Highly cross-linked network chain entanglement

For a loosely cross-linked network, polymerized above the glass transition temperature, R should approach the flexible limit, i.e., R, because the distance from the last attachment to the network is significantly larger and the overall mobility of the system is increased by polymerization above the Tg, As the polymerization temperature is lowered below Tg, the distance back to the last network attachment point (or entanglement) becomes less important, and the mobility of the radical chain end is reduced to the point where it is virtually immobile on the time scale of propagation. In this case, the rigid limit should be applicable, and R should approach R m, just as it would for a highly cross-linked network. 

A new stress-relaxation two-network method is used for a more direct measurement of the equilibrium elastic contribution of chain entangling in highly cross-linked 1,2-polybutadiene. The new method shows clearly, without the need of any theory, that the equilibrium contribution is equal to the non-equilibrium stress-relaxation modulus of the uncross-linked polymer immediately prior to cross-linking. The new method also directly confirms six of the eight assumptions required for the original two-network method. 

Since the excellent work of Moore and Watson (6, who cross-linked natural rubber with t-butylperoxide, most workers have assumed that physical cross-links contribute to the equilibrium elastic properties of cross-linked elastomers. This idea seems to be fully confirmed in work by Graessley and co-workers who used the Langley method on radiation cross-linked polybutadiene (.7) and ethylene-propylene copolymer (8) to study trapped entanglements. Two-network results on 1,2-polybutadiene (9.10) also indicate that the equilibrium elastic contribution from chain entangling at high degrees of cross-linking is quantitatively equal to the pseudoequilibrium rubber plateau modulus (1 1.) of the uncross-linked polymer. 

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