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Hydrogen and deuterium adsorption on uranium decorated graphene nanosheets: A combined molecular dynamics and density functional theory study
Current Applied Physics xxx (xxxx) xxx–xxx
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Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Hydrogen and deuterium adsorption on uranium decorated graphene nanosheets: A combined molecular dynamics and density functional theory study Zahra Ghalamia, Vanik Ghoulipoura,∗, Alireza Khanchib a b
Faculty of Chemistry, Kharazmi University, No. 43, Shahid Mofatteh Ave., Tehran, Iran Nuclear Science and Technology Research Institute, AEOI, P. O. Box 11365/8486, Tehran, Iran
A R T I C LE I N FO
A B S T R A C T
Keywords: Graphene Uranium Deuterium Hydrogen DFT MD
In this study, the combined density functional theory (DFT) and molecular dynamics (MD) simulation methods were carried out to investigate the potential capability of uranium-decorated graphene (U–G) for the separation of deuterium from hydrogen gases. Graphene with hexagonal honeycomb lattice arrangement is suitable for adsorption of individual uranium atoms, with a high binding energy (−1.173 eV) and U-U distance longer than 7 Å. This U-G system has ability to hold up to six H2 (5.16% wt) or seven D2 (11.75% wt) molecules per U atoms. To gain further insights into these interactions, partial electronic density of states (PDOS) and the electron density distribution of the elements were analyzed. The MD results are in reasonable agreement with the results obtained by DFT method. Our calculated results indicate that at room temperature, D2 molecule has higher affinity for U-G system than the H2 molecule. In order to increase the D2 separation factor from H2, the effect of temperature was studied. The results indicated that adsorption ratio of D2 to H2 increases by decreasing the temperature.
1. Introduction In recent years, great attention has been paid to the control of fossil fuels as one of the greatest threats to the environment and public health. New energy resources such as fusion energy seem to play a crucial role in the future. Contrary to fossil fuels, fusion energy has no drawback such as greenhouse effect on the environment. However, an important raw material used for producing fusion energy is deuterium, which is relatively cheap. Furthermore, deuterium tracer applications in medical diagnosis and treatment are of great importance, but the natural content of D2 is only 0.015% [1]. As a result, its separation from other hydrogen isotopes is a critical research subject. The existing methods for the separation of H2 isotopes such as thermal diffusion [2] and cryogenic distillation [3] possess low efficiency and high energy consumption [4–6]. Among the different methods, gas sorption by adsorption in porous materials is considered to be the promising approach. Hydrogen isotopes have common points of similarity, e.g., they have similar chemical properties with only one electron and one proton. Because of large mass differences between hydrogen and deuterium (deuterium is twice heavier than hydrogen), large isotope effects exist in metal-hydrogen systems. The bonding
∗
strength between hydrogen and metal differs slightly due to its mass effect, and equilibrium pressure between hydrogen isotopes is slightly different [7]. Carbon-based nanostructures, such as graphene [8,9], fullerene [10,11], and nanotubes [12] have been reported for solid-state hydrogen storage because of their high specific surface area, fast kinetics, and reversible hydrogen storage etc. Simple carbon nanostructures weakly bind to the H2 molecules [13] and show low H2 adsorption capacity. On the other hand, graphene has opened many opportunities for the development of new materials for hydrogen adsorption and storage due to flexibility in functionalization and modification of surface. Thus, a large number of theoretical studies on doping or surface metal (alkali [14,15]; alkaline-earth [16–18]; transition [19–23]) dispersion have been reported to improve the chemical activity of graphene and graphene-like materials [24,25]. Among these, modification with transition metal (TM) atoms can significantly improve the adsorption energy of hydrogen molecules on graphene [26], This is due to the polarization of H2 molecules by an electric field and/or hybridization of H2 σ or σ* orbitals with TM empty d-orbitals (Kubas type interaction) [27]. In this regard, transition metal (TM) decorated
Corresponding author. E-mail address: [email protected] (V. Ghoulipour).
https://doi.org/10.1016/j.cap.2019.02.011 Received 20 November 2018; Received in revised form 7 January 2019; Accepted 15 February 2019 1567-1739/ Published by Elsevier B.V. on behalf of Korean Physical Society.
Please cite this article as: Zahra Ghalami, Vanik Ghoulipour and Alireza Khanchi, Current Applied Physics, https://doi.org/10.1016/j.cap.2019.02.011
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interaction, a vacuum spacing of 30 Å, along with 6000 H2 and D2 molecules in both sides of graphene layer with 1:1 ratio was set. Each MD simulation was performed in NVT statistical ensemble (constant numbers of atoms N, volume V and temperature T, without external pressure). The time step in our simulations was considered to be 1 fs, and the simulation time t at a specific T was set to 10 ns.
graphene nanostructures have attracted significant attentions. However, the large cohesive energy of TM atoms can simply lead to the aggregation of TMs on graphene. Previous reports demonstrate that the introduction of impurity atoms or vacancies can prevent the TM atoms from formation of clusters, thus increasing the hydrogen storage capacity of graphene [21,28]. The adsorption of some gas molecules on metal oxide based nanoparticles and two-dimensional nanostructures have been investigated in detail [29–33]. Although, of the different hydrogen adsorbent TMs, palladium has received the numerous attention in the past decades [34–38]. Besides, uranium has been widely used for hydrogen isotopes storage [39–45] because of its higher storage capacity per unit volume and higher ability of adsorption in low pressure [46]. On the other hand, due to the higher formation enthalpy of uranium deuteride (−1.40 eV) compared with the uranium hydride (−1.27 eV) [47], it shows a great capability for hydrogen isotopes separations. According to the above-mentioned issues including 1) benefits of graphene nanosheets for gas adsorption 2) improvement the property of graphene through metal decoration and 3) widespread use of uranium in the storage of hydrogen isotopes, this substrate seems to be a good candidate with practical benefits to increase the hydrogen isotopes storage capacity of uranium through increasing surface area with capability of hydrogen/deuterium separation. In the present work, we used MD and DFT methods to calculate the adsorption capability of graphene sheets toward uranium-238 atoms and obtain the most stable configuration of U atoms on graphene sheets. We also examined the adsorption behavior of the resulting material (step 1) onto H2 and D2 molecules.
