Lithium Including Mixed Sodium Inside Graphene Oxide ( GO ) as Anodic Electrodes for ion Batteries

Graphene oxide has a great potential as a suitable material for anodic sodium ion battery (NIBs) due to its unique behavior. The calculated reversible of lithium ion capacity of GO/ Li & Na / GO based anodic materials are widely improved comparing to the conventional graphite-based anodic materials. By this investigation GO sheets have been localized into the graphene as an item for enhancing electrochemical & Physical ratio. Moreover, the structure of GO/Li& Na/GO can be used for improving the capacities and electronics transport in the GO sheets-based NIBs. Therefore, these modifications of GO sheet and designing of GO/Li & Na/GO structures provide a strategy for increasing the performance of GO-based anode. GO/Li & Na/GO could also be accomplished into the freestanding anodes without any of binders or current’s collectors, which will leads to increased energies densities of overall battery’s designing.


INTRODUCTION
Sodium-ion battery is a type of re-chargeable battery which uses sodium-ions as its charge carriers and is very similar to LIBTs in many ways.Na ions are 33% larger in diameter and 2.1 times heavier within lower gravimetric capacities than Li-ion batteries 1 .In addition Na metals are more active than Li with the standard electrode potentials which is ~0.3V higher than Li.
By the Sony it has been realized a commercialization of xC6/Li 1-x CoO 2 cells 1 reaction and mechanism in 1991.LIBs are representative energies storage devices based on electrochemical energies, widely used in small grid storage systems.
Within discovery of high quality reversible, low-voltage 1 Li-intercalations carbonaceous 1 material, the suitable electronic and chemical performances of LIBs concerning energies and power densities 1 , as well as the progress in the cell designing and manufacturing, has been made LIBs extremely successful for mobile equipment.
Although; the Na + cation has a greater radius than the Li + cation, that causes a few of the superior LIB anode's materials un-suitable for [NIBs] 2 , concerns regarding 2 the extra availability of lithium resources 2 is raising.A sodium 2 ion battery has drawn increasing attention 3 due to Na is a abundant 3 element and shares 2 common properties within Li [2][3][4] , specially, graphite 5 is used 6 for anodic electrodes in the present commercial 7 LIBs, while those have been reported for having a very low capacity 6 of when used as an anodic electrode for NIBs [5][6][7] .
Both disordering carbons and Nano-flakes 8 (CNFs) exhibited a high Na intercalation 9 capacities and emerges 8 as the leading candidates for NIB applications 8,9 .In this study we tried to build a model for GO for investigating the mechanisms for Na intercalation 9 into the layered domains 9 .Although, the mechanism 7 of Na + cation inserting into disturbed carbons are still controversial 10 .It is confirmed that a bigger interlayer distances 11 of those carbons, which are bigger than interlayers distances of graphite, help Na + ion intercalation.Consequently, the defects might be enhanced the Na + intercalations through the strong bonding energies for overcoming the van der Waals energies between graphene sheets 12 .In this study it has been evaluated the reliabilities of several semi-empirical corrections and vdW exchange's correlation functional for determining the optimal 12 methods of this work.Graphited electrodes are currently the most general materials used for the anodes of commercial 12 batteries due to its capabilities for reversible 12 lithium intercalation 13 in a layered crystal that represent maximum theoretical sodium storage capacity 13 .
NIBs includes of a positive electrode and a negative electrode with suitable conducting electrolytes where store 14 electric energies as the forming of Na-intercalations compounds 11 .Electrodes 12 , separator 13 , and electrolytes are the major components 14 in the NIB batteries which the anodic electrodes play important behavior in the mechanism of those kind devices 12,13 .
The structures and properties 14 of graphitic oxide depends on a synthesis method or degree of oxidation 13 .In addition graphite, typically preserves 14 the layer structures of those parent graphite, but the layers are buckled 14 and the interlayer's spacing 14 is about two times bigger than the graphite that provides suitable environment for sodium diffusion in a NIBs 11 The detailed 15 structures are still not described because of the strong disordering and irregular 13 packing of those layers 12 .GO layer is about 1.1 ± 0.2 nm thick 10,11 .STM spectroscopy indicates the presences of some regions 14 where the oxygen atoms are arranged 12 in a rectangular 13 pattern within lattice constant 14 0.26 nm × 0.42 nm 11 the edges 15 of one layer is terminated with COOH and CO groups 10 .GO exfoliates 15 and decomposes 16 when heated (rapidly) at moderately 14 high temperatures within the formation 14 of finely dispersed 13 amorphous carbons, somewhat similar for activating carbon 12 .XRD 14 , FTIR 15 , Raman 16 , XPS 15 , AFM 14 , TEM 13 , etc. are some general techniques for characterizing the GO samples 13 .Since the distributions of oxygen's functionalities on GO sheets are poly-disperse fractionations methods using emulsion 16 stabilizations can be used for characterizing and separating "GO" on the basis of oxidation 14 .During of the charging step, the "NIBs" sodium ions released 15 from the cathodes electrodes to move inside the electrolyte and is inserted 16 into the anodes.Upon 15 discharging, sodium ions are extracted 15 from the anode electrodes and move back to the cathode 14 .Although the electrolytes establishes 15 high ionic conductivities between anodes and cathodes, this electrolyte is not responsible 15 for the conduction 16 of those electrons 16 and the half of reaction, so will move through the extra 14 external wires.Several experiments 16 have been performed for confirming the utilization of graphene nano-sheets 16 and nano-ribbons 17 for enhancing lithium capacity to improve the recharge cyclic performances.Furthermore semi-empirical 15 and molecular 17 orbital calculations have been used for investigating sodium ion storage states among the graphene sheets 15 , as well as some heteroatomsubstituted carbon materials 16 .There are several studies on anodic materials [17][18][19][20] and most of them focus on carbons and inorganic materials 18 .
Discharging and charging of LIBTs in graphitized 19 carbon is well investigated up to now 21-24.It has also been established how the repulsive 19 interaction can result in the pure stages during intercalation 22 .Although efforts have been tried for finding suitable replacements 23 , now days only the carbonaceous goods are used for the commercial anodes 25 .Carbonaceous properties widely depends on the preparing materials such as precursor or heat treatment 26 By this work, charging or dis-charging of Na-cations have been investigated 24 in Graphite oxide (GO) with the (+) electrode reaction 25 as: NaCoO 2 Na1-x CoO 2 + x Na+ + x and the (-) electrode mechanism as: xGO + xNa + + x x NaGO , while the whole reaction is: NaCoO 2 + xGO Na 1-x CoO 2 + x Na GO.It has been predicted that a sodium atom is stored 26 through two mechanisms: intercalation 26 and alloying 27 .GO similar Graphite is applied as small band gap semi-metals because of its excellent conduction treatment under the influence 27 of electrical fields 28, 29.Interlayer forces 30 are nothing, and the distances among GO layers 31 are large allowing 29 Na-ions for diffusing between GO sheets 22 .Electrical conductivity of the Na-GO increases, Because of the electron donor nature of the Na 33 .Based on some previous studies we have used several methods to simulate the NIBs and calculated the NMR, solvent effect 24 , voltages, charges and physical properties of our model [32][33][34][35][36][37][38][39][40][41][42][43][77][78][79][80][81] .Typical commercially 31 used sodium -ion battery including several interconnected 32 electrochemical cells, where each one consist of a GO anode, a cathode formed 30 by sodium metal oxide (NaCoO 2 ) and electrolyte same as NaPF 6 embedded in a separator felt 29 .

