Tangential modes

A 9 cm-1 upshift of the tangential mode (G band) vibrational frequency as well as a 90% decrease in intensity was observed by applying 1.0 V between an individual nanotube and a silver reference electrode in a dilute sulfuric acid solution. 

Fig. 13.21 shows another example of oscillatory burning of an RDX-AP composite propellant containing 0.40% A1 particles. The combustion pressure chosen for the burning was 4.5 MPa. The DC component trace indicates that the onset of the instability is 0.31 s after ignition, and that the instability lasts for 0.67 s. The pressure instability then suddenly ceases and the pressure returns to the designed pressure of 4.5 MPa. Close examination of the anomalous bandpass-filtered pressure traces reveals that the excited frequencies in the circular port are between 10 kHz and 30 kHz. The AC components below 10 kHz and above 30 kHz are not excited, as shown in Fig. 13.21. The frequency spectrum of the observed combustion instability is shown in Fig. 13.22. Here, the calculated frequency of the standing waves in the rocket motor is shown as a function of the inner diameter of the port and frequency. The sonic speed is assumed to be 1000 m s and I = 0.25 m. The most excited frequency is 25 kHz, followed by 18 kHz and 32 kHz. When the observed frequencies are compared with the calculated acoustic frequencies shown in Fig. 13.23, the dominant frequency is seen to be that of the first radial mode, with possible inclusion of the second and third tangential modes. The increased DC pressure between 0.31 s and 0.67 s is considered to be caused by a velocity-coupled oscillatory combustion. Such a velocity-coupled oscillation tends to induce erosive burning along the port surface. The maximum amplitude of the AC component pressure is 3.67 MPa between 20 kHz and 30 kHz. - ...

Explosion Properties. Occurence of detonation within rocket engines employing certain aminated fuels and nitric acid propellants are related to the formation of amine or hydrazine nitrates which tend to decompose explosively under the influence of sudden temp or pressure rises (Ref 51). Tangential-mode rocket motor instabilities were analyzed using 1-dimensional, 2-phase... 

Under certain conditions, scale-up of membrane reactors is straightforward. Provided that (i) the reactor contents are well mixed so that the reactor is operated as a CSTR, and that (ii) the membrane is configured for filtration in the tangential mode, the pertinent design criterion, besides constant residence time T in the reactor, is constant fluidity F of the substrate/product solution through the membrane at all reactor scales. Fluidity is defined by Eq. (19.36) (V = ultrafiltered volume, AP = transmembrane pressure, t = filtration time, and A = membrane area). 

The Raman spectrum of HiPco SWNT obtained at the He-Ne laser excitation of 1.96 eV has three characteristic regions four bands in the low frequency region at 100-300 cm 1 (radial breathing mode (RBM)), two intensive bands at 1500-1600 cm 1 (tangential mode (G-mode)) of the spectrum and D mode (near 1300 cm"1) [14-18], At He-Ne laser excitation 4 intensive bands (RBM) are observed in Raman spectra of HiPCO nanotubes, corresponding to SWNTs of different diameters and chirality. 

BN nanotubes treated with tributylamine and trioctylamine showed a band due to the tangential mode around 1367 cm1. These results suffice to demonstrate that the interaction of BN nanotubes with Lewis bases helps to solubilize them in nonpolar solvents. We should note that in the absence of interaction with an amine or a phosphine, BN nanotubes could not be dispersed in toluene and the nanotubes setded to the bottom in a short period. 

Oscillations with only one frequency are monochromatic waves. Thus each normal mode of oscillation [each term in equation (8)] defines a monochromatic wave. There are special shapes of chambers for which more than one mode may have the same frequency this is called degeneracy and admits an infinite variety of monochromatic wave forms (for example, tangential modes in cylindrical chambers). Most of the normal modes describe standing waves, waves having nodal points for the velocity (points where the velocity is always zero) and for the amplitude of the pressure oscillations. Thus, according to equation (8), longitudinal modes have pressure nodes at nz/l = 1, I,..., and they have velocity nodes at nz/l = 0, 1, 2,..., as... 

Raman spectra of SWCNTs as well as the most common experimental techniques of their characterization have been also thoroughly discussed in literature [3, 26]. The strongest Raman bands of SWCNTs are the RBM band (radial breathing mode in the range 100-300 cm ), and the G-band (tangential mode at around 1600 cm ) as shown in Fig. 7.2 [27]. Two more characteristic, but weaker bands are the D-band (disorder-induced band in the range 1300-1400 cm ) and the G -band (sometimes called D -band) at around 2600-2800 cm . ... 

Insight into the changes in the intramolecular bonding of C, on intercalation, and the relevance of the various vibrational modes to the mechanism of superconductivity, can be obtained by comparing the low-temperature INS spectra of K,C,> and Cm,. The striking difference between the two systems is the redistribution of intensity that occurs between the radial and tangential modes. Carbon-60 has intense features up to — 110 meV, followed by many weaker and broader hands up to... 

The Raman spectra of DWCNT s were analysed in terms of chiral, (n,m) assignments for these tubes.266 The Raman spectrum of I2-doped DWCNT gave assignments to radial breathing and tangential modes.267 Resonance Raman spectra of DWCNT were analysed to probe diameters and chiralities.268 The Raman spectra of DWCNT (from fullerene peapods annealed at high temperatures) show that the inner tubes are remarkably defect-free.269 Very low levels of defects were also observed from the Raman spectra of DWCNT produced by the catalytic decomposition of benzene over Fe-Mo/ A1203 catalysts at 900°C (i.e. very weak D-band at 1265.5 cm-1).270... 

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