the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Molecular simulations reveal that heterogeneous ice nucleation occurs at higher temperatures in water under capillary tension
Will Cantrell
Tianshu Li
Issei Nakamura
Raymond A. Shaw
Abstract. Homogeneous ice nucleation rates occur at higher temperatures when water is under tension, otherwise referred to as negative pressure. If also true for heterogeneous ice nucleation rates, then this phenomenon can result in higher heterogeneous freezing temperatures in water capillary bridges, pores, and other geometries where water is subjected to negative Laplace pressure. Using a molecular model of water freezing on a hydrophilic substrate, it is found that heterogeneous ice nucleation rates exhibit a similar temperature increase at negative pressures as homogeneous ice nucleation. For pressures ranging from from 1 atm to −1000 atm, the simulations reveal that the temperature corresponding to the heterogeneous nucleation rate coefficient jhet (m−2 s−1) increases linearly as a function of negative pressure, with a slope that can be approximately predicted by the water density anomaly and the latent heat of fusion at atmospheric pressure.
Simulations of water in capillary bridges confirm that negative Laplace pressure within the water corresponds to an increase in heterogeneous freezing temperature. The freezing temperature in the water capillary bridges increases linearly with inverse capillary height (1/h). Varying the height and width of the capillary bridge reveals the role of geometric factors in heterogeneous ice nucleation. When substrate surfaces are separated by less than approximately h = 20 Angstroms the nucleation rate is enhanced and when the width of the capillary bridge is less than approximately 30 Angstroms the nucleation rate is suppressed. Ice nucleation does not occur in the region within 10 Angstroms of the air-water interface and shows a preference for nucleation in the region just beyond 10 Angstroms.
These results help unify multiple lines of experimental evidence for enhanced nucleation rates due to reduced pressure, either resulting from surface geometry (Laplace pressure) or mechanical agitation of water droplets. This concept is relevant to the phenomenon of contact nucleation and could potentially play a role in a number of different heterogeneous nucleation or secondary ice mechanisms.
Elise Rosky et al.
Status: open (until 12 Apr 2023)
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RC1: 'Comment on egusphere-2023-330', Anonymous Referee #1, 27 Mar 2023
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General Comment
This study investigates the heterogeneous freezing temperature increase at negative pressure with the mW and MLmW water models. Simulations have been carried out at negative pressures of -500 and -1000 atm with water that was in contact with a hydrophilic substrate that promotes ice nucleation. These simulations showed an approximately linear increase in heterogeneous ice nucleation temperature with decreasing pressure. Moreover, water freezing was simulated in water capillary bridges of heights from 3.0 to 1.8 nm. Here, an approximately linear relationship between the capillary bridge width and the heterogeneous ice nucleation temperature was found for unconfined water and water capillary bridges of 3 and 2.4 nm. For capillary bridges of 1.8 nm, an even increased nucleation rate was simulated. Based on these results, a linear relationship between pressure and heterogeneous freezing temperature was derived. This linear relationship was proposed to serve as a basis to estimate the pressure effect on heterogeneous freezing. Moreover, the simulations were used to investigate the location of ice nucleation. It was found that heterogeneous ice nucleation does not occur in the regions within 1.0 nm of the air-water interface.
These are interesting results that are worth publishing in ACP. However, there are weaknesses in the discussion of the results. The ability of the mW and the MLmW water models to describe the pressure dependence of homogeneous and heterogeneous ice nucleation has not been assessed properly. Nevertheless, a parameterization derived from the simulation results was proposed to predict the pressure dependence of freezing temperatures at negative pressure. However, such a recommendation is only justified when the MLmW model is able to describe the pressure dependence of ice nucleation correctly. The comparison to experimental data (Kanno, 1975) reveals that the proposed pressure dependence underpredicts the freezing temperature depression at positive pressure (see specific comments). It should be explained why the proposed pressure dependence should be accurate at negative pressure when the model is not able to describe the pressure dependence at positive pressure correctly. Similarly, the increased nucleation rate in the water capillary bridge is not critically reviewed in view of experiments that show the opposite trend (see e.g. Marcolli, 2014, for a compilation of experiments).
Specific comments
Lines 14–16: “and shows a preference for nucleation in the region just beyond 10 Å”: do you refer here to the distance from the air-water interface or the distance from the substrate? This should be clarified.
Lines 52–55: Here, it is stated that the slope of the freezing temperature as a function of pressure is parallel to the slope of the melting line. However, inspection of Fig. 1 shows that this is not the case. A parallel relationship would only be fulfilled if the enthalpy of fusion and the molar volume difference were independent of temperature.
Figure 1: in Panels c and d, the substrate is only shown below the water bridge. Is this for clarity or is there no substrate above the water bridge? This should be clarified in the figure caption.
Lines 172–175: The surface area of the substrate and the rate at which the system is cooled do not influence Jhet it is formulated as a function of surface area and time. It just influences the time it takes to freeze in the simulation. This needs to be clarified.
Lines 201–202: The data shows indeed a slightly non-linear trend. This sentence should be formulated more carefully.
Line 206–208: the values are still within the uncertainty bounds, but the slope is not strong enough. This weakness in the simulation should be commented.
