the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Sep 2022
Microphysics of liquid water in sub-10 nm ultrafine aerosol particles
Xiaohan Li
Ian C. Bourg
Abstract. Ultrafine aerosol particles with sizes smaller than 50 nm have been shown in recent studies to serve as a large source of cloud condensation nuclei (CCN) that can promote additional cloud droplet formation under supersaturation conditions. Knowledge of the microphysics of liquid water in these droplets remains limited, particularly in the sub-10 nm particle size range, due to experimental and theoretical challenges associated with the complexity of aerosol components and the small length scales of interest (e.g., difficulty of precisely sampling the liquid-air interface, questionable validity of mean-field theoretical representations). Here, we carried out molecular dynamics (MD) simulations of aerosol particles with diameters between 1 and 10 nm and characterized atomistic-level structure and water dynamics in well-mixed and phase-separated system with different particle sizes, NaCl salinities, and organic surface loadings as a function of distance from the time-averaged Gibbs dividing interface or instantaneous water-air interface. We define a sphericity factor (Φ) that can shed light on the phase-mixing state of nanodroplets, and we reveal an unexpected dependence of mixing state on droplet size. Our results also evidence an ion concentration enhancement in ultrafine aerosols, which should modulate salt nucleation kinetics in ultrafine sea salt aerosols, and provide detailed characterization of the influence of droplet size on surface tension and on water self-diffusivity near the interface. Analysis of water evaporation free energy and water activity demonstrates the validity of the Kelvin equation and Köhler theory at droplet sizes larger than 4 nm under moderate salinities and organic loadings and the need for further extension to account for ion concentration enhancement in sub-10 nm aerosols, droplet-size-dependent phase separation effects, and a sharp decrease in the cohesiveness of liquid water in sub-4 nm droplets. Finally, we show that an idealized fractional surface coating factor (fs) can be used to categorize and reconcile water accommodation coefficients (α*) observed in MD simulations and experimental results in the presence of organic coatings, and we resolve the droplet-size dependence of α*.
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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.
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Preprint
(32368 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(32368 KB) - BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Xiaohan Li and Ian C. Bourg
Interactive discussion
Status: closed
-
CC1: 'Comment on egusphere-2022-826', Anthony Wexler, 03 Oct 2022
Summary
This is a comprehensive study of the thermodynamics of nanoscale aerosol particles presenting some unintuitive but well explained results. There are some shortcomings in the work that need to be addressed before it is ready for publication.
Major comments
L13: Relevance to sea spray particles is questionable since (a) particles this small are likely composed primarily of sea surface organics and (b) the physical processes that generated sea spray are not able to generate particles in the ~10nm size range.
L125: what are the implications of a 1.2 nm cut-off for Coulombic and VDW interactions? 1.2 nm is much larger than these molecules and ions and monopole-dipole interactions could be significant. What is the justification for this cut-off.
Equation 1: How is the interfacial width parameter determined? How sensitive are the results to changes in its value? What value was used?
L450-480: This is the opposite trend to what I expected. Since NaCl is concentrated in the core of the particle due to exclusion from the surface, that should lower the water activity in the particle relative that that in the bulk at the same NaCl concentration. The opposite trend is observed. More discussion about this discrepancy is needed.
Minor comments
Equation 2: What are N_w and N_org?
Equation 6: what are P_k and P_U?
L174: vapor pressure of the bulk water?
L269: different numbers of water molecules
L299: diminished
L333: dividing
Citation: https://doi.org/10.5194/egusphere-2022-826-CC1 -
AC1: 'Reply on CC1', Xiaohan Li, 14 Oct 2022
Dear Professor Wexler,
Thanks for your careful reading of our manuscript. We highly appreciate your time and valuable suggestions. Below you will find our replies to your comments in the attched document.
Best wishes,
Xiaohan Li & Ian C. Bourg
Department of Civil and Environmental Engineering, Princeton University
-
AC1: 'Reply on CC1', Xiaohan Li, 14 Oct 2022
-
RC1: 'Comment on egusphere-2022-826', Robert McGraw, 14 Nov 2022
Summary: This is a valuable and comprehensive study that models the interactions between water and typical CCN species, that include ions and organics, using molecular dynamics simulation. The most serious reservation that I have concerns Sec. 2.3 and misuse of the terms equimolecular dividing surface (at Re) and surface tension (see below). Unfortunately, Re is used in the equations, beginning with Eq. 3, instead of the “surface of tension", which should be used. This is likely to affect the calculations that follow, especially if the interfacial structure is broad. The authors should have look at this and comment. Otherwise the paper seems important and should be published. Major points, minor points, and a few typos are listed below.
