Rubber-like elasticity approach

The maximum deformation AD of this 100% hypercrosslinked polymer achieves the value as high as 30% when the temperature approaches 300°C. Although this deformation is characteristic of rubber-like elasticity (Fig. 7.38, plots 1 and 2), no typical plateau can be observed (plot 3). This statement is also valid for the whole set of plots obtained at varying loadings in the interval from 10 to 450 g per bead (Fig. 7.39). AH plots have a flat... 

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... 

In the simplest phenomenological approach for rubber-like elasticity of trapped entanglements at small deformation (210,211), the shear modulus is taken to be the sum of two terms ... 

The phenomenological approach to rubber-like elasticity is based on continuum mechanics and symmetry arguments rather than on molecular concepts [2, 17, 26, 27]. It attempts to fit stress-strain data with a minimum number of parameters, which are then used to predict other mechanical properties of the same material. Its best-known result is the Mooney-Rivlin equation, which states that the modulus of an elastomer should vary linearly with reciprocal elongation [2],... 

Wherever each molecular chain approaches, crystallites are formed, leading to the formation of a 3D network. This structure explains weU the main properties of the gel, such as the melting point, degree of optical rotation, modulus, and rubber-like elasticity. However, a few kinds of networks coexist in the photosensitive material depending on the manufacturing and development methods, the behavior of gelatin gels is very complex. 

Rubber and rubber-like materials are systems of molecules—monomers or mers—that are subject to two types of interactions. The first type are covalent interactions that tie monomers into long chains, which are typically 100 or more mers long. The second type are nonbonded interactions, which occur between pairs of mers that are not covalently bonded to each other. We are concerned here with an examination of how nonbonded interactions are generally treated in theoretical studies of rubber elasticity and with the limitations of this approach. 

The theory in the Gaussian limit has been refined greatly to take into account the possible fluctuations of the junction points. In these approaches, the probability of an internal state of the system is the product of the probabilities Win) for each chain. The entropy is deduced by the Boltzmann equation, and the free energy by equation (26). The three main assumptions introduced in the treatment of elasticity of rubber-like materials are that the intermolecular interactions between chains are independent of the configurations of these chains and thus of the extent of deformation (125,126) the chains are Ganssian, freely jointed, and volumeless and the total number of configurations of an isotropic network is the product of the number of configurations of the individual chains. 

Miehe, C., Goktepe, S. and Lulei, F. (2004) A micro-macro approach to rubber-like materials - part 1 the non-affine micro-sphere model of rubber elasticity. J. Mech. 

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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