2.2. Density functional theory The DFT calculations were performed using DMol3 module of Material Studio (MS) Version 8. A double numerical plus polarization (DNP) basis set was used for all the DFT calculations. A polarization pfunction was adopted for all hydrogen atoms in order to correctly estimate the energy values by considering the hydrogen bonding in the system. The B3LYP hybrid method was used, which produces reliable geometries and energies and requires less time and computer resources. There are a large number of theoretical studies in the literature, which demonstrate the suitability of B3LYP in U coordination complexes [54–56]. The k point was set to 20 × 20 × 1 for the (3 × 3 × 1) graphene cell, with box size of 7.4 Å × 12 Å × 20 Å. The hydrogen or deuterium molecules were placed one by one inside the supercell (seven H2 and ten D2). The convergence tolerance of energy was set to 1.0 × 10−6, and that of maximum force was considered to be 1.0 × 10−4 Hartree/Å (1 Hartree = 27.21 eV). As shown in Fig. 3, the supercell contains 35 C atoms. In the optimization process, all atoms are allowed to relax in all calculations. The binding energy of U atoms onto graphene Eb-U is defined as eq. (3).
Eb − U = [EnU − graphene − (Egraphene + n EU )], 2. Computational details
Where EU-graphene, Egraphene, and EU are the total energies of the system with n U atoms adsorbed on the graphene layer, the energy of the pristine graphene layer, and the energy of one U atom in the same slab, respectively. The binding energy of H2 and D2 molecules onto U-G layer Eb-H2 is defined as eq. (4).
2.1. Molecular dynamic The MD simulations were performed with large-scale atomic/molecular massively parallel simulator (LAMMPS) [48] (lammps-16 February 2016) The intermolecular forces for H2, D2 and C are obtained using atom–atom pair potentials, namely Lennard–Jones (LJ) potential (eq. (1)). The Morse potential is the most popular interatomic potential for metals [49]. Zeng and co-worker demonstrated that the Morse function accurately describes the behavior of the uranium, which is valid to the temperature of 1500 K [50], Thus, we employed Morse potential for uranium atoms in this work (eq. (2)). 12
⎡ σij LJ: U (rij ) = 4εij ⎢ ⎛⎜ ⎞⎟ r ⎣ ⎝ ij ⎠
Eb − H 2 = [EiH 2 + U−graphene − (EU − graphene + i EH 2) ]
(4)
where EiH2+U-graphene, EU-graphene and EH2 denote the total energies of the system with i H2 molecules adsorbed, isolated U-adsorbed graphene, and H2 molecule, respectively. 3. Results and discussion
6
σij ⎤ − ⎛⎜ ⎞⎟ ⎥ ⎝ rij ⎠ ⎦
(3)
3.1. Molecular dynamic predictions (1)
Morse: U (r ) = De (e0−2ß(r − r ) − 2e0−ß(r − r ) )
In order to predict the adsorption capacity of the graphene for uranium atom, we measured the radial distribution functions (RDFs) or g (r) for U-G system, (RDFs) which is a main criterion to evaluate the sorption capability of graphene. This parameter gives the probability of finding uranium atoms at a distance of r away from one of carbon atoms of graphene with respect that for a completely random distribution of the same density of uranium atoms [57]. Then, we averaged the RDF values that calculated for each carbon atoms, and plotted the obtained results. The RDF plots for adsorption of uranium on graphene and that of hydrogen/deuterium on U-G system were shown in Fig. 1a–b. The sorption capacity of U-G for hydrogen and deuterium can be estimated from RDF plots. As can be seen from Fig. 1a, the sharp peak between 3 and 4 Å shows the mean distance between uranium atom and graphene. The result of area calculation of the first peak (about 3.4 Å) in RDF plot shows that 418 uranium atoms were adsorbed on graphene sheet. This means that for the remaining 16 carbon atoms of graphene, only one atom of uranium can be adsorbed. In Fig. 1b, a measure of the surface area of the RDF plot indicates that 2900 D2 molecules (11.75% wt) and 2553 H2 molecules (5.16% wt) are adsorbed on 418 uranium atoms of
(2)
The parameters used for H2, D2, C and U are listed in Table 1. HeH and DeD bond lengths were calculated to be dH-H = 0.741 Å and to dD-D = 0.742 Å, which are in reasonable agreement with the experimental values [53]. Three-dimensional periodic boundary conditions were applied in each direction of the simulation cell. The van der Waals interactions were evaluated within a cutoff length set to the value of 9 Å. The computational unit cell consists of a 50 × 30 × 1 graphene supercell with box size of 13 n × 13 n × 20 n. In order to minimize the interlayer Table 1 Potential parameters for different intermolecular pair interactions [50–52]. pair
Ɛ (eV)
σ (Å)
HeH DeD CeC UeU
0.0031625 0.003033 0.002413 De = 2.273
2.9644 2.9544 3.36945 β = 1.121
r0 = 3.1043
2
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Fig. 1. The RDF plots of (a) uranium adsorption on graphene and (b) H2 (solid line) and D2 (dashed line) adsorption on U-G system at room temperature.
