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 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
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].
Figure 2.9 (a) The body‐centered cubic arrangement of the dodecahedral cages (blue color) in the structure I unit cell. Note that the dodecahedral cage in the center of the unit cell is rotated 90° with respect to the other cages. The space between the dodecahedral cages is divided into tetrakaidecahedral cages. (b) In the structure II unit cell, the dodecahedra are placed between non‐adjacent points of a diamond lattice shown by red spheres. The dashed red line connecting the diamond lattice points passes through the opposing pentagonal faces of the dodecahedral cage. (c) The packing of the properly placed dodecahedral cages (in blue) within the diamond lattice gives rise to hexakaidecahedral cages (clear color) surrounding the diamond lattice points. See Chapters 3 and 4 for a full discussion of these structures. Source: Figure prepared Dr. S. Takeya.
Figure 2.10 Pioneers of clathrate science in the mid‐1900s. Top row, George A. Jeffrey. Bottom row from left to right, Joan H. van der Waals, Donald W. Davidson, and Yuri A. Dyadin. Source: Reproduced with permission from International Union of Crystallography, Reproduced with permission from the Royal Netherlands Academy of Arts and Sciences, Reproduced with permission from Elsevier.
With the knowledge of the structures of hydrates in hand, what remained to be explained was the quantitative nature of the guest–host association, which was neither covalent nor ionic. This came by way of a statistical thermodynamic model of clathrate structures developed by Joan H. van der Waals (Figure 2.10), later collaborating with J.C. Platteeuw and coworkers, then working at Shell Laboratories in Amsterdam [95]. In this model, the guest molecules are “dissolved” in a host lattice of water molecules, hence the name “solid solution model.” The impetus for this work came from Powell's groundbreaking solution of the crystal structure of quinol guest–host compounds, the first clathrates. van der Waals' first model dealt with the quinol clathrates with space‐filling cavities of a single kind, which he later extended to clathrate hydrates with multiple cage types and guest molecules of one or more kinds. By assuming a specific mathematical form for the guest–host interaction potential, the solid solution theory provided a formalism to calculate cage occupancies at different temperatures and pressures, guest hydration numbers, and heats of enclathration. The potential chosen to describe guest–host interaction was the Lennard‐Jones 12–6 potential, thus allowing neutral, non‐polar guest molecules to be treated. After the model successfully described xenon hydrate properties, van der Waals and Platteeuw cautiously suggested that a hydrate with a non‐polar polyatomic guest molecule like methane might also be modeled this way. The van der Waals–Platteeuw theory is discussed in detail in Chapter 7.
2.7 Clathrate Hydrate Science – A New Era
With a successful description of hydrate structures and development of a statistical thermodynamic model, a new era in clathrate hydrate research began. In summary, up until 1960, except for a few isolated contributions (especially the diffraction studies in the 1950s), hydrate scientific research was dominated by European researchers stumbling across hydrates while doing other work, and, later, by doing concentrated curiosity‐driven scientific research on hydrates.
Starting in the 1950s and 1960s, physical chemistry‐based laboratory work of note in the area of gas hydrate research was carried out in the Applied Thermodynamics Laboratory in Delft (G.A.M. Diepen), the Institute of Inorganic Chemistry, Soviet (now Russian) Academy of Sciences, Siberian Branch, Novosibirsk (Yuri A. Dyadin, Figure 2.10), and the University of Pittsburgh (George A. Jeffrey). At the National Research Council of Canada in Ottawa, Donald Davidson (Figure 2.10) started a fundamental gas hydrate research program featuring multi‐technique approaches to study hydrate properties and dynamics. Contributions of these scientists are discussed in detail in the chapters that follow.
2.8 Clathrate Hydrates in Engineering
In contrast to the largely European efforts in developing clathrate hydrate science, the early North American hydrate experiences fell much more along practical lines. E. Hammerschmidt (see Figure 2.8), an engineer at Texoma Energy, read Schröder's book1 and review article, and in 1933, this led him to the realization that it was gas hydrates (and not ice) that formed plugs in gas
