Li-functionalized Carbon Nanotubes for Hydrogen Storage

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Cite This: ACS Appl. Nano Mater. 2019, 2, 3021−3030

Li-Functionalized Carbon Nanotubes for Hydrogen Storage: Importance of Size Effects Ekaterina Anikina,†,‡ Amitava Banerjee,*,§ Valery Beskachko,‡ and Rajeev Ahuja†,§ †

Materials Theory Division, Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden Institute of Natural Sciences and Mathematics, South Ural State University, 76, Lenin Prospekt, Chelyabinsk 454080, Russia § Applied Materials Physics, Department of Materials and Engineering, KTH Royal Institute of Technology, S-100 44 Stockholm, Sweden Downloaded via UNIV OF SOUTHERN INDIANA on July 20, 2019 at 20:17:28 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: We investigated Li-doped carbon nanotubes (CNTs) as a promising hydrogen storage media. In this computational model, we considered isolated lithium atom adsorbed on a CNT wall as an adsorption site for hydrogen. We focused on the influence of size effects on the structural and energetic characteristics of CNT(n,n)@Li+kH2 complexes where n = 5, 7, 9; k = 1, ..., 6; Nc = 4, 5, 6 (Nc is translation length of CNT, expressed in terms of a number of CNT unit cells). We proved that modeled CNT length substantially influences internal sorption of Li and hydrogen on the narrow tube (5,5), which subsequently alters the adsorption energies of H2 molecules and causes the deformation of the carbon framework. Moreover, the size effects are not pronounced in the case of external sorption for all considered CNT translation lengths and diameters. We have not observed any noticeable qualitative difference between internal and external hydrogen sorption in the nanotube wider than CNT(5,5). In the case of external adsorption on all considered nanotubes, doping with Li increases hydrogen adsorption energies of up to four H2 molecules by 100 meV in comparison with pure CNTs. And the local density approximation estimations (∼250 meV/H2) of adsorption energy on Li-decorated CNTs exceed the lowest requirement proposed by the U.S. Department of Energy (200 meV/H2). In the case of internal sorption on Li-functionalized tubes, the generalized gradient approximation also gives hydrogen adsorption energies in the desired range of 200−600 meV/H2. However, steric hindrances could prevent sufficient hydrogen uptakes (less than 2 wt % inside CNT(5,5)). We believe that our findings on the size effects are important for estimation of CNT’s hydrogen storage properties. KEYWORDS: carbon nanotubes, hydrogen adsorption, Li-functionalization, DFT, periodic boundary condition

1. INTRODUCTION

specified target (6.5 wt %) for room temperature applications.13 This happens because of insufficiently strong van der Waals interactions between H2 molecules and pure CNT surfaces in the case of physisorption.14 Room-temperature reversible sorption−desorption cycles can be obtained when the adsorption energy per one hydrogen molecule, Ebind, falls in the range of 200−600 meV, 15 which is in between chemisorption and physisorption. Therefore, it is necessary to tune this Ebind, which can be achieved by forming more active adsorption sites on CNT surface, for example, through metal atom decoration.16−25 Previously, we showed that doping CNTs with Li atom increases the adsorption energy of H2 molecule for single molecule adsorption, and the Ebind of the hydrogen molecule

Compact, safe, and efficient hydrogen storage remains one of the problems to solve on the way to ecofriendly hydrogen economy. Among the thoroughly investigated candidates for such storages are carbon-based nanomaterials (graphene and its allotropic forms, templated carbons, carbon nanotubes, carbon aerogel, etc.) due to their low density, porosity, high thermal and chemical stability, the simplicity and low cost of production.1 More details on the properties and hydrogen storage performance of carbon-based nanomaterials as well as hydrogen adsorption mechanisms (such as chemisorption, physisorption, spillover, etc.) could be found in thorough reviews2,3 Out of these materials, carbon nanotubes (CNTs) have also superior mechanical, unique electrical, and capillary features, having drawn researchers’ attention for a long time.4,5 However, both experimental6−10 and theoretical11,12 investigations showed that the amount of molecular hydrogen adsorbed by pure CNTs is inadequate to achieve the U.S. DOE © 2019 American Chemical Society

