Cylindrical structure model

So, despite the very small diameter of the MWCNT with respeet to the de Broglie wavelengths of the charge carriers, the cylindrical structure of the honeycomb lattice gives rise to a 2D electron gas for both weak localisation and UCF effects. Indeed, both the amplitude and the temperature dependence of the conductance fluctuations were found to be consistent with the universal conductance fluctuations models for mesoscopic 2D systems applied to the particular cylindrical structure of MWCNTs [10]. 

The analytical structural model for the topology of the nanostructure is defined in Isr (5). For many imaginable topologies such models can be derived by application of scattering theory. Several publications consider layer topologies [9,84,231] and structural entities built from cylindrical particles [240,241], In the following sections let us demonstrate the principle procedure by means of a typical study [84],... 

The structural model of GebeF and its recent overhaul by Schmidt-Rohr o show no indicahon of hydrophobic pores these models correspond to hydrated cylindrical fibrils or water-containing inverted cylinders with rather uniform distribution of charged surface groups at polymer-water interfaces. 

Wheeler s treatment of the intraparticle diffusion problem invokes reaction in single pores and may be applied to relatively simple porous structures (such as a straight non-intersecting cylindrical pore model) with moderate success. An alternative approach is to assume that the porous structure is characterised by means of the effective diffusivity. (referred to in Sect. 2.1) which can be measured for a given gaseous component. In order to develop the principles relating to the effects of diffusion on reaction selectivity, selectivity in isothermal catalyst pellets will be discussed. 

The three-way helical junctions all play key roles in directing the architecture of the ribozyme. The low-resolution electron density envelope is good enough to fit cylindrical representations of helical segments and has provided a starting point for more detailed structural modeling of the VS ribozyme to include the junctions and tertiary interactions. 

Because of the conceptual and mathematical simplicity of these models, they have been used recently to describe adsorption in zeolite and clay structures,53,54,55,56 based on either a cylindrical pore model or a packed sphere model. 

The common elements in the cited examples are the mechanical characteristics and the insulation properties. These advantages come, not only from macroscopic configuration of these materials (the hollow cylindrical structure of stubble for instance), but, mainly, from their microscopic structure. Most the vegetal fibres can be described by two models wood fibres and cotton fibres, which will be presented later. In order to better understand the mechanical properties of these fibres, let us first consider their molecular constitution, then their hierarchical structure. 

For studies where the periodicity of the graphite surface plays a role in the determination of properties, (e.g., low-temperature determinations of the structure of layers adsorbed on graphite), the Fourier expanded molecule-surface potential of Steele is commonly used [4—6, 19]. For complex geometries such as heterogeneous surfaces (see Bojan et al., coal pores [20]) and fuUerenes [21] (Martinez-Alonso et al., Ar on C q), a fuU sum of the direct atom—atom potentials is needed. In the recent simulation studies of carbon nanotubes, some studies have used asummed atom-atom potential description (e.g., see the work of Stan et al. [22]) while others use a continuum cylindrical pore model [23, 24]. 

As mentioned earlier, a structural model that many workers over the years had suggested for the bacterial photosynthetic apparatus consisted of the reaction center inside a cylinder of the core antenna. Based on the cylindrical structures ofLH2 ofRp. acidophila and LHl ofRs. rubrum, Kiihlbrandt presented a model in 19% for the bacterial photosynthetic unit as shown in Fig. 12 (A). It is of interest to note that in 1997 Walz and Ghosh prepared two-dimensional crystals ofthe LH1 RC complex from Rs. rubrum and obtained electron micrographs which confirmed that the RC is located inside the LHl cylinder, as LHl in the undissociated RC LHl complex has the same ring diameter as that for the reconstituted LHl reported by Karrasch et al . ... 

Gel-type, microporous, resins must swell to expose their catalytically active sites, whereas macroreticular resins have a permanent pore structure (inside these pores, catalytically active sites reside). Pores of the macroreticular resins can be described acceptably in terms of the conventional cylindrical pore model (pore diameter and volume). Pore structure, size, pore volume, and so on have been studied intensively in recent years. Examples of analytical techniques include X-ray microprobe analysis, ESR spectroscopy, NMR, and inverse steric exclusion chromatography (ISEC) the latter yields the best quantitative assessment of the nanomorphology of swollen resins. 

The structure of a tissue influences its resistance to the diffusional spread of molecules, as discussed previously (see Figure 4.18). Similarly, the structure of a tissue will influence its resistance to the flow of fluid. If Darcy s law is assumed, then the hydraulic conductivity, k, depends on tissue structure. Models of porous media are available in the simplest model, the medium is modeled as a network of cylindrical pores of constant length, but variable diameter. This model produces a relationship between conductivity and geometry ... 

A regular pore structure is found in crystalline zeolites or molecular sieves but when these materials are used as catalysts, tiny zeolite crystals (1-2 fj,m) are combined with a binder to make practical-size pellets (1-5 mm). Spaces between the cemented crystals are macropores of irregular shape and size, and diffusion in these macropores has to be considered as well as diffusion in the micropores of the zeolite crystals. The cylindrical capillary model is used to describe diffusion in zeolite catalyst and other catalysts and porous solids because of its simplicity and because most of the literature values for average pore size are based on this model. However, the... 

Other anisometric viruses have rod-like helical or cylindrical structures, such as tobacco mosaic virus [495,496,509,533] or alfalfa mosaic virus [551,561,562]. Thus cross-sectional parameters can be determined using / xs Q) Q q->o addition to Rq d I 0) data [537,550]. Stuhrmann plots of the / xs data lead to information on the cross-sectional distribution of protein and RNA. Shell models for the cross-section can likewise be made by analogy with the isometric viruses [550,561,562]. The radial scattering density of the cross-section can be calculated by applying the Hankel transformation to the scattering curve [509]. 

Recently, we studied the water dependence in mixtures of water and the protonated form of Nafion [53] using both standard force field models and an empirical valence bond model to account for the Grotthuss structural diffusion mechanism of aqueous proton transport. Results showed a transition of an irregularly shaped filamentous (cylindrical) structure in the case of low water (A = 5, where A is defined as the ratio of water molecules to sulfonate groups) to a structure more in accord with the above-discussed models of nano-separation, where larger clusters form which are connected by narrow bridges. A comparison of aqueous cluster sizes indicated, for a simulation time of 30 ns, no percolating clusters for A = 5, whereas at A = 10 most water molecules were located in a connected cluster (see [53]). Other structural... 

Gas adsorption is by far the most common technique used to gain information about the porous structure from the adsorption/desorption isotherms. As adsorbent, nitrogen is the most commonly used. The treatment of results here is based on a cylindrical pore model. 

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