Night-time oxidation at the air – water interface: co-surfactant e ﬀ ects in binary mixtures †

The ageing of organic-coated aqueous aerosols at night is investigated by reacting NO 3 with binary surfactant mixtures ﬂ oating on water. The surfactants are oleic acid (OA), methyl oleate (MO) and stearic acid (SA). Deuterated surfactants mixed with hydrogenous surfactants were studied using neutron re ﬂ ectometry to determine the reaction kinetics of organic two-component monolayers with NO 3 at the air – water interface for the ﬁ rst time. We measured the rate coe ﬃ cients for OA monolayers, mixed with hydrogenous co-surfactant MO or SA to be (3 (cid:1) 1) (cid:3) 10 (cid:4) 8 cm 2 per molecule per s or (3.6 (cid:1) 0.9) (cid:3) 10 (cid:4) 8 cm 2 per molecule per s and MO monolayers mixed with hydrogenous co-surfactant OA or SA to be (0.7 (cid:1) 0.4) (cid:3) 10 (cid:4) 8 cm 2 per molecule per s or (3 (cid:1) 1) (cid:3) 10 (cid:4) 8 cm 2 per molecule per s. The initial desorption lifetimes of NO 3 , s d,NO 3,1 , were 8 (cid:1) 3 ns, 14 (cid:1) 4 ns, 12 (cid:1) 3 ns and 21 (cid:1) 10 ns. The approximately doubled desorption lifetime for MO – SA compared to the other mixtures is consistent with a more accessible double bond associated with the larger area per molecule of MO in the presence of SA facilitating NO 3 attack. The signi ﬁ cantly slower reactive loss of MO – OA compared to a MO monolayer demonstrates that multi-component surfactant mixtures need to be studied in addition to single-component monolayers. Such a retarded decay would cause the residence time to change from ca. 4 to 22 minutes associated with increased transport distances of surfactant species together with any other pollutants that may be protected underneath the surfactant ﬁ lm.


Introduction
Atmospheric aerosols are of key importance because of their impact on Earth's radiative balance and on cloud formation, [1][2][3] but also due to their link to air pollution. 4These aerosols originate both from natural and man-made sources.6][7] Organic components of atmospheric aerosols are oen surface-active including organic acids and diacids, proteins and humic-like substances (HULIS). 8Key components of surface-active organic aerosols are fatty acids; [9][10][11][12][13][14] it is important to note that phase behaviour especially for fatty acids is highly temperature dependent, 8 and little data are available for temperatures lower than ambient e.g.][10][11][12][13][14] Atmospheric fatty acids include saturated (such as palmitic acid 16 ) and unsaturated acids in particular oleic acid which is found both in marine [17][18][19] and cooking [20][21][22] aerosols.Cooking emissions have been proposed to contribute ca.10% to the man-made emission of small particulate matter (PM 2.5 ) at 320 mg per person per day based on measurements in London. 23The atmospheric lifetime of aerosol particles is largely determined by chemical ageing initiated by the oxidants nitrate radicals (NO 3 ), hydroxyl radicals (OH) and ozone (O 3 ).For investigation of this chemical aerosol ageing, it is crucial to study the heterogeneous reactions occurring between the aerosol and these gas-phase oxidants.Homogeneous chemistry is relatively well understood at a molecular level, while the details of heterogeneous chemistry remain largely unknown.Field measurements suggest that heterogeneous reactions substantially affect the chemical composition of particles, in particular that of their surface lms. 24Such reactions may alter key particle properties such as aerosol hydrophilicity, toxicity as well as their optical properties.7][28] The vast majority of studies to date have investigated the heterogeneous reactions of organic aerosols with O 3 and OH, which are the main oxidants during daytime.During nighttime, [OH] is very low while the concentration of the photolabile NO 3 will build up, so that NO 3 becomes highly signicant.0][31][32] Khan and co-workers 33 reported increases in NO 3 of up to 15 ppt from pre-industrial times to the present day.
In many cases heterogeneous reactions have been studied using organic droplets or thick lms. 34,35However, it has been shown that experimental studies of organic molecules selfassembled at the surface of water rather than purely organic aerosols alone are key to understanding atmospheric ageing of aerosols covered in organic material. 7,36n the work presented here organic monolayers at the airwater interface are used as proxies for organic-coated aqueous atmospheric aerosols, and their reactions with NO 3 are studied.2][43] Furthermore, the majority of the previous investigations has described the reaction of one surfactant with the oxidant, while it is increasingly clear that it is needed to include more than one surfactant species when mimicking the organic coated atmospheric aerosols.
The surfactant species chosen are oleic acid (OA), methyl oleate (MO) and stearic acid (SA).OA, 35,37,38,41,44,45 MO 26,39,41,42,[46][47][48][49] and SA 50 are popular model systems for atmospheric surfactants.MO, the methyl ester of OA, is a main component of biodiesel (chemical name: fatty acid methyl esters or 'FAME'), 51 likely leading to an increased atmospheric abundance in the future given up to 7% of FAME is added to standard petroleum diesel in the EU to reduce greenhouse gas emissions; higher proportions of FAME in petroleum diesel (10% FAME sold as 'B10' and 20% FAME sold as 'B20') and pure FAME ('B100') become increasingly common fuel alternatives across a number of European countries such as Germany, France and Finland.
This range of molecules allows the investigation of the effects of head group and degree of unsaturation on the reaction kinetics and products formed.Building on our previous work on single surfactants, 41 we focussed this study on the impact of co-surfactants on the NO 3 -initiated oxidation of these surfactants in binary mixtures.
