X-Doped Graphene Interaction with Anodic Materiallibs

Introduction

Thecarbonadoessuch as graphite are layered materials composed of hexagonal lattices sheets; graphite^1,2 is including ofcarbon atoms at all direction in the lattice points, while the h-BN is consist of alternating atoms from boron and nitrogen respectively. The lattice constants for graphite and h-BN are 2.46 Å and 2.50 Å repectively^1,2.In other side, layered BN is transparent and is an insulator^2,3 compare to graphite.The layers of h-BN are arranged as boron atoms in one layer which are located directly² on the top of nitrogen² atoms in a neighboring section and vice versa³.In graphite structures, stacking³ is slightly different²whilehexagons are offset² and cannot lie on the top of each other so interlayer distances can be consider similar: 3.35 Å for graphite¹and 3.33 Å for h-BN respectively Fig.1.

Recently, the theoretical approaches have been presented the band structures³ of alone layer of graphite and h-BN whilefor a layer of graphite which called graphene, 2 bands cross each other at the Fermi³ energies. For this matter, graphene is a semimetal⁴. In contrast graphene, for a alayer of the h-BN, equivalent⁴ bands cannot cross each other and amount 4.5 eV band gap forms. Via an experiment, h-BN has been calculated to have a band gap around 5.8 eV⁴.

Crystallographic of BN is classified into four polymorphic³ forms: Hexagonal⁴ BN (h-BN) (fig 1(a); rhombohedral^3,4 BN (r–BN); cubic B-N (c–BN); and wurtzite⁴ BN (w–BN).

Figure 1: Crystal structures of (a) graphite; (b) hexagonal boron nitride Click here to View figure

In 1842, Balmain⁵sensitized- BN as reaction products via boric-oxide and potassium cyanide⁵through1 atmosphere pressure. Then, various methods havebeen reported through h-BN and r-BN which formed under ambient⁵ pressure and c-BN has been synthesized from h-BN via high pressure and high temperatures. It is notable that w-BN is prepared from h-BN via high pressure at room temperature⁶.

The discovery of amazing reversible, low-voltage⁷ Li-intercalation carbonaceous⁸ materials, Sony Company realized the commercialization⁷ of xC6/Li _1-x CoO2 cells in 1991⁷. Lithium ion batteries (LIBs) are widely used in small gridstorage systems.

LIBs generally consist of positive and negative electrodes including a conducting electrolytewhere store electrical energy in the two electrodes⁸ in the form of Li-intercalation⁸ compounds. Electrodes, separator, and electrolyte are the main components of the LIB where the anode plays an essential role in the performance of these devices.

In the charging mechanism of the LIBs, Li+ released from the negative electrode and move inside the electrolyte then inserted into the positive electrode. In the discharging mechanism,Li+ are extracted⁸ from the (+) electrode and move back to the (-) electrode. Although the electrolyte establishes high ionic conductivity⁹ between 2 electrodes, the electrolytes⁹ are not responsible^8,9 for the conduction of free-electrons. So the electrons complete the 1/2 reaction will move in the way of an extra⁹ external wire.

Various experiments have accomplished for confirming the utilization of graphene in the forms of nano-sheets or nano-ribbons for enhancing lithium storage⁹ capacities and for improving recharge performance^9-11. Furthermore in this study, semi-empirical MM calculations have been donefor investigatingLi+ storage between 2 graphene¹¹sheets¹², as well as a few heteroatom-substituted¹¹carbon materials¹³.

Dis-charging or charging of Li+ in carbonadoes iswell established and arrangedup to now^18-21. It has also been exhibitedthe mechanism of the repulsive forces¹³ in the mixed stages which can result in the pure stages during intercalation^19-23. In this study, chargingand discharging of Li-ions has investigated in h-BN with the positive electrode reaction as: Li

and the negative electrode reaction as:

while the whole reaction is:

It has been suggested²² that lithium atoms are stored²³ via two mechanisms: intercalation and alloying²⁴.

Recently many works has been established for describing the intercalation and diffusion of Li+ at different sites on carbonadoes graphite and many studies have been performed in order to explain the mechanism by which Li+ s are stored in electrodes, including theoretical works^13-24 .

The electricalconductivitiesfor the Li+-Graphene increases²⁵via increasing intercalation levels due to the donor²⁶ nature of electronsfor the lithium. This is in contrast of ionic conduction²⁶ in which diffusivity²⁷ decreases²⁶ due to theinsertion of Li-ions²⁷. In the case of amorphous²⁶ carbon as thedisorder²⁸ increases electrical conductivity²⁸ significantly decreases²⁹.

Recently, Fisher group fabricated^29-30 a tube-in-tube structure with Li+ intercalation capacities2 times higher than that of the template-synthesized^30-40 Carbon-NTs, as the inner tubules provided more electrochemical^40-43 active sites for intercalation of Li ions^28-51.

