Three-dimensional ordering

Eurther heat treatment in excess of 2000°C is referred to as graphitization. Eiber stmcture further densifies as molecular packing and orientation increase. At temperatures of 3000°C or above, the fiber stmcture begins to approach a truly graphitic stmcture with three-dimensional order. Typically, fiber strain to failure decreases as the carbonization temperature exceeds 1500°C because of reaction of impurities with the carbon fiber and the development of an increasingly flaw-sensitive graphitic stmcture (31,34)... 

Regarding Case 1, it is known that the rotator phases of -paraffins are three dimensionally ordered solids with molecules in aW-trans conformation, their specific volumes, Vh, and specific entropies, Sh, are closer to corresponding values and for the orthorhombic phases than they are to those for the melt and Sm In contrast,... 

For rigid-chain crystallizable polymers, spontaneous transition into the nematic phase is accompanied by crystallization intermolecular interactions should lead to the formation of a three-dimensional ordered crystalline phase. 

In the first case, there is only partial instead of complete long-range three-dimensional order. Fiber spectrum features are diffuse haloes (besides sharp reflections) on the layer lines. 

Let us consider a structural limiting model, in which the polymer molecules, presenting a periodic conformation, are packed in a crystal lattice with a perfect three-dimensional order. Besides this limiting ordered model, it is possible to consider models of disordered structures having a substantially identical lattice geometry. 

Here, we have arranged the layers on a two-dimensional structure, even though the layers are arranged in three dimensional order. Note that only two crystallographic axes are indicated. We call this the natural stacking sequence because of the nature of the hexagonal close- packed lattice. 

In a crystal atoms are joined to form a larger network with a periodical order in three dimensions. The spatial order of the atoms is called the crystal structure. When we connect the periodically repeated atoms of one kind in three space directions to a three-dimensional grid, we obtain the crystal lattice. The crystal lattice represents a three-dimensional order of points all points of the lattice are completely equivalent and have the same surroundings. We can think of the crystal lattice as generated by periodically repeating a small parallelepiped in three dimensions without gaps (Fig. 2.4 parallelepiped = body limited by six faces that are parallel in pairs). The parallelepiped is called the unit cell. 

Sadakane, M., Asanuma, T., Kubo, J. et al. (2005) Facile procedure to prepare three-dimensionally ordered macroporous (3DOM) perovskite-type mixed metal oxides by colloidal crystal templating method, Chem. Mater. 17, 3546. 

Examples of mesomorphic forms characterized by disorder in the conformation of the chains have already been described in Section 2.6. For instance, a mesomorphic form is present in the high-temperature form I of polytetrafluoro-ethylene.106,107 In this phase the chains are in disordered conformation due to the presence of helix reversals along the chains.108-110 Moreover, intermolec-ular disorder is also present due to the random rotations of the chains around the chain axes.109 A long-range three-dimensional order is present only in the pseudohexagonal placement of the chain axes.107,109... 

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