H 2 SO 4 and particle production in a photolytic flow reactor : chemical modeling , cluster thermodynamics and contamination issues

Size distributions of particles formed from sulfuric acid (H2SO4) and water vapor in a photolytic flow reactor (PhoFR) were measured with a nanoparticle mobility sizing system. Experiments with added ammonia and dimethylamine were also performed. H2SO4(g) was synthesized from HONO, sulfur dioxide and water vapor, initiating OH oxidation by HONO photolysis. Experiments were performed at 296 K over a range of sulfuric acid production levels and for 16 % to 82 % relative humidity. Measured distributions generally had a large-particle mode that was roughly lognormal; mean diameters ranged from 3 to 12 nm and widths (lnσ ) were ∼ 0.3. Particle formation conditions were stable over many months. Addition of single-digit pmol mol−1 mixing ratios of dimethylamine led to very large increases in particle number density. Particles produced with ammonia, even at 2000 pmol mol−1, showed that NH3 is a much less effective nucleator than dimethylamine. A two-dimensional simulation of particle formation in PhoFR is also presented that starts with gas-phase photolytic production of H2SO4, followed by kinetic formation of molecular clusters and their decomposition, which is determined by their thermodynamics. Comparisons with model predictions of the experimental result’s dependency on HONO and water vapor concentrations yield phenomenological cluster thermodynamics and help delineate the effects of potential contaminants. The added-base simulations and experimental results provide support for previously published dimethylamine– H2SO4 cluster thermodynamics and provide a phenomenological set of ammonia–sulfuric acid thermodynamics.

. CPC Raw count rates vs. time for the channels (i.e. particle sizes) monitored with the DEG system. Each channel's set voltage for the nanoDMA's high-voltage source are indicated in the figure: due to electrical offsets, the voltages applied were actually 2 V higher (see Table S1). The thick red line is the flow rate of the HONO mixture and the pink squares joined by slanted lines mark each time-selected range of data for averaging to yield a size distribution. At 13:20, ammonia at 440 pptv was added at the top of PhoFR (2018Jun13). Table S1. Voltage on the nanoDMA center rod, mobility diameter, and the overall correction factor for particle losses, charging efficiency etc. (Jiang et al. 2011.) S1.1 S1.1 S1.1 S1.1 Leading edge of the s Leading edge of the s Leading edge of the s Leading edge of the size distributions ize distributions ize distributions ize distributions The leading edge mode of the size distributions were fit to log-normal functions using an Excel add-in (written in Visual Basic, "LgnFit.xlam", M. R. Stolzenburg, private communication). The routine 'LgnFit' fits a log-normal to the upper portion of a measured distribution, resulting in leading-edge parameters D le , lnσ le and N p,le . Shown in Fig. S2 are a typical measured distribution and two lognormals, one using LgnFit and one that was manually fit to the leading edge particles. The fitting routine included the 4.3 nm data and thus resulted in a wider distribution. Which of the two lognormals is best for interpreting the data may depend on what physical process is being probed. In terms of the size to which the largest particles can grow, the mode diameters of these lognormals are not significantly different.
We have identified a "leading edge" of the size distribution which is "leading" in terms of particle growth. This "leading edge" terminology refers to the large-particles at the leading edge of the distribution and here we clarify this further. This is beyond what one would naturally think of as the leading edge particularly as we fit lognormals to this data which requires to some extent data on both sides of a peak. So if the large particle peak is prominent, data for the fit should extend from the "leading edge" at the far right all the way down in size to an inflection point between the large particle peak and the minimum towards smaller sizes. Note that N p is for "large particles" that are defined differently: all those with D p >= 2.4 nm. It is important to maintain the distinction of which criterion was used to derive any particular parameter (e.g. D le , not D p ). In practice, the integration of the lognormal fit and N p do not differ appreciably.
