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Reactive uptake kinetics of NO3 on multicomponent and multiphase organic mixtures containing unsaturated.. Xiao, Song; Bertram, Allan K. 2011-02-03

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6628 Phys. Chem. Chem. Phys., 2011, 13, 6628–6636 This journal iscthe Owner Societies 2011Citethis: Phys. Chem. Chem. Phys.,2011,13, 6628–6636Reactive uptake kinetics of NO3on multicomponent and multiphaseorganic mixtures containing unsaturated and saturated organicsS. Xiao and A. K. Bertram*Received 27th November 2010, Accepted 3rd February 2011DOI: 10.1039/c0cp02682dWe 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 studieswere carried out to better understand the reactivity of unsaturated organics in multicomponentand multiphase atmospheric particles. For liquid binary mixtures the reactivity of methyl oleatedepended on the matrix molecule. Assuming a bulk reaction, HmatrixffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmatrixkoleatepvaried by afactor of 2.7, and assuming a surface reaction HSmatrixKSmatrixkSoleatevaried by a factor of 3.6, whereHmatrixffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmatrixkoleatepand HSmatrixKSmatrixkSoleateare constants extracted from the data using theresistor model. For solid–liquid mixtures, the reactive uptake coefficient depended on exposuretime: the uptake decreased by a factor of 10 after exposure to NO3for approximately 90 min.By assuming either a bulk or surface reaction, the atmospheric lifetime of methyl oleate indifferent matrices was estimated for moderately polluted atmospheric conditions. For all liquidmixtures, the lifetime was in the order of a few minutes (with an upper limit of 35 min). Theselifetimes can be used as lower limits to the lifetimes in semi-solid mixtures. Our studies emphasizethat the lifetime of unsaturated organics (similar to methyl oleate) is likely short if the particlematrix is in a liquid state.1. IntroductionOrganic material contributes about 20–90% to the total fineaerosol mass in the troposphere.1,2This organic material canbe in the form of pure organic particles or alternatively theorganic can be internally mixed with inorganic material.3,4Adding to the complexity, the organic material can consist ofthousands of different organic compounds with a range offunctional groups.5,6Organic and mixed organic–inorganicparticles can also be solids, liquids, liquid–liquid mixtures,liquid–solid mixtures or glasses.7–16While in the atmosphere these organic and mixedorganic–inorganic particles can undergo reactions with gas-phase species such as OH,17–20O3,21–25NO326–33and Cl.34–36These heterogeneous reactions can be important for severalreasons.18,37–39As an example, heterogeneous reactions haveimplications for source apportionment. Specific organic speciesoften serve as molecular markers for probing sources oforganic particles. If heterogeneous reactions change the concen-trations of the selected molecular markers they can lead toerrors when calculating source strengths.40Despite the potential importance of organic heterogeneouschemistry in the atmosphere and the fact that organic particlesin the atmosphere are complex, there have been relatively fewheterogeneous chemistry studies using multicomponent ormultiphase organic mixtures. Recent studies using multi-component and multiphase organics have mainly involvedO3, OH and Cl chemistry. See for example ref. 9, 21, 24, 29,34, 35, 41–59.Recently we studied the reactive uptake coefficient ofNO3on single-component organics and concluded that theNO3-alkene reaction could potentially be an importantloss process of particle-phase unsaturated organic compoundsin the atmosphere and in laboratory secondary organicaerosol studies.27However, these conclusions were based onmeasurements with single-component substrates. The NO3kinetics may be different in multicomponent and multiphasemixtures based on past studies using multicomponent andmultiphase mixtures with O3, OH and Cl. See for exampleref. 