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Reactive uptake kinetics of NO3 on multicomponent and multiphase organic mixtures containing unsaturated.. Xiao, Song; Bertram, Allan K. 2011

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View Online  PCCP  Dynamic Article Links  Cite this: Phys. Chem. Chem. Phys., 2011, 13, 6628–6636  PAPER  www.rsc.org/pccp  Reactive uptake kinetics of NO3 on multicomponent and multiphase organic mixtures containing unsaturated and saturated organics  Downloaded by The University of British Columbia Library on 18 April 2011 Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682D  S. Xiao and A. K. Bertram* Received 27th November 2010, Accepted 3rd February 2011 DOI: 10.1039/c0cp02682d We investigated the reactive uptake of NO3 (an important night-time oxidant in the atmosphere) on binary mixtures containing an unsaturated organic (methyl oleate) and saturated molecules (diethyl sebacate, dioctyl sebacate, and squalane) which we call matrix molecules. These studies were carried out to better understand the reactivity of unsaturated organics in multicomponent and multiphase atmospheric particles. For liquid binary mixtures the reactivity of methyl oleate pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi depended on the matrix molecule. Assuming a bulk reaction, Hmatrix Dmatrix koleate varied by a factor of 2.7, and assuming a surface reaction HSmatrixKSmatrixkSoleate varied by a factor of 3.6, where pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Hmatrix Dmatrix koleate and HSmatrixKSmatrixkSoleate are constants extracted from the data using the resistor model. For solid–liquid mixtures, the reactive uptake coefficient depended on exposure time: the uptake decreased by a factor of 10 after exposure to NO3 for approximately 90 min. By assuming either a bulk or surface reaction, the atmospheric lifetime of methyl oleate in different matrices was estimated for moderately polluted atmospheric conditions. For all liquid mixtures, the lifetime was in the order of a few minutes (with an upper limit of 35 min). These lifetimes can be used as lower limits to the lifetimes in semi-solid mixtures. Our studies emphasize that the lifetime of unsaturated organics (similar to methyl oleate) is likely short if the particle matrix is in a liquid state.  1. Introduction Organic material contributes about 20–90% to the total fine aerosol mass in the troposphere.1,2 This organic material can be in the form of pure organic particles or alternatively the organic can be internally mixed with inorganic material.3,4 Adding to the complexity, the organic material can consist of thousands of different organic compounds with a range of functional groups.5,6 Organic and mixed organic–inorganic particles can also be solids, liquids, liquid–liquid mixtures, liquid–solid mixtures or glasses.7–16 While in the atmosphere these organic and mixed organic–inorganic particles can undergo reactions with gasphase species such as OH,17–20 O3,21–25 NO326–33 and Cl.34–36 These heterogeneous reactions can be important for several reasons.18,37–39 As an example, heterogeneous reactions have implications for source apportionment. 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.40 Despite the potential importance of organic heterogeneous chemistry in the atmosphere and the fact that organic particles Department of Chemistry, University of British Columbia, Vancouver, British Columbia, Canada  6628  Phys. Chem. Chem. Phys., 2011, 13, 6628–6636  in the atmosphere are complex, there have been relatively few heterogeneous chemistry studies using multicomponent or multiphase organic mixtures. Recent studies using multicomponent and multiphase organics have mainly involved O3, OH and Cl chemistry. See for example ref. 9, 21, 24, 29, 34, 35, 41–59. Recently we studied the reactive uptake coefficient of NO3 on single-component organics and concluded that the NO3-alkene reaction could potentially be an important loss process of particle-phase unsaturated organic compounds in the atmosphere and in laboratory secondary organic aerosol studies.27 However, these conclusions were based on measurements with single-component substrates. The NO3 kinetics may be different in multicomponent and multiphase mixtures based on past studies using multicomponent and multiphase mixtures with O3, OH and