Boron nitride tubes(BN-NT), which firstly predicted and synthesized by Rubio and Chopra respectively^40-48, has a structural similar to Carbon-NTs but,in contrast to the Carbon-NTs being metallic⁴⁰(semiconductor) depending on chirality^42-46. BNNTs are usually can be an insulator regardless of their helicity, tube diameters and number of tube walls^42-49.

Experimental results have exhibited that small SW-Carbon-NTs are usually found inside multi-walled Carbon-NTs ^40-51. There is, therefore⁴⁹, also a strong motivation to study in detail the stability and interaction of small Boron-Nitride-NTs inside a larger one (viewpoint of diameters), which makes easier to understandthe experimental results. Besides, the study on double-walled Boron-Nitride-NTs (DBN-NTs) has demonstrated an interesting variation in their electronic⁵⁰ properties when compared with those of freestanding⁴⁹ component of BNNTs^48-51. So it is also important to see the inter-wall coupling behavior and interaction energies associated with the small Boron-Nitride-NTs.

In summary, Graphene and h-BN compounds as one kind of classical materials⁴² with a mature studied history will play asignificant role in the battery market of the near future,but how to combine hybrid materials together to obtainsafe, stable, and high-capacity electrodes has always beenthe radical problem that many researchers are trying tosolve.

Theoretical Background

Diffus ion properties^45-51 of Li-ion cell determines some of the keys performance metrics of Li+ ion batteries cells, consist fo the charges anddischarges rate, practical capacities and cycling stabilities. The governing equation describing the diffusion process is known as Fick’slaw as:

and

where “j_i” is ionic flux, molcm⁻² s⁻¹, D_i is diffusivity of solute (i =1, 2), cm² s⁻¹ and C_i  is concentration of species i , (molcm3).The proportionality ^40-50 factor D is the diffusivity or diffusion coefficient as

Li+-ion cells consist of, all Keyes phenomena involves conducting charged particles as a primary cell from cathodes to anode or vice versa as a secondarycell from anode to cathodes.

Typical commercially used lithium-ion battery consists of several interconnected electrochemical cells, where each cell is composed of a graphite anode (such as Meso-carbon microbeads), a cathode formed by lithium metal oxide (such as LiCoO2) and electrolyte (such as LiPF6 dissolved in ethylene carbonate/dimethyl carbonate mixture) embedded in a separator felt.

Anode Materials

In the case of anode, Li metal is found to be the most electropositive (-3.04 V versus standard hydrogen electrode) with large reversible capacity (≈ 4000 A h kg-1). However, due to safety considerations (explosion hazards as a result of dendrite growth during cycling), metallic Li has been substituted by various carbonaceous materials.

During discharge, Li+ ions are extracted from the layered graphite, they pass⁵⁵ through the electrolytes and intercalate among the LiCoO2 layers (Fig.2.).

Figure 2: A typical commercial lithium-ion battery Click here to View figure

Density and Energy of Lithium in Diffusion Model

The electron densities has been defined as

Where η_i is occupational number of orbitals (i), φ are orbitals wave functions, Χ  is basis function and C is coefficient matrix, the element of i_th row j_th column⁵² corresponds to the expansion coefficient of orbital j respect to basis function i. Atomic unit for electron density can be explicitly ⁵⁴ written as e/Bohr³

Electron localization and chemical reactivityies⁵⁵ have been built by Bader⁵⁵.

The Hamiltonian Kinetics Energies Densities K(r)

The kinetic energies densities are not defined, since it has been expected value for kinetic energies operators

has been recovered via integrating kinetic energies densities from an alternative definition. One of general used definition can be demonstrated as:

“G(r)” is famous as positive definite kinetic energies densities.

K(r) and G(r) are directly related by Laplacian of electron density

Electron Localization Function (ELF)

Becke and Edgecombe noted that spherically averaged likespin conditional pair probability has direct correlation with the Fermi hole and then suggested electron localization function (ELF)^53-54.

where

and

for close-shell system, since

D and D0 terms can be simplified as

Savin, has reinterpreted the ELF⁵² in the view of kinetics energies^52-58.

Where

Do (r) for spin-polarized system and close-shell system are defined in the same way as in ELF⁵³.

Local Entropies

Local information entropiesare quantification of information, which was proposed by Shannonto decompose di-atomic and tri-atomic molecules into space by a minimized information entropy^52-57.

Parr has discussed the relationship between information entropies and atom partition as well as molecular⁵⁴ similarity⁵⁴. Noorizadeh and Shakerzadeh suggested using information entropy to study aromaticity. probability function is

If P (x) is replaced by

then the integrand can be called LIE of electrons.

Where, N is the total number of electrons in current system.

At each inter-tube configuration, a single-point calculation is carried out and the total energy is recorded.The resulting sliding-rotation energy surfaces are used to fix our model in better position.