9, 18, 23, 24, 29, 35, 41–44, 46, 47, 52, 54, 57, 58 and 60.In the following we investigate NO3reactive uptakeon multicomponent and multiphase mixtures containing anunsaturated organic. For the unsaturated organic we usedmethyl oleate (see Fig. 1). Based on previous work we expectthat the reaction between NO3and the carbon–carbon doublebond is efficient and the ester functional group does not play asignificant role in the chemistry or kinetics.27Other moleculesused in this study were diethyl sebacate (DES), dioctyl sebacate(DOS) and squalane. These molecules cover a range of viscosities,Department of Chemistry, University of British Columbia, Vancouver,British Columbia, CanadaPCCPDynamic Article Linkswww.rsc.org/pccp PAPERDownloaded by The University of British Columbia Library on 18 April 2011Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682DView OnlineThis journal iscthe Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 6628–6636 6629molecular weights and functional groups (See Fig. 1 andTable 1). Also these molecules have low vapor pressures(which is a prerequisite for the flow tube studies). Here werefer to these saturated organics as matrix molecules.At a temperature of 278 K we studied the following binarymixtures: methyl oleate–DES, methyl oleate–DOS and methyloleate–squalane. At this temperature the mixtures were allliquid. This allowed us to probe multicomponent liquidmixtures and assess the effect of the matrix molecules on theNO3uptake kinetics. At 268 K we studied binary mixtures ofmethyl oleate–DES.At thistemperature thebinarysystem wasa solid–liquid mixture. This allowed us to probe the effect ofparticle phase on the NO3chemistry. In all experiments theconcentration of methyl oleate in the binary mixtures werealways kept less than 4 wt% methyl oleate. At these concen-trations physical properties of the binary mixtures, such assolubility and moleculardiffusion, will be controlledmainly bythe matrix molecules.In this paper we present the reactive uptake coefficientmeasurements for these multicomponent and multiphasemixtures. The reactive uptake coefficient (g) is defined as thefraction of collisions with a surface that leads to reactive loss.The results are analyzed using the resistor model, and theresults from this analysis are then used to assess the effect ofthe matrix molecules on the NO3uptake kinetics and thelifetime of unsaturated organics in the atmosphere.2. Experimental2.1 Experimental setupExperiments were conducted in a cylindrical, rotating-wallflow tube reactor coupled to a chemical ionization massspectrometer (CIMS). The setup and procedure are similarto several recent studies.9A rotating Pyrex tube (B12 cmlength, 1.77 cm inner diameter) fitted snugly inside the flowtube reactor. The inside wall of the glass tube provided asurface for a thin coating of the studied organic material. NO3entered the flow tube through a movable injector. By varyingthe distance between the injector tip and the exit of the flowtube, loss of NO3can be determined as a function of reactiondistance and thus reaction time.NO3radicals were obtained by thermal conversion ofgaseous N2O5to NO3and NO2at 430 K in a Teflon coatedglass oven before entering the movable injector. N2O5wasgenerated by reacting NO2with an excess amount of O3in aflow system as described by Schott and Davidson61andCosman et al.62N2O5was trapped and stored as solid whitecrystals at 197 K.After thermal conversion of N2O5to NO3and NO2, therecombination of NO3and NO2was negligible due to theshort residence time of the gases in the flow tube reactor(typically 20–100 ms), NO3was detected as NO3C0in the massspectrometer after chemical ionization by IC0which wasgenerated by passing a trace amount of CH3IinN2througha210Po source (model Po-2031, NRD).Total pressures in the flow cell during experiments weretypically 2.6–3.2 Torr whereas flow velocities ranged from380–600 cm sC01. The carrier gas through the cell was amixture of O2(B10–15%) in He. NO3concentrations for allexperiments were estimated as (3.5–16) C2 1010molecules cmC03by assuming that all N2O5is converted to NO3and NO2andapproximately 20% of the NO3thermally dissociates in theTeflon coated glass oven based on well-known gas-phasereaction rates and modeling studies using the Acuchemchemical kinetics simulation program.63Quantitative conversionofN2O5toNO3and NO2intheoven was confirmedby addinghigh levels of NO to the exit of the flow tube. This conversionreaction with NO also served as a convenient way to quantifythe background signal in the NO3experiments. NO was addedin excess which completely titrated NO3to NO2.Anyremainingsignal at mass 62 after titration by NO was assigned to thebackground. The background signal was typically less than10% of the total signal. The uncertainty of the NO3concen-tration, based on the uncertainty of the rate constant for thegas-phase N2O5+IC0reaction, is 40%.64Fig. 1 Molecular