Welcome to the IKCEST
Predicting heterogeneous ice nucleation with a data-driven approach
  1. 1.

    Kiselev, A. et al. Active sites in heterogeneous ice nucleation-the example of k-rich feldspars. Science 355, 367–371 (2017).

    ADS  CAS  Google Scholar 

  2. 2.

    Friedman, B. et al. Ice nucleation and droplet formation by bare and coated soot particles. J. Geophys. Res.: Atmos. 116, D17203 (2011).

    ADS  Google Scholar 

  3. 3.

    Wilson, T. W. et al. A marine biogenic source of atmospheric ice-nucleating particles. Nature 525, 234–238 (2015).

    ADS  CAS  PubMed  Google Scholar 

  4. 4.

    Bartels-Rausch, T. Chemistry: ten things we need to know about ice and snow. Nature 494, 27–29 (2013).

    ADS  CAS  PubMed  Google Scholar 

  5. 5.

    Vonnegut, B. The nucleation of ice formation by silver iodide. J. Appl. Phys. 18, 593–595 (1947).

    ADS  CAS  Google Scholar 

  6. 6.

    Vonnegut, B. Variation with temperature of the nucleation rate of supercooled liquid tin and water drops. J. Colloid Interface Sci. 3, 563–569 (1948).

    CAS  Google Scholar 

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    Turnbull, D. & Vonnegut, B. Nucleation catalysis. Ind. Eng. Chem. 44, 1292–1298 (1952).

    CAS  Google Scholar 

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    Conrad, P., Ewing, G. E., Karlinsey, R. L. & Sadtchenko, V. Ice nucleation on BaF2(111). J. Chem. Phys. 122, 064709 (2005).

    ADS  PubMed  Google Scholar 

  9. 9.

    Cardellach, M., Verdaguer, A., Santiso, J. & Fraxedas, J. Two-dimensional wetting: The role of atomic steps on the nucleation of thin water films on BaF2(111) at ambient conditions. J. Chem. Phys. 132, 234708 (2010).

    ADS  CAS  PubMed  Google Scholar 

  10. 10.

    Kaya, S. et al. Highly compressed two-dimensional form of water at ambient conditions. Sci. Rep. 3, 1074 (2013).

    PubMed  PubMed Central  Google Scholar 

  11. 11.

    Pruppacher, H. & Klett, J. Microphysics of Clouds and Precipitation. Atmospheric and Oceanographic Sciences Library (Springer, 1997).

  12. 12.

    Zuberi, B., Bertram, A. K., Koop, T., Molina, L. T. & Molina, M. J. Heterogeneous freezing of aqueous particles induced by crystallized (NH4)SO4, ice, and letovicite. J. Phys. Chem. A 105, 6458–6464 (2001).

    CAS  Google Scholar 

  13. 13.

    Murray, B. J. et al. Heterogeneous nucleation of ice particles on glassy aerosols under cirrus conditions. Nat. Geosci. 3, 233–237 (2010).

    ADS  CAS  Google Scholar 

  14. 14.

    Knopf, D. A., Wang, B., Laskin, A., Moffet, R. C. & Gilles, M. K. Heterogeneous nucleation of ice on anthropogenic organic particles collected in Mexico City. Geophys. Res. Lett. 37, L11803 (2010).

    ADS  Google Scholar 

  15. 15.

    Hu, J., Xiao, X.-D., Ogletree, D. & Salmeron, M. Imaging the condensation and evaporation of molecularly thin films of water with nanometer resolution. Science 268, 267–269 (1995).

    ADS  CAS  Google Scholar 

  16. 16.

    Xu, K., Cao, P. & Heath, J. R. Graphene visualizes the first water adlayers on mica at ambient conditions. Science 329, 1188–1191 (2010).

    ADS  CAS  Google Scholar 

  17. 17.

    Michaelides, A. & Morgenstern, K. Ice nanoclusters at hydrophobic metal surfaces. Nat. Mater. 6, 597–601 (2007).

    CAS  PubMed  Google Scholar 

  18. 18.

    Carrasco, J., Hodgson, A. & Michaelides, A. A molecular perspective of water at metal interfaces. Nat. Mater. 11, 667–674 (2012).