Received: March 4, 2019 Accepted: May 3, 2019 Published: May 3, 2019 3021

DOI: 10.1021/acsanm.9b00406 ACS Appl. Nano Mater. 2019, 2, 3021−3030

Article

ACS Applied Nano Materials

Figure 1. Relaxed geometry and charge difference isosurfaces (0.0025e) of the complex CNT(5,5)@Li (Nc = 4): (a) cross section and (b) side view of internally sorbed Li atom; (c) cross section and (d) side view of externally sorbed Li atom. Carbon and Li atoms are represented as gray and green color balls, respectively. Yellow and cyan regions depict depletion and accumulation of charge density, respectively. All structure pictures were obtained using VESTA 3 software package.30

adsorbed inside the nanotube is in the desirable range.26 However, the hydrogen uptake of a CNT@Li-based material could be accessed once we defined the maximum H2 binding capability of the Li adatom. To be more precise, we need to know the structural and energetic characteristics of CNT@Li +kH2 complexes, k = 1, 2, ..., kmax, where kmax is the maximum quantity of H2 molecules. However, with modeling extended structures without translation symmetry, we can run into issues connected with periodic boundary conditions (PBCs). This problem is a result of size effects, i.e., the dependence of model characteristics on the simulated cell size (CNT radius and translational length in our case). These effects originate from spurious interactions of symmetry-breaking objects (like a complex of Li adatom and hydrogen molecules around it) with its images. Hunt et al.27 investigated the case when such objects are structural defects of a nanotube. They showed that in defect energy calculations, size effects are considerable even for very big simulation cells, which have too many atoms for ab initio modeling with reasonable calculation time. Sozykin et al.28 discussed the role of size effects in adsorption energy assessment of Li atoms located near CNT structural defects. They demonstrated that in that case, size effects are not so pronounced, which allowed the researchers to use much smaller simulation cells. However, the importance of these size effects in the case of CNT@Li+kH2 complexes is not clear yet. We expect that size effects may display themselves differently for external and internal adsorption of molecular hydrogen. And they could be more distinct during internal sorption on nanotubes with a small radius, where the steric hindrances could cause the

elongation of hydrogen complex along the CNT axis. As far as we know, quantitative investigation of this effect has not yet been completed. However, it is essential to understand the feasibility of applying the complexes mentioned above for hydrogen storage. All these facts certainly motivate us to study the dependence of hydrogen adsorption energy on simulation cell size and to define the optimal CNT translation length, which will be a compromise between the calculation accuracy and computational expenses.

2. COMPUTATIONAL METHODS Throughout this work we consider the armchair carbon nanotubes (pure and Li doped on internal and external surfaces; see Figure 1) with indexes (n, n), n = 5, 7, 9 and diameters 6.75, 9.46, and 12.20 Å, respectively. Unit cells of these tubes contain ncell(n) = 4n atoms. So CNT fragments that are modeled with PBC should consist of Ncalc atoms per simulation cell: Ncalc = Ncncell, where Nc is the number of CNT unit cells in a model. For nanotubes (5,5), (7,7), and (9,9) ncell = 20, 28, and 36, respectively. To determine the dependence of adsorption energies on CNT translational length, we have considered CNT(5,5) and CNT(7,7) models with Nc = 4, 5, 6. At distances for less than four CNT unit cells, we cannot neglect the spurious interaction between Li atom and its image.29 Hence, the size of chosen models (with Li and H2 molecules) does not exceed two hundred atoms. In the case of Li-functionalized CNTs hydrogen molecules were at the same side of a nanotube as the Li atom. We have performed first-principles DFT based spinpolarized electronic structure calculations as implemented in 3022