Major
Section 2.2 System prep and MD simulations: I have some points of confusion after reading this section. The first concerns the underlying model consisting of cubic cells with periodic boundary conditions and edge length exceeding the droplet diameter – a figure here would help the reader. Second, what is the advantage of periodic boundaries, with so much extra space in each cell? How is the Ewald sum applied in this model? Usually Ewald sums are applied to extended periodic structures - not to a period set of droplets with space around each one. More details here would be helpful.
Having called attention to Ewald sums I might point out a clever test that evaluates the accuracy of intermolecular water potentials. This by comparing the computationally relaxed structures with the 3D structure parameters and densities available for ice structures from x-ray diffraction [Morse and Rice, 1981]. For what its worth, the ST2 water potential performed quite well in the test while another did poorly.
Section 2.3. The author’s description of the Gibb’s dividing surface seems to this reviewer a misrepresentation of this important concept. Specifically, the authors use of surface tension at the equimolar (equimolecular might be better in context of MD) is said to “correspond to a vanishing adsorption … ensuring that the surface free energy per unit area so defined corresponds to the surface tension”. Actually the equimolecular surface does neither! It is the dividing surface located at the “surface of tension” that has these properties. As for adsorption, the Gibbs adsorption isotherm applies only at the surface of tension. Moreover, the pressure difference across the surface of tension is the only one that appears in the standard Laplace and Kelvin relations (otherwise additional terms added to these relations are required) . See [McGraw and Laaksonen, 1997] and especially the citation to Ono and Kondo, an excellent review of the subject, therein.
Related: Eq. 7 is similar to the equation developed by Gibbs for the work to form a capillary drop from vapor. This formula can be applied even to droplets having a broadened interfacial region - provided the radius at the surface of tension is used.
Finally, a couple of comments on the “validity of the Kelvin and Kohler theory at droplet sizes larger than 4nm under moderate salinities and organic loadings and the need to account for ion-concentration enhancement in sub-10nm particles” mentioned in the Abstract. This is an important theme that runs through and adds value to the paper. With respect to the Kelvin relation this has been confirmed for the Kelvin (pure water) and Kelvin-Thomson (ionic solution) relations [Winkler et al., 2012]. For Kohler theory, on the other hand, this is unlikely to be the case for organics. The latter tend to partition between the bulk and surface phases, whereas the standard Kohler and kappa-Kohler models pertain only to fully water-soluble species. A recent extension of Kohler theory, based on analysis of droplet stability, takes into account the partitioning of both water-soluble and surface-active species in a unified way for applications to cloud activation [McGraw and Wang, 2021].
McGraw, R. and A. Laaksonen (1997), J. Chem. Phys. 106, 5284-5287.
Morse, M. D. and S. A. Rice (1981), J. Chem. Phys. 74, 6514-6516.
Winkler, P. M., et. al. (2012), Phys. Rev. Letts. 108, 085701.
McGraw, R. and J. Wang (2021), J. Chem. Phys. 154, 024707; doi: 10.1063/5.0031436
Minor points and typos:
Eq. 9 (previously just below Eq. 5) rho_0 was used, which I assume is the density at the center of the drop. Why the switch to rho_w, which I assume is the bulk density of water? I don't see these symbols defined.
The switch from molecular units, kT, to moler units, RT, in equation 9 and back to kT in Eq. 10 can be avoided using consistent units.
Line 777. The correct authorciting should be to Lewis and Schwartz, 2004. Same in line 102: change Lewis et. al. to Lewis and Schwartz, 2004.
Citation: https://doi.org/10.5194/egusphere-2022-826-RC1 -
AC2: 'Reply on RC1', Xiaohan Li, 17 Nov 2022
Dear Dr. McGraw,
Thanks for your careful reading of our manuscript entitled “Microphysics of liquid water in sub-10 nm ultrafine aerosol particles”. We highly appreciate your time and valuable suggestions. You will find our replies to your comments in the attached document.
