the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Feb 2021
Energetic analysis of succinic acid in water droplets: insight into the size-dependent solubility of atmospheric nanoparticles
Abstract. Size-dependent solubility is prevalent in atmospheric nanoparticles, but a molecular level understanding is still insufficient, especially for organic compounds. Here, we performed molecular dynamics simulations to investigate the size dependence of succinic acid solvation on the scale of ~1–4 nm with the potential of mean forces method. Our analyses reveal that the surface preference of succinic acid is stronger for a droplet than the slab of the same size, and the surface propensity is enhanced due to the curvature effect as the droplet becomes smaller. Energetic analyses show that such surface preference is primarily an enthalpic effect in both systems, while the entropic effect further enhances the surface propensity in droplets. On the other hand, with decreasing droplet size, the solubility of succinic acid in the internal bulk volume may decrease, imposing an opposite effect on the size dependence of solubility as compared with the enhanced surface propensity. Meanwhile, structural analyses, however, show that the surface to internal bulk volume ratio increases drastically, especially when considering the surface in respect to succinic acid, e.g., for droplet with radius of 1 nm, the internal bulk volume would be already close to zero for the succinic acid molecule.
This preprint has been withdrawn.
-
Withdrawal notice
This preprint has been withdrawn.
-
Preprint
(927 KB)
-
Supplement
(151 KB)
-
This preprint has been withdrawn.
- Preprint
(927 KB) - Metadata XML
-
Supplement
(151 KB) - BibTeX
- EndNote
Interactive discussion
Status: closed
-
RC1: 'Comment on acp-2020-1329', Anonymous Referee #1, 16 Mar 2021
The solvation of succinic acid has been investigated in this interesting piece of work. The simulations were conducted for a single succinic acid molecule for different sizes of water nanodroplets (i.e., droplet 255 radius from ~1 nm to 4 nm) and different thickness of water planar slabs (i.e., half slab thickness from ~1 nm to 4 nm). These simulations reveal a stronger surface propensity for succinic acid to stay on the surface of a curved surface rather than on a planar one, due to changes on the hydration energetics associated with the curvature of the nanodroplets.
This is an interesting finding that may have impact for the description of the chemistry of nanodroplets and maybe atmospheric aerosols, even if the later link is not fully established in this work.
It has been shown in previous studies that indeed there is an energy minimum at the air/water interface, which may indeed lead to isolated molecule to have a propensity to stay on the surface. Is this study another simple highlight of the compound dependent feature or is there a benefit of the present work? Maybe the authors could strengthen their message to underline better their key findings (such as the size dependence)? (Note that a revision of the use of the English language would also help, as a several sentences are difficult to follow).
Obviously, one key finding can be found in the observed size and shape dependence. However, the simulations were made on very small objects with limited amount of water, where one can wonder if the difference between bulk and surface is real (especially when the surface region is mentioned to be one nm thick). This is certainly an obvious comment that the authors could address easily for the wider audience of ACP.
While the choice of succinic acid is relevant to the atmosphere, this diacid certainly require an extra amount of water for full solvation. In a context of a limited amount of water (fixed by definition on these simulations), this reviewer was wondering if this would also affect the observations made here where this molecule was pushed to the surface?
Finally, to get closer to atmospheric applications is there any indication for which droplet size this “surface push” is applicable.
Citation: https://doi.org/10.5194/acp-2020-1329-RC1 -
RC2: 'Comment on acp-2020-1329', Anonymous Referee #2, 24 May 2021
Chen et al. report results of a comprehensive study of the bulk/surface partitioning and its energetics of aqueous succinic acid solution nano-droplets using MD simulations. The authors use established methods to obtain the potential of mean force (PMF) experienced by a succinic acid molecule along a reaction coordinate across the liquid-vacuum interface and discuss the effects of curvature on the energetics.
The study is carefully conducted and sound, and the results are interesting from a molecular perspective. However, given the scope of ACP, the authors should reflect more thoroughly on relevance of this work in the atmospheric context. This is important particularly in the light of earlier investigations (especially Werner et al. 2016 which the authors cite) that found the direct changes in CCN activity due to the surface composition in this system to be rather insignificant. It therefore remains to put the current results better into an atmospheric context and emphasize their relevance. Furthermore, the readability and the language of the manuscript needs to be reviewed and improved, and key concepts clarified throughout the manuscript, where possible.