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ACS Applied Nano Materials the open source SIESTA suite.31,32 The local density approximation, LDA (Ceperley−Alder functional33), and the generalized gradient approximation, GGA (Perdew−Burke− Ernzerhof functional34), have been employed as the exchange− correlation functional to obtain the ground state structure. These exchange−correlation approximations do not describe van der Waals (vdW) interactions, which could further tune the binding of hydrogen to CNT@Li complex, although LDA and GGA overestimate and underestimate the absolute value of dispersion contribution, respectively.35 Indeed, the calculations based on more accurate (but computationally expensive) methods showed that the adsorption energy of a hydrogen molecule on carbon-based structures (graphene and benzene molecule) lies between GGA and LDA results.36 We also performed hydrogen adsorption energies calculations for pure and Li-doped CNT(7,7) with Nc = 4 with Grimme37 DFT-D2 corrections (see Table S1). The obtained results are close to the LDA estimations; therefore, we believe that by using only GGA and LDA approximations, it is possible to find the similar trends, independent of a choice of approximation. All the pseudopotentials have been taken from the FHI pseudodatabase.38 The full structural relaxation of structures mentioned above has been achieved with the conjugategradient method (the force convergence criterion is 10−4 Ry/ bohr). We optimized double-ζ polarized basis set39,40 for atoms in our models. The orbital cutoff radius for 1s H, 2s C, and 2p C is ∼6.0, 8.0, and 10.0 bohr, respectively, and SplitNorm is approximately 0.50, 0.30, and 0.25, respectively. For Li, these parameters are close to the default. The mesh cutoff39 is 360 and 210 Ry for GGA and LDA calculations, respectively, and the 1 × 1 × 32 Monkhorst−Pack set of kpoints have been considered to calculate adsorption energies within a numerical precision of ∼7 meV. Before hydrogen sorption modeling we have calculated the equilibrium translation parameter of all basic structures (pure CNT and CNT@Li with all considered Nc) by total energy minimization. For GGA (LDA) calculations these equilibrium distances are 9.87 Å (9.79 Å), 12.34 Å (12.23 Å), and 14.80 Å (14.67 Å) for Nc = 4, 5, and 6, respectively. In nonperiodic directions we put not less than 100 Å.

Table 1. Binding Energy (meV) of Single Hydrogen in Molecule on External (Eext bind) and Internal (Ebind) Surfaces of CNT(5,5) and CNT(5,5)@Li CNT(5,5) Einbind

Eext bind

Einbind

Nc

GGA

LDA

GGA

LDA

GGA

LDA

GGA

LDA

4 5 6

47 48 48

138 142 141

263 263 263

473 473 473

142 144 145

246 247 247

274 273 274

508 508 509

LDA). Calculated Ebind for CNT(5,5)@Li agrees with the previously reported similar complexes.41−43 Table 1 shows that for both Li-doped and pure CNT, the Ebind is always higher in LDA than in GGA. Moreover, the Ebind of the internal adsorption is much higher than that of the external adsorption. To get insight into these findings, we carried out further analysis, as shown in Table 2. In Table 2, Table 2. Differences in Ebind (meV) Induced by (I) Choice of Approximation LDA/GGA, (II) Li Doping, (III) Sorption Surface Curvature Sign (I) LDA vs GGA CNT(5,5) ΔEext L‑G 91−94

CNT(5,5)@Li ΔEinL‑G

ΔEext L‑G

ΔEinL‑G

210 102−104 (II) CNT(5,5)@Li vs CNT(5,5) ΔEext LDA

ΔEext GGA 95−97

234−235

ΔEinGGA

ΔEinLDA

105−108 10−11 (III) Internal vs External

35−36

CNT(5,5)

