Introduction

Water is an exceptionally abundant and essential liquid in nature, facilitating a wide range of critical physical, chemical, and biological processes1,2,3. Although water is composed of simple atoms, it exhibits complex structures and anomalous behaviors under specific conditions, such as supercooling, interfaces, and confinement2,4,5. Especially, at the interface, it is well acknowledged that there is a thin layer of disordered film – this phenomenon is referred to as premelting6.

Premelting forms a thin, quasi-liquid layer on the surface of a solid due to the interfacial interactions to minimize interfacial free energy7. This phenomenon can occur at three different types of interfaces: (1) surface melting between a solid and its vapor or gaseous atmosphere, (2) grain-boundary melting between crystals of the same material, and (3) interfacial melting in contact with foreign solid or liquid8. For the purpose of consistency, quasi-liquid layers at various interfaces are collectively referred to as “film water” in this study. Premelting in frozen soil has significant implications for various environmental problems in cold regions, such as frost heave8. Specifically, under unsaturated condition, when the frozen soil contains solid particles, water, ice and air, all three types of interfaces present. To maintain consistency, the term ‘film water’ in this study refers to the water layer attached to the surface, regardless of the surface material.

Film water properties are fundamentally related to its thickness, as it measures the spatial extent of the film water layer where the chemical reactions and exchange processes are promoted9. The film water thickness undergoes changes with temperature and diverges as it approaches the melting point8. Nevertheless, a consensus regarding the estimated thickness of the liquid-like layer has not been reached, owing to discrepancies among various methods such as experimental techniques, numerical simulations and theoretical approaches10. Various experimental methods have been employed to detect the thin film thickness on ice surfaces, including X-ray diffraction11, ellipsometry12, atomic force microscopy (AFM)13,14, and spectroscopy15,16. Interfacial melting of ice on foreign substrate, such as silica, can be challenging to investigate, therefore, has been only studied by indirect methods such as NMR17. These measurements typically cover an extent range from 1 to 100 nm. Molecular dynamics (MD) simulations are also widely used to assess the thickness of film water. Conde et al. (2008) estimated the film water thickness on free ice surfaces to be within 1 nm with 2 types of water models and 2 types of ice surfaces, and the separation between film water and ice was based on structural arrangement18. Similarly, Gladich et al. (2011) obtained comparable film water thickness using a different water model, and the separation also considered the dynamic properties19. At the interface between silica and ice, where the silica surfaces are either amorphous or crystalline, the thickness of the water film was found to be up to 1.1 nm20. Besides MD simulations, Dash et al. (2006) applied a theoretical thermodynamic solution, and the determined film water thickness can be up to 2 nm8.

Both molecular dynamics (MD) simulations and theoretical predictions yielded remarkedly lower results compared to the laboratory data. This discrepancy can be partially attributed to the fact that MD and theoretical studies assume ideal conditions and pure systems, while the ice surface is sensitive to perturbations and impurities encountered in the laboratory experiments, as discussed by Mitsui and Aoki (2019)21. In addition, the variation in MD simulations can be attributed to the chosen water models and exposed surface of ice, and the methods to identify film water. Laboratory data displayed the most substantial variability, especially when different techniques were employed. That is mainly because distinct physical quantities are measured to determine the film water thickness using different experimental techniques as it is not directly observable, and another reason is that techniques such as AFM can affect the tested sample22.

The mobility of film water is also important, for example, in permafrost, as it measures the ability of this unique water layer to serve as a potential channel for mass transport and ice growth in cold regions23,24. Viscosity can be the most critical parameter in water dynamic, which is also closely related to the diffusion coefficient25. However, determining the dynamic properties of film water experimentally can be challenging, due to the microscale of film water and the need for precise laboratory conditions26. Molecular dynamics (MD) simulations prove to be a useful tool for probing molecular-level phenomena, thus facilitating an in-depth understanding of thin water films. Kling et al. (2018) found that diffusion coefficient in film water was considerably small at low temperatures, resembling the behavior of amorphous materials22. Pfalzgraff et al. (2011) investigated various ice planes exposed to vapor, including basal, prismatic, and pyramidal facets, and figured out that the diffusion coefficient is intrinsically connected to the ice morphology27. Moreover, Gladich et al. (2011) revealed diffusion coefficient anisotropy at lower temperatures (less than 250 K) as film water resembles the structure of ice, but this anisotropy gradually smears when temperature increases as the structure shifts towards that of water19. Molecular dynamics (MD) studies have also explored the water behavior near the silica surface28,29. These studies all either focus on ice-air/vacuum interfaces or water-silica interactions, while very few study investigates specific interaction between silica and ice, and even fewer consider the influence of gas at the same time.

