Introduction

Aerosols play a key role in cloud formation and climate, [1][2][3] substantially offsetting the warming by greenhouse gases. 4 It is therefore important to understand what mechanisms are driving the formation and growth of aerosols, so that climate models can include them. Of equal importance, nucleation and growth of aerosols leads to persistent pollution in megacities, which can also be responsible for changes in local weather systems and local climate forcing. 5,6 In addition, particulate pollution causes millions of premature deaths annually, and is one of the leading causes of deaths globally. [7][8][9] Once new particles have been formed, they are able to grow via condensation of vapours. The growth must be fast enough to rival coagulation with larger particles, referred to as the coagulation sink. Particles smaller than 10 nm have high Brownian diffusivity and are therefore most vulnerable to coagulation loss. 10 The likelihood of a particle's survival is dependent on a balance between growth rate and coagulation sink. Previous understanding was that growth rates in cities are only up to a few times greater than those in clean environments. 11 Therefore, under highly polluted conditions seen in cities, newly formed particles are not expected to survive very long before sticking to larger particles. However, intense new particle formation events are regularly observed under these conditions, with particle formation rates up to hundreds of times higher than in clean environments, [12][13][14][15][16] despite the high loss rates of nucleated clusters. Currently, there is a major gap in our understanding as to how the particle number concentration can be sustained under such highly polluted conditions. Higher than expected cluster survival through the most critical size range (the so-called "valley of death" between nucleated particles and $10 nm) implies either ineffective scavenging by pre-existing particles or a missing growth mechanism. 17 Recently, Wang et al. (2020) 18 presented a new mechanism of rapid particle growth, affecting particles as small as a few nanometers, via condensation of HNO 3 and NH 3 . Ammonium nitrate is an important semi-volatile constituent of large particles, previously thought to be too volatile to contribute to early growth. However, Wang et al. (2020) demonstrated that in conditions of excess NH 3 and HNO 3 mixing ratios, with respect to ammonium nitrate saturation ratios, particles as small as a few nanometers can be activated to rapidly grow to much larger sizes, analogous to CCN activation. Ammonium nitrate growth affects particles once they reach a critical diameter, referred to as the activation diameter. This growth mechanism could play a key role in high survival of small particles and therefore explain the maintenance of high particle number concentration under highly polluted conditions. An alternative mechanism that has been also suggested would be that our current understanding of loss rates is incomplete, and clusters are not efficiently lost to large particles. 17 However, neither theory has been experimentally tested or veried to date. In this work, we present the rst combined experimental and model results of survival of small particles in the presence of a high coagulation sink, analogous to haze.

Methods

The CLOUD chamber at CERN The experiments presented were undertaken at the CLOUD (Cosmics Leaving OUtdoor Droplets) chamber at CERN (European Organization for Nuclear Research). The conditions in the chamber were controlled to 5 C and 60% relative humidity (RH). Further details on the CLOUD chamber experiments can be found in the ESI. † Nucleation experiments. We begin the nucleation experiments with a clean chamber and constant gas concentrations. The experiments start by injecting several precursor gases which would be expected in a city, namely NO, SO 2 , toluene, apinene, HONO, NH 3 , O 3 , and dimethylamine. Through photolysis of HONO (UVA generated at 385 nm by a 400 W UVA LED saber, LS3) and/or O 3 (170 W quartz-clad high intensity Hg lamp, saber, LS1) OH radicals were produced, and subsequently condensable gases, leading to nucleation and growth of particles. HNO 3 was formed through reaction of cOH with NO 2 ; organic oxidation products through reaction of cOH with volatile organic compounds (VOCs); and H 2 SO 4 through reaction of cOH with SO 2 . In certain experiments, HNO 3 was also injected directly into the chamber. We then monitor the nucleation and growth, and when the stage is deemed nished, the lights are turned off and cleaning and preparation for the next stage begins.

High condensation sink experiments. In the high condensation sink experiments, before nucleation attempts began, we generated a high condensation sink, consisting of particles around 100 nm and larger. This was achieved by rapidly growing particles with a high amount of condensable gases (H 2 SO 4 , HNO 3 , NH 3 , DMA, and toluene organic oxidation products). Once the condensation sink reached values above 0.06 s À1 , the lights were turned off to halt further gas production, and the fan speed in the chamber was increased, to remove small particles and condensable gases. Aer the cleaning step, the experimental run was undertaken as described previously (see Nucleation experiments).

