Skeletal vibrations, intramolecular

Now, in aromatic hydrocarbons intramolecular skeletal vibrations, rather than C—H vibrations, dominate the vibronic coupling contribution to the term J m = — . Furthermore, intermolecular vibrations will have negligible effect on the coupling of the electronic states of interest. Thus, in the case of internal conversion, where the (relatively large) matrix elements are solely determined by intramolecular vibronic coupling, no appreciable medium effect on the nonradiative lifetime is to be expected. On the other hand, intersystem crossing processes are enhanced by the external heavy atom effect, which leads to a contribution to the electronic coupling term. 

Heat capacity theory permits a correlation with the chemical structure of the repeating unit (U). In the solid state, only vibrational contributions need to be considered (skeletal and group vibrations). For an approximate discussion of the skeletal vibrations, the molecule is considered to be a string of structureless beads of the given formula weight. For linear macromolecules with similar backbones, the geometry and force constants are similar so that intramolecular skeletal vibrations are fixed by the mass of the structureless bead. The inter-molecular vibrations of linear macromolecules have quite low... 

The addition scheme of group contributions helps to connect larger bodies of data for liquid polymers. In the Uquid state one is always at a sufficiently high temperature so that the intermolecular skeletal vibrations are ftdly excited so that additivity holds for both the intramolecular skeletal vibrations and the group vibrations. Figure 2.59 shows the experimental data for the liquids for the same series of polyoxides as analyzed for the soUd state. The equation in the top of the graph represents all the thin lines, while the thick hnes represent the experimental data. The equation for Cp was arrived at by least-squares fitting of all experiments and seems more precise than any of the separate experiments. 

More refined models of the heat capacities of polymers can be obtained by deconvoluting the "skeletal vibrations" of chain molecules from their set of discrete "atomistic group vibrations", and by further deconvoluting the "intramolecular" component of the skeletal vibrations from the "intermolecular" (i.e., interchain) component. The major portion of the heat capacity at temperatures of practical interest (i.e., temperatures which are not too low) is accounted for by the atomistic group vibrations. The remaining portion of the heat capacity arises from skeletal modes. Detailed discussion of these issues is beyond the scope of this chapter. The reader is referred to the reviews provided by references [1-3] for further details and lists of the original publications. 

Improvements beyond the empirical, direct additivity of heat capacities is needed at low temperatures, where skeletal vibrations govern the heat capacities. With only few measured points it is possible to establish the functional relationship of the 0, and 3 temperatures with concentration for the inter- and intramolecular vibrations (see Sect. 2.3). The group-vibration frequencies are strictiy additive, so that heat capacities of complete copolymer systems can be calculated using the ATHAS, as discussed in Sect. 2.3.7. hi Fig. 2.70 the glass transition changes with concentration, to reach 373 K for the pure polystyrene, as for the previously discussed copolymer systems with polystyrene. Below T, the solid Cp of both components needs to be added for the heat capacity of the copolymer, above, the liquid Cp must be used. The glass transition retains the same shape and width as seen in Fig. 7.68 on the example of brominated poly(oxy-2,6-dimethyl-l,4-phenylene) [29]. 

Overall, these molecular dynamics crystal simulations showed that random, uncorrelated conformational disorder was governed by three processes (1) the intramolecular dynamics leading to local isomeric transition (2) the number of intermolecular collisions and (3) the restrictiveness of the crystal environment [5b]. These initial conformational defects do not corr pond to a potential energy minimum and thus cannot easily be predicted by molecular mechanics calculations. They are the result of the dynamic interaction of skeletal vibrations... 

The application of Stepanov s theory to intramolecular F bonded systems has been criticized [42], In this case the low frequency vibration described above as vXH Y is also partly constrained by a more nearly harmonic vibration involving skeletal bending motions of the rest of the molecule, and the X, H, and Y atoms are not collinear. These factors would seem to suggest that (I) the vXll Y type of vibration will be of higher frequency than in the usual case (perhaps 200-300 cm"1 rather than 100-200 cm"1) so that the sub-bands will be more widely spaced and may not be recognised as part of the rXH band (2) the motion of the H atom will have less effect on rXY and (3) H-bond bending vibrations may also couple considerably with vXH. The observation of rather smaller frequency shifts for vXR and narrower absorption bands w such cases are in reasonable agreement with this picture,... 

Following the classical approach of vibrational dynamics (as in the case of o--bonded polymers) [67], the experimental data from the oligomers could in principle be used to obtain the phonon dispersion curves of the ideally infinite polymer. In the case of 7r-bonded systems, complications arise because the skeletal modes are strongly CL-dependent and cannot be treated in the standard way. The rationalization of the behavior of the totally symmetric Raman-active normal modes leads to the definition of a CL-dependent intramolecular potential on which the effective conjugation coordinate (ECO theory is based (see Section IV). 

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