In the context of cryosphere hydrological models at the continuum scale, the components of water (such as capillary water and film water) are crucial for representing the freeze-thaw characteristics of porous media and determining the soil’s hydraulic properties30. This water retention ability in porous media can be described by the soil freezing characteristic curve (SFCC), which illustrates the relationship between subzero temperatures and unfrozen water content31. In SFCC, it is commonly assumed that soil water is retained by capillary forces32. Consequently, film water has not been systematically considered in permafrost models. While some models simply do not include film water32,33, other models with film water in the framework have dynamic properties (e.g., viscosity) assumed to be similar to capillary water or defined arbitrarily34. However, film water becomes dominant at lower temperatures, as it is typically more resistant to freezing35. Therefore, it is essential to incorporate film water into permafrost models to improve their accuracy and predictive capabilities. As for film water properties, the characteristics of film water at interfaces differ significantly from those of bulk water, which has been realized36, but not systematically investigated. Film water may exhibit heterogeneity and anisotropy in its properties27 due to the influences of different interfaces such as water-air and water-minerals and symmetry breaking the configuration. However, the influences of interfaces on water flow remain unclear, and thus have not been collectively considered in the study of permafrost system. Furthermore, previous investigations have often examined the diffusion coefficient (D) over a broad temperature range, including temperatures as low as − 40 K below the melting point, with coarse resolution (typically with an interval of 10 K)19. However, in the study of natural frozen soils, it is practically important to consider temperatures within 10 K below the melting point, and the evolution of 1 K could induce significant changes.

In order to bridge these research gaps, the present study utilizes MD simulations to investigate key parameters associated with the film water, including the thickness of the water film and its dynamic properties (diffusion coefficient D, and viscosity). The study places particular emphasis on temperatures close to the melting point, subjecting this range to a higher resolution (1 K) analysis. We consider two main types of interfaces in the frozen soil system: the air-ice interface, where a thin layer of water exists on the ice surface and in contact with air, and the soil-ice interface, where water is absorbed onto the soil particle surface and also constrained by ice. These are differentiated as “film water” at the silica-water (SW) interface and “film water” at the air-water (AW) interface. By doing so, the study aims to draw parallels to the characteristics observed in unsaturated frozen soil systems.

Methods

MD simulation

The initial model configuration, with air, silica, ice, and water coexisting, is depicted in Fig. 1. Silica is suited to act as a representative of soils in studies examining water-soil interactions, given its status as the most abundant component in soils37. This configuration is achieved through the coexistence technique38, where each layer of material was placed in direct contact with one another. Within the system, the 5 nm void between the ice and the top silica slab was established to simulate the gas phase, which was widely adopted by the MD investigations on the premelting of the free ice surface22,27. The silica utilized in this study was represented by the most stable form found in soils—α-quartz, with the thermodynamically dominant exposed planes (001), and was fully saturated by hydroxyl groups, as a common physicochemical reaction in nature39,40,41. The unit cell parameters of α-quartz adopted in comparison to the experimental data are listed in Table 1. The simulated ice in the system is the widely occurring hexagonal ice Ih, with the secondary prismatic plane exposed known for its efficient nucleation rate18. The ice serves as a template to facilitate the crystallization process, considering that homogeneous nucleation would be extremely time-consuming in the MD simulation42. Additionally, a 5 nm vacuum area from the top silica surface to the edge of the simulation domain was included to eliminate unwanted interactions across the boundaries. Distances between two silica slabs were varied to test the effect of pore size, which was achieved by applying water layers of different thicknesses while maintaining the constant 5 nm vacuum area, namely constant gas volume. Specifically, the water layer thickness varied from 3 to 5 nm with the cases labeled as “siw3,” “siw4,” and “siw5” (Fig. 1a–c). The pore size effect in this study accounts for the joint changes in both the number of water molecules and the interaction distances between water and silica particles, which are associated with changes in water layer thickness. The unit cell size of the simulation box is 5.88 nm along the x-axis and 4.90 nm along the y-axis. The z-axis lengths are dependent on the system size. Detailed information regarding the length of z direction of simulation box and the number of molecules in each system is provided in Table 2.

Based on these configurations, the process of water phase change against the silica slab was simulated. To simulate the interaction between water and silica at low temperatures, the TIP4P/Ice water model43 was utilized in combination with CLAYFF model44. The detailed information of TIP4P/Ice water model and CLAYFF model has been added in the Supporting Information (S1). During the simulation, all atoms in the silica slab were held fixed, with the exception of -OH groups on the surface. This setting allows the -OH groups to vibrate, imparting the motion necessary for important physical-chemical processes on the solid surface, while eliminating the risk of slab collapse45. The OH groups are free to move but a constant bond length of 0.1 nm is maintained, as specified by the CLAYFF force field46. These settings follows the methodology employed in previous studies46,47.

