Enhanced Hydrogen Purification in Nanoporous Phosphorene

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Enhanced Hydrogen Purification in Nanoporous Phosphorene Membrane With Applied Electric Field Xiongyi Liang, Siu Pang Ng, Ning Ding, and Chi-Man Lawrence Wu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12283 • Publication Date (Web): 25 Jan 2018 Downloaded from http://pubs.acs.org on January 30, 2018

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The Journal of Physical Chemistry

Enhanced Hydrogen Purification in Nanoporous Phosphorene Membrane with Applied Electric Field

Xiongyi Liang†, Siu-Pang Ng†, Ning Ding†,‡,and Chi-Man Lawrence Wu*,†,‡ †

Department of Materials Science and Engineering, City University of Hong Kong,

Hong Kong SAR, People’s Republic of China ‡

Key Laboratory for Applied Technology of Sophisticated Analytical Instruments,

Shandong Academy of Sciences, Qilu University of Technology, Jinan 250014, People’s Republic of China

Abstract: As a feasibility study for hydrogen purification, the mechanisms of H2, CO2, N2, CO, and CH4 penetrating through self-passivated porous phosphorene membranes with different pore size were systematically investigated by density functional theory. The thermal stability of porous phosphorene membranes with various pore sizes was studied by ab initio molecular dynamic. By applying an external electric field perpendicular to the porous phosphorene membrane, the diffusion of CO2 and N2 through the pores was remarkably suppressed due to the polarizability of these molecules, whereas the energy barrier and permeance of H2 passing though the membrane is virtually unaffected. Thus, the application of the electric field improves the performance of hydrogen purification further. This finding opens up a new avenue to optimally tune the performance of 2D materials for gas separation by applying an external electric field.

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1.

Introduction Hydrogen (H2) is regarded as a promising green energy source because of many

advantages, including high energy density per unit mass, high conversion efficiency, pollutant-free, renewability and abundancy.1-2 In addition, hydrogen is an important industrial chemical, which is widely used in semiconductor and electronics production processes.3-6 In these processes, the purity of hydrogen is critical to control the quality of products. However, existing production methods of hydrogen inevitably introduce undesirable byproducts, e.g. CO2, N2, CO, CH4, thus hindering the development of high purity hydrogen production.7 Therefore, it is desirable to develop a highly effective and selective technology for hydrogen purification. In comparison with traditional hydrogen purification technologies, for example, pressure swing absorption and cryogenic distillation,8 2D material-based membrane separation has competitive advantages, such as superior permeance due to its ultrathin structural feature, controllable pore size and low energy cost.9-14 For example, graphene, a monolayer graphite with unique structure and many excellent properties, has been theoretically proved by Tao et al.15 to be feasible for hydrogen separation. However, edged carbon atoms with dangling bonds in porous graphene possess high chemical reactivity and should be protected by decorating with H or N atoms, thus hindering the application of graphene in hydrogen separation.16-17 In addition, other 2D materials such as graphene oxide18, h-BN19-20 and silicene21 were studied by computational methods to investigate the feasibility in hydrogen purification. In 2014, a new 2D material, phosphorene, which is a monolayer of black phosphorus, has been successfully exfoliated.22-23 Unlike graphene and h-BN with planar structure, phosphorene has honeycomb lattice and buckled geometry. In addition, phosphorene has superior electronic, chemical and mechanical properties. It is worth noting that Hashmi et al.24 have theoretically predicted the superior thermal stability of porous phosphorene, showing that the edge atoms in porous phosphorene with even number of atom vacancies will reform three sp3 covalent bonds with three other neighboring P atoms similar to pristine phosphorene layer without any dangling 2 ACS Paragon Plus Environment

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bond. This self-passivated effect dramatically stabilizes the porous phosphorene and is more effective than that of edge passivation with H and O atoms. Interestingly, some reports showed that phosphorene exhibits superior gas sensing power.25-28 This means that phosphorene interacts with such gas molecules, thus opens up the possibility of its gas-related applications. Experimentally, nanopores in phosphorene can be fabricated from pristine phosphorene by using e-beam treatment, heavy ion bombardment, and by oxidative etching.24,

