Rubber network elasticity

If the proposed model of a fixed liquid, a lower transition, a rubber network elasticity, and a higher transition associated with loss of the entanglement network is correct, it should be able to "explain" the characteristics of the transition region as presented in the early sections of this paper. 

Langley, N.R. and Polmanteer, K.E., Relation of elastic modulus to crosslink and entanglement concentrations in rubber networks. J. Polym. Sci. Polym. Phys. Ed., 12(6), 1023-1034 (1974). 

Mark, J. E. The Use of Model Polymer Networks to Elucidate Molecular Aspects of Rubber like Elasticity. Vol. 44, pp. 1-26. 

The ratios of mean-squared dimensions appearing in Equation (13) are microscopic quantities. To express the elastic free energy of a network in terms of the macroscopic (laboratory) state of deformation, an assumption has to be made to relate microscopic chain dimensions to macroscopic deformation. Their relation to macroscopic deformations imposed on the network has been a main area of research in the area of rubber-like elasticity. Several models have been proposed for this purpose, which are discussed in the following sections. Before that, however, we describe the macroscopic deformation, stress, and the modulus of a network. 

J.E. Mark and B. Erman, Molecular aspects of rubber-like elasticity. In R.F.T. Stepto (Ed.), Polymer Networks, Blackie Academic, Chapman Hall, Glasgow, 1998. 

The two-network method has been carefully examined. All the previous two-network results were obtained in simple extension for which the Gaussian composite network theory was found to be inadequate. Results obtained on composite networks of 1,2-polybutadiene for three different types of strain, namely equibiaxial extension, pure shear, and simple extension, are discussed in the present paper. The Gaussian composite network elastic free energy relation is found to be adequate in equibiaxial extension and possibly pure shear. Extrapolation to zero strain gives the same result for all three types of strain The contribution from chain entangling at elastic equilibrium is found to be approximately equal to the pseudo-equilibrium rubber plateau modulus and about three times larger than the contribution from chemical cross-links. 

It is evident that composite or heterogeneous networks, which result from macro- and micro-syneresis respectively, are not suitable for the verification of basic rubber-elasticity theories. The interpretation of their behaviour in the light of existing network elasticity theories should be quite complicated. Especially for heterogeneous networks, additional... 

The gelation process that leads to the network structures required for rubber-like elasticity have been extensively studied, by experiments, theory, and simulations.245-249 In some case, the gelation can be made to be reversible.250... 

Priss LS (1981) Molecular origin of constants in the theory of rubber-like elasticity considering network chains steric interactions. J Pure Appl Chem 53 1581-1596 Priss LS, Gamlitski YuA (1983) Mechanism of conformation transitions in polymer chains. Polym Sci USSR 25 117-123... 

A good understanding of the structure of the network in filled rubbers is of great importance, because the rubber s elastic properties are determined primarily by the density of chemical and physical network junctions and their ability to fluctuate. The following types of network junctions occur in filled rubbers ... 

This brings us to the elastic behavior of rubber networks. There are a number of problems involved in developing a good theory, not the least of which is the fact chat real networks are not perfect. If natural rubber is vulcanized there are all sorts of defects in the resulting network dangling ends and... 

The average length (or molecular weight) of network chains in a crosslinked polymer can be experimentally determined from the equilibrium rubbery modulus. This relationship is a direct result of the statistical theory of rubber-like elasticity . In the last decade or so, modem theories of rubber-like elasticity 2127) further refined this relationship but have not altered its basic foundation. In essence, it is... 

Thus, the level of sophistication which one may consider for the application of rubber-like elasticity theory to epoxy networks may depend on the application. For highly crosslinked systems (M < 1,000), a quantitative dependence of the rubbery modulus on network chain length has recently been demonstrated , but the relevance of higher order refinements in elasticity theory is questionable. Less densely crosslinked epoxies, however, are potentially suitable for testing modern elasticity theories because they form via near quantitative stepwise reactions. Detailed investigations of such networks have been reported by Dusek and coworkers in recent studies ... 

C. Menduina, C. McBride, and C. Vega (2001) Correctly averaged Non-Gaussian theory of rubber-like elasticity - application to the description of the behavior of poly(dimethylsiloxane) bimodal networks. Phys. Chem,. Chem. Phys. 3, p. 1289... 

As shown in Fig. 7.41, the deformation of all hypercrossHnked beads noticeably increases at a temperature above 100°C. However, this phenomenon is not related to trivial transition of polystyrene segments from glassy to rubber-Hke state. The very nature of deformation of hypercrosslinked materials differs fundamentally from the deformation of conventional networks under rubber-Hke elasticity. 

Several approaches to the description of molecular entanglements in polymers are available at present. A brief outline will be given here. The best known is the version of the binary hook [9,10] with some network features. At temperatures (T) exceeding the temperature of glass transition (Tg) for the polymer, the network density V(,i, is usually determined in the framework of the rubber-like elasticity, while for Tentanglement network is proven both theoretically and... 

Rubber networks will imbibe solvent liquids until the elastic retractive force of the network crosslinks counterbalances the swelling force exerted by the liquid. If no crosslinks are present, the rubber dissolves completely on immersion in an excess of solvent. The degree of swelling is thus a function of crosslink density. As crosslink density increases, the degree of swelling decreases and vice versa. The average crosslink between junction points can be related to swelling measurements from potential considerations, as shown below. 

From the reaction of such polyiners with silicone crosslinkers, which need to have at least three reactive groups, three-dimensional networks with rubber-like elasticity are obtained. The chemical nature of the silicone crosslinker to be used depends on the crosslinking system, further details of which are given in the next Chapter. 

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... 

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