Concentration of elastically active network chains

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. 

To obtain accurate values of the sol, thin specimens (1 mm) in one study (13) were kept in the solvent for six weeks in another study (14), thin specimens were extracted for more than 18 days in Soxhlet extractors. When the present experimental data were obtained (6), there was little interest in knowing the sol fraction accurately. However, as discussed subsequently, to compute the extent of the curing reactions and the concentration of elastically active network chains, the sol fraction must be known accurately. 

Note 4 Loose ends and ring structures reduce the concentration of elastically active network chains and result in the shear modulus and Young s modulus of the rubbery networks being less than the values expected for a perfect network structure. 

Using the values of the modulus G, measured just after preparation (X = 1), one can determine the concentration of elastically active network chains (EANC), vd, related to the dry state... 

The concentrations of elastically active network chains related to the dry state vd series A-F were [26] vd = 3.6, 5.7, 6.3, 7.1, 10.9 and 15.2 x 10 5 molcm 3 (structure formation at high dilution in the system. Using vd values together with other molecular parameters, the dependences of y vs ip 2 were calculated and both the extent of the collapse, A, and the critical value,... 

Assuming that no internal elastic chains are activated, the concentration of elastically active network chains per unit mass, ve, may be calculated... 

In the case of unsaturated polyesters, nondegraded samples made from a prepolymer of molar mass M and a styrene mass fraction s have a chain-ends concentration b = [2(1 — s)/M]p, where p is the density. If ve is the actual concentration of elastically active network chains, an ideal network would be obtained by welding each chain end to another one, leading to... 

Weakly crosslinked epoxy-amine networks above their Tg exhibit rubbery behaviour like vulcanized rubbers and the theory of rubber elasticity can be applied to their mechanical behaviour. The equilibrium stress-strain data can be correlated with the concentration of elastically active network chains (EANC) and other statistical characteristics of the gel. This correlation is important not only for verification of the theory but also for application of crosslinked epoxies above their Tg. 

Fig. 16. Time dependence of the gel fraction, w, and concentration of elastically active network chains, v, in the stoichiometric mixture of azelaic acid and DGEBA...

Along with T, further structural parameters of networks, e.g. the sol fraction, w, and the concentration of elastically active network chains in the gel, s v /(l — w, ... 

Since at long times pendant chains do not contribute to permanent elastic properties, the elastic equilibrium behavior of networks containing these chains should not differ substantially from that of regular networks. The elastic modulus from a network with pendant chains can then be obtained from the molecular theories of rubber elasticity provided that the concentration of elastically active network chains (v) can be calculated accurately. Depending on the different approaches that can be used for the rubber elasticity theory, the calculation of some other parameters, like the concentration of junctions points (p) and trapped entanglements (Te), also may be needed. 

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