CNT(5,5)@Li

ΔEin‑ext GGA

ΔEin‑ext LDA

ΔEin‑ext GGA

ΔEin‑ext LDA

215−216

331−335

129−132

261−262

in ΔEext L‑G (ΔEL‑G) is the difference between LDA- and GGApredicted binding energy for external (internal) sorption; ext ΔEext GGA (ΔELDA) is the difference of GGA-predicted (LDAin predicted) Eext bind for Li-doped and pure CNT (similarly, ΔEGGA in in‑ext in‑ext and ΔELDA for internal sorption); and ΔEGGA (ΔELDA ) is the difference between GGA-predicted (LDA-predicted) Einbind and Eext bind. The range of values in the Table 2 actually suggests the limits in which the calculated energy difference changes depending on the choice of Nc. Table 2 indicates that ΔEL‑G significantly depends on the curvature sign of the sorption surface (ΔEinL‑G is 2 times higher than ΔEext L‑G), whereas addition of Li atom changes the ΔEL‑G by only 10% with respect to pure CNT. Moreover, the differences in the Ebind with and without Li adatom for both approximations of the exchange−correlation functional are in the comparable range (∼100 meV for external sorption and ∼10−40 meV for internal sorption). Therefore, from the application point of view, the internal CNT surface is more promising than external based on the ΔEin‑ext value, which again strongly depends on the choice of the exchange− correlation approximation and the presence of Li atom. However, despite the adsorption energy differences mentioned above, with the given calculation accuracy in all considered structures there is no visible effect of the structure size as assessed by parameter Nc. Therefore, in all cases (external/internal adsorption, pure/doped CNTs) we could

3. RESULTS AND DISCUSSION 3.1. Adsorption of Single Hydrogen Molecule on Pure CNT(5,5) and CNT(5,5)@Li. First, we studied the influence of translation length on the binding energy of single H2 molecule outside and inside a pure and a Li-doped nanotube (5,5). The hydrogen binding energy Ebind was calculated as E bind = Eframe + E H2 − Eframe + H2

CNT(5,5)@Li

Eext bind

(1)

where Eframe+H2 is the total energy of the complex (CNT(5,5)+H2 or CNT(5,5)@Li+H2), Eframe is the total energy of the same complex without hydrogen, and EH2 is the total energy of H2 molecule. Note the “reverse” order in eq 1, which means if Ebind > 0, the hydrogen molecule attracts to the adsorbent, and the bigger is the Ebind, the stronger is this binding. Subsequently, if Ebind < 0, the hydrogen molecule repels from the adsorbent. Table 1 depicts the Ebind for all in considered cases, such as external (Eext bind) and internal (Ebind) adsorption on pure CNT(5,5) and CNT(5,5)@Li with both approximations of exchange−correlation functional (GGA and 3023


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Figure 2. Relaxed geometry of the complex CNT(5,5)@Li+6H2 (external sorption, Nc = 4) from which hydrogen molecules were desorbed: (a) side and (b) cross-section views. Carbon atoms are gray, Li atoms are green, and hydrogen atoms are red.

with consequent structural optimization at every step (the translation length was fixed). If the binding energy of the removed H2 molecule, ELi bind, is higher than the adsorption energy of H2 molecule on a pure CNT, Epure bind, we regarded this molecule as a part of a Li-associated hydrogen complex. For the minimal system size, Nc = 4, we considered all symmetrically nonequivalent positions of removed H 2 molecules at each step, and for the next step, we chose the structure with the lowest total energy as the initial configuration. As a result, we found the “optimal” desorption pathway of hydrogen. In the case of Nc = 5 and 6, for every k we considered only the hydrogen configurations chosen as “optimal”. The adsorption energy of H2 molecule is calculated by using the following formula:

model CNT fragments of minimal possible length by choosing, for example, Nc = 4 for small adsorption complexes with a single H2 molecule. 3.2. External Sorption of Several Hydrogen Molecules on CNT(5,5)@Li. We observed that the behavior of a hydrogen complex of minimal size does not change with an increase of the translation parameter. However, a rise in the number of hydrogen molecules in the structure CNT(5,5)@Li +kH2 could cause the elongation of the hydrogen complex along the CNT axis, and for the correct description of hydrogen complex characteristics we will need a bigger translation length. To investigate this issue, we modeled the external and internal sorption of several H2 molecules. Initial configurations for bigger complexes are constructed as follows. During test calculations, we found that with the increase of hydrogen molecules to k = 3−4, these molecules are arranged symmetrically around the Li atom. This arrangement could be the result of the symmetric Coulomb potential of Li+ ions (Figure 1), since the Li atom, when adsorbed on CNT surface, donates almost all its valence electron to the tube.29 Thus, for k ≥ 5 we considered symmetrical starting configurations where the H2 molecules are located compactly near the Li adatom. However, structural optimization of a few initial configurations for k = 6 (as shown in Supporting Information) resulted in the spread of hydrogen onto the nanotube. So some H2 molecules are no longer geometrically close to Li as shown in Figure S1 and S2; i.e., the adatom did not influence these molecules significantly. For example, the starting configuration of hydrogen molecules, arranged in an almost regular hexagon around Li (G configuration), transferred to configuration S+2 after optimization, where a Li atom is in the center of a square formed by four H2 molecules, while the other two H2 molecules are located symmetrically in Li second neighbor’s sphere as shown in Figure S1. Similarly, another initial configuration, in which four hydrogen molecules were located around a lithium atom in one plane, and two on top of Li (R +2u), subsequently evolved to configuration R+2 (Figure S2), where the Li atom is in the rhomb center, and two “upper” H2 molecules are closer to the nanotube surface and farther from the Li atom. Configuration P+1, where five hydrogen molecules almost form a regular pentagon and one molecule is on top of Li (as shown in Figure 2), turned out to be the most energetically favorable. Also, its geometry remains the same after the optimization. Hence, we chose this configuration for further analysis of external sorption. Subsequently, hydrogen desorption was simulated by removing hydrogen molecules one by one from k = kmax = 6,

E bind = −Ek + Ek − 1 + E H2

(2)

where Ek is the total energy of a CNT(5,5)@Li+kH2 complex with k adsorbed hydrogen molecules and EH2 is the total energy of hydrogen molecule. Note again the “reverse” order of terms, as in eq 1 (here, positive Ebind also stands for attraction). The dependencies of H2 molecule adsorption energy on the hydrogen complex size k (on “optimal” desorption pathway) are depicted in Figure 3. Figure 3 shows that the predicted adsorption energies are not influenced by the model size Nc at all k. However, the Ebind substantially depends on the choice of exchange−correlation

Figure 3. Binding energies of H2 molecules externally adsorbed on CNT(5,5)@Li with Nc = 4 (gray bars), 5 (red bars), and 6 (green bars). GGA and LDA results are drawn as net pattern and solid color, respectively. Adsorption energies on pure CNT are noted as solid lines (for both GGA and LDA). 3024


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Figure 4. Starting configurations of the complex CNT(5,5)@Li+6H2 (internal sorption) after geometry optimization. (a) Cross section and (b) side view of configuration I with deformation energy of CNT@Li Edef = 101 (94) meV; 2a = 7.09 (7.14) Å, 2b = 6.51 (6.60) Å, e = 0.39 (0.38). (c) Cross section and (d) side view of configuration II with deformation energy of CNT@Li Edef = 95 meV; 2a = 7.08 Å, 2b = 6.58 Å, e = 0.37. (e) Cross section and (f) side view of configuration III with deformation energy of CNT@Li Edef = 120 (104) meV; 2a = 7.08 (7.12) Å, 2b = 6.52 (6.61) Å, e = 0.39 (0.37). GGA results are noted in parentheses. Nc = 4.