    ADS  CAS  PubMed  Google Scholar 

  19. 19.

    Gerrard, N., Gattinoni, C., McBride, F., Michaelides, A. & Hodgson, A. Strain relief during ice growth on a hexagonal template. J. Am. Chem. Soc. 141, 8599–8607 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  20. 20.

    Ma, R. et al. Atomic imaging of the edge structure and growth of a two-dimensional hexagonal ice. Nature 577, 60–63 (2020).

    ADS  CAS  PubMed  Google Scholar 

  21. 21.

    Murray, B. J., O’Sullivan, D., Atkinson, J. D. & Webb, M. E. Ice nucleation by particles immersed in supercooled cloud droplets. Chem. Soc. Rev. 41, 6519–6554 (2012).

    CAS  PubMed  Google Scholar 

  22. 22.

    Atkinson, J. D. et al. The importance of feldspar for ice nucleation by mineral dust in mixed-phase clouds. Nature 498, 355–358 (2013).

    ADS  CAS  PubMed  Google Scholar 

  23. 23.

    Holden, M. A. et al. High-speed imaging of ice nucleation in water proves the existence of active sites. Sci. Adv. 5, eaav4316 (2019).

  24. 24.

    Sosso, G. C. et al. Unravelling the origins of ice nucleation on organic crystals. Chem. Sci. 9, 8077–8088 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  25. 25.

    Wu, S. et al. Heterogeneous ice nucleation correlates with bulk-like interfacial water. Sci. Adv. 5, eaat9825 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  26. 26.

    Bai, G., Gao, D., Liu, Z., Zhou, X. & Wang, J. Probing the critical nucleus size for ice formation with graphene oxide nanosheets. Nature 576, 437–441 (2019).

    ADS  CAS  PubMed  Google Scholar 

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    Lukas, M. et al. Electrostatic interactions control the functionality of bacterial ice nucleators. J. Am. Chem. Soc. 142, 6842–6846 (2020).

    CAS  PubMed  Google Scholar 

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    Fitzner, M., Sosso, G. C., Pietrucci, F., Pipolo, S. & Michaelides, A. Pre-critical fluctuations and what they disclose about heterogeneous crystal nucleation. Nat. Commun. 8, 2257 (2017).

    ADS  PubMed  PubMed Central  Google Scholar 

  29. 29.

    Bi, Y., Cao, B. & Li, T. Enhanced heterogeneous ice nucleation by special surface geometry. Nat. Commun. 8, 15372 (2017).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  30. 30.

    Sosso, G. C. et al. Crystal nucleation in liquids: open questions and future challenges in molecular dynamics simulations. Chem. Rev. 116, 7078–7116 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  31. 31.

    Hudait, A. & Molinero, V. Ice crystallization in ultrafine water-salt aerosols: nucleation, ice-solution equilibrium, and internal structure. J. Am. Chem. Soc. 136, 8081–8093 (2014).

    CAS  PubMed  Google Scholar 

  32. 32.

    Lupi, L., Peters, B. & Molinero, V. Pre-ordering of interfacial water in the pathway of heterogeneous ice nucleation does not lead to a two-step crystallization mechanism. J. Chem. Phys. 145, 211910 (2016).

    ADS  PubMed  Google Scholar 

  33. 33.

    Qiu, Y., Hudait, A. & Molinero, V. How size and aggregation of ice-binding proteins control their ice nucleation efficiency. J. Am. Chem. Soc. 141, 7439–7452 (2019).

    CAS  PubMed  Google Scholar 

  34. 34.

    Li, T., Donadio, D. & Galli, G. Ice nucleation at the nanoscale probes no man’s land of water. Nat. Commun. 4, 1887 (2013).

    ADS  PubMed  Google Scholar 

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    Lupi, L. et al. Role of stacking disorder in ice nucleation. Nature 551, 218 (2017).

    ADS  CAS  Google Scholar 

  36. 36.

    Fitzner, M., Sosso, G. C., Cox, S. J. & Michaelides, A. Ice is born in low-mobility regions of supercooled liquid water. Proc. Natl Acad. Sci. USA 116, 2009–2014 (2019).

