From the journal Environmental Science: Atmospheres Peer review history

19-Jan-2022

Dear Dr Kontkanen:

Manuscript ID: EA-ART-12-2021-000103
TITLE: What controls the observed size-dependency of the growth rates of sub-10 nm atmospheric particles?

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Reviewer 1

This manuscript explores various factors influencing the early growth of freshly nucleated particles, focusing on CLOUD experiments with sulfuric acid, ammonia, and organics as well as simulations of these experiments. Overall, the paper is interesting and useful. I recommend publication once the following are addressed.

However, firstly, I’m not sure if the submitted manuscript was following the journal standards or something else, but I found it very hard to review in this format. There are no line numbers. This made writing up this review very hard. There were places where I have minor suggested writing edits that I think could help the paper, but I just don’t have the energy to figure out and write “4th sentence of the 5th paragraph of page 12” for minor suggestions on how to make a sentence more clear. Please always have line numbers (or if the journal standard is to not have line numbers, then this should be changed).

There are no indents at the start of paragraph (or extra whitespace between paragraphs, which also would be fine), and the reader needs to rely on there being trailing whitespace after the paragraph to know where paragraphs end (and often the last sentences go to near the end of the line). I also found that there was not much space to write notes between lines. Overall, I found it strange and challenging to review in the submitted format, and I hope it is not the journal standard.


Specific comments

Last paragraph of Section 1: “(2) what does this imply…” would be parallel structure with #1. Also, there should be question marks (or at least one at the end) for these questions.

Section 2.2, 2nd paragraph: What RH (or range of RHs) are these acid/base/water ratios based on and/or appropriate for?

Table 1. and discussion of the molecular weights. For the “SA” species, is the diffusivity of this species based on the molecular weight in this table or on sulfuric acid? I would guess that sulfuric acid is more appropriate since sulfuric acid condensation should be limiting the rate of the uptake of the bases and water.

Section 2.4 (and the associate results in 3.4): Please add some physical intuition as to why the ratio of the 2nd to 1st derivatives provides the threshold of the diameter where stochastic effects no longer matter… enough such that people don’t need to seek out Olenius et al. to get this intuition. I think that exploring stochastic effects is important, but I’m left feeling like I have an empty understanding of the results (perhaps this is on me for not being tuned-in enough, but I suspect that I won’t be the only reader feeling this way).

Continued: I’m currently also struggling with this ratio of derivatives since (1) the ratio can be positive and negative in different parts of the size distribution and for different reasons (negative when either the 1st or 2nd derivative is negative and positive when both derivatives either negative or both are positive), and (2) the ratio of the derivatives is not only size dependent but time dependent (though I guess it may approach steady-state values for the smallest particle sizes in chamber experiments when vapor and particle sinks are ~constant… but in a general sense, it’s time dependent as the size distribution evolves). If text can be added to help make sense of these points, please add.

Tables 3 and 4: Was there a reason why the simulations were not set to correspond exactly to the 11 experiments? Maybe it was mentioned and I missed it, but if it wasn’t, a sentence or 2 on this would be helpful. Was it because HOMs and HOM dimers don’t correspond exactly to ELVOCs and LVOCs, so exact matches were not possible?

Figure 3: Please make the y axis of the right panel go to 0. The current y-axis extent makes the simulations seem like they have a larger relative error than they do.

Middle of first paragraph on page 12 (discussing Figure 5). When discussing the maxima in the simulated vapor concentrations that does not appear in the experiments, a reason for the maxima in the simulations is given. However, it’s not clear to me why the explanation would not apply to the experiments as well. Please clarify in the text why the experiments lack the vapor maxima.

Section 3.3, first sentence of 2nd paragraph. “In the simulations with only LVOC…” This confused me for a while because I could not find the simulations with only LVOCs in Figures 7 and S3 even though these figures had just been introduced. I eventually realized that only Table 4 has these sims. I suspect that this will confuse other readers. Please either add the LVOC-only sims to the figures or make it clear that these results are only in Table 4 at the start of this paragraph.