Modelling ammonium sulfate

The sulfuric acid and ammonia nucleation and growth model is based on the model described in detail in Xiao et al. (2021) 11 which is developed from the general dynamic equation. 19 Briey, the model calculates particle and gas concentrations for each time step via a sum of production and losses for each gas, cluster or particle size bin. When organic oxidation products were present in the experiments, nucleation and growth were parameterised in the model to that of the experiment. This was achieved by increasing the H 2 SO 4 concentration used in the model to account for enhanced growth rates since this model does not include organic oxidation products.

Particle loss rates

For the particle loss rates in the chamber, we consider wall loss, dilution loss, and coagulation loss (or gain). We calculate the coagulation change in each size bin using the coagulation coefficient and the general dynamic equation from Seinfeld and Pandis (2006) 19 and solving for the change in particle number for each size bin for each time step. 11,20

Modelling ammonium nitrate

We developed an ammonium nitrate growth model addition to the ammonium sulfate model. It is a polydisperse growth model, with 150 bins ranging from one ammonium sulfate cluster to 1000 nm, which also provides the time evolution of particle size and composition. We predict condensation of ammonium nitrate based on the equilibrium of NH 3 and HNO 3 in the gas phase. NH 3 and HNO 3 concentrations are also calculated by summing up production and losses at each time step (injection, photolysis, wall loss, dilution loss, condensation, etc.). For some experiments, gas phase concentration or formation rates were constrained from measurements. As shown in Wang et al. (2020) 18 ammonium nitrate condensation behaves much like CCN activation, and the behaviour is consistent with the nano-Köhler theory. A mass ux is established, based on whether the ammonium nitrate is in supersaturation or not. The supersaturation was calculated based on the dissociation constant K p , 21 dened as the equilibrium product of gas phase NH 3 and HNO 3 . Supersaturation of ammonium nitrate is equal to ([NH 3 ] g  [HNO 3 ] g )/K p . The uxes of HNO 3 and NH 3 are considered to be equal and dependent on the limiting gas, since formation of ammonium nitrate is equimolar. Therefore, we calculate the net ux of NH 3 and HNO 3 at every time step and include a Kelvin term and activity term in order to calculate the different uxes for different particle sizes (see eqn (S.3) ESI † -Modelling ammonium nitrate).

Results

Modelling rapid growth from ammonium nitrate condensation

Experiments were undertaken at the CLOUD chamber at CERN under various concentrations of H 2 SO 4 , NH 3 and HNO 3 at 5 C

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Environmental Science: Atmospheres and 60% relative humidity, and in some instances in the presence of dimethyl amine and/or organic oxidation products formed from a-pinene or toluene. Fig. 1(c) shows experimental CLOUD (2018) and kinetic model results and the dependence of the growth rate of particles aer activation by ammonium nitrate on the excess ammonium nitrate concentration. The excess ammonium nitrate is calculated by subtracting the dissociation constant K p from the product of the gas phase NH 3 and HNO 3 concentrations, this represents the amount of gas available for condensational growth, once the particles have grown as large as the activation diameter. In the majority of CLOUD experiments presented, the limiting gas for condensation was HNO 3 , as the experimental design was intended to be comparable to ambient conditions where NH 3 is usually in excess. The modelled growth rates are in good agreement with measured growth rates from CLOUD, and the model replicates qualitatively and quantitatively the evolution of the entire size distribution with particles rapidly growing by ammonium nitrate condensation once they reach a critical diameter of $4 nm for the experiment shown.

The effect of high growth rates in the presence of high coagulation sink

We generated a high condensation sink (CS), with loss rates comparable to those found during haze, in order to verify experimentally the loss rates of small clusters, and to test the effect of high growth rates on the survival of small particles.