Best wishes,
Xiaohan Li & Ian C. Bourg
Department of Civil and Environmental Engineering, Princeton University
-
AC2: 'Reply on RC1', Xiaohan Li, 17 Nov 2022
-
RC2: 'Comment on egusphere-2022-826', Anonymous Referee #2, 25 Nov 2022
The authors present a theoretical study of nanoparticle morphology and gas/droplet partitioning behavior of water using systems consisting of sodium chloride, water, and pimelic acid. The authors discover several parameters - sphericity and fractional surface coverage - that aptly describe chemical morphology as a function of composition and size regimes and variation in mass accommodation coefficients. The authors also report a threshold for the validity of continuum theories. The paper is well-written and is of interest to the Atmospheric Chemistry and Physics community, and is recommended for publication after the following general comments have been addressed.As the authors note in Section 3.4, classical water models are known to have biases in errors in reproducing experimental surface tensions - though with SPC/E having one of the smallest errors (Vega and de Miguel, 2007). Additionally, a study (Lbadaoui-Darvas and Takahama, 2019) suggest that carboxylic acid-water dynamics are not well captured in equilibrium MD simulations and lead to deviations in predictions of water activity even above 0.95. On the other hand, the water activity calculations seem to suggest that the simulation results are in good agreement - with observations - is this due to canceling of errors (e.g., with molar volume) or the relatively small magnitude of the error in surface tension by these models?
Many of the conclusions summarize the effect of "organic loadings" but the simulations use a specific type of organic, namely pimelic acid. Many studies on the other hand suggest the importance of alcohols in marine aerosols (e.g., Russell et al., 2010). Is there reason that the authors can justify broadening the conclusion from a particular "organic acid" to "organics" generally? Other abundant dicarboxylic acids (e.g., oxalic acid) may also exhibit different bulk/surface partitioning behavior than demarcated by the sphericity factor. The main question is whether parts of the manuscript should be more clear in what is meant by "organic loading" in this work.
References:
Lbadaoui-Darvas, Mária, and Satoshi Takahama. “Water Activity from Equilibrium Molecular Dynamics Simulations and Kirkwood-Buff Theory.” The Journal of Physical Chemistry B 123, no. 50 (December 19, 2019): 10757–68. https://doi.org/10.1021/acs.jpcb.9b06735.
Russell, L. M., L. N. Hawkins, A. A. Frossard, P. K. Quinn, and T. S. Bates. “Carbohydrate-like Composition of Submicron Atmospheric Particles and Their Production from Ocean Bubble Bursting.” Proceedings of the National Academy of Sciences of the United States of America 107, no. 15 (2010): 6652–57. https://doi.org/10.1073/pnas.0908905107.
Vega, C., and E. de Miguel. “Surface Tension of the Most Popular Models of Water by Using the Test-Area Simulation Method.” The Journal of Chemical Physics 126, no. 15 (2007): 154707. https://doi.org/10.1063/1.2715577.
Citation: https://doi.org/10.5194/egusphere-2022-826-RC2 -
AC3: 'Reply on RC2', Xiaohan Li, 01 Dec 2022
Dear Reviewer,
Thanks for your careful reading of our manuscript entitled “Microphysics of liquid water in sub-10 nm ultrafine aerosol particles”. We highly appreciate your time and valuable suggestions. You will find our replies to your comments in the attached document.
Best wishes,
Xiaohan Li & Ian C. Bourg
Department of Civil and Environmental Engineering, Princeton University
-
AC3: 'Reply on RC2', Xiaohan Li, 01 Dec 2022
Interactive discussion
Status: closed
-
CC1: 'Comment on egusphere-2022-826', Anthony Wexler, 03 Oct 2022
Summary
This is a comprehensive study of the thermodynamics of nanoscale aerosol particles presenting some unintuitive but well explained results. There are some shortcomings in the work that need to be addressed before it is ready for publication.
Major comments
L13: Relevance to sea spray particles is questionable since (a) particles this small are likely composed primarily of sea surface organics and (b) the physical processes that generated sea spray are not able to generate particles in the ~10nm size range.
L125: what are the implications of a 1.2 nm cut-off for Coulombic and VDW interactions? 1.2 nm is much larger than these molecules and ions and monopole-dipole interactions could be significant. What is the justification for this cut-off.
Equation 1: How is the interfacial width parameter determined? How sensitive are the results to changes in its value? What value was used?
L450-480: This is the opposite trend to what I expected. Since NaCl is concentrated in the core of the particle due to exclusion from the surface, that should lower the water activity in the particle relative that that in the bulk at the same NaCl concentration. The opposite trend is observed. More discussion about this discrepancy is needed.
Minor comments
Equation 2: What are N_w and N_org?
Equation 6: what are P_k and P_U?
L174: vapor pressure of the bulk water?
