Phantom chain simulations for fracture of star polymer networks on the effect of arm molecular weight

Despite many efforts, the fracture of network polymers under extension is yet to be elucidated. This study investigated the effect of strand molecular weight on the fracture characteristics of the networks made from star-branched prepolymers with various node functionalities $3 \le f \le 8$ and conversion ratios $0.6 \le {\phi}_c \le 0.95$ via molecular simulations with phantom chains. The networks were created via end-linking reactions of star polymers with the arm molecular weight $N_a$ = 2, 5, and 10, simulated by a Brownian dynamics scheme. The cycle rank of the percolated network ${\xi}$ was entirely consistent with the mean-field theory, implying that the reaction occurred independently and the network connectivity was statistically fair. Afterward, the networks were alternatively subjected to energy minimization and uniaxial stretch until the break. From the stress-strain curves recorded during the stretch, the stretch and stress at the break, ${\lambda}_b$ and ${\sigma}_b$, and work for fracture $W_b$ were obtained. For these values, the following relations were found: ${\lambda}_b \sim N_a^{(1/2)} {\xi}^{(-1/3)}$, ${\sigma}_b \sim {\nu}_{br} N_a^{(4/3)} {\xi}^{(2/3)}$, and $W_b \sim {\nu}_{br} N_a^{(4/3)} {\xi}^{(2/3)}$, where ${\nu}_{br}$ is the branch point density.