Longitudinal acoustical vibration

Already Kohlrausch (1943) has pointed out that linear paraffines shows a Raman band in the range 250. .. 400 cm the frequency of which decreases with increasing length of the chain. Schaufele and Shimanouchi (1967) have demonstrated that this longitudinal acoustical vibration can be observed in the Raman spectra of crystalline linear hydrocarbons as well as in polymers with folded chains. 

Thus, for the motion of the next state along the chain it is necessary to repolarize the chain into its initial state, which can be achieved by Bjerrum-fault transfer. The semiphenomenological theory of proton transfer along the hydrogen-bonded chain of the ice-like structure, developed in Ref. 161, includes the influence of longitudinal acoustic vibrations of the chain sites on the proton subsystem. Reference 162, in which the dynamics of the ionic state formation in the hydrogen-bonded chains is considered, resembles roughly Ref. 161. 

Schaufele, R. F. and Shimanouchi, T. (1967) Longitudinal acoustical vibrations of finite polymethylene chains, /. Chem. Phys., 47, 3605 3610. 

The earliest observation of a Raman active fundamental mode in n-paraffins was made in 1949 (103). The characteristics of this vibration are its extremely strong intensity and the fact that the observed frequency is inversely proportional to the straight chain segment length. This mode was hypothesized to be related to the longitudinal acoustic vibration along the backbone of the entire chain segment. The frequency of vibrations is then related by the expression shown below. 

Shimanouchi, T. Longitudinal acoustic vibrations of finite polyethylene chains. J. diem. Phys. 47, 3605—3610 (1967). 

The complementary use of the Raman and INS techniques allowed the observation and assignment of the whole set of longitudinal acoustic vibrational modes (LAM s) for these amines, both for their undeuterated and N-deuterated forms (44) (Figure lA), as well as of the corresponding transverse modes (TAM s). The INS experimental LAM s are in good accordance with the LAM s of the corresponding w-alkanes (49), which supports the idea of a significant conformational similarity (in the solid state) between these two sets of compounds. 

The frequency bands due to longitudinal acoustic vibrations which, as mentioned previously, are not observed in infrared spectra but occur in Raman spectra, are inversely proportional to lamella thickness. These bands are usually difficult to observe. For example, a low frequency band due to a longitudinal acoustic vibration has been found in the Raman spectra of polyethylene and polypropylene which is related to the chain length and the lamellar thickness. - The longitudinal acoustic vibration is dependent on the force constant (dependent on the chain s longitudinal Young s modulus), the interlamellar forces, structure of the chain folding sequence, the proportions of the amorphous and crystalline components and the density of the polymer. 

Raman spectroscopy is a technique appropriate for the analysis and characterization of polymers, as it provides information on the chemical and morphological structures of polymers. One advantage of Raman spectroscopy over IR spectroscopy is the greater sensitivity to homonuclear bonds such as >C—C<, —C=C—, and —C=C—. Raman spectroscopy can serve to measure the degree of crystallinity of partly crystalline polymers, and notable in this context are the longitudinal acoustic vibrations in linear chain polymers (also... 

According to Eq. (II.7), co = 0 for k = 0 in the center of BZ 1. With these values Eqs. (II. 1)—(II.3) lead to the relation UA = UB. This means that both sets of atoms vibrate with the same amplitude and in phase (because they have the same sign). A translation of the whole chain results which corresponds to an acoustical wave with X = °°. This is called a longitudinal acoustical branch (LA). 

The vibration spectruin of GaAs, calculated by using the C, and C l values of Tabic 8-4 (TO = transverse optical LO = longitudinal optical LA = longitudinal acoustical TA = transverse acoustical). Experimental points arc from Dolling and Waugh (1965). 

Wurtzite ZnO structure with four atoms in the unit cell has a total of 12 phonon modes (one longitudinal acoustic (LA), two transverse acoustic (TA), three longitudinal optical (LO), and six transverse optical (TO) branches). The optical phonons at the r point of the Brillouin zone in their irreducible representation belong to Ai and Ei branches that are both Raman and infrared active, the two nonpolar 2 branches are only Raman active, and the Bi branches are inactive (silent modes). Furthermore, the Ai and Ei modes are each spht into LO and TO components with different frequencies. For the Ai and Ei mode lattice vibrations, the atoms move parallel and perpendicular to the c-axis, respectively. On the other hand, 2 modes are due to the vibration of only the Zn sublattice ( 2-low) or O sublattice ( 2-high). The expected Raman peaks for bulk ZnO are at 101 cm ( 2-low), 380 cm (Ai-TO), 407 cm ( i-TO), 437 cm ( 2-high), and 583 cm ( j-LO). 

The substrate (or adsorbent) was modelled in one dimension by a linear chain of five carbon atoms, (We could have chosen any other atom.) A terminal carbon atom represents a surface atom and the remaining atoms the bulk. There is only one force constant, the C-C stretching force constant (C—C of C2 12.16 mdyn A" ). The dynamics were treated by the Wilson GF method. The substrate then had four vibrations similar to longitudinal acoustic modes (LAM) ( 10.1.2) LAM1,170 cm LAM2, 330 cm LAM3, 455 cm LAM4, 535 cm. The calculated INS spectrum comprised four bands of equal, weak intensity. 

Some interesting and important conclusions were drawn by separating the phonon spectrum in accordance with the polarization of the oscillations [15]. The whole spectrum was divided into six branches, each of which has an almost Gaussian form of the distribution curve g( ). For cubic crystals, these six branches consist of three acoustical branches (one branch of longitudinal and two branches of transverse waves) and three optical branches (one longitudinal and two transverse waves). The acoustical vibrations can be compared with the vibrations of atoms in a unit cell, and the optical vibrations with mutual oscillations of the sublattices in relation to one another. The curves of the density distribution of oscillations in each [Pg.180]

Analysis of Structural Unit-SiZG. The strength of vibrational spectroscopy lies in its ability to characterize chemical composition and localized structure of polymers. The observation of the intense longitudinal acoustic mode (LAM) in the extremely low frequency region (<50 cm ) of the Raman spectra of semicrystalline polymers provides a very different morphological tool for measurement of structural subunits in the order of several hundreds of angstroms. 

In addition to longitudinal acoustic modes (section 4.10), the low-frequency regions of Raman spectra often contain rather broad, ill-defined bands. While these can sometimes be ascribed to specific intra- or inter-molecular vibrations, work has suggested they may be due to fracton vibrational modes localised in disordered regions or blobs [241]. Analysis of the bandshape has been used to measure the size of the disordered regions for example, -50A blobs were found in amorphous PET and PMMA [242]. 

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