Frequency shift from

The metal substrate evidently affords a huge ( 10 and even as high as 10 [84, 85]) increase in the cross-section for Raman scattering of the adsorbate. There are two broad classes of mechanisms which are said to contribute to this enhancenient [, and Ml- The first is based on electromagnetic effects and the second on cheniicaT effects. Of these two classes the fomier is better understood and, for the most part, the specific mechanisms are agreed upon the latter is more complicated and is less well understood. SERS enhancenient can take place in either physisorbed or chemisorbed situations, with the chemisorbed case typically characterized by larger Raman frequency shifts from the bulk phase. 

FREQUENCY SHIFT FROM CENTER OF GAIN CURVE (GH ... 

Vanadium atom depositions were further studied in alkane matrices 109) in an effort to observe the influence of other low-temperature, matrix environments on the optical spectra and clustering properties of metal atoms. Thus, vanadium atoms were deposited with a series of normal, branched, and cyclic alkanes over a wide range of temperature. The atomic spectra were somewhat broadened compared to those in argon, but the matrix-induced, frequency shifts from gas-phase values were smaller. As shown in Fig. 3, these shifts decrease with in-... 

The molecular collective behavior of surfactant molecules has been analyzed using the time courses of capillary wave frequency after injection of surfactant aqueous solution onto the liquid-liquid interface [5,8]. Typical power spectra for capillary waves excited at the water-nitrobenzene interface are shown in Fig. 3 (a) without CTAB (cetyltrimethy-lammonium bromide) molecules, and (b) 10 s after the injection of CTAB solution to the water phase [5]. The peak appearing around 10-13 kHz represents the beat frequency, i.e., the capillary wave frequency. The peak of the capillary wave frequency shifts from 12.5 to 10.0kHz on the injection of CTAB solution. This is due to the decrease in interfacial tension caused by the increased number density of surfactant molecules at the interface. Time courses of capillary wave frequency after the injection of different CTAB concentrations into the aqueous phase are reproduced in Fig. 4. An anomalous temporary decrease in capillary wave frequency is observed when the CTAB solution beyond the CMC (critical micelle concentration) was injected. The capillary wave frequency decreases rapidly on injection, and after attaining its minimum value, it increases... 

The first term on the right corresponds to Raleigh scattering. The second term suggests an energy-exchange interaction that depends on the anisotropy of the polarizability and involves frequencies shifted from that of the incident radiation by an amount which depends on twice the rotational or vibrational frequency of the molecules in the sample. 

The ratio of symmetry numbers s s° in equation 11.40 merely represents the relative probabilities of forming symmetrical and unsymmetrical molecules, and ni and nf are the masses of exchanging molecules (the translational contribution to the partition function ratio is at all T equal to the power ratio of the inverse molecular weight). Denoting as AX, the vibrational frequency shift from isotopically heavy to light molecules (i.e., AX, = X° — X ) and assuming AX, to be intrinsically positive, equation 11.40 can be transated into... 

Fig. 2 Temperature dependence of the - 1/2 -0-+ 1/2 NMR spectrum in the region of the PE-FE phase transition for D-RADP-20 (Bo c). The positive frequency shift from the pure PE line to the pure FE line amounts to 8 kHz. The change in the line shape clearly indicates the coexistence of both phase states over a wide temperature range [17]...

The instantaneous OH frequency was calculated at each time step in an adiabatic approximation (fast quantal vibration in a slow classical bath ). We applied second-order perturbation theory, in which the instantaneous solvent-induced frequency shift from the gas-phase value is obtained from the solute-solvent forces and their derivatives acting on a rigid OH bond. This method is both numerically advantageous and allows exploration of sources of various solvent contributions to the frequency shift. 

KGS632). The weak band which appears as a shoulder ca. 20 cm 1 to low frequency of the main NH band in very dilute solutions and of roughly one-twentieth of its intensity has become a classical example of a hot band (64JCP(4l)3274) similar bands have been identified in substituted pyrroles. The position of the NH stretching vibration is sensitive to the number, type and position of ring substituents effects of substituents are additive and independent provided that adjacent substituents do not experience severe, mutual steric interactions. The effect of a substituent is always greater when at an a- rather than a /3-position. Frequency shifts from 3496 cm-1 are listed in Table 26. 

