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The influence of node functionality (f) on the fracture of polymer networksremains unclear. While many studies have focused on multi-functional nodes withf>4, recent research suggests that networks with f=3 exhibit superior fractureproperties compared to those with f=4. To clarify this discrepancy, weconducted phantom chain simulations for star-polymer networks varying f between3 and 8. Our simulations utilized equimolar binary mixtures of star branchprepolymers with a uniform arm length. We employed a Brownian dynamics schemeto equilibrate sols and induce gelation through end-linking reactions. Weprevented the formation of odd-order loops owing to the binary reaction andsecond-order loops algorithmically. We stored network structures at variousconversion ratios ({\phi}_c) and minimized energy to reduce computation costsinduced by structural relaxation. We subjected the networks to stretching untilfracture to determine stress and strain at break and work for fracture,{\epsilon}_b, {\sigma}_b, and W_b. These fracture characteristics are highlydependent on {\phi}_c for networks with small f but relatively insensitive forthose with large f. Thus, the networks with small f exhibit greater fractureproperties than those with large f at high {\phi}_c, whereas the oppositerelationship occurs at low {\phi}_c. We analyzed {\epsilon}_b, {\sigma}_b, andW_b concerning the cycle rank {\xi} and the broken strand fraction {\phi}_bb.We found {\epsilon}_b, {\sigma}_b/{\phi}_bb, and W_b/{\phi}_bb monotonicallydecrease with increasing {\xi}, and the data for various f and {\phi}_csuperpose with each other to draw master curves. These results imply that themechanical superiority of the networks with small f comes from their smaller{\xi} that gives higher {\epsilon}_b, {\sigma}_b/{\phi}_bb, and W_b/{\phi}_bbthan the networks with large f.

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