L269: different numbers of water molecules
L299: diminished
L333: dividing
Citation: https://doi.org/10.5194/egusphere-2022-826-CC1 -
AC1: 'Reply on CC1', Xiaohan Li, 14 Oct 2022
Dear Professor Wexler,
Thanks for your careful reading of our manuscript. We highly appreciate your time and valuable suggestions. Below you will find our replies to your comments in the attched document.
Best wishes,
Xiaohan Li & Ian C. Bourg
Department of Civil and Environmental Engineering, Princeton University
-
AC1: 'Reply on CC1', Xiaohan Li, 14 Oct 2022
-
RC1: 'Comment on egusphere-2022-826', Robert McGraw, 14 Nov 2022
Summary: This is a valuable and comprehensive study that models the interactions between water and typical CCN species, that include ions and organics, using molecular dynamics simulation. The most serious reservation that I have concerns Sec. 2.3 and misuse of the terms equimolecular dividing surface (at Re) and surface tension (see below). Unfortunately, Re is used in the equations, beginning with Eq. 3, instead of the “surface of tension", which should be used. This is likely to affect the calculations that follow, especially if the interfacial structure is broad. The authors should have look at this and comment. Otherwise the paper seems important and should be published. Major points, minor points, and a few typos are listed below.
Major
Section 2.2 System prep and MD simulations: I have some points of confusion after reading this section. The first concerns the underlying model consisting of cubic cells with periodic boundary conditions and edge length exceeding the droplet diameter – a figure here would help the reader. Second, what is the advantage of periodic boundaries, with so much extra space in each cell? How is the Ewald sum applied in this model? Usually Ewald sums are applied to extended periodic structures - not to a period set of droplets with space around each one. More details here would be helpful.
Having called attention to Ewald sums I might point out a clever test that evaluates the accuracy of intermolecular water potentials. This by comparing the computationally relaxed structures with the 3D structure parameters and densities available for ice structures from x-ray diffraction [Morse and Rice, 1981]. For what its worth, the ST2 water potential performed quite well in the test while another did poorly.
Section 2.3. The author’s description of the Gibb’s dividing surface seems to this reviewer a misrepresentation of this important concept. Specifically, the authors use of surface tension at the equimolar (equimolecular might be better in context of MD) is said to “correspond to a vanishing adsorption … ensuring that the surface free energy per unit area so defined corresponds to the surface tension”. Actually the equimolecular surface does neither! It is the dividing surface located at the “surface of tension” that has these properties. As for adsorption, the Gibbs adsorption isotherm applies only at the surface of tension. Moreover, the pressure difference across the surface of tension is the only one that appears in the standard Laplace and Kelvin relations (otherwise additional terms added to these relations are required) . See [McGraw and Laaksonen, 1997] and especially the citation to Ono and Kondo, an excellent review of the subject, therein.
Related: Eq. 7 is similar to the equation developed by Gibbs for the work to form a capillary drop from vapor. This formula can be applied even to droplets having a broadened interfacial region - provided the radius at the surface of tension is used.
Finally, a couple of comments on the “validity of the Kelvin and Kohler theory at droplet sizes larger than 4nm under moderate salinities and organic loadings and the need to account for ion-concentration enhancement in sub-10nm particles” mentioned in the Abstract. This is an important theme that runs through and adds value to the paper. With respect to the Kelvin relation this has been confirmed for the Kelvin (pure water) and Kelvin-Thomson (ionic solution) relations [Winkler et al., 2012]. For Kohler theory, on the other hand, this is unlikely to be the case for organics. The latter tend to partition between the bulk and surface phases, whereas the standard Kohler and kappa-Kohler models pertain only to fully water-soluble species. A recent extension of Kohler theory, based on analysis of droplet stability, takes into account the partitioning of both water-soluble and surface-active species in a unified way for applications to cloud activation [McGraw and Wang, 2021].
McGraw, R. and A. Laaksonen (1997), J. Chem. Phys. 106, 5284-5287.
Morse, M. D. and S. A. Rice (1981), J. Chem. Phys. 74, 6514-6516.
Winkler, P. M., et. al. (2012), Phys. Rev. Letts. 108, 085701.
McGraw, R. and J. Wang (2021), J. Chem. Phys. 154, 024707; doi: 10.1063/5.0031436
Minor points and typos:
Eq. 9 (previously just below Eq. 5) rho_0 was used, which I assume is the density at the center of the drop. Why the switch to rho_w, which I assume is the bulk density of water? I don't see these symbols defined.