Table 1 Lattice parameters of α-quartz from the experiment48 and used in this study respectively. Unit: Å.
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Table 2 Number of water molecules in initial configurations of different sizes.
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Fig. 1
figure 1

Initial configuration of the ice-water-silica-gas coexisted system, with different sizes: (a) siw3; (b) siw4; (c) siw5; (d) schematic diagram of film water at AW and SW interfaces; red particle represents oxygen atom, white particle represents hydrogen atom, and yellow particle represents silicon atom. The visualization was generated by Visual Molecular Dynamics (VMD) software49.

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The MD simulations were conducted using the open-source software GROMACS-2021.4 (https://www.gromacs.org/)50. The Newton’s equations of motion are integrated using the leap-frog algorithm, employing a timestep of 2 fs. The NVT ensemble was applied to keep constant temperature and volume of the system during the simulation. Temperature control was achieved by employing the Nosé-Hoover thermostat with a relaxation time of 1 ps51,52. Periodic boundary conditions (PBC) were implemented in all three spatial dimensions to simulate a parallelly infinite system. To enhance the simulation efficiency, the short-range interactions and the real part of the long-range interactions were truncated at a distance of 1.2 nm. Long-range interactions beyond this cutoff range were computed using the three-dimensional particle mesh Ewald summation (PME) package53. The LINCS algorithm was used to maintain the length of the water hydrogen bond constant54.

Higher temperatures compared to a previous study (−40 ℃)19, ranging within 10 K below the melting temperature, were set with an interval of 1 K to generate different simulation cases. Note that this temperature range is of particular interest for the study for permafrost in nature, as this is a critical temperature range where the water behavior undergoes substantial transformations. Moreover, within this temperature range, the diffusion coefficient is less influenced by the ice morphology and exhibits isotropic behavior, as highlighted by Gladich et al. (2011)19. As the melting temperature is subject to the system size (represented by the total water content in this study), the simulation results of systems with different sizes were presented over different temperature ranges. The lower temperature thresholds for all systems were uniformly established at a frozen temperature of 255 K, whereas the upper temperature boundaries were chosen to be precisely 1 K below the respective critical points for each distinct system. The melting points of water for all simulation cases were determined using the potential energy method, following the approach described by Conde et al. (2017)55, and the detailed information regarding this process can be found in the Supporting Information (S2). For all the simulations with different seeds, only the frozen cases were considered for further analysis, as in melted cases the phenomenon of premelting disappear.

Analysis of film water properties

Film water thickness

The method of identifying the liquid-like water molecules from the ice crystal is vital in determination of film water thickness. In previous studies, the order parameter qt was utilized to determine the quantity of molecules exhibiting liquid-like properties18,19. The order parameter qt distinguishes unfrozen water from ice based on their distinct structures, as water molecules are randomly distributed, while ice crystals are characterized by the tetrahedral structure. However, as water undergoes supercooling, it also becomes increasingly tetrahedral56. Besides, the choice of the qt varies across different water models and can be subjective19. Consequently, it is challenging in accurately distinguishing between ice and liquid-like molecules, and this could result in an inaccurate estimation of the thickness of the water film. The Chill+ algorithm used in this study identifies the state of water molecules based on the correlation of orientational order with its four closest neighbors57. This Chill+ algorithm is open-source and has been integrated into the visualization software Ovito. By determining the number of unfrozen water molecules, it is possible to calculate the thickness of the water film using Eq. (1)18:

$$\xi =\frac{{N}_{l}M}{\rho {N}_{A}{L}_{x}{L}_{y}}$$
(1)

where \(\xi\) represents the thickness of the film water, \({N}_{l}\) denotes the number of unfrozen water molecules at equilibrium, M represents the molecular weight of water (18.02 g/mol), \({N}_{A}\) is Avogadro’s number, the product of \({L}_{x}\) and \({L}_{y}\) represents the area of the interface, and ρ denotes the density of liquid water.

