Entanglements in polymer melts

The Edwards tube model of polymer entanglements was already discussed in Section 7.3.1. The topological constraints imposed by neighbouring chains on a given chain restrict its motion to a tube-like region (see Fig. 7.10) called the confining tube. The motion of the chain along the contour of- 

The tube can be thought of as being composed of NjN sections of size a, with each section containing monomers. The chain can be considered as either a random walk of entanglement strands NjNc strands of size a) or a random walk of monomers (A monomers of size b). 

The average contour length (L) of the primitive path (the centre of the confining tube, see Fig. 7.10) is the product of the entanglement strand length a and the average number of entanglement strands per chain N/N.  

The average primitive path contour length (L) is shorter than the contour length of the chain bNhy the factor afb because each entanglement 

One manifestation of entanglement in long chains (N Ne) is the appearance of a wide region in time (or frequency) where the modulus is 

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Table 9.1 shows and calculated from the measured plateau modulus. All flexible polymers have Pg —20 overlapping entanglement strands defining the entanglement volume a, which is the overlap criterion for entanglement in polymer melts. 

Colby, R. H., Rubinstein, M., Viovy, J.-L. Chain entanglements in polymer melts. Macromol (1992)... 

Polymer chains are strongly entangled in the melt but despite this they behave in a way that is thermodynamically ideal. This surprising fact was first reported by P. J. Rory in 1949, but may be readily understood. If we... 

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]. 

Figure 4.53 Schematic illustration of the reptation process in polymer melts, showing chain entanglements (light arrows), the wriggling motion of the polymer chain (darker arrows), and the primitive path of the polymer chain (dark Une). Reprinted, by permission, from G. Strobl, The Physics of Polymers, 2nd ed., p. 283. Copyright 1997 by Springer-Verlag.

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. 

In order to test the model of intrinsic craze initiation it would be desirable to produce entanglement networks of different structures and study X as a function X. This may be achieved by pre-orientation of PC above T. In fact, there is much evidence that the entanglement network in polymer melts is modified increasingly with the magnitude of deformation i32,i5o.i59,i6i> -j-jjg modification must be assumed to arise... 

Chains in polymer melts and entangled polymer solutions form an effective... 

There are four different regimes of monomer displacement in entangled linear polymer melts, shown in Fig. 9.20. The subdiffusive regime for the mean-square monomer displacement is a unique characteristic of Rouse motion of a chain confined to a tube, which has been found in both NMR experiments and computer simulations. 

At a given polymer coneentration, increased MW gives more effective DR. Polymers with MW lower than 100,000 are likely to be ineffective.Liaw, Zakin, and Patterson, introduced a reduced MW, m = MW/Mc, which takes into account the entanglement capacity of a polymer chain to compare MW effects of different polymers.is the minimum chain size for molecular entanglements to occur in polymer melts. 

Minimum MW for entanglements to occur in polymer melts (g/mol) Molecular weight (g/mol)... 

Polymer chains are strongly entangled in the melt but despite this they behave in a way that is thermodynamically ideal. This surprising fact was first reported by P. J. Flory in 1949, but may be readily understood. If we consider the repulsion potential, U, experienced by a monomer unit of a polymer in the melt, we can divide U into two terms, one due to repulsion by other monomer units of the same molecule, U, and the other due to repulsion by monomer units in different polymer mcdecules, f/,i, i.e. 

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