in heterogeneous ice nucleation—the example of K-rich feldspars. Science 355, 367-371 (2017).83 83. A. Cacciuto, S. Auer, and D. Frenkel, Onset of heterogeneous crystal nucleation in colloidal suspensions. Nature 428, 404-406 (2004).
84 84. M. Matsumoto, S. Saito, and I. Ohmine, Molecular dynamics simulation of the ice nucleation and growth process leading to water freezing. Nature 416, 409-413 (2002).
85 85. A. Filipponi, A. Di Cicco, and E. Principi, Crystalline nucleation in under-cooled liquids: A Bayesian data-analysis approach for a nonhomogeneous Poisson process. Phys. Rev. E 86, 066701 (2012).
86 86. N. Miljkovic, R. Enright, and E.N. Wang, Modeling and optimization of superhydrophobic condensation. J. Heat Transfer 135, 111004 (2013).
87 87. M. Watkins, D. Pan, E.G. Wang, A. Michaelides, J. VandeVondele, and B. Slater, Large variation of vacancy formation energies in the surface of crystalline ice. Nat. Mater. 10, 794-798 (2011).
88 88. R.S. Smith and B.D. Kay, The existence of supercooled liquid water at 150 K. Nature 398, 788-791 (1999).
89 89. J. Wölk and R. Strey, Homogeneous nucleation of H2O and D2O in comparison: The isotope effect. J. Phys. Chem. B 105, 11683-11701 (2001).
90 90. B.N. Hale, Temperature dependence of homogeneous nucleation rates for water: Near equivalence of the empirical fit of Wölk and Strey, and the scaled nucleation model. J. Chem. Phys. 122, 204509 (2005).
91 91. S. Prestipino, A. Laio, and E. Tosatti, Systematic improvement of classical nucleation theory. Phys. Rev. Lett. 108, 225701 (2012).
92 92. L. Dufour and R. Defay, Thermodynamics of Clouds. Academic Press, New York and London (1963).
93 93. M. Sokuler, G.K. Auernhammer, M. Roth, C. Liu, E. Bonacurrso, and H.-J. Butt, The softer the better: fast condensation on soft surfaces. Langmuir 26, 1544-1547 (2010).
94 94. F. Eslami and J.A.W. Elliott, Thermodynamic investigation of the barrier for heterogeneous nucleation on a fluid surface in comparison with a rigid surface. J. Phys. Chem. B 115, 10646-10653 (2011).
95 95. T. Kajiya, F. Schellenberger, P. Papadopoulos, D. Vollmer, and H.-J. Butt, 3D imaging of water-drop condensation on hydrophobic and hydrophilic lubricant-impregnated surfaces. Sci. Rep. 6, 23687 (2016).
96 96. S. Kim, D. Kim, J. Kim, S. An, and W. Jhe, Direct evidence for curvature-dependent surface tension in capillary condensation: Kelvin equation at molecular scale. Phys. Rev. X 8, 041046 (2018).
97 97. F. Pellerey, M. Shaked, and J. Zinn, Nonhomogeneous Poisson processes and logconcavity. Probab. Eng. Inform. Sc. 14, 353-373 (2000).
98 98. T.L. Liu and C.-J.C. Kim, Turning a surface superrepellent even to completely wetting liquids. Science 346, 1096-1100 (2014).
99 99. S. Engemann, H. Reichert, H. Dosch, J. Bilgram, V. Honkimäki, and A. Snigirev, Interfacial melting of ice in contact with SiO2. Phys. Rev. Lett. 92, 205701 (2004).
100 100. M. Mezger, S. Schöder, H. Reichert, H. Schröder, J. Okasinski, V. Honkimäki, J. Ralston, J. Bilgram, R. Roth, and H. Dosch, Water and ice in contact with octadecyl-trichlorosilane functionalized surfaces: A high resolution x-ray reflectivity study. J. Chem. Phys. 128, 244705 (2008).
101 101. G. Malenkov, Liquid water and ices: understanding the structure and physical properties. J. Phys.: Condens. Matter 21, 283101 (2009).
