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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Distinct Understanding of Constant-Volume/variablePressure Experimental Method on the CO Capture Using Graphtriyne Membrane Through the Atomistic Approach 2

Amin Khorsandi-Langol, and Seyed Majid Hashemianzadeh J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01988 • Publication Date (Web): 06 Jun 2019 Downloaded from http://pubs.acs.org on June 7, 2019

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The Journal of Physical Chemistry

Distinct understanding of constant-volume/variablepressure experimental method on the CO2 capture using graphtriyne membrane through the atomistic approach Amin Khorsandi-Langol a, Seyed Majid Hashemianzadeh a,* a

Molecular Simulation Research Laboratory, Department of Chemistry, Iran University of Science & Technology, Tehran, Iran * To whom correspondence should be addressed: P.O. Box: 16846-13114. Fax: (+98) 2177491204. Phone: (+98) 2177240287. E-mail: [email protected], [email protected]

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Abstract

In this research, the non-equilibrium thermodynamic of gas permeation process based on the constant-volume/variable-pressure experimental method was explored with the novel algorithm using atomistic simulation. The hybrid force field and the in-house FORTRAN code was used in the proposed algorithm and the pressure was considered through exerted spring force within the NVT ensemble .The graphtriyne layers were utilized as a porous membrane for investigation of N2 and CO2 permeation. Two parameters of free tendency and channel cross-sectional area (CCSA) were introduced to analyze the result of the simulation. The result of the simulation revealed that the effect of CCSA on the N2 permeation decreases as the number of graphtriyne layers increases while the CO2 permeation through the membrane is independent of the CCSA. Also, there is a distinct permeation behavior for CO2 and N2 so that first CO2 is trapped within the graphtriyne layers and then permeation is started, in contrast, trapping of N2 increases with increasing the number of graphtriyne layers in permeation process. This trend originated from the higher free tendency of CO2 relative to N2 which is confirmed by time dependent density parameter. Hence, it is possible to make the membrane permselective by adjusting the pressure and number of graphtriyne layers.

Keywords: Gas permeation, Molecular dynamics simulation, Graphtriyne, Constantvolume/variable-pressure, Non-equilibrium thermodynamic.


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1. Introduction Global warming originated from greenhouse gases is the world crisis which should be considered seriously. Sea level rise, climate change, and ocean acidification are some consequences of greenhouse gases in the atmosphere which can impress the human societies.1,2 Nevertheless, the human activities are the main source of greenhouse gas emission in the atmosphere regarding to the fossil fuels in electricity production, transportation, and industry.3 The carbon dioxide as a main product of fossil fuels combustion plays a key role in heat trapping and global warming. Therefore, research in the field of CO2 capture has been increased drastically since the past decades.4,5 Membranes technologies have been proved to be an efficient separation method of CO2 in the view point of the energy cost.6,7 In this regard, a literature survey shows that there is a trade-off between permeability and selectivity to achieve a better separation.8 In other words, having simultaneous high permeability and selectivity properties in a membrane is the main challenge. Nonetheless, among the various membrane, the graphene-based structures such as nanoporous graphene,9 graphene oxide,10 reduced graphene oxide

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and graphene oxide framework

shown great potential for gas separation. The single atomic layer structure

13,

12

have

and nanoscale

porosity are two distinct characteristics of this class of materials which satisfies either permeability or selectivity.10 Recently, experimental and computational studies have demonstrated the potential of these novel materials. Various research has been carried out in the CO2 separation field using graphene-based material, such as examination of nanoporous graphene for the separation of N2 from CO2,14 prediction of CO2 and CH4 gas molecules permeation through sub-nanometer graphene pores,15 study the effect of oxidation degree, interlayer spacing and channel length for CO2/N2 separation through graphene oxide,16 investigation of diffusion coefficient of different


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gases in graphene oxide,10 CO2 capture by polyethylenimine-functionalized graphene oxide 17 and using Boron functionalized graphene oxide-organic frameworks for highly efficient CO2 Capture 18.

