Relaxation terminal chain

Whichever process relaxes the chain faster is the one that controls terminal dynamics. 

It is noteworthy that when Schweizer worked out his equation for entangled polymer melts, he did not obtain a stretch exponential that has exponent P = 0.57 or 0.59 that would have let him obtain the experimental or the dependence of the terminal relaxation time in order to be consistent with the experiment. On the other hand, as hinted by Schweizer (1989), Property (ii) of the CM when applied to terminal chain relaxation time xr of PI in blends with PtBS leads to the relation,... 

Component B represents motions in the chain-mode regime between Tg and the terminal chain relaxation time. On a time scale up to the longest chainmode relaxation time, which in terms of the Rouse model is given by Tr (see Eq. 54), it is independent of the molecular mass. A relatively weak molecular... 

Component C finally terminates component B and may become visible in the experimentally accessible frequency window of field-cycling NMR relax-ometry in the form of a crossover to an extreme-narrowing plateau [2]. Since this crossover is coimected with the terminal chain relaxation time T(, it will be strongly dependent on the molecular mass. This effect, however, will show up in the experimentally accessible frequency window of NMR re-laxometry only for relatively small molecular masses (in contrast to the NMR diffusometry experiments). 

Remarkably, a series of distinct and apparently universal NMR relaxation dispersion regimes can be identified from the data in Figs. 28 to 34 for the diverse polymer species. We consider the time/frequency window Tt Ts (see Fig. 5). The terminal chain relaxation time, Tt> is in-... 

Chain reactions, 181 branching, 189 initiation step, 182 propagation steps, 182 rate laws for, 188 termination step, 182 well-behaved, 187 Chemical mechanism, 9 Chemical relaxation, 255-260 Coalescence temperature, 262 Col, 170... 

Reaction scheme, defined, 9 Reactions back, 26 branching, 189 chain, 181-182, 187-189 competition, 105. 106 concurrent, 58-64 consecutive, 70, 130 diffusion-controlled, 199-202 elementary, 2, 4, 5, 12, 55 exchange, kinetics of, 55-58, 176 induced, 102 opposing, 49-55 oscillating, 190-192 parallel, 58-64, 129 product-catalyzed, 36-37 reversible, 46-55 termination, 182 trapping, 2, 102, 126 Reactivity, 112 Reactivity pattern, 106 Reactivity-selectivity principle, 238 Relaxation kinetics, 52, 257 -260 Relaxation time, 257 Reorganization energy, 241 Reversible reactions, 46-55 concentration-jump technique for, 52-55... 

Some information concerning the intramolecular relaxation of the hyperbranched polymers can be obtained from an analysis of the viscoelastic characteristics within the range between the segmental and the terminal relaxation times. In contrast to the behavior of melts with linear chains, in the case of hyperbranched polymers, the range between the distinguished local and terminal relaxations can be characterized by the values of G and G" changing nearly in parallel and by the viscosity variation having a frequency with a considerably different exponent 0. This can be considered as an indication of the extremely broad spectrum of internal relaxations in these macromolecules. To illustrate this effect, the frequency dependences of the complex viscosities for both linear... 

In the case of polymer samples, it is expected that, at the temperatures and frequencies at which the rheological measurements were carried out, the polymer chains should be fully relaxed and exhibit characteristic homo-polymer-like terminal flow behavior (i.e., the curves can be expressed by a power-law of G oc co2 and G" oc co). 

The longest relaxation time. t,. corresponds to p = 1. The important characteristics of the polymer are its steady-state viscosity > at zero rate of shear, molecular weight A/, and its density p at temperature 7" R is the gas constant, and N is the number of statistical segments in the polymer chain. For vinyl polymers N contains about 10 to 20 monomer units. This equation holds only for the longer relaxation times (i.e., in the terminal zone). In this region the stress-relaxation curve is now given by a sum of exponential terms just as in equation (10), but the number of terms in the sum and the relationship between the T S of each term is specified completely. Thus... 

In particular it has been conjectured that the terminal relaxation of star polymers might be the most sensitive test of the dilution exponent P in Go theta solvents suggest a mean value of nearer 2.3 [32]. A physically reasonable scahng assumption for the density of topological entanglements in a melt of Gaussian chains leads to a value of 7/3 [31]. 

---