structures of the organic compounds used in thisstudy.Table 1 Properties of the organic compounds used in this studyCompound Molecular Formula Molecular weight (g molC01) Viscosity at 293–298 K (mPa s) Diffusion Coefficientaat 293 K (cm2sC01)Methyl oleate C19H36O2296.49 N/A N/ADES C14H26O4258.36 5.88781.8 C2 10C06DOS C26H50O4426.67 25b4.3 C2 10C07Squalane C30H62422.81 36.0793.0 C2 10C07aThediffusioncoefficientiscalculatedbytheStokes–Einsteinequation27andbyassumingtheradiusofthediffusingspecies(NO3)wasthesameasO3as done in a recent paper.80 bTaken from www.kicgroup.com/dos.htm.Downloaded by The University of British Columbia Library on 18 April 2011Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682DView Online6630 Phys. Chem. Chem. Phys., 2011, 13, 6628–6636 This journal iscthe Owner Societies 2011Observed first-order loss rate coefficients, kobs, were calculatedfrom the depletion of the oxidant signal with increasingreaction time. Typical plots of the natural logarithm of theNO3signal as a function of time are shown in Fig. 2. Theslopes of the linear fits were used to determine kobs, which wasin turn corrected for concentration gradients that formed closeto the flow-tube wall by using the procedure described byBrown.65Uptake coefficients (g) were calculated from thecorrected rate constants, kcorr, using a standard procedure.9Diffusion coefficients of NO3used in these calculations weretaken from Rudich et al.66The two main sources of uncertainty for the uptakecoefficient measurements were the gas phase NO3diffusioncoefficient and the measurement of kobs. We calculated theerror from gas phase diffusion by assuming a 20% uncertaintyfor the NO3diffusion coefficient.67The uncertainty for the gasphase diffusion coefficient of NO3in Helium is about 8%, andfor NO3in O2is about 20%. In our study, the carrier gas is amixture of He and O2. To be conservative we used the largeruncertainty (20%) as the uncertainty of NO3in the He–O2mixture. For the uncertainty of kobs, we used the standarddeviation (1s) of the measurements. Reported errors includeboth the uncertainty from the diffusion coefficient anduncertainty from measuring kobs. The vapor pressure of puremethyl oleate is 4 C2 10C05Torr at 25 1C, and in the mixtures itshould be decreased by more than an order of magnitudeassuming Raoult’s Law behaviour. At these low vaporpressures, the loss due to gas-phase reactions between methyloleate and NO3should be less than 0.1% of the observed lossof NO3.For reactive uptake studies on liquids, approximately 0.5 to0.8 ml of the liquid was added to the inner wall of a rotatingglass cylinder. A rotation rate of B10 rotations minC01wasused for all experiments to ensure an even coating of the liquidon the inside of the glass tube.For reactive uptake studies on solid–liquid mixtures, asmoothsolid–liquidfilmwaspreparedfollowingtheprocedureoutlined by Knopf et al.9First a liquid mixture of methyloleate in DES (1.4 wt% methyl oleate) was prepared. Thisliquid mixture was added to a glass tube at room temperatureand rotated. Next, the glass tube was rapidly immersed intoliquid N2. Subsequently, the tube was taken out of the liquidN2and located inside the flow tube reactor at (268 C6 1) K.There was no apparent change in the phase after the reactions.2.2 Measurements of the temperature-composition phasediagram for mixtures of methyl oleate in DESThe temperature-composition phase diagram for methyloleate–DES mixtures is not known. We determined this phasediagram by means of differential scanning calorimetry (DSC).The phase diagram was necessary to determine properties ofthe solid phase (e.g. pure solid DES or a solid solutioncontainingmethyloleateandDES)thatformedintheexperimentsmentioned above as well as determine mass partitioningbetween solid and liquid phases.Determination of the phase diagram consisted of thefollowing steps: 40 mL of liquid mixture (methyl oleate andDES) were added to a sample pan. The temperature of thesample was decreased to C050 1C, and then increased to 30 1Cat a rate of 5 1C minC01. The phase diagram was constructedfrom the melting peaks in the thermogram.682.3 ChemicalsDiethyl sebacate (98%) and squalane (99%) were obtainedfrom Sigma-Aldrich; Methyl oleate (Z99%) and dioctylsebacate (Z97%) were purchased from Fluka; NO2waspurchased from Matheson. N2(99.999%), O2(99.993%),and He (99.999%) were purchased from Praxair. O3wasproduced by photolysis of O2.3. Results3.1 Reactive uptake coefficients of NO3on single