The bending rigidity of two-dimensional (2D) materials is a key parameter for understanding the mechanics of 2D NEMS devices. The apparent bending rigidity of graphene membranes at macroscopic scale differs from theoretical predictions at micro-scale. This difference is believed to originate from thermally induced dynamic ripples in these atomically thin membranes. In this paper, we perform modal analysis to estimate the effective bending rigidity of graphene membranes from the frequency spectrum of their Brownian motion. Our method is based on fitting the resonance frequencies obtained from the Brownian motion in molecular dynamics simulations, to those obtained from a continuum mechanics model, with bending rigidity and pretension as the fit parameters. In this way, the effective bending rigidity of the membrane and its temperature and size dependence, are extracted, while including the effects of dynamic ripples and thermal fluctuations. The proposed method provides a framework for estimating the macroscopic mechanical properties in other 2D nanostructures at finite temperatures.

Thermal degradation under wet conditions is considered as an important aging mechanism in polyamide 6,6 (PA 6,6). The effect of water on thermal degradation of amorphous PA 6,6 is investigated at relatively low temperatures, varying from 1000 to 2000 K, using reactive force field molecular dynamics (MD) and collective variable-driven hyperdynamics simulations. The simulation of the related long-term chemical reactions is made possible thanks to the self-learning accelerated MD concept of hyperdynamics in combination with the corresponding accurate reproduction of the correct dynamics, consistent with unbiased MD simulations. The kinetics of cleavage reactions of the amide bonds in the backbone of the polymer chains, responsible for the thermal degradation of the polymer, is studied, and the influence of water content on the activation energy and pre-exponential factor of the cleavage reactions is explored. The results show that activation energy and pre-exponential factor are in agreement with experimental data. The proposed simulation framework not only estimates kinetic properties of thermal degradation that are consistent with experimental observations but also provides a predictive tool for studying long-term thermal degradation of PA 6,6.