Lines 211–212: “While the linear nature of ΔT/ΔP” is apparent in our results”. This is an exaggeration. The results are in agreement with a linear relationship given the uncertainty bounds. This sentence needs to be adjusted in this sense.
Lines 213–214: Do you refer here to the values given in Table 1 (last line)? If yes, a reference to Table 1 could be given here.
Lines 219–220: Here, it is hypothesized that the thermodynamic properties of mW water are less influenced near the substrate compared to the MLmW model. Couldn’t this be found out by inspecting the simulation?
Lines 221–225: This paragraph is written as if the MLmW model could correctly predict the dependence of freezing temperature as a function of pressure. This assumption needs to be tested by simulating ice nucleation in the positive pressure range and comparing the results to measurements. Such a comparison can be done for homogeneous ice nucleation. See also general comment.
Figure 3: It should be stated whether the dotted line is a fit line or based on the pressure values given in Table 1.
Lines 249–253: The calculation of the Laplace pressure by estimating the contact angle from the simulation is indirect. What is relevant for the Laplace pressure is the radius of the meniscus, which could be directly determined from the simulation. Could this still be done to validate the assumed tension within the capillary bridge?
Figure 5: Reading the figure caption and the text, it seems that Panels a and b show the same simulation viewed in different 2D projections. Yet, the colour scale in the panels are different: in Panel a, it is from 231–234 K and in Panel b, it is from 231–238 K. Is this a mistake? Please explain.
Figure 5b: the air-water interface (red shaded stripes) seems to be too narrow. It should be broader in the projection because the interface is curved. How was the distance from the air-water interface evaluated? Based on the projection or was the actual distance to the interface taken?
Lines 303–305: A higher nucleation rate for pores narrower than 2 nm is in contradiction with DSC experiments performed on slurries of mesoporous silica materials with pores in this size range, for which no freezing peak at all was observed (see e.g. Marcolli, 2014, for a compilation). This should be commented.
Lines 323–325: Here, the simulation results should be critically reviewed in view of the experimental evidence.
Lines 323–327: Here, it is written: “Therefore, the linear approximation can serve as the basis for a straightforward parameterization of the pressure effect.” And: “Essentially, the temperature increase for heterogeneous freezing is determined in large part by the volume difference between liquid and ice.” These two sentences together imply a linear dependence of the volume difference on pressure. Do the authors really want to imply such a linear pressure dependence? It would be interesting to know whether the simulations support such a linear pressure dependence.
Line 328: If the proposed dependence of freezing temperature on pressure is extrapolated to positive pressure, a freezing point depression of 7.3 K would be expected at 1000 atm. Yet, experimental data by Kanno et al. (1975) show that the freezing point depression is already 7 K at 500 atm and increases to 17 K at 1000 atm. Is there any evidence that the simulations are better in predicting pressure dependence for negative than for positive pressure?
Lines 340–341: “Our findings provide additional perspectives to those of Lintunen et al. (2013), who showed a tendency for suppression of ice nucleation in the xylem of vascular plants”. What is meant by this sentence?
Lines 342–343: what is meant here by "significant"? In the order of kPa or in the order of MPa? The order of magnitude is decisive for the impact negative pressure has on the ice nucleation rate and should be mentioned.
Technical comments
Table captions should be above the tables.
References: Journal titles are not abbreviated according to the journal’s guidelines. Also, they are not consistently formatted: Some are with and some without DOIs; some use capital letters in article titles while others do not.
Line 6: There are two ”from”. One should be deleted.
Line 116: “feasibly be achieved”: either just “feasible” or just “be achieved”.
Line 125: the abbreviation“NVT” should be explained.
Line 139– 41: this sentence should be improved.
Line 179: “comparison with Rosky et al.” instead of “comparison from Rosky et al.”
Line 196: Do you mean Equation (2) instead of Equation (1)? Moreover, in most parameterizations, the pre-factor “A” is different for homogeneous and heterogeneous ice nucleation.
Lines 210–211: this sentence is incomplete.
Line 276: “a capillary bridge” or “capillary bridges”.
Figure 4: Panel b of this figure is explained only after Fig. 5. The manuscript should be reorganized in a way that the figures are explained in the right sequence.
Figure 5: The legend and axis numbers and the colour scale numbers are two small and should be increased.
Line 389: “adobpting”: remove the “b”
Line 460: the paper title is not correctly displayed.
References
Kanno, H., Speedy, R. J., and Angell, C. A.: Supercooling of water to 92_ C under pressure, Science, 189, 880–881, https://doi.org/10.1126/science.189.4206.880, 1975.
Marcolli, C.: Deposition nucleation viewed as homogeneous or immersion freezing in pores and cavities, Atmos. Chem. Phys., 14, 2071–2104, https://doi.org/10.5194/acp-14-2071-2014, 2014.
Citation: https://doi.org/10.5194/egusphere-2023-330-RC1
Elise Rosky et al.
Data sets
Molecular dynamics simulation data: mW and MLmW water model ice nucleation on a hydrophilic substrate with negative pressure W. Cantrell, T. Li, I. Nakamura, E. Rosky, and R. Shaw http://doi.org/10.37099/mtu.dc.all-datasets/41
Elise Rosky et al.
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