Segmental mode

Different methods can be applied for the split into segments. Mode 111222333 denotes that the first n/s (rounded to integer) objects are put into segment 1, the next n/s objects into segment 2, and so on. Mode 123123123 puts object 1 into segment 1, object 2 into segment 2, and so on. Mode random makes a random split but usually without any user control. We recommend to sort the objects by a user-created random permutation of the numbers 1 to n, and then to apply mode 111222333 —and to repeat this several times. 

Fig. 4.7 Temperature dependence of the mean relaxation time (r) divided by the rheological shift factor for the dielectric normal mode (plus) the dielectric segmental mode (cross) and NSE at Qinax=l-44 A (empty circle) and Q=1.92 A (empty square) [7] (Reprinted with permission from [8]. Copyright 1992 Elsevier)...

Due to the coupling of segmental modes of motion, macromolecular dynamics cover a range of 10 orders in magnitude in time. Slow dynamics, however, allow the formation of persistent metastable and intermediate states. Still supramolecular organization under nonequilibrium conditions is a rather unexplored field and there is an urgent need to learn about the scope and the limitations for the formation of supramolecular structures far away from the equilibrium state. 

Note that for POB there is a dielectrically active normal mode at lower frequencies, which has different P and T dependences than the local segmental mode. The T—P superposition at fixed xa holds also for PVME (Fig. 14), EVA (Fig. 15), PMPS (Fig. 16), PVE (Fig. 17), PPG-4000 (Fig. 18), and PiBVE (Fig. 19). For PMPS this superposition is maintained even when xa varies. 

As expected, two relaxation processes are observed for PIP in the bulk the segmental mode, related to the dynamic glass transition representing the dynamics of the polymer segments, and the normal mode, sensing the chain dynamics (Fig. 9). 

The overall dynamics of PIP in the context of dependence on the confinement size is illustrated in Fig. 11, showing the temperature dependence of the dielectric loss of PIP (Mw = 52 kg/mol) down to a him thickness smaller than the end-to-end distance of the polymer chains. The confinement-induced mode becomes faster with decreasing him thickness and approaches the segmental mode, while its relaxation strength increases at the expense of the normal mode, which decreases (Figs. 11 and 12). 

The segmental mode is not shifted in its relaxation rate with decreasing film thickness because it takes place on a length scale much smaller than the confinement size. 

One of the principal advantages of CPMAS experiments is that resolution in the solid state allows individual-carbon relaxation experiments to be performed. If a sufficient number of unique resonances exist, the results can be interpreted in terms of rigid-body and local motions (e.g., methyl rotation, segmental modes in polymers, etc.) (1,2). This presents a distinct advantage over the more common proton relaxation measurements, in which efficient spin diffusion usually results in averaging of relaxation behavior over the ensemble of protons to yield a single relaxation time for all protons. This makes interpretation of the data in terms of unique motions difficult. 

It is to expect that the segmental mode does not depend on the molecular weight of the chain (Fig. 21.10). In contrast... 

FIGURE 21.10. (a) Activation piot for the segmentai mode and the normal mode of c/s-1,4-polyisoprene samples with molecular weights of /H < Me A. PIP-05 , PIP-08 x, PIP-12. The solid lines represent the WLF fit with the fit parameters given in Table 21.3. (b) Activation plot for the segmental mode and the normal mode of c/s-1,4-polyisoprene samples with molecular weights of > Me. , PIP-12 , PIP-17 , PIP-38 PIP-65 T, PIP-97. The solid lines represent the... 

Code Segmental mode To = 250K Normal mode To = 300K... 

Figure 8.10 The temperature dependence of e" (at 1 x 10 Hz) for the unfilled and nanocomposite NR samples after crosslinking. For vulcanized NR the main process is associated with the segmental mode (SM). For the nanocomposite an additional slower relaxation (SR) appears at higher temperatures.

In the above description of local motions, characterizes the segmental modes. In order to know whether these segmental motions observed by NMR in bulk at temperatures well above the glass-transition temperature belong to the glass-transition processes, it is of interest to compare the variations of Ti as a function of temperature with the predictions of the Williams-Landel-Ferry (WLF) equation [19]. The WLF equation describes the frequency dependence of the motional processes associated with the glass-transition phenomena. It can be written as [20]... 

Star-branched polymers contain a center to which chains ( arms ) of usually equal length are linked. Experiments were pioneered by Stockmayer and Burke and theoretical studies by Ham and Zimm and Kilb. Of special interest are cis-PI star polymers, " because in these systems the molecular dynamics can be traced on two different length scales the segmental mode corresponding to fluctuations of a few polymer segments, and the normal mode representing fluctuations of the end-to-end vector of the arms by BDS. The arm fluctuations have to be considered as that of a tethered chain, because the chain end at the star center is fixed. This bormdary condition carrses, compared to a linear chain, a retardation of the normal-mode relaxation by a factor of 4 ... 

Figure 25) delivers a similar picture Two segmental mode relaxations of the different blocks take place which are well separated in time. It is remarkable that the fluctuation of the end-to-end vector (normal mode) has a similar temperature dependence as in the PI homopolymer. A closer look reveals... 

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