Force-induced breakdown of flexible polymerized membrane

We consider the fracture of a free-standing two-dimensional (2D) elastic-brittle network to be used as protective coating subject to constant tensile stress applied on its rim. Using a Molecular Dynamics simulation with Langevin thermostat, we investigate the scission and recombination of bonds, and the formation of cracks in the 2D graphene-like hexagonal sheet for different pulling force $f$ and temperature $T$. We find that bond rupture occurs almost always at the sheet periphery and the First Mean Breakage Time $<tau>$ of bonds decays with membrane size as $<tau> propto N^{-beta}$ where $beta approx 0.50pm 0.03$ and $N$ denotes the number of atoms in the membrane. The probability distribution of bond scission times $t$ is given by a Poisson function $W(t) propto t^{1/3} exp (-t / <tau>)$. The mean failure time $<tau_r>$ that takes to rip-off the sheet declines with growing size $N$ as a power law $<tau_r> propto N^{-phi(f)}$. We also find $<tau_r> propto exp(Delta U_0/k_BT)$ where the nucleation barrier for crack formation $Delta U_0 propto f^{-2}$, in agreement with Griffiths theory. $<tau_r>$ displays an Arrhenian dependence of $<tau_r>$ on temperature $T$. Our results indicate a rapid increase in crack spreading velocity with growing external tension $f$.

Thermal decomposition of a honeycomb-network sheet - A Molecular Dynamics simulation study

The thermal degradation of a graphene-like two-dimensional triangular membrane with bonds undergoing temperature-induced scission is studied by means of Molecular Dynamics simulation using Langevin thermostat. We demonstrate that the probability distribution of breaking bonds is highly peaked at the rim of the membrane sheet at lower temperature whereas at higher temperature bonds break at random anywhere in the hexagonal flake. The mean breakage time $tau$ is found to decrease with the total number of network nodes $N$ by a power law $tau propto N^{-0.5}$ and reveals an Arrhenian dependence on temperature $T$. Scission times are themselves exponentially distributed. The fragmentation kinetics of the average number of clusters can be described by first-order chemical reactions between network nodes $n_i$ of different coordination. The distribution of fragments sizes evolves with time elapsed from a $delta$-function through a bimodal one into a single-peaked again at late times. Our simulation results are complemented by a set of $1^{st}$-order kinetic differential equations for $n_i$ which can be solved exactly and compared to data derived from the computer experiment, providing deeper insight into the thermolysis mechanism.