Polyhedral deformation

Pre-organizing for metallacarboranes to be deliberately overcrowded can have significant structural effects. Work in our group has focused on polyhedral deformation and on low-temperature isomerization. 

Polyhedral deformation can result in unusual, open pseudocloso) structures, which, although not represented on the Wade-Williams matrix, appear structurally to lie between closo and hypercloso forms. The further discovery of partially deformed (semipseudocloso) species supports the idea of a continuum of structure type, which can, at least in part, be controlled by judicious use of substituents with differing steric demands. 

As was mentioned in the introduction, HIPEs contain an internal phase volume fraction greater than 0.74. Since this is the maximum volume which can be occupied by uniform, undeformed spherical particles, the dispersed phase droplets must either be non-uniform, i.e. polydisperse, or deformed into non-spheri-cal, polyhedral cells. 

A foam consists of a high volume fraction of gas dispersed in a liquid where the liquid forms a continuous phase. Wet foams with a high water content, e.g. immediately after the formation, can have more or less spherical bubbles. As a consequence of a drainage process of the foam lamellae, the wet foam loses water with time. Due to the resulting high volume fraction of gas, the bubbles are no longer spherical but they are deformed into a polyhedral shape. The polyhedra are separated from each other by thin liquid films. The intersection lines of the lamella are termed plateau borders (see Figure 3.28). 

In a monodisperse foam the deformation of spherical bubbles and formation of films at the places of their contact starts when the gas content in the system reaches - 50% (vol.) for simple cubic bubble packing or 74% for close (face-centred) cubic or hexagonal packing (foam expansion ratio - 4). In a polydisperse foam the transition to polyhedral structure starts at expansion ratio n - 10-20, according to [ 10] but, as reported in [51], this can occur at n < 4, the latter being more probable. The structure which corresponds to the transition of bubbles from spherical to polyhedral shape is called occasionally honeycomb structure. 

In [64] the possible stable configurations of films in polyhedral foams is discussed from the thermodynamic point of view that any disperse system tends to minimum surface energy. Almgren and Taylor [64] modelled the shape of the films and the angles between them with wire devices and studied several film configurations. They established that only film configurations which obey Plateau laws are stable with respect to minor deformations. 

Further studies by electron microscopy on some of the samples exhibiting the Pm3n cubic phase show the existence of grain bormdaries and stacking faults [118]. These are all consistent with the presence of quasi-spherical assemblies or more precisely to polyhedral-like micelles, and moreover suggest that the supramolecular spheres are deformable, interacting with one another through a relatively soft pair potential [119]. The majority of such quasi-spherical assemblies are thus distorted into an oblate shape. 

A foam is a disperse system that consists of gas bubbles separated by liquid layers. Because of the significant density difference between the gas bubbles and the medium, the system quickly separates into two layers, with the gas bubbles rising to the top, which may undergo deformation to form polyhedral structures this process will be discussed in detail below. 

Another striking example is the T symmetry of tetrakis[trimethylsilyl] silane (25), the discussion of which is deferred to the last section, dealing with high-symmetry chiral polyhedral symmetry. An interesting conformational deformation in a crystal lattice has been analyzed by X-ray crystallography coupled with force-field calculations (26). 

A polyhedral isomerization may be defined as a deformation of a specific polyhedron until its vertices define a new polyhedron t 2. Of particular interest are sequences of two polyhedral isomerization steps in which the polyhedron... 

The role of polyhedra in the static description of chemical structures, including those of coordination compounds, makes the dynamic properties of polyhedra also of considerable interest. The central concept in the study of dynamic properties of polyhedra is that of a polyhedral isomerization, which may be defined as the deformation of a specific polyhedron lIi until the vertices define a new polyhedron II2. Of particular interest are sequences of two polyhedral isomerization steps Hi 112 113 in which the polyhedron II3 is equivalent to the polyhedron Hi but with some permutation of the vertices. Such a polyhedral isomerization process is called a degenerate polyhedral isomerization with II2 as the intermediate polyhedron. A degenerate polyhedral isomerization in which the intermediate II2 is a planar polygon may be called a planar polyhedral isomerization. 

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