Interlayer distances

A second calculation was done for a two-layer tubule using density functional theory in the local density approximation to establish the optimum interlayer distance between an inner (5,5) armchair tubule and an outer armchair (10,10) tubule. The result of this calculation yielded a 3.39 A interlayer separation... 

Abstract—The geometrical conditions pertaining to closure, helicity, and interlayer distance between successive layers with circular cross-sections in carbon tubules (nanotubes) have been examined. Both the intralayer length of the C—C bonds and the interlayer distance between successive layers must vary with the radius of the layers. The division into groups of the sheets in nanotubes is found to be due to the reciprocal interaction of the interlayer distance variations and of the conditions required to maintain constancy of the pitch angle. 

Key Words—Carbon nanotubes, pitch angle, helix angle, interlayer distance, carbon-carbon intralayer distance. 

The consequence of the presence of scroll helicity in a tubule is expected to be that any increase (decrease) of the intralayer C—C distance G will increase (decrease) the local length of the spiral, but not necessarily the mean interlayer distance, since the scroll can easily adapt its radius of curvature to minimize, if necessary, any energetic strain due to a stress in the local bond lengths. 

Referring now to the symmetric tubule, the interlayer distance between two layers of radii r and... 

We observed in some cases coaxial arrangement of the outermost and an inner tube. The outer tube may be terminated and the adjacent inner one is imaged si-multaneously[4]. We measure an interlayer spacing of 3.4 A, which is about the graphite interlayer distance (3.35 A). 

If one attempts to build a second coaxial knee around the ideal (12,0)-(7,7) knee at an interlayer distance of 3.46 A, the second layer requires a (21,0)-( 12,12) knee. In this case, the axis going through the centers of the heptagon and of the pentagon of each tubule are not aligned. Moreover, the difference of diameter between the two connected segments of each knee is not the same for the two knees [Fig. 3(b)]. 

The optimised interlayer distance of a concentric bilayered CNT by density-functional theory treatment was calculated to be 3.39 A [23] compared with the experimental value of 3.4 A [24]. Modification of the electronic structure (especially metallic state) due to the inner tube has been examined for two kinds of models of concentric bilayered CNT, (5, 5)-(10, 10) and (9, 0)-(18, 0), in the framework of the Huckel-type treatment [25]. The stacked layer patterns considered are illustrated in Fig. 8. It has been predicted that metallic property would not change within this stacking mode due to symmetry reason, which is almost similar to the case in the interlayer interaction of two graphene sheets [26]. Moreover, in the three-dimensional graphite, the interlayer distance of which is 3.35 A [27], there is only a slight overlapping (0.03-0.04 eV) of the HO and the LU bands at the Fermi level of a sheet of graphite plane [28,29],... 

These batteries incorporate a polyacenic semiconductor (PAS) for the active material of the positive electrode, lithium for that of the negative electrode and an organic solvent for the electrolyte. PAS is essentially amorphous with a rather loose structure of molecular-size order with an interlayer distance of 4.0 A, which is larger than the 3.35 A of graphite [56, 57]. 

Coke materials are generally made by heat-treatment of petroleum pitch or coal-tar pitch in an N2 atmosphere. Coke made from petroleum is called "petroleum coke" and that from coal is called "pitch coke". These materials have the closest-packed hexagonal structures. The crystallinity of coke materials is not so high as that of graphite. The crystallite size of coke along the c-axis (Lc) is small (about 10-20 A) and the interlayer distance (d value about 3.38-3.80 A) is large. 

Compound or mineral Approximate formula Symmetry Space Lattice constants Interlayer -distance (pm) Reference... 

Figure 4. Change in interlayer distance between Ni02 sheets upon charge for an Li/LiNi02 cell. The gap (shrinkage) of ca.0.3 A in the interlayer distance is associated with the formation of nickel dioxide (kNi02) for 0.75

Figure 9.7 Proposed structural models for Ru(OOOl) oxidation, where the O, S, and Ru atoms are represented by the open, lightly shaded, and heavily shaded circles, respectively. The interlayer distances are in nanometers and coverage in monolayers (ML). (Reproduced with permission from Wang et al. [2001].)...

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