In-plane diffusion coefficient

The transition of ice from a solid to a liquid state has been observed to occur through a two-dimensional phase-transition process, taking place layer by layer58,59. As the PBCs were applied, water diffusion along the coordinates parallel to the interface (x and y) is unbounded. As a result, our attention was directed towards understanding D parallel to the silica slab within the interfacial region, which corresponds to the thickness of the water film. In the context of bulk fluids, the most employed method for determining diffusion coefficient D is the Einstein relation that relies on the mean square displacement (MSD)60. However, this approach is not applicable to systems with interfaces or confined fluids. In these cases, molecules within the region of interest only remain for a limited time before entering other regions, and the asymmetry of the interface introduces unique characteristics in interfacial self-diffusion. To address this, Liu et al. (2004) proposed a method that enforces virtual boundary conditions on the molecular system, enabling the layering of the system in specific regions of interest61. For calculation of layer-specific D, a layer with boundaries {l, h} was assumed, and the MSD within this range in one-dimension (e.g., x-direction) can be expressed as:

$${ \langle \varDelta {x}^{2}({\uptau },{\updelta }) \rangle }_{\{l,h\}}=\frac{1}{{N}_{{\uptau }}}\sum _{\delta =1}^{{N}_{{\uptau }}}\left(\frac{1}{{N}_{p}\left(\delta , \delta +\tau \right)}\sum _{n=1}^{n\in \zeta (\delta , \delta +{\uptau })}{\left|\overrightarrow{{x}_{n}\left(\delta +{\uptau }\right)}-\overrightarrow{{x}_{n}\left(\delta \right)}\right|}^{2}\right)$$
(2)

where the set ζ(δ, δ + τ) represents all the particles that remain within the layer during the time interval between δ and δ + τ, \({N}_{p}\left(\delta , \delta +\tau \right)\) denotes the number of particles in this set. It is crucial to mention that only the molecules that remain within the studied regions are taken into account. By doing so, it becomes possible to calculate the interfacial D by obtaining survival probabilities within these regions, which is determined by Eq. (3):

$$P\left({\uptau }\right)=\frac{1}{T}\sum _{\delta =1}^{T}\frac{N\left(\delta ,\delta +{\uptau } \right)}{N\left(\delta \right)}$$
(3)

Hence, we can derive the expression for the one-dimensional Dxx:

$${D}_{xx}\left(\left\{l,h\right\}\right)=\underset{{\uptau }\to {\infty }}{\text{lim}}\frac{{\langle \varDelta {x}^{2}\left({\uptau }\right) \rangle }_{\{a,b\}}}{2P\left({\uptau }\right)}$$
(4)

Based on the same method, Dyy can be calculated, and then the parallel diffusion coefficient Dxy can be obtained by:

$${D}_{xy}\left(\left\{l,h\right\}\right)=\frac{{D}_{xx}+{D}_{yy}}{2}$$
(5)

During the calculation, the virtual boundaries were determined by the thickness of film water.

The TIP4P-Ice water model has a known problem of underestimating the diffusion coefficient by nearly 2 times62. Consequently, the determination of D for film water may be significantly lower than the actual value for bulk water due to the specific water model employed. Therefore, in order to analyze the trend of D in film water, the estimated D will be compared to the bulk value obtained using the same water model, rather than the real value for water. The calculated D of bulk water using the TIP4P-Ice model, obtained using the same method employed to determine the in-plane diffusion coefficient, is 2.00 × 10−6 cm2/s at 260 K. This value deviates from the reported value of 2.15 × 10−6 cm2/s for bulk water applying TIP4P/Ice63 by only 7%, demonstrating the reliability of this method for determining the diffusion coefficient. Furthermore, a series of bulk diffusion coefficients of pure water was simulated to enable comparisons with the local D at the same temperature ranges.

Viscosity

The viscosity and diffusion coefficient are interrelated, as proposed by Louden and Gezelter (2018) and mathematically expressed by Eq. (6)25:

$${\eta }_{s}=\frac{{D}_{bulk}}{{D}_{s}}{\eta }_{bulk}$$
(6)

where \({\eta }_{s}\) and \({\eta }_{bulk}\) represent viscosity in film water layer and bulk water, respectively, \({D}_{s}\)and \({D}_{bulk}\) represent diffusion coefficient in the film water layer and bulk water, respectively. Notably, the viscosity of TIP4P-Ice water model is different from the actual water as well. Therefore, the viscosity of bulk water predicted by TIP4P-Ice water model64 was selected for the calculation of film water viscosity.

