Entanglement density, control

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. 

The different experimental systems all yield a similar pattern of variation of toughness with interface width. The toughness initially increases slowly with width at low interface width, and then increases rapidly with width and saturates at high width at a value close to the bulk toughness. If the density of entangled strands controlled the toughness, then the interface width at which the toughness... 

Wu [1985, 1990] postulated that the brittle/ ductile behavior of a neat amorphous polymer is controlled by two intrinsic molecular parameters the entanglement density, v., and the chain stiffness (given by the characteristic chain constant C. ). Assuming that crazing involves chain scission, the stress, o, should be proportional to and the yield stress, proportional to C . In consequence c,/c, where... 

According to the Eq. 11.7 both and Coo provide a consistent prediction of the deformation behavior. It seems, however, that the entanglement density Vg can be considered as the primary parameter which controls the crazing behavior, whereas the chain stiffness parameter C o is predominant in controlling the shear yielding behavior. 

The idea described above for glassy amorphous homopolymers can be extended to include miscible amorphous polymer blends, such as PS/PPO. Furthermore, a low degree of covalent cross-links can be considered as equivalent to entanglements for controlling the deformation mode. The strand density of cross-linked polymers is defined as the sum of the entanglement density and the covalent cross-link density [18] as... 

For imperfect epoxy-amine or polyoxypropylene-urethane networks (Mc=103-10 ), the front factor, A, in the rubber elasticity theories was always higher than the phantom value which may be due to a contribution by trapped entanglements. The crosslinking density of the networks was controlled by excess amine or hydroxyl groups, respectively, or by addition of monoepoxide. The reduced equilibrium moduli (equal to the concentration of elastically active network chains) of epoxy networks were the same in dry and swollen states and fitted equally well the theory with chemical contribution and A 1 or the phantom network value of A and a trapped entanglement contribution due to the similar shape of both contributions. For polyurethane networks from polyoxypro-pylene triol (M=2700), A 2 if only the chemical contribution was considered which could be explained by a trapped entanglement contribution. 

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