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 multifunctional 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 the sols and induce gelation through end-linking reactions. We prevented the formation of odd-order loops algorithmically, owing to the binary reaction and second-order loops. We stored network structures at various conversion ratios (fc) 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 fractures, eb, sb, and W b. These fracture characteristics are highly dependent on fc for networks with a small f but relatively insensitive for those with a large f. Thus, the networks with small f exhibit greater fracture properties than those with large f at high fc, whereas the opposite relationship occurs at low fc. We analyzed eb, sb, and W b concerning cycle rank ? and broken strand fraction fbb. We found that eb, sb/fbb, and W b/fbb monotonically decrease with increasing ?, and the data for various f and fc 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 ? that gives higher eb, sb/fbb, and W b/fbb than the networks with large f.