Results

Thickness of film water layer

The variation of film water thickness with temperature differs at the two different interfaces for systems of various sizes according to Fig. 2a. For all the systems, the film water thickness at the air-water interface (AW) is highly dependent on temperature, as an increase in temperature leads to a substantial thickening in the unfrozen water layer, and the increase rate also rises with temperature. When the temperature approaches the melting point, the thickness of the water film at the AW increases by up to 154.8–224% compared to that at 255 K. Conversely, the film water thickness at the silica-water interface (SW) appears to be unaffected by temperature variations, maintaining a value of approximately 0.5 nm. Notably, at the lowest selected temperature of 255 K, the film water thickness at the AW interface is observed to be even marginally thinner than that at the silica-water (SW) interface. This reaffirms the strong temperature dependence of film water associated with the air interface, in contrast to the relative insensitivity of SW interface film water to temperature changes. This finding indicates that different interfaces can have distinct impacts on the freezing process.

Pore size effect was also observed in the film water thickness among different systems (Fig. 2a). The thickness of the film water layer connecting to air is subject to influence of the system size, as siw4 and siw5 exhibit thicker film water layers than siw3, which can also be observed for the layer at the silica side, but to a much less extent. At the AW interface, the influence of pore size contributes to an increase of 5–45% in the film water thickness from siw3 to siw4 at temperature increases from 255 K to 263 K. The subsequent increase from siw4 to siw5 is relatively moderate, ranging from 1 to 13%. The diminishing rate of increase in the water film thickness as pore size further expands indicates a decreasing influence of pore size on the film thickness, suggesting a transition towards a nearly size-independent behavior in further larger pores. In contrast, at the SW interface, the impact of pore size results in increases of less than 15% across all cases. The effects of pore size have been noted in Fig. 2a. These trends in film water thickness can be related to the change in melting point due to the pore size effect. It was observed that as the pore size increases, the melting point decreases (see Supporting Information S2, Fig. S1), which corresponds to an increase in film water thickness.

Systems of varying sizes require different amounts of time to equilibrate. Figure 2b–d demonstrates the determined water film thickness at two consecutive time intervals. Based on Fig. 2b, it can be observed that in the smaller siw3 case, the film water thicknesses calculated at 50 ns show minimal variation (within 10%) when compared to those at 40 ns, across different temperatures. This finding implies that the MD simulation for the siw3 system has reached equilibrium after 50 ns. Similar equilibrium has not been observed until at 80 ns for the larger siw4 case (Fig. 2c), and at 140 ns for the largest siw5 case (Fig. 2d). Film water at the SW interface generally shows less variation compared to that at the AW interface, as indicated by the error bar, which demonstrates the stability of film water at the SW interface. When approaching the melting point, this variation could become larger, as seen in the siw5 case.

In summary, the presence of water at the air-water (AW) interface (i.e., film water layer between ice and air) is influenced by both the temperature and pore size, and temperature plays a dominant role in thickening the film water layer. However, film water at the SW interface is much less affected compared to that at the AW interface.

Fig. 2
figure 2

Variations of film water thickness with temperature for (a) all systems at the AW and SW interfaces within their respective temperature ranges at their equilibrium time; (b) siw3 at 40 and 50 ns; (c) siw4 at 70 and 80 ns; and (d) siw5 at 130 and 140 ns. The green arrows indicate the change caused by pore size at AW interface, while the yellow arrow indicates the change caused by pore size at SW interface.

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Dynamic properties of film water layer

The average lateral diffusion coefficients (D) within the film water layer vary at the two different interfaces in all systems, as shown in Fig. 3a. The specific ranges of D for AW and SW at different systems are detailed in Table 3. The average lateral diffusion coefficients of film water are generally lower than those of bulk water (indicated by the dashed line). Lower temperature, such as 255 K in siw3, results in an in-plane diffusion coefficient nearly two magnitudes lower than that of bulk water for AW. The much lower D is also found in the film water layer at the SW interface for all the cases with all the temperatures. However, as the temperature increases towards the melting point, the lateral D of film water near the AW interface approaches that of bulk water.

The lateral D of water molecules at the SW interface remains relatively constant regardless of temperature and pore size compared to that at the AW interface, similar to what is found in the film water thickness. For the small system siw3, the lateral D of film water at AW interface shows a substantial increase as the temperature rises from 255 K to 264 K, by approximately two orders of magnitude. For larger cases siw4 and siw5, significant increases of 23 and 13 times are observed as the temperature approaches the melting point (262 K and 261 K), respectively. These findings clearly indicate that the diffusion coefficient at the AW interface is highly dependent on temperature. The error bars represent variations among simulations with different seeds, which become significant particularly at temperatures near the melting point; note this is clearer with a normal scale along the vertical axis than the log scale here. The increase in pore size from siw3 to siw4 contributes to an average 1.3-fold increase in lateral D of film water at the AW interface. However, there is an insignificant increase in D from siw4 to siw5. This phenomenon can be attributed to the diminishing impact of pore size as it increases further, indicating that there could be an upper limit for local D with increasing size prior to reaching the melting temperature.

