Layer planes

The smectic A phase is a liquid in two dimensions, i.e. in tire layer planes, but behaves elastically as a solid in the remaining direction. However, tme long-range order in tliis one-dimensional solid is suppressed by logaritlimic growth of tliennal layer fluctuations, an effect known as tire Landau-Peierls instability [H, 12 and 13]... 

Mechanical Properties. The hexagonal symmetry of a graphite crystal causes the elastic properties to be transversely isotropic ia the layer plane only five independent constants are necessary to define the complete set. The self-consistent set of elastic constants given ia Table 2 has been measured ia air at room temperature for highly ordered pyrolytic graphite (20). With the exception of these values are expected to be representative of... 

The stmcture of activated carbon is best described as a twisted network of defective carbon layer planes, cross-linked by aHphatic bridging groups (6). X-ray diffraction patterns of activated carbon reveal that it is nongraphitic, remaining amorphous because the randomly cross-linked network inhibits reordering of the stmcture even when heated to 3000°C (7). This property of activated carbon contributes to its most unique feature, namely, the highly developed and accessible internal pore stmcture. The surface area, dimensions, and distribution of the pores depend on the precursor and on the conditions of carbonization and activation. Pore sizes are classified (8) by the International Union of Pure and AppHed Chemistry (lUPAC) as micropores (pore width <2 nm), mesopores (pore width 2—50 nm), and macropores (pore width >50 nm) (see Adsorption). 

The word particle has become so widely used ia the technical mbber and carbon black Hterature that it is convenient to retain the term when ia fact nodule is meant. The layer planes are curved, distorted, and of varyiag size. They also iatersect and interconnect one particle or nodule with its neighbors. This type of stmcture has been termed paracrystalline. It is obvious that iadividual particles do not exist ia carbon blacks, with the exception of thermal... 

Fig. 6. Aromatic layer plane with functional side groups.

Surfaces that do not have strong surface chemical bonds that were broken tend to be nonpolar and are not readily wetted. Substances such as graphite and talc are examples that can be broken along weakly bonded layer planes without rupturing strong chemical bonds. These solids are naturally floatable. Also, polymeric particles possess... 

For both forms of graphite the in-plane C-C distanee is 142 pm, i.e., intermediate between Csp Csp and CspMl sp bond lengths, 153 and 132 pm respeetively. Table 1. Consideration of the resonanee struetures between earbon atoms in the plane show that eaeh C-C bond in the earbon layer plane has about one third double bond character. Carbon layer planes (of various dimensions... 

The 8 functions limit the non-vanishing regions of / -space to discrete layer planes perpendicular to k. These layer planes are infinitely sharp, because the helix was assumed to be infinitely long. Limiting the summation to a finite length of the helix would lead to broadening of these layer planes. 

Figure 8.16 Layer-plane sequence along the c-axis for graphite in various stage I -5 of alkali-metal graphite intercalation compounds. Comparison with Fig. 8.15 shows that the horizontal planes are being viewed diagonally across the figure. /,. is the interlayer repeat distance along the c-axis.

As expected from their structures, the elements are poor conductors of electricity solid F2 and CI2 have negligible conductivity and Br2 has a value of 5 X 10 ohm cm just below the mp. Iodine single crystals at room temperature have a conductivity of 5 x 10 ohm cm perpendicular to the be layer plane but this increases to 1.7 x 10 ohm cm" within this plane indeed, the element is a two-dimensional semiconductor with a band gap g 1.3eV (125kJmol" ). Even more remarkably, when crystals of iodine are compressed they become metallic, and at 350kbar have a conductivity of 10" ohm" cm", The metallic nature of the conductivity is confirmed by its negative temperature coefficient. 

Figure 15. Arrangement of the Mn - O layers and separating sheets according to Giovanoli [3]. The layer structure can be (a) completely ordered or (d) completely disordered (turbostratic disorder). The cases (h) and (c) represent situation between the two extremes, (b) Disorder of the interlayer atoms or molecules but an ordered stacking of the Mn - O layers with constant layer distance, (c) Disorder of the interlayer atoms and an incommensurate shift of the complete Mn - O sheet within the layer plane, resulting in an incommensurate superstructure along the r -direction (perpendicular to the layer) and in a diffuse distribution of the electron density in this layer, resulting in a lower contribution of this layer to the 0 0 / reflections. (Adapted from Ref. [47]).

HOPG cylinders showed that intercalation starts close to the basal planes and proceeds thence to the central layers. Cylinders capped at both ends with glass caps and grease are not intercalated. The layer system is split into a number of discs at a rate that increases with the degree of alignment of layer planes. For non-heat-treated PG, the threshold pressure increases with the number of layer planes in the sample. Similar results confirming this mechanism have been obtained with metal halides (H13). A mechanism of intercalation based on these results has been discussed by Hooley (H22). 

Kurogoshi and Hori [ 104] determined the crystal structures of the mesogenic ethyl and butyl 4-[4-(4-n-octyloxybenzoyloxy)benzylidene]aminobenzoates. The compounds have different phase sequences crystal-smectic A-nematic-isotropic and crystal-smectic C-smectic A-nematic-isotropic for the ethyl and butyl compounds, respectively. Both compounds have layer structures in the solid phase. The butyl compound contains two crystallographically independent molecules. Within the layers, adjacent molecules are arranged alternately so as to cancel their longitudinal dipole moments with each other. In the ethyl compound the core moieties are almost perpendicular to the layer plane, while in the butyl compound these moieties are tilted in the layer. 

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