Because of the unique properties of carbon, it seems, there is no end for the allotropes of this element. Apart from different types of these allotropes, two dimensional structures similar to graphene were predicted by Baughman et al.19 which provided a new facility for gas separation. Also, these structures have been synthesized experimentally.20,21 The graphyne is a new carbon allotrope which has been formed by joining hexagonal rings through triple carbon bond. This structure provides triangle nanopores between hexagonal rings so that the nanopore size depends on the number of triple carbon bond.19 Therefore, properties such as the adjustable size of nanopores and single atomic layer, make graphyne-based material, ideal candidate as a molecular sieve for gas separation. Accordingly, there are several attempts for theoretical studies along with practical construction of graphyne-based structures. Some computational studies include water purification,22,23 hydrogen adsorption and purification 24,25 and post-combustion CO2 capture 26,27. Apart from the few studies in the field of CO2 separation using graphtriyne structures, there is not much attention paid to the non-equilibrium thermodynamic rules that govern on the permeation process. Hereupon, in this research, molecular dynamics (MD) simulation was applied for modeling of experimental set-up of gas separation relying on the aforementioned challenge. Several innovations were incorporated to simulate the overall membrane separation process according to the common experimental method of constant-volume/variable-pressure used in the permeation measurement. For this purpose, MD simulation was carried out by considering a box divided to three regions including feed reservoir, membrane and dead-volume of the downstream chamber similar to the practical setup commonly used in the experiments. This innovative idea


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was used to scrutinize the permeation of CO2 and N2 gas through the graphtriyne structure as a membrane. The different pressure (i.e., 10 up to 50 bar) under NVT ensemble was accomplished by adjusting the spring force. Moreover, the effect of the different number of graphtriyne layers (up to nine layers) on the permeation of gas molecules was investigated to find the bulk properties of graphtriyne membrane. With the aid of the in-house FORTRAN code, the overall MD simulation run was split up to several sub-MD simulations to model the flow of gas molecules under NVT ensemble and non-periodic conditions. Finally, the results were analyzed based on the two introduced parameters of free tendency and channel cross-sectional area which is not well understood in gas permeation process in the literature. 2. Computational Method 2.1. MD Simulations Details All calculations have been performed using MD simulation as implemented in the LAMMPS 28 suite of package. The MD simulations were carried out under NVT ensemble (constant particle number, volume, and temperature). The Nose-Hoover thermostat was applied for controlling the temperature at 298 K. Cut-off distance for electrostatic, and van der Waals forces were considered as 15 Å and 16 Å, respectively. Two potential walls were placed at the bottom and top edge of the simulation box (z-direction) to confine gas molecules between two edges. The multilevel summation method (MSM)

29

was used to calculate long-range electrostatic interactions due to

non-periodic conditions in the z-direction. The adaptive intermolecular reactive empirical bond order (AREBO) force filed

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was only employed for simulation of intramolecular interaction of

graphtriyne structure to achieve more accurate results. Additionally, force filed parameters for CO2 and N2 were obtained from literature (more details are in Table 1).31-34 Three sites model was


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selected for the N2 based on recent reports 33 which consists of a mass-less dummy atom locating in the middle of two nitrogen atoms (see Figure 1). The interactions between gas molecules and graphtriyne layers were given by consistent valence force field (CVFF)

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model. The sigma,

epsilon and charge parameters in CVFF were assigned to graphtriyne structures considering interactions of graphtriyne structures and gases molecules (refer to Table1). Finally, Lorentz– Berthelot combination rules were used for cross term pairwise Lennard-Jones interactions, due to the incorporation of hybrid force filed (AREBO and CVFF). 2.2. Molecular System Preparation The MD simulation was performed for modeling of the experimental set-up for gas permeation based on the constant-volume/variable-pressure method as shown in Figure 2 (a). Gases permeability through mentioned set up is calculated according to the Eq. (1),36

273.15  1010Vl  dp  P   760  AT  P0  76  / 14.7   dt 

(1)

Where P is the gas permeability across the membrane in Barrer (1.0 Barrer = 1×10-10 cm3 (STP) cm/cm2 s cmHg), V is the dead-volume of the downstream chamber (cm3), l is the membrane thickness (cm), T is the experimental temperature (K), A is the effective membrane area (cm2), P0 is the upstream feed gas pressure (psia) and finally (

dp ) is the steady-state rate of pressure change dt

gradient in the downstream side (mmHg s-1) (derivation of Eq. (1) is indicated in supporting information (S1)). Also, the selectivity of two gases in the same condition is calculated using Eq. (2). a

PA PB

(2)

Where PA and PB are the permeability of pure gas molecules of A and B, respectively.