29-30

Inspired by these reports, it is

conceived that self-passivated porous phosphorene can be made for hydrogen separation from other gases (i.e. CO2, N2, CO, and CH4). Furthermore, the properties of 2D materials can be tuned by applying an external electric field.31-34 For example, an electric field can enhance the adsorption of NO2 on Ga-doped graphene in the presence of an appropriate electric field.35 Ao et al. also found that electric field could act as a controller for the uptake or release process of hydrogen on N-doped graphene by computational simulation.36 Additionally, Lee et al. showed that the valley Hall effect in MoS2 transistors can be controlled by electric field.37 Therefore, the gas filtration performance of 2D material-based devices can be promisingly regulated by external electric field. In this work, the performance of self-passivated porous phosphorene in hydrogen purification from CO2, N2, CO, and CH4 is systematically investigated by density functional theory (DFT). CO2, N2, CO, and CH4 were chosen so that the results can be compared with those of previous investigators. The effects of pore size of self-passivated porous phosphorene and external electric field are studied by calculating the penetration energy barrier, selectivity and permeance. Also, ab initio molecular dynamics (AIMD) is performed to explore the thermal stability of self-passivated phosphorene with different pore sizes. 2.

Computational details All calculations were performed by DFT method in DMol3 of Materials studio38

with Perdew-Burke-Ernzerhof (PBE) functional of the

generalized-gradient

approximation (GGA).39 In order to correct the effects of dispersion potential and van 3 ACS Paragon Plus Environment


der waals (vdW) interactions between gas molecules and porous phosphorene, DFT-T of Grimme was implemented.40 The atomic orbital was specified by double numerical plus polarization (DNP) and the core treatment was set by all electrons to treat core electrons in the same manner as valence electrons. Spin-unrestricted calculation was selected to use different orbitals for different spins. To obtain high quality results, the self-consistent field tolerance, energy threshold and force cutoff was set to 10-6 a.u., 10-5 a.u. and 0.002 a.u. respectively. All simulations were based on a 6×6 supercell (27.72 Å×19.80 Å) of phosphorene with periodic boundary conditions. The Brillouin zone was represented by a 6×6×1 Monkhorst-Pack k-point meshes41 and a sufficiently large vacuum slab with a height of 25 Å was introduced along the z direction to avoid interlayer interactions. In addition, the electric field is applied perpendicular to the phosphorene sheet, and the upward (downward) direction was denoted by a positive (negative) value, as shown in Figure S1. To compute the effect of external electric field on the properties of 2D materials or bulk surfaces based on experimental configuration,42-43 the nano-scale electric field of 1.0 V/Å is usually applied.44-45 Thus, the effect of electric field ranging from -1.0 V/Å to +1.0 V/Å is considered in this work. To investigate the thermal stability of porous phosphorene, AIMD calculations46-48 were employed under constant temperature condition (NVT) at 300K for 2 ps with time step of 2 fs.49 The Nosé-Hoover thermostat50 was used to control the temperature of the NVT simulation. The Nosé Q ratio and Yoshida parameter was set to 2 and 3, respectively.51 3.

Results and discussion

First, the optimized structure of the pristine phosphorene after full relaxation with lattice constants of a = 4.62 Å and b = 3.30 Å, as well as buckled height of 2.12 Å is shown in Figure S2. The results agreed well with previous reports.49, 52-54 Then, four self-passivated porous phosphorene with different pore sizes are designed by removing 6, 8, 10, 12 phosphorous atoms (namely D6, D8, D10 and D12), and the geometric parameters of pores are labeled, as shown in Figure 1. In general, larger pore sizes may cause very low selectivity, while H2 molecules are difficult to 4 ACS Paragon Plus Environment

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penetrate a smaller pore, e.g. D2 and D4. Thus, these four self-passivated porous phosphorene are considered to explore the feasibility for hydrogen purification. It was confirmed that self-passivation effect occurs in edge atoms in all porous phosphorene without any dangling bond, and agrees well with previous reports. In addition, no magnetic moment and spin is observed in all porous phosphorene. Prior to investigating gas separation performance, the thermal stability of various self-passivated porous phosphorene membranes were studied by computing the formation energy and performing AIMD simulation.55-57 It was found that D6 configuration is most easily formed in phosphorene with a small formation energy of 3.22eV (See Table S1), which is also more easily formed than vacancy defect in graphene.58 The AIMD results showed that all structures were kinetically stable at 300K and the porous structure of phosphorene will not be disrupted during the total simulation time of 2 ps (See Figure S3). In addition, the total energy of all self-passivated porous phosphorene shows small oscillation after relatively strong fluctuation at the beginning of the simulations (See Figure S4). All these results reveal that all self-passivated porous phosphorene membranes have good thermal stability at 300K, suggesting that the self-passivated porous phosphorene is capable of performing gas separation at room temperature.



