Scission, entangled chains

The toughness Gc (Eq. 20) is related to material features such as the surface density of entangled chains in the fibrils vs and the force for chain scission /b. The value of vs depends on the amount of disentanglement induced by the fibrillation together with the initial entanglement density of the bulk. 

Craze breakdown is experimentally characterized by a critical craze thickness Acr which is primarily dependent (Eq. 20) on the craze stress ac, the force for chain scission, and the entangled chain density along the craze surface vs. The craze stress ac is assumed to be rate and temperature depen-... 

We first compute the probability p that at least one entangled chain is left unbroken in a given entanglement transfer length. Since for the assumed random chain scission the probability of a certain number of breaks follows a binomial distribution one finds... 

Casale and Porter (1978) brought together much of the early work on the theory of mechanical generation of free radicals. Much of the theory for radical formation in the rubbery state bas developed from tbe ideas of Buecbe regarding tbe scission of entangled cbains. Tbe entangled chain does not permit tbe rotation of tbe entire chain to dissipate energy when shear is applied and, furthermore, tensions reach a maximum at the centre of the chain. The number of scissions will decline exponentially with distance from the centre of the chain such that at link q from the centre the ratio of the number of scissions, ng, to that at the centre, no, is... 

The techniques described above have been used to demonstrate that failure can occur by (1) simple chain pull-out, (2) chain scission close to the interface, or (3) chain scission within one of the blocks (typically PS). The transition from chain pull-out to scission is essentially controlled by molecular weight whilst the location of the scission seems to depend on the entanglement density. Fig. 2 shows the transition between (2) and (3) as E is increased. 

M. Cates. Reptation of living polymers Dynamics of entangled polymers in the presence of reversible chain-scission reactions. Macromolecules 20 2289-2296, 1987. 

In the semi-dilute regime, the rate of shear degradation was found to decrease with the polymer concentration [132, 170]. By extrapolation to the dilute regime, it is frequently argued that chain scission should be nonexistent in the absence of entanglements under laminar conditions. No definite proof for this statement has been reported yet and the problem of isolated polymer chain degradation in simple shear flow remains open to further investigation. 

The small values of the quantity 100(f-f )/f prove that chain scission is absent or small for this system. his is important since the interpretation of the experimental results would be difficult or even impossible in the case of substantial chain scission. It should also be stressed that the functionality of the cross-links need not be known, and that a distribution of cross-link functionalities as well as Inhomogeneous cross-linking is unimportant. The reason being that the cross-links merely serve the purpose of trapping the entangled structure. 

An alternative pathway for entanglement loss is chain scission (Fig. 3.2, process B), in which a covalent bond along the polymer main chain is broken and a stress-bearing, otherwise elastic, chain is lost. Chain scission reactions, for example, homolytic carbon-carbon cleavage, have obviously high activation energies. The stress-free rates of these reactions are therefore typically extremely low. 

Figure 3.3 Entanglement response to a mechanical force in a supramolecular system process A, chain slippage via reptation process B, chain scission via breaking of the supramolecular bond.

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