the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 Jul 2024
The role of interfacial tension in the size-dependent phase separation of atmospheric aerosol particles
Abstract. Atmospheric aerosol particles span orders of magnitude in size. In ultrafine particles, the energetic contributions of surfaces and interfaces to the Gibbs energy become significant and increase in importance as particle diameter decreases. For these particles, the thermodynamic equilibrium state depends on size, composition, and temperature. Various aerosol systems have been observed to undergo liquid–liquid phase separation (LLPS), impacting equilibrium gas–particle partitioning, modifying physicochemical properties of the particle phases, and influencing cloud droplet activation. Numerous laboratory experiments have characterized the onset relative humidity of LLPS in larger aerosol particles and macroscopic bulk systems. However, in sufficiently small particles, the interfacial tension between two liquid phases constitutes an energetic barrier that may prevent the formation of an additional liquid phase. Determining said small-size limit is a key question.
We introduce a predictive droplet model based on the Aerosol Inorganic–Organic Mixtures Functional groups Activity Coefficients model. This model enables size-dependent computations of surface and interfacial tension effects on bulk–surface partitioning within phase-separated and single-phase particles. We evaluate four approaches for computing interfacial tension in multicomponent droplets, including a new method introduced in this work. Of the approaches tested, Antonov's rule best matches observed liquid–liquid interfacial tensions in highly immiscible mixtures, while a modified Butler equation fits well in more miscible systems. We find that two approaches substantially lower the onset relative humidity of LLPS for the studied systems.
-
Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
-
Preprint
(954 KB)
-
Supplement
(303 KB)
-
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(954 KB) - Metadata XML
-
Supplement
(303 KB) - BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
-
CC1: 'Comment on egusphere-2024-1690', Alison Bain, 09 Jul 2024
Schmedding and Zuend provide a very nice comparison of four methods to predict the interfacial tension between two liquid phases and their ability to predict the onset of liquid-liquid phase separation observed in aerosol droplets. I have a few minor comments about the manuscript.
1. There seems to be a discrepancy between Fig 2A caption and the rest of the text. Fig. 2A caption says the system is glutaric acid and water but in the discussion of the figure in the text (~line 307 page 11) ethanol/water is mentioned. I also see ethanol but not glutaric acid in Table S3.
2. It would be helpful to the reader to have a note somewhere (maybe near the top of section 3.1) that the dry aerosol component mass fractions for all systems investigated are in Table S3. Table S3 would also be more clear if it a) had the figure number where the system result is shown or b) was in the same order as systems are introduced in the main text.
3. There seems to be a discrepancy between Fig 4C caption and the rest of the text. Fig 4C caption is labeled dodecane-lithium-chloride, but in Table S3 and main text (~line 333, page 12) dodecane-KCl is mentioned.
4. page 14 line 399 - during the discussion of Fig. 7, I do not understand the reference to Fig S2 which is for PEG400 - AS (not one of the systems in Fig. 7). OIR is also mentioned on this line but is not defined in the main text.
5. small typo, there is an extra '-' in 10 - 50 nm on line 527.
Citation: https://doi.org/10.5194/egusphere-2024-1690-CC1 -
AC1: 'Reply on CC1', Ryan Schmedding, 09 Jul 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1690/egusphere-2024-1690-AC1-supplement.pdf
-
AC1: 'Reply on CC1', Ryan Schmedding, 09 Jul 2024
-
RC1: 'Comment on egusphere-2024-1690', Anonymous Referee #1, 29 Jul 2024
Most existing thermodynamic models for calculating liquid-liquid phase separation effectively simulate bulk matter and neglect surface/interfacial effects, which can be important at the small sizes relevant in aerosol particles. This manuscript presents a model that is able to incorporate these surface/interfacial effects and evaluates four different methods of computing interfacial tensions. This manuscript represents an important contribution to the literature and I have only a few minor comments, described below:
Scientific points:
- Line 90 gives a constraint on the value of φ, but is there any independent method of estimating φ independent of comparison with experimental values of σαβ, or is this essentially a purely empirical factor? Some additional discussion of this parameter would he helpful.
- What a Guggenheim interface is, which is mentioned on lines 124 and 205, should be briefly explained.
Minor presentation points:
- The first paragraph of the results section, lines 287 to 297 do not really seem to contain results, but rather some definitions and background information that would benefit the reader to see earlier in the manuscript. I would suggest that this section/information be moved to the introduction section.
- In the paragraph starting on Line 320, the authors switch back and forth between referring to the different approaches by name and by equation number. For the sake of the reader, it would be helpful to stick to one consistent naming throughout the manuscript, rather than switching back and forth. Related, the shorthand ‘Butler equation’ is used on line 338 for ‘Butler equation with geometric mean activity coefficients’ (line 323), but the figure just uses ‘Geom. Mean. Act. Coeffs.’ Consistency would improve clarity.
Citation: https://doi.org/10.5194/egusphere-2024-1690-RC1 - AC2: 'Reply on RC1', Ryan Schmedding, 19 Sep 2024
- AC4: 'Reply on RC1', Ryan Schmedding, 18 Oct 2024
-
RC2: 'Comment on egusphere-2024-1690', Anonymous Referee #2, 18 Sep 2024
In this manuscript, Schmedding and Zuend present a mathematical framework for predicting the surface and interfacial tensions of a droplet with liquid-liquid-vapor equilibrium, and they compare their predictions with several case studies and comparisons to literature. They provide thorough documentation of their methodology, both in the main text and in the supplement. The authors draw from classical relationships for interfacial tension, propose a new relationship, and test all for their predictive ability. This paper is an important contribution, and publication is recommended.