I don’t see Figure 8 discussed in the text… only Figure 8b being mentioned. Maybe I missed it.

Figure 8: Related to the earlier comment, why don’t the simulations correspond exactly to the experiments such that there could be x’s and o’s of the same color and we can compare the simulations and experiments directly.

Page 14 and around. The “fluxes” due to each process may be better described as “partial fluxes” to help show that it’s the flux due to each isolated process. However, I personally would find partial growth rates (the growth rate due to each process) to be a more intuitive parameter because (1) it does not depend on the number concentrations of particles at each side and takes away the decrease in fluxes with increasing size due to coagulational losses, and (2) I think values of nm/hr (0.1-10s of nm/hr) is something people have more of a feel for than the flux values. I recommend switching unless there is something that flux is showing that growth rates would not.

Figure 10 vs. discussion in the text. I was confused for a while because Figure 10 was showing the experimental growth rates to be too large even above the Dp,th values listed in the text. I then realized that this is because the simulations in Figure 10 also include collisions of small clusters contributing to growth whereas the single-particle estimates do not (discussed at the end of the 2nd to last paragraph in Section 3.4). Hence, it is hard for me to get much out of Figure 10 because I don’t know how much of the difference between the model and single-particle estimates is because of stochastic effects vs. small-cluster condensation.

Reviewer 2

In this submission to Environmental Science: Atmospheres, the authors analyze the growth of sub-10nm atmospheric particles. They unravel which factors affect the growth, analyze these factors, and comment on their role with a detailed discussion. The authors are aware of previous studies in this area because many related studies are referenced in the introduction section of the manuscript. The originality of this paper is from my point of view in the chosen particle size range. The authors chose some approximations to run simulations from gas molecules up to several-nm particles. Both simulations and experiments support their results and qualitatively match. Not all results match quantitatively though. However, the reasons behind this are well elaborated. Therefore, I find the paper reliable. I believe that the discussion on the disentangled factors (role of stochastic fluctuations, molecule concentration+volatility, etc.) is essential and will impact future studies that will address sub-10nm particle growth. Hence, I recommend publishing this article after the authors address my minor questions/comments.

QUESTIONS/COMMENTS:
Equation (1): I am almost sure you should remove both 1/2 factors. I have seen this written already in McGrath et al. (2012). However, I think this is a mistake that should not propagate to further future articles. If I am wrong, please explain why the halves should stay there.

Page 7, 2nd paragraph: Besel et al. indeed used DLPNO-CCSD(T) method but only to perform electronic energy single-point correction for structures optimized at DFT level of theory with vibrational analysis also at DFT level. The electronic binding energy is the most crucial factor in the free energy calculations. However, with improvements in computational chemistry, I would not be surprised if DLPNO-CCSD(T) would be in the future used to numerical optimizations of structures together with vibrational analysis. Therefore, I think that you should mention that these structures were optimized at DFT and subsequently corrected with the DLPNO-CCSD(T) method.

Also, the method used by Besel et al. is slightly under-binding (makes clusters less stable). This could be an additional explanation why some simulation results with “2 comp. QC data” lead to lower concentrations or growth rates.

The SA abbreviation: Although this could be easily confused with SA = sulphuric acid, I fully respect that in your manuscript SA = sulf.acid+ammonia mixture. However, I have been confused in several places if you mean only sulfuric acid or the mixture.
- For instance, on Page 12, 1st paragraph: when you speak about high sulphuric acid concentration, you mean SA concentration, right?
This brings me to another question: you compare results between experiment and simulation and show SA concentration. Do you mean the sulphuric acid concentration (in the experiments)? or do you mean the sum of ammonia and sulphuric acid concentration? Why do you not mention the ammonia concentrations for those experiments and simulations where you explicitly treat ammonia molecules? Or is it everywhere in 1:2 ratio with sulphuric acid concentration?
- Most confusing is for me Figure 4. For instance, what does mean sulfuric acid dimer? (H2SO4)2 or sum[(H2SO4)2(NH3)n] or the most stable (H2SO4)2(NH3)n?

