Reduced density, rubber elasticity

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. 

In Section I, the discussion dealt with the significant role of nonbonded interactions in the development of the full stress tensor, mean plus deviatoric, in rubber elasticity, in the important high reduced density regime p > 1. Here, we present some concepts and formulations that apply to this regime. 

The Epons 828,1001,1002,1004, and 1007 fully cured with stoichiometeric amounts of DDS are examples of well-characterized networks. Therefore, mechanical measurements on them offer insight into the viscoelastic properties of rubber networks. The shear creep compliance J t) of these Epons were measured above their glass temperatures [11, 12, 14]. From the statistical theory of rubber elasticity [1-5, 29-33] the equilibrium modulus Ge is proportional to the product Tp, where p is the density at temperature T, and hence the equilibrium compliance is proportional to (Tpy Thus J t) is expected to be proportional to and J(t)Tp is the quantity which should be compared at different temperatures. Actually the reduced creep compliance... 

Because G is proportional to temperature T (in degrees Kelvin) and to density, p, according to the theory of rubber elasticity, the reduced modulus,... 

In appearance, HR resembles natural crepe rubber, since it is an aliphatic, hydrocarbon polymer the density being the minimum (0.91) attainable for elastic materials of this type. In HR, the original unsaturation is very small, and even this low unsaturation is greatly reduced and may even be entirely eliminated during the compounding and curing process. The fact that once vulcanised it is extremely resistant to chemical attack is understandable because it becomes, after vulcanisation, not only a nonthermoplastic strong elastic material, but also essentially a chemically saturated product as well. This means that whilst physically vulcanised HR resembles soft vulcanised natural rubber, chemically it may be considered most similar to ebonite almost devoid of any unsaturation. 

Simo [51] proposed to penalize the classic elastic strain energy densities, Wo(F)> designed to fit the hyperelastic stress-strain responses of rubber-like materials submitted to the deformation gradient F, by a reducing parameter of the Kachanov form [99]. 

The general effect of cross-link density on the elastic modulus of an elastomer is indicated by Eq. 2.3. In their paper Landel and Fedors [189] consider the influence of a time-dependent cross-link density on the shape of the stress-strain curves of silicon, butyl, natural, and fluorinated rubbers. Introducing an additional shift-factor a related to the cross-link density, they were able to represent reduced breaking stresses as a function of reduced time in one common master curve. 

Since the epoxy resin binder is a rigid three-dimensicHial polymer, the findings should be interpreted from the point of view of a change in the density of the network cross-links. With this aim we carried out measurements of the equilibrium modulus of rubber-like elasticity of filled spedn ns. It was shown that the network density with the polymeric filler concentrations reduces. 

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