Condensation is a sink for condensable gases and depends on ] gives an activation diameter of $7.5 nm, i.e. particles larger than 7.5 nm are in supersaturated conditions. Under these conditions, we measure steady new particle formation (J 2.5 ¼ 5-10 cm À3 s À1 ; panel f) and rapid growth of both the newly formed and the pre-existing particles, which maintains a high CS despite dilution of the chamber contents (panel g). (i) Model simulation of the second CLOUD experiment. The initial vapour product for the simulation has an activation diameter of 2.5 nm, i.e. particles larger than 2.5 nm are in supersaturated conditions. The model predicts continuous new particle formation as well as rapid growth of both the new particles and the pre-existing particles. The reason for the different appearance of the measured (h) and simulated (i) size distributions is due to varying experimental conditions (see text). (j) Size and time dependent growth rates calculated using the INSIDE method.

the surface area, and coagulation is a sink for particles that depends on the diameter of the colliding particles. In Fig. 2 we present two CLOUD experiments (one longer than the other) at 5 C and 60% relative humidity, summarising the observations (panels a-c, e and f-h, j) and our kinetic model results (panels d and i). Run 1 of the CLOUD measurements shown in Fig. 2(a-c ande) presents results of an experiment in which we observed no nucleation under the initial high CS. The initial concentrations of this experiment were $2.5 Â 10 6 molecules per cm 3 H 2 SO 4 , $0.03 ppbv HNO 3 , $6 ppbv NH 3 and an initial CS of $0.06 s À1 . During the experiment the CS steadily decayed due to dilution in the CLOUD chamber, as well as evaporation of NH 4 NO 3 due to sub-saturated conditions of gas phase NH 3 and HNO 3 . The gas phase NH 3 was constantly increasing, although the injection rate was constant, most likely due to increased production rate of NH 3 by evaporation, combined with a decreasing loss rate to the CS resulting in a higher steady state concentration. HNO 3 should experience the same changes in loss and production rates, but the increase in concentration in Fig. 2(a) is delayed. This is probably due to its higher wall loss rate (i.e. the walls are not an effective source and act as a sink), and the fact that HNO 3 is not in steady state at the beginning of the experiment, as each run starts with the onset of lights and therefore HNO 3 production. Nucleation of particles commenced once the CS dropped to approximately 0.03 s À1 (indicated with a vertical orange line). As the condensation sink decreased further, the nucleation rate continued to increase and the particles continued to grow, although at relatively slow rates. In this experiment, neither particle formation and growth nor condensation to the larger mode was sufficient to sustain the particle number and the CS.

Run 2 of the CLOUD measurements in Fig. 2(f-h and j) shows a second experiment, with similar initial conditions but higher HNO 3 concentration ($6 Â 10 6 cm À3 H 2 SO 4 , $0.2 ppbv HNO 3 , $1.7 ppbv NH 3 , and an initial CS of $0.06 s À1 ). We observe that not only were the condensation sink and particle number sustained, but small particles were present from the beginning of the experiment, with measurable and continuous formation of 2.5 nm particles (J 2.5 ) as well as high growth rates. Since loss rates of particles to dilution are the same between the two runs, comparing the progression of the large particle mode in Fig. 2(c andh) can elucidate much about the growth of particles. Although growth does not manifest as a typical new particle formation (NPF) and growth event in Fig. 2(h), it is clear from comparing to Fig. 2(c) that rapid and continuous growth is occurring. In Fig. 2(c), the lower end of the large pre-existing particle mode increases in diameter due to slow growth of the particles, while the CS and particle number decreases. However, in Fig. 2(h) there are continuous particle concentrations around 10 nm and a steady CS, which can only be explained by new particle formation and rapid growth. Furthermore, as time progresses in Fig. 2(h), the particle number concentration at large sizes (indicated by colour) increases, whereas for Fig. 2(c) it is decreasing. These results indicate that, with sufficient HNO 3 and NH 3 , higher growth rates at small particle sizes can shepherd small particles to larger sizes through the so-called "valley of death", and thus sustain particle number concentration and CS during haze events. Panels e and j present size and time dependent growth rates calculated using the INSIDE method. 22,23 Panel e shows that initially, before the onset of nucleation, the only measured growth is slow growth of large particles, most likely caused by condensable gases present other than NH 3 and HNO 3 . While there are relatively low growth rates for the newly formed particles (<4 nm) in panel j, as soon as the activation diameter is reached the particles experience extremely rapid and continuous growth just above the activation diameter, leading to rapid condensational loss, resulting in the apparent gap in the particle-number size distribution. Similar observations of apparent gaps in the particle size distribution, due to ammonium nitrate growth, were also reported in Wang et al. (2020). 18 The activation diameter is increasing during the rst 20 minutes of run 2; this is visible as the leading edge of the nucleation mode is increasing in diameter (Fig. 2(h)), concurrent with lower growth rates (Fig. 2(j)). As the gas phase NH 3 and HNO 3 concentrations stabilise (Fig. 2(f)) the activation diameter also stabilises.