Cl. See for example ref. 9, 18, 23, 24, 29, 35, 41–44, 46, 47, 52, 54, 57, 58 and 60. In the following we investigate NO3 reactive uptake on multicomponent and multiphase mixtures containing an unsaturated organic. For the unsaturated organic we used methyl oleate (see Fig. 1). Based on previous work we expect that the reaction between NO3 and the carbon–carbon double bond is efficient and the ester functional group does not play a significant role in the chemistry or kinetics.27 Other molecules used in this study were diethyl sebacate (DES), dioctyl sebacate (DOS) and squalane. These molecules cover a range of viscosities, This journal is  c  the Owner Societies 2011  View Online  2. Experimental  Downloaded by The University of British Columbia Library on 18 April 2011 Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682D  2.1 Experimental setup  Fig. 1 Molecular structures of the organic compounds used in this study.  molecular weights and functional groups (See Fig. 1 and Table 1). Also these molecules have low vapor pressures (which is a prerequisite for the flow tube studies). Here we refer to these saturated organics as matrix molecules. At a temperature of 278 K we studied the following binary mixtures: methyl oleate–DES, methyl oleate–DOS and methyl oleate–squalane. At this temperature the mixtures were all liquid. This allowed us to probe multicomponent liquid mixtures and assess the effect of the matrix molecules on the NO3 uptake kinetics. At 268 K we studied binary mixtures of methyl oleate–DES. At this temperature the binary system was a solid–liquid mixture. This allowed us to probe the effect of particle phase on the NO3 chemistry. In all experiments the concentration of methyl oleate in the binary mixtures were always kept less than 4 wt% methyl oleate. At these concentrations physical properties of the binary mixtures, such as solubility and molecular diffusion, will be controlled mainly by the matrix molecules. In this paper we present the reactive uptake coefficient measurements for these multicomponent and multiphase mixtures. The reactive uptake coefficient (g) is defined as the fraction of collisions with a surface that leads to reactive loss. The results are analyzed using the resistor model, and the results from this analysis are then used to assess the effect of the matrix molecules on the NO3 uptake kinetics and the lifetime of unsaturated organics in the atmosphere.  Table 1  Experiments were conducted in a cylindrical, rotating-wall flow tube reactor coupled to a chemical ionization mass spectrometer (CIMS). The setup and procedure are similar to several recent studies.9 A rotating Pyrex tube (B12 cm length, 1.77 cm inner diameter) fitted snugly inside the flow tube reactor. The inside wall of the glass tube provided a surface for a thin coating of the studied organic material. NO3 entered the flow tube through a movable injector. By varying the distance between the injector tip and the exit of the flow tube, loss of NO3 can be determined as a function of reaction distance and thus reaction time. 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. N2O5 was generated by reacting NO2 with an excess amount of O3 in a flow system as described by Schott and Davidson61 and Cosman et al.62 N2O5 was trapped and stored as solid white crystals at 197 K. After thermal conversion of N2O5 to NO3 and NO2, the recombination of NO3 and NO2 was negligible due to the short residence time of the gases in the flow tube reactor (typically 20–100 ms), NO3 was detected as NO3À in the mass spectrometer after chemical ionization by IÀ which was generated by passing a trace amount of CH3I in N2 through a 210Po source (model Po-2031, NRD). Total pressures in the flow cell during experiments were typically 2.6–3.2 Torr whereas flow velocities ranged from 380–600 cm sÀ1. The carrier gas through the cell was a mixture of O2 (B10–15%) in He. NO3 concentrations for all experiments were estimated as (3.5–16)  1010 molecules cmÀ3 by assuming that all N2O5 is converted to NO3 and NO2 and approximately 20% of the NO3 thermally dissociates in the Teflon coated glass oven based on well-known gas-phase reaction rates and modeling studies using the Acuchem chemical kinetics simulation program.63 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 reaction with NO also served as a convenient way to quantify the background signal in the NO3 experiments. 