Figure 2: The error bars show the uncertainty of the measured particle diameter and the appearance time. However, these results do not say anything about impurities in the experiments. The particle growth rate would undoubtedly be affected by any contaminants. Can you estimate if those play any significant role in your experiments?

Simply out of curiosity: Using the appearance time method for estimating the particle growth rate is very much dependent on the cluster population evolution and generally on cluster concentrations. However, the particle growth rate is defined as the growth rate of the diameter of a single particle per time, right? Thus, could it be possible to calculate the growth rate in your simulation only from fluxes at each cluster size?

Otherwise, I have enjoyed reading the result and discussion sections and found them very educative.

REPLIES TO REFEREES

We thank the referees for their encouraging comments and insightful suggestions that improved our manuscript. We have answered to each of the comments below.

REPLY TO REFEREE #1
Referee #1:

Comments to the Author

This manuscript explores various factors influencing the early growth of freshly nucleated particles, focusing on CLOUD experiments with sulfuric acid, ammonia, and organics as well as simulations of these experiments. Overall, the paper is interesting and useful. I recommend publication once the following are addressed.

However, firstly, I’m not sure if the submitted manuscript was following the journal standards or something else, but I found it very hard to review in this format. There are no line numbers. This made writing up this review very hard. There were places where I have minor suggested writing edits that I think could help the paper, but I just don’t have the energy to figure out and write “4th sentence of the 5th paragraph of page 12” for minor suggestions on how to make a sentence more clear. Please always have line numbers (or if the journal standard is to not have line numbers, then this should be changed).

There are no indents at the start of paragraph (or extra whitespace between paragraphs, which also would be fine), and the reader needs to rely on there being trailing whitespace after the paragraph to know where paragraphs end (and often the last sentences go to near the end of the line). I also found that there was not much space to write notes between lines. Overall, I found it strange and challenging to review in the submitted format, and I hope it is not the journal standard.

Our answer: We apologize for the inconvenience. The manuscript follows the journal’s template.

Specific comments

Referee #1: Last paragraph of Section 1: “(2) what does this imply…” would be parallel structure with #1. Also, there should be question marks (or at least one at the end) for these questions.

Our answer: We corrected this.

Referee #1: Section 2.2, 2nd paragraph: What RH (or range of RHs) are these acid/base/water ratios based on and/or appropriate for?

Our answer: Theoretical results cited here were derived for RH = 50%, and the experimental results obtained from experiments with RH = 38% (experiments including organics) and 38% or 60% (pure inorganic experiments). Furthermore, the minor effect of water on pure sulfuric acid growth between 38% and 60% RH has been discussed in Stolzenburg et al. (2020).

Referee #1: Table 1. and discussion of the molecular weights. For the “SA” species, is the diffusivity of this species based on the molecular weight in this table or on sulfuric acid? I would guess that sulfuric acid is more appropriate since sulfuric acid condensation should be limiting the rate of the uptake of the bases and water.

Our answer: In our cluster population model, we do not treat condensation using mass transfer equations based on diffusion and including vapor diffusivities. Instead, we consider all possible collisions and evaporations between different vapor molecules and clusters, as described in Sect. 2.2.1. The collision rates are calculated assuming hard sphere collisions and in the free-molecular regime (below ~10 nm) they only depend on temperature and the molecular masses of the model compounds shown in Table 1. The referee is correct that for the collision rate, hydrated sulfuric acid should be assumed while for the mass added in a collision, the mass of ammonia should also be included (as done currently). However, the error introduced by this small simplification (i.e. using the same mass in the collision kernel and for the cluster molecular weight) is less than 3% below 10 nm.