Some distributions without base added do not exhibit a prominent large particle peak. In these cases either no or an inappropriate inflection point was selected. When no inflection point is exhibited, they were not able to be fit automatically. These cases were not included in the D le plots but we note that lognormals fitted by eye, using an average width from contemporary distributions, yield D le values that fall within the scatter of the expected values. Some distributions yielded automatic fits that exhibited widths that were very large because the inflection point was too low in diameter. In these cases, the routine was forced to ignore one or two of the smallest diameter data points. A width criteria was used in these cases: the smallest diameter data were excluded one at a time until lnσ ≤ 0.4 for Q 4 ≤ 4.3 sccm and lnσ ≤ 0.55 at higher Q 4 . Fig. S2 below for a Q 4 = 4.3 sccm distribution is one such case. For this data set, the inflection point criteria in the automatic fitting routine also included the next smallest diameter data point and resulted in a lnσ = 0.5. Including the data point at 3.3 nm brings in smaller particles that probably did not originate in the top 1/3 of the flow reactor. S1.2 Typical me S1.2 Typical me S1.2 Typical me S1.2 Typical measured size distributions. asured size distributions. asured size distributions. asured size distributions.
Depicted in Figs. S1.2.1 are representative particle size distributions as a function of N 2 flow through the HONO source, Q 4 , a proxy for HONO abundance. Q 4 was varied from 1.6 to 5.3 sccm while the abundances of the other reactants were held constant. The size distributions are strongly dependent on HONO over this range, with concentrations increasing by a factor of ~ten at small sizes and the large particle abundance by a hundred-fold. Log-normal distributions are also shown as the dashed lines in the figure with leading-edge mode diameter D le and lnσ noted in the legend. The log-normals shown in the figure were not those from the fitting procedure (see S1.1 for a discussion of the fitting procedure) because the fits failed for the two lowest Q 4 . For a consistent presentation, lnσ was fixed and each log-normal was adjusted visually to best cover the four or five points nearest the peak of each distribution. Note that raw count rates at the smallest size for the three lowest Q 4 are roughly 0.1 s -1 and, statistically, they are not significantly different. This is slightly above the background count rate of ~0.05 s -1 . The volume mean diameters from nearly all of the measured nominally-binary size distributions are plotted vs. Q 4 in Fig. S1.2.2(a-c). Panel (a) shows D V.l.e. as a function of Q 4 , panel (b) is D V.l.e. vs. relative humidity and (c) is D V.l.e. as a function of SO 2 abundance. Not all experiments yielded leading-edge log-normal fits; these were primarily for Q 4 values less than or equal to 2.2 sccm in (a).
The data is linear in plot (a) over the range 2.2 to 8.5 sccm in Fig. S1.2.2(a) and a linear fit is shown as the line. The largest Q 4 data points fall a little below the line and perhaps the distribution of H 2 SO 4 is significantly perturbed by the large particle surface area, decreasing the connection between Q 4 and growth. Plot (b) also shows a linear relationship between size and relative humidity, a phenomenological finding that has a slightly higher RH dependency than a simple swelling of the particles due to uptake of water vapor (see the solid line). Plot (c) shows the experimental and growth-rate calculated diameter as a function of SO 2 .
Fig. S1.2.2. Volume mean diameter of the particles in the leading edge of the particle distributions, D V,le = D le *exp(1.5lnσ σ σ σ 2 ). Top plot (a) D Vl.e. vs. Q 4 at 52 % RH. Data from those distributions that had a local minimum between the smallest particles and the peak at large diameters that allowed for fit. (b) D Vl.e. vs. RH at Q 4 = 4.2 sccm. A linear fit is shown as the dashed line (phenomenological) while the solid line is the diameter increase based on water uptake using bulk values for the density and mass fraction of H 2 SO 4 as a function of RH (Wexler and Clegg, 2002). (c) D Vl.e. vs. Q 1 , the flow rate of the SO 2 mixture for 52 % RH and Q 4 = 4.2 sccm. The dashed and solid lines are diameters derived from simulated growth rates without and with, respectively, a reaction included for HO 2 with SO 2 . The size was estimated from the H 2 SO 4 growth rate and particle transit time assuming particles nucleate at 1 nm mass diameter. Also applied was the mobility to mass size difference of 0.3 nm (Larriba et al.) Finally, size distributions for Q 4 = 4.2 sccm and Q 1 > 16 sccm for the bulk of the measurement period are shown in Fig. S1.2.3. The scatter in the measurements is clearly the dominant feature in these plots. Yet in an overall sense, it appears that particles taken in the latter time period are somewhat less abundant. However, any differences are obscured by the overlap of the scatter in the individual distributions.

