Phantom Network Simulations for Rupture of Polymer Networks

The relationship between network structure and fracture properties in polymer networks remains a complex, unresolved issue. For instance, the effect of node functionality (f) is contentious, with conflicting experimental reports; some suggest that higher f improves strength, whereas recent studies demonstrate that lower f can be superior. This review summarizes a series of studies that utilize phantom chain simulations to investigate network fracture systematically. The model employs Rouse-Hamm type phantom chains, forming networks via end-linking of star-shaped prepolymers (mimicking Tetra-PEG gels). These networks were uniaxially stretched using a quasi-static process based on energy minimization. The simulations successfully reproduced the contradictory effects of f, revealing a strong dependence on the reaction conversion (p). Specifically, a higher f is advantageous at low p, but this trend reverses at high p, where a lower f yields better fracture properties6. The central discovery is that the cycle rank, which represents the density of independent loops, unifies the complex effects of f and p. Fracture properties—including strain at break, stress at break, and work of rupture—all collapse onto universal master curves when plotted against cycle rank.