Simulation Study On The Structure And Flexibility Of Egg-tray Graphene

Graphene is an important material expected to be applied to flexible electronics technology.However,in the process of synthesis and application of graphene,lots of intrinsic defects and doping are often randomly and uncontrollably generated.Thus,a series of functionalized graphene and graphene allotropes with rippled geometry are obtained due to the rotation,deletion and rearrangement of carbon-carbon bonds,and the presence of oxygen-containing functional groups,doping and gain boundaries.In addition,the presence of non-hexagonal carbon rings and doping can significantly affect the geometry,thickness and properties of graphene,especially opening band gap which limits application of graphene in flexible electronics.Meanwhile,thickness is usually considered to be one of the key parameters to determine the flexibility of two-dimensional materials.Moreover,the egg-tray graphene models with similar structural pattern provide the possibility to explore the relationship between bending modulus and thickness.Therefore,we can change the structure of egg-tray graphene by tuning the structural pattern and doping,aiming to explore the effects of structural pattern,thickness,curvature,and doping on the flexibility,electronic structures and optical properties of rippled graphene and control them.Here,we constructed a series of egg-tray graphene configurations with a similar structural pattern but different thicknesses,and explored the optimal sites of monoatomic doping,diatomic doping and co-doping of nitrogen and boron.Employing the software based on density functional theory,we studied the relationship between the bending modulus and the structural pattern,thickness,curvature and doping,as well as the influences of non-hexagonal carbon rings and doping on the electronic and optical properties.It was found that the bending modulus of egg-tray graphene shows a complex dependence on the structural pattern,thickness and curvature.After eliminating the influences of structural pattern and curvature,there is a simple linear relationship between the bending modulus and thickness,and its determination coefficient（r²）is 0.986.Moreover,this linear relationship is not affected by curvature,calculation method and parameters,r² is always above 0.984（even up to 0.995）,and shows strong stability.Meanwhile,the multi-electron nitrogen atom is more suitable for doping in the five-membered carbon ring with one less carbon atom,and the less-electron boron atom is more suitable for doping in the seven-membered carbon ring.In addition,two different heteroatoms tend to be adjacent to each other for bonding,and two identical heteroatoms will be as far away from each other as possible.Except that BN-doping has little effect on its thickness and bending modulus,both N doping and B doping can reduce its thickness and bending modulus.A single nitrogen atom can reduce the thickness of t₁-4 configuration from 2.517 to 2.382（?）,and its bending modulus from 12.086 to 11.505 eV;a single boron atom can also reduce the thickness and bending modulus of t₁-4 configuration to 2.311（?）and 9.785 eV.However,after eliminating the influence of structural pattern and curvature,the bending modulus of doped egg-tray graphene is still mainly determined by the thickness,and increases linearly with it,and r² is always around 0.99.Finally,as for the electronic properties,although the egg-tray graphene commonly has a band gap（up to 600 meV）which oscillates with the configuration due to the breaking ofπbonds by incorporating non-hexagonal carbon rings,and t₂ is a semiconductor configuration with a band gap of 0.29 eV,the t₂-2 configuration is metallic,and N doping can also eliminate the band gap.Besides,doping of nitrogen and boron will separately cause blue shift and red shift of the light absorption peak of egg-tray graphene（about 0.3 and 0.2 eV,respectively）,which is useful in optical detection.