What is lacking so far in the literature is the link between laboratory studies of single component surfactant lms and real atmospheric surfactant materials.Key questions are if studies of single surfactants can be combined in modelling studies to describe more complex real surfactant compositions and also if co-surfactants will affect the loss of the reactive surfactant species.Xiao and Bertram 42 investigated NO 3 -initiated oxidation of binary mixtures containing the unsaturated organic MO and saturated molecules (diethyl sebacate, dioctyl sebacate, and squalane) as matrix molecules.They have used a rotating-wall ow tube reactor coupled to a chemical ionization mass spectrometer (CIMS) with the aim to better understand the reactivity of unsaturated organics in multicomponent and multiphase atmospheric particles; their results suggest that for liquid binary mixtures the reactivity of methyl oleate depended on the matrix molecule.Our method of neutron reectometry (NR) is particularly well suited for the study of these mixtures, since deuteration of one of the surfactants in the binary mixture Fig. 1 The mixture of deuterated and hydrogenous organic molecules self-assembles at the air-water interface as a monolayer and the gas species, NO 3 and NO 2 , are expected to interact with both species.However, when monitoring the surface excess with neutron reflectometry, only the deuterated molecules are visible and hence the data collected provide information only on the reaction kinetic of the deuterated molecules.The red arrow shows chemical reaction, while the green arrows show the transport fluxes.
allowed us to follow the kinetics of the deuterated component and then reverse deuteration enabled us to follow the kinetics of the other surfactant with molecular resolution (see Fig. 1).The surface excess of the organic molecule during the oxidation reaction is monitored by NR at the air-ACMW (air-contrast matched water) interface, 52 and information about reaction mechanisms can even be accessed thanks to partial deuteration of the surfactant. 53,54Furthermore, the surface composition of mixed systems can be resolved in situ during dynamic processes by the selective deuteration of different components, 55,56 and therefore the reaction rates of individual components in mixtures can be determined.NR is an ideal technique to resolve kinetic and dynamic processes at uid interfaces on the second time scale: 39,57 in the present work NR is used effectively to measure the surface excess of the deuterated component of binary surfactant mixtures during reactions with gas-phase NO 3 .NO 3 is produced in situ by reacting O 3 with NO 2 , the dependence of [NO 3 ] on the initial [NO 2 ] and [O 3 ] is modelled, and to determine the concentration of NO 3 , the steady state concentrations of NO 2 and N 2 O 5 are measured using FTIR spectroscopy as a function of the initial [NO 2 ]. 41 The analysis of the kinetic experiments of the binary mixtures was based on the modelling approach developed in our previous work, 41 where we took into account all the key reactions and processes.Briey, in order to describe the NO 3 -initiated oxidation we used a model, which considers, in addition to reactions, other mechanisms, such as accommodation, desorption, competition for adsorption sites and transport of the gas-phase species (see Sebastiani et al. 41 ).This model builds on the formalism and terminology of the "PRA framework" (introduced by Pöschl, Rudich and Ammann 58 ).It is a combination of K2-SURF, kinetic double-layer surface model 59 and KM-SUB, kinetic multi-layer model of aerosol surface and bulk chemistry, 60 but has been adapted to a planar geometry (see Sebastiani et al. 41 ).KM-SUB and K2-SURF have been applied to describe a range of experimental datasets and conditions. 48,61,62Both models describe the evolution of the kinetic parameters of an organic droplet exposed to oxidants.We have adapted the model to a monomolecular organic layer at the air-water interface for analysis and interpretation of the experimental data presented here.In the binary mixture, only the surface excess of the deuterated component is detected and hence the kinetic modelling describes the reaction of the deuterated surfactant.The kinetic parameters embed both the oxidant and the cosurfactant effect on the reaction with the deuterated component.The kinetic analysis of the measured surface excess decays for the four reaction systems provides information on the rate coefficients of the heterogeneous reaction as well as indirect information on the effect of the co-surfactant and the formation of surface-active products.The results obtained for the different molecules will be discussed in relation of their chemical structures.Furthermore, the comparison between NO 3 and other oxidants species indicates to what extent night-time oxidation is important to atmospheric aerosol ageing.We also estimated oxidant uptake coefficients and compared those to literature data on similar organic molecules that have been studied in the condensed phase (i.e.droplets or thick lms 34,35 ).16 COOH, Sigma-Aldrich, purity 98.5%); further details may be found in Section 1 of the ESI; † the chemical structures of the molecules studied are displayed in Scheme 1.The subphase was a mixture of 8.1% by volume D 2 O (Sigma Aldrich, 99.9%) in pure H 2 O (generated using a Millipore purication unit, 18.2 MU cm), referred to as air-contrast matched water (ACMW).Chloroform (Sigma-Aldrich, >99.8%) and O 2 (Air Liquide, France, >99.9%) were used as supplied.NO 2 was supplied in small gas cylinders (112 dm 3 ) by Scientic and Technical Gases Ltd (Newcastle-under-Lyme, UK) and provided as a mixture of 1000 ppm of NO 2 in synthetic air with an analytical tolerance of AE2%.The solutions of organic molecules in chloroform were prepared shortly before the experiments and then mixed in a 1 : 1 molar ratio, the concentrations are given in mM: for d 34 OA-hMO 4.17 mM, for d 34 OA-hSA 4.37 mM, for d 33 MO-hOA 4.05 mM and for d 33 MO-hSA 3.77 mM.
