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Freezing of water confined in porous materials: role of adsorption and unfreezable threshold

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Abstract

It has been widely accepted in scientific communities that water confined in porous materials gradually freezes from large pores to small pores at subfreezing temperatures (< 0 °C), though we still describe a soil as frozen or unfrozen in engineering practice and daily life. Therefore, it is more accurate to say “how frozen” instead of “whether frozen.” This gradual freezing process is temperature-dependent because water in pores of different sizes has different energy levels, which requires different temperatures for its phase transition, leading to a relationship between unfrozen water content and temperature in soils. However, the understanding of this relationship, i.e., the Phase Composition Curves (PCC), is still incomplete, especially in the low-temperature range. We still lack answers to even the most fundamental questions for frozen soils and their PCCs: (1) How much pore water could be frozen? (2) How do capillarity and adsorption control the freezing of pore water? This study investigates two basic physical mechanisms, i.e., unfreezable threshold and adsorption, for their dominant roles in the low-temperature range of the PCC. To quantify the effects of the unfreezable threshold, molecular dynamics simulation was employed to identify the unfreezable threshold of cylindrical pores. The simulation results, for the first time, revealed that the unfreezable threshold corresponds to a pore diameter of 2.3 ± 0.1 nm and is independent of the wettability of the solid substrates. Combining this unfreezable threshold with a modified Gibbs–Thomson equation, a mathematical model was proposed to predict the melting temperature in pores of different sizes, which considers both unfreezable threshold and adsorption. Comparisons of the results calculated with the new model and other two conventional equations against experimental results indicated that the model can improve conventional equations which have been used for centuries by including the two mechanisms, which significantly improved our understanding of frozen soils.

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References

  1. Alba-Simionesco C, Coasne B, Dosseh G, Dudziak G, Gubbins K, Radhakrishnan R, Sliwinska-Bartkowiak M (2006) Effects of confinement on freezing and melting. J Phys Condens Matter 18(6):R15

    Article  Google Scholar 

  2. Amarasinghe PM, Anandarajah A (2011) Influence of fabric variables on clay–water–air capillary meniscus. Can Geotech J 48:987–995

    Article  Google Scholar 

  3. Anandarajah A, Amarasinghe PM (2011) Microstructural investigation of soil suction and hysteresis of fine-grained soils. J Geotech Geoenviron Eng 138(1):38–46

    Article  Google Scholar 

  4. Baker R, Frydman S (2009) Unsaturated soil mechanics: critical review of physical foundations. Eng Geol 106(1):26–39

    Article  Google Scholar 

  5. Berendsen HJ, Postma JP, van Gunsteren WF, Hermans J (1981) Interaction models for water in relation to protein hydration. In: Intermolecular forces. Springer, Berlin, pp 331–342

  6. Berendsen HJC, Grigera JR, Straatsma TP (1987) The missing term in effective pair potentials. J Phys Chem-Us 91(24):6269–6271. https://doi.org/10.1021/j100308a038

    Article  Google Scholar 

  7. Borja RI (2013) Plasticity: modeling and computation. Springer, Berlin

    Book  MATH  Google Scholar 

  8. Borja RI, Song X, Wu W (2013) Critical state plasticity. Part VII: triggering a shear band in variably saturated porous media. Comput Method Appl Mech Eng 261:66–82

    Article  MATH  Google Scholar 

  9. Cahn J, Dash J, Fu H (1992) Theory of ice premelting in monosized powders. J Cryst Growth 123(1–2):101–108

    Article  Google Scholar 

  10. Cheng SF, Robbins MO (2014) Capillary adhesion at the nanometer scale. Phys Rev E 89(6):62402. https://doi.org/10.1103/physreve.89.062402

    Article  Google Scholar 

  11. Churaev NV, Derjaguin BV, Muller VM (2013) Surface forces. Springer, New York

    Google Scholar 

  12. Findenegg GH, Jähnert S, Akcakayiran D, Schreiber A (2008) Freezing and melting of water confined in silica nanopores. Chem Phys Chem 9(18):2651–2659