The difference between film water D at different interfaces is represented by the ratio of D at the SW to AW interface (refer to Fig. 3b). When the temperature is as low as 255 K, siw3 has even lower lateral D of film water at AW than SW. As the temperature rises, D in the AW film water layer increases, surpassing that of SW film water. At 259 K, the ratio of film water D at the SW to AW interface is approximately 35% in siw3, while at 264 K, this ratio becomes less than 5%. For larger systems, the differences of film water D between the SW and AW interfaces are relatively small in siw4 and siw5 at low temperatures 255 K. As the temperature approaches the melting point, the differences enlarge with the ratio of D at SW to AW interface down to approximately 5% for siw4, and even lower for siw5.

The general trends agree well with that obtained by Gladich et al. (2011) (lateral D on the free ice surface)19 and Carignano et al. (2005) (D of bulk water)65, where the diffusion coefficient of film water at free ice surface is observed to be lower than that of bulk water and always increases with temperature. Data from Gladich et al. (2011) span within a temperature range from 230 to 290 K with a 10 K interval. To facilitate comparison with our data (255–264 K), we fitted Gladich et al.‘s data to obtain D values at 255–265 K with a 1 K interval. The D values computed by Gladich et al. (2011) at 261 K are very close to those of siw5 and siw4 at the AW interface in the present study, with a deviation of only 17.51% (Fig. 3a). However, the discrepancy becomes pronounced at temperatures below 261 K, where the D values determined in this study are notably lower. This discrepancy can be attributed to the different methodologies employed for calculating the local diffusion coefficient. In the study of Gladich et al. (2011), the in-plane diffusion coefficient of film water is assumed to be proportionable to the bulk system, and the number reported is scaled according to the volume fraction of film water within a fixed domain. The approach adopted in the present study directly calculates the local diffusion coefficient.

Our findings reveal that the film water at the SW interface exhibits limited mobility with increasing temperature and pore size, indicating a more restrained water molecular environment. In contrast, the film water at the AW interface demonstrates enhanced mobility, particularly as the temperature is lower than the melting point.

Table 3 Lateral diffusion coefficient range for systems of different sizes from 255 K to 264 K. Unit: 10e−8 cm2/s.
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Fig. 3
figure 3

(a) Lateral diffusion coefficients; (b) The ratio between diffusion coefficients of SW and AW film water for siw3, siw4 and siw5 within their respective temperature ranges.

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Viscosity

We calculated the viscosity of film water at different interfaces based on the diffusion coefficient data, as shown in Fig. 4. The viscosity profile mirrors that of the local diffusion coefficient, albeit in an inverse relationship according to Eq. (6). Specifically, across the three systems examined, viscosities of film water at the AW interface are notably high at low temperatures, declining progressively as temperatures increases, and eventually converge towards the bulk water viscosity as the temperatures rise to the melting point. In contrast, for the SW interface, the average film water viscosities across systems were significantly elevated, with an average of 237.68 mPa·s—this is approximately 32 times greater than the bulk water value of the TIP4P-Ice water model (7.2 mPa·s). Besides, these high viscosities remain largely invariant over the simulated temperature range. A higher viscosity indicates a reduced fluid dynamics rate. Therefore, the water film present on the soil surface can be considered as being relatively immobile, while that on the free ice surface is more dynamic depending on the temperature.

Fig. 4
figure 4

Viscosities of film water near the SW and AW interfaces for siw3, siw4 and siw5 over their respective temperature ranges.

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Discussion

Film water behaviors at two interfaces

The density profile of oxygen atoms in film water were analyzed to learn more about the layer-specific structural properties (Fig. 5). Using the siw4 system as an example, with the z direction perpendicular to the ice plane and assuming the lower silica end as the starting point, it was observed that the density at SW interface (as high as 1400 kg/cm3, indicated by yellow dashed box) is higher than that of bulk water (1000 kg/m3), while density at AW interface (indicated by red dashed box) is always lower. Additionally, the density of film water at the AW interface is more responsive to temperature changes, displaying a decrease with increasing temperature. In contrast, the density at the SW interface remains relatively unaffected by temperature variations.

The properties of film water at different interfaces have been examined from various dimensions, including film thickness, dynamic properties, and density profiles. The distinct behaviors of film water at these interfaces in response to temperature can be attributed to the unique bonding interactions between water molecules and their neighboring surfaces.