I therefore feel that this manuscript requires major revision before it can be published within ACP, and elaborate further on these comments in the following:
General comments:
- A more elaborate and specific discussion about the relevance for atmospheric chemistry and physics is missing especially in Abstract, Introduction and Conclusions, given the placement in this journal. How are the simulations of nanometer-sized droplets relevant in the atmosphere? What is the relevance of the studied system (i.e. succinic acid)? What implications might the observed phenomena have and can they be generalized to a larger set of atmospherically relevant compounds? Can the authors please put their results in a larger context to link the physical chemistry results of their work to atmospheric processes? Where will these results lead?
- Furthermore, a brief discussion on the applicability, strengths and weaknesses for this type of molecular dynamics simulations in addressing the problem of atmospheric phase state would be appropriate under Results and Discussion.
Specific comments:
- Please simplify the last sentence of the abstract: “Meanwhile, structural analyses, however, …” (remove “Meanwhile”?)
- Introduction: “compositions” -> “compounds”?
- Throughout the manuscript: Please check the use of tenses (“was” vs. “has been” vs. “is”).
- L 4: remove “area”?
- L 36: Which “observed phenomenon” do you mean? Please specify.
- L 39: “Higher relative humidity” than what? Please specify. Please also clarify the the connection to the following sentence starting with “And Cheng et al. (2015)…”. Please clarify what exactly you would like to say with these two sentences.
- L 43: “is dependent” -> “depends”
- L 55: Werner et al. 2016 also state that “… this direct effect of the aqueous surface composition on the CCN activation is very small…”. Please re-phrase.
- L 58: “organic composition solvation” -> “organic compound solvation”
- L 59: “surrogate” of what?
- Top of page 4: I have concerns about the restraining potential (top of page 4) preventing water molecules to evaporate: Droplets of such small sizes undergo relatively strong deforming fluctuations which would be dampened by the artificial potential if the allowed radius is too small. How do the authors exclude this to be significant for the interfacial structure? From own MD simulations we obtain the radius fluctuation’s amplitude to be √ (Δ r)2 ~ 0.15 nm for a droplet of average radius <r> = 4 nm at a temperature of T = 280 K. Can the authors confirm this and put the result in relation to the width of the restraining potential?
- L 107: How is the thickness of the spherical shell determined? Please add the unit of \Delta{}r.
- Eq. 5: Why not just refer to Eq. 3 which is identical?
- Eq. 4: The shape of the harmonic umbrella potential has already been defined in Eq. 1, it is sufficient to mention that the radial distance from the droplet center is replaced by the distance from the slab center perpendicular to the surface with corresponding spacings along the reaction coordinate and refer to Eq. 1.
- Fig. 1: There are numbers missing on the r-axis of the figure – I can only guess that the tick marks are at -1 and 1 nm, respectively?
- Fig. 1: Where exactly is the succinic acid molecule when it is in the PMF minimum at the interface? Is it “on top” of the water molecule’s instantaneous surface (in the sense of Willard & Chandler, J. Phys. Chem. B, 2010) or fully hydrated?
- L 140 ff: what does it mean to “statistically” calculate or average? Please revise or remove.
- L 143: I assume that Eq. 7 was fitted to the density profiles and not the other way around?
- L 150: Could the authors more precisely describe “minimum at the surface region”? It would be interesting to know whether or not the succinic acid molecule is fully hydrated in this “surface state” or if it rather lies “on top” of the instantaneous liquid surface, see earlier comments on Fig. 1.
- L 155: ΔGsb is a PMF difference and I would rather say the difference is larger for the droplets, the current phrasing depends on the reference.
- L 161: It might not be immediately clear to the reader what is “smaller”/”larger”, the negative number or the difference. Maybe it would help to say “more/less negative”?
- L 177: “weaken” -> “weakened”
- 3a: both ΔGba and ΔGsb are r-dependent. At what r were the values in Fig. 3a obtained?
- In the droplet case, the coordinate r is defined radially outwards from the COM of the droplet. In the PMF plots, the origin is moved to the interface. Is this still consistent with Eq. 3? Or are these different r’s?
- L 180: Please rewrite “This result shows that different from thin slabs:” – do you mean “This results shows that nanodroplets behave differently from thin slabs.”?
- L 194: The “slight jump in the internal PMF”, is this the barrier-like bump located around r = -0.5 nm? Please rephrase for clarity. I’m also not quite sure what the “internal” PMF is.
- L 196: Do you mean “behavior” instead of “performance”?