2.1.2Gas delivery.Nitrate radicals, NO 3 , were produced in situ from the reaction of O 3 with NO 2 as described in our previous work. 41O 3 was generated by the exposure of molecular oxygen to UV light (the procedure has been described in Pfrang et al. 39 ).[NO 3 ] was regulated by changing the ow rate of NO 2 in the range 0.045-0.23 dm 3 min À1 while [O 3 ] was kept constant at 3.9 ppm (i.e. using a constant UV exposure of the O 2 molecules and a xed O 2 ow rate of 1.2 dm 3 min À1 ).A ow of the NO 3 -NO 2 -N 2 O 5 -O 2 mixture was then admitted to the reaction chamber 41,47 (we ensured complete consumption of O 3 prior to owing the gas mixture into the reaction chamber) and the organic monolayer was oxidised at a rate that was determined by [NO 3 ]; reaction chamber and reaction bulb, where NO 2 was allowed to react with O 3 to form NO 3 , were kept in the dark to avoid any photolysis of the photolabile NO 3 .Measurements of Scheme 1 Chemical structure of the organic molecules studied.
NO 2 and N 2 O 5 were carried out using IR absorption spectroscopy to establish the concentrations, [NO 2 ] and [N 2 O 5 ], and their uncertainties.Modelling of the well-known reaction scheme allowed the estimation of [NO 3 ].At a total ow rate of l.2 to 1.5 dm 3 min À1 , [NO 3 ] ranged from (3.5 AE 1.5) Â 10 8 molecule per cm 3 (13 AE 5 ppt) to (2.6 AE 1.0) Â 10 9 molecule per cm 3 (100 AE 40 ppt) in the experiments presented here; [NO 3 ] and NO 2 ow rates are given in Table 1.In line with previous work, 41,63 the range of NO 3 concentrations is representative for a range of atmospheric mixing ratios, 5-50 ppt, that are encountered in the atmosphere owing to spatial and seasonal uctuations.At night, NO 3 mixing ratios can reach 100 ppt and more. 64For further details on the gas reaction model we refer to our previous paper. 41.1.3Neutron reectometry (NR).NR measurements of the oxidation of deuterated monolayers by NO 3 in a custom-made reaction chamber 47 were carried out on the FIGARO instrument at the Institut Laue-Langevin. 65As in our previous work on monomolecular lms, 41 high ux settings were used to maximise the data acquisition rate involving an incident angle, q, of 0.62 , a wavelength, l, range of 2-20 Å, and a constant resolution in momentum transfer, q, of 11% over the probed q-range of 0.007 to 0.07 ÅÀ1 , where q ¼ 4p sin w/l.
Only a brief description of the physical basis of NR with reference to its application is given here while more details may be found in ref. 52, 57, 66 and 67.NR is a technique that allows measuring the surface excess of oil-like lms at the air-water interface.Neutron scattering is related to the coherent cross sections of the atoms with which the neutrons interact, and these values vary non-monotonically for different isotopes of the same atom and different atoms across the periodic table.In particular, swapping hydrogen for deuterium changes signicantly the scattering, and as such mixing of hydrogenous and deuterated materials enables contrast matching.
We followed the change in reectivity of a deuterated monolayer at the air-water interface using the time-of-ight mode measuring the entire q-range stated above with respect to the time of the oxidation reaction.For a deuterated surfactant monolayer at the air-ACMW interface the reectivity, R, can be expressed by: R y 16p 2 q 4 4b 2 n 2 sin 2 qd 2 where b is the scattering length of the surfactant, in fm, n is the number density, in ÅÀ3 , d is the thickness of the layer in Å, and bn ¼ r is the scattering length density.The surface excess, G, is given by: where A hg is the area per molecule (or per head group).The surface excess, G, is calculated from the scattering length density, r, which results from tting the reectivity prole with the eqn (1) as a model.A surface excess for insoluble molecules corresponds to surface concentration.A stratied layer model was applied to the experimental data involving a single layer for the deuterated surfactant.It has been shown that in this low q-range (<0.07 ÅÀ1 ), the value of G is very insensitive to specic details of the model applied. 68Fitting of the thickness with an arbitrary xed value of the density or tting of the density with an arbitrary xed value of the thickness (to within reasonable bounds) gives equivalent results to within an added uncertainty of less than 2%.In our case, we chose to t r while xing d at the value obtained by tting data recorded over a wider q-range (up to 0.25 ÅÀ1 ).
Normalisation of the reectivity data was carried out with respect to the total reection of an air-D 2 O measurement.The sample stage was equipped both with passive and active antivibration controls.The reaction chamber was mounted on the sample stage, interfaced with the gas setup, and the trough (13 Â 10 cm) was lled with 80 ml of ACMW. 47,47,52,53 The volume of solution spread was 26 ml for d 34 OA-hMO, 25 ml for d 34 OA-hSA, 27 ml for d 33 MO-hOA and 29 ml for d 33 MO-hSA.The solvent was allowed to evaporate before closing the chamber.Since we used a barrier-less trough the desired surface pressure (16 to 25 mN m À1 depending on the molecule) was achieved by spreading a calculated number of molecules on the surface as described earlier. 41From the surface excess obtained by NR the reproducibility is found to be within 1 to 14%, depending on the binary mixture.The choice of initial surface pressure and surface excess was based on the requirement of maximising the signal-to-noise ratio for NR measurements while having a reaction that lasts long enough to be analysed for kinetic parameters.A reduction of the initial surface pressure is not expected to affect the kinetic behaviour, i.e. the G(t) will start from a lower value and the curve will extend on a shorter time and less data will be available for the kinetic tting.The monolayer was further characterised with compression-expansion isotherms with a Langmuir trough off-line, while recording Brewster-angle microscopy (BAM) images at different surface pressure values, and these results are shown in the ESI Section 1. † Data were recorded for several minutes before NO 3 was admitted into the reaction chamber.The time resolution was set to 2 s.The alignment of the interface was maintained to a precision of 2.2 Kinetic modelling NO 3 -initiated oxidation of organic compounds proceeds generally via two reaction channels: rapid addition to the double bond of unsaturated species as well as slower abstraction of hydrogen atoms particularly relevant for saturated compounds. 29These mechanisms need to be described together with transport processes occurring in the experimental system to t our data.Based on the PRA-framework 58-60,69-72 a specic model has been developed for the heterogeneous reaction of a monomolecular organic layer at the air-water interface. 41This model was applied to the binary mixture without changes: in the binary mixture only one component is deuterated and hence visible to the NR technique.Details of the modelling approach are described in Sebastiani et al. 41 and we only give a brief overview below.
