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RBM frequencies ω RBM = A/ d + B versus nanotube diameter for (i) A = 234 cm -1 nm and B = 10 cm -1 , for SWNT bundles (dashed curve); (ii) A = 248 cm -1 nm and B = 0, for isolated SWNTs (solid curve). Adapted from A. Jorio, M. A. Pimenta, A. G. S. Filho, R. Saito, G. Dresselhaus, and M. S. Dresselhaus, New J. Phys. , 2003, 5 , 139.

Hence, a single Raman measurement gives an idea of the tubes that are in resonance with the laser line, but does not give a complete characterization of the diameter distribution of the sample. However, by taking Raman spectra using many laser lines, a good characterization of the diameter distributions in the sample can be obtained. Also, natural line widths observed for isolated SWNTs are ω RBM = 3 cm -1 , but as the tube diameter is increased, broadening is observed which is denoted by Γ RBM . It has been observed that for d >2 nm, Γ RBM >20 cm -1 . For SWNT bundles, the line width does not reflect Γ RMB , it rather reflects an ensemble of tubes in resonance with the energy of laser.

Variation of rbm intensities upon functionalization

Functionalization of SWNTs leads to variations of relative intensities of RBM compared to the starting material (unfunctionalized SWNTs). Owing to the diameter dependence of the RBM frequency and the resonant nature of the Raman scattering process, chemical reactions that are sensitive to the diameter as well as the electronic structure, i.e., metallic or semiconducting of the SWNTs can be sorted out. The difference in Raman spectra is usually inferred by thermal defunctionalization, where the functional groups are removed by annealing. The basis of using annealing for defunctionalizing SWNTs is based on the fact that annealing restores the Raman intensities, in contrast to other treatments where a complete disintegration of the SWNTs occurs. [link] shows the Raman spectra of the pristine, functionalized and annealed SWNTs. It can be observed that the absolute intensities of the radial breathing modes is drastically reduced after functionalization. This decrease can be attributed to vHs, which themselves are a consequence of translational symmetry of the SWNTs. Since the translational symmetry of the SWNTs is broken as a result of irregular distribution of the sp 3 -sites due to the functionalization, these vHs are broadened and strongly reduced in intensity. As a result, the resonant Raman cross section of all modes is strongly reduced as well.

Raman spectra of sidewall functionalized SWNTs of (A) pristine material, (B) functionalized SWNTs, and (C) after annealing at 750 °C in Ar. Adapted from R. Graupner, J. Raman Spectrosc. , 2007, 38 , 673.

For an ensemble of functionalized SWNTs, a decrease in high wavenumber RBM intensities has been observed which leads to an inference that destruction of small diameter SWNT takes place. Also, after prolonged treatment with nitric acid and subsequent annealing in oxygen or vacuum, diameter enlargement of SWNTs is observed from the disappearance of RBMs from small diameter SWNTs and the appearance of new RBMs characteristic of SWNTs with larger diameters. In addition, laser irradiation seems to damage preferentially small diameter SWNTs. In all cases, the decrease of RBM intensities is either attributed to the complete disintegration of SWNTs or reduction in resonance enhancement of selectively functionalized SWNTs. However, change in RBM intensities can also have other reasons. One reason is doping induced bleaching of electronic transitions in SWNTs. When a dopant is added, a previously occupied electronic state can be filled or emptied, as a result of which E f in the SWNTs is shifted. If this shift is large enough and the conduction band vHs corresponding to the respective E ii transition that is excited by the laser light gets occupied (n-type doping) or the valence band vHs is emptied (p-type doping), the resonant enhancement is lost as the electronic transitions are quenched.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
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2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
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Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
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A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Source:  OpenStax, Nanomaterials and nanotechnology. OpenStax CNX. May 07, 2014 Download for free at http://legacy.cnx.org/content/col10700/1.13
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