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Figure 1. The optimized atomistic structures of self-passivated porous phosphorene with different pore sizes (a) D6, (b) D8, (c) D10 and (d) D12. The orange balls represent the P atoms. In order to evaluate the permeation of the five gases considered, the interaction energies, Eint(h), of the five gas molecules passing the center of the pore of various porous phosphorene membranes, as a function of adsorption height, are calculated. Eint(h) is defined as: ℎ ℎ ℎ ℎ

(1)

where Etotal(h), Egas(h) and Esheet(h) represent the total energy of gas molecule and porous phosphorene, the energy of isolated gas and the energy of isolated porous phosphorene at a particular adsorption height h, respectively (See Figure S5). The adsorption height is defined as the distance between the center of mass of the gas molecules to the center of the pore.15 To minimize the energy barriers for gas molecules penetration, for the linear molecules (i.e. H2, CO2, N2, and CO), the 6 ACS Paragon Plus Environment

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molecular axes are aligned perpendicular to the phosphorene plane. On the other hand, the configuration of the tetrahedral CH4 molecule is that three of the C-H bonds point toward the phosphorene plane, and the fourth C-H bond point away from the centre of the pore,14, 59 as shown in Figure 2 and Figure S6. The calculated interaction energies between the gas molecules considered and the porous phosphorene membranes with various pore sizes as a function of adsorption height are shown in Figure 3. The energy barrier for gas molecule to diffuse through the pore, which can be obtained from Figure 3 and defined as the difference between the maximum (defined as transition state) and minimum (defined as stable state) values (i.e. Eb = ETS – ESS), are summarized and listed in Table 1 and Table S2. It is worth noting that the adsorption height dependence interaction energy curves are not symmetrical due to the buckled structure of porous phosphorene and the asymmetric structure of the CO molecule. Interestingly, the transition states of H2 are located at 1.2-1.6 Å for these four porous phosphorene membranes, and are totally different from those of other molecules at the adsorption height close to 0 Å. It is noted that the interaction energies of H2 in all these four porous phosphorene membranes remain negative even at transition states (See Figure 2(a) and Figure 3), which means that the H2 molecules are slightly physisorbed by porous phosphorene membranes during the whole penetration process. In addition, the energy barrier of H2 is only 0.012 to 0.085 eV and decreases with increasing pore sizes. These results suggest that H2 molecules can easily diffuse through porous phosphorene membranes at room temperature and pressure. On the other hand, all the energy barriers of CO2, N2, CO, and CH4 are much larger than that of H2, and the repulsive interactions of CO2, N2, CO, and CH4 molecules within the pores (i.e. the adsorption height close to 0) can be observed. These indicate that the porous phosphorene membranes could block these four gases from penetration. The differences in the energy barrier among the gas molecules considered can be explained by the difference in kinetic diameters of gas molecules (H2: 2.9 Å, CO2: 3.3 Å, N2: 3.6 Å, CO: 3.8 Å, and CH4: 3.8 Å) and can be understood by electron density isosurfaces for transition states of gases molecules passing through the porous 7 ACS Paragon Plus Environment


phosphorene membranes (See Figure S7). From the analyses of electron density, no electron overlap between H2 molecule and porous phosphorene membrane at transition state can be observed due to the smaller molecule size and kinetic diameter. In contrast, other gas molecules, especially CH4, show obvious electron density overlap with membrane at transition state, which demonstrates that electron density overlapping causes repulsive force, resulting in blocking of gas molecules from penetration through the membrane. In addition, for crosscheck purpose, the transition states were searched by the synchronous method with conjugated gradient (CG) refinements,60 as shown in Table S3. The results show that the transition state for all gas molecules passing through the porous phosphorene with different pores sizes are in excellent agreement with the transition states obtained from interaction methods.