simulation cell. Therefore, the enhanced adsorption of U on graphene can be attributed to the electrostatic attraction between negatively charged graphene and positive charge of U species. Besides, electrostatic repulsion between the positively charged U atoms prevents uranium clustering. Since the charged uranium atoms are the nucleation centers for hydrogen and deuterium adsorption, the available surface area for hydrogen and deuterium storage is increased with increasing U atoms on both sides of the graphene sheet [60–62]. For this reason, the adsorption of two U atoms on both sides of the graphene layer and the most stable configuration for two adsorbed uranium atoms were considered here. As shown in Fig. 3a, there are many different sites for the second U atom to be positioned on the other side of the graphene layer. After geometry optimization of these configurations, we found that the lowest-energy configuration for adsorption of the second U atom belongs to the hollow site of the third ring from uranium decorated ring on opposite side of the previous uranium, as shown in Fig. 3b. The calculated binding energy is about Eb-U = −1.657 eV, and the average Eb-U for two U atoms is −1.415 eV/U. These results are consistent with MD simulations, which the most stable configuration contains two uranium atoms adsorbed by 35 carbon atoms. As shown in Fig. 3b, the most stable adsorption mode occurs when two U atoms are positioned on two carbon hexagons in the opposite sides of graphene layer (indicated by small circles) with an empty honeycomb at the center. Two uranium atoms can be placed on the same side of graphene sheet with three empty honeycombs at the center. However their thermodynamic stabilities are less than “two opposite sides” configuration. In addition, opposite sides are the closest situation, in which two U single atoms can get close without clustering. Negative charge on the carbon atoms screens the repulsive coulomb interaction between the positively charged U atoms on both sides of the graphene plane. As compared with the previous single U atom case, the graphene layer is more negatively charged, and U atoms are less positively charged (the charges of the U and C atoms are given in Fig. 3b). This gives rise to a weaker binding energy of the U atoms on the graphene sheet. Furthermore, d1 is calculated to be 3.303 Å, which is almost the same as that of single side U adsorption mode. The reason is that the charges of U atoms located in two sides of the graphene layer were screened by the charged graphene layer. Meanwhile, the repulsion between the uranium atoms approaches to zero, and the distance
U-G system. This means that 6.941 molecules of D2 and 6.092 molecules of H2 are adsorbed per uranium atom. Fig. 2a–b shows the optimized geometry configuration of six and seven H2 and D2 molecules adsorbed on U-G system, respectively. However, the above results indicate that the system has a rather high hydrogen and deuterium storage capacity at room temperature. Furthermore, density functional theory (DFT) calculations were performed to evaluate the validity of molecular dynamic (MD) simulation and obtain the binding energies of H2 and D2 molecules adsorbed on UG system. 3.2. Density functional theory calculations 3.2.1. Uranium decorated graphene sheet TM atoms basically tend to aggregate into clusters rather than being individually dispersed on nanomaterials because of the large cohesive energy of bulk TMs [58] (for U, the cohesive energy is −4.2 eV/U) [59]. This phenomenon considerably reduces the hydrogen and deuterium storage capacity of uranium. To examine the validity of our simulation based on MD results, a unit cell consisting of 35 C and 1 U atoms was considered. The considered unit cell of graphene with adsorbed uranium was depicted in Fig. 3. The U: C ratio of 1:35 was chosen so that a relatively high storage capacity could be provided. This result ensures that the UeU distance is sufficiently large (at least 7 Å in x and y directions) and prevents clustering of U on graphene. The adsorption site of this decorated graphene was then determined. As can be seen from Fig. 3a, three adsorption positions were analyzed including the hollow site of the carbon hexagon (H), the bridge site of CeC bond (B), and the top site of the C atom (T). The adsorption energy results indicate that the adsorption of U occurs at the lowest energy position, (H site). Thus, the hollow site provides an energy favorable adsorption configuration with a calculated binding energy of −1.173 eV, and the distance between U atom and the graphene sheet, d1, is about 3.308 Å. In Fig. 3, the charge distribution near the adsorbed U atom is estimated using Mulliken analysis. The adsorbed U atom has a positive charge of 0.907 e, and each neighboring C atom possesses a negative charge of −0.082 e. It is also worth noting that the rest of the negative electron charge is provided by participation of other C atoms in the
Fig. 2. Side views of the adsorption configurations of U-G system with (a) six adsorbed H2 and (b) seven adsorbed D2 molecules. Colors represent atoms accordingly: Carbon in gray, Uranium in blue, Hydrogen in white and Deuterium in yellow. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
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Fig. 3. The charges of carbon atoms near the adsorbed U atom in (a) one side U-G system and (b) two sides U-G system, where the unit of charge is one electron charge e, which is not given in the Figure for clarity. In addition, three different sites for a U atom adsorption on graphene were considered. H, B, and T denote the hollow of hexagon, bridge of C-C bond, and top site of C atom, respectively. The gray and blue balls represent C and U atoms, respectively, and dark blue is uranium atom. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
computational method:
between them remains almost unchanged.
1 The vertical distance between H2 molecules and the graphene layer (d2) is 3.852 Å when d1 decreases slightly to 3.305 Å, 2 The adsorption energy for the first H2 molecule (Eb-H2) is calculated to be −0.505 eV, 3 The vertical distance between the D2 molecules and the graphene layer (d2) is 3.630 Å When d1 decreases to 3.219 Å. 4 The adsorption energy for the first D2 molecule (Eb-D2) is −0.600 eV.
