Supplemental Information for : Understanding Interactions of Organic Nitrates with the Surface and Bulk of Organic Films : Implications for Particle Growth in the Atmosphere

Understanding impacts of secondary organic aerosol (SOA) in air requires a molecular-level understanding of particle growth via interactions between gases and particle surfaces. The interactions of three gaseous organic nitrates with selected organic substrates were measured at 296 K using attenuated total reflection Fourier transform infrared spectroscopy. The organic substrates included a long chain alkane (triacontane, TC), a keto-acid (pinonic acid, PA), an amorphous ester oligomer (poly(ethylene adipate) di-hydroxy terminated, PEA), and laboratory-generated SOA from α-pinene ozonolysis. There was no uptake of the organic nitrates on the non-polar TC substrate, but significant uptake occurred on PEA, PA, and α-pinene SOA. Net uptake coefficients (γ) at the shortest reaction times accessible in these experiments ranged from 3 × 10-4 to 9 × 10-6 and partition coefficients (K) from 1 × 107 to 9 × 104. Trends in γ did not quantitatively follow trends in K, suggesting that the intermolecular forces involved in gas-surface interactions are not the same as those in the bulk, which is supported by theoretical calculations. Kinetic modeling showed that nitrates diffused throughout the organic films over several minutes, and that the bulk diffusion coefficients evolved as uptake/desorption occurred. A plasticizing effect occurred upon incorporation of the organic nitrates, whereas desorption caused decreases in diffusion coefficients in the upper layers, suggesting a crusting effect. Accurate predictions of particle growth in the atmosphere will require knowledge of uptake coefficients, which are likely to be several orders of magnitude less than one, and of the intermolecular interactions of gases with particle surfaces as well as with the particle bulk.


Section 2-FTIR Absorption Cross Sections
Absorption cross sections for each organic nitrate and substrate were obtained using transmission through a 0.5 mm pathlength KBr cell or by filling the ATR cell with a solution of known concentrations ranging from 1 to 10 -3 M, and covering the cell with a glass lid to prevent evaporation.Solutions for FTIR cross section measurements were made in either dodecane, methanol, or acetonitrile.
To calculate the pathlength within the ATR cell through a thick film such as the case when the cell is filled with solution, the effective thickness (de) of the solution in the cell was calculated using the wavelength of interest, and the refractive indices of the Ge crystal and the solvent. 1 Accounting for the 10 bounces within the crystal, the effective pathlength (leff) through for example an acetonitrile solution was 3.0 μm at 1730 cm -1 , 3.2 μm at 1630 cm -1 , and 4.0 μm at 1280 cm -1 respectively.The measured cross sections from the two methods agreed within 5% and averages are provided in Table S1, which includes the cross section at 1280 cm -1 for each organic nitrate, as well as the carbonyl cross section for PA, PEA and a proxy cross section for SOA comprised of the average of the cross sections of PA, tartaric acid, valeric acid and 2nonanone.
Table S1: FTIR cross sections in cm 2 mole -1 -ONO2 or cm 2 mole -1 C=O (base 10) for the organic nitrates, PA, PEA, and a proxy SOA at a resolution of 8 cm -1 .

Compound
σ a,b (Units of 10 b Cross sections were determined from the height of the characteristic peaks for each compound (1280 cm -1 for organic nitrates, and 1700-1730 cm -1 for C=O) using standard solutions, and for carbonyl-containing compounds normalized to the number of carbonyls on the molecule.For PEA, six subunits of the polymer were assumed, resulting in a total of 12 C=O for every PEA molecule.Carbonyl cross section for SOA was estimated as the average of the cross sections for pinonic acid, tartaric acid, valeric acid, and nonanone.
The ATR-FTIR spectra for a solid PA film and a standard solution are shown in Figure S5.The presence of hydrogen bonding in the solid caused overlap of the acid and ketone carbonyl peaks, whereas in solution these are two distinct peaks.Due to this overlap in the solid phase, the peak cross section at 1704 cm -1 for the liquid solution was used to quantify the thickness of solid PA films.For all nitrates and substrates, the quantification was made based on the cross section determined from the liquid solutions.The amount of organic substrate on the crystal was varied to ensure the film thickness was below the depth of penetration (dp) of the infrared evanescent wave.The depth of penetration was calculated from the wavelength of the peak of interest and the refractive indices of the Ge crystal and air to be 0.35 μm at 1730 cm -1 , 0.37 μm at 1630 cm -1 , and 0.47 μm at 1280 cm -1 . 1,2 or a sufficiently thin film, the path length (l) of the infrared beam through the organic film can be estimated using dp and factoring in the 10 bounces of the beam within the ATR crystal, giving total path lengths of 3.5 μm at 1730 cm -1 , 3.7 μm at 1630 cm -1 , and 4.7 μm at 1280 cm -1 . 1 The 1280 cm -1 peak was used for analysis of the organic nitrates since there was some overlap of the substrate carbonyl peaks with the 1630 cm -1 peak of the -ONO2 group.
Using both the amount of substrate deposited and the amount of nitrate taken up, partition coefficients and net uptake coefficients were quantified as described in the main text.