- L 198: Please clarify what you mean by “more active molecule interactions…”
- L 206: What is the difference between “internal bulk” and “bulk”? Do the authors want to point out the difference between surface propensity of flat vs curved surfaces and isn’t the bulk of the solution always bulk? If the latter is not the case, please precisely define “bulk” and “internal bulk”.
- L 215: Constant with what? Slab thickness?
- L 233: As far as I understand, Wang et al. 2019 discuss capillary waves in slab simulations rather than droplets? Could the authors please elaborate on this point and/or provide a suitable reference, e.g. one of those referred to in the discussion of Wang et al. 2019?
- L 409-412: Please clarify how the uncertainty estimates presented in Fig. 5 are calculated. In particular, one would expect the uncertainties of the MOL-SOL contribution to be larger than SOL-SOL given the statistics (see especially Fig. 5c)?
Citation: https://doi.org/10.5194/acp-2020-1329-RC2 -
RC3: 'Comment on acp-2020-1329', Anonymous Referee #3, 31 May 2021
This study presents a detailed analysis of the energy profiles of a single succinic acid molecule as it is moved from the middle of a droplet to the surface. This transect is compared with the one of a flat slab. Enthalpic (split up in solvent-solvent and solute-solvent contributions) as well as entropic energy terms as a function of droplet radius and half slab thickness (both varying from 1 to 4 nm) were calculated. The results were discussed in the context with previous molecular dynamics studies and experimental work (Sayou et al., 2017; Werner et al., 2016). The authors found that the surface preference of succinic acid is stronger for a droplet than the slab of the same size, and that the surface propensity is enhanced due to the curvature effect. Moreover, they found that the surface preference is primarily an enthalpic effect, both, in the droplet and in the slab. Yet, if fluctuations are considered (Figs. 4 and 5) the surface propensity of succinic acid seems to become irrelevant compared with the huge effect of the internal bulk volume to surface ratio, which strongly increases with increasing droplet size from radii of one to four nanometers. To give relevance to their work, the authors should therefore add a statement whether the size dependence due to the enthalpic effect is relevant at all and whether it needs to be considered when analyzing surface/bulk partitioning of organic species. This question becomes even more relevant considering that the droplets under investigation are very small and thus the curvature effects are maximized. Based on their size, the droplets would be nucleation-mode aerosol particles, but considering their strong dilution, they rather represent particles during cloud droplet activation. Yet, so small particles (and such a strong curvature) is unrealistic for cloud droplet activation. The authors should therefore better motivate the relevance of the chosen system and explain for what atmospheric processes it might be relevant. Moreover, the relevance of internal pressure arising through the high curvature in small droplets could be discussed more explicitly and quantitatively. The internal pressure within the droplet could be quantified and related to the solvation energy of succinic acid. To find out whether the size dependence of the solvation energy is depending on the internal pressure, bulk systems with increasing internal pressure could be calculated as a reference. Overall, the discussion and the English should be improved to increase readability.
Specific comments
Line 15, “with the potential of mean forces method”: rephrase.
Line 19: why only “may”? Please be more specific.
Line 58, “organic composition solvation”: rephrase.
Line 60: By simulating only one succinic acid molecule in water, you neglect solute-solute interactions, which are highly important in aerosol particles. Please comment on this restriction.
Line 86: Having only one succinic acid molecule together with so many water molecules corresponds to very high dilution. At such high dilution succinic acid dissociation becomes relevant. Please comment on this.
Line 156: It would be interesting to relate the curvature effect to internal pressure.
Line 159–160: What is meant here? Just a surface enrichment or an increase of surface enrichment?
Line 162: Figure 3b shows the opposite or do you mean "less negative"?
Lines 174–175: Why “at the considered temperature”? For what temperature would the pressure be relevant for a flat slab?
Lines 177–179: The discussion of Fig. 3 should be improved. It should be tried to rationalize the molecular dynamics simulation rather than just describe the curves.
Line 180, “This result shows that different from thin slabs”: rephrase.
Line 181: quantify the pressure.
Lines 192–194: Please explain better.
Lines 201–206: This needs to be formulated better.
Lines 216–217: rephrase.
Line 246: explain Panel 6b better.
Line 250: can you specify the long-range forces?
Figure 1: Could you add an image where the succinic acid molecule is directly on the surface to visualize surface hydration?
Figure 2: In panel (c) (3 nm) the curves of the droplet and the slab overlap at the interface, while in all other panels (1, 2, 4 nm) this is not the case. Do you have an explanation?
