Coarse-grained molecular dynamics simulations and structural analysis of end-linked polymer networks under different cross-linking protocols

Abstract Crosslinked rubbers and gels derive their softness and toughness from a three-dimensional network of junction points connected by polymer strands. Classical affine and phantom network models qualitatively relate the network architecture to the shear modulus but fail to predict absolute values owing to elastically ineffective defects such as loops and dangling chains. In the present study, we employed coarse-grained molecular dynamics simulations combined with an iterative defect-removal algorithm to compare four model networks formed under various cross-linking protocols and binding ratios: three-/four-armed star polymer networks (SPNs) and three-/four-armed telechelic polymer networks (TPNs). We directly counted elastically effective junctions and eliminated primitive and even higher-order defects. The SPNs exhibited higher shear moduli than the TPNs did, which was a consequence of more rapid generation and greater density of effective junctions as well as suppressed loop formation. Remarkably, in both network types, the simulated modulus G obeyed: $$G\approx {2G}_{{{{\rm{ph}}}}},$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> <mml:mo>≈</mml:mo> <mml:msub> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>G</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>ph</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> </mml:math> where G ph represents the prediction by the phantom network model using the actual effective junction, which is independent of the cross-linking protocols, binding ratio, or functionality.