The Effects of Random Porosities in Resonant Frequencies of Graphene Based on the Monte Carlo Stochastic Finite Element Model

Abstract

With the distinguished properties in electronics, thermal conductivity, optical transparence and mechanics, graphene has a powerful potential in nanosensors, nano-resonators, supercapacitors, batteries, etc. The resonant frequency of graphene is an important factor in its application and working environment. However, the random dispersed porosities in graphene evidently change the lattice structure and destroy the integrity and geometrical periodicity. This paper focuses on the effects of random porosities in resonant frequencies of graphene. Monte Carlo simulation is applied to propagate the porosities in the finite element model of pristine graphene. The statistical results and probability density distribution of porous graphene with atomic vacancy defects are computed based on the Monte Carlo finite element model. The results of porous graphene with atomic vacancy defects are compared and discussed with the results of graphene with bond vacancy defects. The enhancement effects of atomic vacancy defects are confirmed in porous graphene. The influences of atomic vacancy defects on displacement and rotation vector sums of porous graphene are more concentrated in local places.

The Fingerprints of Resonant Frequency for Atomic Vacancy Defect Identification in Graphene

“…The geometrical configuration of graphene lattice and the corresponding geometri and material parameters are defined as above, while the resonant frequencies and def mations under different vibration modes are computed based on the finite eleme method. The first four order resonant frequencies of the pristine graphene without v cancy defects are 1.7282, 3.2925, 3.7442, and 5.189 THz, respectively, which reaches go agreement with the reported literature [28,30,31].…”

“…The geometrical parameters involving the length of carbon covalent bonds and the diameter of the cross-section of the beam (thickness of graphene) are 0.27 nm and 0.032 nm, respectively. The material properties, namely Young's modulus, Poisson's ratio, and mass density, are settled as 1.2 TPa, 0.2, and 2700 Kg/m 3 , respectively, according to the reported literature [7,[28][29][30].…”

The Uncertainty Propagation for Carbon Atomic Interactions in Graphene under Resonant Vibration Based on Stochastic Finite Element Model

“…In addition to the related geometrical parameters in the finite plane element model of graphene, the material parameters are listed in Table 1 . According to the reported literature [ 10 , 11 ], the distinguished mechanical properties are measured and predicted. However, the uncertainty and obvious fluctuations of mechanical properties are the essential issues that require effective solutions.…”

“…However, the uncertainty and obvious fluctuations of mechanical properties are the essential issues that require effective solutions. In this paper, the specific value intervals of the geometrical and material parameters are provided according to the data in the literature [ 10 , 11 ] and presented in Table 1 .…”

“…The finite element method has long-term development in terms of nonlinear problem solutions, parallel computing, dynamic motion modeling, etc. [ 10 ]. The high computational performance and fast convergence speed of the finite element method make it a competitive alternative to the numerical simulation of graphene.…”