Two key features of our model description are: (i) the oxidant loss due to the reaction and transport to the bulk water; and (ii) the reaction products are divided into three categories: volatile, soluble and surface-active species (the branching ratios for volatile and soluble products are based on literature values, and for surface-active products an estimation was based on G(t) at long reaction times when the value of G(t) is above the detection limit).It should be noted that the technique used in this study monitors the deuterium concentration at the interface and that we could have described the reaction system by assuming only two types of products: surface active and non-surface active.However, we decided to distinguish non-surface active compounds between volatile and soluble products in order to make our model suitable for description of experimental data probing the partitioning to subphase and/or gas-phase.Due to the chosen NO 3 delivery method (see Sebastiani et al. 41 ) [NO 2 ]/ [NO 3 ] ratios increase from 10 5 to 10 7 as [NO 3 ] decreases from 10 9 to 10 8 molecule per cm 3 .NO 2 can adsorb and desorb from the organic layer (compare to King et al. 44 ), occupying reactive sites for an average time represented by the desorption lifetime, so that the loss of organic material due to reaction with NO 3 could be affected: NO 2 occupies a reactive site, which becomes unavailable for NO 3 oxidation, and hence reduces the number of reactive sites available, in turn slowing down the apparent reaction rate.Especially for high [NO 2 ]/[NO 3 ] ratios the reactant loss rate will be lower than the loss rate recorded for lower [NO 2 ]/[NO 3 ] ratios.As a consequence, we had to include the absorption and desorption of NO 2 in the model and describe this with a parameter called desorption lifetime, s d,NO 2 , following the approach used by Shiraiwa et al. 59 The effect of N 2 O 5 is not considered in the model, since the concentration was constant for all conditions.Experimental investigations of NO 3 and N 2 O 5 uptake [73][74][75][76][77] have shown that NO 3 uptake is much higher compared to N 2 O 5 .The reaction system is described as a gas phase (labelled g) and a near-surface gas phase (gs), above a sorption layer (s), a surface layer (ss), a near-surface bulk (nb) and the bulk (b), following the formalism of Shiraiwa et al. 60 (as illustrated in Fig. 1).
Gas-phase species (NO 3 and NO 2 ) can adsorb to the sorption layer and interact with the organic molecules in the surface layer.The reaction products can stay at the surface layer, or they can be lost through solubilisation into the bulk or by evaporation into the gas phase.
The evolution of the gas species surface concentration, [X i ] s , is described by considering adsorption, desorption, transport and reaction (see ESI † for further details).The key equations that describe the reactions are discussed below (the nomenclature is based on the PRA framework [58][59][60]69,78 ).
In the model, the gas-phase compound NO 3 reacts with the organic layer and its loss, L surf,Y,NO 3 , is described with the second-order rate coefficient k surf,Y,NO 3 : The evolution of the NO 3 surface and bulk concentrations can be described as: where A is the water surface area and V is the total water volume.
The ux of adsorbed gas molecules, J ads,NO 3 , is proportional to the surface accommodation coefficient, a s,NO 3 , which is determined by the product of the surface accommodation coefficient on an adsorbate-free surface, a s,0,NO 3 , and the sorption layer coverage, q s , given by the sum of the surface coverage of all competing adsorbate species.The ux of desorption, J des,NO ), or in the gas-like state (s d,NO 3,2 À1 ): The organic reactant, Y, (e.g.oleic acid) is lost only through reaction with NO 3 at the surface, described as: The products (Z) of the heterogeneous reaction cannot be identied individually at the air-water interface in our experiments, so we described them as three key categories: surfaceactive (i.e.remaining at the surface and directly measurable by NR, Z S ), volatile (i.e.escaping into the gas-phase, Z G ) and soluble (i.e.accumulating in the water bulk, Z B ) compounds.Since the surface-active products (Z S ) will remain at the airwater interface, the surface-bulk transport is negligible: where c S is the branching ratio for the surface-active products.
The volatile products (Z G ) will leave the surface based on their vapour pressures.The soluble products (Z B ) will diffuse into the water bulk depending on the diffusion coefficient.All equations describing the evolution of the various species can be found in the ESI.† This system of equations cannot be solved analytically, hence the ODE solver of MATLAB® (2011) has been used for numerical solving.In order to t G(t), provided by NR, a minimisation of the value of c 2 has been performed using the FMINUIT package. 79

Results and discussion
Two of the organic molecules considered in this work (OA and MO) contain one unsaturated C]C bond in the aliphatic tail while one molecule (SA) is fully saturated.Among the unsaturated surfactants, MO is a methyl ester in comparison with the fatty acid OA.The double bond is expected to be the key reactive site for NO 3 .Kinetic data on the two reactive unsaturated surfactants in the presence of a co-surfactant are presented in Sections 3.1 and 3.2.When a deuterated surfactant is mixed with a hydrogenous surfactant the reaction of the rst molecule can be followed in the presence of the second.Each section will illustrate the data collected for the 1 : 1 mixture (by mole) of deuterated and hydrogenous same molecule, then the deuterated surfactant mixed with saturated molecule (SA) and nally the deuterated surfactant mixed with the other unsaturated molecule in its hydrogenous form.