Figure 2. The configurations for (a) H2, (b) CO2, (c) N2, (d) CO, and (e) CH4 passing various D6 membrane. First, second and third row is top view, side view of transition states and stable states, respectively. The white, grey, blue, red and orange balls represent H, C, N, O and P atoms, respectively.


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Figure 3. Interaction energies between the gas molecules considered and (a) D6, (b) D8, (c) D10 and (d) D12, as a function of adsorption height (Å).

Table 1. Energy barrier (eV) of H2, CO2, N2, CO, and CH4 for passing various porous phosphorene membranes. D6 D8 D10 D12

To

H2 0.085 0.028 0.012 0.030

CO2 1.045 0.372 0.212 0.464

quantitatively evaluate

N2 0.684 0.308 0.216 0.263

the

CO 0.777 0.317 0.272 0.284

performance

CH4 1.506 0.826 0.689 0.741

of self-passivated porous

phosphorene for hydrogen purification, the selectivity of H2 over CO2, N2, CO, and CH4 and the permeance are two important parameters to consider. First, the selectivity of H2 over other four gases can be estimated by the Arrhenius equation:61



⁄

e ⁄ 2 e ⁄

where r is the diffusion rate, A is the diffusion prefactor, E is the diffusion barrier, R is the molar gas constant and T is the temperature. As the prefactor for all gases are about 10 THz, it is assumed that A are identical for all gases being studied.61 The Arrhenius equation implies that the higher the selectivity the better filtration effectiveness for that particular gas molecule. The calculated selectivities of various pore sizes for H2 over CO2, N2, CO, and CH4 at room temperature (300K) are summarized in Table 2. It is found that the selectivity of H2 decreases with increasing pore sizes. Interestingly, D10 shows the lowest selectivity instead of D12 that has the largest pore area, indicating that selectivity is not only determined by the pore size but also affected by the pore shape. By comparing the electron density isosurfaces of D10 and D12 in Figure S7, the intervention of electron density between gas molecules and D12 membranes was found to be more significant than that of D10. Therefore, D10 shows the lower energy barriers and lower selectivities to the gas molecules than D12. Among the four porous phosphorene configurations, the D6 configuration exhibits the highest selectivity of 1.3×1016, 1.1×1010, 4.2×1011, and 7.3×1023 for H2 over CO2, N2, CO, and CH4, respectively. Obviously, the D6 configuration also competes favorably over other 2D materials, except g-C3N3 for CH4 as shown in Table 2. Although g-C3N3 shows better selectivity of H2 over CH4, the selectivities over N2 and CO of D6 membrane are much better than those of g-C3N3. In addition, H2 only requires to overcome an energy barrier of 0.085 eV passing though D6 membrane, which is much lower than that of g-C3N3. Thus, D6 has the best overall hydrogen purification performance amongst all the membranes considered in Table 2.


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Table 2. Comparison of the selectivies (SH2/gas) of various porous phosphorene configurations for H2 over CO2, N2, CO, and CH4 at room temperature, as well as those of other 2D materials. Membrane D6 (this work) D8 (this work) D10 (this work) D12 (this work) graphene62 silicene21 g-C3N363

CO2

N2 16

CO 10

1.3×10 6.0×105 2.3×103 2.0×107 1011 -

1.1×10 5.0×104 2.6×103 2.1×104 1010 106

CH4 11

4.2×10 7.1×104 2.3×104 4.5×104 1010 104

7.3×1023 2.6×1013 2.4×1011 2.2×1012 1022, 108 1022 1026

Furthermore, permeance is another essential factor for hydrogen mixtures purification. Permeance can be determined by Maxwell-Boltzmann distribution and the kinetic theory of gases. Permeance is defined as the molar amount of gas through the membrane per unit area per unit time and per unit pressure. In addition, permeance can be calculated by Pgas = F/∆P, in which F represents the molar flux (mol m-2 s-1) of gas molecules and ∆P represents the difference in partial pressure (Pa) of the gas.13, 19, 59, 64

