Nonaffine chain and primitive path deformation in crosslinked polymers

Chains in a polymer network deform nonaffinely at small length scales due to the ability for extensive microscopic rearrangement. Classically, the conformations of an individual chain can be described solely by an end-to-end length. This picture neglects interchain interactions and therefore does not represent the behavior of a real polymer network. The primitive path concept provides the additional detail to represent interchain entanglements, and techniques have recently been developed to identify the network of primitive paths in a polymer simulation. We use coarse-grained molecular dynamics (MD) to track both chain end-to-end and primitive path deformation in crosslinked polymer networks. The range of simulated materials includes short chain unentangled networks to long, entangled chain networks. Both chain end-to-end and primitive path length are found to be linear functions of the applied deformation, and a simple relationship describes the behavior of a network in response to large stretch uniaxial, pure shear, and equibiaxial deformations. As expected, end-to-end chain length deformation is nonaffine for short chain networks, and becomes closer to affine for networks of long, entangled chains. However, primitive path deformation is found to always be nonaffine, even for long, entangled chains. We demonstrate how the microscopic constraints of crosslinks and entanglements affect nonaffine chain deformation as well as the simulated elastic behavior of the different networks.