Polymers rotational modes

As is well known, molecular motions such as local mode relaxation of the main chain and rotational mode relaxation of the side chain are not frozra-in at T. The typical temperature dependence of viscoelastic properties is shown schranatkally in Fig. 3 for both crystalline and amoridious polymers. Sub ass transitions (Tp, T, Tg, etc.) corresponding to the freezing of these local motions appear as peaks in a tan temperature curve. 

Good agreement with experimental viscoelastic measurements on several helical polymers has been obtained with an empirical hybrid relaxation spectrum in which a separate rotational mode (relaxation time tq) has been added to a set of mechanisms attributed to internal motions and spaced in accordance with the Zimm spectrum (tj, T2,. . The appropriate equations for [(/ ] and are as follows ... 

The invariance of relaxation frequency with molecular wei t may not be apparent at finite concentrations of polymer, because cofl — c< interactions can effect the relaxation of internal modes as well as the first order, rotational mode. There have been a number of studies of the concentration dependence of dielectric loss processes some of which show weU the continuous trend in behawour from dilute solution to the bulk state. Temperature variation can provide useful information on the enthalpies of activation of local mode motions. Finally, since such local modes are very structure sensitive, differences in chain tacticity would be expected, and do cause changes in loss behaviour. This prediction has been authenticated for such polymers as poly(methyl methacrylate) and poly(ethyl acrylate). ... 

For the two acoustic branches of an isolated polymer chain, vibrational frequencies are reduced to v = 0 for the phase difference of 5 = 0 and vibrational modes are reduced to the translational mode along the chain axis and the rotational mode about the chain axis. For the polyethylene chain, the unit rotation angle is 6 = 7t, and two acoustic branches are again reduced to v = 0 for 5 = 6 = 7t and vibrational modes are reduced to the translational modes perpendicular to the chain axis. 

Besides polydispersity effects, which are neglected in the following discussion, internal modes of motion for flexible polymers, rotational diffusion for rigid rods, hydrodynamic interaction and long range intermolecular potentials may cause the partly pronounced q-dependence of D,pp(q). 

For a molecule consisting of N atoms, the number of vibrational degrees of freedom is 3N -6, leading to the same number of normal modes of vibration. For linear molecules, where low rotational modes are equivalent, the number of vibrational degrees of freedom is represented by 3N-5 (Campbell et al., 2000 Stuart, 2004). The degrees of freedom for polyatomic molecules, eg, polymers, are summarized in Table 7.2. 

It has to be noted that Kremer et al conducted their studies on purposely unoriented samples. They did so because the presence of the optically active end groups in the side mesogen chains usually leads to chirality of the mesophase. As a result, polymers 31, 37, 39, 41 and 43 exhibit the cholesteric (chiral nematic) phase, and polymer 40, 41 and 43 the chiral smectic C phase.Since the smectic C shows ferroelectric-ity, in order to separate the molecular rotational modes from the ferroelectric Goldstone and soft modes (cf. Section 4.3), samples should be unoriented. On the other hand, measurements performed on the oriented sample of the chiral C phase of polymer 43 led Vallerien et al to the observation of ferroelectric modes. 

The compounding was done using a Leistrez twin-screw extruder operated in co-rotating mode. The L/D ratio of the extruder was 40 1. All fillers were fed into the polymer using a loss-on-weight feeder. The conqwunded sanples were then injection molded into ASTM test specimens. 

The main mode of action of plasticisers appears to be to act as spacers at the molecular level. Hence less energy is required to free the molecules sufficiently to allow substantial rotation about the C—C bonds thus is lowered. So, too, is the temperature at which the polymer begins to flow. 

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