Panels d and i of Fig. 2 show the kinetic modelling results of these runs. Each model run had initial and boundary conditions consistent with the corresponding experimental run. We initialized both simulations with a condensation sink of $0.06 s À1 , comprising particles with a 100 nm modal diameter. We constrained J 2.5 and the concentrations of NH 3 and HNO 3 to the experimental values and the production rate of H 2 SO 4 . For run 1 (a-e), the model agrees qualitatively and quantitatively with the observations. For run 2 (f-j) the model agrees qualitatively but with evident differences that we shall discuss. In run 1, even with the rise in J 2.5 aer $65 min, the particles only grow a few nm before being lost, and the CS declines steadily due to ventilation without being counterbalanced by newly formed growing particles. A second simulation with J 2.5 constrained to 10 cm À3 s À1 throughout the run shows very similar results, with essentially no growth before 65 min and only feeble growth aerwards (Fig. S1(a andb) †). Sensitivity tests show that the differences in H 2 SO 4 and NH 3 between the experiments also do not have a strong inuence on the particle size distribution (Fig. S1(c andd) †). With these experiments, we demonstrate that our current understanding of coagulation loss rates of small particles, which we use in the model, is correct as the results match well with the experiments, i.e. clusters and small particles are efficiently lost to large particles, and inefficient coagulation is not the explanation for measured J rates in polluted conditions.

For run 2 (f-j) model simulation we found the lower limit where we could reproduce this experiment was at concentrations of $0.3 ppbv HNO 3 and $3.8 ppbv NH 3 , around two times larger than the estimated concentrations in the chamber. This discrepancy is within the estimated errors of gas concentrations for these runs (see ESI †). The model reproduces the observed "smear" of particles across the size distribution, with an indistinct minimum near 5 nm. However, the "CS mode" at 100 nm also grows rapidly, in contrast to the observations. The rapidly increasing diameter of the gap in between the

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Environmental Science: Atmospheres nucleation and Aitken modes in panel (i) is most likely an artefact of the initial conditions. We thus conrm the high particle survival as well as the persistent CS, which is sustained against losses as the result of ammonium nitrate-enabled particle activation. The model-measurement differences likely arise from multiple factors, predominantly because experimental conditions were changing dynamically, making it more difficult to constrain the model accurately. As seen in Fig. S2-S4 (ESI †) the activation diameter and especially the growth rate are very sensitive to the experimental, or ambient, conditions. Specically, the growth rate depends on the diameter, and close to the activation diameter, d act , the growth rate rapidly increases with increasing diameter. The sensitivity is especially high when HNO 3 and NH 3 are near stoichiometric equivalence, such as in this case (Fig. S4 †). The activation diameter is then also sensitive to the saturation concentration, S where a small change in S can result in a large change in activation diameter. Finally, certain data limitations (lack of particle composition measurements, lack of HNO 3 measurements etc.) meant that the model could not be constrained to all experimental conditions. The result of these effects is that, in a dynamic situation such as in the CLOUD experiments or ambient environments, we expect to observe a size distribution as we have observed, due to changes in sinks and sources resulting in rapid changes in growth rate and activation. The differences in Fig. 2(h andi) indicate that ammonium nitrate growth would not necessarily be classied as a NPF event, and thus could be overlooked in ambient data. We also do not yet include the effect of van der Waals forces, which for sulfuric acid -NH 3 growth can enhance sub-10 nm growth by up to a factor of 2. 20 While van der Waals forces have a small effect on the overall results, they might contribute to high growth rates in the smallest particles without causing a higher growth at larger sizes (see ESI † -Modelling ammonium nitrate).