Some minor suggestions on presentation include:
1. On line 130 or elsewhere, it may be good to briefly describe how the partial molar area of each component is determined in the studied systems.
2. On lines 243-247, it could be better to have these equations as displayed, numbered equations on separate lines, as it could be difficult for a general reader to easily parse these in-line equations.
3. In Fig 3, Equation 15 could be referred to in the caption for the reader to be reminded of how σs,∗ is defined.Citation: https://doi.org/10.5194/egusphere-2024-1690-RC2 - AC3: 'Reply on RC2', Ryan Schmedding, 19 Sep 2024
Interactive discussion
Status: closed
-
CC1: 'Comment on egusphere-2024-1690', Alison Bain, 09 Jul 2024
Schmedding and Zuend provide a very nice comparison of four methods to predict the interfacial tension between two liquid phases and their ability to predict the onset of liquid-liquid phase separation observed in aerosol droplets. I have a few minor comments about the manuscript.
1. There seems to be a discrepancy between Fig 2A caption and the rest of the text. Fig. 2A caption says the system is glutaric acid and water but in the discussion of the figure in the text (~line 307 page 11) ethanol/water is mentioned. I also see ethanol but not glutaric acid in Table S3.
2. It would be helpful to the reader to have a note somewhere (maybe near the top of section 3.1) that the dry aerosol component mass fractions for all systems investigated are in Table S3. Table S3 would also be more clear if it a) had the figure number where the system result is shown or b) was in the same order as systems are introduced in the main text.
3. There seems to be a discrepancy between Fig 4C caption and the rest of the text. Fig 4C caption is labeled dodecane-lithium-chloride, but in Table S3 and main text (~line 333, page 12) dodecane-KCl is mentioned.
4. page 14 line 399 - during the discussion of Fig. 7, I do not understand the reference to Fig S2 which is for PEG400 - AS (not one of the systems in Fig. 7). OIR is also mentioned on this line but is not defined in the main text.
5. small typo, there is an extra '-' in 10 - 50 nm on line 527.
Citation: https://doi.org/10.5194/egusphere-2024-1690-CC1 -
AC1: 'Reply on CC1', Ryan Schmedding, 09 Jul 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-1690/egusphere-2024-1690-AC1-supplement.pdf
-
AC1: 'Reply on CC1', Ryan Schmedding, 09 Jul 2024
-
RC1: 'Comment on egusphere-2024-1690', Anonymous Referee #1, 29 Jul 2024
Most existing thermodynamic models for calculating liquid-liquid phase separation effectively simulate bulk matter and neglect surface/interfacial effects, which can be important at the small sizes relevant in aerosol particles. This manuscript presents a model that is able to incorporate these surface/interfacial effects and evaluates four different methods of computing interfacial tensions. This manuscript represents an important contribution to the literature and I have only a few minor comments, described below:
Scientific points:
- Line 90 gives a constraint on the value of φ, but is there any independent method of estimating φ independent of comparison with experimental values of σαβ, or is this essentially a purely empirical factor? Some additional discussion of this parameter would he helpful.
- What a Guggenheim interface is, which is mentioned on lines 124 and 205, should be briefly explained.
Minor presentation points:
- The first paragraph of the results section, lines 287 to 297 do not really seem to contain results, but rather some definitions and background information that would benefit the reader to see earlier in the manuscript. I would suggest that this section/information be moved to the introduction section.
- In the paragraph starting on Line 320, the authors switch back and forth between referring to the different approaches by name and by equation number. For the sake of the reader, it would be helpful to stick to one consistent naming throughout the manuscript, rather than switching back and forth. Related, the shorthand ‘Butler equation’ is used on line 338 for ‘Butler equation with geometric mean activity coefficients’ (line 323), but the figure just uses ‘Geom. Mean. Act. Coeffs.’ Consistency would improve clarity.
Citation: https://doi.org/10.5194/egusphere-2024-1690-RC1 - AC2: 'Reply on RC1', Ryan Schmedding, 19 Sep 2024
- AC4: 'Reply on RC1', Ryan Schmedding, 18 Oct 2024
-
RC2: 'Comment on egusphere-2024-1690', Anonymous Referee #2, 18 Sep 2024
In this manuscript, Schmedding and Zuend present a mathematical framework for predicting the surface and interfacial tensions of a droplet with liquid-liquid-vapor equilibrium, and they compare their predictions with several case studies and comparisons to literature. They provide thorough documentation of their methodology, both in the main text and in the supplement. The authors draw from classical relationships for interfacial tension, propose a new relationship, and test all for their predictive ability. This paper is an important contribution, and publication is recommended.
Some minor suggestions on presentation include:
1. On line 130 or elsewhere, it may be good to briefly describe how the partial molar area of each component is determined in the studied systems.
2. On lines 243-247, it could be better to have these equations as displayed, numbered equations on separate lines, as it could be difficult for a general reader to easily parse these in-line equations.
3. In Fig 3, Equation 15 could be referred to in the caption for the reader to be reminded of how σs,∗ is defined.Citation: https://doi.org/10.5194/egusphere-2024-1690-RC2 - AC3: 'Reply on RC2', Ryan Schmedding, 19 Sep 2024
Peer review completion
Journal article(s) based on this preprint
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 358 | 125 | 456 | 939 | 45 | 13 | 12 |
- HTML: 358
- PDF: 125
- XML: 456
- Total: 939
- Supplement: 45
- BibTeX: 13
- EndNote: 12
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Ryan Schmedding
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(954 KB) - Metadata XML
-
Supplement
(303 KB) - BibTeX
- EndNote
- Final revised paper