comparison with the Ebind of hydrogen molecules on pure CNT(5,5), which agrees with the previous results for CNT(8,0)@Li.44,45 Thus, four CNT unit cells are sufficient for modeling sorption on the external surface of CNT(5,5) and nanotubes with a bigger radius. Further increase of nanotube translation length does not change hydrogen adsorption energies in the considered complexes. 3.3. Internal Sorption of Several Hydrogen Molecules on CNT(5,5)@Li. Similar methodology (as for external sorption) was followed. However, in this case, hydrogen molecules could not exit the CNT(5,5) inner cavity. Because of PBC, “endless” tubes were simulated, in which molecular

approximation. In particular, these approximations estimate the maximal size of Li-associated hydrogen complex, kmax, based on pure pure the criterion ELi bind > Ebind (Ebind is taken from Table 1 and represented as horizontal lines on Figure 3) differently. In GGA kmax = 4−5, and in LDA kmax = 6 (additional LDA calculations demonstrated that binding energy of seventh hydrogen molecule was 85 meV, which is considerably less than Epure bind). This fact can be explained by GGA/LDA specifics in vdW interaction description, as mentioned previously. Still, in both approximations, only four hydrogen molecules show a notable increase in binding energies in the presence of the Li atom. The mean adsorption energy of the four last H2 molecules rose by ∼168% in GGA and by ∼75% in LDA in 3025


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ing to Nc = 4, is too small for six hydrogen molecules, which are forced by PBC to spread over the nanotube cavity. To check this speculation, we have performed calculations for bigger models with Nc = 5, 6. The dependence of Edef on Nc is shown in Figure 5, which demonstrates that with higher Nc,

hydrogen cannot leave through the absent nanotubes edges or nanotube’s wall due to the high potential barrier.46 Starting complexes of CNT(5,5)@Li+6H2 were constructed in the same way as in the case of external adsorption. The minimum energy configuration was confirmed by considering several symmetrical configurations of hydrogen molecules, namely, G, R+2u, and P+1, which after the geometry relaxation in LDA transformed into configurations I, II, and III, respectively. The first two structures (Figure 4a−d) have similar total energies (with a minor difference of 17 meV). However, the energy of III (Figure 4e,f) is higher than the energy of II by 241 meV, so we excluded it from consideration. In GGA simulations, configuration II does not form, and both starting complexes G and R+2u transformed to configuration I. Moreover, configuration III has the same geometry as in LDA, and its total energy is higher than the energy of I by 250 meV. Therefore, again, for GGA calculations with Nc = 5, 6 we did not consider configuration III. Further, we considered configurations I and II with LDA in more detail. Parts a−d of Figure 4 show a similar distribution of H2 molecules over lithium coordination spheres. The crosssection views (Figure 4a,c) depict that six hydrogen molecules are arranged into two groups of three molecules, whereas the side views (Figure 4b,d) show that those molecules are extended along the tube axis and located symmetrically with respect to it. The distance between the two opposite edge H2 molecules is ∼8.3 Å, which is close to the translational length of the tube (∼8.56 Å). This means that for Nc = 4 the complex Li+6H2 has the maximal size compatible with the PBC. Moreover, configurations I and II differ by the position of the Li atom with respect to the neighboring hydrogen molecules. This fact could indicate that Li plays a less important role than steric constraints of carbon frameworks during the formation of Li+6H2 complex inside the tube. Subsequently, with the removal of two H2 molecules, both configurations have been transformed to the same CNT@Li +4H2 complex. Therefore, for LDA calculations on longer tubes, we have purposely chosen configuration I as the same geometry for the corresponding complex was predicted with GGA approximation. The CNT of configuration I (Figure 4a,b) has been deformed slightly during relaxation with both LDA and GGA. This deformation could be quantified by fitting the cross section of the tube with an ellipse. In GGA, the ellipse major and minor axes are 2a ≅ 7.14 and 2b ≅ 6.60 Å, respectively, and its eccentricity is e = (1 − (b/a)2)1/2 ≅ 0.38. With LDA, the deformation is almost the same: e ≅ 0.39. We have calculated the energy of hydrogen-induced deformation by using the following formula: Edef = E0tot − Etot, where E0tot is the total energy of the relaxed complex CNT(5,5)@Li, and Etot is the total energy of the same complex with the geometry obtained (without relaxation) by removing only the H2 molecules from the ground state structure of CNT(5,5)@Li +6H2. For Nc = 4 we have obtained Edef ≅ 0.1 eV in both approximations of the exchange−correlation functional. In configuration I, the major axis of the elliptic cross section lies in the plane of H2 molecules centers as shown in Figure 4a. Moreover, for Nc = 4, this elliptic fitting of the tube cross section is valid throughout the whole tube length (not only centered at Li position) with roughly the same eccentricity, which indicates again the main role of hydrogen (not lithium) in CNT deformation. Deformation uniformity could also be connected with the fact that translational length, correspond-

