  We present a loop-opening model that accounts for the molecular details of
the intrinsic fracture energy for fracturing polymer networks. This model
includes not only the energy released from the scission of bridging chains but
also the subsequent energy released from the network continuum. Scission of a
bridging chain releases the crosslinks and opens the corresponding topological
loop. The released crosslinks will be caught by the opened loop to reach a new
force-balanced state. The amount of energy released from the network continuum
is limited by the stretchability of the opened loop. Based on this loop-opening
process, we suggest that the intrinsics fracture energy per broken chain
approximately scales with the product of the fracture force and the contour
length of the opened loop. This model predicts an intrinsic fracture energy
that aligns well with various experimental data on the fracture of polymer
networks.
