Rubber elasticity bonded interactions

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 early molecular theories of rubber elasticity were based on models of networks of long chains in molecules, each acting as an entropic spring. That is, because the configurational entropy of a chain increased as the distance between the atoms decreased, an external force was necessary to prevent its collapse. It was understood that collapse of the network to zero volume in the absence of an externally applied stress was prevented by repulsive excluded volume (EV) interactions. The term nonbonded interactions was applied to those between atom pairs that were not neighboring atoms along a chain and interacting via a covalent bond. 

Chain extender choice influences elastomer properties considerably. When a diamine is employed as extender, a higher level of physical properties usually results than if a diol were used, probably due to the introduction of urea linkages which enter into strong hydrogen-bonded interactions. A diamine is usually chosen as the chain extender when a relatively unsymmetrical diisocyanate is employed this is particularly true of polymers made by the prepolymer route and applies especially to the use of mixed toluene diisocyanates and to methylene diisocyanates whose bulky or hindered structure and, to some extent, their stereo configurations (see Fig. 3.5), limit the linearity in the polymer chain which is an essential feature of strength and elasticity in all rubber materials. 

Obviously, the temperature dependent parameter indicates the difference between the real chain and rwm structure. A review of the Cpf values for a great number of polymers can be found in reference [11]. The unperturbed real chain exhibits swelled conformations (in contrast to the rwm approximation) due to the iutra-molecular short-range interactions and almost fixed bond angles. This consequently leads to the temperature dependent end-to-end distance and other peculiarities such as the non-zero energy term in the rubber elastic response of real polymers [12]. 

The model network employed is described in detail in Gao and Weiner [2] and [3], Briefly put, the model chains are freely jointed, and the covalent bonds are represented by a linear, stiff spring of equilibrium length a the noncovalent interaction is the repulsive portion of a Lennard-Jones potential which approximates a hard-sphere interaction of diameter a. The network corresponds to the familiar three-chain model of rubber elasticity (see Treloar [10]). In the reference state, three chains, one in each coordinate direction, have their end atoms fixed in the center of the faces of a cube of side L periodic boundary conditions are employed to remove surface effects as is customary in molecular dynamics simulations. The system is siibjected to a uniaxial deformation at constant volume so that the cube side in the x direction has length XL while the other two sides have lengtn... 

Here./g is called the energetic elasticity, and/ is called the entropic elasticity. For instance, the spring exhibits a high elasticity mainly contributed by the energetic elasticity due to the metallic bonds for the strong interactions of iron atoms, while the rubber exhibits a high elasticity mainly contributed by the entropic elasticity due to the chain conformations for the large deformations of polymers. 

The influence of the structme of the elastomer on reinforcement is linked with the effects of localization of stresses, because the stress, occmring on the smface of the filler particles, is a fiinction of the elastic properties of the material. This explains the fact that for an equal nrunber of polymer-filler bonds and crosslinks, the reinforcement effects are still different for different rubbers. The predominance of physical interactions between rubber and black corresponds well with the mechanism of equahzing of the stresses on stretching. Stronger in-... 

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