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 10% of the total signal. The uncertainty of the NO3 concentration, based on the uncertainty of the rate constant for the gas-phase N2O5 + IÀ reaction, is 40%.64  Properties of the organic compounds used in this study  Compound  Molecular Formula  Molecular weight (g molÀ1)  Viscosity at 293–298 K (mPa s)  Diffusion Coefficienta at 293 K (cm2 sÀ1)  Methyl oleate DES DOS Squalane  C19H36O2 C14H26O4 C26H50O4 C30H62  296.49 258.36 426.67 422.81  N/A 5.8878 25b 36.079  N/A 1.8  10À6 4.3  10À7 3.0  10À7  The diffusion coefficient is calculated by the Stokes–Einstein equation27 and by assuming the radius of the diffusing species (NO3) was the same as O3 as done in a recent paper.80 b Taken from www.kicgroup.com/dos.htm. a  This journal is  c  the Owner Societies 2011  Phys. Chem. Chem. Phys., 2011, 13, 6628–6636  6629  View Online  liquid mixture was added to a glass tube at room temperature and rotated. Next, the glass tube was rapidly immersed into liquid N2. Subsequently, the tube was taken out of the liquid N2 and located inside the flow tube reactor at (268 Æ 1) K. There was no apparent change in the phase after the reactions.  Downloaded by The University of British Columbia Library on 18 April 2011 Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682D  2.2 Measurements of the temperature-composition phase diagram for mixtures of methyl oleate in DES  Fig. 2 Plot of the natural logarithm of the NO3 signal vs. reaction time from several experiments. The substrates used in these studies were liquid DES and two liquid binary mixtures of methyl oleate and DES (0.57 and 1.72 wt% methyl oleate).  Observed first-order loss rate coefficients, kobs, were calculated from the depletion of the oxidant signal with increasing reaction time. Typical plots of the natural logarithm of the NO3 signal as a function of time are shown in Fig. 2. The slopes of the linear fits were used to determine kobs, which was in turn corrected for concentration gradients that formed close to the flow-tube wall by using the procedure described by Brown.65 Uptake coefficients (g) were calculated from the corrected rate constants, kcorr, using a standard procedure.9 Diffusion coefficients of NO3 used in these calculations were taken from Rudich et al.66 The two main sources of uncertainty for the uptake coefficient measurements were the gas phase NO3 diffusion coefficient and the measurement of kobs. We calculated the error from gas phase diffusion by assuming a 20% uncertainty for the NO3 diffusion coefficient.67 The uncertainty for the gas phase diffusion coefficient of NO3 in Helium is about 8%, and for NO3 in O2 is about 20%. In our study, the carrier gas is a mixture of He and O2. To be conservative we used the larger uncertainty (20%) as the uncertainty of NO3 in the He–O2 mixture. For the uncertainty of kobs, we used the standard deviation (1s) of the measurements. Reported errors include both the uncertainty from the diffusion coefficient and uncertainty from measuring kobs. The vapor pressure of pure methyl oleate is 4  10À5 Torr at 25 1C, and in the mixtures it should be decreased by more than an order of magnitude assuming Raoult’s Law behaviour. At these low vapor pressures, the loss due to gas-phase reactions between methyl oleate and NO3 should be less than 0.1% of the observed loss of NO3. For reactive uptake studies on liquids, approximately 0.5 to 0.8 ml of the liquid was added to the inner wall of a rotating glass cylinder. A rotation rate of B10 rotations minÀ1 was used for all experiments to ensure an even coating of the liquid on the inside of the glass tube. For reactive uptake studies on solid–liquid mixtures, a smooth solid–liquid film was prepared following the procedure outlined by Knopf et al.9 First a liquid mixture of methyl oleate in DES (1.4 wt% methyl oleate) was prepared. This 6630  Phys. Chem. Chem. Phys., 2011, 13, 6628–6636  The temperature-composition phase diagram for methyl oleate–DES mixtures is not known. We determined this phase diagram by means of differential scanning calorimetry (DSC). The phase diagram was necessary to determine properties of the solid phase (e.g. pure solid DES or a solid solution containing methyl oleate and DES) that formed in the experiments mentioned