componentorganicsThe resistor model is used to analyze the reactive uptake datafor binary mixtures. Ideally, for this analysis the NO3reactiveuptake coefficients on the pure matrix molecules are available.Table 2 provides the uptake coefficients for NO3on the purematrix molecules, as well as the uptake on pure methyl oleatefor comparison.The uptake result for methyl oleate is in good agreementwith measurements of other unsaturated organics (oleic acid,linoleic acid and conjugated linoleic acid).27Also, the uptakecoefficient of NO3on methyl oleate is about 2–3 orders ofmagnitude higher than those of NO3on saturated organics(DES, DOS and squalane). This trend is roughly consistentwith the trend observed in the gas phase.69The uptakeFig. 2 Plot of the natural logarithm of the NO3signal vs. reactiontime from several experiments. The substrates used in these studieswere liquid DES and two liquid binary mixtures of methyl oleate andDES (0.57 and 1.72 wt% methyl oleate).Table 2 Measured uptake coefficients of NO3on single-componentorganic compoundsCompound T (K) Phase gDES 278 Liquid (4.4 C6 0.4) C2 10C03DES 272 Solid (3.6 C6 0.5) C2 10C04aDOS 278 Liquid (3.9 C6 0.3) C2 10C03Squalane 278 Liquid (5.2 C6 0.4) C2 10C03Methyl oleate 278 Liquid (1.4 +8.6/C00.5) C2 10C01aThis uptake coefficient was obtained from our previous work.27Downloaded by The University of British Columbia Library on 18 April 2011Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682DView OnlineThis journal iscthe Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 6628–6636 6631coefficient of NO3with solid DES is about 90% lower than thecorresponding liquid-phase data.3.2 Reactive uptake coefficients of NO3on binary liquidmixtures containing methyl oleateFig. 3 shows the measured uptake coefficients of NO3ondifferent binary mixtures as a function of the methyl oleateconcentration. For all matrices studied the addition of smallamounts of methyl oleate (less than 4 wt%) significantlyincreases the reactive uptake coefficient. Also, the magnitudeof increase depends of the type of matrix. For example atapproximately 2.3 wt% methyl oleate the reactive uptakecoefficient in DES increased by a factor of 20 compared tothe pure case, but in squalane the reactive uptake coefficientonly increased by a factor of 4.To check whether the uptake is reversible or irreversible, atthe end of every experiment we moved the injector to aposition where the coated organic mixture was no longerexposed to the NO3flow. The absence of any release of NO3indicated that the uptake was irreversible.3.3 Analysis of the reactive uptake coefficient data using theresistor modelTo analyze the liquid uptake results presented in Fig. 3, weused the resistor model for gas-substrate interactions.70If thereaction occurs in the bulk and the reactive uptake coefficientis 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 liquidmixtures (see Appendix).g2mixtureC0 g2matrix¼ð4HmatrixRTÞ2Dmatrixkoleatec2NO3Moleateð1Þwhere gmixtureis the reactive uptake coefficient of NO3in thetwo component mixture, gmatrixis the reactive uptakecoefficient of NO3with the pure matrix molecules, Hmatrixisthe Henry’s law solubility constant of NO3in the matrix, R isthe gas constant, T is the temperature, Dmatrixis the diffusioncoefficient for NO3in the matrix, koleateis the bulk second-order rate constant for the NO3reaction with methyl oleate,cNO3is the mean molecular velocity of NO3, and Moleateis themolarity of the methyl oleate in each matrix. According toeqn (1), a plot of (g2mixtureC0 g2matrix) vs. Moleateis expected toyield a straight line.In contrast to eqn (1), if the reaction occurs on the surfaceand assuming the reactive uptake coefficient is not limited bythe adsorption coefficient, the following equation applies forour binary liquid mixtures (see Appendix).gmixtureC0 gmatrix¼4HSmatrixRTKSmatrixkSoleatecNO3Moleateð2Þwhere gmixtureis the reactive uptake coefficient of NO3with thebinary mixture, gmatrixis the reactive uptake coefficientof NO3with the corresponding pure matrix, HSmatrixisthe surface Henry’s law equilibrium analogous to a Henry’slaw equilibrium for bulk condensed phase, KSmatrixisan equilibrium constant linking the surface concentrationto the bulk concentration of the organic liquid, kSoleateisthe second-order rate constant for the NO3reaction withmethyl oleate at the surface, and Moleateis the molarity ofmethyl oleate in each matrix. If the reaction occurs at thesurface and the assumptions