Mingzhe
Shao
abc,
Chuanbiao
Zhang†
b,
Chonghai
Qi
d,
Chunlei
Wang
d,
Jianjun
Wang
c,
Fangfu
Ye
b and
Xin
Zhou
*b
aCollege of Light Industry Science and Engineering, Tianjin University of Science and Technology, Tianjin, China
bSchool of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China. E-mail: xzhou@ucas.ac.cn
cInstitute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
dInstitute of Applied Physics, Chinese Academy of Sciences, Shanghai, China
First published on 22nd November 2019
Using all-atomic molecular dynamics (MD) simulations, we show that the structure of interfacial water (IW) induced by substrates characterizes the ability of a substrate to nucleate ice. We probe the shape and structure of ice nuclei and the corresponding supercooling temperatures to measure the ability of IW with various hydrogen polarities for ice nucleation, and find that the hydrogen polarization of IW even with the ice-like oxygen lattice increases the contact angle of the ice nucleus on IW, thus lifting the free energy barrier of heterogeneous ice nucleation. The results show that not only the oxygen lattice order but the hydrogen disorder of IW on substrates are required to effectively facilitate the freezing of top water.
While the various kinds of aspects of different materials are hard to universally describe, all these different substrates induce atomic rearrangement of the first layers of interfacial water (IW), and regulate the freezing of top water. It has found that the molecules of the first layers of the interfacial liquid on substrates rearrange and these first layers dominate supercooling,29,30 wetting,31–34 adsorption20 and evaporation35 of the top liquids. It would be desirable to investigate the correlation between the atomic reconstruction of IW and freezing of water on various kinds of substrates, which might provide a universal understanding about the effects of various kinds of substrates on ice nucleation.
Recently, a number of MD simulations focusing on the rearrangement of IW have already revealed its significance on affecting ice nucleation. It was found that the oxygen atoms of the first layer of IW on β-AgI were almost perfectly ice-like, and promoted the formation of an ice-like lattice in the next water layers thus freezing all of the top water.16,17 The polarity of the substrate was also found to be crucial in heterogeneous ice nucleation as well, and a charge-induced α-alumina surface suppresses ice nucleation upon it irrespective of the sign of the surface charge.20,36 Moreover, the adsorption energy of a polar monomer on the ice surface exhibits a strong correlation with the IW orientation. These recognitions emphasize the role of IW in heterogeneous ice nucleation, and inspires our interest in pursuing a more detailed perception of the specific effects of transitional and rotational order of IW. To our best knowledge, there is no report on the hydrogen rearrangement influence on ice nucleation with oxygen lattice interference eliminated up to now.
In this article, based on all-atomic MD simulations, we found that the formation of an ice-like oxygen lattice of IW alone is not sufficient to aid ice nucleation, and the hydrogen polarization of IW induced by substrates also sensitively regulates freezing of the top water. This hydrogen dominating ice nucleation will generate fresh insight into the molecular mechanism of heterogeneous ice nucleation, and a broader perspective on the lattice matching mechanism as well.
In the simulations, the Coulombic interaction is calculated based on the particle mesh Ewald method with slab correction.39 It has been noted that the water structures for this model of AgI with the slab correction are very likely unphysical.40 However, in this work, we apply the AgI-like substrate to achieve the polarized IW rather than to direct study the ice nucleation on the real AgI surfaces. The possible effects of the unphysical water structure is not key for our purpose. We generated the polarized IW without the AgI-like substrate to verify this in this work.
For probing the freezing of water, we count the number of maximal ice clusters during a 50 ns regular MD simulation, following the method of Dellago and Doye;41–43 here a molecule is identified as ice or water based on its orientational order,44 and we group hydrogen-bonded ice molecules as clusters.
(1) |
(2) |
Here water molecules in ice are classified into five types according to the direction of its OH bond, and the numbers (or concentrations) of the five types of water are denoted as ck, k = 1,…,5, respectively, see Fig. 1. For example, as the ordered form of ice Ih, ice XI (ξ = 1) only has type 1 and 2 water molecules. There is no significant statistical difference between these two hydrogen polarity definitions in our cases.
Fig. 1 Five kinds of water molecules in ice with different OH directions. A guide view for different ice structures with the same lattice but different hydrogen polarity is also presented. |
On AgI substrates,17 we verify the formation of the IW layer with almost perfect ice lattice, and the freezing of water on the surfaces happens within 10 nanoseconds at 260 K. To study if IW with ice-like lattice but various polarizations facilitates the freezing of top water, we apply soft harmonic springs (k = 50 kcal mol−1 Å−2) to constrain the oxygen atoms of the first IW layer to keep its ice-like lattice. Additional charge (by directly changing the charge of the cation and anion of the AgI substrate) is applied to polarize the IW. The ice lattice structure remains and the hydrogen polarity increases from 0 to 0.3 while increasing the charge of the ions of AgI from 0.3e to 1.8e. The original AgI has the ion charge 0.6e, where e is the basic unit of charge, equal to that of a proton.