above as well as determine mass partitioning between solid and liquid phases. Determination of the phase diagram consisted of the following steps: 40 mL of liquid mixture (methyl oleate and DES) were added to a sample pan. The temperature of the sample was decreased to À50 1C, and then increased to 30 1C at a rate of 5 1C minÀ1. The phase diagram was constructed from the melting peaks in the thermogram.68 2.3 Chemicals Diethyl sebacate (98%) and squalane (99%) were obtained from Sigma-Aldrich; Methyl oleate ( Z 99%) and dioctyl sebacate ( Z 97%) were purchased from Fluka; NO2 was purchased from Matheson. N2 (99.999%), O2 (99.993%), and He (99.999%) were purchased from Praxair. O3 was produced by photolysis of O2.  3. Results 3.1 Reactive uptake coefficients of NO3 on single component organics The resistor model is used to analyze the reactive uptake data for binary mixtures. Ideally, for this analysis the NO3 reactive uptake coefficients on the pure matrix molecules are available. Table 2 provides the uptake coefficients for NO3 on the pure matrix molecules, as well as the uptake on pure methyl oleate for comparison. The uptake result for methyl oleate is in good agreement with measurements of other unsaturated organics (oleic acid, linoleic acid and conjugated linoleic acid).27 Also, the uptake coefficient of NO3 on methyl oleate is about 2–3 orders of magnitude higher than those of NO3 on saturated organics (DES, DOS and squalane). This trend is roughly consistent with the trend observed in the gas phase.69 The uptake Table 2 Measured uptake coefficients of NO3 on single-component organic compounds Compound  T (K)  Phase  g  DES DES DOS Squalane Methyl oleate  278 272 278 278 278  Liquid Solid Liquid Liquid Liquid  (4.4 (3.6 (3.9 (5.2 (1.4  a  Æ 0.4)  10À3 Æ 0.5)  10À4a Æ 0.3)  10À3 Æ 0.4)  10À3 +8.6/À0.5)  10À1  This uptake coefficient was obtained from our previous work.27  This journal is  c  the Owner Societies 2011  View Online  coefficient of NO3 with solid DES is about 90% lower than the corresponding liquid-phase data.  Downloaded by The University of British Columbia Library on 18 April 2011 Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682D  3.2 Reactive uptake coefficients of NO3 on binary liquid mixtures containing methyl oleate Fig. 3 shows the measured uptake coefficients of NO3 on different binary mixtures as a function of the methyl oleate concentration. For all matrices studied the addition of small amounts of methyl oleate (less than 4 wt%) significantly increases the reactive uptake coefficient. Also, the magnitude of increase depends of the type of matrix. For example at approximately 2.3 wt% methyl oleate the reactive uptake coefficient in DES increased by a factor of 20 compared to the pure case, but in squalane the reactive uptake coefficient only increased by a factor of 4. To check whether the uptake is reversible or irreversible, at the end of every experiment we moved the injector 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. 3.3 Analysis of the reactive uptake coefficient data using the resistor model To analyze the liquid uptake results presented in Fig. 3, we used the resistor model for gas-substrate interactions.70 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 our binary liquid mixtures (see Appendix). g2mixture À g2matrix ¼  ð4Hmatrix RTÞ2 Dmatrix koleate Moleate c2NO3  ð1Þ  Fig. 3 Measured uptake coefficients of NO3 on binary liquid mixtures containing methyl oleate. Some of the error bars for methyl oleate in DES exceed maximum y-values shown in this figure. Typically, when the g value is greater than 0.05 such as the last three data points for the methyl oleate–DES mixtures, the gas-phase diffusion of NO3 to the reactive surface greatly influences the measured g values. In this case, a small uncertainty in the diffusion coefficient will result in a large uncertainty in the measured g value. All experiments were carried out at (278 Æ 1) K.  This journal is  c  the Owner Societies 2011  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, R is the gas constant, T is the temperature, Dmatrix is the diffusion coefficient for NO3 in the matrix, koleate is the bulk secondorder rate constant for the NO3 reaction with methyl oleate, cNO3 is the mean molecular velocity of NO3, and Moleate is the molarity of the methyl oleate in each matrix. According to eqn (1), a plot of (g2mixture À g2matrix) vs. Moleate 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 our binary liquid mixtures (see Appendix).  