Deformation of elastomeric networks: Relation between molecular level deformation and classical statistical mechanics models of rubber elasticity

In this work, molecular simulations are conducted to provide details of the underlying micromechanisms governing the observed macroscopic behavior of elastomeric materials. The polymer microstructure is modeled as a collectio n of unified atoms interacting by two-body potentials of bonded and nonbond ed type. Representative volume elements (RVEs) containing a network of 200 molecular chains of 100 bond lengths are constructed. The evolution of the RVEs with uniaxial deformation was studied using a molecular dynamics techn ique. The simulations enable observation of structural features with deform ation including bond lengths and angles as well as chain lengths and angles . The simulations also enable calculation of the macroscopic stress-strain behavior and its decomposition into bonded and nonbonded contributions. The distribution in initial end-to-end chain lengths is consistent with Gaussi an statistics treatments of rubber elasticity. It is shown that application of an axial strain of +/-0.7 (a logarithmic strain measure is used) only c auses a change in the average bond angle of +/-5 degrees, indicating the fr eedom of bonds to sample space at these low to moderate deformations; the s ame strain causes the average chain angle to change by +/-20 degrees. Rando mly selected individual chains are monitored during deformation; their indi vidual chain lengths and angles are found to evolve in an essentially affin e manner consistent with Gaussian statistics treatments of rubber elasticit y. The average chain length and angle are found to evolve in a manner consi stent with the eight-chain network model of rubber elasticity. Energy quant ities are found to remain constant during deformation consistent with the n ature of rubber elasticity being entropic in origin. The stress-strain resp onse is found to have important bonded and nonbonded contributions. The bon ded contributions arise from the rotations of the bonds toward the maximum principal stretch axis(es) in tensile (compressive) loading.