Figure 5. Dependence of CNT@Li deformation energy (induced by presence of six H2 molecules) on the number of CNT unit cells Nc.

this hydrogen-induced CNT deformation is almost negligible with both approximations. It is possible that this deformation could be localized, but even Nc = 6 is not enough to consider the Li+6H2 as an isolated complex. Figure 6a shows Ebind of hydrogen molecules calculated by using eq 2 in the case of internal adsorption on CNT(5,5)@Li with Nc = 4, 5, 6. Similar to the external sorption, LDA predicts significantly larger values of Ebind than GGA. Moreover, in LDA, Ebind(k) > 0 for all considered k and Nc, whereas in GGA, this inequality is fulfilled for k ≤ 3 (Nc = 4) and k ≤ 4 (Nc = 5). For k = 6, Ebind < 0 for all considered values of Nc, as shown in Figure 6a. All this means that the considered systems can adsorb no more than 2.42 wt % (with LDA estimation for six hydrogen molecules and Nc = 4) or even 1.36 wt % (with GGA estimation for five hydrogen molecules and Nc = 6). It is quite interesting to see that in GGA, the inner surface of CNT(5,5) with Nc = m is able to adsorb only m − 1 H2 molecules (for mth molecule Ebind(m) < 0). The corresponding H2 gravimetric density GDH could be estimated as GDH =

2WH(m − 1) 2m − 2 = ncellWCm + WLi + 2WH(m − 1) 122m + 1 (3)

which in the m → ∞ limit gives 1.64 wt % (here W represents the corresponding atomic weight, ncell = 20, the number of carbon atoms in the CNT(5,5) unit cell). For larger amounts of hydrogen, internal sorption is energetically unfavorable from a GGA point of view. Even lower numbers of hydrogen molecules have adsorption energies of 200−600 meV per molecule, which corresponds to the gravimetric density of the order of 1.6 wt % with LDA estimation for k = 4 and Nc = 4 and 1.3 wt % with GGA estimation for k = 4 and Nc = 5. Finally, Figure 6a indicates that the presence of the Li adatom does not substantially influence hydrogen adsorption as the Ebind for k = 1−3 (nearest neighbors of Li) exceeds Epure bind only by around 8% in LDA and by 4% in GGA. From the above discussion we can conclude that the considerable differences between external and internal hydrogen sorption on Li-doped CNT(5,5) arise from the high curvature of CNT surface and small specific (per unit length) volume. We can expect that with a decrease in curvature, some 3026


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another geometrical parameter, diameter, could also play an important role. To clarify this point, we modeled hydrogen desorption following the procedure mentioned above for CNT(7,7) (both pure and with externally adsorbed Li atom) and for CNT(9,9) (pure and with Li atom, adsorbed on external and internal surfaces of the nanotube). For all nanotubes we took the minimal system size, Nc = 4, as mentioned above. Results of these calculations are presented in Figure S3. Figure S3 shows that in the case of external adsorption on both CNT(7,7)@Li and CNT(9,9)@Li the energetic characteristics of hydrogen complex are similar to the considered case of external sorption on CNT(5,5)@Li. And internal sorption on CNT(9,9)@Li is similar to that on CNT(7,7)@Li. Calculated Ebind for CNT(7,7)@Li and CNT(9,9)@Li agrees with the previously reported similar complexes.47−49 To compare hydrogen adsorption energies, we plotted Ebind in case of external and internal sorption on CNT(n,n) and CNT(n,n)@Li, where n = 5, 7, 9 and Nc = 4 (Figure 7). For

Figure 6. Binding energies of H2 molecules internally adsorbed on (a) CNT(5,5)@Li and (b) CNT(7,7)@Li complexes with Nc = 4 (gray bars), 5 (red bars), and 6 (green bars). GGA and LDA results are drawn as net pattern and solid color, respectively. Adsorption energies on pure CNT are noted as solid lines (for both GGA and LDA).

