Phantom Chain Simulations for the Fracture of Energy-Minimized Tetra- and Tri-Branched Networks

Abstract

Effects of branch functionality on mechanical properties of polymer networks are yet to be fully elucidated, although multi-functional approaches have been mainly attempted. For instance, Fujiyabu et al. [Sci. Adv. 2022, 8, abk0010] recently reported that polymer networks made from tri-branch prepolymers exhibit superior mechanical properties to tetra-branch analogues. Although they attribute the difference to stretch-induced crystallization observed in tri-branch poly (ethylene glycol) networks, the mechanism still needs to be clarified. In this study, we performed coarse-grained molecular simulations to extract the effect of branch functionality. The prepolymers were replaced by bead-spring phantom chains, and gelation was simulated by a Brownian dynamics scheme. We subjected the resultant networks to energy minimization and uniaxial stretch by introducing breakage for elongated segments. In the stress−strain relation thus obtained, stress and strain at the break were larger for tri-branch networks than that for tetra-branch analogues, consistent with the experiment. The superiority of tri-branch networks is observed in a wide range of the conversion ratio in gelation, molecular weights of prepolymers, and polymer concentrations. The result implies that the mechanical superiority of tri-branch networks to tetra-branch ones is due to a fundamental structural difference generated during gelation.

Phantom-Chain Simulations for the Effect of Node Functionality on the Fracture of Star-Polymer Networks

“…Panels (h) and (i) show the development of stress σ and unconnected strand fraction ϕ u during the stretch. We employ true stress and true strain to be consistent with our previous work . Note that ϕ u starts at 0.1, which is consistent with ϕ c = 0.9.…”

“…One may argue that this thought contradicts earlier studies in which f = 3 networks show superior fracture characteristics than f = 4, even if the modulus is the same. , However, we note that the master curves are observed for σ b /ϕ bb and W b /ϕ bb , not for σ b and W b . Indeed, our simulation is consistent with the earlier studies , on the superiority of small- f networks with similar G values. Figure shows an example where the stress–strain curves are shown for different f networks with similar G values.…”

“…We distributed M prepolymers with f branching arms, each consisting of N a beads in the simulation box under periodic boundary conditions. According to the previous study, we chose N a = 5 and M = 1600, whereas we varied f ranging from 3 to 8. The effects of system size and prepolymer molecular weight were discussed in our previous study .…”

“…According to the previous study, we chose N a = 5 and M = 1600, whereas we varied f ranging from 3 to 8. The effects of system size and prepolymer molecular weight were discussed in our previous study . The simulation box dimension was set to realize the bead number density ρ, chosen at 8.…”

“…Motivated by the work of Fujiyabu et al, we previously performed phantom chain simulations where networks with f = 3 and 4 were constructed via the gelation of star-branched prepolymers . The simulation of gelation was performed with a Brownian dynamics scheme.…”