Referee #1: Section 2.4 (and the associate results in 3.4): Please add some physical intuition as to why the ratio of the 2nd to 1st derivatives provides the threshold of the diameter where stochastic effects no longer matter… enough such that people don’t need to seek out Olenius et al. to get this intuition. I think that exploring stochastic effects is important, but I’m left feeling like I have an empty understanding of the results (perhaps this is on me for not being tuned-in enough, but I suspect that I won’t be the only reader feeling this way).

Our answer: We agree, and have added the following in Section 2.4:

The idea behind the metric can be understood by considering that the representation of condensational growth in single-particle and aerosol dynamics models is based on the continuous GDE, which is derived from the explicit discrete GDE by approximating particle size as a continuous variable. This leads to a condensational growth flux equation that is analogous to the convection-diffusion equation, with a first-order drift term (∝ ∂c/∂i) corresponding to the driving force of condensation (the difference between the collision and evaporation rate constants) and a second-order diffusion term (∝ ∂^2c/∂i^2) corresponding to stochastic molecular collisions and evaporations. For larger aerosol particles the latter term is generally omitted, but should be included if it is comparable to the first-order term, that is, ∂^2:∂ >> 0.

Referee #1: Continued: I’m currently also struggling with this ratio of derivatives since (1) the ratio can be positive and negative in different parts of the size distribution and for different reasons (negative when either the 1st or 2nd derivative is negative and positive when both derivatives either negative or both are positive), and (2) the ratio of the derivatives is not only size dependent but time dependent (though I guess it may approach steady-state values for the smallest particle sizes in chamber experiments when vapor and particle sinks are ~constant… but in a general sense, it’s time dependent as the size distribution evolves). If text can be added to help make sense of these points, please add.

Our answer: We agree that these issues need clarification and have modified the text accordingly. As for point (1), the ratio is in fact that of the absolute values of the derivatives, as the important parameters are their magnitudes instead of their signs. This is now clarified in Section 2.4:

The metric is based on studying the ratio of the absolute values of the second and first derivatives of the particle size distribution:
|(∂^2 c)/(∂i^2 )|⁄|∂c/∂i| ≡∂^2:∂.

Regarding point (2), ∂^2:∂ is indeed also time-dependent, although at the particle appearance times the particle distribution can be expected to approach the final steady-state conditions (see Supplementary Information Section 2.3 in Olenius et al. 2018). Here, we determine ∂^2:∂ at the final steady-state situation, as the experimental size distribution data involves less noise and fluctuations at the final state. Stochastic effects are most important for the so-called “sub-critical” sizes for which evaporation dominates over growth by molecular collisions, and these sizes are evident by ∂^2:∂ also at the steady state.

We now clarify this in Section 2.4:

We determined Dp,th both from experimental data and simulations using the size distributions under steady-state condition, as the experimental data fluctuates less at the final state.

Referee #1: Tables 3 and 4: Was there a reason why the simulations were not set to correspond exactly to the 11 experiments? Maybe it was mentioned and I missed it, but if it wasn’t, a sentence or 2 on this would be helpful. Was it because HOMs and HOM dimers don’t correspond exactly to ELVOCs and LVOCs, so exact matches were not possible?

Our answer: Thanks for the comment, we agree that this should be clarified in the manuscript. In the simulations involving only SA (representing a mixture of sulfuric acid and ammonia), we used similar vapor concentrations to those in sulfuric acid–ammonia experiments (experiments 9-11 in Table 3 and simulations 2-7 in Table 4). However, for organic vapors, we chose not to match the simulated vapor concentrations with measured concentrations due to the following reasons: (1) Computational reasons limited the number of organic compounds to maximum two in pure organic simulations (ELVOC and LVOC) and to one in inorganic-organic simulations (LVOC), while in reality there exist a variety of organics with different volatilities. (2) As quantum-chemistry based evaporation rate data for organic compounds is very limited, we used classical evaporation rates, which are known to be uncertain. (3) Experimental organic measurements also suffer from an incomplete detection of all organic compounds (see Stolzenburg et al. 2018). We now clarify this in the end of Sect. 2.2.3:

For SA, we used similar vapor concentrations in the simulations to those observed in the corresponding experiments. However, for organic compounds, we did not exactly match the simulated vapor concentrations with the measured values, due to the limited number of different organic vapors in the simulations and high uncertainties in their evaporation rates. Instead, the simulated organic concentrations correspond to the approximate range of vapor concentrations in the studied experiments.