gmixture À gmatrix ¼  S S 4Hmatrix RTKmatrix kSoleate Moleate cNO3  ð2Þ  where gmixture is the reactive uptake coefficient of NO3 with the binary mixture, gmatrix is the reactive uptake coefficient of NO3 with the corresponding pure matrix, HSmatrix is the surface Henry’s law equilibrium analogous to a Henry’s law equilibrium for bulk condensed phase, KSmatrix is an equilibrium constant linking the surface concentration to the bulk concentration of the organic liquid, kSoleate is the second-order rate constant for the NO3 reaction with methyl oleate at the surface, and Moleate is the molarity of methyl oleate in each matrix. If the reaction occurs at the surface and the assumptions outlined above are valid, then a plot of (gmixture À gmatrix) vs. Moleate is expected to yield a straight line. In Fig. 4 panels a–c, we have plotted (g2mixture À g2matrix) vs. Moleate and panels d–f, we have plotted (gmixture À gmatrix) vs. Moleate. Fig. 4 shows that the data can be fit reasonably well by assuming either a bulk reaction or a surface reaction. To evaluate the goodness-of-fit for the two different models (bulk and surface), we calculated w2 values. Smaller w2 values represents a better fit to the data. The results from these calculations are included in Fig. 4. Based on the w2 values, kinetics for DOS and squalane mixtures is explained well by both the bulk and surface model. For DES, the kinetic data fit better to the surface model than the bulk model, although even the bulk model does a reasonable job of describing the trend in the reactive uptake data. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Table 3 shows values of Hmatrix Dmatrix koleate and S S S HmatrixKmatrixkoleate determined from the slopes of the lines shown in p Fig. 4. If the reaction occurs in the bulk, then ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the Hmatrix Dmatrix koleate values vary by a factor of 2.7. If the reaction occurs on the surface, then the HSmatrixKSmatrixkSoleate values vary by a factor of 3.6. This shows that the matrix has an effect on the kinetics as expected. It is also interesting to compare the trends observed for the different matrices. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi For example, the trend in Hmatrix Dmatrix koleate is DES > DOS > squalane. This trend is the same as the trend in the diffusion coefficients (Dmatrix) of the matrices (see Table 1). Phys. Chem. Chem. Phys., 2011, 13, 6628–6636  6631  Downloaded by The University of British Columbia Library on 18 April 2011 Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682D  View Online  Fig. 4 Plot (g2mixture À g2matrix) (panel a, b, c) and (gmixture À gmatrix) (panel d, e, f) as a function of Moleate. Panel a and d correspond to the reaction of NO3 with a methyl oleate–DES mixture, panel b and e correspond to the reaction of NO3 with methyl oleate–DOS mixtures, panel c and f correspond to the reaction of NO3 with methyl oleate–squalane mixtures. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Table 3 Hmatrix Dmatrix koleate and HSmatrixKSmatrixkSoleate values determined from the slopes of the lines in Fig. 4. The reported uncertainties are based on the standard deviation (1s) of the slopes in Fig. 4 Matrix molecule  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Hmatrix Dmatrix koleate ðcm M 1=2 atmÀ1 sÀ1 Þ  HSmatrixKSmatrixkSoleate (L cmÀ2 atmÀ1 sÀ1)  DES DOS Squalane  69.4 Æ 5.8 35.4 Æ 2.4 26.1 Æ 1.5  281.3 Æ 11.8 120.9 Æ 4.2 78.0 Æ 2.7  3.4 Temperature-composition phase diagram for methyl oleate–DES mixtures Shown in Fig. 5 are results from the differential calorimetry measurements. According to the phase diagram, methyl oleate and DES are miscible in the liquid state but immiscible in the solid state. The eutectic temperature for the binary system was determined to be (250.7 Æ 0.5) K. 3.5 Reactive uptake coefficient measurements of NO3 on solid–liquid mixtures containing methyl oleate and DES The solid triangle in Fig. 5 shows the temperature and composition at which we studied the reactive uptake coefficient of partially solid mixtures of methyl oleate and DES. According to the phase diagram, the mixture consists of solid DES in equilibrium