outlined above are valid, then aplot of (gmixtureC0 gmatrix) vs. Moleateis expected to yield astraight line.In Fig. 4 panels a–c, we have plotted (g2mixtureC0 g2matrix) vs.Moleateand panels d–f, we have plotted (gmixtureC0 gmatrix) vs.Moleate. Fig. 4 shows that the data can be fit reasonably well byassuming either a bulk reaction or a surface reaction. Toevaluate the goodness-of-fit for the two different models (bulkand surface), we calculated w2values. Smaller w2valuesrepresents a better fit to the data. The results from thesecalculations are included in Fig. 4. Based on the w2values,kinetics for DOS and squalane mixtures is explained well byboth the bulk and surface model. For DES, the kinetic data fitbetter tothesurfacemodelthanthebulk model,although eventhe bulk model does a reasonable job of describing the trend inthe reactive uptake data.Table 3 shows values of HmatrixffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmatrixkoleatepandHSmatrixKSmatrixkSoleatedetermined from the slopes of the linesshown in Fig. 4. If the reaction occurs in the bulk, thenthe HmatrixffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmatrixkoleatepvalues vary by a factor of 2.7. If thereaction occurs on the surface, then the HSmatrixKSmatrixkSoleatevalues vary by a factor of 3.6. This shows that the matrixhas an effect on the kinetics as expected. It is also interestingto compare the trends observed for the different matrices.For example, the trend in HmatrixffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmatrixkoleatepisDES > DOS > squalane. This trend is the same as the trendin the diffusion coefficients (Dmatrix) of the matrices (seeTable 1).Fig. 3 Measured uptake coefficients of NO3on binary liquid mix-tures containing methyl oleate. Some of the error bars for methyloleate 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 pointsfor the methyl oleate–DES mixtures, the gas-phase diffusionof NO3tothe reactive surface greatly influences the measured g values. In thiscase,asmalluncertaintyinthe diffusioncoefficient willresultinalargeuncertainty in the measured g value. All experiments were carried outat (278 C6 1) K.Downloaded by The University of British Columbia Library on 18 April 2011Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682DView Online6632 Phys. Chem. Chem. Phys., 2011, 13, 6628–6636 This journal iscthe Owner Societies 20113.4 Temperature-composition phase diagram for methyloleate–DES mixturesShown in Fig. 5 are results from the differential calorimetrymeasurements. According to the phase diagram, methyl oleateand DES are miscible in the liquid state but immiscible in thesolid state. The eutectic temperature for the binary system wasdetermined to be (250.7 C6 0.5) K.3.5 Reactive uptake coefficient measurements of NO3onsolid–liquid mixtures containing methyl oleate and DESThe solid triangle in Fig. 5 shows the temperature andcomposition at which we studied the reactive uptakecoefficient of partially solid mixtures of methyl oleate andDES. According to the phase diagram, the mixture consists ofsolid DES in equilibrium with a binary liquid mixture ofapproximately 45 wt% methyl oleate in DES.Contrary to measurements with liquids, the measuredreactive uptake coefficients for these mixtures decrease withtime. This is illustrated in Fig. 6. After approximately 90 minthe reactive uptake coefficient on the solid–liquid mixturedecreased by a factor of 10. In contrast the reactive uptakecoefficient ofNO3on a liquid methyl oleate–DES mixture withthe same weight percent methyl oleate did not decrease withtime as expected. Fig. 6 illustrates that the phase of themixture can significantly influence the kinetics, consistent withprevious 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 asurface that is partially solid DES and partially a liquidmixture of methyl oleate and DES. As the carbon–carbondouble bonds in the exposed liquid regions are oxidized, theuptake is expected to decrease, consistent with observations.During the 90 min exposure approximately 4 C2 1016moleculesof NO3were lost to the surface. Assuming that one moleculeof NO3reacts with one molecule of methyl oleate and thatone monolayer of methyl oleate corresponds to roughly6 C2 1014molecules cmC02, then during the 90 min exposureapproximately 10 monolayers of methyl oleate is oxidized.This is consistent with only the top few monolayers of thematerial being available for reaction when the material is inthe semi-solid state.4. Atmospheric implications4.1 Lifetime of unsaturated organics in liquid organic particlesNext we use the kinetic parameters for the liquids, to estimatethe lifetime of condensed-phase unsaturated organics in theFig. 