Transient chains

Fig. 11). It is, therefore, highly probable that the bulky filler particles impose geometrical hindrances (entropy constraints) for the chain dynamics at the time scale of the NMR experiment (of the order of 1 ms). This effect may be compared with the effect of transient chain entanglements on chain dynamics in polymer melts. It should be remarked that the entanglements density estimated for PDMS melts by NMR is close to its value fi om mechanical experiments [38]. Therefore, it can be assimied that topological hindrances from the filler particles can also be of importance in the stress-strain behavior of filled elastomers. 

Rotational convection and angular Brownian motion of clusters, as well as ather-mal nucleation resulting from transient free energy of the system are considered. One concludes that the cluster growth mechanism dominates the other mechanisms of oriented nucleation in the systems with transient chain deformation and orientation. Example computations illustrating transient effects in oriented nucleation are presented for the case of uniaxial elongational flow. 

The example indicates that, due to the transient chain deformation between the initial affine and the steady state mode, we expect transient effects in free energy and, in consequence, in the kinetics of crystal nucleation also at fixed deformation rates applied to the system. With a time-dependent deformation rates, ej(t), the transient effects are more complex. But they are tractable in terms of the present model where a numerical solution of (4.11) is needed for specified time dependent elongation rates. 

We have studied self-diffusion in polymer-like networks self-diffusion of transient chains (long entangled micelles) and tracer diffusion in the solvent (silica gels). Our results illustrate the role of reversible chain breaking and the scale-dependence of diffusion in the solvent. 

Equations 11.23 through 11.26 are the counterparts to Eqs. 11.14 through 11.17 of the MED theory. In Eq. 11.23, the CCR term is just Ir S, similar to the CCR term K S - XlA) in the MED theory, but without the transient chain retraction rate A/ /I. (In Eq. 11.23, an absolute value must be taken of the CCR term at S to keep its value positive, while in the MED theory, this term is kept positive through the stretch equation 11.16.) The expression Eq. 11.23 for the orientational relaxation time contains not only the reptation time and the rate of convective constraint release k S, but also the stretch time t. This guarantees that even for velocity gradients greater than 1 /Tj, the rate of orientational relaxation remains bounded by 1 /Tj. This effectively switches off the CCR effect for fast flows, and so functions in much the same way as the switch function/(A) in the MED theory. Hence, no explicit switch function is present in Eq. 11.23. 

The analysis of steady-state and transient reactor behavior requires the calculation of reaction rates of neutrons with various materials. If the number density of neutrons at a point is n and their characteristic speed is v, a flux effective area of a nucleus as a cross section O, and a target atom number density N, a macroscopic cross section E = Na can be defined, and the reaction rate per unit volume is R = 0S. This relation may be appHed to the processes of neutron scattering, absorption, and fission in balance equations lea ding to predictions of or to the determination of flux distribution. The consumption of nuclear fuels is governed by time-dependent differential equations analogous to those of Bateman for radioactive decay chains. The rate of change in number of atoms N owing to absorption is as follows ... 

A number of proteins are known to pass through a transient intermediate state, the so-called molten globule state. The precise stmctural features of this state are not known, but appear to be compact, and contain most of the regular stmcture of the folded protein, yet have a large side-chain disorder (9). 

In Fig. 20 we show the MSQ of a system of GM [66] with different mean chain lengths (depending on 7, cf. Eq. (12)) for three values of LO=l, 0.1, 0. 01. Since the individual chains have only transient identity, it is meaningless to discuss their center of mass diffusion. It is evident from Fig. 20 that the MSQ of the segments, g t) = ([x( ) - x(O)j ), follows an intermediate sub-diffusive regime, g(t) oc which is later replaced by conventional diffusion at some characteristic crossover time which grows... 

The existence of kinks was recently explicitly taken into account by Larson (Fig. 14) as a possible model for chain unravelling in the flow [69]. At the same time, Kausch developed a similar model to explain degradation results measured in transient elongational flow (Fig. 15) [70]. With this difference from the Larson model, kinks in the latter model can support compressive stress chain elastic modulii range from 16 to 110 GPa, depending on the number of defects within the kinked region. 

In transient elongational flow degradation, it was determined in the authors laboratory, by a detailed mass balance, that main chain scission accounted for >95% of the degradation in dilute solution. Any other type of depolymerization, if present, should then be of minor importance. 

The exponent x is an empirical parameter to be determined from experiments. For a fully extended chain in stagnant elongational flow, x is equal to 2 whereas a value of 1 was found under transient flow conditions (Sect. 5.4). 

From the weak dependence of ef on the surrounding medium viscosity, it was proposed that the activation energy for bond scission proceeds from the intramolecular friction between polymer segments rather than from the polymer-solvent interactions. Instead of the bulk viscosity, the rate of chain scission is now related to the internal viscosity of the molecular coil which is strain rate dependent and could reach a much higher value than r s during a fast transient deformation (Eqs. 17 and 18). This representation is similar to the large loops internal viscosity model proposed by de Gennes [38]. It fails, however, to predict the independence of the scission yield on solvent quality (if this proves to be correct). 

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