Longitudinal acoustic modes, LAM

Low-frequency Raman spectroscopy (LFRS) has been used to measure the longitudinal acoustic mode (LAM) of semicrystalline diblocks containing poly(ethylene oxide) (Mai et at. 1996 Viras et at. 1988 Yang et at. 1995), The LAM mode frequency is inversely proportional to the crystal stem length, and indicates whether chains are folded or extended. 

Fig. 5.16 Low-frequency Raman spectrum of a PP07PE075PP07 triblock at -10 °C (Viras et al. 1988). The band between 8 and 12 cm 1 is assigned to the longitudinal acoustic mode (LAM) of the copolymer.

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. 

Below 600 cm are the V5 in-plane C—C—C bending modes (longitudinal acoustic modes, LAMs), the V9 out-of-plane C—C—C bending modes (transverse acoustic modes, TAMs) and the 12 lattice modes. These comprise in-phase and out-of-phase pairs of librations about the three axes, giving six modes, three optic translation and three... 

S.F. Parker, D.A. Braden, J. Tomkinson B.S. Hudson (1998). J. Phys. Chem. B, 102, 5955-5956. Full longitudinal acoustic mode (LAM) spectrum of an n-alkane comparison of observed and computed incoherent inelastic neutron scattering spectmm of n-octadecane. 

Long period spacing and lamellae thickness A Raman longitudinal acoustic mode (LAM) and small-angle X-ray scattering (SAXS) See Table 4 (5,24, 35-37)... 

At the extreme low-frequency end of the Raman spectrum, the so-called longitudinal acoustic modes (LAM), probe the lamellar structure, including the fold surfaces. These lattice modes correspond to accordionlike deformations of the chain. The lamella thickness is related to the frequency of these modes. A quantitative expression has not been found for helical PP, but an inverse relation has been proved. LAM bands in the range 10-20 cm have been used to compare PP samples in terms of lamella thicknesses. A similar mode exists in the amorphous phase the so-called disoriented LAM (DLAM). A DLAM doublet observed near 220 cm in iPP melts has been associated with 3, helix segments. 

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. 

The longitudinal acoustic mode (LAM), measured by Raman spectroscopy, continues to be a powerful means of measuring the average stem length in crystalline polymers. Its application has been extended to polyethers, poly-thioether," and also polytetrafluorethylene and its oligomers. ... 

One of the main uses of Raman spectroscopy in morphological analysis is the measurement of the longitudinal acoustic mode (LAM) in polyethylene which goes back to relatively early work (1949) on paraffins. The LAM frequency (u(LAM- )) can be converted to all-tmns chain length or crystal thickness (Lc) according to the following formula ... 

The longitudinal acoustic mode (LAM) is found in a number of semicrystalline polymers. The LAM mode for the all-trans -alkanes is a symmetric accordion-like... 

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