The study of multilayer graphene membrane performance in O 2 purification process: Molecular dynamics simulation

: We use molecular dynamics (MD) method to describe the atomic behavior of Graphene nanostructure for Oxygen molecules (O 2 ) separation from Carbon dioxide (CO 2 ) molecules. Technically, for the simulation of graphene-based membrane and O 2 -CO 2 gas mixture, we used Tersoff and DREIDING force fields, respectively. The result of equilibrium process of these structures indicated the good stability of them. Physically, this behavior arises from the appropriate MD simulation settings. Furthermore, to describe the purification performance of graphene-based membrane, we report some physical parameters such as purification value, impurity rate, and permeability of membrane after atomic filtering process. Numerically, by defined membranes optimization, the purification value of them reach to 97.31%. Also, by using these atomic structures the CO 2 impurity which passed from graphene-based membrane reach to zero value.


Introduction
Atomic membranes are a new class of low-dimensional, free standing, physically stable, and virtually impermeable materials [1][2][3][4] .The common 2D atomic membrane is graphene nanosheet, a twodimensional lattice entirely made of carbon atoms, but other interesting structures such as the multilayer graphene offer new properties [5][6][7][8] .Structurally, graphene nanosheet is a layer of carbon atoms which are bonded together with covalent interaction in honeycomb lattice.This atomic structure shows promising properties including a high specific surface area, good thermal conductivity, proper mechanical behavior, and excellent charge mobility [9,10] .Due to these interesting properties, this atomic layer has remained at the core of scientific research since its advent, with many of its successful accomplishments being transformed into various applications.Today, graphene-based nanostructures are used commonly in fuel cells [11,12] , supercapacitor [13,14] , capacitive deionization [15][16][17] , desalination [18][19][20] .Furthermore, graphene-based membranes are the other class of this atomic structure applications.These atomic membranes are capable of creating an appropriate barrier when dealing with liquids and gasses particles.Graphene-based membranes effectively separate target atoms from liquid and gasses environment.Physically, due to the repulsive interaction of the π-bond orbital electron distrobution in graphene nanosheet, this atomic structure is not permeable to liquid or gas environment [21] .These practical properties of graphene membrane can be studied with experimental and theoretical approaches.Molecular Dynamics (MD) method is one of the important methods in the atomic study of various nanostructures [22][23][24][25] .Previously, this computational method used for graphene-based membrane study.Cohen-Tanugi and Grossman [26] showed that nanoporous graphene membranes can remove NaCl from H2O molecules.In their work, simulation results show the single layer membranes delivery capacity reach to 66 L/(cm 2 • day• MPa).In other work, this research group used single layer graphene as a reference structure to explore the possibility of multilayer graphene membranes [27] .The result of this computational work show the appropriate properties of multilayer grapgene structures as atomic membrane.Kim et al. [28] described the transport of H2O molecules and atomic ions in the pores of the graphene nanosheet.The MD results indicated the use of hydroxylated graphene pores can improve the membrane efficiency for actual applications.Also, Wang et al. [29] used graphene nanosheet on polyacrylonitrile matrix to introduce an effective graphene oxide membrane.It was found that with graphene oxide thickness increasing, the H2O molecules flux decreased appreciably.So, due to the appropriate performance of MD simulations in the study of graphene-based membranes behavior, in this work we use of this approach to describe of multilayer (3-layers) graphene membrane performance in O2 purification process from O2-CO2 gas mixture for the first time.In our MD simulations, the distance between various sheets and porous radius changes to designing optimized atomic membrane for O2 molecules purification process to actual applications.