Section 3-SOA Generation and Characterization
All reactants were introduced in the initial mixing section of the reactor. 3Gas phase αpinene (250 ppb) was generated by injection of the pure liquid from an automated syringe pump (New Era Pump Systems Inc., Model NE-1000) into a stream of clean, dry air flowing at 10 L min -1 from a purge gas generator (Parker Balston, model 75-62), carbon/alumina media (Perma Pure, LLC) and an inline 0.1 µm filter (Headline Filters, DIF-N70).Ozone was generated by flowing 0.4 L min -1 O2 gas through a UV lamp (UVP), and subsequently was diluted with 9.6 L min -1 of air before being introduced to the reactor, with resulting reactor concentrations of 250-350 ppb O3 verified using an ozone monitor (Teledyne Photometric O3 Analyzer -Model 400E).
An additional 14 L min -1 of air was introduced to create a total flow rate of 34 L min -1 .
Experiments were performed under ambient temperature and pressure, and dry conditions (RH < 5%), without OH scavenger or seed particles.
Gas phase concentrations of α-pinene in the reactor were monitored using GC-MS with electron impact ionization (Agilent 7890A GC system with a 5975C MS detector) with the particles and ozone filtered out using a quartz filter and a KI ozone scrubber.Elemental ratios of SOA particles were measured using an aerosol mass spectrometer (Aerodyne, HR-ToF-AMS) 4 that sampled directly from the flow reactor with a diluter in some cases.Values of O/C = 0.50  0.03 (2σ) and H/C = 1.61  0.02 (2σ) were determined using the method of Canagaratna et al. 5 Particle size distributions were monitored using a scanning mobility particle sizer (SMPS, TSI), equipped with a model 3071A classifier and 3022A CPC, and an aerodynamic particle sizer (APS, TSI Model 3321).The size distributions were combined using the SMPS data below 11 500 nm and APS data above 700 nm mobility diameter assuming a particle density of 1.2 g cm - 3 , 6 and fit with a Weibull 5-parameter distribution as described by Perraud et al. 7 To check the validity of the Weibull fit, an Aerodynamic Aerosol Classifier (AAC, Cambustion Ltd., UK) was used with a CPC (TSI, model 3776) to scan the entirety of the range covered by the SMPS and the APS.The AAC measures aerodynamic diameter and these diameters were converted to mobility diameters using a particle density, p, of 1.2 g cm -3 for pinene SOA and the Cunningham slip correction factors as a function of diameter, Cc(d), as in equation (S2) 8 where 0 is the standard density (1.0 g cm -3 ).

Section 4-KM-GAP parameters
The bulk diffusion coefficients of the nitrate (Db,nit) and substrate (Db,sub) were treated to be composition-dependant using Vignes-type equations 9,10 as shown below: Db,sub = (Db,sub,nit)   respectively. Fsub is the molar fraction of the substrate in the bulk layers and a is a correction factor which takes the form of an activity coefficient. Te parameter a was required in Equation 8in order to reproduce the experimental data using a value for Db,nit,nit which was in the liquid range.a was assumed to be composition dependent and was parameterized using the equation shown below, which has been used successfully in previous work.9,10 ln  =   2 ( + 3 − 4 sub ) The constants C and D as well as other parameters such as the film thickness and diffusion coefficients were determined using the Monte Carlo Genetic Algorithm (MCGA) method. 11This method consists of two steps: during the Monte Carlo step, parameters are randomly varied over a range of values and a residual between the experimental data and the output is calculated.
During the genetic algorithm step, the best parameter sets are optimized using processes such as survival, recombination and mutation.
Table S2 summarizes the parameters used in the KM-GAP model that provided the best fit to the experimental data.The values of Knit were fixed to values which had been determined experimentally for the specific experiments which were modeled.The value of Db,nit,nit was fixed to 1× 10 -8 cm 2 s -1 for all nitrates and is a reasonable value for the self-diffusion of the nitrates, which are liquids at room temperature.Only upper limits of Db,sub,nit and Db,sub,sub are given in Table S2 as lower values had a negligible impact on the modeling results.Other input parameters in the model were the desorption lifetimes of the nitrates which were set to one μs, and the surface mass accommodations of the nitrates, which were fixed to be one.is not shown due to variations in the CO2 (g) in the sampling compartment.

Figure S2 :
Figure S2: The GC-MS data for solutions (approximately 100 mM in dichloromethane) of a)

Figure S4 :
Figure S4: DART-MS spectra for the vapors from the headspace of a) pure HPN in the glass

Figure S5 :
Figure S5: ATR-FTIR spectra for a solid PA film (red), and a liquid PA solution in acetonitrile

Figure S6 :
Figure S6: Typical films of a) PEA, b) PA, and c) SOA.The white regions on the crystal face

Figure
Figure S6a shows an example data set of the SMPS, APS, and Weibull fit for a

Figure S7 :
Figure S7: a) The SMPS, APS, and Weibull fit data for a representative particle number

Figure S9 :Section 7 -Figure S10 :
Figure S9: The optimized structures for binding of one PEA subunit to a) two 2EHN, b) two HPN, and c) two

Table S2 :
Input parameters used in the KM-GAP model to fit the experimental data.

Table S3 :
Binding energies for systems of one nitrate molecule binding to one PEA subunit, and two nitrate