|Comments on the revised manuscript by Yu et al.|
I’m happy to see that the authors have included more data in the measurement comparisons, and also made the discussion more balanced. I have one main suggestion regarding the new comparison (Figure 8):
As discussed, the agreement between CLOUD measurements and the presented model becomes worse when (1) temperature increases, and (2) ions are not present. It would be good to note that these are the conditions when the role of cluster evaporation (i.e. thermodynamics) becomes more important (i.e. higher evaporation and/or generally less tightly bound clusters), and thus they are likely to reveal the biases of the used thermochemistry. This naturally applies to all thermodynamic data sets, PW91PW91/6-311++G(3df,3pd) and other, regardless of the kinetic model framework used.
Also, will the model be freely available?
In addition, some of the replies to my previous comments were slightly inadequate. For instance, the following points would still need a bit of elaboration:
Comment on the model being quasi-unary: The authors reply that “the model is multicomponent” - I agree that the thermodynamic data is multi-component, but the kinetic model is not. The kinetic equations consider only the number of H2SO4 molecules i in each particle (page 7): “Ni is the total number concentration (cm-3) of all cluster/particles (binary + ternary) in the bin i. For small clusters (i≤id), Ni is the number concentration (cm-3) of all clusters containing i H2SO4 molecules.” To the best of my knowledge, this means that the model is quasi-unary, and also the authors have used the same term for the previous versions of the model (Yu, J. Chem. Phys., 127, 054301, 2007). If the model was explicitly multi-component, then there would be no reason to apply the equilibrium assumptions for e.g. ammonia.
Comment 1: I did not ask about the QC data, I asked if the different approaches to assess the thermochemistry of clusters and particles of different sizes, compositions and charging states (QC, Eq. (10), experimental liquid data…) could be presented in an easy-to-read way. How about including this information e.g. in Figure 1? That is, explain for each charging state which size range is described with which thermochemical data; it would be much easier than digging the information from the text.
Comment 17: I don’t understand why you artificially set the cumulative Gibbs free energy to zero when it should be negative. Free energy profiles exhibiting both a minimum and a maximum can naturally occur, especially for charged clusters (see e.g. Figure 2 in Vehkamäki and Riipinen, Chem. Soc. Rev. 41, 5160-5173, 2012), and it simply means that there exist stable “pre-nucleation” clusters.
Comment 18: The vapor concentrations were probably also used to convert the QC data to the given conditions (through the law of mass action)?
Comment 24: I understand that parameter c is an approximation, but the statement “We estimated c based on QC data” still does not answer the question about how c is exactly calculated.
Comment 25: I fully agree that “the formation of small clusters are limiting steps”, but the particle formation process is limited by cluster stability throughout the size range where the clusters are not stable, which is at least up to the barrier maximum. This is clear e.g. from simplified kinetic models such as classical nucleation theory, where the cluster free energy at the maximum of the barrier (the “critical cluster”) is the only free energy determining the particle formation rate. I am sure the authors agree, since they have recently used such critical-cluster-based approaches themselves (Yu et al., Atmos. Chem. Phys. 17, 4997-5005, 2017).
Also, repeating that the model is “in excellent agreement with CLOUD measurements” is not helpful, when Figure 8 tells that this is not the case in all conditions. Thus, there is no need to commend a model when it is not justifiable, but it is instead good to point out the weaker features (as the authors already have nicely done in replies to some other comments).
Comment 26: It might be good to clearly note then, that the model scheme is probably not suitable for situations where ammonia concentration is not substantially higher than H2SO4 concentration. To amend a few issues:
“Please note that the nucleation rates measured in CLOUD are also steady state values”: Equilibrium and steady state are two different things, and the fact that CLOUD formation rates are assessed for a steady state has nothing to do with the assumption regarding cluster equilibration with respect to ammonia. (Equilibrium is a steady state with no net formation or growth of particles. A steady state where particle formation occurs is not equilibrium, but instead any time-independent situation with or without cluster equilibration with respect to some chemical compound.)
“It should be noted that all previous ternary nucleation models discussed in Section 2.1 assume the equilibrium with respect to NH3”: No, they actually don’t. For instance, the acid-base scheme used by Chen et al. (Proc. Nat. Acad. Sci., 109, 18713-18718, 2012), and further developed by Jen et al. (J. Geophys. Res. Atmos., 119, 7502-7514, 2014), assumes two separate acid dimers (clusters containing two acid molecules) that have different base content. ACDC (McGrath et al., Atmos. Chem. Phys., 12, 2345-2355, 2012) does not make any equilibrium assumptions with respect to ammonia.
Comment 27: Please add these clarifications also to the manuscript (I was not able to find them there).
Comment 28: If Eqs. (1) and (2) correspond to H+AaWw and NO3-, in which equation is the bisulfate ion HSO4- included, i.e. does index i in Eq. (5) refer to the sum of H2SO4 and HSO4-? What does the second term of Eq. (2) describe; is NO3- evaporating from a negative cluster or HSO4-?
Comment 29: Yes, but isn’t the double count canceled also for the evaporation term? This is because the evaporation rate constant gamma *includes* the collision rate constant beta as given by Eq. (7), and the permutation factor of 1/2 should be included in beta. Or is the beta in Eq. (7) defined differently than the beta in Eq. (3)?
Comment 31: There’s something wrong with the updated Eqs. (7) and (8), since the H2SO4 concentration N1,0 doesn’t cancel out; please fix this. In any case, there is no reason to include any H2SO4 concentrations in the equation of evaporation rate, as they are not needed there.
The original comment was mainly related to the statement “N0 is the number concentration of H2SO4 at a given T under the reference vapor pressure P of 1 atm”. In QC methods, N0 is the arbitrary number concentration of a hypothetical gas consisting solely of the species for which the calculation is performed (which can be a single molecule or a cluster), and doesn’t have to do with any concrete H2SO4 or other vapor concentration. Conversions are not needed, as they cancel out in the evaporation rate anyway, as the authors state.
Comment 43: It is still claimed in Section 3 of the revised manuscript (page 18, line 554) that the ACDC model neglects the effect of water.