Ultralow-Density Clathrate Ices and Phase Diagram under Negative Pressure
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摘要: 水不仅在地球上无处不在，而且在太阳系中（如彗星、小行星及巨行星的卫星上）也普遍存在。因此，探索存在于不同环境条件下不同形态的水冰晶体对物理学、化学、生物学、地球科学以及行星科学都有着重要意义。根据周围的环境条件（压强和温度），冰呈现出极其丰富和复杂的相图。目前，实验上已合成了18个晶体冰相，分别是ice Ic、ice Ih、ice II 直至ice XVII。此外，还有一些来自于笼形包合物的假想超低密度冰相，分别是I型、II型、H型、K型和T型笼形冰。近期，在实验室中合成的II型笼形冰（即ice XVI）出现在了水的负压相图中，极大地激发了人们去探索其他低密度笼形冰。结合带有色散修正的密度泛函理论计算和经典的蒙特卡罗、分子动力学模拟，我们预测了两个具有超低密度的立方笼形冰相，将其依次命名为s-III笼形冰（ρ=0.593 g/cm3）和s-IV笼形冰（ρ=0.506 g/cm3）。s-III笼形冰的元胞由2个二十六面体的大笼子（8668412）和6个十面体的小笼子（8248）组成。s-IV笼形冰的元胞中含有8个二十六面体的大笼子（12464418）、8个十二面体的中等尺寸笼子（6646）和6个八面体的小笼子（6246）。对于这两种笼形冰，超大尺寸的二十六面体水笼子以及不同笼子之间的独特堆积方式使它们的密度极低。把所有低密度冰相（其密度小于或者等于ice XI）考虑在内，我们基于TIP4P/2005模型势函数构建了水在负压下的p-T（压强-温度）相图。在s-II笼形冰下方的极低负压区域内，s-III和s-IV笼形冰取代了之前认为的s-H笼形冰，分别占据了高温和低温部分，因此在相图中产生了一个三相点（T=115 K，p=–488.2 MPa）。密度泛函理论计算表明，通过在二十六面体大笼子中添加合适尺寸的客体分子，比如十二面烷（C20H20）和富勒烯（C60），能够分别充分地稳定s-III和s-IV笼形冰晶格。基于实验室中已经制备出的无客体分子填充的s-II笼形冰，且被认定为ice XVI相，那么s-III和s-IV笼形冰很可能是ice XVIII或ice XIX的候选结构。它们一旦在实验室中被合成，则可以作为一种储存气体的材料用来封装气体分子（如H2、CH4、CO2等）。计算表明：s-III笼形冰在低温和室温下的储氢能力均为s-II的两倍左右，达到了美国能源部在海陆运输上制订的储氢目标。Abstract: Water is not only omnipresent on the Earth but also ubiquitous in the solar system such as on comets, asteroids, or icy moons of the giant planets. Hence, exploration of different forms of ice in different environment has significant implication to physical science, chemical science, bioscience, geoscience and planetary science. Depending on the surrounding conditions of pressure and temperature, water ice exhibits an exceptionally rich and complicated phase diagram. To date, at least eighteen crystalline ice phases (ice Ih, Ic, ice II to ice XVII) have been identified under laboratory conditions. In addition, there are many hypothetical ultralow-density ice phases from clathrate hydrates, such as structure I (s-I), structure II (s-II), structure H (s-H), structure K (s-K) and structure T (s-T) ices. Recently, the s-II clathrate ice (ice XVI) produced in the laboratory emerges in the negative pressure part of phase diagram, which stimulates greatly people to explore the other low-density clathrate ices. Using extensive Monte Carlo packing algorithm, classical molecular dynamins simulations, and dispersion-corrected density functional theory optimization, we predict two cubic clathrate ices with ultralow densities, and name them as s-III (ρ=0.593 g/cm3) and s-IV (ρ=0.506 g/cm3) clathrate ices. The unit cell of s-III clathrate ice is composed of two large icosihexahedral cavities (8668412) and six small decahedral cavities (8248), while the unit cell of s-IV clathrate ice is constructed by eight large icosihexahedral cavities (12464418), eight intermediate dodecahedral cavities (6646), and six small octahedral cavities (6246). For these two clathrate ices, the large-sized icosihexahedral cavities and the unique packed patterns among different cavities result in their record low densities. Considering all the low-density (lower than ice XI or equal to ice XI) ices, we construct a new p-T (pressure-temperature) phase diagram of water with TIP4P/2005 model potential under negative pressures. Below the deeply negative-pressure region of s-II clathrate ice, s-III and s-IV clathrate ices replace s-H clathrate ice, arising as the most stable ice phases in the high-temperature part and the low-temperature part, respectively. As a result, a triple point (T = 115 K, p = –488.2 MPa) appears in the phase diagram. The density functional theory calculations suggest that the s-III and s-IV clathrate ices can be fully stabilized by encapsulating an appropriate guest molecule such as dodecahedrane molecule (C 20H20) and fullerene molecule (C60) in the large cavity, respectively. Considering that the guest-free s-II clathrate ice has been produced in the laboratory, which is also recognized as ice XVI, both the s-III and s-IV clathrate ices can be viewed as potential candidates of ice XVIII or ice XIX. Computations show that the hydrogen storage capacities of s-III ice clathrate amount to nearly twice of those for the s-II ice clathrate at low temperature and room temperature, which satisfies the DOE ultimate target for on-board hydrogen storage.
