Predicting failure locations in model end-linked polymer networks

The fracture of polymer networks and gels has a significant impact on the performance of these versatile and widely used materials, and a molecular-level understanding of the fracture process is crucial for the design of new materials. Combining molecular dynamics simulations and network analysis techniques, we demonstrate that in the initial undeformed state of model end-linked polymer networks, polymer strands with fewer topological defects in their local surroundings, higher geodesic edge betweenness centrality values compared to the system average, and greater alignment to the loading direction are more prone to breaking under uniaxial tensile deformation.

Figure 1

For the $N=5$ system, (a) distribution of probability of breaking ($P_{\text{break}}$) of polymer strands obtained from the isoconfigurational ensemble (blue) and the random sampling (orange); (b) schematic illustration showing the first three generations of the local structure of a polymer strand, with strands and crosslinkers at the same generation from the root (G0) strand labeled with the same color; (c) average primary loop fraction as a function of generation index for strands with different $P_{\text{break}}$ in the isoconfigurational ensemble, zoomed in the low generation index region. The plot with the full range of values is available in the Supplemental Material [53].

Figure 2

Probability distribution function of (a) GEBC and (b) $P_2$ for the $N=5$, 15, and 50 systems. GEBC and $P_2$ are calculated from the initial undeformed state of the network. GEBC of each polymer strand is normalized by the average value of all strands in the network.

Figure 3

For the $N=5$, 15, and 50 network systems, average (a) GEBC and (b) $P_2$ for polymer strands with the same $P_{\text{break}}$. Average $P_{\text{break}}$ for polymer strands that have (c) GEBC and (d) $P_{2,\text{loading}}$ above certain thresholds. Average $P_{\text{break}}$ is also plotted as a function of both GEBC and $P_{2,\text{loading}}$ for the (e) $N=5$ and (f) $N=50$ systems.

Figure 4

Average (a) GEBC and (b) $P_{2,\text{loading}}$ as a function of the strand breaking order for the $N=5$, 15, and 50 systems. Black lines are linear fittings of each data set.