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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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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