We further calculated the interaction energy between x lithiuman h-BN sheets.

The interaction energy was calculated via an Mp6 method in all items according to

Where the “ΔE_s ” is the stability energy of system.

The contour line map has drawn via Multiwfn software^52-54. The graphs are exhabited on interactive interfaces and the methods in this work has based on our previous work^59-99.

Result and Discussion

We have listed the data of Density, energy, electron localization function (ELF), localized orbital locator (LOL) and local entropy, gap energy, charge from ESP, electrostatic potential ,ionization energy,the charges of two doped grap hene electrodes and the stability energy of X-G-(h-BN) -X-G and dielectric  in 4 tables (tables1-6) and these data have plotted in 10 the figures (figs.1-10)

We have calculated the gradient norm and the Laplacian of electron density via equals 7 and 8 for the lithium diffused in the X-G/(h-BN)/X-G system respectively and the data are listed in table 1. For calculation the electron spin density from the difference between alpha and beta density, we have Used

then the spin polarization parameter function will be returned instead of spin density

The absolute value of ξ going from zero to unity corresponds to the local region going from un-polarized case to completely polarized case Table 1.

In this work it has been calculated the local Information entropies for each of Li atoms via eqs. 19-20 and the   integrating of those functions over whole spaces yield the information entropies. The data of local Information entropies are listed in Tables 1-5

Weak interaction (equals 20 and 21) has significant influence on conformation of macro-molecules, however reproduction of electron densities by ab initio and grids data calculation of reduced density gradient (RDG) for such huge systems are always too time-consuming.

In this work it has been exhibited the complex of X-G/(h-BN)/X-G which demonstrate a high electrical  conductivity and a good mechanical strength, excellentflexibility, great chemical stabilities and high specific surfaces area. Thoseare especially noticeable when the graphene are chemically converted via greater proportion of functional groups, proving that they are suited for using as the basecomposite electrodes materials as wellas enhancing the electrode’s mechanical stabilities. As a result, X-G/(h-BN)/X-G containing electrode materials have highcapacity and good rate performance. X-G/(h-BN)/X-Gflexibilities makes thoseas an idealmaterial for buffering metal electrode’s volume expansionand contraction during the charge or discharge phenomenon.

Further, the excellent electrical properties of X-G/(h-BN)/X-Gcan enhance the conductivity of metal electrodematerial. Finally, the lithium storage capacity for mostmetal oxide composite materials with X-G/(h-BN)/X-Gcan be useful greatly.

Figure 3: h-BN sandwich inside two boron graphene doped as two electrodes of B-G/h-BN/B-G and Be-G/h-BN/Be-G capacitors Click here to View figure

 

Figure 4: six diffused ion lithium between h-BN and B& Be doped graphene sheet layers Click here to View figure

 

Table 1: Density, energy, Electron localization function (ELF), Localized orbital locator (LOL) and Local Entropy for each Li of 6 lithium diffused on X-G/(h-BN)/X-G (X=B,N and Be) mixed layers

LithiumNo.	Density of all electron (10-4)	Density of electron (10-4)	Density of electron (10-4)	Spin density of electron	Potential energy β ensity ( 10-3J)	Hamiltonian  kinetic Energy ( 10-4J)	LOL 10-3	LocalEntropy 10-6	Ellipticity	ELF 10-7	Eta index
X=B
Li+(2)	0.30	0.15	0.15	0.0	-0.23	-0.15	0.16	0.50	-0.15	0.31	0.16
Li+(4)	0.26	0.13	0.13	0.0	-0.29	-0.15	0.18	0.52	-0.30	0.32	0.14
Li+(6)	0.38	0.19	0.19	0.0	-0.27	-0.12	0.17	0.53	-0.22	0.31	0.17
X=Be
Li+(2)	0.22	0.11	0.11	0.0	-0.28	-0.14	0.21	0.50	-0.19	0.38	0.17
Li+(4)	0.26	0.13	0.13	0.0	-0.27	-0.13	0.18	0.54	-0.12	0.35	0.13
Li+(6)	0.34	0.17	0.17	0.0	-0.25	-0.15	0.19	0.51	-0.41	0.36	0.16

 

Table 2: The Charges of two doped graphene electrodes and the stability energy of x-G/(h-BN)/x-G X= 6 atoms of Be, B and NClick here to View table

 

Table 3: The dielectric of X-G/(h-BN) /X-G modeled in various Lithium number Click here to View table

 

Table 4: Nucleor list and HOMO/LUMO and Gap energy for the B-C/h-BN/B-GClick here to View table

 

Figure 5: ELF of B-G/h-BN/B-G for Click here to View figure

 

Figure 6: K(r)of 3 lithium diffusion inside Be-G/h-BN/Be-G  Click here to View table

 

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