Oleic acid (d 34 OA) exposed to nitrate radicals (NO 3 ) in the presence of a co-surfactant
We investigated the time evolution of the two-component lms when following the decay of deuterated oleic acid (d 34 OA) component mixed with hydrogenous oleic acid (dOAhOA), the saturated surfactant stearic acid (dOAhSA) and its methyl ester (dOAhMO).Fig. 2 shows the surface excess decays of d 34 OA monolayers at the air-ACMW interface as a function of time with respect to different [NO 3 ] in the presence of hOA, hSA and hMO.The NO 3 -initiated oxidation leads to a non-zero surface excess value (4-6 Â 10 13 molecule per cm 2 ) at the end of the reactive decay.This plateau value is reached following an initial decay, which lasts between 5 min and well over 1 h depending on [NO 3 ].[NO 3 ] ranges from (13 AE 6) to (86 AE 45) ppt.For several gas conditions, the oxidation was carried out twice, demonstrating a good reproducibility for high [NO 3 ] (>35 ppt), and visually higher variability for lower concentrations.However, the uncertainty in [NO 3 ], for [NO 3 ] < 35 ppt, is $30%, which means that even a small variation in concentration produces a measurable change in the rate of loss of the deuterated surfactant.The oxidant is admitted into the chamber at t ¼ 0 s, and the decay of the surface excess starts almost immediately suggesting that the monolayer begins to be consumed as soon as the oxidant is admitted.The surface excess of d 34 OA was monitored also for exposure to O 2 when mixed with hSA and hMO, and for exposure to NO 2 only when mixed with hMO in order to assess a mechanical loss due to gas ux and isomerisation effects due to the presence of NO 2 (compare to King et al. 44 ).All blanks show a very stable surface excess for d 34 OA over the relevant timescale.The O 2 blank for d 34 OA-hMO shows a surface excess uctuation of about 5%; this may be due to some mechanical vibrations or other intermittent interference during this particular experimental run, but given the stability of this lm in the presence of NO 2 (and all other lms in the presence of O 2 ) and the fact that the reactive decays are all very clearly distinct from the apparent, but comparatively small uctuations in this run, we did not explore these uctuations further within the tight timeframe of these neutron beamtime experiments.
The kinetic tting was performed taking into account the variability of the gas concentrations (both for NO 3 and NO 2 ) and the initial surface excess was set to a value that takes into account only the d 34 OA, since the hydrogenous surfactant was effectively invisible to the NR technique (the scattering length of the hydrogenous material is only about 1% of the deuterated form).An example of the kinetic t is displayed in Fig. 2C (see Section 3.2 of the ESI † for the complete data set).The modelling of the data followed the same approach as that for the single component monolayers; 41 the kinetic parameters are discussed in comparison to the results for single molecule monolayers reported earlier 41 with our new data allowing us now to explore the effect of the co-surfactant presence which is crucial to link the results for the frequently studied monomolecular lms to complex, multi-component surfactant materials encountered in the real atmosphere.
The range of data we used for the kinetic tting starts very close to the beginning of the reactive decay when NO 3 is admitted to the chamber (t ¼ 0 s), and ends at a surface excess value of 5 Â 10 13 molecule per cm 2 : data below this value are excluded from the tting for two main reasons: (i) at low coverage the data become more sensitive to experimental details such as the precise background subtraction, so the parameters that affect the kinetic model are better determined without increasing sensitivity to these factors; and (ii) at low coverage some surfactants can segregate into domains which are inhomogeneous laterally (especially when mixing saturated and unsaturated surfactants), and the NR model does not have the resolution to distinguish this effect but the results are modestly affected, so again it is better to desensitize the kinetic parameters from this effect.The tted curve, which results from the sum of the surface excesses of d 34 OA and the products, is shown as a solid red line in the insert of Fig. 2C.Since NR effectively measures the quantity of deuterium atoms at the air-ACMW interface, a distinction between reactant and products is not possible from NR data; hence the tting function needs to take into account the contribution to G from both d 34 OA and its reaction products.The product yields are taken from our previous work; 41 we assumed that at t ¼ 0 s the signal is arising solely from d 34 OA, while the signal for long reaction time when the reactive decay has ceased (e.g.t > 1000 s for [NO 3 ] ¼ 86 ppt) is entirely due to the surface-active products.Also, the products 43,80 are assumed to have a similar scattering length density to d 34 OA, since oxidation of d 34 OA is expected to break the molecule into two parts, 43,80 which each maintains almost the same ratio between scattering length and molecular volume.The scattering length of the products is thus likely to be ca.half of the scattering length of d 34 OA and the product lm also likely possesses ca.half of the d 34 OA lm thickness.Given that and considering eqn (2), the resulting surface excess of the products corresponds to the value calculated with r, d and b of d 34 OA.This approximation is not valid in the extreme case of the products being only surface-active, since the packing would be two times denser than that for oleic acid, and this should be considered in the surface excess calculation and consequent modelling.In our study, the surface-active product yield is between 22% and 33%, and it has been taken into account that the total number of product molecules (surfaceactive, volatile and soluble) was twice the number of the reactant molecules.
