Rotation of the chain

This decrease in effective flexibility can be attained by extending the macromolecules in a mechanical or stationary hydrodynamic field3). The extending fields decrease the freedom of internal rotation of the chain units, and the new effective flexibility parameter now becomes ... 

Fig. 10 Shear deformation of a domain shown in Figs. 5 and 6 results in a rotation of the chain axes and in a relative displacement x of the chains, which is proportional to the shear angle or the shear strain 2(0-0)...

So far we have employed in this discussion a critical shear stress as a criterion for fibre fracture. In Sect. 4 it will be shown that a critical shear strain or a maximum rotation of the chain axis is a more appropriate criterion when the time dependence of the strength is considered. 

During the creep of PET and PpPTA fibres it has been observed that the sonic compliance decreases linearly with the creep strain, implying that the orientation distribution contracts [ 56,57]. Thus, the rotation of the chain axes during creep is caused by viscoelastic shear deformation. Hence, for a creep stress larger than the yield stress, Oy,the orientation angle is a decreasing function of the time. Consequently, we can write for the viscoelastic extension of the fibre... 

Examples of mesomorphic forms characterized by disorder in the conformation of the chains have already been described in Section 2.6. For instance, a mesomorphic form is present in the high-temperature form I of polytetrafluoro-ethylene.106,107 In this phase the chains are in disordered conformation due to the presence of helix reversals along the chains.108-110 Moreover, intermolec-ular disorder is also present due to the random rotations of the chains around the chain axes.109 A long-range three-dimensional order is present only in the pseudohexagonal placement of the chain axes.107,109... 

Because of the orderly arrangement of pendant methyl groups, which allows the units to fit well together, rotation of the chain is restricted. ft-PP has a relatively high Tt (—18 C) and a relatively high Tm (176 C). 

If we neglect the distortion of the segment distribution in the fuzzy cylinder by the shear flow, we can apply Doi s stress expression, Eq. (61), to fuzzy cylinder systems as it stands. The neglect of the distortion may be justified when the shear-rate is low. Equation (61) expresses the contribution of the end-over-end rotation of the chain to asegment distribution is not distorted, the orientational entropy term Sor in the static free energy expression contains only the orientational entropy loss of the entire chain, but not the conformational entropy loss cf. Sect. 2.3. 

The rotational diffusion coefficient Dr of a rodlike polymer in isotropic solutions can be measured by electric, flow, and magnetic birefringence, dynamic light scattering, and dielectric dispersion. However, if the polymer has some flexibility, its internal motion makes it difficult to extract Dr for the end-over-end rotation of the chain from data of these measurements. In other words, Dr can be measured only for nearly rodlike polymers. 

It is known that crystalloid lum an influence on the position of the glass transition temperature. For instance, amorphous poly (ethylene terephthalate) has a TfJ of 67°C. This increases to 81 C. for the crystallized polymer (11). This is explained by the fact that the rotation of the chain segments, which is made possible at the glass transition, is hindered tn the proence of the crystallites. 

The described chain migratory insertion mechanism, which operates in olefin polymerisation with metallocene-based single-site catalysts, follows that proposed by Cossee [268,277,278] for olefin polymerisation with heterogeneous catalysts there is, however, no back skip of the polymer chain to the previously occupied position prior to the coordination of the next monomer molecule, but rotation of the chain around the axis of the Mt-CH2 bond takes place (Figure 3.19) [358],... 

A schematic representation of the domain contributions to the tensile deformation of a fibre is depicted in Fig. 13.97 and shows that the total deformation consists of chain stretching and shear deformation resulting in rotation of the chain axis. For an infinitesimal deformation and well-oriented fibres Northolt and Baltussen found for the initial modulus, El, and for the initial compliance,S[n, of the fibre... 

Removal of a proton from C4 forms an extended enol, which can be protonated at C2 or C4. Proto nation at C4 is thermodynamically favoured as it leads to the conjugated alkene. But protonation at C2 is kinetically favoured, and this leads to the nonconjugated alkene. The geometry of the new alkene depends on the conformation of the chain when the first (deprotonation) step occurs. It is thought that this is the best conformation for the previous reaction, the dehydration step, and that no rotation of the chain occurs before the isomerase gets to work. 

A planar form of the growing chain end is, of course, much more frequent. Most hydrocarbon radicals, carbenium ions, and carbanions are in the sp2 state. From a planar chain end, a specific structure is only formed after the addition of a further unit. When the possibility of (momentary) rotation of the chain end is excluded the sp3 configuration generated from the sp2 state depends on the direction of monomer approach, which is thus one of the factors determining the stereochemistry of addition... 

However, in any conformation the chain as a whole has a dipole moment m being the vector sum of dipole moments Mq of all its polar groups. The rotating moment exhibited by the dipole p in the electric field, can lead to the orientation of p in the field direction through rotation of the chain molecule as a whole (large-scale motion). In this case, the mechanism of the appearance of the polarization and macroscopic solution anisotropy may be called orientational mechanism. 

Figure 7.26 shows the temperature dependence of ESR spectra of PE chain end type of propagating radical tethered to a PTFE surface [27]. The radicals were produced by ball-milling of PTFE with a large amount of ethylene monomer. The dotted spectra at 15 and 30 K were calculated using the site exchange rates of 10 and 56 MHz, respectively. The spectrum observed at 95 K could be simulated by the rotation of the chain end about the chain axis along with the site exchange motion. The oscillation amplitude was also estimated from the values of SPLIT A and B, shown in Fig. 7.26. The ESR spectra of the end type of scission radicals produced by the mechanical fracture of PE were also simulated by the site exchange model between the sites 1 and 2 as described in Fig. 7.50 (in Appendix A7.1). The reason...

To fix our ideas consider again the simple model for the polethylene fibre with full orientation, but where there is rotation of the chain around its axis (at a frequency greater than the line width in Hz, i.e. lO -lO Hz for proton resonance with Hq 10 kg). The length of the internuclear vector r is unchanged by the motion and we have for the proton pair interaction only ... 

The modified series model shown in Fig. 21 has been extended to include the viscoelastic behaviour. To this end the simple assumption is made that the time-dependent part of the creep strain arises solely from the rotation of the chains towards the direction of the fibre axis as a result of the shear deformation of the crystallites. This yields for the fiber extension as a function of the time t during creep caused by a stress CTq... 

In a real polymer coil, not all angles r are possible. As one can see in Fig. 8.3, in a real polymer chain, the bond angle r is fixed and the rotation of the chain is restricted and reduced to the most probable torsion angle 0. Additional short-range interactions of the polymer chain segments can be captured with an additional factor In consideration of all these short-range interactions, the end-to-end distance of a polymer coil in its unperturbed dimensions, o, can be described with the following expression ... 

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