Swollen state network density

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. 

If we exclude the case of pre-existing order, we have so far considered a network as a random, but completely homogeneous structure. It should now be mentioned that the crosslinking process itself may give rise to "aggregation of network elements and therefore, in the swollen state, to significant fluctuations in segment density. 

Inordinately low M may result from an anomaly associated with polyurethane networks (12). The persistence of hydrogen bonding in the swollen state may lead to high apparent crosslink density and low values of Mc. In addition, it is possible that the Gaussian approximation implicit in all our treatments is inadequate for an extensively swollen network. 

Similar to the gel-type styrene copolymers, the hypercrosslinked networks based on both linear polystyrene and styrene-DVB copolymers are transparent materials, being in dry or swollen state. Nevertheless, alternatively to the conventional copolymers, the hypercrosslinked networks exhibit very low apparent density (Papp) when isolated from the reaction media and dried. The apparent density of the polymers (I) based on linear polystyrene (Table 7.7) decreases with increasing the degree of crosslinking ... 

Here Xn is the Flory solvent-polymer interaction parameter and p is the network density (mass per unit volume). The volume fraction of the polymer in the swollen state can be easily determined experimentally by measuring the volume of the swollen sample Vs and of the dry sample 02 = Vd/Vsw... 

Fedors, R.F. and Landel, R.F. (1978) Determination of network density of composites containing inert fillers from stress-strain measurements in the swollen state. Polymer, 19,1189-94. 

As pointed out in Chapter III, Section 1 some specific diluent effects, or even remnants of the excluded volume effect on chain dimensions, may be present in swollen networks. Flory and Hoeve (88, 89) have stated never to have found such effects, but especially Rijke s experiments on highly swollen poly(methyl methacrylates) do point in this direction. Fig. 15 shows the relation between q0 in a series of diluents (Rijke assumed A = 1) and the second virial coefficient of the uncrosslinked polymer in those solvents. Apparently a relation, which could be interpreted as pointing to an excluded volume effect in q0, exists. A criticism which could be raised against Rijke s work lies in the fact that he determined % in a separate osmotic experiment on the polymer solutions. This introduces an uncertainty because % in the network may be different. More fundamentally incorrect is the use of the Flory-Huggins free enthalpy expression because it implies constant segment density in the swollen network. We have seen that this means that the reference dimensions excluded volume effect. 

The state of cure of the phases in a blend can be determined from changes in the magnitude of the damping peaks [37a] and from freezing-point-depression measurements on swollen networks. HonibaU and McGill [37b] have employed the freezing point depression of solvent-swelled NR-BR blends to determine the crosslink densities of the individual polymer phases. 

Most of the above cross-linked polymers were considered in the dry state, although the Flory-Rehner theory (Section 9.12) made use of equilibrium swollen gels in the evaluation of the cross-link density. Generally, a polymeric gel is defined as a system consisting of a polymer network swollen with solvent. It must be understood that the solvent is dissolved in the polymer, not the other way around. 

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