柔性聚合物膜的力致击穿
Force-induced breakdown of flexible polymerized membrane
摘要：
我们考虑一个独立的二维（2D）的弹性脆性网络的断裂被用作保护涂层受到恒定的拉伸应力施加在其边缘。采用分子动力学方法，利用Langevin恒温器模拟了二维类石墨烯六方片层在不同的拉力$f$和温度$T$作用下的键断裂、重组和裂纹形成.我们发现，键断裂几乎总是发生在片的周边和第一平均断裂时间$<τ>$的债券衰减与膜的大小为$<τ> \propto N^{-β}$其中$β\approx 0.50\pm 0.03$和$N$表示的原子数在膜中。键断裂时间$t$的概率分布由泊松函数$W(t) \propto t^{1/3} \exp (-t / <τ>)$给出。平均破坏时间$<τ_r>$随尺寸$N$的增大呈幂律$<τ_r> \propto N^{-ϕ(f)}$下降。我们还发现$<τ_r> \propto \exp(ΔU_0/k_BT)$的裂纹形成的成核障碍$ΔU_0 \propto f^{-2}$，与格里菲斯的理论。$<τ_r>$显示出$<τ_r>$对温度$T$的Arrhenius依赖性。我们的研究结果表明，裂纹扩展速度与增长的外部张力$f$迅速增加。
英文摘要：
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 $<τ>$ of bonds decays with membrane size as $<τ> \propto N^{-β}$ where $β\approx 0.50\pm 0.03$ and $N$ denotes the number of atoms in the membrane. The probability distribution of bond scission times $t$ is given by a Poisson function $W(t) \propto t^{1/3} \exp (-t / <τ>)$. The mean failure time $<τ_r>$ that takes to rip-off the sheet declines with growing size $N$ as a power law $<τ_r> \propto N^{-ϕ(f)}$. We also find $<τ_r> \propto \exp(ΔU_0/k_BT)$ where the nucleation barrier for crack formation $ΔU_0 \propto f^{-2}$, in agreement with Griffith's theory. $<τ_r>$ displays an Arrhenian dependence of $<τ_r>$ on temperature $T$. Our results indicate a rapid increase in crack spreading velocity with growing external tension $f$.
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