Deformed entanglement network

Reasons have been advanced for both an increase and a decrease of the tube diameter with strain. A justification of the former view might be the retraction process itself [38]. If it acts in a similar way to the dynamic dilution and the effective concentration of entanglement network follows the retraction then Cgjy < E.u > so that a < E.u On the other hand one might guess that at large strains the tube deforms at constant tube volume La. The tube length must increase as < E.u >,so from this effect a < E.u > . Indeed, Marrucci has recently proposed that both these effects exist and remain unnoticed in step strain because they cancel [69] Of course this is far from idle speculation because there is another situation in which such effects would have important consequences. This is in conditions of continuous deformation, to which we now turn. 

The front factor g as defined above5 is unity in all the earlier theories (17). Recently Duiser and Staverman (233) have obtained g = j and Imai and Gordon (259) g — 0.54 with Rouse model theories which make no a priori assumptions about the junction point locations after deformation. Edwards (260) also arrives at and Freed (261) deduces that g= 1 is an upper bound by similar approaches. The front factor usually assumed in the shifted relaxation theory of the plateau modulus is g = 1, although Chompff and Duiser (232) obtain g = j through their extension of the Duiser-Staverman result to entanglement networks. The physical reasons for the different values of g in different treatments are not clear at present. 

In addition to the compression loading, uniaxial extension of entangled PDMS chains have been investigated by pulling a small portion of the material and measuring elastic response before the rupture happens [419]. The multiple ruptures observed in the force-distance curves (Fig. 43) have been interpreted as fractures of an entangled network of PDMS chains formed between the tip and the silica grafted surface. At small deformations, also the capillary forces were shown to contribute in the force. The elastic part of the curves was described us-... 

Production. Recognition that the shish-kebab fibers produced by the surface-growth procedure result from the deformation of a gel-like entangled network layer at the rotor surface led to the development of gel-spun polyethylene fibers. The fiber is made by the solution spinning method. The polymer is... 

In section 3.1.3. we proposed a simple model to calculate the anisotropic form factor of the chains in a uniaxially deformed polymer melt. The only parameters are the deformation ratio X of the entanglement network (which was assumed to be identical to the macroscopic recoverable strain) and the number n, of entanglements per chain. For a chain with dangling end submolecules the mean square dimension in a principal direction of orientation is then given by Eq. 19. As seen in section 3.1.3. for low stress levels n can be estimated from the plateau modulus and the molecular weight of the chain (n 5 por polymer SI). 

Fig. 18. Experimental extension ratios of deformation zones in various homopolymers and copolymers plotted against the theoretical maximum extension ratios of a single entangled chain and the entanglement network, and net respectively...

It has become apparent in the previous section that intrinsic crazing of PC is a postyield phenomenon which occurs at high deformations of the material. There is much evidence that such phenomena are strongly affected by the existence of an entanglement network frozen-in during the glass transition p j. example,... 

In order to test the model of intrinsic craze initiation it would be desirable to produce entanglement networks of different structures and study X as a function X. This may be achieved by pre-orientation of PC above T. In fact, there is much evidence that the entanglement network in polymer melts is modified increasingly with the magnitude of deformation i32,i5o.i59,i6i> -j-jjg modification must be assumed to arise... 

The (schizophrenic) existence of both deformation modes is made possible by the long-chain macromolecular structure of polymers. The entangled network... 

The results in this section were all derived for unentangled networks. The Edwards tube model for entangled networks gives identical results with N replaced by N, the number of Kuhn monomers in an entanglement strand in the preparation state, because both entanglement strands and network strands are assumed to deform affinely in the Edwards tube model. If the Edwards tube model were correct, the universal relations [Eqs (7.91) and (7.92)] would still apply for entangled networks, since they are independent of N. However, the non-affine tube models predict that entangled networks will swell considerably more than the Edwards tube model predicts. 

Under compression or shear most polymers show qualitatively similar behaviour. However, under the application of tensile stress, two different deformation processes after the yield point are known. Ductile polymers elongate in an irreversible process similar to flow, while brittle systems whiten due the formation of microvoids. These voids rapidly grow and lead to sample failure [50, 51]. The reason for these conspicuously different deformation mechanisms are thought to be related to the local dynamics of the polymer chains and to the entanglement network density. 

Two deformation schemes are commonly used to account for molecular orientation. These are the so-called affine and pseudoaffine schemes whose description, along with their applicability to real polymers, it given in a series papers [5, 6]. However, it turns out that the behaviour of the real polymers (amorphous as well as the semicrystalline ones) differs essentially from these schemes, entailing mmierous modifications [5, 6]. The main principle of all these modified and unmodified deformation schemes is the presence of a molecular entanglement network [7, 8]. 

A number of features of the behaviour of the oriented polymers, that fits weakly to the version of macromolecular entanglement network, has been revealed during detailed revision of some results of [5-9, 14, 15]. Thereby, the direct application of the two deformation schemes mentioned previously is prohibited. These features are ... 

For the purpose of considering both rubbers with fully recoverable deformation and glassy polymers that exhibit rubbery behavior above their Tg through the presence of entanglement networks, we distinguish two separate families of material (a) rubbers that have been cross linked through vulcanization and (b) some glassy polymers that show prominent rubbery behavior in their mechanical responses above their Tg for short periods. 

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