The molar flux F can be obtained by F = N×f, where N and f is the number of gas

molecules colliding with the wall and the probability for a gas molecule penetrate through the pore, respectively. According to the kinetic theory, N can be expressed by N = P/(A×(2πmkBT)1/2), in which P, A, m, kB, T represents the pressure, Avogadro constant, molecular mass, Boltzmann constant and temperature, respectively. f is given by %

! " !# d# 3 &'

where f(v) and vB represent the Maxwell velocity distribution and the velocity corresponding to energy barriers.65 Pressure P and pressure difference ∆P is assumed to be 3×105 Pa and 1×105 Pa, respectively.10 Figure 4 reveals the permeances for the gases considered when passing through porous phosphorene with various pore sizes at 300 K, and the dashed line indicates the accepted permeance for gas separation 11 ACS Paragon Plus Environment


industrial wide.66-67 It is noted that the permeances for all gases increase with increasing pores size, which is consistent with the calculation by energy barrier. Obviously, the four porous phosphorene membranes exhibit excellent permeance of H2 at room temperature (300 K), reaching 1.5×10-3 mol m-2 s-1 Pa-1 for D6 and increasing to 1.4×10-2 mol m-2 s-1 Pa-1 for D10, which exceeds the industrial standard by more than 4 orders of magnitude. Thus, it can be inferred that H2 can freely penetrate through the porous phosphorene membranes. However, the permeance of N2 and CO with a magnitude of 10-6 can also be obtained in D8, D10 and D12, which suggests that D8, D10 and D12 do not show industrially acceptable selectivity for H2 over N2 and CO. Therefore, it can be summarized that with excellent permeance of H2 and industrially acceptable selectivity at 300 K, D6 is suitable to be used in hydrogen separation. Interestingly, the D10 configuration possesses good permeance of H2, CO2, N2 and CO, and exceeds the industrial standard, except for CH4 at 300 K. Using the Arrhenius equation, the selectivity of H2/CH4, CO2/ CH4, N2/ CH4 and CO/ CH4, is calculated as 2.4×1011, 1.0×108, 9.0×107 and 1.0×107. Therefore, the D10 membrane can be used for methane upgrading (i.e. retaining methane from a mixture of these gases) to improve the calorific value and applicability in natural gas.13

Figure 4. Permeance for gas molecules passing porous phosphorene with various pore sizes at 300K. The dashed line indicates the industrially acceptable permeance for gas separation. In order to verify and crosscheck the permeances determined by energy barrier and based on kinetic theory, classical molecular dynamics (MD) was implemented to study the permeance of D6 for gaseous mixture (H2, CO2, N2, CO and CH4) at 300 K. 12 ACS Paragon Plus Environment

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The details of the computational method are given in the supporting information. The MD results show that only H2 molecules can penetrate through the D6 membranes into the vacuum boxes during the total simulation time of 2 ns and the permeance of D6 for H2 within gaseous mixture at 300 K is 1.7×10-3 mol m-2 s-1 Pa-1, which agrees well with the values calculated by DFT methods. The simulation methods used in this work, which compare results of DFT calculation with MD simulation have been confirmed in previous reports13-14, 64 and suggest that the present DFT simulations and parameters setting are reliable and acceptable. In the following part, the enhancement effect of external electric field on performance of hydrogen purification for D6 is explored by the same DFT methods. The electric field is applied perpendicular to the phosphorene sheet, and the upward (downward) direction is denoted by a positive (negative) value. The electric field dependent diffusion properties of H2, CO2, N2, CO, and CH4 for passing D6 are shown in Figure 5. It is evident that the energy barriers of all gas molecules passing through D6 membrane increase as the intensity of external electric field increase, and exhibit second order relation with electric field with a quadratic coefficient of 0.040 to 0.240 for different gas molecules and different direction of electric field. (The fitting functions are shown in Figure 5(a).) Interestingly, CO and CH4 show different quadratic trends under positive and negative electric field due to asymmetric structure of CO molecule and the penetrating configuration of tetrahedral CH4 molecule. In general, the penetrating configurations with smaller energy barrier are selected to explore the gas diffusion. The energy barrier of H2 slightly increases from 0.085 eV to 0.158 eV under an electric field of ±1.0 V/Å, but the H2 molecules can still freely penetrate the D6 membranes. On the other hand, the energy barrier of CO2 is very sensitive to electric field, with significant growth from 1.045 eV to 1.241 eV in the presence of electric field of ±1.0 V/Å, i.e. about 20% increase. Also, a relatively large increase in energy barrier with electric field can be found in the case of N2 with a quadratic coefficient of 0.118 (See Figure S8). This phenomenon can be explained by two main reasons: 1) an external electric 13 ACS Paragon Plus Environment