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As initial configuration, graphtriyne layers as membrane were placed in the xy-plane which are perpendicular to the z-direction. Therefore, two regions can be considered in the simulation box. The bottom region of the membrane was considered as dead-volume of the downstream chamber. This region was empty at the onset of simulation. Also, the upper region of the membrane was considered as gas reservoir similar to experimental set-up and gas molecules were loaded inside it (Figure 2 (b)). Since the number of loaded molecules (CO2 and N2) are same in the reservoir under different pressure, therefore the height of upper region was adjusted to simulate the various applied pressure as shown is Figure 3 (a) to (e). 2.2.1. Pressure Exerting on NVT Conditions Pressure exerting was accomplished by spring force f ( z )  k ( zt  z0 ) where k is spring constant (force/distance units), z0 is equilibrium distance from tether point (distance units) and zt is the membrane distance (z-component) at any time step (time-dependent variable) from tether point, while the MD simulations were carried out under NVT ensemble. The lowest layer of the membrane was tethered to the upper side (positive z-direction) of the box by the hypothetical spring. According to Figure 3 (F), the relaxation position of spring was settled at z0 = 0, so that the initial position of the membrane in the simulation box indicates the stretched condition of spring. This means that membrane (graphtriyne layers) inclines to turn back to the upper side of the box to reach the equilibrium condition at z0 =0. The k values as spring constant were calculated in such a way that the membrane can exert specific pressure to molecules in the gas reservoir during the permeation process. Two approach were considered for spring constants estimation. Firstly, based on the Hooke’s law, the force is proportional to the extension. Hereupon, the distance of the lowest layer of membrane from the upper side of simulation box (i.e., Δz) was considered as the extension value at the onset of simulation (Figure S1). The second approach is related to spring laws. The


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membrane movement toward upper side of simulation box (MD simulations carried out under NVT ensemble) can be imagined as the membrane is fixed and upper side of box moves toward membrane. This case is similar to a piston that pushes gas molecules into the membrane (Figure 3S). It should be noted that the simulation box is non-periodic in the z-direction due applying the potential wall. The potential wall acts like a continuous surface in our simulations. According to this argument, the pressure can be calculated through the hook’s law (see Eq. 3). F  kz or PA  kz

(3)

Where F ,k ,Δz ,P and A are force, spring constant, membrane distance from upper side of simulation box, pressure and cross-section area of simulation box. The corresponding k values to the given pressure has been listed in Table 2. Also, the pressure dropping of reservoir resulted from gas permeation through the membrane can be compensated by spring force so that the pressure remains constant in the upper region during the MD simulations.

2.2.2. Permeation Algorithm The increasing number of gas molecules in the bottom region (dead volume) resulted by gas permeation leads to an increase in the dead volume pressure which can push back the membrane towards upper-side. This phenomenon will corrupt the gas permeation procedure under desired pressure because dead volume pressure will exert excess pressure to membrane. In addition, membrane movement toward the upper side of the box causes two other challenges. Beside the increase in the height of dead-volume region, membrane movement by spring force toward the upper side of the box, decreases the Δz and the force decreases due to decreasing of Δz, when spring constant remains constant during the simulation. Therefore, three strategies were considered to keep the constant pressure (first and second strategy), and the fix the height of dead-volume


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(second strategy) similar to experimental set-up during simulation. As the first strategy, any MD simulation was divided into sub-MD simulations so that any sub-MD simulation carried out over 50000 femtoseconds. Those gas molecules in the bottom region which follow the

(𝑍𝑙𝑜𝑤𝑒𝑟 𝑙𝑎𝑦𝑒𝑟 𝑜𝑓 𝑔𝑟𝑎𝑝ℎ𝑡𝑟𝑖𝑦𝑛𝑒 ― 𝑍𝑔𝑎𝑠) ≥ 50 Å condition, were deleted after each sub-MD simulations and before starting next sub-MD simulations. The selection of distance of 50 Å and beyond the 50 Å away from the lowest layer of graphtriyne, ensures no return of any permeated molecules. Additionally, two potential walls were incorporated at the bottom of the simulation box. The distance of the potential walls was about 2 Å with different sigma, epsilon and cut-off radius. This trick causes the gas molecules to be trapped between two potential walls (refer to Figure 4). Therefore, the first strategy helps to prevent the accumulation of molecules in the bottom region during the permeation process. As the second strategy, in-house FORTRAN code was incorporated to calculate the Δz and updates spring constant at the end of each sub-MD simulation and before starting of next sub-MD simulation (50000 fs). Results shows that the average of membrane movement during any sub-MD simulation is small so that the force changing is negligible at any sub-MD simulation. For example, average of membrane movement is equal to 1.3 Å under 50 bar as the maximum studied pressure and consequently maximum possible movement (Figure S2). In the third strategy, the lower side of the box (z-direction) was located at the distance of 100 Å from the membrane at the end of each sub-MD simulation and before starting of next sub-MD simulation (Figure 4). Finally, a virtual reservoir was considered to simulate the constant volume reservoir (Figure 2 (a)) similar to the experimental set-up. For calculation of pressure changes in the constant volume reservoir over the time (

dp ), the deleted gas molecules were collected in the virtual dt

reservoir. The volume of a virtual reservoir was set equivalent to the volume of 1106 particle at 1.0 bar, so that the ideal gas law was met. The sub-MD simulations were continued until 90% of


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gas molecules permeated through the membrane. Since the gases molecules in the reservoir is limited, the pressure cannot be considered constant at the end of the permeation process. Thus, to achieve reliable accuracy for results under constant pressure, (

dp ) was reported based on the 50% dt

of the permeation process. According to the Eq. (1), variables of V, l, A and T are constant and same for both gases, so permeation (P) is proportional to (

dp dp ). Consequently, ( ) was dt dt

investigated as the representative of the permeation parameter.

