Phantom-Chain Simulations for the Effect of Node Functionality on the Fracture of Star-Polymer Networks

The influence of node functionality (f) on the fracture of polymer networks remains unclear. While many studies have focused on multi-functional nodes with f>4, recent research suggests that networks with f=3 exhibit superior fracture properties compared to those with f=4. To clarify this discrepancy, we conducted phantom chain simulations for star-polymer networks varying f between 3 and 8. Our simulations utilized equimolar binary mixtures of star branch prepolymers with a uniform arm length. We employed a Brownian dynamics scheme to equilibrate sols and induce gelation through end-linking reactions. We prevented the formation of odd-order loops owing to the binary reaction and second-order loops algorithmically. We stored network structures at various conversion ratios (φ_c) and minimized energy to reduce computation costs induced by structural relaxation. We subjected the networks to stretching until fracture to determine stress and strain at break and work for fracture, ε_b, σ_b, and W_b. These fracture characteristics are highly dependent on φ_c for networks with small f but relatively insensitive for those with large f. Thus, the networks with small f exhibit greater fracture properties than those with large f at high φ_c, whereas the opposite relationship occurs at low φ_c. We analyzed ε_b, σ_b, and W_b concerning the cycle rank ξ and the broken strand fraction φ_bb. We found ε_b, σ_b/φ_bb, and W_b/φ_bb monotonically decrease with increasing ξ, and the data for various f and φ_c superpose with each other to draw master curves. These results imply that the mechanical superiority of the networks with small f comes from their smaller ξ that gives higher ε_b, σ_b/φ_bb, and W_b/φ_bb than the networks with large f.