    Article  Google Scholar 

  13. Gonzalez Solveyra E, De La Llave E, Scherlis DA, Molinero V (2011) Melting and crystallization of ice in partially filled nanopores. J Phys Chem B 115(48):14196–14204

    Article  Google Scholar 

  14. Hockney RW, Eastwood JW (1988) Computer simulation using particles. CRC Press, Boca Raton

    Book  MATH  Google Scholar 

  15. Ishizaki T, Maruyama M, Furukawa Y, Dash J (1996) Premelting of ice in porous silica glass. J Cryst Growth 163(4):455–460

    Article  Google Scholar 

  16. Iwata S, Tabuchi T, Warkentin BP (1995) Soil–water interactions: mechanisms and applications, vol 2. Marcel Dekker, Inc, New York

    Google Scholar 

  17. Jähnert S, Chavez FV, Schaumann G, Schreiber A, Schönhoff M, Findenegg G (2008) Melting and freezing of water in cylindrical silica nanopores. Phys Chem Chem Phys 10(39):6039–6051

    Article  Google Scholar 

  18. Jorgensen WL, Tirado-Rives J (2005) Potential energy functions for atomic-level simulations of water and organic and biomolecular systems. Proc Natl Acad Sci USA 102(19):6665–6670

    Article  Google Scholar 

  19. Katti DR, Schmidt SR, Ghosh P, Katti KS (2007) Molecular modeling of the mechanical behavior and interactions in dry and slightly hydrated sodium montmorillonite interlayer. Can Geotech J 44(4):425–435. https://doi.org/10.1139/T06-127

    Article  Google Scholar 

  20. Katti DR, Srinivasamurthy L, Katti KS (2015) Molecular modeling of initiation of interlayer swelling in Na-montmorillonite expansive clay. Can Geotech J 52:1385–1395

    Article  Google Scholar 

  21. Koga K, Gao G, Tanaka H, Zeng XC (2001) Formation of ordered ice nanotubes inside carbon nanotubes. Nature 412(6849):802–805

    Article  Google Scholar 

  22. Konrad J-M, Morgenstern NR (1980) A mechanistic theory of ice lens formation in fine-grained soils. Can Geotech J 17(4):473–486

    Article  Google Scholar 

  23. Konrad J-M, Morgenstern NR (1981) The segregation potential of a freezing soil. Can Geotech J 18(4):482–491

    Article  Google Scholar 

  24. Koopmans RWR, Miller R (1966) Soil freezing and soil water characteristic curves. Soil Sci Soc Am J 30(6):680–685

    Article  Google Scholar 

  25. Kurylyk BL, Watanabe K (2013) The mathematical representation of freezing and thawing processes in variably-saturated, non-deformable soils. Adv Water Resour 60:160–177

    Article  Google Scholar 

  26. Laplace PS (1806) Supplement to book 10 of Mecanique Celeste. Crapelet, Courcier, Bachelier

    Google Scholar 

  27. Liao M, Lai Y, Liu E, Wan X (2017) A fractional order creep constitutive model of warm frozen silt. Acta Geotech 12(2):377–389

    Article  Google Scholar 

  28. Likos WJ, Yao J (2014) Effects of constraints on van Genuchten Parameters for modeling soil–water characteristic curves. J Geotech Geoenviron 140(12):06014013

    Article  Google Scholar 

  29. Liu Z, Yu X (2013) Physically based equation for phase composition curve of frozen soils. Transp Res Rec J Transp Res Board 2349:93–99

    Article  Google Scholar 

  30. Liu Z, Sun Y, Yu XB (2012) Theoretical basis for modeling porous geomaterials under frost actions: a review. Soil Sci Soc Am J 76(2):313–330