3. Results and Discussion

With the aid of the simulation box, the effect of pressure and number of graphtriyne layer on the permeation of CO2 and N2 were investigated. The first question that comes to mind is how many layers of graphtriyne in atomistic scale represents the bulk properties. The cut off was utilized for answering this question. The average distance of graphtriyne interlayer based on the AREBO force field under periodic boundary conditions was calculated as 3.46 Å. Nonetheless, the average interlayer distance of graphtriyne in the designed simulation box (Figure 2 (b)), under non-periodic boundary condition was estimated as 3.50 Å. Also, results indicate that the graphtriyne interlayer distance was independent of different pressure. Hence, the number of layers must be nine at least by considering the selected cut off radius for this work (15 Å) and graphtriyne interlayer distance (3.5 Å). This means that when one gas molecule places in the middle of fourth and sixth layers of membrane, its distance from gas molecules in the reservoir is out of interaction range (out of the cut off radius). In other words, only the inter-layer interaction has been considered for permeation of the respective molecule. Therefore, nine layers of graphtriyne have been investigated.


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3.1. The Free Tendency of Gases towards the Graphtriyne The free tendency of gas molecules towards graphtriyne can be one of the important parameters in the permeation process. In other words, free tendency describes how gas behaves in the presence of membrane. It can be said that the gas behavior toward membrane is affected by the type and magnitude of interaction energy between them. In this regard, chemical potential is appropriate to show the interaction between gas molecules and membrane. In thermodynamic, chemical potential of a species is energy that can be absorbed or released due to a change of the number of particles in the given species. Also, the self-diffusivity arises from adsorption effects and intermolecular interactions of membrane and gases molecules as well as the size and shape of gas molecules. Accordingly, self-diffusivity and isothermal adsorption behavior were selected to clarify free tendency of related gases. The self-diffusion coefficient is proportional to the slope of MSD curve vs. time according to Einstein’s equation 37 that in order to reduce statistical errors in simulations, the self-diffusivity is defined from ensemble averaging Einstein’s equation over a large enough number of molecules 38 (Eq. 4). Ds  (

 1 N 1  )  lim rk (t )  rk (0) 6 N k 1 t  t



2

(4)



Where Ds, N, rk (t ) and are rk (0) self-diffusivity, number of molecules, the position of the k-th molecule of species i at time t and the reference position of the k-th molecule of species i at t=0, respectively. Also, the center of mass of each particle was considered as the position of that particle. Simulations were carried out to show the effect of a number of graphtriyne layers on the diffusion coefficient under 10 bar and 298 K. The data acquisition for MSD calculation was performed in 0.2 nanoseconds after equilibration of the system. The results have been summarized in Table 3 and Figure 5. According to Table 3, the diffusion coefficient of pure CO2 and N2 are


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the same approximately. After putting the first graphtriyne layer in the middle of the simulation box, the difference between the diffusivity of gases becomes considerable. The impact of onelayer graphtriyne on the CO2 diffusivity is more significant than this effect on N2 diffusivity. Numerically, the CO2 diffusion coefficient has been dropped about 85% of its initial value while N2 diffusivity was declined nearly 33% relative to its initial value. Figure 6 (a) shows the effect of a number of layers on the diffusivity of CO2 and N2. Moreover, the results of interaction energy between gas molecules and one-layer graphtriyne are indicated in Table 4. Results of interaction energy show that electrostatic contribution to the binding energy plays a crucial role in CO2 free tendency towards graphtriyne sheet. Also, gas adsorption was conducted under isothermal condition (298 K) through Grand Canonical Monte Carlo (GCMC) for two gases, individually. As shown in Figure 6 (b), there is a significant difference between the free tendency of CO2 and N2 at the ambient temperature and pressure. However, the average loading of N2 approach to that of CO2 at high pressures. 3.2. Effect of Channel Cross-Sectional Area on the Permeation Several open channels can be produced by overlapping the triangle surface area of multiple graphtriyne layers. These channels are considered as a pass way for gas molecules to go through the membrane. In another word, the cross-sectional area (CSA) of channels can influence the permeation of gases through graphtriyne membrane. Nevertheless, CSA of open channels can be confined by sliding of layers over each other. In an ideal condition, the cross section of an open channel can be a maximum value when the triangle area of each layer is placed alongside each other as shown in Figure 7 (a) and (b). At any other arrangement of layers, the different CSA can be formed. Some of these configurations are depicted in Figure 7 (c) to (f). To show the variation of CSA of channels resulted from sliding of layers over each other, MD simulations were carried


