Molecular Dynamics Study on the Validity of Miller-Macosko Theory for Entanglement and Crosslink Contributions to the Elastic Modulus of End-Linked Polymer Networks

Stress-relaxation molecular dynamics simulations are performed to obtain estimates of the shear modulus of "real " end-linked poly(dimethylsiloxane) networks with excluded-volume interaction between the strands. Computer microstructures with up to 104 identical strands end-linked by tri-or tetrafunctional crosslinks are studied. A representative range of extents of reaction and strand molar masses is considered. It is found that for the entire range, the additivity assumption for the contributions of the chemical crosslinks and entanglements to the modulus is remarkably valid even though the topological factors of the real and their topologically equivalent phantom networks differ very substantially and that for the real networks the affine deformation requirement is not satisfied. It is demonstrated that the classical additive mean-field Miller-Macosko theory, which does not explicitly address the underlying microscopic mechanisms, gives consistently accurate predictions for both real and phantom moduli of studied end-linked polymer networks, and the predictions are achieved using a quick arithmetic calculation.