    Article  Google Scholar 

  31. Lu N, Likos WJ (2004) Unsaturated soil mechanics. Wiley, New York

    Google Scholar 

  32. Luan B, Robbins MO (2005) The breakdown of continuum models for mechanical contacts. Nature 435(7044):929–932

    Article  Google Scholar 

  33. Ma L, Qi J, Yu F, Yao X (2016) Experimental study on variability in mechanical properties of a frozen sand as determined in triaxial compression tests. Acta Geotech 11(1):61–70

    Article  Google Scholar 

  34. Martínez L, Andrade R, Birgin EG, Martínez JM (2009) PACKMOL: a package for building initial configurations for molecular dynamics simulations. J Comput Chem 30(13):2157–2164. https://doi.org/10.1002/jcc.21224

    Article  Google Scholar 

  35. Mitchell JK, Soga K (2005) Fundamentals of soil behavior. Wiley, New York

    Google Scholar 

  36. Molinero V, Moore EB (2008) Water modeled as an intermediate element between carbon and silicon†. J Phys Chem B 113(13):4008–4016

    Article  Google Scholar 

  37. Moore EB, Molinero V (2011) Structural transformation in supercooled water controls the crystallization rate of ice. Nature 479(7374):506–508

    Article  Google Scholar 

  38. Moore EB, Allen JT, Molinero V (2012) Liquid-ice coexistence below the melting temperature for water confined in hydrophilic and hydrophobic nanopores. J Phys Chem C 116(13):7507–7514

    Article  Google Scholar 

  39. Morishige K, Kawano K (1999) Freezing and melting of water in a single cylindrical pore: the pore-size dependence of freezing and melting behavior. J Chem Phys 110(10):4867–4872

    Article  Google Scholar 

  40. Noy-Meir I, Ginzburg B (1967) An analysis of the water potential isotherm in plant tissue. Aust J Biol Sci 22(1):35–52

    Google Scholar 

  41. Painter SL, Karra S (2014) Constitutive model for unfrozen water content in subfreezing unsaturated soils. Vadose Zone J 13(4):1–8

    Article  Google Scholar 

  42. Plimpton S (1995) Fast parallel algorithms for short-range molecular-dynamics. J Comput Phys 117(1):1–19. https://doi.org/10.1006/jcph.1995.1039

    Article  MATH  Google Scholar 

  43. Plimpton S, Crozier P, Thompson A (2007) LAMMPS-large-scale atomic/molecular massively parallel simulator, vol 18. Sandia National Laboratories, Livermore

    Google Scholar 

  44. Schmidt R, Hansen EW, Stoecker M, Akporiaye D, Ellestad OH (1995) Pore size determination of MCM-51 mesoporous materials by means of 1H NMR spectroscopy, N2 adsorption, and HREM: a preliminary study. J Am Chem Soc 117(14):4049–4056

    Article  Google Scholar 

  45. Schofield R (1935) The pF of the water in soil. In: Transactions of 3rd international congress of soil science, pp 37–48

  46. Schreiber A, Ketelsen I, Findenegg GH (2001) Melting and freezing of water in ordered mesoporous silica materials. Phys Chem Chem Phys 3(7):1185–1195

    Article  Google Scholar 

  47. Schuur EA, Bockheim J, Canadell JG, Euskirchen E, Field CB, Goryachkin SV, Hagemann S, Kuhry P, Lafleur PM, Lee H (2008) Vulnerability of permafrost carbon to climate change: implications for the global carbon cycle. Bioscience 58(8):701–714

    Article  Google Scholar 

  48. Sheng D, Zhang S, Yu Z, Zhang J (2013) Assessing frost susceptibility of soils using PCHeave. Cold Reg Sci Technol 95:27–38

    Article  Google Scholar 

  49. Shiomi J, Kimura T, Maruyama S (2007) Molecular dynamics of ice-nanotube formation inside carbon nanotubes. J Phys Chem C 111(33):12188–12193

    Article  Google Scholar 

  50. Song X, Borja RI (2014) Mathematical framework for unsaturated flow in the finite deformation range. Int J Numer Meth Eng 97(9):658–682