with a binary liquid mixture of approximately 45 wt% methyl oleate in DES. Contrary to measurements with liquids, the measured reactive uptake coefficients for these mixtures decrease with time. This is illustrated in Fig. 6. After approximately 90 min the reactive uptake coefficient on the solid–liquid mixture decreased by a factor of 10. In contrast the reactive uptake coefficient of NO3 on a liquid methyl oleate–DES mixture with the same weight percent methyl oleate did not decrease with 6632  Phys. Chem. Chem. Phys., 2011, 13, 6628–6636  time as expected. Fig. 6 illustrates that the phase of the mixture can significantly influence the kinetics, consistent with previous measurements using O3, Cl and OH as the oxidants. See for example ref. 9, 18, 29, 35, 41–44, 47, 52, 54 and 60. In our studies the liquid–solid mixture is likely to have a surface that is partially solid DES and partially a liquid mixture of methyl oleate and DES. As the carbon–carbon double bonds in the exposed liquid regions are oxidized, the uptake is expected to decrease, consistent with observations. During the 90 min exposure approximately 4  1016 molecules of NO3 were lost to the surface. Assuming that one molecule of NO3 reacts with one molecule of methyl oleate and that one monolayer of methyl oleate corresponds to roughly 6  1014 molecules cmÀ2, then during the 90 min exposure approximately 10 monolayers of methyl oleate is oxidized. This is consistent with only the top few monolayers of the material being available for reaction when the material is in the semi-solid state.  4. Atmospheric implications 4.1 Lifetime of unsaturated organics in liquid organic particles Next we use the kinetic parameters for the liquids, to estimate the lifetime of condensed-phase unsaturated organics in the This journal is  c  the Owner Societies 2011  View Online  atmosphere. If the reaction occurs in the bulk then the following equation can be used together with parameters shown in Table 3 to estimate the atmospheric lifetime.71–73 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½UnsaturatedOrganicŠt ¼ ½UnsaturatedOrganicŠ0 À  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3PNO3 Hmatrix Dmatrix koleate t 2rparticle  Downloaded by The University of British Columbia Library on 18 April 2011 Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682D  ð3Þ  Fig. 5 Temperature-composition phase diagram for the methyl oleate–DES system. S and L indicate solid and liquid phases, respectively. MO represents methyl oleate. The symbols ’ and . represent the melting temperatures of DES and methyl oleate, respectively, in the binary mixtures. The symbol K represents the measured eutectic temperature of the mixture. Each point represents the average of two runs. The symbol m represents the conditions at which the uptake kinetics was investigated. The line and curves were added to guide the eye.  where PNO3 is the NO3 partial pressure in the atmosphere, rparticle is the radius of the particle in the atmosphere, [UnsaturatedOrganic]0 is the initial concentration of the unsaturated organic in the particle and [UnsaturatedOrganic]t is the concentration of an unsaturated organic after reaction time t. If the reaction occurs at the surface then the following equation together with parameters in Table 3 can be used to estimate the lifetime of an unsaturated organic in the atmosphere.71  ln  S S 3PNO3 Hmatrix Kmatrix kSoleate ½UnsaturatedOrganicŠt ¼À t ½UnsaturatedOrganicŠ0 rparticle  ð4Þ  Fig. 6 Measured uptake coefficient (g) of NO3 on mixtures of methyl oleate with DES (composition = 1.37 wt% methyl oleate). Experiments were carried out by continuously exposing the surface to NO3, and periodically measuring the NO3 uptake coefficients. The open symbols represent experiments carried out at 278 K and correspond to a liquid, whereas the solid symbols represent experiments carried out at 268 K and correspond to a solid–liquid mixture.  