Phantom chain simulations for the fracture of star polymer networks with various strand densities

Despite many attempts, the relationship between the fracture and structure of polymer networks is yet to be clarified. For this problem, a recent study on phantom chain simulations [Y. Masubuchi et al., Macromolecules, 2023, 56, 9359-9367.] has demonstrated that the fracture characteristics obtained for polymer networks with various node functionalities and conversion ratios lie on master curves if they are plotted against cycle rank, which is the number of closed loops in the network per network node. In this study, we extended the simulation to the effect of prepolymer concentration c on the relationships between the cycle rank and fracture characteristics within the concentration range of 1 ≲ c/c* ≲ 10, concerning the overlapping concentration c*. We created networks from sols of star-branched phantom bead-spring chains via an end-linking reaction between different chains through Brownian dynamics simulations upon varying the number of branching arms f from 1 to 8, and the conversion ratio φ_c from 0.6 to 0.95. For the resultant networks, the cycle rank ξ was consistent with the mean-field theory. The networks were uniaxially stretched with energy minimization until break to obtain modulus G, strain at break ε_b, stress at break σ_b, and work for fracture W_b. As reported earlier, ε_b data for various f and φ_c are located on a master curve if plotted against ξ. The other quantities also draw master curves as functions of ξ if normalized by the branch point density υ_br. The master curves depend on c; as c increases, all the mechanical characteristics monotonically increase. If we plot σ_b/υ_br and W_b/υ_br against G/υ_br, the data for various f and φ_c lie on master curves but depending on c. Consequently, the fracture characteristics are not solely described by the modulus.