    ADS  CAS  PubMed  Google Scholar 

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    Sanz, E. et al. Homogeneous ice nucleation at moderate supercooling from molecular simulation. J. Am. Chem. Soc. 135, 15008–15017 (2013).

    CAS  PubMed  Google Scholar 

  38. 38.

    Espinosa, J. R. et al. Role of salt, pressure, and water activity on homogeneous ice nucleation. J. Phys. Chem. Lett. 8, 4486–4491 (2017).

    CAS  PubMed  Google Scholar 

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    Lupi, L., Hudait, A. & Molinero, V. Heterogeneous nucleation of ice on carbon surfaces. J. Am. Chem. Soc. 136, 3156–3164 (2014).

    CAS  PubMed  Google Scholar 

  40. 40.

    Lupi, L. & Molinero, V. Does hydrophilicity of carbon particles improve their ice nucleation ability? J. Phys. Chem. A 118, 7330–7337 (2014).

    CAS  PubMed  Google Scholar 

  41. 41.

    Fitzner, M., Sosso, G. C., Cox, S. J. & Michaelides, A. The many faces of heterogeneous ice nucleation: Interplay between surface morphology and hydrophobicity. J. Am. Chem. Soc. 137, 13658–13669 (2015).

    CAS  PubMed  Google Scholar 

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    Cabriolu, R. & Li, T. Ice nucleation on carbon surface supports the classical theory for heterogeneous nucleation. Phys. Rev. E 91, 052402 (2015).

    ADS  Google Scholar 

  43. 43.

    Cox, S. J., Kathmann, S. M., Slater, B. & Michaelides, A. Molecular simulations of heterogeneous ice nucleation. II. Peeling back the layers. J. Chem. Phys. 142, 184705 (2015).

    ADS  PubMed  Google Scholar 

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    Cox, S. J., Kathmann, S. M., Slater, B. & Michaelides, A. Molecular simulations of heterogeneous ice nucleation. I. Controlling ice nucleation through surface hydrophilicity. J. Chem. Phys. 142, 184704 (2015).

    ADS  PubMed  Google Scholar 

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    Zielke, S. A., Bertram, A. K. & Patey, G. Simulations of ice nucleation by kaolinite (001) with rigid and flexible surfaces. J. Phys. Chem. B 120, 1726–1734 (2015).

    PubMed  Google Scholar 

  46. 46.

    Sosso, G. C., Tribello, G. A., Zen, A., Pedevilla, P. & Michaelides, A. Ice formation on kaolinite: Insights from molecular dynamics simulations. J. Chem. Phys. 145, 211927 (2016).

    ADS  PubMed  Google Scholar 

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    Pedevilla, P., Fitzner, M. & Michaelides, A. What makes a good descriptor for heterogeneous ice nucleation on oh-patterned surfaces. Phys. Rev. B 96, 115441 (2017).

    ADS  Google Scholar 

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    Glatz, B. & Sarupria, S. The surface charge distribution affects the ice nucleating efficiency of silver iodide. J. Chem. Phys. 145, 211924 (2016).

    ADS  PubMed  Google Scholar 

  49. 49.

    Metya, A. K., Singh, J. K. & Müller-Plathe, F. Ice nucleation on nanotextured surfaces: the influence of surface fraction, pillar height and wetting states. Phys. Chem. Chem. Phys. 18, 26796–26806 (2016).

    CAS  PubMed  Google Scholar 

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    Molinero, V. & Moore, E. B. Water modeled as an intermediate element between carbon and silicon. J. Phys. Chem. B 113, 4008–4016 (2009).

    CAS  Google Scholar 

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    ADS  CAS  PubMed  Google Scholar 

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    Haji-Akbari, A. & Debenedetti, P. G. Direct calculation of ice homogeneous nucleation rate for a molecular model of water. Proc. Natl Acad. Sci. USA 112, 10582–10588 (2015).

    ADS  CAS  PubMed  Google Scholar 

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    Sosso, G. C., Li, T., Donadio, D., Tribello, G. A. & Michaelides, A. Microscopic mechanism and kinetics of ice formation at complex interfaces: Zooming in on kaolinite. J. Phys. Chem. Lett. 7, 2350–2355 (2016).

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Original Text (This is the original text for your reference.)

