Entanglement Effects in Polymer Melts

Entanglements constitute a major feature of the structure in pol3mier melts and strongly affect the d3mamics. Because they interpenetrate each other (the more they interpenetrate, the higher the molar mass), pol3mier molecules become entangled. Since the chains are linearly connected objects that cannot cross each other, the individual motions become constrained, and it is impossible for the chain to move freely as a whole in all directions. 

We have already met several manifestations of the entanglements, in particular 

the effect of the entanglements is two-fold, since both the elastic and the viscous properties are concerned. The observations all indicate the existence of a critical molar mass, introduced earlier as the critical molar mass at the entanglement limit, denoted by Me. Polymers with low molar masses, M Me, exhibit no entanglement effects, but for M Me they show up and become dominant. All properties that are founded on motions on length scales corresponding to a molar mass above Me are affected. This holds, in particular, for the viscosity and the dielectric normal mode since these include the whole polymer chain. On the other hand. Rouse dynamics is maintained within the sequences between the entanglement points, as has already been mentioned. 

If the motion of the chains in the melt is not restricted, the long-time limit of the pair correlation function is given by 

As a consequence, the intermediate scattering function vanishes for long times 

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Kremer K, Grest GS (1995) Entanglement effects in polymer melts and networks. In Binder K (ed) Monte Carlo and molecular dynamics methods in polymer science. Oxford University... 

ENTANGLEMENT EFFECTS IN POLYMER MELTS Within this scheme the relaxation modulus of the melt is given by ... 

Chains in Networks. One of the first studies of chains in networks is by Gao and Weiner (235) where they performed extended simulations of short chains with fixed (affinely moving) end-to-end vectors. The first extensive molecular dynamics simulations of realistic networks were performed by Kremer and collaborators (236). These calculations were based on a molecular dynamics method that has been applied to study entanglement effects in polymer melts (237). The networks obtained by cross-linking the melts were then used to study the effect of entanglements on the motion of the cross-links and the moduU of the networks. The moduli calculated without any adjustable parameters were close to the phantom network model for short chains, and supported the Edwards tube model for long ones. Similar molecular dynamics analyses were used to understand the role of entanglements in deformed networks in subsequent studies (238-240). 

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