Effect of NH 3 and HNO 3 concentrations on particle survival

Results from Fig. 1 and 2 indicate that the model accurately captures the growth by ammonium nitrate, as well as particle Fig. 3 Survival parameter of newly formed particles versus condensation sink: the survival parameter is defined as the particle formation rate at 6 nm divided by the formation rate at 2.5 nm, i.e. J 6 /J 2.5 . CLOUD measurements are indicated by diamond symbols and model simulations by square symbols without outlines. The points are coloured according to the particle growth rate at 3 nm, calculated from the measured HNO 3 and NH 3 concentrations (Fig. 1), the fuchsia colour indicates conditions of either no growth (GR ¼ 0) or evaporation of NH 4 NO 3 (GR < 0). The CLOUD experiments are those shown in Fig. 2, the experimental conditions are listed in its caption. All the model simulations assume kinetic nucleation (zero evaporation), and $10 nm h À1 early growth (from H 2 SO 4 ) for non-activated particles, in the absence of any particle condensation sink. The model assumes a constant J 2.5 of 10 cm À3 s À1 . The model conditions are 5 C, HNO 3 and NH 3 between 400 pptv and 4 ppbv, and a condensation sink between 0.01 and 0.13 s À1 . Experiments where the activation diameter is sufficiently low that the non-activated growth surpasses it result in activation of particles. Activated particles grow rapidly enough to survive loss in the presence of high condensation sinks whereas non-activated particles have very low survival probabilities. The experimental measurements show that the rapid particle growth rates from ammonium nitrate formation are sufficient to overcome losses of newly formed particles in high condensation sink environments. The good agreement of the model with the experimental data confirms that particle scavenging involves unit sticking probability, as expected from previous measurements in low condensation sink environments.

loss rates; therefore, the model most likely accurately represents the underlying physics and chemistry of particle growth associated with ammonium nitrate activation. We now use the model to explore under which atmospherically relevant conditions ammonium nitrate condensation could enhance the survival of newly formed particles.

The model was run at 5 C with NH 3 and HNO 3 concentrations ranging from 400 pptv to 4 ppbv and the condensation sink ranging from 0.01 to 0.13 s À1 covering a range of low particle surface area to extremely high limits. We dene the survival parameter as the ratio of the formation rate of 6 nm (J 6 ) particles to that of 2.5 nm (J 2.5 ) particles at steady state, i.e. the proportion of how many particles survived between 2.5 and 6 nm. We feed the model with 2.5 nm particles (J 2.5 ¼ 10 cm À3 s À1 ) and assume no evaporation of clusters of H 2 SO 4 (kinetic nucleation). All model runs have the same production rate of H 2 SO 4 , which, in the absence of a condensation sink, leads to $10 nm h À1 early growth (1.8-3.2 nm) for non-activated particles.

Fig. 3 indicates the calculated ammonium-nitrate-driven growth rate at 3 nm of model and CLOUD experiments via symbol colour, with points plotted as survival parameter against condensation sink. The fuchsia diamond symbols represent a CLOUD run with low amounts of HNO 3 , as in Fig. 2, panels ac. We can see that as the CS decayed and particles began to grow that the survival signicantly increased compared to at higher CS. The purple diamond symbols represent the run with higher HNO 3 (Fig. 2 panels f-h and j), and these points along with the model points show us that at high growth rates, the condensation sink has little effect on the survival, and these points even approach unity. Although there is relatively high survival at low condensation sinks ($0.01 s À1 ), even with slower growth rates, at high condensation sinks the only experiments that saw high survival were those with activation and high growth rates. This conrms our theory that high growth rates are able to "shepherd" small particles through size ranges where they are most vulnerable to loss.