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out at 298 K and 1.0 bar under periodic boundary condition. Figure 8 illustrates the CSA distribution of channels for each configuration (i.e., 1 layer, 2 layers, etc.) obtained by an in-house FORTRAN code numerically. It can be seen that distribution curves shift toward to lower CSA with increasing the number of graphtriyne layers, which confirm the inverse relation of CSA of channels and number of graphtriyne layers. It is clear that the effective cross-sectional area (ECSA) of open channels for passing gas molecules are less than CSA due to Van der Waals radius of atoms. According to Lorentz– Berthelot combination rules, the ECSA of open channels in graphtriyne membrane depends on the type of gases which permeates through the membrane. Therefore, assigning the absolute ECSA to graphtriyne is incorrect and unreasonable. Accordingly, the ECSA was estimated for the vertical and horizontal orientation of gas molecules toward graphtriyne layer (see Figure 9 (i)). For this purpose, the interaction energy of the gas molecules and graphtriyne as a function of distance was 

assessed. According to Figure 9 (j), gas molecules were moved from y1 to y2 point along the a

vector. The distance of the central atom of gas molecules (i.e., C atom in the CO2 molecule and Nmid atom in N2 molecule) from the y1 point was considered as distance parameter in interaction energy calculation. As clearly illustrated in Figure 10 (a), the  as a measure of ECSA of CO2 which is equal to |𝜎4 ― 𝜎1|, is greater than that of N2 molecule (i.e., |𝜎3 ― 𝜎2|) in the vertical orientation. It should be noted that σ is the distance at which the binding energy between gas molecules and graphtriyne sheet is zero (refer to Figure 9 (k)). Furthermore, the center of mass of the triangle surface is the minimum point of interaction energy for two gas molecules. However, the minimum point of interaction energy for two gas molecules of CO2 relative to that of N2 is indicative of more tendency of CO2 in vertical orientation towards graphtriyne sheet. In contrast, the size of two gas molecules is effective in the binding energy in the horizontal orientation of


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molecules toward graphtriyne. Referring to Figure 10 (b) in the horizontal orientation, the positive value of binding energy for CO2 shows that permeation of CO2 is prohibited while N2 can permeate through graphtriyne due to its negative binding energy. Analysis of interaction energy derived from Figure 10 are given in Table 5. Hereupon, it can be concluded that the N2 permeation is feasible under the vertical and horizontal orientation of molecules unlike to CO2 permeation which can only occur in the vertical orientation of molecules toward graphtriyne sheet. Consequently, CSA of channels is the most important parameter in N2 permeation based on the lower free tendency of N2 relative to CO2. Another issue is finding the number of layers of graphtriyne in which the permeation of N2 through channel cross-sectional area parameter is blocked due to the sliding of layers over each other and consequently decreasing the CSA. In this way, the minimum value of ECSA (MECSA) was determined based on the vertical orientation of linear molecules rather than horizontal orientation. This basis was selected because the required area for passage of molecules in the vertical orientation is less than horizontal orientation. N2 molecules cannot permeate through the graphtriyne membrane bearing the ECSA equal to or less than the MECSA value. The data related to molecules in the vertical orientation in Table 5 was used to calculate the MECSA in N2 permeation process. To calculate the MECSA with appropriate accuracy, the shape of ECSA is preferred to be in circular form. Since the ECSA is elliptical due to inequality of the σ2 and σ3, the average of two parameters of σ2 and σ3 () (i.e.,

2  3 2

) should be calculated. In this way, the

elliptical form of ECSA was converted to the circular form. When the ECSA is circular, the MECSA can be calculated based on the radius of the circle inscribed in an equilateral triangle. The radius of the inscribed circle (r) in an equilateral triangle is presented in Eq. (5) according to


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geometry rules. The surface area of the equilateral triangle (Atriangle) can be calculated according to Eq. (6). r

3 a 6

Atriangle 

(5) 3 2 a 4

(6)