Figure 3: Are the points depicted in these plots averages or evaluated at the center of the slab/droplet? Can you explain the reversal of trends found in panels (a) and (b) with increasing droplet radius/slab thickness?
Figure 6: explain how t is evaluated. Are the differences relevant considering the fluctuations shown in Figs. 4 and 5?
Citation: https://doi.org/10.5194/acp-2020-1329-RC3
Interactive discussion
Status: closed
-
RC1: 'Comment on acp-2020-1329', Anonymous Referee #1, 16 Mar 2021
The solvation of succinic acid has been investigated in this interesting piece of work. The simulations were conducted for a single succinic acid molecule for different sizes of water nanodroplets (i.e., droplet 255 radius from ~1 nm to 4 nm) and different thickness of water planar slabs (i.e., half slab thickness from ~1 nm to 4 nm). These simulations reveal a stronger surface propensity for succinic acid to stay on the surface of a curved surface rather than on a planar one, due to changes on the hydration energetics associated with the curvature of the nanodroplets.
This is an interesting finding that may have impact for the description of the chemistry of nanodroplets and maybe atmospheric aerosols, even if the later link is not fully established in this work.
It has been shown in previous studies that indeed there is an energy minimum at the air/water interface, which may indeed lead to isolated molecule to have a propensity to stay on the surface. Is this study another simple highlight of the compound dependent feature or is there a benefit of the present work? Maybe the authors could strengthen their message to underline better their key findings (such as the size dependence)? (Note that a revision of the use of the English language would also help, as a several sentences are difficult to follow).
Obviously, one key finding can be found in the observed size and shape dependence. However, the simulations were made on very small objects with limited amount of water, where one can wonder if the difference between bulk and surface is real (especially when the surface region is mentioned to be one nm thick). This is certainly an obvious comment that the authors could address easily for the wider audience of ACP.
While the choice of succinic acid is relevant to the atmosphere, this diacid certainly require an extra amount of water for full solvation. In a context of a limited amount of water (fixed by definition on these simulations), this reviewer was wondering if this would also affect the observations made here where this molecule was pushed to the surface?
Finally, to get closer to atmospheric applications is there any indication for which droplet size this “surface push” is applicable.
Citation: https://doi.org/10.5194/acp-2020-1329-RC1 -
RC2: 'Comment on acp-2020-1329', Anonymous Referee #2, 24 May 2021
Chen et al. report results of a comprehensive study of the bulk/surface partitioning and its energetics of aqueous succinic acid solution nano-droplets using MD simulations. The authors use established methods to obtain the potential of mean force (PMF) experienced by a succinic acid molecule along a reaction coordinate across the liquid-vacuum interface and discuss the effects of curvature on the energetics.
The study is carefully conducted and sound, and the results are interesting from a molecular perspective. However, given the scope of ACP, the authors should reflect more thoroughly on relevance of this work in the atmospheric context. This is important particularly in the light of earlier investigations (especially Werner et al. 2016 which the authors cite) that found the direct changes in CCN activity due to the surface composition in this system to be rather insignificant. It therefore remains to put the current results better into an atmospheric context and emphasize their relevance. Furthermore, the readability and the language of the manuscript needs to be reviewed and improved, and key concepts clarified throughout the manuscript, where possible.
I therefore feel that this manuscript requires major revision before it can be published within ACP, and elaborate further on these comments in the following:
General comments:
- A more elaborate and specific discussion about the relevance for atmospheric chemistry and physics is missing especially in Abstract, Introduction and Conclusions, given the placement in this journal. How are the simulations of nanometer-sized droplets relevant in the atmosphere? What is the relevance of the studied system (i.e. succinic acid)? What implications might the observed phenomena have and can they be generalized to a larger set of atmospherically relevant compounds? Can the authors please put their results in a larger context to link the physical chemistry results of their work to atmospheric processes? Where will these results lead?
- Furthermore, a brief discussion on the applicability, strengths and weaknesses for this type of molecular dynamics simulations in addressing the problem of atmospheric phase state would be appropriate under Results and Discussion.
Specific comments:
- Please simplify the last sentence of the abstract: “Meanwhile, structural analyses, however, …” (remove “Meanwhile”?)
- Introduction: “compositions” -> “compounds”?
- Throughout the manuscript: Please check the use of tenses (“was” vs. “has been” vs. “is”).
- L 4: remove “area”?
