Libration polymer motion

This model can also be extended to further levels of librational motion, each with its own order parameter and correlation time, and has been underpinned more formally in the three-r case of two librational levels plus rotation [7]. It is clearly of a general nature. One may indeed choose to abandon relationship (4.23) and to re-interpret in (4.24) as a more general order parameter. One thereby achieves a model-free theory, which has advantages over alternative, more specific models for polymer motion (see chapter 6), when the motional details are not clear. 

In addition to these elementary motions, the C T measurements have shown that a much faster anisotropic motion occurs, correjgondlng to a libration motion of the CH bonds inside a cone. Recent C Tj measurements ( 10 ) performed on bulk polybutadiene containing both cis 1,4 and trans 1,4 sequences have shown a lower mobility of the trans sequences relatiy to the cis units. This result illustrates the main interest of studies, allowing one to reach more detailed information on the dynamics of each group in the polymer chain and thus yielding a way of setting up a relationship between the chemical structure and the dynamic behavior of bulk polymers. 

PPP is a typical conjugated polymer with nondegenerate ground states in bond alternation. The crystal structure is orthorhombic/monoclinic similar to PA, but a degree of molecular motion in the crystal in particular the librational motion of the ring is reasonably larger than in the case of /rans-PA [2,23]. 

If the molecule also undergoes slow isotropic rotation as before, then this will also tend to reduce G(t) towards zero, but much more slowly than the timescale for libration. (The same will often turn out to be true for the looping motions of a polymer chain). Thus,... 

Although the ratio is not determined to a good accuracy when it reaches large values, interpretation of data shows that Tq is at least 150 or 200 times shorter than for each polymer under investigation. This implies that the anisotropic mode, which is observed in addition to the segmental reorientation in the NMR relaxation experiments, is indeed a very fast process. The high frequency of this motion is one of the main reasons for its assignment to a libration of the internuclear vector about its rest position. 

It has been shown in chapters 4 and 6 that the individual mechanisms describing polymer chain motion in the bulk are often complex. An individual segment may simultaneously execute small-angle libration or rotational diffusion (10 < Tc < 10 s) and rotational jump motion with a broad distribution of correlation times (10 < < 10 s). An amorphous material may... 

In side-chain LC polymers, the molecular dynamics of the mesogenic groups is decoupled from the main chain by use of a flexible (aliphatic) spacer. Three relaxation processes typically take place. (1) The p-relaxation which is assigned to librational fluctuation of the mesogen arotmd the long molecular axis. (2) The 5-relaxation process corresponding to librational fluctuation around the short molecular axis. (3) And finally, the a-relaxation process corresponds to the motion of the polymer backbone at the dynamical glass transition. It should be... 

The correlation time p characterizes three-bond jumps, and the correlation time B characterizes other processes. Bendler and Yaris have also reconsidered the diamond lattice model, and replaced the discrete jump kinetic formulation by a continuum with adjustable cut-offs in the frequency spectrum. The high cut-off arises from the finite size of the smallest displaceable unit, and the low cut-off from the fact that chain displacements will be damped out as they travel down the chain. Librational motions, hitherto neglected, have been considered by Howarth, with success in interpreting relaxation data on proteins. It is possible that this factor should also be taken into account for synthetic polymers. 

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