For film water at the SW interface, the OH groups on the silica surface exhibit strong affinity for water molecules, leading to changes in their distribution and orientation, facilitated the hydrogen bonding between them20,66. This interaction promotes the formation of hydration layers—a more ordered and dense arrangement of water molecules on the edge surfaces of silica. The effect of the strong interactions extends to a certain spatial extent, maintaining a stable film thickness even at higher temperatures (still below the melting point) and resisting freezing at low temperatures. Consequently, water molecules near the SW interface form a solid-like, relatively constant layer that is distinct from ice. The dense structure induced by these interactions result in lower mobility compared to bulk water. This phenomenon is not limited to systems containing ice but is also observed in configurations consisting of silica and water, where interfacial water exhibits higher density and slower displacement compared to bulk water67. Therefore, the structural and dynamic properties of the film water layer at the SW interface are relatively insensitive to changes in temperature. Extensively, we speculate for film water in contact with a hydrophilic foreign material, the water molecules are strongly attracted and remain relatively stable, forming a solid-like structure with reduced mobility.

The formation of film water at the AW interface has been a long-debated topic, as systematically reviewed by Sun et al. (2023)68. One prominent theory is the molecular undercoordination theory, which points out that surface molecules are inherently unstable due to the lack of neighboring molecules above, prompting the formation of a liquid phase. According to our simulation results, the film of water observed at the AW interface was generated by simulating initially intact ice at temperatures even well below the melting point. Despite these low temperatures, the film of water remains unfrozen even at equilibrium. This observation supports the molecular undercoordination theory. Therefore, the film water at the AW interface is formed by weak bonding interactions at the free ice surface, while the state of ice is highly sensitive to temperature. As the temperature increases, the ice melts accordingly, leading to the increase in the film water thickness at the AW interface. This results in a higher diffusion coefficient of the film water at this interface.

Limitation and implication of this study

Although this study discovers distinct film water behavior at different interfaces in the unsaturated frozen soil systems, we recognize that there are aspects that could benefit from additional investigation. First, the availability of data for validation is limited, and thus the results in this study are validated indirectly. As discussed in section “Introduction”, there are significant differences (up to two orders of magnitude) in film water thickness measurements among various techniques, and most of these studies focus on film water at the AW interface. Consequently, it is challenging to directly validate the estimated film water thickness based on data from previous studies using different techniques. As for molecular dynamics (MD) simulations, previous results vary according to the force field, boundary or initial conditions, and those conditions are not identical to this study. Overall, we have only compared the general trends rather than exact numbers in the film water thickness.

For the diffusion coefficient D, we first compared the D of a pure water system from this study with that reported in a previous study also using TIP4P/Ice water model. The good match supports the rational of chosen model parameter and calculation method of lateral D. Additionally, the lateral D of film water was compared with those from previous studies (Gladich et al., 2011; Carignano et al., 2005) (Fig. 3a), and the trends show good agreement with our results. The discrepancies in precise values can also be attributed to the specific method used to calculate the local diffusion coefficient (D). Our method is more direct and therefore provides a clearer and more accurate representation of the local diffusion behavior.

As the melting point is a vital criterion for evaluating the performance of water models in phase change simulations, we have added simulations of well-studied systems, including fully saturated systems with varying sizes, to estimate their melting points as a function of pore size (see Supporting Information S3, Figs. S2, S3). The results show consistency with previous work (Findenegg et al., 2008), further validating our simulation protocol for the freezing-thawing process. In addition, the simulated results align well with the established theoretical framework proposed by previous studies, which further validates these outcomes, as discussed in section “Discussion”.

Second, pore size effects inherently involve changes in both the number of water molecules and the pore size (interactive distance). These two effects are difficult to separate and tend to work in tandem. Even when the distance between silica slabs is kept constant, the gap thickness (interactive distance) will vary as the number of water layers increases. In the current cases, we maintained a constant gap thickness, which resulted in variations in the pore size. To decouple the mixed effects due to pore size changes, we try to investigate this system in another perspective by establishing new configurations with a constant pore size but varied water number and gap thickness. Three new cases, labeled siw3*, siw4*, and siw5*, are shown in Fig. S4 in the Supporting Information.

The calculated film water thickness in the new cases versus temperature and pore size do not differ significantly from the previous cases when the gap thickness is changed. For the trend in film water thickness, as temperature and pore size increase, the film water thickness at SW interface remains relatively insensitive, while a more pronounced increase is observed at the AW interface (Fig. S5). Compared to the siw systems, the siw* systems exhibit a deviation in film water thicknesses of less than 10% at the SW interface and less than 20% at the AW interface (Fig. S6). A detailed discussion is provided in the Supporting Information (S4). Despite the different settings for the position of the top silica slab in cases with the minimal gap thickness of 5 nm, we observe similar results in the film water thickness. The strong correlation between film water thickness and the number of water molecules, still, can be attributed to (1) the thickness of water/ice layer and (2) the interaction distance to the bottom slab. These two factors are strongly coupled in all cases. In summary, the effect of the number of water molecules and pore size is inherently coupled, while the effect of the distant (> = 5 nm) top slab is not significant.