S1
. S1. S1. S1.3 3 3 3 Modeled size distributions. Modeled size distributions. Modeled size distributions. Modeled size distributions. Fig. S1.3.1a,b,c below are typical model results for nucleation due to only the binary system (a) as incorporated for 52 % RH, and nucleation with 200 pptv NH 3 added (b) using a new set of NH 3 -H 2 SO 4 thermodynamics, scheme NH3_52 (aka B52#ZtriplePrime). These thermodynamics are presented in S8 below. The development of the size distributions are illustrated in a series of distributions at different lengths down the flow reactor for a HONO source flow of Q 4 = 2.1 sccm. Clusters up to 250 H 2 SO 4 molecules were simulated. Panel c shows the size distributions at Z = 120 cm where particles are sampled for the binary and added ammonia cases from a and b as well as a size distribution for 0.005 pptv added dimethylamine. Shown in Fig.  S1.3.2 are the R = 0 concentrations vs. axial distance of a few select clusters for the simulation shown in Fig.  S1.3.1b.

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The characteristics of the distributions change in expected ways along the length of the flow reactor. The binary system results ( Fig. S1.3.1a) have N p increase dramatically with distance along the flow reactor (N p /cm -3 is the second column in the legend; N p is the sum of all particles with mobility diameters D p > 2 nm which are cluster sizes > 10 H 2 SO 4 molecules), while N p in the added NH 3 case is relatively constant in the lower half of the reactor. From 80 to 120 cm, the number of large particles increases by a factor of 20 in the binary case while in the added NH 3 case this number increases by a factor of only 1.4. The "large particles" in general grow larger as they flow down the reactor with this growth best exhibited in the added-NH 3 case with a nice progression in the peak towards large sizes in the distributions from 60 to 120 cm.
Comparing the simulated 120 cm distributions with and without added base ( Fig.S1.3.1c where additional simulations where 0.005 and 2 pptv dimethylamine were included) illustrates how the size distributions form.
The smallest clusters of D p < 1.8 nm have high concentrations in all cases at the end of the reactor because of the peak in H 2 SO 4 in that region. The large particle mode is apparent in all cases as well but the shapes and abundances are different. In the case of added NH 3 , the large particle mode is indicated by a strong leading edge with a peak at 4 nm while the binary only size distribution is smaller with a shallow peak at 2.6 nm. Ammonia's influence is large for large particles, those that nucleate near the top of PhoFR but the mid-sized particle numbers are also significantly increased. Despite its rapid diffusion and loss on the wall, enough ammonia makes it far enough into the reactor to affect the mid-sized particles: the model (Fig. S1.3.2) shows that about 10 % of the initial [NH 3 ] is present on axis, halfway down the tube. The 5 ppqv dimethylamine simulation shows that this slower diffusing base species, which will be true for any amine or amide compared to ammonia, can have a relatively large impact on the mid-sized particles. The interplay between the effects on the size distributions depends on what type of impurity is present and where it originates. There is excellent agreement between simulated and experimental for the 2 pptv dimethylamine-added case except towards large particles.
