Phantom-Chain Simulations for the Effect of Node Functionality on the Fracture of Star-Polymer Networks
Yuichi Masubuchi, Yuya Doi, Takato Ishida, Naoyuki Sakumichi, Takamasa Sakai, Koichi Mayumi, Kotaro Satoh, Takashi Uneyama
Abstract
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 (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 fractures, ε b, σ b, and W b . These fracture characteristics are highly dependent on φ c 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 φ c, whereas the opposite relationship occurs at low φ c . We analyzed ε b, σ b, and W b concerning cycle rank ξ and broken strand fraction φ bb . We found that 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 .