Entanglements in polymers

Both the questions of the transition from Rouse to reptation dynamics and of what fixes the average distance between entanglements in polymer liquids has been the subject of a number of recent theoretical and experimental investigations. 

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. 

Several approaches to the description of molecular entanglements in polymers are available at present. A brief outline will be given here. The best known is the version of the binary hook [9,10] with some network features. At temperatures (T) exceeding the temperature of glass transition (Tg) for the polymer, the network density V(,i, is usually determined in the framework of the rubber-like elasticity, while for Tentanglement network is proven both theoretically and... 

Gent, A. N. Liu, G. L. Mazurek, M., Experimental-Study of Molecular Entanglement in Polymer Networks. J. Polym. Set, Part B Polym. Phys. 1994, 32... 

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

Next let us consider the differences in molecular architecture between polymers which exclusively display viscous flow and those which display a purely elastic response. To attribute the entire effect to molecular structure we assume the polymers are compared at the same temperature. Crosslinking between different chains is the structural feature responsible for elastic response in polymer samples. If the crosslinking is totally effective, we can regard the entire sample as one giant molecule, since the entire volume is permeated by a continuous network of chains. This result was anticipated in the discussion of the Bueche theory for chain entanglements in the last chapter, when we observed that viscosity would be infinite with entanglements if there were no slippage between chains. 

In the rubbery plateau, a new impediment to movement must be overcome entanglements along the polymer chain. In discussing the effects of entanglements in Chap. 2, we compared them to crosslinks. Is it any surprise, then, that rubbery behavior similar to that shown by cross-linked elastomers characterizes this region ... 

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. 

Langley, N.R. and Polmanteer, K.E., Role of chain entanglements in rubber elasticity. Polym. Prep. Am. Chem. Soc. Div. Polym. Chem., 13(1), 235-240 (1972). 

The mechanism by which the primers are thought to work is relatively straightforward. The primer first diffuses into the polyolefin surface, and subsequently becomes entangled in the polyolefin. The primer molecule can then act as an anchor in the substrate surface for the adhesive polymer, which forms after the primer initiates polymerization of the alkyl cyanoacrylate monomer [37]. 

The rigid chemical structure of a conjugated polymer helps in the movement of electrons. That stiff structure, however, has limited its use. They are like uncooked spaghetti and do not easily entangle themselves. Polymer chain entanglements are necessary to achieve high viscosities, which are required to create fibers out of these polymers. 

Due to dieir compact, branched structure and to die resulting lack of chain entanglement, dendritic polymers exhibit much lower melt and solution viscosity dian their lineal" counterparts. Low a-values in die Mark-Houwink-Sakurada intrinsic viscosity-molar mass equation have been reported for hyperbranched polyesters.198 199 Dendrimers do not obey diis equation, a maximum being observed in die corresponding log-log viscosity-molar mass curves.200 The lack of chain entanglements, which are responsible for most of the polymer mechanical properties, also explains why hyperbranched polymers cannot be used as diermoplastics for structural applications. Aldiough some crystalline or liquid... 

The remaining problem in the model development is to estimate the decrease in kp as a function of conversion. As the reaction proceeds beyond the point of chain entanglement, a critical conversion is reached where the propagation reaction becomes diffusion controlled and kp begins to fall with further increase in polymer concentration. At the critical conversion, one may write... 

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... 

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