Molecular motions, entangled polymer chains

In nondilute polymer solutions and melts, the polymer coils interpenetrate each other enough that the molecular motions of one chain are greatly slowed by the interfering effects of other chains. These interferences are attributed to intermolecular entanglements. 

This chapter has illustrated how stress relaxation, creep, and rheology in polymers depend on the rate of molecular motion of the chains and on the presence of entanglements. It must be remembered that aU macroscopic deformations of matter depend ultimately on molecular motion. In the case of high polymers, the chain s radius of gyration is changed during initial deformation or flow. Thermal motions tend to return the polymer to its initial conformation, thus raising its entropy. Clearly, there is a direct relationship between the mechanical or viscous behavior of polymeric materials and their molecular behavior. 

The interdiffusion of polymer chains occurs by two basic processes. When the joint is first made chain loops between entanglements cross the interface but this motion is restricted by the entanglements and independent of molecular weight. Whole chains also start to cross the interface by reptation, but this is a rather slower process and requires that the diffusion of the chain across the interface is led by a chain end. The initial rate of this process is thus strongly influenced by the distribution of the chain ends close to the interface. Although these diffusion processes are fairly well understood, it is clear from the discussion above on immiscible polymers that the relationships between the failure stress of the interface and the interface structure are less understood. The most common assumptions used have been that the interface can bear a stress that is either proportional to the length of chain that has reptated across the interface or proportional to some measure of the density of cross interface entanglements or loops. Each of these criteria can be used with the micro-mechanical models but it is unclear which, if either, assumption is correct. 

There have been several attempts to relate Kg to the critical molecular weight (Mcr, which is discussed in Chapter 13) based on considerations of the effects of polymer chain entanglements on the large-scale cooperative motions of chain segments involved in the glass transition for example, see references [97-99]. It was also suggested [100,101], from considerations of chain stiffness and the statistics of chain conformations, that Kg should be proportional to a power of... 

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