3.2.2. Adsorption of H2 and D2 gases on one-sided U-G In order to determine the hydrogen and deuterium adsorption capabilities, we added the considered molecules to the one-sided U-G system, and obtained the optimized configurations. Fig. 6 a-b show the configuration of the first H2 and D2 molecules adsorbed on the 3 × 3 × 1 supercell of single side graphene sheet with adsorbed U atom. The following data are obtained from the aforementioned
Table 2 lists the calculated values of binding energy (Eb), HeH bond length (dH-H) and D-D bond length (dD-D) for one, two, three, four, five, six and seven H2 and D2 adsorbed on U-G system, respectively. As can be seen from this table, with gradual addition of either hydrogen or deuterium on U-G structure, their adsorption energies decrease until the next molecules will no longer adsorb on the U-G sheets. Therefore, we can conclude that the ultimate numbers of H2 and D2 molecules adsorbed on single-side U-G system are six and seven, respectively, which are in reasonable accordance with MD calculations. To gain further insights into the interaction between U atoms and the graphene, PDOS plots of the s, d and f orbitals of U and the s and p orbitals of graphene were analyzed and displayed in Fig. 4. As can be seen from this figure, the d orbital of uranium atom interacts with C atoms at the energy values of 1.95 eV and 0.96 eV, while the s orbital of uranium atom interacts with C atoms at the energy value of −0.1 eV. Therefore, the interaction between U atoms and the pristine graphene at the positions indicated by the dashed lines is very strong because of the large PDOS overlaps, which confirms the high binding of U atom to the graphene sheet. Important to note is that the f orbital of uranium atom remains almost unaltered after adsorption and does not show an overlap with C atom. It indicates that the f orbital does not contribute in the interaction anymore. The PDOS spectra of the adsorbed H2, D2, decorated U, and the C atoms in both H2/U-G and D2/U-G systems are plotted and shown in Fig. 5a and b. Fig. 5a shows the PDOS of the H2/U-G system. The main peak of H2 was located at −8.87 eV, which shows overlapping with
Fig. 4. The PDOS plots of adsorbed U and graphene systems. The Fermi level is set to 0 eV. 4
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Fig. 5. The PDOS plots of adsorbed H2, D2, decorated U, and graphene in (a) H2/U-G and (b) D2/U-G systems. The Fermi level is set to 0 eV.
carbon atoms of graphene. H2 molecule interacts with both the decorated U and the C atoms simultaneously at 1.6 eV (the positions are indicated by the dashed lines). Alternatively, for the D2/U-G system shown in Fig. 5b, the main peak of D2 is located at −7.6 eV, which represents overlap with carbon atoms of graphene. D2 bonds interact with both the decorated U and the C atoms simultaneously at 1.31 eV (the positions are indicated by the dashed lines), implying a strong interaction between D2 and the U decorated graphene. Fig. 6 shows the electron density distribution for the D2/U-G and H2/U-G systems. Note that significant amount of electrons appear in the region between the graphene layer and the adsorbed U atom. It is obvious from these electron density plots that the U atoms are strongly adsorbed on the graphene layer. It was found that the adsorbed D2 molecules were located parallel to the graphene layer, whereas adsorbed H2 molecules tend to be positioned perpendicular towards the graphene layer. This is due to the more affinity of deuterium to substrate than hydrogen. As can be seen from Fig. 5, the difference between peak of the PDOS plot of C atoms and that of D2 molecule is the location of the main peak of graphene (at −7.6 eV), which indicates the stronger interaction between the D2 and C atoms than H2 and C atoms. Also, in Fig. 6, more electronic distribution appears in the region between the D2 molecules and the graphene layer than the H2 molecules and the graphene layer. At the same time, the binding energy of D2 molecule to the U atom is generally more than that of H2 molecule, which is in line with the reports of Abraham (1955) using the heats of formation [47]. These imply that the U-G system possesses stronger ability to attract D2 molecules as compared with the H2 molecules.
Fig. 6. Electron density distributions in the (a) H2+U-G system and (b) D2+UG system (side view).
Table 2 Calculated binding energies per H2 and D2 molecule and bond lengths of hydrogen and deuterium molecules for gradual increase of H2 and D2 molecules on U-G structure at 298 K. n #of H2 per U
Eb (eV/H2)
dH-H (Å)
n #of D2 per U
Eb (eV/D2)
dD-D (Å)
1 2 3 4 5 6 7
−0.505 −0.466 −0.454 −0.433 −0.404 −0.380 −0.101
0.84 0.78 0.82 0.8 0.76 0.84 0.76
1 2 3 4 5 6 7 8
−0.600 −0.559 −0.522 −0.485 −0.450 −0.433 −0.405 −0.025
0.83 0.79 0.81 0.81 0.77 0.84 0.77 0.78
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Table 3 Number of D2 and H2 molecules adsorbed per uranium on one-sided U-G at different temperatures. Tem. (K)
nH2/U
nD2/U
Molar ratio (nD2/nH2)
273 298 373
7 6 5
10 7 5
1.43 1.17 1
[9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
3.2.3. Temperature effect To understand how the ratio of absorption of D2 to H2 is improved at different temperatures, we measured the absorbance of these two gases on U-G at temperatures of 273, 298 and 373 K. The results are listed in Table 3. The results of this table show that D2 adsorption decreases by a slope higher than H2 with increasing temperature. In fact, the molar ratio of adsorbed D2 to H2 at 273 K is greater than that at 373 K, which indicates its suitability for separation.
[20] [21] [22] [23] [24] [25] [26] [27] [28]
4. Conclusions
[29] [30] [31] [32] [33] [34] [35] [36] [37]
In the present study, the combination of MD and DFT simulations was successful to investigate the adsorption of hydrogen and deuterium on U-G surface. The obtained results indicated that apart from the significant tendency of uranium to interact with graphene, the resulted U-decorated graphene-based nanostructures can serve as a highly efficient storage surface for hydrogen and deuterium adsorption. By decreasing the temperature, the amount of D2 adsorption shows a further increase in comparison with H2 adsorption, which can be used to separate these two gases. Therefore, U-G has the potential to be applied as an effective sorbent for the storage of hydrogen and deuterium even on industrial scale because of operational benefits such as excellent sorption capacity and simple operational process (There is no need for pretreatment, modification and immobilization). As a result, we concluded that U-G surface will open a new area and play significant roles in the removal, enrichment of hydrogen and deuterium in the future.
