# The Impacts of Random Distributed Vacancy Defects in Steady-State Thermal Conduction of Graphene
###### Abstract  
The unavoidable vacancy defects dispersed throughout the entire pristine graphene tailor to the integrity of the lattice structure and thereby have complicated impacts on the mechanical and thermal properties of graphene. In order to analyze the influence of vacancy defects on the extraordinary thermal conductivity of graphene, three typical kinds of vacancy defects--namely center concentrated, periodic, and random distributed vacancy defects--are compared and discussed. In the steady-state thermal conduction, the finite element method (FEM) is performed to calculate the total thermal energy and temperature field. The equivalent coefficient of thermal conductivity is derived from thermal energy, amount of vacancy defects, and boundary condition. The chirality in graphene is discussed by the location of its heat source. Moreover, the Monte Carlo simulation is applied to propagate the uncertainty of random vacancy defects in the finite element model of pristine graphene. In this paper, we provide the robustness to defend the impacts of vacancy defects on thermal conduction and the fluctuation and divergence caused by a certain number of random vacancy defects. v 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 2019 2  
suspended graphene [13]. The range in the interval from 1500-5000 W/mK is reported for the thermal conductivity of suspended graphene [14]. In the investigation process, theoretical and analytical methods are available alternatives of experimental measurements. The theoretical results obtained for heat conduction can be tested and compared with the experiments of high-quality suspended graphene with few layers [15; 16; 17; 18]. Previously, graphene's thermal conductivity was computed using relaxation-time approximation (RTA) [19]. Based on the Klemens theory, thermal conductivity is predicted with divergence in layer, grain size, and substrate [20; 21]. In addition, the molecular dynamics (MD) simulation also provided 9000 W/mK for graphene near room temperature [22]. Heat conduction in graphene nanoribbons with uncertain length, existence of edge roughness, and unavoidable defect concentration has Tersoff and Brenner potential, [23; 24; 25; 26; 27; 28]. The rough edges in graphene contribute to the reduction of thermal conductivity by orders of magnitude [29; 30]. Usually, theoretical description of thermal properties of graphene closely corresponds to that of carbon nanotubes [31]. The extraordinary thermal conductivity of graphene is confirmed both in experimental measurements and theoretical analysis results. However, there are still challenging issues. First, whether the contribution and importance of Z axial acoustic phonons in graphene is negligible [32; 33] or dominant, it is still not clearly defined. Second, thermal conductivity non-linearly depends on the temperature [34], which is proofed in the experimental [35] and theoretical [36] data. Third, the optical absorption under the conditions of the experiment [37] leads to underestimated thermal conductivity. It is hard to compare directly its accuracy of Raman optothermal technique with that of the thermal-bridge or 3-\(\omega\) techniques [38; 39; 40; 41]. Lastly, the parameters of geometrical properties are ambiguous and the defects are difficult to precisely define. Based on the inter-atomic potential [42], the graphene thickness equals 0.34 nm, but based on [PERSON]'s modulus and tensile strength [43], the thickness ranges from 0.06-0.69 nm. The inevitable vacancy defects dispersed throughout the entire pristine graphene tailor to the integrity of the lattice structure and impact the thermal conductivity of graphene. It is necessary to quantitatively analyze the influence of vacancy defects in graphene's thermal conduction. In this paper, three typical kinds of vacancy defects--namely center concentrated, periodic, and random distributed vacancy defects--are introduced in the pristine graphene. The chirality of graphene is considered by using the boundary condition as a location of its heat source.