- L 36: Which “observed phenomenon” do you mean? Please specify.
- L 39: “Higher relative humidity” than what? Please specify. Please also clarify the the connection to the following sentence starting with “And Cheng et al. (2015)…”. Please clarify what exactly you would like to say with these two sentences.
- L 43: “is dependent” -> “depends”
- L 55: Werner et al. 2016 also state that “… this direct effect of the aqueous surface composition on the CCN activation is very small…”. Please re-phrase.
- L 58: “organic composition solvation” -> “organic compound solvation”
- L 59: “surrogate” of what?
- Top of page 4: I have concerns about the restraining potential (top of page 4) preventing water molecules to evaporate: Droplets of such small sizes undergo relatively strong deforming fluctuations which would be dampened by the artificial potential if the allowed radius is too small. How do the authors exclude this to be significant for the interfacial structure? From own MD simulations we obtain the radius fluctuation’s amplitude to be √ (Δ r)2 ~ 0.15 nm for a droplet of average radius <r> = 4 nm at a temperature of T = 280 K. Can the authors confirm this and put the result in relation to the width of the restraining potential?
- L 107: How is the thickness of the spherical shell determined? Please add the unit of \Delta{}r.
- Eq. 5: Why not just refer to Eq. 3 which is identical?
- Eq. 4: The shape of the harmonic umbrella potential has already been defined in Eq. 1, it is sufficient to mention that the radial distance from the droplet center is replaced by the distance from the slab center perpendicular to the surface with corresponding spacings along the reaction coordinate and refer to Eq. 1.
- Fig. 1: There are numbers missing on the r-axis of the figure – I can only guess that the tick marks are at -1 and 1 nm, respectively?
- Fig. 1: Where exactly is the succinic acid molecule when it is in the PMF minimum at the interface? Is it “on top” of the water molecule’s instantaneous surface (in the sense of Willard & Chandler, J. Phys. Chem. B, 2010) or fully hydrated?
- L 140 ff: what does it mean to “statistically” calculate or average? Please revise or remove.
- L 143: I assume that Eq. 7 was fitted to the density profiles and not the other way around?
- L 150: Could the authors more precisely describe “minimum at the surface region”? It would be interesting to know whether or not the succinic acid molecule is fully hydrated in this “surface state” or if it rather lies “on top” of the instantaneous liquid surface, see earlier comments on Fig. 1.
- L 155: ΔGsb is a PMF difference and I would rather say the difference is larger for the droplets, the current phrasing depends on the reference.
- L 161: It might not be immediately clear to the reader what is “smaller”/”larger”, the negative number or the difference. Maybe it would help to say “more/less negative”?
- L 177: “weaken” -> “weakened”
- 3a: both ΔGba and ΔGsb are r-dependent. At what r were the values in Fig. 3a obtained?
- In the droplet case, the coordinate r is defined radially outwards from the COM of the droplet. In the PMF plots, the origin is moved to the interface. Is this still consistent with Eq. 3? Or are these different r’s?
- L 180: Please rewrite “This result shows that different from thin slabs:” – do you mean “This results shows that nanodroplets behave differently from thin slabs.”?
- L 194: The “slight jump in the internal PMF”, is this the barrier-like bump located around r = -0.5 nm? Please rephrase for clarity. I’m also not quite sure what the “internal” PMF is.
- L 196: Do you mean “behavior” instead of “performance”?
- L 198: Please clarify what you mean by “more active molecule interactions…”
- L 206: What is the difference between “internal bulk” and “bulk”? Do the authors want to point out the difference between surface propensity of flat vs curved surfaces and isn’t the bulk of the solution always bulk? If the latter is not the case, please precisely define “bulk” and “internal bulk”.
- L 215: Constant with what? Slab thickness?
- L 233: As far as I understand, Wang et al. 2019 discuss capillary waves in slab simulations rather than droplets? Could the authors please elaborate on this point and/or provide a suitable reference, e.g. one of those referred to in the discussion of Wang et al. 2019?
- L 409-412: Please clarify how the uncertainty estimates presented in Fig. 5 are calculated. In particular, one would expect the uncertainties of the MOL-SOL contribution to be larger than SOL-SOL given the statistics (see especially Fig. 5c)?