Shown in Table 4 are the calculated lifetimes of unsaturated organics using eqn (3) and (4) and the parameters listed in Table 3, and assuming a radius of 100 nm, and a NO3 concentration of 25 ppt NO3 (24 h average). The NO3 concentration corresponds to roughly moderately polluted levels.74 Several conclusions can be drawn from Table 4. First, comparing the calculations assuming bulk with the calculations assuming surface, the lifetimes only differ by a factor of 1.5. Second, the lifetimes differ by only factor of 3 when comparing different liquid matrices. Third, regardless of the liquid matrix, or the assumption of surface vs. bulk, the lifetimes are short (all less than 35 min) for liquids. Hence we can conclude that the lifetime of unsaturated organics (similar to methyl oleate) are likely short in the atmosphere if the particle matrix is in a liquid state and NO3 concentrations are approximately 25 ppt. These lifetimes are comparable to the lifetimes reported for O3 with oleic acid9,40 (a molecule similar to methyl oleate) but are considerably shorter than the lifetimes for OH with oleic acid.40 Significant amounts of oleic acid, an unsaturated compound similar to methyl oleate, have been observed in the atmosphere.  Table 4 Estimated atmospheric lifetimes of unsaturated organics, tunsaturated, using parameters determined from studies with methyl oleate in different matrices (DES, DOS and squalane) tunsaturated (min)a System used for determining kinetic parameters  Assuming bulk reaction  Assuming surface reaction  Liquid mixture of methyl oleate in DES Liquid mixture of methyl oleate in DOS Liquid mixture of methyl oleate in squalane  13.0 25.7 34.8  8.0 18.4 28.5  a  When calculating the atmospheric lifetime it was assumed that the mole fraction of the unsaturated organic in the particle was 0.1 and the particle diameter was 200 nm.  This journal is  c  the Owner Societies 2011  Phys. Chem. Chem. Phys., 2011, 13, 6628–6636  6633  View Online  This suggests that particles containing oleic acid in the atmosphere are most likely not liquids, rather solids, semisolids or glasses, based on our NO3 kinetics. A similar conclusion has been made by others based on measured reaction rates between O3 and liquid oleic acid in the laboratory.  Downloaded by The University of British Columbia Library on 18 April 2011 Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682D  4.2 Lifetime of unsaturated organics in semi-solid organic matrices The lifetime of unsaturated organics in semi-solid organic matrices is difficult to estimate from our measurements. Until further measurements are available, the results for the liquid mixtures can be used as a lower limit to the lifetime of unsaturated organics in semi-solid organic matrices based on Fig. 6.  Appendix 1.  Derivation of eqn (1)  According to the resistor model, if the reaction occurs in the bulk, and if NO3 can react with both methyl oleate 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:70,75,76 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4Hmixture RT Dmixture ðkmatrix Mmatrix þ koleate Moleate Þ gmixture ¼ 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, kmatrix is the secondorder 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 (methyl oleate) is always small (wt% o 4%) in the mixture. As a result 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 equation.  g2mixture  ð4Hmatrix RTÞ2 Dmatrix ¼ kmatrix Mmatrix c2NO3 þ  ð4Hmatrix RTÞ2 Dmatrix koleate Moleate c2NO3  ðA2Þ  For our study, g2mixture varies at least by a factor of 5, 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 which can be 6634  Phys. Chem. Chem. Phys., 2011, 13, 6628–6636  calculated from the g value in Table 1. After making this assumption and substitution we have the following:  g2mixture À g2matrix ¼  ð4Hmatrix RTÞ2 Dmatrix koleate Moleate ðA3Þ c2NO3  Eqn (A3) is equivalent to eqn (1) above. A similar equation to eqn (A3) was used 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.75,76 2.  Derivation of eqn (2)  According to the resistor model, if NO3 can react with both methyl oleate 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.70,71,77 gmixture ¼  S S 4RTHmixture Kmixture kSmatrix Mmatrix cNO3  þ  S S 4RTHmixture Kmixture kSoleate Moleate cNO3  ðA4Þ  Employing approximations similar to the ones used to derive eqn (A2) above, we derive eqn (A5) below. gmixture ¼  S S 4RTHmatrix Kmatrix kSmatrix Mmatrix cNO3  þ  S S 4RTHmatrix Kmatrix kSoleate Moleate cNO3  ðA5Þ  Employing approximations similar to the ones used to derive eqn (A3) above, we derive eqn (A6): gmixture À gmatrix ¼  S S 4RTHmatrix Kmatrix kSoleate Moleate cNO3  ðA6Þ  Eqn (A6) is equivalent to eqn (2) in the main text.  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