Referee #1: Figure 3: Please make the y axis of the right panel go to 0. The current y-axis extent makes the simulations seem like they have a larger relative error than they do.

Our answer: We fixed this.

Referee #1: Middle of first paragraph on page 12 (discussing Figure 5). When discussing the maxima in the simulated vapor concentrations that does not appear in the experiments, a reason for the maxima in the simulations is given. However, it’s not clear to me why the explanation would not apply to the experiments as well. Please clarify in the text why the experiments lack the vapor maxima.

Our answer: The reason for the measured vapor concentration not exhibiting a maximum is that in the experiments with sulfuric acid and ammonia, cluster concentrations are low, and thus they do not act as a significant sink for vapor. However, in the experiments (not analyzed in this study) involving sulfuric acid and dimethylamine, which is a stronger base than ammonia and thus form more stable clusters, a similar behavior with a maximum in vapor concentration has been detected. We clarified the issue by adding a following sentence to this paragraph:

A similar behavior is not observed in the experiments, because the concentrations of clusters are low, and thus, they do not act as a significant sink for the vapor.

Referee #1: Section 3.3, first sentence of 2nd paragraph. “In the simulations with only LVOC…” This confused me for a while because I could not find the simulations with only LVOCs in Figures 7 and S3 even though these figures had just been introduced. I eventually realized that only Table 4 has these sims. I suspect that this will confuse other readers. Please either add the LVOC-only sims to the figures or make it clear that these results are only in Table 4 at the start of this paragraph.

Our answer: As suggested by the referee, we now mention in the beginning of this paragraph that the results on growth rates in LVOC simulations are only visible in Table 4:

In the simulations with only LVOC, the size-dependence of growth rate depends on LVOC concentration (shown only in Table 4).

Referee #1: I don’t see Figure 8 discussed in the text… only Figure 8b being mentioned. Maybe I missed it.

Our answer: Figure 8a (that the referee probably means here) is discussed in the third paragraph of Sect 3.3: “Figure 8a shows the comparison between growth rates in the experiments and simulations involving only organic vapors…”

Referee #1: Figure 8: Related to the earlier comment, why don’t the simulations correspond exactly to the experiments such that there could be x’s and o’s of the same color and we can compare the simulations and experiments directly.

Our answer: As discussed above, due to the limitations of our simulations involving organic vapors, we did not perform simulations matching exactly specific experiments. Therefore, in Figure 8 we are unable to mark the simulations and the corresponding experiments with a similar marker. Note that for the revised manuscript, we modified Figure 8b slightly by moving the legend so that it would not hide one simulation point.

Referee #1: Page 14 and around. The “fluxes” due to each process may be better described as “partial fluxes” to help show that it’s the flux due to each isolated process. However, I personally would find partial growth rates (the growth rate due to each process) to be a more intuitive parameter because (1) it does not depend on the number concentrations of particles at each side and takes away the decrease in fluxes with increasing size due to coagulational losses, and (2) I think values of nm/hr (0.1-10s of nm/hr) is something people have more of a feel for than the flux values. I recommend switching unless there is something that flux is showing that growth rates would not.