102 102. E.B. Moore, E. de la Llave, K. Welke, D.A. Scherlis, and V. Molinero, Freezing, melting and structure of ice in a hydrophilic nanopore. Phys. Chem. Chem. Phys. 12, 4124-4134 (2010).
103 103. E. González Solveyra, E. de la Llave, D.A. Scherlis, and V. Molinero, Melting and crystallization of ice in partially filled nanopores. J. Phys. Chem. B 115, 14196-14204 (2011).
104 104. H. Li, M. Bier, J. Mars, H. Weiss, A.-C. Dippel, O. Gutowski, V. Honkimäki, and M. Mezger, Interfacial premelting of ice in nano composite materials. Phys. Chem. Chem. Phys. 21, 3734-3741 (2019).
105 105. R.R. Vanfleet and J.M. Mochel, Thermodynamics of melting and freezing in small particles. Surf Sci. 341, 40-50 (1995).
106 106. Y. Suzuki, H. Duran, M. Steinhart, M. Kappl, H.-J. Butt, and G. Floudas, Homogeneous nucleation of predominantly cubic ice confined in nanoporous alumina. Nano Lett. 15, 1987-1992 (2015).
107 107. Y. Suzuki, M. Steinhart, H.-J. Butt, and G. Floudas, Kinetics of ice nucleation confined in nanoporous alumina. J. Phys. Chem. B 119, 11960-11966 (2015).
108 108. Y. Yao, P. Ruckdeschel, R. Graf, H.-J. Butt, M. Retsch, and G. Floudas, Homogeneous nucleation of ice confined in hollow silica spheres. J. Phys. Chem. B 121, 306-313 (2017).
109 109. L. Lupi, A. Hudait, and V. Molinero, Heterogeneous nucleation of ice on carbon surfaces. J. Am. Chem. Soc. 136, 3156-3164 (2014).
110 110. K. Koga, G.T. Gao, H. Tanaka, and X.C. Zeng, Formation of ordered ice nanotubes inside carbon nanotubes. Nature 412, 802-805 (2001).
111 111. M. Raju, A. van Duin, and M. Ihme, Phase transitions of ordered ice in graphene nanocapillaries and carbon nanotubes. Sci. Rep. 8, 3851 (2018).
112 112. S.J. Cox, Z. Raza, S.M. Kathmann, B. Slater, and A. Michaelides, The microscopic features of heterogeneous ice nucleation may affect the macroscopic morphology of atmospheric ice crystals. Faraday Discuss. 167, 389-403 (2013).
Notes
1 * Corresponding authors: [email protected]
2 † Corresponding authors: [email protected]
3 Physics of Ice Nucleation and Growth on a Surface
Alireza Hakimian, Sina Nazifi and Hadi Ghasemi1*
Department of Mechanical Engineering, University of Houston, Houston, Texas, USA
Abstract
Fundamental understanding of ice formation on a surface, i.e. heterogeneous formation, is critical to suppress ice accretion on the surfaces. Ice formation on a surface includes two steps of ice nucleation and further ice growth. As water droplet is placed on a sub-zero surface, with a time delay, ice nucleolus forms on the surface. Ice nucleation is governed by thermodynamics of ice-water-surface system and it is described by Gibbs energy barrier, ΔG*, which strongly depends on surface factor, f (m, x). Surface factor is a function of surface geometry, i.e. nano or micro, as well as surface free energy and through manipulating these parameters, ice nucleation can be controlled. After ice nucleation, ice further grows in a process which is controlled through heat transfer. Ice growth could be described by two extreme scenarios. In the first one, ice formation occurs with no airflow around where heat transfer through the substrate determines ice growth rate. In the second scenario, ice growth occurs in an environment with external airflow in which ice growth rate is controlled mainly by convective heat transfer. All of mentioned theories about ice formation on a surface are applicable for a single, isolated droplet. However, in reality existence of many droplets on a surface can interfere with ice nucleation and growth of