4 Plot (g2mixtureC0 g2matrix) (panel a, b, c) and (gmixtureC0 gmatrix) (panel d, e, f) as a function of Moleate. Panel a and d correspond to the reactionof NO3with a methyl oleate–DES mixture, panel b and e correspond to the reaction of NO3with methyl oleate–DOS mixtures, panel c and fcorrespond to the reaction of NO3with methyl oleate–squalane mixtures.Table 3 HmatrixffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmatrixkoleatepand HSmatrixKSmatrixkSoleatevalues determined from the slopes of the lines in Fig. 4. The reported uncertainties arebased on the standard deviation (1s) of the slopes in Fig. 4Matrix molecule HmatrixffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmatrixkoleatepðcmM1=2atmC01sC01Þ HSmatrixKSmatrixkSoleate(L cmC02atmC01sC01)DES 69.4 C6 5.8 281.3 C6 11.8DOS 35.4 C6 2.4 120.9 C6 4.2Squalane 26.1 C6 1.5 78.0 C6 2.7Downloaded by The University of British Columbia Library on 18 April 2011Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682DView OnlineThis journal iscthe Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 6628–6636 6633atmosphere. If the reaction occurs in the bulk then thefollowing equation can be used together with parametersshown in Table 3 to estimate the atmospheric lifetime.71–73ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½UnsaturatedOrganicC138tq¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½UnsaturatedOrganicC1380qC03PNO3HmatrixffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmatrixkoleatep2rparticletð3Þwhere PNO3is the NO3partial pressure in the atmosphere,rparticleis the radius of the particle in the atmosphere,[UnsaturatedOrganic]0is the initial concentration of theunsaturated organic in the particle and [UnsaturatedOrganic]tis the concentration of an unsaturated organic after reactiontime t.If the reaction occurs at the surface then the followingequation together with parameters in Table 3 can be usedto estimate the lifetime of an unsaturated organic in theatmosphere.71ln½UnsaturatedOrganicC138t½UnsaturatedOrganicC1380¼C03PNO3HSmatrixKSmatrixkSoleaterparticletð4ÞShown in Table 4 are the calculated lifetimes of unsaturatedorganics using eqn (3) and (4) and the parameters listed inTable 3, and assuming a radius of 100 nm, and a NO3concentration of 25 ppt NO3(24 h average). The NO3concentration corresponds to roughly moderately pollutedlevels.74Several conclusions can be drawn from Table 4. First,comparing the calculations assuming bulk with the calculationsassuming surface, the lifetimes only differ by a factor of 1.5.Second,the lifetimes differ byonlyfactor of3whencomparingdifferent 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 thatthe lifetime of unsaturated organics (similar to methyl oleate)are likely short in the atmosphere if the particle matrix is in aliquid state and NO3concentrations are approximately 25 ppt.These lifetimes are comparable to the lifetimes reported for O3with oleic acid9,40(a molecule similar to methyl oleate) but areconsiderably shorter than the lifetimes for OH with oleicacid.40Significant amounts of oleic acid, an unsaturated compoundsimilar to methyl oleate, have been observed in the atmosphere.Fig. 6 Measured uptake coefficient (g)ofNO3on mixtures ofmethyl oleate with DES (composition = 1.37 wt% methyl oleate).Experiments were carried out by continuously exposing the surfaceto NO3, and periodically measuring the NO3uptake coefficients.The open symbols represent experiments carried out at 278 Kand correspond to a liquid, whereas the solid symbols representexperiments carried out at 268 K and correspond to a solid–liquidmixture.Table 4 Estimated atmospheric lifetimes of unsaturated organics, tunsaturated, using parameters determined from studies with methyl oleate indifferent matrices (DES, DOS and squalane)System used for determining kinetic parameterstunsaturated(min)aAssuming bulk reaction Assuming surface reactionLiquid mixture of methyl oleate in DES 13.0 8.0Liquid mixture of methyl oleate in DOS 25.7 18.4Liquid mixture of methyl oleate in squalane 34.8 28.5aWhencalculatingtheatmosphericlifetimeitwasassumedthatthemolefractionoftheunsaturated organicintheparticlewas0.1andtheparticlediameter was 200 nm.Fig. 5 Temperature-composition phase diagram for the methyloleate–DES system.S