Our answer: It is indeed true that in aerosol research community, particle growth rate is a more well-known variable than particle flux. Also, when using single particle models to simulate particle growth, it is common to determine growth rate due to a certain vapor from its mass flux onto a particle. However, here, we simulate the time development of the whole cluster population, considering all possible collisions and evaporations between different vapor molecules and clusters, instead of a following the growth of a single particle. Thus, the particle fluxes analyzed in our study do not correspond to a particle flux onto a single particle, but instead, the particle flux past certain sizes (Eulerian approach). We feel that this is the most straightforward approach to assess the mechanisms that drive the growth of the population of small nanoparticles.

It would be possible to derive so-called flux equivalent particle growth rates from these fluxes (see Kontkanen et al. 2016 as well as the answer to the last comment by Referee #2) but these growth rates would not correspond to any observed particle growth rate and they would contain uncertainties related to the conversion between fluxes and growth rates. More generally, as illustrated by our results, growth rate is not a well-defined variable for nanometer-sized particles, for which stochastic effects are important, and therefore all similar-sized particles do not grow at the same rate. The flux past a given threshold size may also be due to coagulation of clusters of different sizes below the threshold and thus does not correspond to the growth of one specific particle size, making the concept of growth rate even more ambiguous. For these reasons, we choose to show the particle fluxes, determined considering different collisions and evaporations past a certain size. We now clarify this in the end of Sect 2.3:

To assess the mechanisms driving particle growth in our simulations, we also investigated particle fluxes due to different collisions and evaporations past selected threshold sizes. We chose not to convert these to flux equivalent particle growth rates (see Kontkanen et al.43), as the resulting growth rates would not correspond to any observed particle growth rate and they would contain uncertainties related to the conversion.

In addition, following the referee’s suggestion, we changed “fluxes” to “partial fluxes” in suitable places.

Referee #1: Figure 10 vs. discussion in the text. I was confused for a while because Figure 10 was showing the experimental growth rates to be too large even above the Dp,th values listed in the text. I then realized that this is because the simulations in Figure 10 also include collisions of small clusters contributing to growth whereas the single-particle estimates do not (discussed at the end of the 2nd to last paragraph in Section 3.4). Hence, it is hard for me to get much out of Figure 10 because I don’t know how much of the difference between the model and single-particle estimates is because of stochastic effects vs. small-cluster condensation.

Our answer: It is true that besides the stochastic effects, the differences in the growth rates between the cluster population model and the single particle model stem from other population dynamics effects, especially the contribution of small clusters to the growth. However, we are unable to separate the impacts of stochastics and cluster-cluster collisions on appearance-time particle growth rates derived from population simulations. Moreover, as our cluster population simulations show that using classical, Kelvin-based, thermodynamics at high vapor concentrations leads to an important role of clusters in particle growth, forcing the simulations not to include the contribution of small clusters would be unphysical. For this same reason, modelling particle growth with single particle growth models (that are unable to consider the contribution of clusters to growth) at high vapor concentrations is inconsistent, as mentioned in the end of Sect. 3.2. To clarify the reasons for the differences between the growth rates derived using the two approaches in Figure 10, we added the following sentence in the discussed paragraph:

One should note that in addition to the stochastic effects, the differences between the two approaches stem from other population dynamics effects (such as cluster-cluster collisions) influencing the growth rates derived from population simulations. This applies generally to appearance-time-based growth rates and is relevant to analysis of experimental growth rates in the presence of efficiently clustering chemical compounds14.


REPLY TO REFEREE #2

Referee #2: Comments to the Author

In this submission to Environmental Science: Atmospheres, the authors analyze the growth of sub-10nm atmospheric particles. They unravel which factors affect the growth, analyze these factors, and comment on their role with a detailed discussion. The authors are aware of previous studies in this area because many related studies are referenced in the introduction section of the manuscript. The originality of this paper is from my point of view in the chosen particle size range. The authors chose some approximations to run simulations from gas molecules up to several-nm particles. Both simulations and experiments support their results and qualitatively match. Not all results match quantitatively though. However, the reasons behind this are well elaborated. Therefore, I find the paper reliable. I believe that the discussion on the disentangled factors (role of stochastic fluctuations, molecule concentration+volatility, etc.) is essential and will impact future studies that will address sub-10nm particle growth. Hence, I recommend publishing this article after the authors address my minor questions/comments.