Computational method
In this MD study, graphene membrane and initial mixture gas (O2-CO2) interact with each other for the t = 2 ns.This atomic procedure determines the graphene membrane filtering performance in O2 purification process.In our computational approach, simulations were done by LAMMPS package [30][31][32][33] .By using this computational package, multi-layer graphene membrane and O2-CO2 gas mixture simulated as C, H, and O atoms arrangement as depicted in Figure 1.This atomic structure depicted by OVITO (Open Visualization Tool) software [34] .Computationally, in depicted atomic structures, fix boundary conditions were used in x direction and periodic style implemented to y and z directions [35] .After atomic modeling, NVT ensemble used in our MD simulations to equilibrate the temperature of structures [36,37] .This computational ensemble equilibrate the modeled samples at T 0 = 300 K with 0.001 damping value for temperature.Atomic force-field is an important parameter in common MD simulations.To simulate the atomic structures inside MD box, we use DREIDING and Tersoff force-fields [38,39] .In DREIDING force-field, the atomic interactions were presented by non-bonded and bonded terms.The non-bond term in atomic structures simulation defined by the Lennard-Jones (LJ) equation (12-6 type) as reported in Equation (1).Historically, this mathematical function was introduced by John Lennard Jones for the first time as Equation (1) [40] : In Equation (1), ε is the depth of the potential well, σ is the distance at which the potential function is zero and r ij is the atomic distance.These physical parameters selected with type of atoms in simulated structures.So, these parameters value for all atoms in our MD simulation reported in Table 1 [39] .
Table 1.The ε and σ constants for LJ interactions in our MD simulation box [39] .The bonded term of atomic interactions consists of simple and angle strengths.The bond and angle strengths in DREIDING force-field is calculated by harmonic oscillator formalism as Equations ( 2) and (3), respectively [39] : In Equations ( 2) and ( 3), K r and Kθ are the constants of harmonic oscillator.Also, r 0 and θ 0 are the equilibrium value of bond length and angle, respectively.Harmonic oscillator constants (K r and Kθ) in DREIDING force-field set to 700 (kcal/mol)/ Å 2 for each atomic bond and 100 (kcal/mol)/degree 2 for all bond angle bend.Furthermore, the equilibrium value of bond length and angle in our simulated structures listed in Table 2 [39] .
Table 2.The r0 and θ0 values for the bond strength and angle bend of simulated structures by MD method [39] .
As mentioned before, Tersoff force-field used for C atoms interaction in graphene nanosheets as below [38] : (5) where f R is a two-body term and f A include three-body interactions.The summations in Equation ( 5) are over all neighbors j and k of atom i within a cutoff radius.After defining an appropriate force-field to O2-CO2 gas mixture and graphene-based membrane, MD study was fulfilled.Then, to describe the atomic structures time evolution inside MD box, Newton's law's is used as the gradient of selected force-fields [35] : = −∇  (7)   From these base equations, the atomic momentum   can be defined as Equation ( 8) [37] : In the stated equations, to integrate the Newton's law's, the association of equation ( 6) is done by the Velocity-Verlet algorithm as below [35] : In Equations ( 9) and (10), ( + ), ( + )is the position and velocity of atoms in t + δt and r(t), v(t) is the value of these physical quantities in t.Furthermore, in MD simulation approach, Gaussian distribution is implemented for temperature calculating in atomic arrangement as Equation ( 11) [35] : Finally, the instantaneous temperature variation is calculated from Equation ( 12) [35] : where, N sf is the degree of freedom of the atomic systems.According to the reported descriptions, MD simulations in current computational study carried out as below:  Step 1: CO2-O2 gas mixture and graphene-based membrane was simulated with DREIDING and Tersoff force-fields and equilibrated by NVT ensemble for 1,000,000 time steps with Δt = 1 fs.For this purpose, atomic structures temperature set at T 0 = 300 K as initial condition.After, atomic structures reached to equilibrium phase, the stability of them reported by temperature and potential energy calculating. Step 2: Next, atomic purification process settings implemented to equilibrated structures for 1,000,000 time steps with NVE ensemble (t = 1 ns).For this purpose, dynamic graphene sheet displaces in MD simulation box with constant velocity (see Figure 2).After this process, physical parameters such as: purification and permeability values reported to describe the atomic behavior of graphene-based membrane in O2 purification process.

