Interaction interlayer

Of particular importance to carbon nanotube physics are the many possible symmetries or geometries that can be realized on a cylindrical surface in carbon nanotubes without the introduction of strain. For ID systems on a cylindrical surface, translational symmetry with a screw axis could affect the electronic structure and related properties. The exotic electronic properties of ID carbon nanotubes are seen to arise predominately from intralayer interactions, rather than from interlayer interactions between multilayers within a single carbon nanotube or between two different nanotubes. Since the symmetry of a single nanotube is essential for understanding the basic physics of carbon nanotubes, most of this article focuses on the symmetry properties of single layer nanotubes, with a brief discussion also provided for two-layer nanotubes and an ordered array of similar nanotubes. 

However, in graphite, consistent with the weak interlayer interaction, the phonon dispersion parallel to... 

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],... 

Thus it seems that the electronic structure of the inner tube does not seriously affect that of the most outside tube in MWCNT. More detailed theoretical and experimental examination on MWCNT is obviously desirable for complete understanding of miscellaneous interlayer interaction. 

Realistic samples contain CNTs with different layer numbers, circumferences, and orientations. If effects of small interlayer interactions are neglected, the magnetic properties of a multi-walled CNT (MWCNT) are given by those of an ensemble of single-walled CNTs (SWCNTs). The distribution function for the circumference, p(L), is not known and therefore we shall consider following two different kinds. The first is the rectangular distribution, p(L) = mn)... 

The electronic properties of CNTs are of particular importance for hybrid materials and strongly depend on the structure of the CNTs. Theoretical [45-48] and experimental results [49] reveal that SWCNTs are either metallic or semiconducting depending on diameter and chirality, while MWCNTs are generally metallic (due to band alignment upon interlayer interactions). 

Roux, D. and Safinya, C.R. (1988) A synchrotron X-ray study of competing undulation and electrostatic interlayer interactions in fluid multimembrane lyotropic phases. J. Physique France, 49, 307-318. 

Some multilayered HTSC, for example Bi2Sr2CaCu20x, show an anisotropy of the elastic moduli inherent for layered crystals, and negative thermal expansion in a direction within the layer [16], which can be described by formula (2). At the same time for multilayered structures such as HTSC 1-2-3, where the interlayer interaction between all layers is of the same order, the intralayer interaction essentially varies from one layer to another layer. Local anisotropy of chain type is characteristic for layers with weak intralayer interaction (a layer of the rare earth and a layer of chains Cu-O). In these layers the root-mean-square displacement of atoms in a direction within the plane is beyond the classical limit at lower temperatures, and is appreciably higher than the root-mean-square... 

Detailed reviews of the physical properties of fullerenes under pressure already exist [13,14] and only a few important parameters will be discussed here. Since fullerene molecules have been found to be very incompressible the primary effect of high pressure is to decrease the intermolecular distance, which leads to changes in most physical properties. To a first approximation, solid molecular fullerites can be described as three-dimensional graphite , in the sense that the molecular interaction is similar to the interlayer interaction in graphite, and because compression can occur in three dimensions the bulk modulus B is close to one third of that of graphite. However, the molecular reorientation from a P-oriented to an H-oriented structure with increasing pressure leads to anomalies... 

The tt tt overlap interaction is the force that holds together two or more aromatic rings that tend to be parallel to each other in molecular packing. The most well-known example is the interlayer interaction in graphite, where the distance separating layers measures 335 pm. 

A reasonable question to ask is the following. If one layer (the acceptor layer) in CaBe2Ge2 is more stable than the other, the donor layer, why does the CaBe2Ge2 structure form at all Why doesn t it go into a ThCr2Si2 structure based on the acceptor layer alone The answer lies in the balance of covalent and dative interactions for some elements the binding energy gained in donor-acceptor interlayer interactions overcomes the inherent stability of one layer isolated.39c... 

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