Na + Diffusion
Diffusion of Na + in the cells determine the key performance 31 of Na-ion batteries cells, with the charge and discharge rates, practical and cycling capacities and stabilities respectively.The governing 45 equations describing 44 the diffusion 44 process are famous as Fick's law as: ji=(1)-D i ∇C i & (2): =∇.(D∇C i )which ji is an ion in flux condition, molcm −2 s −1 , are diffusivities of solute (i=1,2), cm 2 s −1 and C i are concentrations of species i, (molcm3) 44 .
The proportionalities 44 factors D are the diffusivities or diffusion coefficients as D i = (3) 44,45 .In condensed systems both liquid & solid, diffusion 45 is governed 45 by random particles, leads to a position exchanges by its neighbor.The kinetic parameter of these processes are temperatures depend to an Arrhenius types relationships rate≈exp (4) 46 .
In liquid phase, the temperature related of diffusion 45 is less than the solid form.There are no successful 44 first-principle calculations which have been made, because of in-sufficient interpretation of the liquid structure 44 .Therefore, an easy expression 44 is gotten from Stoke's drag law which is used as an alternative 45 for a diffusivities expression in the liquids 55 frequently (Eq.3).Na + is quite big comparing to electrons 46 ; the radius of a Na-ion is larger than that of an electron (electron: 10 "22 m) 46 .The motions of Na-ions are strongly impeded through the ions as discussed below 47 .

Anode materials
In the anode, Na + are found to be the suitable electropositive particles with large reversible capacities.However, due to safety considerations 51 , metallic Na has been substituted by various carbonaceous materials such as GO.
GO-sodium anode has much lower gravimetric and volumetric energies density than pure sodium which leads toward the development of 3d transition metal oxides 51 .(M x O y , M = Fe, Co, Ni, Mn, Cu).These materials are able to incorporate more than one Na + per metal through conversion reactions giving higher capacities in comparison to carbon anodes 51 .During discharge, Na + ion is extracted 52 from the internal layered of graphite, those passes through the electrolyte 63 and intercalated between the NaCoO 2 compounds Figure .2.

