Thermal Vibrations Of Single‐layered Graphene Sheets

Graphene is one of the most watchable nanomaterials for its excellent properties in electrical,chemical, and mechanical. The dynamic behavior of graphene received extensive attention.Experiments, quantum mechanics, molecular mechanics (MD) and continuum mechanics are used tostudy the problem. In this thesis, dynamics problems in the thermal vibration of single-layeredgraphene sheets (SLGSs) are investigated using MD method and continuum mechanics. Wavelettransform (WT) is used to process the SLGSs’ thermal vibration signals. The main progresses andcontributions of the thesis are as follows.Dynamics problems of isolated SLGSs are investigated using MD method based on theBrenner’s second-generation reactive empirical bond order (REBO) potential. The in plane stiffnessand Poisson ratio of SLGSs are calculated by stretching SLGSs. The effective thickness of SLGSs isobtained by MD simulations for the thermal vibration of SLGSs through the natural frequency. Thenatural frequencies for SLGSs of different sizes with initial stress in different temperatures arecalculated through MD. The thin plate theory can predict the MD results very well in a certain rangeof strain. For the nonlinear relation between stress and strain when the strain is very large, thedeviation between the MD results and plate theory becomes larger when the strain increases. Thedifference between the plate theory and the MD results becomes more and more obvious, when thesize of graphene sheet is very small.The thermal vibration of SLGSs embedded in the inert gas environment is investigated using MDmethod based on the condensed-phase Optimized Molecular Potentials for Atomistic SimulationStudies (COMPASS) force field. The root-of-mean-squared (RMS) amplitudes for SLGSs in differenttemperatures are calculated through MD. It is contrasted with the results calculated by the thin platemodel together with the law of energy equipartition. At the center of SLGS, the thin plate theory canpredict the MD results very well. The deviation between the MD results and plate theory becomeslarger at the edge of SLGS.Wavelet transform (WT) is used to analysis the SLGSs’ thermal vibration signals. It is found thatusing a suitable wavelet for wavelet analysis can extract some vibration information about naturalfrequency.