In order to emphasize the role of IW rather than the substrates, we also generate a pure polarized ice slab (without any another substrate surface) as the IW with ice-like lattice. Many different methods can be applied to generate this kind of polarized IW. For example, we may fix oxygens of the regular ice Ih and apply a strong electric field to get a polarized ice slab. In this work, we follow another way, first relaxing the hydrogens of some layers of ice XI at a higher temperature to achieve a few layers of ice with layer-varied partial polarity, then applying an electric field (one between −0.8 and 1.2 V nm−1, along the c axis) which makes the polarity of every ice layer be the same as any desired value between 0 to 0.7. The obtained ice-like slab is applied as the substrate by constraining all of its oxygen and hydrogen positions for checking the effect on ice nucleation on IW.
Pedevilla and coworkers presented a heterogeneous seeding approach (HSEED)53 to overcome the difficulty, which enables the assessment of the ice nucleation ability upon crystalline substrates. The HSEED approach presets multiple possible ice nuclei, e.g., five initial combinations of crystal polytype and face exposed to the substrate: Ih(001), Ih(100), Ih(110), Ic(001), and Ic(111), and calculates the adsorption energy of water molecules on the nuclei, to pinpoint which nucleus is most likely to form on substrates.
Here, we present a different implementation to achieve the suitable ice nucleus on a substrate by gradually adjusting the shape, crystal polytype, position and face of the ice nucleus on the substrate through a repeated melting and growing process: (1) we preset a sphere-cap (or a spherical) hexagonal ice (Ih) nucleus and locate it nearby the substrate then immerse in supercooled water as the initial conformation; (2) we choose a few supercooled temperatures within a (small) range where the ice nucleus is predicted to be able to grow obviously at its low limit but melt obviously at the high limit. Then we simulate the system from the initial conformation for a segment of time, e.g., 10 ns, at each of these temperatures, respectively, to adjust the ice nucleus; (3) we choose one from these trajectories where the size and shape of the ice nucleus was most obviously adjusted (but not completely melting out or growing up too large). The final conformation is resetting the chosen trajectory as a new initial conformation to repeat the step (2) and (3). The corresponding temperature and a few of its neighbor values were applied as the new simulation temperatures to adjust the ice nucleus. The steps were repeated a few times, until the shape and size of the ice nucleus had already changed a lot and did not change obviously any more. Thus we achieved a suitable ice nucleus on the substrate, and the middle value of the two neighboring temperatures where the ice nucleus grows and shrinks respectively during the final simulation segment is the corresponding temperature where the ice nucleus is critical.
The freezing processes upon IW with different hydrogen polarities ξ are shown in Fig. 2. For small ξ, an ice-like IW layer can quickly form with the ice Ih lattice within 10 nanoseconds at T = 260 K, and grow fast, similar to previous results.16,17 However, as ξ increases by increasing the charge of the cation and anion of the AgI substrate, the formation of ice clusters becomes difficult. The hydrogen bond network of IW is fractured when ξ > 0.2, and water on top cannot freeze within the 50 ns, even though the IW remains the same ice-like oxygen lattice by constraining these oxygen atoms.
As shown in the inset of Fig. 3a, while ξ = 0.09 (the corresponding charge of ions is about 0.6e, similar to that of the original AgI), the hydroxyl groups of IW almost equally point to the two sides of IW, where ice nucleation is easy. But when ξ = 0.21 (the corresponding charge of the ions is about 1.4e, similar to that of BaF2), more hydroxyl groups point toward the substrate and fewer hydroxyl groups point to the reverse direction, the water side, where the ice nucleation is difficult. Thus, the IW with ice-like lattice can be hydrogen ordered20,45,54 (large ξ) or hydrogen disordered (small ξ) providing different abilities to facilitate ice nucleation of top water.
By simulating 50 ns each from initial liquid water at various temperatures, we get an approximate phase diagram of water freezing on substrates with the ice-like lattice but hydrogen polarized IW, see Fig. 3b. The freezing temperature of water abruptly decreases with the increasing ξ of IW. When ξ ≈ 0, water freezes at 269 K, approaching the melting temperature of the applied TIP4P/ice water model, 272 K. On increasing the hydrogen polarity of IW, when ξ ≈ 0.09, water is found to freeze around 265 K, and when ξ ≈ 0.21 the freezing temperature decreases to about 250 K.
As shown in Fig. 4, in the absence of AgI-like substrates, the freezing of supercooled water is also found to become more difficult as the hydrogen polarity of the ice-like polarized IW increases. At 265 K, water freezes on the ice-like polarized IW layers (usually 4–6 layers) with ξ = 0.10, but does not form an ice cluster at ξ = 0.18 during 20 ns regular MD simulations. We also carried out simulations at 255 K, where water freezes at ξ = 0.10 and ξ = 0.18, but not at ξ = 0.43 within 20 ns. This result indicates that the heterogeneous free energy barrier of ice nucleation is obviously dependent on the hydrogen polarity of the ice-like IW. This result is in agreement with the phase diagram of ice nucleation on AgI-like substrates shown in Fig. 3b.
