Theoretical models, nanotube

In this paper, we review progress in the experimental detection and theoretical modeling of the normal modes of vibration of carbon nanotubes. Insofar as the theoretical calculations are concerned, a carbon nanotube is assumed to be an infinitely long cylinder with a mono-layer of hexagonally ordered carbon atoms in the tube wall. A carbon nanotube is, therefore, a one-dimensional system in which the cyclic boundary condition around the tube wall, as well as the periodic structure along the tube axis, determine the degeneracies and symmetry classes of the one-dimensional vibrational branches [1-3] and the electronic energy bands[4-12]. 

Theoretical model of hydrogen adsorption on nanotube surface... 

S. Irle, A. Mews and K. Morokuma, Theoretical study of structure and Raman spectra for model nanotubes in their pristine and oxidized forms, J. Phys. Chem. A 106, 11973-11980 (2002). 

Abstract This chapter focuses on the performances of gas sensors based on single-walled carbon nanotubes (SWCNTs).The chapter first reviews chemiresistor and field-effect transistor sensor architectures. Theoretical models based on doping effect and Schottky barrier modulation are correlated to the percolation of metallic carbon nanotubes. The functionalisation strategies of carbon nanotubes, used to acquire a gas selectivity, are discussed and offer promising application for the monitoring of air quality, or military and medical applications. 

It can be seen that, with regard to the pure matrix, the elastic modulus, tensile strength and strain at break increase with nanotube loading. On the other hand, the addition of 10 MWNTs impart to the matrix a higher level of reinforcement than 10 phr of carbon black. Many factors could potentially explain the superior reinforcing efficiency of carbon nanotubes and among them, the filler aspect ratio is expected to play an important role in the mechanical response of the composite. Experimental data can be usefully compared to theoretical model predictions, especially those of Guth [71] and Halpin-Tsai [72]. 

Abstract—Experimental and theoretical studies of the vibrational modes of carbon nanotubes are reviewed. The closing of a 2D graphene sheet into a tubule is found to lead to several new infrared (IR)- and Raman-active modes. The number of these modes is found to depend on the tubule symmetry and not on the diameter. Their diameter-dependent frequencies are calculated using a zone-folding model. Results of Raman scattering studies on arc-derived carbons containing nested or single-wall nanotubes are discussed. They are compared to theory and to that observed for other sp carbons also present in the sample. 

The simple relation (4) is in good agreement with existing data from billiard gas channels to nonlinear lattices, and even single walled nanotubes(Li et al, 2005). This is shown in Fig. 5, where we compare the theoretical prediction (4) with existing data in different models. 

Margulis, VI.A., Muryumin, E.E. and Tomilin, O.B. (2004) Theoretical study of atomic chemisorption on single-walled carbon nanotubes. Application of Anderson-Newns model, PhysicaB 353(3-4), 314-323. 

Mechanical properties - Numerous theoretical works have been done to predict the mechanical properties of reinforced composites. Some of these models are more sophisticated, but in order to understand why nanotubes are ideal reinforcement particles, the rule of... 

In order to estimate the theoretical upper bounds for the electrical conductivities of polymer nanotube composites, equation (15.1) was used to calculate conductivity values for model composites based on both SWNT and MWNT. The values are included in Table 15.2 together with the electrical conductivities of individual CNTs as reported in the literature. Although arc-synthesized MWNTs are likely to possess higher conductivities than CVD-grown ones, no distinction is made in the present analysis between the two types due to the unavailability of reliable data. An electrical conductivity of IE-9 S/m is taken to represent the conductivity of a typical polymer matrix. 

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