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Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Hydrogen and deuterium adsorption on uranium decorated graphene nanosheets: A combined molecular dynamics and density functional theory study Zahra Ghalamia, Vanik Ghoulipoura,∗, Alireza Khanchib a b
Faculty of Chemistry, Kharazmi University, No. 43, Shahid Mofatteh Ave., Tehran, Iran Nuclear Science and Technology Research Institute, AEOI, P. O. Box 11365/8486, Tehran, Iran
A R T I C LE I N FO
A B S T R A C T
Keywords: Graphene Uranium Deuterium Hydrogen DFT MD
In this study, the combined density functional theory (DFT) and molecular dynamics (MD) simulation methods were carried out to investigate the potential capability of uranium-decorated graphene (U–G) for the separation of deuterium from hydrogen gases. Graphene with hexagonal honeycomb lattice arrangement is suitable for adsorption of individual uranium atoms, with a high binding energy (−1.173 eV) and U-U distance longer than 7 Å. This U-G system has ability to hold up to six H2 (5.16% wt) or seven D2 (11.75% wt) molecules per U atoms. To gain further insights into these interactions, partial electronic density of states (PDOS) and the electron density distribution of the elements were analyzed. The MD results are in reasonable agreement with the results obtained by DFT method. Our calculated results indicate that at room temperature, D2 molecule has higher affinity for U-G system than the H2 molecule. In order to increase the D2 separation factor from H2, the effect of temperature was studied. The results indicated that adsorption ratio of D2 to H2 increases by decreasing the temperature.
1. Introduction In recent years, great attention has been paid to the control of fossil fuels as one of the greatest threats to the environment and public health. New energy resources such as fusion energy seem to play a crucial role in the future. Contrary to fossil fuels, fusion energy has no drawback such as greenhouse effect on the environment. However, an important raw material used for producing fusion energy is deuterium, which is relatively cheap. Furthermore, deuterium tracer applications in medical diagnosis and treatment are of great importance, but the natural content of D2 is only 0.015% [1]. As a result, its separation from other hydrogen isotopes is a critical research subject. The existing methods for the separation of H2 isotopes such as thermal diffusion [2] and cryogenic distillation [3] possess low efficiency and high energy consumption [4–6]. Among the different methods, gas sorption by adsorption in porous materials is considered to be the promising approach. Hydrogen isotopes have common points of similarity, e.g., they have similar chemical properties with only one electron and one proton. Because of large mass differences between hydrogen and deuterium (deuterium is twice heavier than hydrogen), large isotope effects exist in metal-hydrogen systems. The bonding
∗
strength between hydrogen and metal differs slightly due to its mass effect, and equilibrium pressure between hydrogen isotopes is slightly different [7]. Carbon-based nanostructures, such as graphene [8,9], fullerene [10,11], and nanotubes [12] have been reported for solid-state hydrogen storage because of their high specific surface area, fast kinetics, and reversible hydrogen storage etc. Simple carbon nanostructures weakly bind to the H2 molecules [13] and show low H2 adsorption capacity. On the other hand, graphene has opened many opportunities for the development of new materials for hydrogen adsorption and storage due to flexibility in functionalization and modification of surface. Thus, a large number of theoretical studies on doping or surface metal (alkali [14,15]; alkaline-earth [16–18]; transition [19–23]) dispersion have been reported to improve the chemical activity of graphene and graphene-like materials [24,25]. Among these, modification with transition metal (TM) atoms can significantly improve the adsorption energy of hydrogen molecules on graphene [26], This is due to the polarization of H2 molecules by an electric field and/or hybridization of H2 σ or σ* orbitals with TM empty d-orbitals (Kubas type interaction) [27]. In this regard, transition metal (TM) decorated
Corresponding author. E-mail address: [email protected] (V. Ghoulipour).
https://doi.org/10.1016/j.cap.2019.02.011 Received 20 November 2018; Received in revised form 7 January 2019; Accepted 15 February 2019 1567-1739/ Published by Elsevier B.V. on behalf of Korean Physical Society.
Please cite this article as: Zahra Ghalami, Vanik Ghoulipour and Alireza Khanchi, Current Applied Physics, https://doi.org/10.1016/j.cap.2019.02.011
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interaction, a vacuum spacing of 30 Å, along with 6000 H2 and D2 molecules in both sides of graphene layer with 1:1 ratio was set. Each MD simulation was performed in NVT statistical ensemble (constant numbers of atoms N, volume V and temperature T, without external pressure). The time step in our simulations was considered to be 1 fs, and the simulation time t at a specific T was set to 10 ns.
graphene nanostructures have attracted significant attentions. However, the large cohesive energy of TM atoms can simply lead to the aggregation of TMs on graphene. Previous reports demonstrate that the introduction of impurity atoms or vacancies can prevent the TM atoms from formation of clusters, thus increasing the hydrogen storage capacity of graphene [21,28]. The adsorption of some gas molecules on metal oxide based nanoparticles and two-dimensional nanostructures have been investigated in detail [29–33]. Although, of the different hydrogen adsorbent TMs, palladium has received the numerous attention in the past decades [34–38]. Besides, uranium has been widely used for hydrogen isotopes storage [39–45] because of its higher storage capacity per unit volume and higher ability of adsorption in low pressure [46]. On the other hand, due to the higher formation enthalpy of uranium deuteride (−1.40 eV) compared with the uranium hydride (−1.27 eV) [47], it shows a great capability for hydrogen isotopes separations. According to the above-mentioned issues including 1) benefits of graphene nanosheets for gas adsorption 2) improvement the property of graphene through metal decoration and 3) widespread use of uranium in the storage of hydrogen isotopes, this substrate seems to be a good candidate with practical benefits to increase the hydrogen isotopes storage capacity of uranium through increasing surface area with capability of hydrogen/deuterium separation. In the present work, we used MD and DFT methods to calculate the adsorption capability of graphene sheets toward uranium-238 atoms and obtain the most stable configuration of U atoms on graphene sheets. We also examined the adsorption behavior of the resulting material (step 1) onto H2 and D2 molecules.
