Entanglements and reptation

PART FIVE ENTANGLEMENT AND REPTATION OF POLYMER MELTS AND NETWORKS... 

There are a number of important concepts which emerge in our discussion of viscosity. Most of these will come up again in subsequent chapters as we discuss other mechanical states of polymers. The important concepts include free volume, relaxation time, spectrum of relaxation times, entanglement, the friction factor, and reptation. Special attention should be paid to these terms as they are introduced. 

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. 

For (p>(pe, entanglement effects control chain dynamics and the reptation model must be used as described below. Between the overlap concentration and the entanglement concentration (cp <solution model of Section 8.5 describes dynamics. The width of this semidilute unentangled regime is given by the ratio of Eqs (9.33) and (9.32) ... 

These tube length fluctuation modes (see Section 9.4.5) of the neighbouring chains affect the constraint release modes of a given chain. If entanglements between chains are assumed to be binary, there should be a duality between constraint release events and chain in a tube relaxation events. A release of an entanglement by reptation or tube length fluctuation of one chain in its tube leads to a release of the constraint on the second chain. If this duality is accepted, the distribution of constraint release rates can be determined self-consistently from the stress relaxation modulus of the tube model. 

Part I summarizes the main ideas of de Gennes, Doi and Edwards about tube models and reptation in entangled polymer systems. Attention has been limited to properties for which predictions can be made without invoking the independent alignment approximation macromolecular diffusion, linear viscoelasticity in the plateau and terminal regions, stress relaxation following a step strain from rest of arbitrary magnitude, and equilibrium elasticity in networks. 

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