QUESTIONS/COMMENTS:

Referee #2: Equation (1): I am almost sure you should remove both 1/2 factors. I have seen this written already in McGrath et al. (2012). However, I think this is a mistake that should not propagate to further future articles. If I am wrong, please explain why the halves should stay there.

Our answer: Both ½ factors should actually be included in Eq. (1), like they generally are included in the GDE. In the first term of Eq. (1), describing the formation of cluster i in collisions between two smaller clusters, this factor is needed not to count each collision twice. In the case of different-sized clusters this is easy to grasp, but same is true also for the collisions between similar sized clusters, due to indistinguishability of the collision parties. This is nicely explained in Seinfeld & Pandis (2016) on pp. 551–552. For the same reason, the factor ½ is needed in the fourth term, describing the loss of cluster i due to evaporation into smaller clusters.

Referee #2: Page 7, 2nd paragraph: Besel et al. indeed used DLPNO-CCSD(T) method but only to perform electronic energy single-point correction for structures optimized at DFT level of theory with vibrational analysis also at DFT level. The electronic binding energy is the most crucial factor in the free energy calculations. However, with improvements in computational chemistry, I would not be surprised if DLPNO-CCSD(T) would be in the future used to numerical optimizations of structures together with vibrational analysis. Therefore, I think that you should mention that these structures were optimized at DFT and subsequently corrected with the DLPNO-CCSD(T) method.

Our answer: Thanks for this clarification. In the revised manuscript, we mention this in Sect. 2.2.2:

We retrieved from Besel et al.61 Gibbs free energies for the sulfuric acid-ammonia system, which had been obtained by applying a density functional theory (DFT) method for cluster structures and vibrational frequencies and the Domain based Local Pair Natural Orbital Coupled Cluster method (DLPNO-CCSD(T)) for single-point energy calculations. DLPNO-CCSD(T) is considered to be the best available quantum chemical method for atmospheric clusters67.

Referee #2: Also, the method used by Besel et al. is slightly under-binding (makes clusters less stable). This could be an additional explanation why some simulation results with “2 comp. QC data” lead to lower concentrations or growth rates.

Our answer: This is a good point. We now mention this in the end of Sect. 3.2:

The large difference between the dimer concentration in the experiments and in the two-component simulations can result from the tendency of the used quantum chemistry method to slightly underestimate the cluster stability61, illustrating the need to improve these methods (see Elm et al. 67).

Referee #2: The SA abbreviation: Although this could be easily confused with SA = sulphuric acid, I fully respect that in your manuscript SA = sulf.acid+ammonia mixture. However, I have been confused in several places if you mean only sulfuric acid or the mixture.
- For instance, on Page 12, 1st paragraph: when you speak about high sulphuric acid concentration, you mean SA concentration, right?

Our answer: We agree that this could be confusing. The problem is that when discussing experimental results, it should be called “sulfuric acid concentration”, while when discussing simulations, it should be “SA concentration”. For this reason, in some places (for example in the sentence that the referee mentions), where the comparison between experimental and simulation results is discussed, we chose to write “sulfuric acid concentration”, for the sake of simplicity. However, we went through the manuscript and in a few places discussing simulations changed “sulfuric acid” to “SA”.

Referee #2: This brings me to another question: you compare results between experiment and simulation and show SA concentration. Do you mean the sulphuric acid concentration (in the experiments)? or do you mean the sum of ammonia and sulphuric acid concentration? Why do you not mention the ammonia concentrations for those experiments and simulations where you explicitly treat ammonia molecules? Or is it everywhere in 1:2 ratio with sulphuric acid concentration?

