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 φc 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 εb, stress at break σb, and work for fracture Wb. As reported earlier, εb data for various f and φc 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 υbr. The master curves depend on c; as c increases, all the mechanical characteristics monotonically increase. If we plot σb/υbr and Wb/υbr against G/υbr, the data for various f and φc lie on master curves but depending on c. Consequently, the fracture characteristics are not solely described by the modulus.