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 collection of unified atoms interacting by two-body potentials of bonded and nonbonded 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 technique. The simulations enable observation of structural features with deformation 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 Gaussian statistics treatments of rubber elasticity. It is shown that application of an axial strain of +/-0.7 (a logarithmic strain measure is used) only causes a change in the average bond angle of +/-5 degrees, indicating the freedom of bonds to sample space at these low to moderate deformations; the same strain causes the average chain angle to change by +/-20 degrees. Randomly selected individual chains are monitored during deformation; their individual chain lengths and angles are found to evolve in an essentially affine manner consistent with Gaussian statistics treatments of rubber elasticity. The average chain length and angle are found to evolve in a manner consistent with the eight-chain network model of rubber elasticity. Energy quantities are found to remain constant during deformation consistent with the nature of rubber elasticity being entropic in origin. The stress-strain response is found to have important bonded and nonbonded contributions. The bonded contributions arise from the rotations of the bonds toward the maximum principal stretch axis(es) in tensile (compressive) loading.