Third, this work intends to investigate the behavior of water in frozen soil and is grounded in the theoretical frameworks of cryosphere hydrology, where film water is always neglected or simplified. However, the upscaling directly from the molecular scale to the continuum scale and integrating these findings into mathematical models remains a significant challenge that requires further study.

Nonetheless, our research systematically considered film water at two distinct interfaces within a complex system, and provides valuable insights into the physical models of frozen soil, which are crucial for simulation settings. The system examined in this study closely mirrors unsaturated frozen soil systems. The traditional REV (representative elementary volume) scale hydrological model neglects the film water present in the unsaturated frozen soil at the AW, while considering only the film water at the SW interface. The REV scale is the smallest volume of the porous medium that can be considered statistically representative of the entire medium’s properties, which is essential for linking microscale phenomena to macroscopic behavior and simplifying the analysis of transport processes. This study suggests that film water at the AW can exhibit higher water content and faster dynamics within the practical temperature range (within 10 K from the melting point). Consequently, it is imperative to include the film water at the AW within the modeling framework when the unsaturated frozen soil condition is considered.

It is noteworthy that the impact of film water is far beyond hydrology. The study of film water is an important subject in chemical physics and has been a topic of long-standing debate. As discussed in the introduction, relatively little attention has been paid to film water in complex silica-based solid-ice-water-gas systems. Due to the limitations of techniques that focus on different physical quantities, a consensus regarding the film water properties has not yet been reached. This study aims to quantitatively measure the film water thickness and dynamic properties, and proposes assumptions for the underlying mechanisms based on the results, thereby contributing to the film water study.

One of the common questions across various fields is the nature and classification of “water” at interfaces, particularly at the SW interface. These unique water layers raise the need to consider whether this type of “water” should be regarded as a distinct phase or state of water. This is critical, as there is ongoing controversy over whether describing this unique layer in analogy to the liquid phase is a valid and realistic approach, which is a prerequisite for the afterward property parameterization. From a practical perspective, water exhibits active reactions and mass transport. D of the film water at the SW interface falls between the estimated values of bulk water and ice (Fig. 3). At the AW interface, the diffusion coefficient of the film water is nearer to that of bulk water when the temperature is elevated, whereas it approaches that of ice when the temperature decreases. Therefore, the film water at SW exhibits properties distinct from both bulk water and solid crystals. Based on the abnormal properties of interfacial water, especially the structured and dynamic behavior, this study suggests that film water at SW interface may not be classified as conventional liquid water, and that at AW should be considered depending on the temperature.

Fig. 5
figure 5

Density profile of oxygen atoms in the siw4 water system changing with temperature and schematic diagram of film water at SW interface (yellow dashed box) and at SW interface (red dashed box).

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Conclusion

In this study, molecular dynamics (MD) simulations were conducted to investigate the film water, with a focus on determining its thickness, layer-specific diffusion coefficient and viscosity at the silica-water (SW) and air-water (AW) interfaces. The results revealed that the film water at the AW interface is influenced by both temperature and pore size, with temperature exerting a dominant effect. Moreover, the mobility of this layer gets enhanced with rising temperature and pore size. In contrast, the film water at the SW interface remains relatively unaffected by temperature and pore size. This distinction can be attributed to the underlying mechanisms governing film water at different interfaces. The hydroxylated silica surface imposes strong attractive forces and forms hydrogen bonds between water molecules and the -OH groups on the silica surface, leading to the formation of a structured, solid-like layer characterized by high density and low mobility. In contrast, the film water at the AW interface is dependent on the weak bonding of ice and exhibits sensitivity to temperature variations.

The abnormal properties of the water at the silica-water (SW) interface, such as its high density and solid-like structure, suggest that this “water” may not behave like conventional liquid water, which has significant implications for many engineering and research applications. The system studied in this research bears resemblance to unsaturated frozen soil systems. Our finding is different from the traditional Representative Elementary Volume (REV) scale models of unsaturated frozen soil, which typically only considers the water at the SW interface. Instead, it suggests that the film water at the air-water (AW) interface should be considered for a more accurate representation. The findings from this study contribute to enhancing our understanding and predictive capabilities regarding the behavior of ice and frozen soil in both natural and engineered systems.