Following the approach we used for the single component monolayer, 41 the accommodation coefficients for the gas-phase species were xed to one, and the desorption lifetimes were le free to vary in the range 10 À9 to 10 À7 s, which is in agreement with the values suggested by Shiraiwa et al. 78 For the rate coefficient, k surf , the range of variability was optimised through a sensitivity study performed by changing in the Matlab code the value of k surf .The suitable range of values found was (0.7-8) Â 10 À8 cm 2 per molecule per s, which is signicantly higher than the best t value provided by Shiraiwa et al. 70 for abietic acid exposed to NO 3 (1.5 Â 10 À9 cm 2 per molecule per s) and wider than the range used for the single component monolayer study.The optimisation of the kinetic parameters was performed systematically by the c 2 minimisation routine FMINUIT. 79The sensitivity of the model to changes in desorption lifetimes is shown in the ESI.† Fig. 3 The evolution of the surface concentrations obtained from kinetic modelling using the best-fitted parameters for the data shown in Modelled evolutions of the concentrations of reactants and products are exemplied in Fig. 3 with examples taken for the mixtures dOAhMO and dMOhOA.Fig. 3A shows the model for the surface excess of dOA in the mixture dOAhMO and of dMO in the mixture dMOhOA.The steady state [NO 3 ] s for the two mixtures reaches different values (see Fig. 3B): [NO 3 ] s reaches a ca.40% higher value when reacting with dOAhMO than with dMOhOA.This has two reasons: (i) the difference in the initial NO 3 gasphase concentration, in fact while both experimental runs had the same settings for the NO 3 production, the uncertainty in the NO 3 concentration is about 50% (see Table 1) and hence the model accounts for this variability with the best t for the initial NO 3 gas concentration being 27% higher for dOAhMO than for dMOhOA; (ii) the desorption lifetime at low coverage, s d,NO 3,2 , determines how long the NO 3 remains at the sorption layer, and this lifetime is about 60% longer for dOAhMO compared to dMOhOA.Fig. 3C and D show the time evolution of the products; the difference in the amounts of surface-active products, Z S , and soluble products, Z B , depends on the product yields for OA and MO, while the total amount of volatile product, Z G , is comparable for the two reactants if normalized by the respective starting [Y] ss .While visually the Z G peak is signicantly higher for dOAhMO compared to dMOhOA, when comparing the areas below the curves (noting the different timescales for the two reactions), the total amount of Z G for dOAhMO is about 33% higher than for dMOhOA, which is due to the initial reactant amounts differing by about 20% and the fact that reaction for dOAhMO is complete while it is not for dMOhOA (see differences in the surface excesses at t ¼ 0 and at the last time point in Fig. 3A).
This tting approach has been applied to all the molecules studied, while accounting for different product yields and kinetic parameter ranges (see Table 2).
The kinetic parameters related to the products, which have been used as xed input parameters, are taken from our previous work with single component monolayers. 41The product yields were optimised to c S ¼ 0.2 for the surface-active products, c G ¼ 0.45 for the volatile products and c B ¼ 0.35 for the soluble products.The best t values for the kinetic parameters related to the heterogeneous reaction between d 34 OA and NO 3 in the presence of hOA, hSA and hMO are summarised in Table 2.The presence of a co-surfactant can have different effects on the kinetics of the reaction occurring between d 34 OA and NO 3 : for example, the co-surfactant can have a higher reaction rate and compete for NO 3 uptake.Within the monolayer, the co-surfactant will occupy a different area per molecule than d 34 OA; the area will be larger for hMO and smaller for hSA, thus affecting the packing and the availability of the C]C double bond of d 34 OA for NO 3 adsorption.We measured the reaction of d 34 OA in the presence of hOA in order to determine the effect of monitoring the surface excess of only half the molecules exposed to NO 3 and we found similar results as for the fully deuterated monolayer.The rate coefficient for d 34 OA-hOA exposed to NO 3 was found to be (3.2AE 0.2) Â 10 À8 cm 2 per molecule per s.The fast desorption time obtained for NO 3 is (8 AE 2) Â 10 À9 s and the slow desorption is about 2.5 times longer, while the desorption time for NO 2 (NO 2 is present in our NO 3 oxidation experiments together with O 2 ) is four times  longer.The introduction of two desorption times reects the change of orientation of the organic molecules at the interface, i.e. for a highly packed monolayer the reactive site is less accessible, and the oxidant has less affinity for other parts of the molecules hence the desorption is faster.When the organic surface coverage decreases the reactive sites become more accessible and the desorption is slowed down.The rate coefficient for d 34 OA-hSA exposed to NO 3 was found to be (3.6 AE 0.9) Â 10 À8 cm 2 per molecule per s.It should be noted that the loss of surfactant material due to O 2 ow only (see black symbols in Fig. 2) leads to an apparent loss rate coefficient in the order of 10 À11 cm 2 per molecule per s, which is well within the uncertainty of the reactive rate coefficient.The fast desorption time obtained for NO 3 is (14 AE 4) Â 10 À9 s and the slow desorption is about the same value, while the NO 2 desorption time is about three times longer.The fact that s d,NO3,1 and s d,NO 3,2 have similar values agrees well with the idea that the area per molecule of d 34 OA is larger and the C]C double bond is more readily available when mixed with the same number of hSA molecules than when in a pure system, since hSA has a smaller area per molecule and packs more tightly than OA (see section 1 of ESI †).
