Resonance Vibrations

Infrared and Raman spectroscopy each probe vibrational motion, but respond to a different manifestation of it. Infrared spectroscopy is sensitive to a change in the dipole moment as a function of the vibrational motion, whereas Raman spectroscopy probes the change in polarizability as the molecule undergoes vibrations. Resonance Raman spectroscopy also couples to excited electronic states, and can yield fiirtlier infomiation regarding the identity of the vibration. Raman and IR spectroscopy are often complementary, both in the type of systems tliat can be studied, as well as the infomiation obtained. 

Labuda M J and Wright J C 1997 Measurement of vibrationally resonant and the feasibility of new vibrational spectroscopies Phys. Rev. Lett. 79 2446-9... 

Dynamic techniques are used to determine storage and loss moduli, G and G respectively, and the loss tangent, tan 5. Some instmments are sensitive enough for the study of Hquids and can be used to measure the dynamic viscosity T 7 Measurements are made as a function of temperature, time, or frequency, and results can be used to determine transitions and chemical reactions as well as the properties noted above. Dynamic mechanical techniques for sohds can be grouped into three main areas free vibration, resonance-forced vibrations, and nonresonance-forced vibrations. Dynamic techniques have been described in detail (242,251,255,266,269—279). A number of instmments are Hsted in Table 8. Related ASTM standards are Hsted in Table 9. 

Resonance-Forced Vibration. Resonance-forced vibration devices drive the vibration of the specimen. This can be over a range of frequencies that includes the resonant frequency, which is detected as a maximum in the ampHtude, or the instmment can be designed to detect the resonant frequency and drive the specimen at that frequency. An example of the resonance-forced vibration technique is the vibrating reed. A specimen in... 

Resonant vibration. Any of the forced vibration loads, such as cyclic or misalignment loads, may have a frequency that coincides with a natural frequency of the rotating-shaft system, or any component of the complete power plant and its foundation, and may, thus, excite vibration resonance. 

When equipment receives impulses at its own natural frequency of vibration, excessive vibration (resonance) occurs, and this can lead to rapid failure. A control valve was fitted with a new spindle with slightly different dimensions. This changed its natural frequency of vibration to that of the impulses of the liquid passing through it (the frequency of rotation of the pump times the number of passages in the impeller). The spindle failed after three months. Even a small change in the size of spindle is a modification [24]. 

Einstein (f,) remarked that this point of view can be carried over to the theory of the energy content of a solid body if we suppose that the positive ions of Drude s theory ( 198) may be looked upon as the vibrating resonators, and the seat of the heat content of the body (Korperwarme). He calculated the expression ... 

Rothschild W. G. Vibrational resonance energy transfer and dephasing in liquid nitrogen near its boiling point molecular computations, J. Chem. Phys. 65, 2958-61 (1976). 

A spontaneous Raman spectra is shown in Figure 2.8d in which the on- and off-resonant frequencies are indicated. The DNA bundles are observed at the resonant frequency, as shown in Figure 2.8a, while they cannot be seen at the off-resonant frequency in Figure 2.8b. This indicates that the observed contrast is dominated by the vibrationally resonant CARS signals. Figure 2.8c shows a cross-section of Figure 2.8a denoted by two solid arrows, which were acquired with a 5 nm step. The FWHM of... 

An SFG signal exhibits characteristic features at frequencies of molecular vibrational resonances similar to the vibrational fingerprints of conventional IR... 

When the gap is large, the sketch in Fig. 9 shows that a second channel will open when there is a vibrational resonance - that is, when eV = ho, with o one of the vibrational frequencies of the molecule. This is vibronic resonance, and energy will transfer from the momentum of the tunneling electrons into the vibrations of the molecule. The interaction is quite weak (because the tunneling time is so short) ... 

It was noted early by Reed and others that the IETS spectrum could exhibit both absorption and emission peaks - that is, the plots of Fig. 9 could have positive excursions and negative excursions called peaks and dips. The simple analysis suggested in Fig. 9 implies that it should always be absorptive behavior, and therefore that there should always be a peak (a maximum, an enhancement) in the IETS spectrum at the vibrational resonances. It has been observed, however, that dips sometimes occur in these spectra. These have been particularly visible in small molecules in junctions, such as in the work of van Ruitenbeek [92, 109] (Fig. 12). Here, formal analysis indicates that, as the injection gap gets smaller, the existence of an inelastic vibrational channel does not contribute a second independent channel to the transport, but rather opens up an interference [100]. This interference can actually impede transport, resulting in a dip in the spectrum. Qualitatively, this occurs because the system is close to an electronic resonance without the vibrational coupling the conductance is close to g0, and the interference subtracts from the current. 

Engel, Y. M., and Levine, R. D. (1989), Vibration-Vibration Resonance Conditions in Intramolecular Classical Dynamics of Triatomic and Larger Molecules, Chem. Phys. Lett. 164, 270. 

ISO 3597-2 2003 Textile-glass-reinforced plastics - Determination of mechanical properties on rods made of roving-reinforced resin - Part 2 Determination of flexural strength ISO 5893 2002 Rubber and plastics test equipment - Tensile, flexural and compression types (constant rate of traverse) - Specification ISO 6721-3 1995 Plastics - Determination of dynamic mechanical properties - Part 3 Flexural vibration - Resonance-curve method... 

Detection sensitivity is one of the key issues in CARS microscopy. This is an especially acute problem in applications where chemical selectivity of CARS perfectly suits the tracking of small changes in cells related to specific protein and DNA distributions, external drug delivery/distribution, etc. There is, however, a component in CARS signal that is not associated with a particular vibration resonance and therefore does not carry chemically specific information. Unfortunately, in many cases, it can distort and even overwhelm the resonant signal of interest. In modeled approach, the CARS response originates from the third-order nonlinear susceptibility, which... 

FIGURE 7.11 Time-resolved single-beam CARS transients (left column) and corresponding Fourier spectra (right column) for bromotrichloromethane (CBrClj), chloroform (CHClj), bromoform (CHBrj) and a mixture of the three constituents. This result shows that the different components can clearly be distinguished by their characteristic vibrational resonances, (von Vacano and Motzkus 2007b). (From von Vacano and Motzkus, Phys. Chem. Chem. Phys., 10 681-691, 2008. Used with permission.)... 

Fourier transform for different, chemically very similar halomethanes and a mixture thereof. The time-domain data in Figure 7.11 can be directly interpreted as an observation of molecular motion in real time, made possible by the compressed ultrashort pulses in the microscope. From the presence of different oscillatory patterns and beatings, it already becomes clear that the different molecules can be discriminated with high resolution. Correspondingly, the Fourier spectra in Figure 7.11 show markedly different vibrational resonances, which can also be discriminated in the ternary mixture of all components. 

The components of the third-order nonlinear susceptibility relevant to the CARS process are conveniently subdivided into two terms vibrationally resonant (X, ) and vibrationally nonresonant (Xnr) components. The total response of the material depends on the sum of these two terms ... 

This phase shift is akin to the phase shift experienced by a damped harmonic oscillator driven in the vicinity of the oscillator s eigenfreqnency Hence, the presence of a vibrational resonance not only changes the amplitnde of the signal field, bnt also its phase. To incorporate this effect, the resonant nonlinear susceptibility is no longer real as it contains imaginary contributions ... 

The main source of contrast in FE-CARS is based on differences in the amplitude and phase of The spectral phase plays an important role in FE-CARS. While the phase of the nonresonant CARS signal is independent of co, the resonant part of exhibits a characteristic r-jump in the vicinity of a vibrational resonance Or. In the presence of a spatial r-step in focus, the nonresonant background destructively... 

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