Entanglement density, effect

From the foregoing it will be clear that whenever entanglements and long chain branching are both present the dynamics in a polymer melt are highly co-operative. The orientational relaxation time of chain segments is exponentially dependent on both the contour distance to the nearest effective free end and on the effective entanglement density of its enviroiunent at all previous timescales. 

Such an intramolecular cooperativity plays quite an important role, in particular in fracture behaviour. Indeed, when considering the effect of replacing iso- by tere-phthalic units, in most cases it has not been possible to account for the results by considering the entanglement density, nor the yield stress. Only the occurrence of intramolecular cooperativity leads to consistent expla-... 

The way to remove entanglements, viz. the manner in which topological constraints limit the drawability, is seemingly well understood and crystallization from semi-dilute solution is an effective and simple route to make disentangled precursors for subsequent drawing into fibers and tapes [ 17,18]. A simple 2D model visualizing the entanglement density is shown in Fig. 3. Here 0 is the polymer concentration in solution and 0 is the critical overlap concentration for polymer chains. 

Moreover, Wu related AGR for miscible polymers to entanglement density 134]. For AG < 0 the entanglement density in the miscible system is reduced compared to additivity behavior which means that the different chain molecules tend to align in the mixture. This is the same effect as stated above. The shift of the spinodal temperature caused by flow can be estimated easily as follows. The spinodal may be given as in the case of a system at rest... 

The functions g(9) and h 6) represent two separate effects of disentanglement g(6) is the fractional reduction of entanglement density due to steady shear flow and h(ff) is the fractional reduction in energy dissipation rate per molecule due to dis-entanglement in steady shear flow (for details, see Graessley, 1974, Chap. 8). Eqs. (16.52)-(16.55) define an implicit expression for the master curve rj/rj0 vs. qzn, the reduced viscosity also being present in the arguments of the functions g(6) and h(6). 

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. 

Having set out a detailed model of craze growth, we now compare its predictions with recent experiments in two principal areas 1) the effects of entanglement density and 2) the effects of temperature. 

The first molecular variable to be considered is chain entanglement density. It is known that this factor, as well as a related parameter, viz. the average chain contour length between entanglements, can have an appreciable effect on deformation modes observed in thin films and on various aspects of crazing such as the craze stress and the craze fibril extension ratio. Examples of these effects will be presented and dis-... 

A careful inspection of Tables 4 and 5 shows that changes, even limited, in the details of SAPA chemical structure may affect noticeably their fracture behavior. Although it has been carried out [1], a systematic study of their effects falls out of the scope of this article, because too many parameters are concerned. They include yield stress, p relaxation characteristics, tensile modulus, entanglement density, Mw / ratio, and also, in the high temperature range, the gap (Ta-T) between Ta and the test temperature T. Instead, emphasis will just be put here on two features whose explanation is quite simple. 

In the above expression, a is the dissociation energy, R is the gas constant, while B and D are material parameters. Such evolution of the entanglement density is used to model a reduction of the hardening with temperature. Consistent with the above-mentioned assumption that the effects of chain entanglement when T > Tg are considered to be lumped into q and m, we shall here employ the side condition that n(T g) = 0. Mth this, it is seen that the parameters in (5) need to satisfy B/D = exp(- a/ 7g)-... 

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