Polyethylene frequency spectrum

Myers, W., J. L. Donovan, and J. S. King Polyethylene frequency spectrum... 

Myers,W., Donovan,J.L., King,J.S. Polyethylene frequency spectrum from warm-neutron scattering. J. Chem. Phys. 42, 4299—4 X) (1%5). 

Using Eq. (51) and the known polyethylene frequency spectrum, heat capacities can be calculated within experimental error between 180° K and the glass transition temperature. At low temperatures the calculated values are too small (50% at 50° K), an indication that the C-Cl vibrations couple with the skeletal C-C vibrations and decrease the skeletal frequencies relative to pol5rethylene. Lebedev, Rabinovich and Budarina (1967) used Tarasov expression [see Eq. (8)] with 0 = 350° K and 08 = 175° K per 4.5 modes of vibration per mole to describe their low... 

The graphs of Fig. 5.17 illustrate the experimental heat capacities for polyethylene. A number of other polymers are described in the ATHAS Data Bank in the Appendix. The curves in the upper left graph show linear crystallinity dependence. For the fiilly crystalline sample (w. = 1.0) there is a temperature dependence of the heat capacity up to 10 K (single point in the graph), as is required for the low-temperature limit of a three-dimensional Deltye function. One concludes that the beginning of the frequency spectrum is, as also documented for diamond and graphite in Fig. 5.16, quadratic in... 

Interchain potential, frequency spectrum, specific heat and root-mean-squared displacements in polyethylene crystal. Rept. Progr. Polymer Phys. Japan 11,219—222 (1968a). 

The deuteropolyethylene heat capacity was discussed in terms of the changed frequency spectrum due to the isotope effect by Rabinovich, Pavlinov, and Krylova (1967). The -value changed to = 112 K. Agreement between calculation and experiment seems similar to polyethylene. 

An early analysis of the heat capacity of polytetrafluoroethylene was made by Starkweather (1960). He fitted the Stockmayer and Hecht frequency spectrum (see Fig. IIL15B) in the region of 15 to 75° K using a maximum frequency of 8.3 10 cps.The number of vibrators was 2.83 in contrast to polyethylene with closer to two skeletal vibrations. A more detailed analysis was performed by Gotlib and Sochava (1962). They compared polytetrafluoroethylene with polyethylene assuming a planar... 

Such normal vibration analyses have been applied to the spectra of macromolecules to only a limited extent. In the first place, the only structure which has been analyzed in detail is that of the planar zig-zag chain of CHg groups, i.e., polyethylene. Neither substituted planar zig-zag chains nor the helical chain structures characteristic of many polymers [Bunn and Holmes (28)] have been submitted to such a theoretical analysis. In the second place, even for the case of polyethylene the answers are not in all instances unambiguous. Different assumptions as to the nature of the force field, and lack of knowledge of some of the force constants, has led to varying predictions of band positions in the observed spectrum. For the identification of certain modes, viz., those which retain the characteristics of separable group frequencies, such an analysis is not of primary importance, but for knowledge of skeletal frequencies and of interactions... 

It passes through the sample absorption cell made of Pyrex with polyethylene windows and is detected with a liquid helium cooled bolometer. One of the lasers is frequency-modulated at 1 kHz and the detector output is processed with a lock-in amplifier, as shown. Far-infrared rotational spectra of CO, HC1 and HF have been recorded [67], and as an example of the excellent sensitivity achieved, we refer the reader to the spectrum of the OH radical [68] shown later in this chapter. Evenson s spectrometer operates over a wide range of the far-infrared region up to 9 THz, with excellent frequency stability. 

In the infrared spectrum of polyethylene (Fig. 4.1-2A) this band is split into a doublet at 720 and 731 cm This factor group splitting (Fig. 2.6-1 and Sec. 2.7.6.4) is a result of the interaction between the molecules in crystalline lattice areas. It may be used to investigate the crystallinity of polymers (Drushel and Iddings, 1963 Luongo, 1964). Polyethylene has a unit cell of the factor group Dih (compare Secs. 2.7.5 and 2.7.6.3) which contains a -CH2-CH2- section of two neighboring chains. Each of these sections has a center of inversion in the middle of the C-C bond (Fig. 4.1-3). Therefore the rule of mutual exclusion (Sec. 2.7.3.4) becomes effective The vibrations of the C-C bonds cannot be infrared active and further there are no coincidences of vibrational frequencies in the infrared and Raman spectrum of linear polyethylene. 

Figure 13. Stress growth function for blends of linear low density polyethylene, LLDPE, with (left) another type of LLDPE (miscible, Series-I) and (right) with low density polyethylene (immiscible. Series II). Broken lines experimental data in elongation triangles experimental data in steady state shearing at y - O.Ols". Solid lines were computed from the frequency relaxation spectrum. (Adapted from ref. 14.)...

In the region around k = 0.5, especially in the longer chains, several vibrations with frequencies close to (fi>rAM)max occur and the spectrum becomes congested into a band-head reminiscent of polyethylene. 

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