Authors: Jacob Davidson and Nakhiah Goulbourne
Dept. of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48105
Elastomers are polymers able to undergo large, reversible deformations due to the added chemical crosslinks which link chains together. The mechanical properties of the material depend on the chain chemistry and on the topology of the resulting interconnected network of chains. Recently, network theoretical methods have received increased attention in the application to characterizing and understanding complex networks ranging from social to technological to biological. In this work we employ a network description to characterize molecular dynamics (MD) simulations of crosslinked polymers constructed via the Kremer & Grest bead-spring model. The chain length and the density at which crosslinking is performed is varied in order to produce systems ranging from crosslink-dominated to highly entangled. Large deformation mechanical testing using the coarse-grained MD model reveals the important differences in properties of these different materials. A network analysis along with primitive path techniques is used to identify the characteristic chemical and topological properties that lead to this behavior. The spectrum of the crosslink adjacency matrix is shown to resemble a sparse regular graph, and spectrum of the intermolecular chain entanglement matrix for the highly entangled systems is shown to resemble the characteristic semi-circle of a random matrix; however, deviations are noted which require further study. These metrics along with the degree distribution of entanglements can be used to identify and differentiate between the different simulated materials. A comparison of the stress-stretch behavior with the network properties allows for multiscale connections to be made relating the chemistry and network topology to the elastic and viscoelastic properties. These results demonstrate that network theoretical methods may be applied to understand and model the behavior of crosslinked polymers and suggest directions for future modeling work.
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