Equilibration process of atomic structures
In the first step of our computational work, the atomic behavior of O2-CO2 gas mixture and graphene-based membrane was studied at initial temperature (T0 = 300 K) for 1 ns.Our simulation results, showed the initial arrangement of particles in simulation box adopted with DREIDING and Tersoff force-fields [38,39] .This atomic phase of simulated structures reported by temperature and potential energy calculations.The simulated structures temperature changes as a function of simulation time as depicted in Figure 2. From calculated results, we conclude the atomic structures equilibrated after 1,000,000 time steps (t = 1 ns).Physically, this thermal equilibrium arises from atomic oscillation reducing which indicted our MD simulation settings validity [35] .Also, Figure 3 shows the potential energy changes in atomic systems as a function of MD simulation time in this computational step.From this figure, we conclude the simulated structures potential energy converged after 1,000,000 time steps to constant value.Numerically, potential energy of graphene membrane and CO2-O2 gas mixture reached to −399 eV after 1 ns.Theoretically, this physical parameter has reciprocal relation by mean distance of atoms.By increasing the potential energy magnitude, the atomic stability of target system increased.Figure 3 indicated, by increasing the initial porous radius (R) from 3 Å to 5 Å and 7 Å, the atomic system doesn't disrupted and so, stable phase of them can be detected after equilibrium process.Our calculations show the temperature of equilibrated structures reach to 300 K in the final step of simulations.Physically, atomic stability of initial membrane decreases by porous radius increasing.Numerically, by porous enlarging, the magnitude of potential energy parameter decreases to −376.81 eV from −406.69 eV.This behavior arises from carbon atom missing in membrane structure and interatomic force (by attraction type) decrease in defined layer system.Atomic layer distance between graphene sheets (D) is another important parameter for graphene-based membrane stability.By this parameter changes from 5 Å to 7.5 Å and 10 Å, the potential energy of the total atomic system decreases to −402.70 eV and −397.97 eV, respectively.This behavior arises from mutual interaction between carbon atoms which cause saving energy in MD simulation box.We can say the atomic stability of simulated membrane decreased by these potential energy's magnitude decreasing.

Atomic behavior of pristine graphene membrane
In this step, MD settings implemented to pristine graphene membrane to study of O2 molecules purification efficiency with this atomic arrangement.Figure 4 shows the evolution of atomic structures after 320,000 time steps (t = 0.32 ns).After the equilibration phase, the number of filtered O2 molecules variation as a function of MD simulation time reported in Figure 5. From this computational result, we conclude the MD simulation time (t = 1 ns) is long enough to the atomic purification process detecting.After this atomic phase, the number of CO2 molecules which passed from graphene membrane reported (see Figure 6).From our MD simulation results, the number of filtered O2 molecules reach to 603 (90.00% ratio) which this calculated value comparable with previous reports [41,42] .Also computed value of CO2 molecules which passed from pristine membrane is 11 molecules (15.71% ratio).Reported atomic behavior of simulated structures in this MD simulation step show the validity of our computational settings and show the appropriate behavior of graphene-based membranes in atomic purification process.

Graphene layers distance effect on atomic behavior of membrane
The results of graphene layers distance effects on carbon-based membrane purification behavior reported in this section of our MD study.The distance of atomic layers (D) which depicted in Figure 1 are set to 5 Å, 7.5 Å, and 10 Å in NVT ensemble by setting initial temperature in T0 = 300 K.After atomic equilibration process simulation for 1,000,000 time steps (t = 1 ns), the atomic structure were for atomic purification process to estimate efficiency of them in this performance.Numerically, by D parameter increasing, the number of O2 molecules which passed from carbon-based membrane decreases to 498 molecules (74.33% ratio) as reported in Figure 7. Furthermore, the CO2 molecules elimination rate improve by D parameter increasing in modeled atomic membrane and the number of CO2 molecules in region 2 reach to zero after 1 ns as depicted in Figure 8. Physically, by graphene layers distance variation, the attraction force which implemented to O2-CO2 gas mixture changes.This type of atomic interaction decreases by D parameter increasing and so the efficiency of graphene membrane improved.Also, the permeability of atomic structures affected by D parameter variation.From Figure 9a we can say the maximum value of this physical parameter reach to 62 L/cm 2 /day/MPa and 43 L/cm 2 /day/MPa by D parameter increasing from 7.5 Å to 10 Å, respectively.Here, the interaction energy between membrane atoms and gas mixture reported for more description of detected atomic phenomenon.This physical parameter indicated the atomic evolution of simulated structures.We report the total component of interaction energy in Figure 9b.MD results show that by D parameter enlarging, the interaction energy between membrane and O2-CO2 system decreases.This behavior arises from atomic distance increasing between simulated components which by this atomic evolution the membrane efficiency decreases.As reported in Figure 9b, D parameter enlarging cause interaction energy changes from −41.32 eV to −32.09 eV.By data analyzing from this section of our MD simulations, we conclude the D parameter increasing, improve the accuracy of atomic purification process and decreases the speed of this atomic phenomenon (as listed Table 3).