2.2. Density functional theory The DFT calculations were performed using DMol3 module of Material Studio (MS) Version 8. A double numerical plus polarization (DNP) basis set was used for all the DFT calculations. A polarization pfunction was adopted for all hydrogen atoms in order to correctly estimate the energy values by considering the hydrogen bonding in the system. The B3LYP hybrid method was used, which produces reliable geometries and energies and requires less time and computer resources. There are a large number of theoretical studies in the literature, which demonstrate the suitability of B3LYP in U coordination complexes [54–56]. The k point was set to 20 × 20 × 1 for the (3 × 3 × 1) graphene cell, with box size of 7.4 Å × 12 Å × 20 Å. The hydrogen or deuterium molecules were placed one by one inside the supercell (seven H2 and ten D2). The convergence tolerance of energy was set to 1.0 × 10−6, and that of maximum force was considered to be 1.0 × 10−4 Hartree/Å (1 Hartree = 27.21 eV). As shown in Fig. 3, the supercell contains 35 C atoms. In the optimization process, all atoms are allowed to relax in all calculations. The binding energy of U atoms onto graphene Eb-U is defined as eq. (3).
Eb − U = [EnU − graphene − (Egraphene + n EU )], 2. Computational details
Where EU-graphene, Egraphene, and EU are the total energies of the system with n U atoms adsorbed on the graphene layer, the energy of the pristine graphene layer, and the energy of one U atom in the same slab, respectively. The binding energy of H2 and D2 molecules onto U-G layer Eb-H2 is defined as eq. (4).
2.1. Molecular dynamic The MD simulations were performed with large-scale atomic/molecular massively parallel simulator (LAMMPS) [48] (lammps-16 February 2016) The intermolecular forces for H2, D2 and C are obtained using atom–atom pair potentials, namely Lennard–Jones (LJ) potential (eq. (1)). The Morse potential is the most popular interatomic potential for metals [49]. Zeng and co-worker demonstrated that the Morse function accurately describes the behavior of the uranium, which is valid to the temperature of 1500 K [50], Thus, we employed Morse potential for uranium atoms in this work (eq. (2)). 12
⎡ σij LJ: U (rij ) = 4εij ⎢ ⎛⎜ ⎞⎟ r ⎣ ⎝ ij ⎠
Eb − H 2 = [EiH 2 + U−graphene − (EU − graphene + i EH 2) ]
(4)
where EiH2+U-graphene, EU-graphene and EH2 denote the total energies of the system with i H2 molecules adsorbed, isolated U-adsorbed graphene, and H2 molecule, respectively. 3. Results and discussion
6
σij ⎤ − ⎛⎜ ⎞⎟ ⎥ ⎝ rij ⎠ ⎦
(3)
3.1. Molecular dynamic predictions (1)
Morse: U (r ) = De (e0−2ß(r − r ) − 2e0−ß(r − r ) )
In order to predict the adsorption capacity of the graphene for uranium atom, we measured the radial distribution functions (RDFs) or g (r) for U-G system, (RDFs) which is a main criterion to evaluate the sorption capability of graphene. This parameter gives the probability of finding uranium atoms at a distance of r away from one of carbon atoms of graphene with respect that for a completely random distribution of the same density of uranium atoms [57]. Then, we averaged the RDF values that calculated for each carbon atoms, and plotted the obtained results. The RDF plots for adsorption of uranium on graphene and that of hydrogen/deuterium on U-G system were shown in Fig. 1a–b. The sorption capacity of U-G for hydrogen and deuterium can be estimated from RDF plots. As can be seen from Fig. 1a, the sharp peak between 3 and 4 Å shows the mean distance between uranium atom and graphene. The result of area calculation of the first peak (about 3.4 Å) in RDF plot shows that 418 uranium atoms were adsorbed on graphene sheet. This means that for the remaining 16 carbon atoms of graphene, only one atom of uranium can be adsorbed. In Fig. 1b, a measure of the surface area of the RDF plot indicates that 2900 D2 molecules (11.75% wt) and 2553 H2 molecules (5.16% wt) are adsorbed on 418 uranium atoms of
(2)
The parameters used for H2, D2, C and U are listed in Table 1. HeH and DeD bond lengths were calculated to be dH-H = 0.741 Å and to dD-D = 0.742 Å, which are in reasonable agreement with the experimental values [53]. Three-dimensional periodic boundary conditions were applied in each direction of the simulation cell. The van der Waals interactions were evaluated within a cutoff length set to the value of 9 Å. The computational unit cell consists of a 50 × 30 × 1 graphene supercell with box size of 13 n × 13 n × 20 n. In order to minimize the interlayer Table 1 Potential parameters for different intermolecular pair interactions [50–52]. pair
Ɛ (eV)
σ (Å)
HeH DeD CeC UeU
0.0031625 0.003033 0.002413 De = 2.273
2.9644 2.9544 3.36945 β = 1.121
r0 = 3.1043
2
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Fig. 1. The RDF plots of (a) uranium adsorption on graphene and (b) H2 (solid line) and D2 (dashed line) adsorption on U-G system at room temperature.