The switch from molecular units, kT, to moler units, RT, in equation 9 and back to kT in Eq. 10 can be avoided using consistent units.
Line 777. The correct authorciting should be to Lewis and Schwartz, 2004. Same in line 102: change Lewis et. al. to Lewis and Schwartz, 2004.
Citation: https://doi.org/10.5194/egusphere-2022-826-RC1 -
AC2: 'Reply on RC1', Xiaohan Li, 17 Nov 2022
Dear Dr. McGraw,
Thanks for your careful reading of our manuscript entitled “Microphysics of liquid water in sub-10 nm ultrafine aerosol particles”. We highly appreciate your time and valuable suggestions. You will find our replies to your comments in the attached document.
Best wishes,
Xiaohan Li & Ian C. Bourg
Department of Civil and Environmental Engineering, Princeton University
-
AC2: 'Reply on RC1', Xiaohan Li, 17 Nov 2022
-
RC2: 'Comment on egusphere-2022-826', Anonymous Referee #2, 25 Nov 2022
The authors present a theoretical study of nanoparticle morphology and gas/droplet partitioning behavior of water using systems consisting of sodium chloride, water, and pimelic acid. The authors discover several parameters - sphericity and fractional surface coverage - that aptly describe chemical morphology as a function of composition and size regimes and variation in mass accommodation coefficients. The authors also report a threshold for the validity of continuum theories. The paper is well-written and is of interest to the Atmospheric Chemistry and Physics community, and is recommended for publication after the following general comments have been addressed.As the authors note in Section 3.4, classical water models are known to have biases in errors in reproducing experimental surface tensions - though with SPC/E having one of the smallest errors (Vega and de Miguel, 2007). Additionally, a study (Lbadaoui-Darvas and Takahama, 2019) suggest that carboxylic acid-water dynamics are not well captured in equilibrium MD simulations and lead to deviations in predictions of water activity even above 0.95. On the other hand, the water activity calculations seem to suggest that the simulation results are in good agreement - with observations - is this due to canceling of errors (e.g., with molar volume) or the relatively small magnitude of the error in surface tension by these models?
Many of the conclusions summarize the effect of "organic loadings" but the simulations use a specific type of organic, namely pimelic acid. Many studies on the other hand suggest the importance of alcohols in marine aerosols (e.g., Russell et al., 2010). Is there reason that the authors can justify broadening the conclusion from a particular "organic acid" to "organics" generally? Other abundant dicarboxylic acids (e.g., oxalic acid) may also exhibit different bulk/surface partitioning behavior than demarcated by the sphericity factor. The main question is whether parts of the manuscript should be more clear in what is meant by "organic loading" in this work.
References:
Lbadaoui-Darvas, Mária, and Satoshi Takahama. “Water Activity from Equilibrium Molecular Dynamics Simulations and Kirkwood-Buff Theory.” The Journal of Physical Chemistry B 123, no. 50 (December 19, 2019): 10757–68. https://doi.org/10.1021/acs.jpcb.9b06735.
Russell, L. M., L. N. Hawkins, A. A. Frossard, P. K. Quinn, and T. S. Bates. “Carbohydrate-like Composition of Submicron Atmospheric Particles and Their Production from Ocean Bubble Bursting.” Proceedings of the National Academy of Sciences of the United States of America 107, no. 15 (2010): 6652–57. https://doi.org/10.1073/pnas.0908905107.
Vega, C., and E. de Miguel. “Surface Tension of the Most Popular Models of Water by Using the Test-Area Simulation Method.” The Journal of Chemical Physics 126, no. 15 (2007): 154707. https://doi.org/10.1063/1.2715577.
Citation: https://doi.org/10.5194/egusphere-2022-826-RC2 -
AC3: 'Reply on RC2', Xiaohan Li, 01 Dec 2022
Dear Reviewer,
Thanks for your careful reading of our manuscript entitled “Microphysics of liquid water in sub-10 nm ultrafine aerosol particles”. We highly appreciate your time and valuable suggestions. You will find our replies to your comments in the attached document.
Best wishes,
Xiaohan Li & Ian C. Bourg
Department of Civil and Environmental Engineering, Princeton University
-
AC3: 'Reply on RC2', Xiaohan Li, 01 Dec 2022
Peer review completion
Journal article(s) based on this preprint
Xiaohan Li and Ian C. Bourg
Xiaohan Li and Ian C. Bourg
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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