    Article  MathSciNet  MATH  Google Scholar 

  51. Song X, Borja RI (2014) Finite deformation and fluid flow in unsaturated soils with random heterogeneity. Vadose Zone J 13(5)

  52. Spaans EJ, Baker JM (1996) The soil freezing characteristic: its measurement and similarity to the soil moisture characteristic. Soil Sci Soc Am J 60(1):13–19

    Article  Google Scholar 

  53. Starov VM, Velarde MG, Radke CJ (2007) Wetting and spreading dynamics, vol 138. CRC Press, Boca Raton

    MATH  Google Scholar 

  54. Stillinger FH, Weber TA (1985) Computer simulation of local order in condensed phases of silicon. Phys Rev B 31:5262

    Article  Google Scholar 

  55. Stukowski A (2010) Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool. Modell Simul Mater Sci Eng 18(1):015012

    Article  Google Scholar 

  56. Tadmor EB, Miller RE (2011) Modeling materials: continuum, atomistic and multiscale techniques. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  57. Watanabe K, Flury M (2008) Capillary bundle model of hydraulic conductivity for frozen soil. Water Resour Res 44(12)

  58. Webb SW (2000) A simple extension of two-phase characteristic curves to include the dry region. Water Resour Res 36(6):1425–1430

    Article  Google Scholar 

  59. Xu G, Wu W, Qi J (2016) Modeling the viscous behavior of frozen soil with hypoplasticity. Int J Numer Anal Met 40(15):2061–2075

    Article  Google Scholar 

  60. Young T (1805) An essay on the cohesion of fluids. In: Philosophical Transactions of the Royal Society of London, pp 65–87

  61. Zhang S, Sheng D, Zhao G, Niu F, He Z (2015) Analysis of frost heave mechanisms in a high-speed railway embankment. Can Geotech J 53(999):1–10

    Google Scholar 

  62. Zhang C, Liu Z, Deng P (2016) Contact angle of soil minerals: a molecular dynamics study. Comput Geotech 75:48–56. https://doi.org/10.1016/j.compgeo.2016.01.012

    Article  Google Scholar 

  63. Zhang C, Liu Z, Deng P (2016) Atomistic-scale investigation of effective stress principle of saturated porous materials by molecular dynamics. Geophys Res Lett 43(19):10257–210265. https://doi.org/10.1002/2016gl070101

    Article  Google Scholar 

  64. Zhang C, Dong Y, Liu Z (2017) Lowest matric potential in quartz: metadynamics evidence. Geophys Res Lett 44(4):1706–1713. https://doi.org/10.1002/2016GL071928

    Article  Google Scholar 

  65. Zhang C, Liu Z, Dong Y (2017) Effects of adsorptive water on the rupture of nanoscale liquid bridges. Appl Clay Sci 146:487–494. https://doi.org/10.1016/j.clay.2017.07.002

    Article  Google Scholar 

  66. Zhao X, Zhou G, Lu G (2017) Strain responses of frozen clay with thermal gradient under triaxial creep. Acta Geotech 12(1):183–193

    Article  Google Scholar 

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Acknowledgements

The financial support from the National Science Foundation (NSF CMMI 1562522) and the Michigan Space Grant Consortium by National Aeronautics and Space Administration (Grant No. MSGC1311039) is gratefully acknowledged. We also acknowledge Superior, a high-performance computing cluster at Michigan Technological University, for providing computational resources to fulfill this study.

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  1. Department of Civil and Environmental Engineering, Michigan Technological University, Houghton, MI, 49931, USA

    Chao Zhang & Zhen Liu

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Correspondence to Zhen Liu.

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Zhang, C., Liu, Z. Freezing of water confined in porous materials: role of adsorption and unfreezable threshold. Acta Geotech. 13, 1203–1213 (2018). https://doi.org/10.1007/s11440-018-0637-6

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