Graphene layers porous size effect on atomic behavior of membrane
In the final step of our computational work, we reported the graphene layers porous size (R) effect on carbon-based membrane purification efficiency.The porous size of graphene sheets set to 3 Å, 5 Å, and 7 Å at T 0 = 300 K.After MD equilibration process implementing for t = 1 ns, the dynamic graphene sheet move by 1 MPa pressure and so atomic purification process fulfilled after 1 ns.Our MD simulation results show that, by R parameter increasing, the number of O2 molecules in region 2 increases from 591 molecules (88.21%) to 623 (92.98%) and 652 (97.31%) molecules (respectively) as reported in Figure 10.Furthermore, the CO2 molecules elimination rate getting worse by R parameter increasing in graphene nanosheets.Numerically, CO2 molecules elimination reach to 24.28% and 32.86% after 1 ns as depicted in Figure 11.Physically, by graphene layers porous size increasing, the atomic interaction between carbon atoms in membrane structure and O2-CO2 gas mixture decreased and the more molecules can be passed from graphene configuration as target membrane.The permeability of graphene membrane also affected by R parameter variation and the maximum value of this atomic separation factor reach to 71 L/cm 2 /day/MPa and 77 L/cm 2 /day/MPa (see Figure 12a).As previous section, interaction energy between atomic membrane and atomic gas mixture reported in Figure 12b.MD outputs in this section indicated the interaction energy get to more values by R parameter enlarging.By this process occur, the number of atoms which attracted by graphene sheets increased and number of passed molecules from target membrane improved.From these calculated results, we can conclude R parameter increasing, decrease the accuracy of purification process and increase the speed of this atomic phenomenon as reported in Table 4.

Conclusion
We use Molecular Dynamics (MD) simulations to describe the behavior of multilayer (3-layers) graphene membrane in gas mixture purification process (O2 molecules purification from O2-CO2 gas system).Our important computational results from MD simulations are as following: • DREIDING and Tersoff force-fields are appropriate functions to MD simulation of graphenebased membrane and O2-CO2 gas mixture inside MD box.

•
MD outputs predicted the number of O2 and CO2 molecules which passed from graphene membrane are 652 (97.31% ratio) and 23 (32.86% ratio) molecules after t = 1 ns.

•
Numerically, the permeability of graphene membrane reach to 77 L/cm 2 /day/MPa value by atomic structure optimization.

•
Increasing of graphene atomic layers distance in simulated membrane, cause the accuracy improve and performance speed decrease in atomic purification process.Numerically, interaction energy between membrane and gas mixture converged to −32.09 eV by this atomic process done.

•
Increasing of graphene atomic layers porous, cause the accuracy decrease and performance speed increase in atomic purification process.Numerically, interaction energy between membrane and gas mixture converged to −49.93 eV by this atomic process done.
These MD simulation results was shown that, the atomic arrangement of carbon atoms in graphene-based membrane can be improve the purification process accuracy or speed.Practically, these estimated results can be implemented in various purification process to optimize the industrial application efficiency.

Figure 1 .
Figure 1.Multi-layer graphene membrane and O2-CO2 gas mixture simulated as C, H, and O atoms arrangement.(a) atomic properties of simulated structures with LAMMPS package; (b) atomic structures arrangement inside MD simulation box.

Figure 2 .
Figure 2. Temperature changes of graphene membrane and CO2-O2 gas mixture as a function of MD simulation time.

Figure 3 .
Figure 3. Potential energy changes of graphene membrane and CO2-O2 gas mixture as a function of porous radius and atomic layers distance.

Figure 5 .
Figure 5. Number of O2 molecules which passed from pristine graphene membrane as a function of MD simulation time.

Figure 6 .
Figure 6.Number of CO2 molecules which passed from pristine graphene membrane as a function of MD simulation time.

Figure 7 .
Figure 7. Number of O2 molecules which passed from pristine graphene membrane as a function of graphene layers distance (D).The total number of O2 molecules inside MD box is 670 molecules.

Figure 8 .Figure 9 .Table 3 .
Figure 8. Number of CO2 molecules which passed from pristine graphene membrane as a function of graphene layers distance (D).The total number of CO2 molecules inside MD box is 70 molecules.

Figure 10 .
Figure 10.Number of O2 molecules which passed from pristine graphene membrane as a function of graphene layers porous size (R).

Figure 11 .
Figure 11.Number of CO2 molecules which passed from pristine graphene membrane as a function of graphene layers porous size (R).

Figure 12 .
Figure 12.(a) Permeability of graphene-based membrane as a function of graphene layers porous size (R); (b) interaction energy between atomic membrane and gas system as a function of R parameter.

Table 4 .
Number of O2 and CO2 molecules which passed from graphene-based membrane and membrane permeability as a function of graphene layers porous size (R).