Elastically effective entanglement points

Table II contains the values for the number of elastically effective entanglement points both as calculated from Gp (ng(exp)) and as calculated theoretically for an ideal network (n (theo)). The ratio ng(exp)/ng(theo) re-...

Table U. Elastically Effective Entanglement Points as Calculated from Gp and...

On the other hand, as the following relationship applies between the mesh width Mg (molecular weight between two entanglement points) and the number of elastically effective covalent entanglement points (n J... 

Hence, the effect of the entanglements is two-fold, since both the elastic and the viscous properties are concerned. The observations all indicate the existence of a critical molar mass, introduced earlier as the critical molar mass at the entanglement limit, denoted by Me. Polymers with low molar masses, M < Me, exhibit no entanglement effects, but for M > Me they show up and become dominant. All properties that are founded on motions on length scales corresponding to a molar mass above Me are affected. This holds, in particular, for the viscosity and the dielectric normal mode since these include the whole polymer chain. On the other hand. Rouse dynamics is maintained within the sequences between the entanglement points, as has already been mentioned. 

Let us now consider the modulus in more detail. It was shown very early that fluctuations in crosslink density modify the modulus and this can be brought into a general context. The modulus is related to the structure of the material as we have seen in the section of network formation. The question raised from the structural point of view is whether there is any concept as to how to count the contribution of elastically effective chains to the modulus. This question is difficult to answer and the main problem is the inffuence of entanglements. 

More elaborate versions of the molecular theory may account for entanglement, loose ends or loose loops, deviations from Gaussian statistics, the statistics of actual chains, excluded-volume effects (real chains with finite thickness cannot interpenetrate each other), the movement of junction points, the contribution of the internal energy to elasticity, changes in volume, etc. 

The chemical nature of the cross-link points is quite unimportant to typical cross-linked network properties such as elasticity and swelling in solvents. Most chemical cross-linking occurs via covalent bonds, but cross-linking can also be achieved with coordinate or electron-deficient bonds. Cross-link-like effects can also be caused by purely physical phenomena, for example, by crystallite regions in partially crystalline polymers, amorphous domains in block polymers, or molecular entanglements in amorphous polymers and polymer melts. 

Polymer chain entanglement has a significant effect on the processing of polymer fibre. According to rubber elasticity theory, the maximum stretch ratio of polymer fibre (A ax) and the number of statistical links of the polymer chain cross-linking points are in the relationship shown in Equation... 

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