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Key words:
- clathrate ice /
- phase diagram /
- negative pressure /
- ultralow-density
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图 2 证实一个大气压存在(a)和Huygens证实负压存在的实验示意(b)（76 cm的水银柱以上表示负压）[39]
Figure 2. Schematic representation of experiment to demonstrate the existence of the atmospheric pressure (a) and Huygens’s experiment to generate negative pressure under laboratory condition (b) (Above the approximately 76 cm mercury line the pressure is below zero[39].)
图 5 s-III笼形冰的结构示意:(a) 组成s-III相的两种水笼子（下面是由48个水分子形成的8668412笼子, 上面是由16个水分子形成的8248笼子；只显示了氧原子骨架）, (b)和(c) 分别是1×2超胞和2×2超胞（蓝色虚线表示氢键，红色球表示氧原子，白色棍棒表示氢原子）
Figure 5. Structure of s-III ice clathrate: (a) Two types of building water cages (bottom: 8668412, 48-molecule; top: 8248, 16-molecule; only oxygen frameworks are shown); repeated unit cells (1×2) (b) and 2×2 unit cells (c) (The hydrogen bond network is shown with blue dash line, red ball for oxygen, and white stick for hydrogen.)
图 6 ice i、ice XI和笼形冰相s-T、s-I、s-II、s-K、SGT及s-H的晶体结构（2 × 2元胞）(蓝色虚线表示氢键，红球表示氧原子，白球表示氢原子)
Figure 6. Crystal structures (2 × 2 unit cells) of ice i, ice XI, and clathrates of s-T, s-I, s-II, s-K, SGT and s-H (blue dash line for hydrogen bond, red ball for oxygen and white stick for hydrogen)
图 7 ice XI、ice i、s-K、s-I、s-II、s-H、s-III、SGT和s-T冰相的晶格结合能（平均到每个分子上）随体积变化的函数曲线（插图是42~48 Å3体积区间内的放大函数曲线。Elatt定义为Elatt = Ew ‒ Ecry/N，其中：N是晶体中水分子的数目，Ecry和Ew分别是晶体的总能和单个水分子的能量。）
Figure 7. Lattice cohesive energies (Elatt) for ice XI, ice i, s-K, s-I, s-II, s-H, s-III, SGT, and s-T clathrates as function of volume per water molecule (Inset is amplification of the region for the volume between 42–48 Å3. Elatt is defined as Elatt = Ew – Ecry/N, where N is the number of water molecules in the crystal, Ecry and Ew are the total energies of the ice/clathrate crystal and an individual water molecule, respectively.)
图 8 s-I、s-II、s-H、s-III、SGT、s-K、s-T和ice i的相对焓 （以ice XI为参考相）随负压变化的函数曲线
Figure 8. Relative enthalpy versus negative pressure for clathrate phases s-I, s-II, s-H, s-III, SGT, s-K, s-T, and ice i with ice XI as a reference
图 10 (a) C20H20分子封装在8668412水笼子中的结构示意；(b) 每个大笼子均被一个C20H20分子占据时s-III笼形冰的结构示意（显示的是2×2的超胞）
Figure 10. (a) Structure of an individual 8668412water cage with a C20H20 molecule encapsulated; (b) Structure of the s-III clathrate with one C20H20 molecule encapsulated in each large cavity (2×2 unit cell is shown for clearer view.)