Citation: https://doi.org/10.5194/acp-2020-1329-RC2 -
RC3: 'Comment on acp-2020-1329', Anonymous Referee #3, 31 May 2021
This study presents a detailed analysis of the energy profiles of a single succinic acid molecule as it is moved from the middle of a droplet to the surface. This transect is compared with the one of a flat slab. Enthalpic (split up in solvent-solvent and solute-solvent contributions) as well as entropic energy terms as a function of droplet radius and half slab thickness (both varying from 1 to 4 nm) were calculated. The results were discussed in the context with previous molecular dynamics studies and experimental work (Sayou et al., 2017; Werner et al., 2016). The authors found that the surface preference of succinic acid is stronger for a droplet than the slab of the same size, and that the surface propensity is enhanced due to the curvature effect. Moreover, they found that the surface preference is primarily an enthalpic effect, both, in the droplet and in the slab. Yet, if fluctuations are considered (Figs. 4 and 5) the surface propensity of succinic acid seems to become irrelevant compared with the huge effect of the internal bulk volume to surface ratio, which strongly increases with increasing droplet size from radii of one to four nanometers. To give relevance to their work, the authors should therefore add a statement whether the size dependence due to the enthalpic effect is relevant at all and whether it needs to be considered when analyzing surface/bulk partitioning of organic species. This question becomes even more relevant considering that the droplets under investigation are very small and thus the curvature effects are maximized. Based on their size, the droplets would be nucleation-mode aerosol particles, but considering their strong dilution, they rather represent particles during cloud droplet activation. Yet, so small particles (and such a strong curvature) is unrealistic for cloud droplet activation. The authors should therefore better motivate the relevance of the chosen system and explain for what atmospheric processes it might be relevant. Moreover, the relevance of internal pressure arising through the high curvature in small droplets could be discussed more explicitly and quantitatively. The internal pressure within the droplet could be quantified and related to the solvation energy of succinic acid. To find out whether the size dependence of the solvation energy is depending on the internal pressure, bulk systems with increasing internal pressure could be calculated as a reference. Overall, the discussion and the English should be improved to increase readability.
Specific comments
Line 15, “with the potential of mean forces method”: rephrase.
Line 19: why only “may”? Please be more specific.
Line 58, “organic composition solvation”: rephrase.
Line 60: By simulating only one succinic acid molecule in water, you neglect solute-solute interactions, which are highly important in aerosol particles. Please comment on this restriction.
Line 86: Having only one succinic acid molecule together with so many water molecules corresponds to very high dilution. At such high dilution succinic acid dissociation becomes relevant. Please comment on this.
Line 156: It would be interesting to relate the curvature effect to internal pressure.
Line 159–160: What is meant here? Just a surface enrichment or an increase of surface enrichment?
Line 162: Figure 3b shows the opposite or do you mean "less negative"?
Lines 174–175: Why “at the considered temperature”? For what temperature would the pressure be relevant for a flat slab?
Lines 177–179: The discussion of Fig. 3 should be improved. It should be tried to rationalize the molecular dynamics simulation rather than just describe the curves.
Line 180, “This result shows that different from thin slabs”: rephrase.
Line 181: quantify the pressure.
Lines 192–194: Please explain better.
Lines 201–206: This needs to be formulated better.
Lines 216–217: rephrase.
Line 246: explain Panel 6b better.
Line 250: can you specify the long-range forces?
Figure 1: Could you add an image where the succinic acid molecule is directly on the surface to visualize surface hydration?
Figure 2: In panel (c) (3 nm) the curves of the droplet and the slab overlap at the interface, while in all other panels (1, 2, 4 nm) this is not the case. Do you have an explanation?
Figure 3: Are the points depicted in these plots averages or evaluated at the center of the slab/droplet? Can you explain the reversal of trends found in panels (a) and (b) with increasing droplet radius/slab thickness?
Figure 6: explain how t is evaluated. Are the differences relevant considering the fluctuations shown in Figs. 4 and 5?
Citation: https://doi.org/10.5194/acp-2020-1329-RC3
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 989 | 477 | 47 | 1,513 | 139 | 50 | 42 |
- HTML: 989
- PDF: 477
- XML: 47
- Total: 1,513
- Supplement: 139
- BibTeX: 50
- EndNote: 42
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Cited
1 citations as recorded by crossref.
Chuchu Chen
Xiaoxiang Wang
Kurt Binder
Mohammad Mehdi Ghahremanpour
David van der Spoel
Ulrich Pöschl
This preprint has been withdrawn.
- Preprint
(927 KB) - Metadata XML
-
Supplement
(151 KB) - BibTeX
- EndNote