simulation cell. Therefore, the enhanced adsorption of U on graphene can be attributed to the electrostatic attraction between negatively charged graphene and positive charge of U species. Besides, electrostatic repulsion between the positively charged U atoms prevents uranium clustering. Since the charged uranium atoms are the nucleation centers for hydrogen and deuterium adsorption, the available surface area for hydrogen and deuterium storage is increased with increasing U atoms on both sides of the graphene sheet [60–62]. For this reason, the adsorption of two U atoms on both sides of the graphene layer and the most stable configuration for two adsorbed uranium atoms were considered here. As shown in Fig. 3a, there are many different sites for the second U atom to be positioned on the other side of the graphene layer. After geometry optimization of these configurations, we found that the lowest-energy configuration for adsorption of the second U atom belongs to the hollow site of the third ring from uranium decorated ring on opposite side of the previous uranium, as shown in Fig. 3b. The calculated binding energy is about Eb-U = −1.657 eV, and the average Eb-U for two U atoms is −1.415 eV/U. These results are consistent with MD simulations, which the most stable configuration contains two uranium atoms adsorbed by 35 carbon atoms. As shown in Fig. 3b, the most stable adsorption mode occurs when two U atoms are positioned on two carbon hexagons in the opposite sides of graphene layer (indicated by small circles) with an empty honeycomb at the center. Two uranium atoms can be placed on the same side of graphene sheet with three empty honeycombs at the center. However their thermodynamic stabilities are less than “two opposite sides” configuration. In addition, opposite sides are the closest situation, in which two U single atoms can get close without clustering. Negative charge on the carbon atoms screens the repulsive coulomb interaction between the positively charged U atoms on both sides of the graphene plane. As compared with the previous single U atom case, the graphene layer is more negatively charged, and U atoms are less positively charged (the charges of the U and C atoms are given in Fig. 3b). This gives rise to a weaker binding energy of the U atoms on the graphene sheet. Furthermore, d1 is calculated to be 3.303 Å, which is almost the same as that of single side U adsorption mode. The reason is that the charges of U atoms located in two sides of the graphene layer were screened by the charged graphene layer. Meanwhile, the repulsion between the uranium atoms approaches to zero, and the distance
U-G system. This means that 6.941 molecules of D2 and 6.092 molecules of H2 are adsorbed per uranium atom. Fig. 2a–b shows the optimized geometry configuration of six and seven H2 and D2 molecules adsorbed on U-G system, respectively. However, the above results indicate that the system has a rather high hydrogen and deuterium storage capacity at room temperature. Furthermore, density functional theory (DFT) calculations were performed to evaluate the validity of molecular dynamic (MD) simulation and obtain the binding energies of H2 and D2 molecules adsorbed on UG system. 3.2. Density functional theory calculations 3.2.1. Uranium decorated graphene sheet TM atoms basically tend to aggregate into clusters rather than being individually dispersed on nanomaterials because of the large cohesive energy of bulk TMs [58] (for U, the cohesive energy is −4.2 eV/U) [59]. This phenomenon considerably reduces the hydrogen and deuterium storage capacity of uranium. To examine the validity of our simulation based on MD results, a unit cell consisting of 35 C and 1 U atoms was considered. The considered unit cell of graphene with adsorbed uranium was depicted in Fig. 3. The U: C ratio of 1:35 was chosen so that a relatively high storage capacity could be provided. This result ensures that the UeU distance is sufficiently large (at least 7 Å in x and y directions) and prevents clustering of U on graphene. The adsorption site of this decorated graphene was then determined. As can be seen from Fig. 3a, three adsorption positions were analyzed including the hollow site of the carbon hexagon (H), the bridge site of CeC bond (B), and the top site of the C atom (T). The adsorption energy results indicate that the adsorption of U occurs at the lowest energy position, (H site). Thus, the hollow site provides an energy favorable adsorption configuration with a calculated binding energy of −1.173 eV, and the distance between U atom and the graphene sheet, d1, is about 3.308 Å. In Fig. 3, the charge distribution near the adsorbed U atom is estimated using Mulliken analysis. The adsorbed U atom has a positive charge of 0.907 e, and each neighboring C atom possesses a negative charge of −0.082 e. It is also worth noting that the rest of the negative electron charge is provided by participation of other C atoms in the
Fig. 2. Side views of the adsorption configurations of U-G system with (a) six adsorbed H2 and (b) seven adsorbed D2 molecules. Colors represent atoms accordingly: Carbon in gray, Uranium in blue, Hydrogen in white and Deuterium in yellow. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
3
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Fig. 3. The charges of carbon atoms near the adsorbed U atom in (a) one side U-G system and (b) two sides U-G system, where the unit of charge is one electron charge e, which is not given in the Figure for clarity. In addition, three different sites for a U atom adsorption on graphene were considered. H, B, and T denote the hollow of hexagon, bridge of C-C bond, and top site of C atom, respectively. The gray and blue balls represent C and U atoms, respectively, and dark blue is uranium atom. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
computational method:
between them remains almost unchanged.
1 The vertical distance between H2 molecules and the graphene layer (d2) is 3.852 Å when d1 decreases slightly to 3.305 Å, 2 The adsorption energy for the first H2 molecule (Eb-H2) is calculated to be −0.505 eV, 3 The vertical distance between the D2 molecules and the graphene layer (d2) is 3.630 Å When d1 decreases to 3.219 Å. 4 The adsorption energy for the first D2 molecule (Eb-D2) is −0.600 eV.