  1. 1.

    Kiselev, A. et al. Active sites in heterogeneous ice nucleation-the example of k-rich feldspars. Science 355, 367–371 (2017).

    ADS  CAS  Google Scholar 

  2. 2.

    Friedman, B. et al. Ice nucleation and droplet formation by bare and coated soot particles. J. Geophys. Res.: Atmos. 116, D17203 (2011).

    ADS  Google Scholar 

  3. 3.

    Wilson, T. W. et al. A marine biogenic source of atmospheric ice-nucleating particles. Nature 525, 234–238 (2015).

    ADS  CAS  PubMed  Google Scholar 

  4. 4.

    Bartels-Rausch, T. Chemistry: ten things we need to know about ice and snow. Nature 494, 27–29 (2013).

    ADS  CAS  PubMed  Google Scholar 

  5. 5.

    Vonnegut, B. The nucleation of ice formation by silver iodide. J. Appl. Phys. 18, 593–595 (1947).

    ADS  CAS  Google Scholar 

  6. 6.

    Vonnegut, B. Variation with temperature of the nucleation rate of supercooled liquid tin and water drops. J. Colloid Interface Sci. 3, 563–569 (1948).

    CAS  Google Scholar 

  7. 7.

    Turnbull, D. & Vonnegut, B. Nucleation catalysis. Ind. Eng. Chem. 44, 1292–1298 (1952).

    CAS  Google Scholar 

  8. 8.

    Conrad, P., Ewing, G. E., Karlinsey, R. L. & Sadtchenko, V. Ice nucleation on BaF2(111). J. Chem. Phys. 122, 064709 (2005).

    ADS  PubMed  Google Scholar 

  9. 9.

    Cardellach, M., Verdaguer, A., Santiso, J. & Fraxedas, J. Two-dimensional wetting: The role of atomic steps on the nucleation of thin water films on BaF2(111) at ambient conditions. J. Chem. Phys. 132, 234708 (2010).

    ADS  CAS  PubMed  Google Scholar 

  10. 10.

    Kaya, S. et al. Highly compressed two-dimensional form of water at ambient conditions. Sci. Rep. 3, 1074 (2013).

    PubMed  PubMed Central  Google Scholar 

  11. 11.

    Pruppacher, H. & Klett, J. Microphysics of Clouds and Precipitation. Atmospheric and Oceanographic Sciences Library (Springer, 1997).

  12. 12.

    Zuberi, B., Bertram, A. K., Koop, T., Molina, L. T. & Molina, M. J. Heterogeneous freezing of aqueous particles induced by crystallized (NH4)SO4, ice, and letovicite. J. Phys. Chem. A 105, 6458–6464 (2001).

    CAS  Google Scholar 

  13. 13.

    Murray, B. J. et al. Heterogeneous nucleation of ice particles on glassy aerosols under cirrus conditions. Nat. Geosci. 3, 233–237 (2010).

    ADS  CAS  Google Scholar 

  14. 14.

    Knopf, D. A., Wang, B., Laskin, A., Moffet, R. C. & Gilles, M. K. Heterogeneous nucleation of ice on anthropogenic organic particles collected in Mexico City. Geophys. Res. Lett. 37, L11803 (2010).

    ADS  Google Scholar 

  15. 15.

    Hu, J., Xiao, X.-D., Ogletree, D. & Salmeron, M. Imaging the condensation and evaporation of molecularly thin films of water with nanometer resolution. Science 268, 267–269 (1995).

    ADS  CAS  Google Scholar 

  16. 16.

    Xu, K., Cao, P. & Heath, J. R. Graphene visualizes the first water adlayers on mica at ambient conditions. Science 329, 1188–1191 (2010).

    ADS  CAS  Google Scholar 

  17. 17.

    Michaelides, A. & Morgenstern, K. Ice nanoclusters at hydrophobic metal surfaces. Nat. Mater. 6, 597–601 (2007).

    CAS  PubMed  Google Scholar 

  18. 18.

    Carrasco, J., Hodgson, A. & Michaelides, A. A molecular perspective of water at metal interfaces. Nat. Mater. 11, 667–674 (2012).

    ADS  CAS  PubMed  Google Scholar 

  19. 19.