图 11 在温度分别为77、240和298 K时，s-III和s-II笼形冰相在不同氢压下对氢气的吸附函数曲线 （中间图形中的黑色方框表示在温度为240 K、压强为300 MPa条件下获取的实验值[48-49]）
Figure 11. Hydrogen uptake versus hydrogen pressure for empty s-III and s-II ice clathrate lattices at temperatures of 77, 240 and 298 K, respectively (In the middle panel, the corresponding experimental value [48-49] for the s-II ice clathrate at 240 K and 300 MPa is marked by a black square.)
图 12 s-IV笼形冰的晶体结构：(a) 3种类型的水笼子（只给出氧原子骨架），从左到右依次是具有T对称性的48元12464418大笼子、具有T对称性的24元6646中等尺寸笼子、具有S6对称性的12元6246小笼子；(b) 和 (c) 是s-IV笼形冰立方元胞示意（蓝色虚线表示氢键，红球代表氧原子，白棍代表氢原子）
Figure 12. Crystalline structure of the s-IV ice clathrate: (a) Three types of cavities (only oxygen frameworks are shown), from left to right they are large cavity—48-member 12464418with T symmetry, intermediate cavity—24-member 6646 with T symmetry, and small cavity—12-member 6246 with S6 symmetry, respectively; (b) and (c) are the cubic unit cell of the s-IV ice clathrate (The hydrogen-bonding network is shown with blue dash line, red for oxygen, white for hydrogen.)
图 13 笼形冰相s-II、s-III和s-IV的相对焓值随压强变化的函数曲线（以ice XI相的焓值为参考）
Figure 13. Relative enthalpy per water molecule as a function of pressure for s-II, s-III, and s-IV ice clathrates, with the ice XI being as a reference
表 1 不同冰相和无客体分子填充的笼形冰的元胞内分子数目(Zcell)、元胞的平衡体积(Vcell)、平均O-O距离(dO-O)、密度(ρ)以及平均到每个分子上的晶格结合能(Elatt)(括号内的数据源于实验值)
Table 1. Number of water molecules per unit cell (Zcell), equilibrium volume of unit cell (Vcell), average distance between oxygen atoms in adjacent water molecules (dO-O), density (ρ), and lattice cohesive energy per water molecule (Elatt) for various ice and guest-free clathrate phases (The values in parenthesis are experimental data.)
Phase Zcell Vcell/Å3 dO-O/Å ρ/(g·cm-3) Elatt/(kJ·mol-1) ice XI 8 266 (257[17]) 2.785 (2.735[17]) 0.900 (0.930[17]) 62.84 (58.86[74]) ice i 8 280 2.785 0.855 61.31 s-I 46 1 692 2.765 0.813 61.38 s-K 80 2 962 2.765 0.808 60.76 s-II 136 5 059 (5 022[22]) 2.865(2.751[22]) 0.804 (0.81[22]) 61.37 s-T 12 453 2.795 0.792 60.23 s-H 34 1 325 2.785 0.768 60.79 SGT 64 2 650 2.765 0.722 59.27 s-III 48 2 423 2.765 0.593 55.77 
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表 2 通过vdW-DF2/DFT计算得到的ice XI、s-II、s-III和s-IV冰相元胞内的分子数目(Zcell)、元胞的平衡体积(Vcell)、平均O-O距离(dO-O)、平均氢键键长(dO···H)、密度(ρ)、平均到每个水分子上的晶格结合能(Elatt)（括号内的数据是实验值）
Table 2. Number of water molecules per unit cell (Zcell), equilibrium volume of unit cell (Vcell), average distance between oxygen atoms in adjacent water molecules (dO-O), average length of hydrogen bond (dO···H), mass density (ρ), and lattice cohesive energy per water molecule (Elatt) from vdW-DF2/DFT calculations for ice XI, s-II, s-III and s-IV ice clathrates (The values in parenthesis are experimental values.)
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