Even though the shapes of the distributions compare favorably with experiment for nominally clean and for added NH 3 , the disparity in the total number of particles indicates there is some deficiency in the phenomenological thermodynamics for these conditions. Yet this could also be due to a contaminant that is more nucleation-active than ammonia such as an amine (Glasoe et al.) and thus it could have an influence even if present at very low levels. The thermodynamics used here (see S8) are phenomenological and set by comparison with the high ammonia data for Q 4 = 4.2 sccm. This was done because under these conditions nucleation will be less influenced by any potential contaminant. So the under-prediction of the simulations at Q 4 = 2.1 sccm may not be a flaw in the thermodynamics but probably indicates a larger sensitivity to contaminant at the lower sulfuric acid conditions. S2. S2. S2. S2. Historical PhoFR Historical PhoFR Historical PhoFR Historical PhoFR data data data data During the course of this study, the experimental apparatus was moved to a lab in a newly-constructed building. The gas source was switched from cleaned air (AADCO 737) to nitrogen from a liquid nitrogen gas-pack dewar (Airgas). This nitrogen is listed as having < 10 ppm oxygen impurity level, and apparently there is enough present as there was little effect on size distributions when oxygen was added. Data for typical baseline conditions for the year previous to this move are presented in Fig. S2.  Over this time period, N p averages about 1x10 5 cm -3 , the mode diameter has an average of about 5 nm, and the majority of the lnσ values are between 0.4 and 0.44. Since late March 2017, when the UV lights were moved a few cm closer to the flow reactor, trends in the data with time are not evident although the scatter remains significant. Three recent data points are not filled in and they were taken just before the NaONO(s) powder was lightly shaken. It is noteworthy that this process makes a difference however the effect is variable, e.g. in early November 2017 the NaONO vessel was shaken and the N p increase was only about 25 %, less than the +100 %/-50 % day-to-day variability. The causes of this variability have not been identified but temperature variations are a likely cause, that of the room as well as that of the HCl-source. When NH 3 is added to PhoFR, the leading-edge particles of the size distributions become very well-defined. This is also true for the measurements presented in Glasoe et al. (2015), but in that case the very low number of particles without the dilution system attached, less than 1 cm -3 , indicated a very clean flow reactor. The probable contaminant amine in the ammonia dilution system used by Glasoe et al. is a separate issue. Fig. S3.1 are representative size distributions for the present measurements taken in PhoFR (2018Jun13) and for measurements in the Nucleation Flow Reactor (NFR) used by Glasoe et al. (2013Jun27) along with a more recent measurement from that apparatus (2016_01_20). The size distribution from January 2016 is very narrow compared to the others and this is probably due to the 25 ⁰C temperature of the mixing region and sulfuric acid reservoir (these were regulated at 35 ⁰C for the Glasoe et al. data set.) Very important to keep in mind is that the abundance of H 2 SO 4 in NFR is much different than it is in PhoFR: it is greatest near the top of NFR and drops by 2/3 or so as the particles travel to the DEG system. There are fewer particles in the present measurements but they are able to grow to larger sizes due to their larger overall exposure to H 2 SO 4 in PhoFR. The size distribution from 2013 from Glasoe et al. is larger and broader than the others.  Bases are added from the dilution systems through a sidearm port at the top of PhoFR, about 10 cm below the Teflon mesh. We have used a similar system for base introduction where the tip of the exit tubing of the dilution system (of 1/8" OD) is installed so that it is flush with the flow reactor wall (Zollner et al., Ball et al., Glasoe et al.) and we found that a net flow of about 50 sccm through this tubing gave maximum particle number densities. In a later publication, (Hanson et al. 2017) we presented experimental and computational fluid dynamics results that showed that a flow of 50 sccm (computational) and 60 sccm (experimental) carrier gas (nitrogen) resulted in a maximum in the number of particles.

