Entangled states entanglement

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. 

Since the slippage factor is a fraction, Eq. (2.59) states in mathematical terms something we realize must be the case, namely, that the effects of entanglements on the neighbors of the original molecule must diminish as we move away from that molecule to prevent the coupling from producing an infinite viscosity. 

Chemical crosslinks and entanglements differ, however. The former is permanent, the latter transient. Given sufficient time, even the effects of entanglements can be overcome and stationary-state flow is achieved. An... 

Cast material is stated to have a number average molecular weight of about 10. Whilst the Tg is about 104°C the molecular entanglements are so extensive that the material is incapable of flow below its decomposition temperature (approx. 170°C). There is thus a reasonably wide rubbery range and it is in this phase that such material is normally shaped. For injection moulding and extrusion much lower molecular weight materials are employed. Such polymers have a reasonable melt viscosity but marginally lower heat distortion temperatures and mechanical properties. 

Amorphous stereotactic polymers can crystallise, in which condition neighbouring chains are parallel. Because of the unavoidable chain entanglement in the amorphous state, only modest alignment of amorphous polymer chains is usually feasible, and moreover complete crystallisation is impossible under most circumstances, and thus many polymers are semi-crystalline. It is this feature, semicrystallinity, which distinguished polymers most sharply from other kinds of materials. Crystallisation can be from solution or from the melt, to form spherulites, or alternatively (as in a rubber or in high-strength fibres) it can be induced by mechanical means. This last is another crucial difference between polymers and other materials. Unit cells in crystals are much smaller than polymer chain lengths, which leads to a unique structural feature which is further discussed below. 

Fig, 14. Disentanglement mechanism (A) Tightened slack between entanglements. (B) Retraction and disentanglement by Rouse relaxation. (C) Critically connected state. 

How does the polymer chain sneak out from the entangled random coil state and how does it order into a crystalline state ... 

Under quiescent conditions, polymer solutions are divided into four categories depending on the average distance separating the centers of mass of the molecular coils the dilute, the semi-dilute (or semi-concentrated), the concentrated and the entangled state. 

Such considerations appear to be very relevant to the deformation of polymethylmethacrylate (PMMA) in the glassy state. At first sight, the development of P200 with draw ratio appears to follow the pseudo-affine deformation scheme rather than the rubber network model. It is, however, not possible to reconcile this conclusion with the temperature dependence of the behaviour where the development of orientation reduces in absolute magnitude with increasing temperature of deformation. It was proposed by Raha and Bowden 25) that an alternative deformation scheme, which fits the data well, is to assume that the deformation is akin to a rubber network, where the number of cross-links systematically reduces as the draw ratio is increased. It is assumed that the reduction in the number of cross-links per unit volume N i.e. molecular entanglements is proportional to the degree of deformation. 

In the molten state, a Newtonian behavior was observed, a consequence of lack of entanglements. The melt behavior is also dependent on die structure of die endgroups. 

In the literature there is only one serious attempt to develop a detailed mechanistic model of free radical polymerization at high conversions (l. > ) This model after Cardenas and 0 Driscoll is discussed in some detail pointing out its important limitations. The present authors then describe the development of a semi-empirical model based on the free volume theory and show that this model adequately accounts for chain entanglements and glassy-state transition in bulk and solution polymerization of methyl methacrylate over wide ranges of temperature and solvent concentration. 

Different lengths of chains play different roles in controlling polymer properties. For instance, shorter chains flow more readily.in the molten state and are more readily incorporated into crystallites because they have fewer entanglements to impede their motion. Conversely, longer chains tend to resist flow and impede crystallization. 

Polymers crystallize when the crystalline state is more thermodynamically stable than the molten one. The system progresses towards a low energy state, but lull crystallization is hindered by chain entanglements, branches, side group interactions, and viscous drag on chains. 

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