Rubber elasticity nonbonded 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. 

In the usual development of the theory, the important assumption was made that the nonbonded interactions, although certainly present, contributed only to the mean stress p and made zero contribution to the deviatoric stress Dty. Because as noted, the earlier restricted theories of rubber elasticity were... 

The assemblage of chains is constructed to represent the affine network model of rubber elasticity in which all network junction positions are subject to the same affine transformation that characterizes the macroscopic deformation. In the affine network model, junction fluctuations are not permitted so the model is simply equivalent to a set of chains whose end-to-end vectors are subject to the same affine transformation. All atoms are subject to nonbonded interactions in the absence of these interactions, the stress response of this model is the same as that of the ideal affine network. 

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. 

This work is based on the molecular dynamic simulation of a monomer scale model corresponding to the affine network model of rubber elasticity.3 However, whereas the classic model has no nonbonded interactions, our model... 

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