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Depicted in Fig. S3.1.3 are experimental results for 300 pptv NH 3 added to PhoFR at standard conditions. It shows that a flow of 35 sccm entering PhoFR from the dilution system gives a peak in the experimental particle number. This is somewhat lower than for our previous experimental work but this is expected as the total flow rate here is 2900 sccm compared to 6000 sccm in that previous work (both flow reactors have 5 cm ID.) Further discussion of base mixing into the main flow is presented in S7.1.   Fig. S3.2 a and b. The zero-added base data between these runs might be affected by dimethylamine holdover but this appears to be small: the N p are within a factor of two of the Q 4 =2.1 sccm data in Fig. 4a. It is clear that more dimethylamine leads to more particles, with N p increasing approximately linearly with dimethylamine abundance.
Particle-particle interactions at large N p may act to weaken the connection between N p and the actual nucleation rate which may contribute to the low dependence of N p on Q 4 in Fig. 4a. Changes in dimethylamine concentrations due to scavenging by particles may also constrain the nucleation rate at the higher Q 4 conditions.  Fig. 4a and (b) were used in Fig. 5. In the legends, the entries with data points indicate Q 4 /sccm (a) and DMA/pptv (b), and the dash-dot labels indicate D p and lnσ σ σ σ. At least daily, the UV lights were turned off to get a measure of the average dark counts. The count rate for these conditions was typically 0.05 s -1 but ranged as low as 0.02 s -1 and it was independent of reactant concentrations. Note that corrections for losses and charging efficiency increase as particles get smaller, thus there is an increase in corrected dark counts towards smaller particles. They can significantly influence the fits at the lowest Q 4 values, 2.2 sccm and lower, introducing additional uncertainty in the log-normal fit parameters.

S4
Having said that, we note that the smallest particles are not included in the Q 4 = 4.2 sccm data thus counting statistics are not a major contributing factor to the scatter evident in Figs. 2a, S3 and S4(a). The fitting procedure for some distributions can sometimes yield a range of log-normals that fit the data equally well however values for N p and D le are not sensitive to the choice of the log-normal. It is difficult-to-pin-down variations in the system that can be responsible for the scatter. As alluded to in S2, we believe the most likely causes are: (i) small temperature fluctuations in the HCl solution for the HONO source and (ii) inadvertent eddies or changes in the flow profile at the top of PhoFR. These may also introduce a bias in addition to scatter (thus a true systematic uncertainty) that may depend on trends in the temperature of the room. Usually, the temperature of the room was between 22 and 24 C but occasionally it was as warm as 26 C. If these temperature excursions also introduce a secular bias in flow patterns (which may have important implications for the modeling effort, see S7.2) is not known.
Large jumps in N p and D le could be due to episodic exposure of the flow reactor to room air and/or to dust, especially upon cylinder changeover. One such episode is depicted in Fig. 2a Vis absorption experiment. The HONO-containing flow was sent through a 1.05 m long absorption cell to assess the HONO level by absorption using a small diode array detector (Red Tide, Ocean Optics, ~ 3 nm resolution). The source was either a small UVA lamp or a white light. Shown in the figure are the transmissions for several measurements and the expected transmission for a HONO level of 20 ppmv (cross section from NASA data panel averaged over 4 nm). The absorptions for the two sources differ perhaps due to differences in scattered light within the instrument. There is a noticeable absorption at 400 nm and longer which can probably be assigned to NO 2 (see absorption due to 5 ppmv in Fig S5.1, NASA-15 cross sections). Syomin and Finlayson-Pitts (2003) saw HONO decay of about 10 % in a 100 min in the presence of 50 % RH. The water content of gas flowing from the HONO source is about 76% RH at 20 C which may decrease to about 50 % at 23-25 C, the temperature of the absorption cell. Some loss of HONO and formation of NO 2 is expected but it is difficult to quantify to what extent from the previous work. It is also difficult to determine where this conversion may have happened.

