Polyethylene, vibrational excitation

Figure Cl.5.9. Vibrationally resolved dispersed fluoreseenee spectra of two different single molecules of tenylene in polyethylene. The excitation wavelength for eaeh moleeule is indicated and the spectra are plotted as the differenee between excitation and emitted wavenumber. Each molecule s spectrum was recorded on a CCD deteetor at two different settings of the speetrograph grating to examine two different regions of the emission speetrum. Type 1 and type 2 speetra were tentatively attributed to tenylene moleeules in very different local environments, although the possibility that type 2 spectra arise from a chemical impurity could not be ruled out. Further details are given in Tehenio [105-107].

An asymmetry, called vibrational fine structure and attributed to C—H vibrational excitation, is observable on C Is spectra recorded on polymers containing saturated hydrocarbon components as polyethylene. ... 

The elementary excitations inside a specimen can cause absorption or emission of IR radiation only when special conditions—selection rules —are met. For example, all three vibrations of the H2O molecule (Vas, Vs, and 5s) and librations (the frustrated rotations of the H2O molecules relative to each other) are active in the IR spectrum of water (Fig. 1.4), whereas the bands of the stretching vibrations of the C C groups are absent in the IR spectra of a polyethylene film (-CH2-CH2 ) . Below we shall formulate these selection rules. Readers interested in this topic should consult Refs. [53-64]. 

The most detailed investigation of single-molecule vibrational spectra has been carried out on the terrylene in polyethylene system by Tchenio et al. [38, 43, 44]. For this study the setup shown in Fig. 8 was used. Single molecule fluorescence spectra were obtained with excitation wavelengths both to the red and slightly to the blue of Aniax (569 nm) of the inhomogeneous distribution. 

Figure 10. Vibrationally resolved fluorescence spectra of terrylene in polyethylene (r= 1.4 K). Tlie bulk spectrum was obtained with excitation near the peak of the inhomogeneously broadened origin band. A-E represent spectra of different molecules which are described in the text. The average time to collect the single molecule spectra was several hundred seconds (from Ref. 38).

In comparison with polyethylene, the low frequencies are excited less rapidly. A fit of the low frequency heat capacities to a one dimensional Debye function (see Eq. 11.161) yidds a j temperature of K compared to the temperature of 540° K of polyethylene. The higher total heat capacity results from the larger number of low frequency vibrations, 7 instead of 4. Very little can be said from h t capacity measurements about the ccnrtributions of the methyl group torsional oscillation or hindered rotation. 

The optical vibrations have also incteased in number by the introduction of the second CHg-group. A look at Tables III. 11 and III. 12 shows that there should only be little effect of the tical vibrations below 150° K. A try to fit a one (or three) dimensional Debye function (Eqs. 11.146 or 11.161) to the data of Table III.15 between 10 and 150° K failed. Neither leads to a constant 0j-temperature as is possible in case of polyethylene, polypropylene and also polystyrene. Of the 10 low frequency vibrations, an average of only 6 seem to be excited at 150° K, indicating that in comparison with polyethylene their average frequencies lie somewhat higher. They must also be higher than comparable frequencies in polypropylene. From the chemical structure of polyisobutylene one would like to conclude that this relative decrease in heat capacity is caused by steric hindrance of the two methyl groups bound to the same carbon atom. 

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