Discussion and conclusions

Fig. 4 illustrates results from model runs over the selected concentration ranges. As can be seen, the results are almost binary, with a sharp transition from a region of no survival to a region of high survival, showing how crucial activation is for survival. In parts b and c, at high HNO 3 concentrations, the effect of the condensation sink is very small. This can also be seen in part d of the Fig. 4, but with the calculated growth rate caused by ammonium nitrate formation (at 3 nm) on the x-axis. Growth rates from ammonium nitrate formation directly scale with the ux of HNO 3 and NH 3 . The ammonium nitrate ux is dependent on the concentration of gas phase NH 3 and HNO 3 , as well as on which gas is limiting, and the size of the particle, the full equations are found in the ESI. † The region between negative and positive growth rates (evaporation and condensation, respectively) is where we see a step in survival, and above this region the condensation sink has a smaller effect. In panel Fig. 4 Illustration of the binary behaviour of modelled survival of newly formed particles due to ammonium nitrate formation: (a-c) modelled particle survival parameter as a function of condensation sink and concentrations of HNO 3 and NH 3 at 5 C. The model assumes constant HNO 3 and NH 3 concentrations and H 2 SO 4 production rate, and simulates a variable CS at 300 nm. The red square in panel c is a model where the CS and J rates did not stabilise within the time of the model. (d) Particle survival parameter versus the calculated growth rate at 3 nm for different condensation sinks. When the growth is not positive, i.e. no condensation, the particle survival parameter, J 6 /J 2.5 , is extremely low and around 5 Â 10 À4 for CS ¼ 0.005 s À1 . However, above the activation diameter, the total particle growth rates increase by up to a factor of 100 or more and the survival parameter approaches unity, even for condensation sinks as high as 0.1 s À1 . The dashed line in between positive and negative growth rates represents a range with no data points. (e) An inset of (d) with only growth rates above 0. d, it is also more visible that at calculated negative growth rates the survival is highly dependent on the condensation sink (though it is always low). In this region, the survival is controlled by H 2 SO 4 and NH 3 growth, as without activation HNO 3 does not contribute to nucleation and growth. Although the calculated ux, and therefore growth rate, of ammonium nitrate is negative, when there is no ammonium nitrate in the particles evaporation will not occur.

Survival of particles will depend on not only the growth rate, but also the activation diameter, since if particles are not large enough for NH 3 and HNO 3 to condense on there will be no activation. Therefore the contribution of activation to survival of particles will also depend on the pre-existing particle distribution. Since we constrain J 2.5 in our model, and the experiments with positive ux shown in Fig. 4(d ande) have activation diameters under 2.5 nm, all of the particles can be activated.

The observed differences in Fig. 2 parts (h) and (i) give a strong indication that although these processes may happen under ambient conditions, they are most probably masked to researchers as they do not appear as typical NPF events. This is especially the case because deviations from equilibrium are expected to be brief in the ambient atmosphere, and vapour concentrations of NH 3 and HNO 3 tend rapidly towards equilibrium. However, even short perturbations above saturation may drive the rapid growth of nucleating particles at rates up to one thousand times faster than growth by H 2 SO 4 condensation, given the disparity between HNO 3 and H 2 SO 4 concentrations. Particles may not experience rapid growth for long, but they can grow sufficiently fast to escape the valley of death and continue to grow via other condensable gases. In ambient conditions, transient deviations from equilibrium are expected to occur, especially in inhomogeneous urban settings with strong local sources of ammonia (e.g. from traffic or urban geometry). Since HNO 3 is usually the limiting gas, inhomogeneities in HNO 3 could have a larger impact on particle size distributions, however since NH 3 is directly emitted by a multitude of sources, it is more likely to be variable and therefore will likely have a larger impact in typical urban environments. Wang et al. (2020) 18 show the strong temperature dependence of ammonium nitrate formation, therefore we also expect temperature changes characteristic of vertical convection to drive the vapour concentrations of NH 3 and HNO 3 out of equilibrium. Future analysis should investigate the effect of urban and vertical mixing on the rapid growth of nucleating particles by NH 3 and HNO 3 condensation.

While Wang et al. (2020) 18 presented the rst evidence of rapid growth by ammonium nitrate condensation, we have additionally provided the rst experimental data and supporting modelling calculations demonstrating efficient scavenging of nucleating molecular clusters by larger sized particles under haze conditions. We also present experimental results of high survival of freshly nucleated particles even in the presence of a high condensation sink, conrming the hypothesis from Wang et al. (2020) 18 that rapid growth caused by NH 4 NO 3 formation can aid in particle survival through the valley of death. These results strongly support the hypothesis that the unexplained survival of particles is due to a missing growth mechanism, and that under typical ambient conditions of a megacity at 5 C, rapid ammonium nitrate condensation could be that missing mechanism, increasing survival of nucleated particles, and thus sustaining particle number and poor visibility during haze.