2;aldehydeMaldehyde cNO3 : ðA5Þ Employing approximations similar to the ones used to derive eqn (A3) above, we derive eqn (A6): gmixture  gmatrix ¼ 4RTHSmatrixKSmatrixkS2;aldehyde cNO3 Maldehyde: ðA6Þ Eqn (A6) is equivalent to eqn (2) in the main text. 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