Where the ‘a’ is the side-length of the equilateral triangle. As shown in Figure 10, the distances of σ2 and σ3 from the center of mass of equilateral triangle (rɛ) are equal to 0.65 and 1.05 angstroms, respectively. So, the sum of these two numbers represents  (i.e., ECSA). The averaged  was used to convert the ECSA of an elliptical shape to circular form (see Eq. 7).

r   2  0.65 geometry rule  rECSA  0.85     ECSA  1.70    r   3  1.05 

(7)

The β value is the vertical distance between the equilateral sides of triangle and center of mass of the equilateral triangle (see Figure 11 (a)). By subtraction of rECSA (i.e., 0.85 Å) from β value, the surface area in which the permeation of N2 is prohibited can be obtained. A circle with a radius of 2.63 Å (i.e., green-colored circle in Figure 11 (b)) can be drawn by subtracting the rECSA from β value. Finally, the MECSA can be calculated by an equilateral triangle (i.e., blue-colored triangle) which circumscribe the green-colored circle as shown in Figure 11 (b). Consequently, MECSA (Atriangle) was calculated as 35.98 Å² according to Eq. (5). By referring to Figure 8, the pink dash line which is settled at 35.98 Å² is considered as a border for permeation of gasses through the membrane. Therefore, for a CSA of channel less than 35.98 Å², the permeation of gasses is not possible. In other words, gases permeation through channel cross-sectional area parameters for those configurations having the number of layers equal and/or more than 8 layers, is not feasible. 3.3. Estimation of Permeation


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The number of graphtriyne layers and operating pressure as two effective parameters on the permeation process have been studied. The GCMC calculations in section 3.1 showed that there is a significant difference between the free tendency of CO2 and N2 to graphtriyne layers at ambient temperature and pressure. Moreover, MSD calculations revealed that the graphtriyne layers has a considerable effect on the diffusivity of CO2 in comparison with N2 at 10 bar. However, the impact of the free tendency in the permeation process will diminish gradually with increasing the pressure. It means that the free tendency of gas molecules for permeation through the membrane is inversely related to the pressure. This relation can be perceived well in gas permeation through one-layer graphtriyne because the CSA parameter is omitted in a one-layer graphtriyne case. Therefore, as shown in Table 6, one layer of graphtriyne demonstrates the better selectivity (α) under low pressure against high pressure conditions. Under 10 bar as the lowest pressure condition in Table 7, for two graphtriyne layers, the permeation value is identical for two gases approximately, due to large enough CSA for permeation of two gases. With increasing the number of graphtriyne layers, the difference between permeation values for two gases become significant, gradually. The effect of CSA on permeation decreases gradually as the number of graphtriyne layers increases. Although the N2 and CO2 permeation can be limited by decreasing the CSA, the permeation of CO2 is higher than that of N2 due to its higher free tendency towards the membrane. The assessment of time-dependent density has been carried out to reveals the useful information about permeation process which was defined by dividing the number of gas molecules into free space volume between graphtriyne layers. There is a maximum value for the time-dependent density of CO2 at the beginning of the permeation process for all layers refer to Figure 12 (a). It means that the releasing of CO2 from membrane does


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not happen until the free space between layers is saturated with CO2. In spite of large CSA of the channels for the two-layer graphtriyne, the trapping of CO2 happens before permeation through the graphtriyne layers. Therefor it can be inferred that trapping is just attributed to the free tendency of CO2 for permeation. But Unlike behavior of CO2 in permeation, time-dependent density for N2 permeation is proportional to the number of graphtriyne layers. As shown in Figure 12 (b), N2 trapping increases through the membrane with the increasing of the number of layers. So, N2 trapping gets enhanced with decreasing of CSA of channels in the membrane with raising the number of graphtriyne layers. Furthermore, the results derived from Figure 12 confirmed the estimated MECSA of channels (i.e., 35.98 Å²) obtained using geometry rule, and also, approved the no permeation of gases for those configurations having the number of layers equal and/or more than 8 layers. Under 20 bar, the N2 permeation is higher than that of CO2 for up to 4 layers of graphtriyne. But this superiority is temporary and vanishes with increasing the number of layers. The decrement of CSA of the channel becomes a serious obstacle especially for N2 with increasing of the number of graphtriyne layers. Also, the trapping trend of gases under 20 bar and 10 bar is similar to each other as can be inferred from Figure 12 (c) and (d). However, there is an appreciable difference between releasing time of CO2 and N2 under 20 bar after trapping procedure. The higher releasing time of CO2 relative to that of N2 return to the higher free tendency of CO2. Although, the increasing of pressure will lead to enhancing the permeation of both gases, but the N2 permeation is higher due to higher trapping of the CO2 relative to N2 molecules when a smaller number of layers are used. Higher permeation of N2 relative to CO2 can be seen for the graphtriyne with up to four layers under 30 bar, up to six layers under 40 bar, and up to seven layers under 50 bar. The