S5.2 S5.2 S5.2 S5.2 PTrMS measurements of isoprene oxidation due to HONO photolysis PTrMS measurements of isoprene oxidation due to HONO photolysis PTrMS measurements of isoprene oxidation due to HONO photolysis
PTrMS measurements of isoprene oxidation due to HONO photolysis. . . . The amount of OH-photolyte generated for typical conditions (Q 4 =4.3 sccm, 3 sLpm total flow) was evaluated by adding isoprene to the flow and monitoring the amount of product methylvinyl ketone (MVK)and methacrolein (macr) using a PTrMS system (Hanson et al. 2009). An aliquot of isoprene in a diffusion tube, immersed in ice was teed into a flow entering PhoFR resulted in a level of isoprene = 6x10 12 cm -3 as determined with a sensitivity of S isop. = 78 ncps (aka Hz/ppbv/MHz) using isotopic ratio and the signal on mass 70: the M.H + signal at 69 u exceeded the linear range of the detector. This value of S isop. was the average of three values, determined from recent calibrations of the PTrMS for methanol, acetone and 3-pentanone and scaling them according to the ratios of sensitivities for isoprene to these compounds reported in Hanson et al. (2009). An increase in the signal at 71 u (M.H + for MVK + macr) of ∆s 71u = 2800 Hz was observed when the UV lights were turned on (see left plot of Fig. S5.2). Assuming enough NO was present, a yield of 70% for these species is applicable (Liu et al., 2013;Wennberg et al., 2018) and assuming reaction with OH is negligible, the average production rate of MVK + macr (in cm -3 s -1 ) in the illuminated portion of PhoFR is given by where the last term converts ppbv to cm -3 , and the 1.6 is from assuming MVK and macr are 1.6 times better detected than isoprene (Warneke et al., 2003). S 0 is the reagent ion signal (S H3O+ + S H3O+.H2O /1.4; the factor 1.4 here is the relative transmission factor determined for the 38 u relative to 21 u, and isotopic factors of 667 and 500 were applied to S 38u and S 21u , resp., to get the water proton signals. The average production rate of OH due to HONO photolysis is balanced by its loss to isoprene: Applying steady-state and: and combining eqns. 5.1, 5.2 and 5.3, an expression for the quantity k I phot. [HONO] is obtained.   We believe the the flow reactor wall became conditioned to ammonia when subjected to large NH 3 exposures: particle counts rose with time and there was occasionally large holdover where residual ammonia affected results for up to several days. This is shown in Fig. S6, a plot of N p vs. date on runs surrounding (red squares depict no base added runs) days when runs with 2000 pptv NH 3 (blue diamonds) was added. On the two days when this amount of NH 3 was added (blue diamonds) N p increased precipitously with time, increasing by more than an order of magnitude before NH 3 was removed.
This amount of ammonia affected experimental conditions, most likely through neutralizing of the acid that had accumulated on the wall. This conditioning is presumably due to ammonium bi-sulfate formation on the walls which will decrease the loss of NH 3 and more NH 3 is transported down the reactor where it can interact with the high SA levels found there. After each of the two additions, N p without added NH 3 was quite high (red squares) and after the second run high N p persisted for several days. The model is a 2D representation of the flow reactor and was built upon the model presented in Hanson et al. (2017), with details of acid-base clustering presented in the Supplement of that work. In addition to changes in the flow rate (2.9 sLpm here), the present simulations included the production of H 2 SO 4 from the photolysis of HONO and subsequent oxidation of SO 2 . The main inputs for the simulation are HONO and SO 2 levels, a 1storder photolysis rate coefficient for HONO and the amount of base in the inlet. The photo-oxidation scheme and rate coefficients are shown in Table S1. The flow rate was varied in the model from 2.8 to 3.0 and the large clusters (i.e., N p ) were insensitive to flow rate. The number of acid molecules in the largest clusters in the simulation was varied from 6, 8, and 10, maintaining a maximum NH 3 -content of 3, and only small variations were observed in the concentration of the largest clusters (summing over base content). This was much in line with what we reported previously (Panta et al. 2012, Hanson et al. 2017. Presented in S1.3 above were runs where clusters were allowed to grow to 250 sulfuric acid molecules. In this work, base was introduced into simulated 2D flow reactor uniformly distributed across the radius of the flow reactor. Section S7.1 below discusses how well this mimics the mixing of the base in the experiment.  (Atkinson et al. 2004.) or NASA-15 except rxn. 13, the upper limit of Burrows et al. (1979). Species designations: 1, OH; 2: NO, 3: HO2, 4:HO2NO2, 5: SO2, 6: NO2, 7: HONO, 8: HNO3, 9: H2O2, 10: HOONO. a: Assumed to be very fast. b: Includes water chaperone effect. c: Speculative rate and products: OH assumed to be produced.