The rate coefficient for d 34 OA-hMO exposed to NO 3 was determined to be (3 AE 1) Â 10 À8 cm 2 per molecule per s.The loss due to O 2 ow alone leads to an apparent rate coefficient in the order of 10 À11 cm 2 per molecule per s, which is again well within the uncertainty of the reactive rate coefficient.The fast desorption time obtained for NO 3 is (8 AE 3) Â 10 À9 s and the slow desorption is about three times longer, while the NO 2 desorption time is about ve times longer.These values are comparable with those found for d 34 OA-hOA which suggests that hMO has no major effect on OA oxidation kinetics, while the presence of SA slightly increases the rate coefficient and prolongs the fast desorption time both leading to a faster surface excess decay.  1 in the ESI †).MO occupies a larger surface area and is less stable at the air-water interface than OA because of its less hydrophilic head group. 41However, the reactive site is in a very similar chemical environment as for OA, and any difference in reaction kinetics is expected to be related to the chain orientation and formation of different products.The exposure to O 2 ow leads to a non-reactive loss that is signicantly larger than the one recorded for d 34 OA, conrming that d 33 MO is not as stable at the air-water interface as d 34 OA, even when mixed with a co-surfactant.The apparent rate coef-cient obtained for the decays in the absence of NO 3 is on the order of 10 À10 cm 2 per molecule per s.The minimum value reached by the surface excess is z2 Â 10 13 molecule per cm 2 , which is at the detection limit as discussed in our previous work. 41Therefore, no surface-active products are expected to remain at the interface as was also found in experiments with d 33 MO exposed to O 3 and NO 3 in the same reaction chamber. 41,47According to this nding, the product yields were chosen as for the single component lm: 41 c S ¼ 0.03, c G ¼ 0.45 and c B ¼ 0.52.The kinetic parameters were constrained to the values displayed in Table 2; for each co-surfactant a different range was optimised.An example of the tting resulting from the kinetic modelling is displayed in the insert of Fig. 4B.The best-t values obtained from the kinetic model are also presented in Table 2.
In the monolayer, the co-surfactant will occupy a different area per molecule than d 33 MO: a smaller area for both hOA and hSA, thus affecting the packing and the availability of the C]C double bond of d 33 MO for NO 3 adsorption.We measured the reaction of d 33 MO in the presence of hMO in order to determine the effect of monitoring the surface excess of only half the molecules exposed to NO 3 and we found similar results as for the fully deuterated monolayer (also consistent with the equivalent test for d/hOA).The rate coef-cient for d 34 MO-hMO exposed to NO 3 in the presence of NO 2 and O 2 was found to be (4.1 AE 0.8) Â 10 À8 cm 2 per molecule  The rate coefficient for d 33 MO-hOA exposed to NO 3 was found to be (0.7 AE 0.4) Â 10 À8 cm 2 per molecule per s.The loss due to O 2 ow only leads to an apparent rate coefficient on the order of 10 À10 cm 2 per molecule per s, which is well within the uncertainty of the reactive rate coefficient.The fast desorption time obtained for NO 3 is (12 AE 3) Â 10 À9 s and the slow desorption is about 50% longer, while the NO 2 desorption time is about three times longer.Interestingly, this rate coefficient is signicantly smaller than those found for d 33 MO-hMO and d 33 MO-hSA, while the desorption times are comparable for all these systems.We were thus able to quantitatively demonstrate that hOA has a signicant inuence on dMO oxidation kinetics.The importance in the atmospheric context of this experimental nding of a substantially altered reactive decay due to the presence of a co-surfactant will be discussed in the subsequent section on Atmospheric implications.hOA leaves surface active products upon NO 3 -initiated oxidation, and those products may compete with MO for the NO 3 uptake or they can arrange around MO molecules making the double bonds less accessible and hence slow down the reaction.All ts are presented in the ESI.†

Atmospheric implications
The kinetic parameters obtained by analysing the NR data allowed investigation of the effects of co-surfactants in binary mixtures.This is a key step from the monomolecular lms that are commonly studied in the laboratory environment towards an understanding of how these laboratory-based kinetic results can be linked to processes happening in the atmosphere where surfactants will exist in a complex matrix of other species including a wide range of saturated and unsaturated surfactants that are most likely to affect the structure at the air-water interface and thus potentially impact on the reactive decay of unsaturated surfactants such as oleic acid.We have carefully selected closely related surfactants that represent saturated (stearic acid) and unsaturated (oleic acid/methyl oleate) species found in the atmosphere.Thanks to our previous work in the same experimental set-up on these species as monomolecular lms, we could focus this study on the quantitative differences in the presence of co-surfactant by selective deuteration of rst one and then the other of the species in the binary mixtures.
As outlined above, most mixtures tested do not show substantially different kinetic behaviours (k surf is in the range of 2.8 to 4.1 Â 10 À8 cm 2 per molecule per s) and the small differences in k surf and the desorption times can be explained by the different structures at the air-water interface that will affect the accessibility of the C]C double bond for the NO 3 radicals.
The most striking result was found when following the decay of dMO in a binary mixture with hOA.We determined a ca.six times slower decay for dMOhOA compared to dMOhMO ((0.7 AE 0.4) Â 10 À8 cm 2 per molecule per s compared to (4.1 AE 0.8) Â 10 À8 cm 2 per molecule per s).We calculated the uptake coefficients for all the binary mixtures (see Table 3) to allow comparison with data collected in different experimental setups, where the direct result is the NO 3 uptake coefficient; and again, we found a lower uptake of NO 3 by dMOhOA compared to the other mixtures.This difference lies well outside the experimental uncertainty and demonstrates that matrix effects of cosurfactants can indeed affect the reaction kinetics and data from monomolecular surfactant experiments cannot simply be added up to understand the decay of these species in more complex and atmospherically relevant mixtures.Such a retardation of oxidative decay was not found for the binary mixtures of the surfactants OA and SA with a carboxylic acid headgroup.It thus seems likely that the less stable species at the air-water interface (such as MO with its methyl ester headgroup and more limited lifetime at the interface) may be more strongly affected  41 .b See ref. 41 for details on the lifetime calculation.c Values determined in our previous work. 41d Value refers to a study with a ow tube coupled to a chemical ionisation mass spectrometer. 81e Value refers to 1-octadecene uptake measured in a rotating wall ow tube. 82f Value refers to binary mixtures of MO and saturated molecules measured in a rotating wall ow tube. 42y co-surfactant effects.These species are harder to study experimentally because of exactly this less stable nature.While there is a considerable uncertainty about the relative proportions of the head groups in surface-active material in the atmosphere, it is clear that fatty acids as well as esters are key classes (e.g.Cheng et al. 83 ).For instance, sea spray aerosols collected over the Mediterranean Sea contained C 14 to C 34 fatty acid methyl esters (mainly methyl palmitate and methyl stearate). 84,85Degradation of particulate matter suspended in seawater by marine organisms has been shown to be a key source of saturated and unsaturated fatty acid methyl esters. 86verall, it seems very likely that atmospheric surface-active materials will not be limited to perfectly hydrophilic headgroups that are most frequently studied in the laboratory.This new insight into the ageing of multi-component monolayers is thus of particular relevance for the formation of secondary organic aerosols in the atmosphere as well as clouds.

