Clathrate Hydrates. Группа авторов

was not settled until Pauling's definitive paper appeared in 1935 [84]. This puts knowledge of the ice structure within the timeframe of von Stackelberg's work.

In the late 1930s, von Stackelberg at the University of Bonn initiated his 20‐year research efforts on the composition, structure, and thermodynamics of hydrates. His pioneering work on crystallographic studies using X‐ray diffraction especially played a key role in revealing the true nature of the hydrates. Von Stackelberg classified the stoichiometry of the hydrates from M·6H₂O to M·15H₂O based on the size of the hydrate forming molecules, see Figure 2.7. The first X‐ray results, for single crystals of SO₂ hydrate and of the double hydrate of CHCl₃ and H₂S and for 10 other polycrystalline hydrates, were published in 1949 [85]. He found a cubic unit cell, space group with a unit cell constant of 12 Å, and, for the double hydrates, a probable space group of P4₂32. As the X‐ray film was lost during the war, proper intensity measurements were not available for the determination of a detailed structure, including the guest positions, in this initial work; however, a structure for the water lattice of the hydrates was proposed. He suggested that the hydrate structure was a kind of ice in which each water molecule was connected to four neighbors which contained voids of two different geometries large enough to hold small molecules. Influenced by Villard's formula, he assumed there were six times as many water molecules as holes and variability of composition was ascribed to variable occupancy of the voids. Von Stackelberg determined the cubic unit cell of the SO₂ hydrate to have a lattice constant of 12 Å and contain 48 water molecules with the ideal gas molecule content of 8. This first structure did provide an explanation of some of the key features of gas hydrates; however, there were some problems that suggested that the hydrate lattice was not easily relatable to the structure of ice, e.g. the O⋯O atom distances (2.42−2.60 Å) were too short and the O–O–O angles (61°–145°) too far from the tetrahedral angle. A year later, it remained for Walter Claussen [86] to use chemical intuition to suggest the pentagonal dodecahedral water cage as the basis for clathrate hydrate structures even before the single‐crystal X‐ray crystal structures of clathrate hydrates were solved.

      Figure 2.7 von Stackelberg's characterization of the stoichiometry of hydrate phase formation based on the size of the hydrate‐forming molecules (Molekelgröße). The maximum molecular dimension (Max. Molekel‐Länge) and guest sizes with no perceived hydrate formers (Keine Hydrate) are indicated. Guests within each size range, which were not considered to form hydrates (Keine Hydratbildner), are shown in the left of the vertical axis, and those that form hydrates (Hydratbildner) are shown on the right. Source: Von Stackelberg [81].

2.6 Solving the Gas Hydrate Puzzle

Finally, the early 1950s saw the definitive structural work on the hydrates as reported by Claussen [86, 87], von Stackelberg and coworkers [88], and Linus Pauling and Richard Marsh [89], who at about the same time showed that the “gas” and “liquid” hydrate structures were clathrates, a term coined a few years earlier by H. Marcus Powell (Figure 2.8) to describe the compounds of the β‐quinol host with small guest molecules [90]. We now know these two clathrate hydrate families as Structure I and Structure II hydrates.

      Figure 2.8 Pioneers of clathrate science in the mid‐1900s. From left to right, E. Hammerschmidt, H. Marcus Powell, and Mark Freiherr von Stackelberg. Source: Reproduced with permission from the Southwest Retort, Reproduced with permission from the Hertford College, University of Oxford, Reproduced with permission from the Department of Chemistry, University of Bonn.

      Claussen started [86] with the notion that the pentagonal dodecahedron should be suitably spherical and have 108° angles at the vertices not appreciably different from the 109.5° tetrahedral angles required to accommodate proper hydrogen bonding in water. This regular convex polyhedron likely would not have been an unfamiliar shape to many researchers: since ancient times, the regular pentagonal dodecahedron has been known as one of the five Platonic solids [91]. It turned out to be a key building block of the three major hydrate structural families. Using atomic model sets, Claussen (with some initial aid from A.M. Bushwell and data from the von Stackelberg group) constructed a cubic unit cell containing 136 water molecules arranged to form 16 dodecahedra and eight larger hexakaidecahedra comprised of 4 hexagonal and 12 pentagonal faces. The structure was obtained by arranging pairs of dodecahedral water cages, diametrically opposed, around the sites of a diamond lattice in a cubic unit cell, see Figure 2.9. Claussen obtained the structure by arranging two diametrically opposed water molecules of dodecahedral water cages on adjacent sites of a diamond lattice in a cubic unit cell. The angles of the water molecules in the dodecahedron were next distorted so the diametrically opposed water molecules make an exact tetrahedral angle, as required by the diamond lattice [86, 92]. This arrangement accounts for the 16 dodecahedral cages of the cubic structure II unit cell. The remaining void space of the unit cell was filled with hexakaidecahedra formed around dodecahedra. An alternative description of the cage arrangements in the unit cell based on the hexakaidecahedra is shown in Figure 2.9. von Stackelberg and Müller [91] confirmed this model as the correct structure for liquid hydrates with large guests like chloroform and ethyl chloride as well for double hydrates with H₂S. The space group was and the unit cell parameter 17.2 Å. The large guests filled all of the large hexakaidecahedral cages (H) in the structure, with the small help gas H₂S molecules occupying the small dodecahedral cages (D), thus giving an ideal composition of 8M_L·16M_S·136H₂O if all cages are filled.

The structure for the gas hydrates, with smaller guest molecules, was solved quickly thereafter, almost simultaneously by Claussen (again using molecular models) [92], Müller and von Stackelberg [93], and Pauling and Marsh [87]. The 12 Å unit cell belonged to the space group and contained 46 water molecules forming two pentagonal dodecahedra and six tetrakaidecahedra (T), each constructed of 12 pentagonal and 2 hexagonal faces. Claussen constructed the structure of this phase by considering a body‐centered cubic lattice of the dodecahedral cages with eight dodecahedral water cages in the corners and one (rotated) cage in the center, see Figure 2.9 [88]. The D cages are connected with appropriate number of water molecules to obtain a space‐filling structure. The large T cages filled in the remaining space in the unit cell. The ideal composition is 2M_S·6M_L·46H₂O (M·5¾H₂O) if all cages are filled, 6M_L·46H₂O (M·7⅔H₂O) if only the large T cages are filled.

      In the 1960s, George A. Jeffrey (Figure 2.10) and coworkers complemented von Stackelberg's structural determinations by performing single‐crystal X‐ray diffraction studies of a number of clathrate hydrate materials [89]. In addition to verifying general aspects of the structures of the hydrate phases, Jeffrey was able to determine guest positions inside hydrate cages. Jeffrey played an important role in the systematic classification of clathrate hydrate phases for a large family of molecular and ionic substances [94].