Frequency Shifts from Dipole-Dipole Interaction... 

Fe with the template ion. DTA studies indicate that Fe-faujasites have lower thermal stability than their Al—analogs.The (OH) vibration frequency shifts from 3540 and 3630 to 3570 and 3643 cm respectively on isomorphous substitution of Al by Fe. Relative changes in the intensity of the ESR peak at g = 4.3 at low temperatures also support the conclusion that iron can be inserted in the fauja-site lattice positions. 

Since experimental results were available for the high-frequency (" -2080 cm-1) diatomic CN in water (as opposed to CH3C1) (17), with an estimated T value of some 25 ps, an MD study was undertaken by Rey and Hynes (29) to clarify the role of Coulomb forces for VET in this accesible case. The charge distribution of CN in the solvent was modeled by a negative charge on N and a finite dipole located on the C site (30). The equilibrium solvent structure about this ion involved greater solvation number on the N end compared to the C end, a result consistent with some small cluster calculations (31). Since the frequency shift from the vacuum and the anharmonicity in the CN bond are both relatively small (29), the static vibrational aspects of the ion are evidently fairly clean. ... 

The resonant frequency also depends on the density and the viscosity of the contacting media. The frequency shift for measurement in air vs. vacuum is smaller than 10 Hz. However, the frequency shift from air to water or aqueous solution, for a 10 MHz crystal is about 4-12 kHz. The magnitude of this shift can be calculated by using the following relationship ... 

A Raman spectrum is excited by irradiating a sample with coherent or non-coherent monochromatic radiation in the ultraviolet, the visible, or the near-infrared range. By an elementary process described in Sec. 2.4, the sample produces usually non-coherent radiation the strong Rayleigh line at the frequency of the exciting radiation and weak lines at frequencies. shifted from the frequency of the exciting radiation by definite quantities, the Raman spectrum. 

Raman peaks in the spectrum are displayed as frequency shifts from the incident laser-line, or Av = vq v. Each peak corresponds to the energy of a vibrational normal, which depends on molecular strucmre as well as the characteristics of chemical bonds comprising each normal mode. Hence, Raman spectrum is called the molecular fingerprint of the molecules and materials. Raman spectra of DNA and proteins, for example, contain rich information on their chemical bonds and stmctures. The Raman spectmm not only provides information about the stmcture, conformation, and identity of the sample but also the dynamics and interactions between biomolecules such as protein folding and DNA-protein interactions. 

Many other examples of stress or strain measurements through Raman spectroscopy are still primarily qualitative [18, 27]. Much of this stems from the fact that Raman spectroscopy provides only limited additional information (generally only in the form of frequency shifts) from potentially complicated strain distributions. Furthermore, care must be taken when extracting stresses from measured Raman shifts as key mechanical properties such as Young s modulus (which is related to the compliance or stiffness matrix elements) may be diameter dependent in NWs [61]. Still, Raman mapping with submicron spatial resolution and careful polarization analyses may help clarify the piezospectroscopic properties of semiconductor NWs in ongoing research. 

Figure 11. Plot of the decay times and the relative intensities of the fluorescence of the styrene-TMA adduct as a function of excess energy (expressed as frequency shift from the system s origin). Note the different pattern observed for the intensity and lifetime in the case of exciplex-type emission. Adapted from Ref. [27].

The abihty to distinguish closely spaced peaks in spectroscopy has received much attention in the classical literature, and many of the same principles apply to Raman spectroscopy. Raman does require fairly high frequency precision and resolution, since one is observing relatively small frequency shifts from a particular laser frequency (see Chapter 10 for more detail). In the context of spectrometer evaluation, it should be noted that most analytical Raman apph-cations involve liquids and solids in which Raman bandwidths are significantly greater than those in the gas phase. The narrowest linewidths encountered in most liquid and solid samples are in the range of 3 to 10 cm". ... 

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