Molecular vibration absorption

Molecular vibration absorptions are typically observed at infrared wavelengths, which correspond to the resonance frequencies for fundamental molecular vibrations. Because of the molecular potential anharmonicity, however, overtone and combination absorption bands also appear at visible and near-infrared wavelengths. The predominant factor for attenuation in POFs has been the stretching overtone absorptions of C-H bonds. 

To understand the overtone absorption of POF materials, let us consider individual chemical bonds in a polymer as the equivalent diatomic molecules with only 

Here r, r, and are the atomic distance, equilibrium bond length, and potential-well depth, respectively. Further, h is Planck s constant and c is the light velocity in vacuum. The potential-curve shapes depend on the parameters and D. By analytically solving the Schrodinger equation with the anharmonic potential (Equation 2.3), one can obtain the vibrational energy levels ofthe Morse molecular oscillator  

The first term on the right-hand side corresponds to the energy levels in the harmonic oscillator approximation for small displacements from equihbrium, where V r) ll2)kg r - The harmonic oscillator frequency is given by 

Here is the effective mass defined in terms of the atom masses nii and m2 as m =m m2l mi + m. On the other hand, the second additional term in Equation 2.4 is the contribution of the oscillator anharmonicity, which depends on the anharmonicity constant 

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Fundamental absorption Molecular vibrational absorption from ground level to level one. 

In general, IR absorption is caused by the interaction between the IR electric field vector and the molecular dipole transition moments related to the molecular vibrations. Absorption is at a maximum when the electric field vector and the dipole transition moment are parallel to each other. In the case of perpendicular orientation, the absorption is zero. Directional absorptions are measured using polarised light. The terms parallel and perpendicular refer to the orientation of the polarised beam with respect to a reference axis. For deformation studies, the reference axis corresponds to the stretching direction. 

The absorption of light in POF materials depends on its frequency or wavelength because materials have various energy levels that are involved in absorption transitions. In the light wavelengths used for data communication with POFs, the intrinsic absorption losses are caused by electronic transition absorptions and/or molecular vibration absorptions. The electronic transition absorption peaks typically appear at ultraviolet wavelengths, and their absorption tails influence the transmission losses of POFs. For example, a POF with a poly(methyl methacrylate) (PMMA) core exhibits n- i transitions due to the ester groups in methyl methacrylate (MMA) molecules, n-a transitions of S-H bonds in chain-transfer... 

Molecular vibration absorption is the vibrational transition from the ground state to an excited state. From Equation 2.4, the resonance absorption frequency for the transition to the nth excited state can be expressed by... 

Infrared Spectroscopy. The infrared spectroscopy of adsorbates has been studied for many years, especially for chemisorbed species (see Section XVIII-2C). In the case of physisorption, where the molecule remains intact, one is interested in how the molecular symmetry is altered on adsorption. Perhaps the conceptually simplest case is that of H2 on NaCl(lOO). Being homo-polar, Ha by itself has no allowed vibrational absorption (except for some weak collision-induced transitions) but when adsorbed, the reduced symmetry allows a vibrational spectrum to be observed. Fig. XVII-16 shows the infrared spectrum at 30 K for various degrees of monolayer coverage [96] (the adsorption is Langmuirian with half-coverage at about 10 atm). The bands labeled sf are for transitions of H2 on a smooth face and are from the 7 = 0 and J = 1 rotational states Q /fR) is assigned as a combination band. The bands labeled... 

Eig. 4. Transmission profile for a siUca-based glass fiber. Region A represents electronic transitions B, the transmission window and C, molecular vibrations. Point LL is the lowest loss observed in an optical fiber. Absorption profiles for (-) OH and ( ) Fe are also shown. See text. 

Infrared spectroscopy has broad appHcations for sensitive molecular speciation. Infrared frequencies depend on the masses of the atoms iavolved ia the various vibrational motions, and on the force constants and geometry of the bonds connecting them band shapes are determined by the rotational stmcture and hence by the molecular symmetry and moments of iaertia. The rovibrational spectmm of a gas thus provides direct molecular stmctural information, resulting ia very high specificity. The vibrational spectmm of any molecule is unique, except for those of optical isomers. Every molecule, except homonuclear diatomics such as O2, N2, and the halogens, has at least one vibrational absorption ia the iafrared. Several texts treat iafrared iastmmentation and techniques (22,36—38) and thek appHcations (39—42). 

Raman spectroscopy detects the scattering of light, not its absorption. Superposed on the frequency of the scattered light are the frequencies of the molecular vibrations. The detection occurs in the IR spectral region while the excitation happens in the visible region. Since laser light sources have become well developed, Raman spectroscopy has become an important tool for the analysis of biomolecules. 

Complementary to other methods that constimte a basis for the investigation of molecular dynamics (Raman scattering, infrared absorption, and neutron scattering), NIS is a site- and isotope-selective technique. It yields the partial density of vibrational states (PDOS). The word partial refers to the selection of molecular vibrations in which the Mossbauer isotope takes part. The first NIS measurements were performed in 1995 to constitute the method and to investigate the PDOS of... 

These selection rules are affected by molecular vibrations, since vibrations distort the symmetry of a molecule in both electronic states. Therefore, an otherwise forbidden transition may be (weakly) allowed. An example is found in the lowest singlet-singlet absorption in benzene at 260 nm. Finally, the Franck-Condon principle restricts the nature of allowed transitions. A large number of calculated Franck-Condon factors are now available for diatomic molecules. 

Apart from molecular vibrations, also rotational states bear a significant influence on the appearance of vibrational spectra. Similar to electronic transitions that are influenced by the vibrational states of the molecules (e.g. fluorescence, Figure 3-f), vibrational transitions involve the rotational state of a molecule. In the gas phase the rotational states may superimpose a rotational fine structure on the (mid-)IR bands, like the multitude of narrow water vapour absorption bands. In condensed phases, intermolecular interactions blur the rotational states, resulting in band broadening and band shifting effects rather than isolated bands. 

When a broadband source of IR energy irradiates a sample, the absorption of IR energy by the sample results from transitions between molecular vibrational and rotational energy levels. A vibrational transition may be approximated by treating two atoms bonded together within a molecule as a harmonic oscillator. 

For a fundamental vibrational mode to be IR-active, a change in the molecular dipole must take place during the molecular vibration. This is described as the IR selection rule. Atoms that possess different electronegativity and are chemically bonded change the net dipole of a molecule during normal molecular vibrations. Typically, antisymmetric vibrational modes and vibrations due to polar groups are more likely to exhibit prominent IR absorption bands. 

Emission or absorption spectra are produced when molecules undergo transitions between quantum states that correspond to two different internal energies. The energy difference AE between the states is related to the frequency of the radiation emitted or absorbed by the equation DE = hn. Infrared frequencies in the wavelength range 1-50 mm are associated with molecular vibration and vibration-rotation spectra. 

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