Contribution of Unbroken Strands to the Fracture of Polymer Networks

We present a modified Lake–Thomas theory that accounts for the molecular details of network connectivity upon crack propagation in polymer networks. This theory includes not only the energy stored in the breaking network strands (bridging strands) but also the energy stored in the tree-like structure of the strands connecting the bridging strands to the network continuum, which remains intact as the crack propagates. The energy stored in each of the generations of this tree depends nonmonotonically on the generation index due to the nonlinear elasticity of the stretched network strands. Further, the energy required to break a single bridging strand is not necessarily dominated by the energy stored in the bridging strand itself but in the higher generations of the tree. We describe the effect of mechanophores with stored length on the energy stored in the tree-like structure. In comparison with the "strong" mechanophores that can only be activated in the bridging strand, "weak" mechanophores that can be activated both in the bridging strand and in other generations could provide more energy dissipation due to their larger contribution to higher generations of the tree.