17


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N2 releasing time decreases significantly under 50 bar against 10 bar, while CO2 releasing time remains almost unchanged at each pressure except for 50 bar as shown in Figure 12 (e) and (f). 4. Conclusion Molecular dynamics simulation was implemented to model the constant-volume/variablepressure method with applying the non-equilibrium thermodynamic rule for gas permeation process. Accordingly, CO2 and N2 gas molecules permeation through graphtriyne structures as membrane was assessed. Permeation was investigated under various conditions such as different pressures (i.e., 10 up to 50 bar) and the number of graphtriyne layer (i.e., 1 up to 9). Regarding the cut off radius, it was understood that the bulk properties could be modeled by nine layers of graphtriyne structure in atomistic scale. Two novel and innovative parameters of free tendency and channel cross-sectional area were introduced to analyze the result of the simulation. The Free tendency was assessed based on the diffusion coefficient of gas molecules under 10 bar at ambient temperature and isothermal adsorption calculation under different pressure at 298K through Grand Canonical Monte Carlo (GCMC). Result confirmed the higher free tendency of CO2 toward membrane than that of N2. Also, by estimation of the effective cross-sectional area, it was found that cross-sectional area (CSA) of channels is the most important parameter in N2 permeation regarding its lower free tendency relative to CO2. Nevertheless, CSA of open channels can be confined by the sliding of layers over each other so that gases permeation through those graphtriyne membrane bearing 8 layers and beyond 8 layers is not feasible. Consequently, CO2 permeation is higher than that of N2 for those configurations having the 8 layers and/or more than 8 layers under different pressure conditions. This CO2 permeation superiority is related to the ineffectiveness of CSA parameter in the N2 permeation process. The permeation in a lower number of graphtriyne layers is pressure dependent. Since the effect of CSA on the permeation of N2 and


18

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CO2 is the same for a lower number of graphtriyne layer, so pressure and free tendency play the main role on the permeation. Moreover, distinct permeation behavior of CO2 and N2 gas molecules are such a way that CO2 permeation from membrane does not happen until the free space between layers is saturated with CO2 gas molecules. The CO2 is trapped without any dependency on the number of graphtriyne layers so that even for the two-layer graphtriyne, the trapping of CO2 happens before permeation through the graphtriyne layers. In contrast, N2 trapping is proportional to the number of graphtriyne layers and get enhanced with the increasing of the number of layers.

Acknowledgements The authors are grateful to Dr. Foad Mehri, Dr. Seyed Vahid Mousavi and Dr. Seyed Mostafa Rahimian for discussions and their friendly supports.

Figure 1. Denoted atomic type of force filed for graphtriyne, CO2 and N2.


19


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Figure 2. Schematic of gas separation (a) experimental set-up and (b) design of MD simulation based on related set-up.


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Figure 3. The height of gas reservoir under different pressure (a, b, c, d, and e). the presentation of hypothetical spring to exert respective pressure schematically (f)


21


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Figure 4. The illustration of the mechanism of gas permeation.


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Figure 5. The effect of the number of graphtriyne layers (no layer (0L) up to 9 layers (9L)) on the free tendency of CO2 and N2.


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Figure 6. Diffusion coefficient vs. the number of graphtriyne layers and adsorption isotherm for (a) presentation of how the number of layers affects diffusivity of CO2 and N2 and (b) plot of adsorption isotherm of CO2 and N2 under room temperature, respectively.


24

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Figure 7. Various Arrangement of CSA. Top (a) and side (b) view of ideal condition with maximum CSA and other configuration of CSA related to 1 layer (c), 3 layers (d), 6 layers (e) and 9 layers (f) from left to right, respectively.


25


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Figure 8. The relationship between the number of graphtriyne layers and CSA of channels. the vertical pink dashed line shows the theoretical prediction of minimum CSA required for passing gas molecules


26

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Figure 9. (i) Different orientation of gas molecules toward the planar graphtriyne in vertical (a and c) and horizontal (b and d) state. Blue and pink contour surfaces around the N2 and CO2 molecules are drawn based on the Van der Waals surface using σN (ra) and σO (rc) receptively, (j) the direction of moving gas molecules from y1 to y2 point and (k) definition of σ as the distance at which the binding energy between gas molecules and graphtriyne sheet is zero.


27


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Figure 10. Binding energy in two states (a) vertical and (b) horizontal orientations.


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Figure 11. The estimation of the minimum of ECSA for gas molecules passing schematically.