field will lead to polarization of the charge density and charge particle and the accumulation of preferential electrons in one particular atom that is close to the positive electrode,68-70 resulting in increased difficulty for gas molecules passing through pore of membrane. The images of charge density difference for gas molecule passing through D6 at transition state and the corresponding interaction energies are shown in Figure 6 and Figure S9, which is an effective visible tool to illustrate the electron transfer and charge density. In Figure 6(a), the charge density of H2 does not show obvious change as an electric field is applied, so a small increase in interaction energy at the transition state occur. In contrast, in Figure 6(b), electron accumulation is evidently unequal for the two O atoms under an applied electric field of 1.0 V/Å, which is indicated by the larger red region at the bottom O atom compared to the other O atom of CO2. On the other hand, the electron density distributes equally over the two O atoms in the absence of electric field. Furthermore, from the atomic charges based on Hirshfeld’s population analysis,71 compared with a minor change in charge transfer of two H atom in H2 molecule (without electric field: -0.05e and -0.02e; with electric field: -0.04e and -0.05e), an obvious change in charge state of CO2 molecule can be observed. Without the external electric field, the charge of the two O atoms is equal, with the value of -0.12e, whereas more electron transfer to the bottom O atom from the top O atom of CO2 (-0.16 e vs. -0.09 e) occurred when the electric field is applied. Accordingly, electron accumulation in one particular atom results in larger electron density overlap, leading to the increase of interaction energy and difficulty for CO2 to pass the pore of D6. In general, CO2 and N2 show stronger atomic and molecular polarizability due to strong electronegativity of O and N atom,72 and experience a significant deformation of charge density under external electric field, which explains the aforementioned results that the energy barrier of CO2 and N2 are much sensitive to electric field than that of H2. In addition, polarization of the charge density due to electric field was also found in D6 membrane as indicated by the atomic charge values in Figure S10 with larger electron density overlapping. 2) Another reason is that the external electric field will evidently enhance the charge 14 ACS Paragon Plus Environment

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transfer between the gas molecules and membrane sheet, which improves the adsorption energy at stable states.34-35 This eventually increases the energy barrier for gas molecule passing through porous membranes. Based on the Hirshfeld’s population analysis, a three-fold of additional electron transfer from porous phosphorene sheet to CO2 molecule occurs with an electric field of 1.0 V/Å (-0.0516e) when compared with that without electric field (-0.0177e). Accordingly, the adsorption energy for CO2 on D6 increase from -0.121 eV to -0.189 eV in the presence of 1.0 V/Å electric field, which is similar to the case of gas molecules on graphene sheet.35 In general, this enhancement effect shows quadratic tendency with electric field due to the second-order stark effect,73 which may explain why the energy barriers of all gas molecules passing through D6 membrane exhibit second order relation with electric field. It can be seen from Figure 5(b) that the selectivities of D6 for H2 over CO2, N2, CO, and CH4 at room temperature all increase under the external electric field. Compared with the absence of electric field, the selectivity for H2 over CO2 has the biggest enhancement (i.e. two orders of magnitude increase) under a electric field of 1.0 V/Å, while the selectivity for H2 over N2, CO, and CH4 also increases by about one order of magnitude under the same condition. In addition, the permeances for the gases considered passing D6 at 300K under different external electric field is shown in Figure 5(c). It is noted that although the permeance of D6 membrane for H2 slightly decrease with increasing intensity of electric field, the D6 membrane still exhibits excellent permeance for H2 at 300 K even under an electric field of ±1.0 V/Å, and exceeding the industrial standard by more than 4 orders of magnitude. By contrast, the permeances of D6 for other gases, especially for CO2 and N2, apparently decrease under external electric field due to the dramatic increase in energy barrier. Similarly, to prove the permeances determined by energy barrier and based on kinetic theory under electric field, MD was also performed to study the permeance of D6 for gaseous mixture (H2, CO2, N2, CO and CH4) at 300 K with a electric field of 1.0 V/Å. The MD results show that the permeance of D6 for H2 within gaseous mixture at 300 15 ACS Paragon Plus Environment