and Lindicate solid and liquid phases,respectively.MO represents methyl oleate. The symbols ’ and . represent themelting temperatures of DES and methyl oleate, respectively, in thebinary mixtures. The symbol K represents the measured eutectictemperature of the mixture. Each point represents the average oftwo runs. The symbolmrepresents the conditions at which the uptakekinetics was investigated. The line and curves were added to guidethe eye.Downloaded by The University of British Columbia Library on 18 April 2011Published on 02 March 2011 on http://pubs.rsc.org | doi:10.1039/C0CP02682DView Online6634 Phys. Chem. Chem. Phys., 2011, 13, 6628–6636 This journal iscthe Owner Societies 2011This suggests that particles containing oleic acid in the atmo-sphere are most likely not liquids, rather solids, semi-solids or glasses, based on our NO3kinetics. A similarconclusion has been made by others based on measured reactionrates between O3and liquid oleic acid in the laboratory.4.2 Lifetime of unsaturated organics in semi-solid organicmatricesThe lifetime of unsaturated organics in semi-solid organicmatrices is difficult to estimate from our measurements. Untilfurther measurements are available, the results for the liquidmixtures can be used as a lower limit to the lifetime ofunsaturated organics in semi-solid organic matrices based onFig. 6.Appendix1. Derivation of eqn (1)According to the resistor model, if the reaction occurs inthe bulk, and if NO3can react with both methyl oleateand the matrix molecules, and if the reactive uptake coefficientis 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 liquidmixtures:70,75,76gmixture¼4HmixtureRTffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmixtureðkmatrixMmatrixþkoleateMoleateÞpcNO3ðA1Þwhere Hmixturecorresponds to the Henry’s law solubilityconstant of NO3in the mixture, Dmixturecorresponds to thediffusion coefficient for NO3in the mixture, kmatrixis the second-order rate constant for the NO3reaction with matrix molecules,and Mmatrixis the molarity of the matrix molecules in themixture.In this study, the amount of the reactant (methyl oleate) isalways small (wt% o 4%) in the mixture. As a result theHenry’s law solubility constant and the diffusion coefficient ofNO3in the mixture is approximately the same as the Henry’slaw solubility constant and the diffusion coefficient of NO3inpure matrix molecules (i.e. HmixtureE Hmatrixand DmixtureEDmatrixwhere Hmatrixis the Henry’s law solubility constant ofNO3in the pure liquid of matrix molecules, and Dmatrixis thediffusion coefficient of NO3in the pure liquid of matrixmolecules). Substituting these approximations into eqn (A1)results in the following equation.g2mixture¼ð4HmatrixRTÞ2Dmatrixc2NO3kmatrixMmatrixþð4HmatrixRTÞ2Dmatrixc2NO3koleateMoleateðA2ÞFor our study, g2mixturevaries at least by a factor of 5, butMmatrixonly varies by 3%.Hence we assume that the first termin eqn (A2) is constant and equal to g2for a pure liquid ofmatrix molecules. We refer to this as g2matrixwhich can becalculated from the g value in Table 1. After making thisassumption and substitution we have the following:g2mixtureC0 g2matrix¼ð4HmatrixRTÞ2Dmatrixkoleatec2NO3MoleateðA3ÞEqn (A3) is equivalent to eqn (1) above. A similar equation toeqn (A3) was used to describe the uptake coefficient of NO3onan aqueous solution that had two parallel bulk reactions: areaction with water and a reaction with ions.75,762. Derivation of eqn (2)According to the resistor model, if NO3can react with bothmethyl oleate and the matrix molecules at the surface and thereactive uptake coefficient is not limited by the adsorptioncoefficient (i.e., S c g, where S is the adsorption coefficient)then the following equation applies for our binary liquidmixtures.70,71,77gmixture¼4RTHSmixtureKSmixturekSmatrixMmatrixcNO3þ4RTHSmixtureKSmixturekSoleateMoleatecNO3ðA4ÞEmploying approximations similar to the ones used to deriveeqn (A2) above, we derive eqn (A5) below.gmixture¼4RTHSmatrixKSmatrixkSmatrixMmatrixcNO3þ4RTHSmatrixKSmatrixkSoleateMoleatecNO3ðA5ÞEmploying approximations similar to the ones used to deriveeqn (A3) above, we derive eqn (A6):gmixtureC0 gmatrix¼4RTHSmatrixKSmatrixkSoleatecNO3MoleateðA6ÞEqn (A6) is equivalent to eqn (2) in the main text.AcknowledgementsThis research was supported by the National Sciences andEngineering Research Council of Canada (NSERC) and theCanada Research Chairs Program.References1 Q. 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