29


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Figure 12. Time-dependent density related to the different number of layers (a, c and e) of CO2 gas molecules and (b, d, and f) N2 gas molecules under 10, 20 and 50 bar.


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Table 1. Applied force field parameters in MD simulations 31-35

Atomic type CCO 2 O CO2 N N2 N mid

cp ct1 ct 2

Parameters Charge (e)

Sigma (Å)

Epsilon (kcal mol⁻1)

Mass (gr mol⁻1)

0.6512 -0.3256 -0.4820 0.9640 0.0852 -0.0852 0.0000

2.7570 3.0330 3.3200 0.0000 3.6171 3.6171 3.6171

0.0559 0.1599 0.0723 0.0000 0.1479 0.1479 0.1479

12.0112 15.9994 14.0067 1.0e-20 12.0112 12.0112 12.0112


31


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Table 2. Calculated spring constants corresponding to different pressure (a) 10 bar (b) 20 bar (c) 30 bar (d) 40 bar (e) 50 bar under NVT ensemble

Number of layers

Spring constant ×10-4, N/Å (b) (c) (d)

(a)

(e)

1

1.405

5.620

12.646

22.481

35.127

2 3 4 5 6 7 8 9

1.394 1.384 1.373 1.363 1.353 1.343 1.333 13.237

5.535 5.453 5.373 5.295 5.219 5.146 5.074 5.005

12.361 12.088 11.828 11.578 11.338 11.109 10.888 10.676

21.811 21.179 20.583 20.019 19.485 18.980 18.499 18.043

33.827 32.620 31.495 30.446 29.464 28.544 27.680 26.866


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Table 3. The effect of the number of graphtriyne layers on the CO2 and N2 diffusion coefficient. Number of layers 0 1 2 3 4 5 6 7 8 9

Diffusion coefficient (cm2 s-1) CO2 N2 2.98E-02 4.44E-03 2.60E-03 1.92E-03 1.14E-03 5.77E-04 2.08E-05 2.21E-05 1.95E-05 7.02E-06

2.03E-02 1.36E-02 1.12E-02 9.51E-03 8.20E-03 6.50E-03 5.53E-03 3.93E-03 5.48E-03 5.07E-03


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Table 4. Interaction energy components between two gases and membrane Total/Component of binding energy Total Van der Waals Electrostatic

Binding energy (kcal mol-1) CO2 N2 -58.777 -4.567 -54.210

-15.202 -7.169 -8.033


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Table. 5. The calculation of the ECSA (  ) and r in angstroms for CO2 and N2 based on Lennard-Jones potential (12-6) CO2

N2

Orientation

1

4

   4   1

r

2

3

   3   2

r

Vertical Horizontal

2.59 ----

5.06 ----

2.47 ----

3.48 3.88

2.83 3.43

4.53 4.13

1.70 0.70

3.48 3.68


35


Table 6. CO2 and N2 permeation values for one-layer graphtriyne under different pressures. Gas parameters One-layer of graphtriyne

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 54

dp )CO dt 2 dp ( )N2 dt PCO2 a PN 2 (

Pressure (bar)

10

20

30

40

50

7.48E-07

1.07E-06

1.46E-06

1.57E-06

1.76E-06

2.62E-07

4.85E-07

6.34E-07

9.15E-07

1.07E-06

2.85

2.21

2.30

1.72

1.65


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Table 7. CO2 and N2 permeation values under different pressure and number of graphtriyne layers (a) 10 bar (b) 20 bar (c) 30 bar (d) 40 bar (e) 50 bar

CO2

N2

dp 10 -7 -1 (bar fs ) )× dt b c CO2 N2 CO2 N2

2

4.90

4.75

6.61

7.79

8.48

10.12

8.85

11.34

9.03

12.80

3

4.31

2.69

6.12

6.23

7.32

8.12

7.63

9.45

8.45

11.28

4

3.26

2.00

5.22

5.59

5.82

7.13

6.70

8.35

6.33

8.76

5

2.74

1.73

4.15

2.76

4.61

3.28

4.57

5.23

5.36

8.86

6

2.49

1.16

3.64

2.71

4.75

3.06

4.52

5.00

6.06

7.15

7

2.01

0.86

2.73

1.79

3.00

2.36

3.03

3.10

3.04

6.25

8

1.70

0.12

1.82

0.74

2.22

0.644

2.40

0.56

2.63

1.13

9

1.22

0.08

1.60

0.52

1.77

0.26

1.84

0.11

1.85

0.11

(

Number of layers

a

d

e

CO2

N2

CO2

N2


37


Page 38 of 54

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“Graphical abstract”


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variable-Pressure

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