3.2.2. Adsorption of H2 and D2 gases on one-sided U-G In order to determine the hydrogen and deuterium adsorption capabilities, we added the considered molecules to the one-sided U-G system, and obtained the optimized configurations. Fig. 6 a-b show the configuration of the first H2 and D2 molecules adsorbed on the 3 × 3 × 1 supercell of single side graphene sheet with adsorbed U atom. The following data are obtained from the aforementioned
Table 2 lists the calculated values of binding energy (Eb), HeH bond length (dH-H) and D-D bond length (dD-D) for one, two, three, four, five, six and seven H2 and D2 adsorbed on U-G system, respectively. As can be seen from this table, with gradual addition of either hydrogen or deuterium on U-G structure, their adsorption energies decrease until the next molecules will no longer adsorb on the U-G sheets. Therefore, we can conclude that the ultimate numbers of H2 and D2 molecules adsorbed on single-side U-G system are six and seven, respectively, which are in reasonable accordance with MD calculations. To gain further insights into the interaction between U atoms and the graphene, PDOS plots of the s, d and f orbitals of U and the s and p orbitals of graphene were analyzed and displayed in Fig. 4. As can be seen from this figure, the d orbital of uranium atom interacts with C atoms at the energy values of 1.95 eV and 0.96 eV, while the s orbital of uranium atom interacts with C atoms at the energy value of −0.1 eV. Therefore, the interaction between U atoms and the pristine graphene at the positions indicated by the dashed lines is very strong because of the large PDOS overlaps, which confirms the high binding of U atom to the graphene sheet. Important to note is that the f orbital of uranium atom remains almost unaltered after adsorption and does not show an overlap with C atom. It indicates that the f orbital does not contribute in the interaction anymore. The PDOS spectra of the adsorbed H2, D2, decorated U, and the C atoms in both H2/U-G and D2/U-G systems are plotted and shown in Fig. 5a and b. Fig. 5a shows the PDOS of the H2/U-G system. The main peak of H2 was located at −8.87 eV, which shows overlapping with
Fig. 4. The PDOS plots of adsorbed U and graphene systems. The Fermi level is set to 0 eV. 4
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Fig. 5. The PDOS plots of adsorbed H2, D2, decorated U, and graphene in (a) H2/U-G and (b) D2/U-G systems. The Fermi level is set to 0 eV.
carbon atoms of graphene. H2 molecule interacts with both the decorated U and the C atoms simultaneously at 1.6 eV (the positions are indicated by the dashed lines). Alternatively, for the D2/U-G system shown in Fig. 5b, the main peak of D2 is located at −7.6 eV, which represents overlap with carbon atoms of graphene. D2 bonds interact with both the decorated U and the C atoms simultaneously at 1.31 eV (the positions are indicated by the dashed lines), implying a strong interaction between D2 and the U decorated graphene. Fig. 6 shows the electron density distribution for the D2/U-G and H2/U-G systems. Note that significant amount of electrons appear in the region between the graphene layer and the adsorbed U atom. It is obvious from these electron density plots that the U atoms are strongly adsorbed on the graphene layer. It was found that the adsorbed D2 molecules were located parallel to the graphene layer, whereas adsorbed H2 molecules tend to be positioned perpendicular towards the graphene layer. This is due to the more affinity of deuterium to substrate than hydrogen. As can be seen from Fig. 5, the difference between peak of the PDOS plot of C atoms and that of D2 molecule is the location of the main peak of graphene (at −7.6 eV), which indicates the stronger interaction between the D2 and C atoms than H2 and C atoms. Also, in Fig. 6, more electronic distribution appears in the region between the D2 molecules and the graphene layer than the H2 molecules and the graphene layer. At the same time, the binding energy of D2 molecule to the U atom is generally more than that of H2 molecule, which is in line with the reports of Abraham (1955) using the heats of formation [47]. These imply that the U-G system possesses stronger ability to attract D2 molecules as compared with the H2 molecules.
Fig. 6. Electron density distributions in the (a) H2+U-G system and (b) D2+UG system (side view).
Table 2 Calculated binding energies per H2 and D2 molecule and bond lengths of hydrogen and deuterium molecules for gradual increase of H2 and D2 molecules on U-G structure at 298 K. n #of H2 per U
Eb (eV/H2)
dH-H (Å)
n #of D2 per U
Eb (eV/D2)
dD-D (Å)
1 2 3 4 5 6 7
−0.505 −0.466 −0.454 −0.433 −0.404 −0.380 −0.101
0.84 0.78 0.82 0.8 0.76 0.84 0.76
1 2 3 4 5 6 7 8
−0.600 −0.559 −0.522 −0.485 −0.450 −0.433 −0.405 −0.025
0.83 0.79 0.81 0.81 0.77 0.84 0.77 0.78
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Table 3 Number of D2 and H2 molecules adsorbed per uranium on one-sided U-G at different temperatures. Tem. (K)
nH2/U
nD2/U
Molar ratio (nD2/nH2)
273 298 373
7 6 5
10 7 5
1.43 1.17 1
[9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
3.2.3. Temperature effect To understand how the ratio of absorption of D2 to H2 is improved at different temperatures, we measured the absorbance of these two gases on U-G at temperatures of 273, 298 and 373 K. The results are listed in Table 3. The results of this table show that D2 adsorption decreases by a slope higher than H2 with increasing temperature. In fact, the molar ratio of adsorbed D2 to H2 at 273 K is greater than that at 373 K, which indicates its suitability for separation.
[20] [21] [22] [23] [24] [25] [26] [27] [28]
4. Conclusions
[29] [30] [31] [32] [33] [34] [35] [36] [37]
In the present study, the combination of MD and DFT simulations was successful to investigate the adsorption of hydrogen and deuterium on U-G surface. The obtained results indicated that apart from the significant tendency of uranium to interact with graphene, the resulted U-decorated graphene-based nanostructures can serve as a highly efficient storage surface for hydrogen and deuterium adsorption. By decreasing the temperature, the amount of D2 adsorption shows a further increase in comparison with H2 adsorption, which can be used to separate these two gases. Therefore, U-G has the potential to be applied as an effective sorbent for the storage of hydrogen and deuterium even on industrial scale because of operational benefits such as excellent sorption capacity and simple operational process (There is no need for pretreatment, modification and immobilization). As a result, we concluded that U-G surface will open a new area and play significant roles in the removal, enrichment of hydrogen and deuterium in the future.
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