Our answer: In the experimental results, sulfuric acid concentration is the concentration of sulfuric acid monomer detected with the CI-APi-TOF as the bisulfate ion (HSO4-) or an ion-cluster with the nitrate reagent ion (HNO3•HSO4-). Because the bisulfate ion acts as conjugate base, the binding strength in the SA cluster decreases and the ammonia is rejected upon charging in the ion source. Therefore, a fraction of detected sulfuric acid monomers can be clustered with ammonia in their neutral form, but we are unable to quantify how high this fraction is (see also the answer to the comment below).

In the sulfuric acid–ammonia experiments, ammonia concentration was 41–45 ppt. This is now clarified in Sect. 2.1.1.:

Sulfur dioxide and ozone were added up to 5 ppb and 30 ppb, respectively, while ammonia concentration was 41–45 ppt.

Correspondingly, in the simulations with the two-component model, treating ammonia explicitly, ammonia concentration was set to 43 ppt. This is now mentioned in Sect. 2.2.2:

Sulfuric acid concentration was varied between 107 and 108 cm-3 and ammonia concentration was set to 43 ppt.

Referee #2: Most confusing is for me Figure 4. For instance, what does mean sulfuric acid dimer? (H2SO4)2 or sum[(H2SO4)2(NH3)n] or the most stable (H2SO4)2(NH3)n?

Our answer: In Figure 4, sulfuric acid dimer concentration from two-component simulations and experiments represent the sum of [(H2SO4)2(NH3)n]. This is because the neutral form of sulfuric acid dimer clusters can contain 0–n ammonia molecules. In the CI-APi-TOF these clusters are detected only as sulfuric acid dimer ions [(H2SO4)HSO4-] as the ammonia is rejected upon charging, due to the basic character of the formed bisulfate ion. Therefore, the information about the number of ammonia molecules inside the neutral cluster is lost and the measured sulfuric acid dimers detected in the instrument represent the sum of all neutral [(H2SO4)2(NH3)n] clusters. The same applies to sulfuric acid monomer, as explained above. We now clarify this in the caption of Figure 4:

In experiments and two-component simulations, sulfuric acid monomer and dimer concentrations include sulfuric acid monomers and dimers with 0–n ammonia molecules.

Referee #2: Figure 2: The error bars show the uncertainty of the measured particle diameter and the appearance time. However, these results do not say anything about impurities in the experiments. The particle growth rate would undoubtedly be affected by any contaminants. Can you estimate if those play any significant role in your experiments?

Our answer: The CLOUD experiment achieves extremely low levels of organic impurities (Schnitzhofer et al., 2014) and can also be kept clean from inorganic contaminants. Therefore, there should not be any contamination from other growth agents. Before the experimental cycles, the chamber is heated, flushed, and cleaned with a Kärcher cleaning system. See also Kirkby et al. (2016) and Kirkby et al. (2011) confirming that the CLOUD experiment achieves unprecedented cleanliness in organic and inorganic experiments.

Referee #2: Simply out of curiosity: Using the appearance time method for estimating the particle growth rate is very much dependent on the cluster population evolution and generally on cluster concentrations. However, the particle growth rate is defined as the growth rate of the diameter of a single particle per time, right? Thus, could it be possible to calculate the growth rate in your simulation only from fluxes at each cluster size?

Our answer: Yes, it could be possible. As mentioned in the answer to Referee #1, it would be possible to derive flux equivalent particle growth rates (see Kontkanen et al., 2016). However, these flux equivalent growth rates would not correspond to any observed particle growth rates. As our objective is to unravel the factors influencing observed particle growth rates, we focus on growth rates derived using the appearance time method, which is commonly used for analyzing experimental data.

Referee #2: Otherwise, I have enjoyed reading the result and discussion sections and found them very educative.

Our answer: We thank the referee for the encouraging comments.

12-Mar-2022

Dear Dr Kontkanen:

Manuscript ID: EA-ART-12-2021-000103.R1
TITLE: What controls the observed size-dependency of the growth rates of sub-10 nm atmospheric particles?

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Reviewer 1

Thanks!