Conclusion
In summary, our results provide clear evidence that multicomponent mixtures need to be carefully considered when trying to establish the lifetimes of lms in the atmosphere.Simply adding up kinetic data obtained for monomolecular lms in the laboratory are unlikely to yield realistic residence times especially if non-perfect headgroups are present in the surface-active material of interest.We could quantify the retardation of the kinetic decay by NO 3 to be ca.a factor of six for the dMO/hOA binary mixture.This would cause the residence time to change from ca. 4 to 22 minutes and could thus lead to substantially increased transport distances of surfactant species together with any other pollutants that may be protected underneath the surfactant lm.
3 , is proportional to the inverse of the desorption lifetime, s d,NO 3 ,eff À1 , which is the average time that the NO 3 molecule occupies an adsorption site.s d,NO 3 ,eff À1 is a combination of two desorption lifetimes, depending on the organic molecule packing at the interface, q ss ¼ [Y] ss (t)/[Y] ss (0); either closely packed (s d,NO 3,1 À1

Fig. 2
Fig. 2 Surface excess decays of dOAhOA (A), dOAhSA (B) and dOAhMO (C) exposed to different [NO 3 ]; mean values of NO 3 mixing ratios are displayed in the legend (1 ppt ¼ 2.7 Â 10 7 molecule per cm 3 ), NO 3 is admitted at t ¼ 0 s.In the insert, data and fit are shown for dOAhMO exposed to [NO 3 ] ¼ 86 ppt.
Fig.3The evolution of the surface concentrations obtained from kinetic modelling using the best-fitted parameters for the data shown in Fig.2Cand 4C for (A) the organic reactant (Y) respectively dOA mixed with hMO (blue) and dMO mixed with hOA (black) exposed to [NO 3 ] ¼ 86 ppt; (B) the surface concentration for the gas-phase species NO 3 reacting with dOAhMO (blue) and dMOhOA (black); and the surface-active (Z S ), volatile (Z G ) and soluble (Z B ) products produced by dOAhMO (C) and dMOhOA (D).

a
Values from Sebastiani et al. 41 bOnly two oxidant conditions were used to determine the kinetic parameters.

3. 2
Methyl oleate (d 33 MO) exposed to nitrate radicals (NO 3 ) in the presence of a co-surfactant Methyl oleate (MO) differs from OA in terms of the head group: instead of a carboxylic acid it has a methyl ester (COOCH 3 ) group.d 33 MO was used to study the oxidation by NO 3 in the presence of a hydrogenous co-surfactant: hMO, hSA and hOA (see Table Fig. 4A-C display the surface excess decays of d 33 MO monolayers at the air-ACMW interface as a function of time with respect to [NO 3 ] in the presence of hMO, hSA and hOA.[NO 3 ] was varied from (13 AE 6) ppt to (100 AE 40) ppt.

Fig. 4
Fig. 4 Surface excess decays of dMOhMO (A), dMOhSA (B), and dMOhOA (C) exposed to different [NO 3 ]; mean values of NO 3 mixing ratios are displayed in the legend (1 ppt ¼ 2.7 Â 10 7 molecule per cm 3 ), NO 3 is admitted at t ¼ 0 s.In the insert, data and fit are shown for dMOhSA exposed to [NO 3 ] ¼ 86 ppt.
per s.The fast desorption time obtained for NO 3 is (8 AE 2) Â 10 À9 s and the slow desorption is about four times longer, while the NO 2 desorption time is six times longer.The rate coefficient for d 34 MO-hSA exposed to NO 3 was found to be (3 AE 1) Â 10 À8 cm 2 per molecule per s.The fast desorption time obtained for NO 3 is (21 AE 10) Â 10 À9 s and the slow desorption is about the same value, while the NO 2 desorption time is about 50% longer.As for d 34 OA, s d,NO 3,1 and s d,NO 3,2 have similar values and this agrees well with the idea that the area per molecule of d 33 MO is larger and C]C double bond is more readily available when mixed with the same number of hSA molecules than when in a pure system, since hSA has a smaller area per molecule and packs tighter than MO (see section 1 of the ESI †).

Table 1
3he concentrations of NO 3 calculated from IR measurements of [NO 2 ] and [N 2O 5] are reported in the first column as molecule per cm3and the corresponding ppt value is given in the second column; in the third column the flow rate of NO 2 is shown (the total gas mixture flow rate is obtained by adding the constant O 2 flow rate of 1.2 dm 3 min À1 to these values)

Table 2
Results of the kinetic modelling of the experimental data for the

Table 3
Kinetic parameters, uptake coefficients and estimated monolayer lifetimes for the compounds studied.Literature values for uptake coefficients on similar compounds are included for comparison Surfactant k surf /cm 2 per molecule per s g/10 3a g lit /10 3 Lifetime b /minute d 34 OA (2.8 AE 0.7) Â 10 À8c 2.1 AE 0.5 c (3 AE 1) Â 10 2d [1.6 AE 0.3] e a Calculated as k surf Â A Â [Y] ss with A a gas constant in seconds and [Y] ss the surface concentration of the deuterated molecule, see ref.