S7.1 Inhomogeneous base concentrations S7.1 Inhomogeneous base concentrations S7.1 Inhomogeneous base concentrations S7.1 Inhomogeneous base concentrations
There is a concern that base in the sidearm flow does not mix into the main flow rapidly enough to match the assumptions in the simulations. For example, base is present in this sidearm flow at a level of about 100 times the value it would be when fully mixed. In our previous work using 3D CFD models of flow reactors with similar base introduction methods (Fig. A11 in Panta et al. 2012; Figure 4 in Hanson et al. 2017), we showed that base diffusion into the sulfuric acid-laden carrier gas was rapid enough that significant cluster formation did not occur until large gradients in [base] were reduced. Appreciable cluster formation began only after base had been dispersed such that [base] was less than 10 % of its initial sidearm concentration. Cluster formation was not immediate even though the highest levels of sulfuric acid were at the top of the flow reactors where the highest levels of base were. A 2D model cannot simulate this sidearm addition of base and a workaround was presented (Hanson et al., 2017) where base was added at four times the desired level but only in the middle 1/4 of the flow, a so-called middle-fake base addition. Shown in the figure below are results from the middle-fake simulations compared to base fully-mixed at the flow reactor inlet. More ammonia makes it down the reactor due to less interaction with the reactor wall than when ammonia is fully mixed (Fig S7.1 right: compare MidFake 40 cm to Normal 40 cm). The effect on the number of particles was an increase of about 40 % when the middle fake was used (Fig. S7.1 left). This is likely due to the increased ammonia levels downstream (compare the 40 cm radial distributions.) This is a significant effect but it is certainly within the scatter of the base-added experiments. It is likely that the effect on N p is not large because the base is able to diffuse and establish the radial profile determined by loss on the wall before sulfuric acid builds (see Fig. S3.1.2) and significant cluster formation has commenced.

S7.2 Flow considerations S7.2 Flow considerations S7.2 Flow considerations S7.2 Flow considerations
The model assumes either a fully-developed laminar or plug flow profile for the entire length of the flow reactor. With a Reynold's number of about 90 and an entrance length of ~14 cm (0.03 times the diameter times the Reynold's number, Goldstein, 1965 p299), it is expected that experimental conditions are best represented in the simulations using laminar flow than plug flow. This is corroborated by comparing simulations to experimental. Shown in Fig. S7.2 are simulated size distributions for laminar and plug flow for Q 4 =2.1 sccm and 230 pptv NH 3 where the experimental mode diameter with ammonia added is about 4 nm (Fig. S1.3.1). The shape and peak of the size distribution for laminar flow agrees best with experiment as the plug flow simulation shows a leading edge mode with an ~8 nm diameter. Note that there is an increase in simulated N p of about 70 % when plug flow was used compared to laminar flow. The results of these simulations reveal that the assumed flow profile does matter, particularly in the shape and peak of the size distribution.