    Gerrard, N., Gattinoni, C., McBride, F., Michaelides, A. & Hodgson, A. Strain relief during ice growth on a hexagonal template. J. Am. Chem. Soc. 141, 8599–8607 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  20. 20.

    Ma, R. et al. Atomic imaging of the edge structure and growth of a two-dimensional hexagonal ice. Nature 577, 60–63 (2020).

    ADS  CAS  PubMed  Google Scholar 

  21. 21.

    Murray, B. J., O’Sullivan, D., Atkinson, J. D. & Webb, M. E. Ice nucleation by particles immersed in supercooled cloud droplets. Chem. Soc. Rev. 41, 6519–6554 (2012).

    CAS  PubMed  Google Scholar 

  22. 22.

    Atkinson, J. D. et al. The importance of feldspar for ice nucleation by mineral dust in mixed-phase clouds. Nature 498, 355–358 (2013).

    ADS  CAS  PubMed  Google Scholar 

  23. 23.

    Holden, M. A. et al. High-speed imaging of ice nucleation in water proves the existence of active sites. Sci. Adv. 5, eaav4316 (2019).

  24. 24.

    Sosso, G. C. et al. Unravelling the origins of ice nucleation on organic crystals. Chem. Sci. 9, 8077–8088 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  25. 25.

    Wu, S. et al. Heterogeneous ice nucleation correlates with bulk-like interfacial water. Sci. Adv. 5, eaat9825 (2019).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  26. 26.

    Bai, G., Gao, D., Liu, Z., Zhou, X. & Wang, J. Probing the critical nucleus size for ice formation with graphene oxide nanosheets. Nature 576, 437–441 (2019).

    ADS  CAS  PubMed  Google Scholar 

  27. 27.

    Lukas, M. et al. Electrostatic interactions control the functionality of bacterial ice nucleators. J. Am. Chem. Soc. 142, 6842–6846 (2020).

    CAS  PubMed  Google Scholar 

  28. 28.

    Fitzner, M., Sosso, G. C., Pietrucci, F., Pipolo, S. & Michaelides, A. Pre-critical fluctuations and what they disclose about heterogeneous crystal nucleation. Nat. Commun. 8, 2257 (2017).

    ADS  PubMed  PubMed Central  Google Scholar 

  29. 29.

    Bi, Y., Cao, B. & Li, T. Enhanced heterogeneous ice nucleation by special surface geometry. Nat. Commun. 8, 15372 (2017).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  30. 30.

    Sosso, G. C. et al. Crystal nucleation in liquids: open questions and future challenges in molecular dynamics simulations. Chem. Rev. 116, 7078–7116 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  31. 31.

    Hudait, A. & Molinero, V. Ice crystallization in ultrafine water-salt aerosols: nucleation, ice-solution equilibrium, and internal structure. J. Am. Chem. Soc. 136, 8081–8093 (2014).

    CAS  PubMed  Google Scholar 

  32. 32.

    Lupi, L., Peters, B. & Molinero, V. Pre-ordering of interfacial water in the pathway of heterogeneous ice nucleation does not lead to a two-step crystallization mechanism. J. Chem. Phys. 145, 211910 (2016).

    ADS  PubMed  Google Scholar 

  33. 33.

    Qiu, Y., Hudait, A. & Molinero, V. How size and aggregation of ice-binding proteins control their ice nucleation efficiency. J. Am. Chem. Soc. 141, 7439–7452 (2019).

    CAS  PubMed  Google Scholar 

  34. 34.

    Li, T., Donadio, D. & Galli, G. Ice nucleation at the nanoscale probes no man’s land of water. Nat. Commun. 4, 1887 (2013).

    ADS  PubMed  Google Scholar 

  35. 35.

    Lupi, L. et al. Role of stacking disorder in ice nucleation. Nature 551, 218 (2017).

    ADS  CAS  Google Scholar 

  36. 36.

    Fitzner, M., Sosso, G. C., Cox, S. J. & Michaelides, A. Ice is born in low-mobility regions of supercooled liquid water. Proc. Natl Acad. Sci. USA 116, 2009–2014 (2019).

    ADS  CAS  PubMed  Google Scholar 

  37. 37.