K is 0.5×10-3 mol m-2 s-1 Pa-1, which agree well with the values calculated by DFT methods of 0.3×10-3 mol m-2 s-1 Pa-1 (See Figure S12 and S13). In summary, the external electric field affects the permeation of H2 insignificantly, whereas an appropriate electric field can notably deter the permeation of other gases. It follows that the use of external electric field can improve the selectivity of H2 over CO2, N2, CO, and CH4, thus improving the performance of porous phosphorene membrane for hydrogen purification even further.


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Figure 5. The electric field dependent (a) energy barriers of H2, CO2, N2, CO, and CH4 for passing D6, (b) the SH2/gas of D6 for H2 over CO2, N2, CO, and CH4 at 300 K, and (c) the permeances for gases passing D6 at 300K.

Figure 6. Electronic deformation density for (a) H2 and (b) CO2 molecule passing through D6 at transition state with and without electric field. The atomic charges of gas molecules from Hirshfeld’s method are labeled and the inset of Figure 6(b) presents atomic charges for CO2 molecule. The red (blue) region corresponds to charge accumulation (loss). The range of isovalue is set to be ± 0.050. 17 ACS Paragon Plus Environment


4.

Conclusions DFT calculations were used to study the diffusion mechanism of H2, CO2, N2,

CO, and CH4 penetrating through self-passivated porous phosphorene membranes with different pore size and the effect of external electric field. The results show that all the considered porous phosphorene configurations are kinetically stable at 300K. Among these, D6 exhibited excellent permeance for H2, as well as significant good selectivity for H2 over CO2, N2, CO, and CH4, suggesting that D6 reveal a great potential for hydrogen purification. Interestingly, D10 should be applicable for methane upgrading with good selectivity. In addition, an external electric field perpendicular to porous phosphorene membrane was applied to improve the performance of these porous phosphorene membranes. It is found that the energy barrier and permeance of H2 passing though D6 are slightly affected by electric field. In contrast, the diffusion properties of other gases, especially CO2 and N2 are very sensitive to external electric field, due to their stronger molecular polarizability. Therefore, an external electric field can remarkably enhance the performance of porous phosphorene membrane for hydrogen purification, in term of improvement of the H2 selectivity. The above results not only demonstrate the feasibility of self-passivated porous phosphorene membranes for gas separation applications, but also provide a new strategy to improve the performance for gas separation by applying external electric field.


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ASSOCIATED CONTENT

Supporting Information

The schematic diagram of direction of external electric field; Optimized atomistic structure of pristine phosphorene; The calculated formation energy for porous phosphorene; The snapshots of porous phosphorene form NVT AIMD at 300K; The simulation time dependent total energy of porous phosphorene form NVT AIMD at 300K; The configurations for the gas molecules passing through porous phosphorene; The transition state (TS) and stable state (SS) of the gas molecules interacted with the porous self-passivated phosphorene membranes and the responding interaction configuration; Electron density isosurfaces for gas molecules passing through the porous phosphorene the transition states; The comparison of barrier energy (eV) obtained from interaction method and synchronous method; Interaction energies between the gas molecules considered and D6 without and with electric field; Electronic deformation density for gas molecule passing through D6 at transition state with and without electric field; The atomic charges (e) of P atoms of D6 around the pore; The details for classical molecular dynamics simulation.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected]. Tel: +852-34428668



ORCID Chi-Man Lawrence Wu: 0000-0002-7190-8855

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work was supported by The National Natural Science Foundation of China (Grant No. 11404192), The Shandong Province Special Grant for High-Level Overseas Talents (Grant No. tshw20120745), and The Research Award Fund for Outstanding Young and Middle-aged Scientists of Shandong Province, China (Grant No. BS2014CL002).

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Enhanced Hydrogen Purification in Nanoporous Phosphorene

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