Nonetheless, the flow at the top of the reactor may not be fully-developed laminar for some length. Since base is added in this section there may be a sensitivity to conditions that would be difficult to explore with the twodimensional simulation. Yet sulfuric acid levels are lowest at the top of PhoFR and the effect of non-laminar flow is probably a secondary issue more related to variability than to a systematic bias, such as a contamination problem as depicted for the high ammonia experiments (Fig. S6) and intermittent dust contamination (Fig 2a).  A set of thermodynamics for ammonia sulfuric acid clusters that merges with the free energies of the no-base clusters for 52 % relative humidity were developed here. The cluster free energies were manually set by running simulations and checking them against the experimental data for Q 4 = 4.2 sccm with ammonia at 500 pptv and higher. This assumes that the effect of contaminants is negligible for these conditions. Any synergistic effects are also assumed to be negligible. Because of these assumptions, the free energies must be put on a phenomenological footing.
Previously, a set of thermodynamics for ammonia-and dimethylamine-sulfuric acid clusters were determined (Hanson et al., 2017) Table S2. Since this is a somewhat arbitrary procedure, it should be considered as exploratory.
The phenomenological ammonia-sulfuric acid thermodynamics developed here were based on the Ortega et al.
(2012) thermodynamics (extended to larger clusters: NH3_I scheme of Hanson et al. (2017)) and adjusting for the 52 % RH binary system thermodynamics. Cluster free energy changes for addition of sulfuric acid were increased regularly and uniformly as ammonia molecules were incorporated into each cluster. We kept the appearance of local minimums in H 2 SO 4 -loss rates from a 2 b 1 and a 2 b 2 in accord with the NH3_I thermodynamics of Hanson et al. (2017) which followed closely the quantum chemical calculations of Ortega et al. (2012). These cluster free energies labeled NH3_52 were extended up to a 10 b 10 clusters and are presented in Table S3. The largest differences from NH3_I, i.e., ∆G(NH3_I)-∆G(NH3_52), are: more stable a 4-8 b 0 clusters (3 to 14 kcal/mol), more stable a 6-8 b 1,2 clusters (2.7 to 10.5 kcal/mol ), and less stable a 3-5 b 3,4 clusters (-8.5 to -3.5 kcal/mol). A large effect on cluster abundances was noted when selecting the free energy of a 1 b 1 : a factor of x3 / divide by 3 in N p occurred when a 1 b 1 was adjusted by 0.5 kcal/mol, down and up, respectively. The free energy for a 1 b 1 in NH3_52 was set to -7.2 kcal/mol, 0.8 kcal/mol less stable than in NH3_I.  Simulated H 2 SO 4 profiles are sensitive to the value of this rate coefficient. Using low values yields smaller dependencies on SO 2 for N p and size: a value of 1x10 -17 cm 3 /s had N p increase by about 50 % as Q 1 was increased from 8 to 50 sccm while a rate coefficient of 1x10 -18 cm 3 /s had a 22 % increase. Increasing this rate coefficient to 1x10 -16 cm 3 /s had large effects: as Q 1 varied from 8 to 50 sccm, particle size roughly doubled and N p increased by an order of magnitude. A value of the order of 10 -16 cm 3 /s along with generation of OH in the reaction is probably the limit for simulations to remain congruent with the data. On the other hand, if a wall loss for HO 2 is significant in the experiment, much larger values for the rate coefficient would be needed in the simulations for the reaction to have significant effects.
Alternative explanations for an SO 2 dependence include uncertainties in HONO concentrations as well other clustering reactions. More HONO in the flow exiting the source (and a smaller first-order photolysis rate to compensate) would cause predicted N p to have an increased dependence on SO 2 . SO 2 may react with oxidants within the small particles, leading to their growth.
The dependencies upon SO 2 were much smaller when minute amounts of dimethylamine were included in the model. Low levels of (0.005 pptv) dimethylamine gave simulated Np in the 10 4 cm -3 range but at this level its ability to influence the change in N p with H 2 SO 4 was limited due to the amine being scavenged by clusters. This suggests that a potential contaminant in our system is not a strong nucleator like dimethylamine.