We preset ice nuclei on the polarized IW with various ξ to get the critical ice nuclei and the corresponding temperatures. Fig. 5 illustrates the whole simulation scheme on the ice-like IW with ξ = 0.16. The ice nucleus is sufficiently adjusted to change its shape and its size (initial 2000, growing to about 3000, and finally back 2350 molecules) after 6 × 10 ns simulations at a few preset temperatures. Then we simulate the final 10 ns trajectories at a few neighboring temperatures to find the ice nucleus shrinks at 259 K but grows at 258 K. Thus we get the middle temperature T = 258.5 K where the ice nucleus is thought to be critical.
By extracting the outlines of the final ice nuclei from the average density of ice nuclei ρ = 0.5ρI, we find that all the critical ice nuclei are approximately sphere-caps, as expected from classical nucleation theory (CNT), except for a small deviation in the first layers for the small and large ξ cases, see Fig. 6. Here ρI is the density of bulk ice, about 0.906 g cm−3 in this model.
The critical temperatures of heterogeneous nuclei (about 2000 molecules) upon IW with different polarities is estimated. As shown in Table 1, the corresponding temperature of the critical ice nuclei with similar size is obviously dependent on the polarization of the IW.
No. of iterations | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
ξ = 0.14 | 263 ± 2 | 263 ± 1 | 263 ± 1 | 262 ± 1 | 262 ± 1 | 262 ± 1 | 262 ± 1 |
ξ = 0.16 | ∼255 | >256 | ∼257 | 257 ± 1 | 258 ± 1 | 258 ± 1 | 258 ± 1 |
ξ = 0.27 | ∼255 | >256 | ∼256 | 257 ± 1 | 258 ± 1 | 257 ± 1 | 257 ± 1 |
ξ = 0.39 | ∼255 | ∼255 | ∼255 | 255 ± 1 | 255 ± 1 | 255 ± 1 | 255 ± 1 |
ξ = 0.53 | ∼255 | ∼255 | ∼254 | ∼254 | 253 ± 1 | 252 ± 1 | 252 ± 1 |
From the simulations, we have the size Nc, radius R, the (apparent) contact angle θ of the sphere-cap critical nucleus, the corresponding (supercooled) temperature and the free energy barrier ΔG of nucleation, shown in Table 2. Here the free energy barriers are estimated from the CNT, . Here is the shape factor of a spherical cap.
ξ | θ | f(θ) | R | T c (K) | ΔG |
---|---|---|---|---|---|
0.14 | 72 | 0.28 | 10.0 | 262 ± 1 | 50 |
0.16 | 78 | 0.35 | 8.8 | 258 ± 1 | 32 |
0.27 | 90 | 0.50 | 7.7 | 257 ± 1 | 40 |
0.39 | 98 | 0.60 | 6.9 | 255 ± 1 | 37 |
0.53 | 134 | 0.94 | 6.1 | 252 ± 1 | 42 |
In Fig. 7, we find that the inverse of the radius R of a critical nucleus is proportional to the corresponding supercooled temperature, 1/R ≈ κΔT, with κ ≈ 0.03 nm−1 K−1. The result is in good agreement with the expectation of CNT, and . Here is about 0.0043 kcal mol−1 K−1,52 the ice-water surface tension γ was chosen as a typical value of about 26 mN m−1, and Δμ is the chemical potential difference between ice and water.
The cosine of contact angle is found to be linearly related to ξ in the whole range 0 < ξ < 1, as shown in Fig. 7. From the Young's equation, we have
(3) |
Considering the fact that the IW with ξ = 0 is similar to the normal hexagonal ice, we have γice,IW(ξ) = γ(δ1 + k1ξ +…), while γwater,IW(ξ) = γ(1 − δ2 + k2ξ +…). Here both δ1 and δ2 are small positive values, and k1 > k2 > 0, since liquid water is more flexible than an ice nucleus in terms of rearranging its conformations on IW. Therefore, we have, δ1 + δ2 ≈ 0.33, and k1 − k2 = 2.57. The higher order dependence of surface tensions on ξ seem very small (or cancel each other) even when ξ approaches unity, where the completely polarized IW distorts the lattice of both itself and the growing ice nucleus to avoid dangling hydrogen bonds. It is a little surprising that the macroscopic-level picture based on surface tension describes well the ice nucleation happening on the nanometer scale. Identifying the physical reason behind this is interesting for the next studies.
Footnote |
† Current address: College of Physics and Electronic Engineering, Heze University, Heze 274015, China. |
This journal is © the Owner Societies 2020 |