Entanglement trapping factor

The entanglement trapping factor changes from zero at the gel point to unity for fully developed networks that have very few defects (formed by... 

Langley used the mean-field percolation model to derive the entanglement trapping factor, assuming that the probability of entanglement between two network strands is proportional to the square of their concentration. The probability Vi that a randomly chosen monomer in a network strand is... 

Transition, isothermal to adiabatic 138f. Trapped entanglement 36, 42 Trapping factor 36 Triads 36... 

Langley trapping factor) is the fraction of trapped entanglements that contribute to the modulus, and G is the plateau modulus related to the molecular weight Me between entanglement by the expression... 

The first term is the pure crosslink contribution and might be of a phantom nature the second is additional due to entanglements. is called the trapping factor, which accounts for the probability of trapping, probability of sliding, and other effects. is the plateau modulus for the corresponding uncrosslinked polymer melt, i.e. for the melt of same molecular weight as the strands between two crosslinks. 

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. 

Ronca and Allegra (12) and Flory ( 1, 2) assume explicitly in their new rubber elasticity theory that trapped entanglements make no contribution to the equilibrium elastic modulus. It is proposed that chain entangling merely serves to suppress junction fluctuations at small deformations, thereby making the network deform affinely at small deformations. This means that the limiting value of the front factor is one for complete suppression of junction fluctuations. 

To the author s knowledge no other evaluations of the g factor have been made on statistical networks under circumstances in which the contribution of trapped entanglements would be expected to be negligible. Aside from Gordon s... 

To probe the 1/N dependence in the slope F, experiments were carried out on model end-linked networks with different precursor chain lengths (average molecular weight Mn varying from 3100 to 23000 g.mol 1) [55, 56]. As expected, the slope F decreases when N increases. However, it does not follow a 1/N variation F varies only by a factor of about 3 as N varies by a factor of 7. In an end-linked network, N should not be simply assimilated with the length of precursor chains, since trapped entanglements may play the role of effective crosslinks (often denoted as physical crosslinks), in addition to chemical... 

The concentrations of network strands terminated by crosslinks (v ) and by trapped entanglements (Vj.) are related to the CKF Theory Coefficients as follows, assuming front factors of unity ... 

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