Hamiltonian kinetic energy density K(r)
It is defined, since the expected values of kinetic energies operator can be rewritten by definitions 53 .One of commonly used definition 55 is: k(r)=½Σ i η i φ i (r)∇ 2 φ i (r) (4) "G(r)" is a positive definition of kinetic energy densities.

ELF or Electronic localization function
Becke and Edgecombe 57 exhibited that spherically averages like-spin pair probability 56,57 are localization functions (ELF).ELF(r) = ( 7) where ( 8) and ( 9) for close-shell system, since the same way as in ELF 61 .

Electrostatic potential (ESP)
The total electrostatic potential measures the set of functions as GIPF 75 which for the molecular surfaces and macro properties 65,66 .There are a lot of reviews on ESP, interested readers are suggested to consult 66, 67.It is accurate in normal cases.Reduced -density -gradient or RDG and Sign (λ2)*ρ are a couple parameter for revealing of the weak interaction region 68 .The basic applications are Carbon-sodium anodes have much lower gravimetric and volumetric energy densities than pure sodium which lead towards the development of interstitial-free 3d transition metal oxides

Computational details
Calculations are performed using both Gaussian and GAMESS-US packages 68 .Pm6, Extended-Huckel and Pm3MM including pseudo=lanl2 calculations 69 .
M06 and m06-L (DFT) functional is based on pseudo-potentials [69][70] .The (PBE) 71 exchangecorrelations functional are made via minimization of the whole energy [69][70][71] .We employed DFT with the van der Waals densities for modeling the van der Waals capacitor 72 in the medium-range 73 interactions such as the interactions 74 of two cylinders.In some further calculation the interaction energy between x sodium and GO sheets.The interaction energy was calculated via the Mp6 method in all items according to ΔΕ s (ev)= {Ε total − (Ε xNa + Ε GOsheets )} + Ε ΒSSE Where the ΔΕ S is the stability energy of system 73 .

RESULT AND DISCUSSION
The Laplacian of electron density via Eqs (7, 8) for the sodium diffused in the GO system which are arranged and listed in Table .1.We have used ρ s (r)=ρ a (r)−ρ β (r) then the polarization-spin valuable will be replaced instead of spin densities Kintic energies, Lagrangien kintic energies densities, and the electrostatic potentials can be calculated as eqs.( 9), (10) and: where RA and ZA denotes vectors charges of atom A, and are listed in tables1,2.
If pseudo-potentials are used, Z is shown the explicitly expression of those electrons.Z can be stand for the atomic charges (the fourth column), at this item is useful for analyzing the differences between exact electrostatic potential and the electrostatic potential reproduced by atomic charges.Notice that at nuclear positions, this function will be infinite and may cause some numerical problems in program; hence at these cases this function always returns 1000 instead of infinity.
In which the a c t u a l k i n e tic energy term in D(r) from eqs. 15-16 is re p l a c e d b y K irzhnits type gradient expansions, which is so that ELF is the kinetic energy term.In this work we have calculated the local information entropies for each sodium atom via eqs.19-20 and the integrating of this function over total space yields the entropy.The calculated data for local entropy are listed in Tables 2-5 Weak interactions (eqs 20-21) have significant influences for conformational structures of the macromolecules, however reproduction by the electron density via ab initio.
As sodium have unpaired electrons, leading to a difference in spin-up & down, when two sodium atoms are adsorbed.
As a result, spin polarized cluster for NIBTs have a gap which size depends on adsorbed spin polarization.And this system can be replaced with LIBTs completely with high performance.

CONCLUSION
In conclusion, our calculations have been designed to study the Na adsorption on graphene oxide with two layers of GO.Our results exhibit that adsorption in GO is much stronger than pristine graphene.
Additionally, it has been found the structure of GO can be to improve the electrical transport in NIBs.Therefore, the modification and design of GO structure provide strategies for improving the performance of GO-based anodes.With the increase in defect density by GO sheets, maximum capacities obtained are much higher than that of graphite.

Fig. 1 .
Fig. 1. the cathode conduction during charge (r)/D o(r) ] 2 D o(r) = (6π 2 ) [ρ a (r) +ρβ(r) ] 05, it can be nullify this treatment by setting the parameter to zero.( ELFs, Localized locators (LOLs) and Local Entropies including ESP charges, potential energies, of two graphene layers (GO sheets) have been listed in tables1-2 and these data have been plotted in seven figures figs.1-7.The values of yielded from zero to the local region of un-polarized cases, are shown as a complete polarized situation and are listed in (Table1).