    Sanz, E. et al. Homogeneous ice nucleation at moderate supercooling from molecular simulation. J. Am. Chem. Soc. 135, 15008–15017 (2013).

    CAS  PubMed  Google Scholar 

  38. 38.

    Espinosa, J. R. et al. Role of salt, pressure, and water activity on homogeneous ice nucleation. J. Phys. Chem. Lett. 8, 4486–4491 (2017).

    CAS  PubMed  Google Scholar 

  39. 39.

    Lupi, L., Hudait, A. & Molinero, V. Heterogeneous nucleation of ice on carbon surfaces. J. Am. Chem. Soc. 136, 3156–3164 (2014).

    CAS  PubMed  Google Scholar 

  40. 40.

    Lupi, L. & Molinero, V. Does hydrophilicity of carbon particles improve their ice nucleation ability? J. Phys. Chem. A 118, 7330–7337 (2014).

    CAS  PubMed  Google Scholar 

  41. 41.

    Fitzner, M., Sosso, G. C., Cox, S. J. & Michaelides, A. The many faces of heterogeneous ice nucleation: Interplay between surface morphology and hydrophobicity. J. Am. Chem. Soc. 137, 13658–13669 (2015).

    CAS  PubMed  Google Scholar 

  42. 42.

    Cabriolu, R. & Li, T. Ice nucleation on carbon surface supports the classical theory for heterogeneous nucleation. Phys. Rev. E 91, 052402 (2015).

    ADS  Google Scholar 

  43. 43.

    Cox, S. J., Kathmann, S. M., Slater, B. & Michaelides, A. Molecular simulations of heterogeneous ice nucleation. II. Peeling back the layers. J. Chem. Phys. 142, 184705 (2015).

    ADS  PubMed  Google Scholar 

  44. 44.

    Cox, S. J., Kathmann, S. M., Slater, B. & Michaelides, A. Molecular simulations of heterogeneous ice nucleation. I. Controlling ice nucleation through surface hydrophilicity. J. Chem. Phys. 142, 184704 (2015).

    ADS  PubMed  Google Scholar 

  45. 45.

    Zielke, S. A., Bertram, A. K. & Patey, G. Simulations of ice nucleation by kaolinite (001) with rigid and flexible surfaces. J. Phys. Chem. B 120, 1726–1734 (2015).

    PubMed  Google Scholar 

  46. 46.

    Sosso, G. C., Tribello, G. A., Zen, A., Pedevilla, P. & Michaelides, A. Ice formation on kaolinite: Insights from molecular dynamics simulations. J. Chem. Phys. 145, 211927 (2016).

    ADS  PubMed  Google Scholar 

  47. 47.

    Pedevilla, P., Fitzner, M. & Michaelides, A. What makes a good descriptor for heterogeneous ice nucleation on oh-patterned surfaces. Phys. Rev. B 96, 115441 (2017).

    ADS  Google Scholar 

  48. 48.

    Glatz, B. & Sarupria, S. The surface charge distribution affects the ice nucleating efficiency of silver iodide. J. Chem. Phys. 145, 211924 (2016).

    ADS  PubMed  Google Scholar 

  49. 49.

    Metya, A. K., Singh, J. K. & Müller-Plathe, F. Ice nucleation on nanotextured surfaces: the influence of surface fraction, pillar height and wetting states. Phys. Chem. Chem. Phys. 18, 26796–26806 (2016).

    CAS  PubMed  Google Scholar 

  50. 50.

    Molinero, V. & Moore, E. B. Water modeled as an intermediate element between carbon and silicon. J. Phys. Chem. B 113, 4008–4016 (2009).

    CAS  Google Scholar 

  51. 51.

    Moore, E. B. & Molinero, V. Structural transformation in supercooled water controls the crystallization rate of ice. Nature 479, 506–508 (2011).

    ADS  CAS  PubMed  Google Scholar 

  52. 52.

    Haji-Akbari, A. & Debenedetti, P. G. Direct calculation of ice homogeneous nucleation rate for a molecular model of water. Proc. Natl Acad. Sci. USA 112, 10582–10588 (2015).

    ADS  CAS  PubMed  Google Scholar 

  53. 53.

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