Figure 7. Dependence of hydrogen adsorption energy on CNT diameter in the case of (a) external and (b) internal sorption. Red rhombic and black square symbols represent GGA and LDA results, respectively. Filled and empty symbols represent the case of Lifunctionalized and pure CNTs, respectively.

of the narrow tube size effects would reduce or even disappear. To evaluate this hypothesis, we repeated the calculations of internal hydrogen sorption on the nanotube (7,7). Its radius is 1.4 times larger than that of CNT(5,5), and volume is 2 times larger. Figure 6b proves that, eventually, with CNT(7,7) all dependencies of hydrogen binding energies on nanotube’s length disappeared for all considered k, regardless of the choice of exchange−correlation approximation. The CNT deformation energies for all considered translational lengths do not exceed 30 meV in GGA and 22 meV in LDA, which indicates lower hydrogen-induced structural changes than in the case of CNT(5,5). Moreover, the values of the Ebind are noticeably reduced in comparison with CNT(5,5): for small k by 50 meV in GGA and by 100 meV in LDA. But now an increase in adsorption energies from the Li adatom was seen for all k in LDA and for k ≤ 3 in GGA, since for small k, the Ebind exceeds Epure bind by ∼30% in LDA and by ∼50% in GGA. Predicted Ebind in LDA landed within the desirable energy range for all investigated k, whereas the same was only true for k ≤ 3 in GGA. 3.4. Dependence of H2 Adsorption on CNT Diameter. In the previous section we showed that the length of a modeled CNT fragment considerably influences hydrogen adsorption energies in the case of a narrow nanotube (5,5). But

pure tubes we took adsorption energy of a single hydrogen molecule. And for Li-functionalized nanotubes we took average adsorption energy for k = 3, as previously we showed that Li atom influences not less than three H2 molecules in all investigated cases. Figure 7a shows that for all considered CNT radii hydrogen adsorption energies behave similarly in terms of the nearly equal difference between LDA and GGA predictions, as well as between pure and Li-doped nanotubes (in all cases Li atom increases Ebind by ∼100 meV in both GGA and LDA). With the rise of CNT radius adsorption energies slightly increase, but GGA predictions even for Li-functionalized CNT(9,9) with the largest considered diameter are still lower than the desired energy range of 200−600 meV per H2 molecule. However, LDA values are quite optimistic for all investigated Li-doped nanotubes. Furthermore, GGA estimations of Ebind in case of external adsorption on pure nanotubes are close to the experimental value of ∼60 meV/H2 molecule obtained on unopened CNTs.50 We estimated hydrogen uptakes in terms of gravimetric density (GD), assuming the LiC6 coverage of a nanotube, as well as the fact that a single Li atom adsorbs three H2 molecules, as follows: 3027


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ACS Applied Nano Materials GD =

[ ncell

6[ ncell 6 ]WH n 6 ]WLi + ncell WC + 6[ cell 6 ]WH

adsorption energies of hydrogen molecules also depend more on the nanotube’s curvature, i.e., the adsorption energies inside CNT(5,5) are much bigger than outside. (III) The distinct differences in the external and internal adsorption on CNT(5,5) originate from the tube’s curvature. Modeling of internal adsorption on CNT(7,7) and CNT(9,9) confirmed this fact. In wider tubes, Epure bind is considerably lower than on CNT(5,5) (and slightly decreases with the rise of a nanotube’s diameter), and the Li adatom increases adsorption energies of hydrogen complexes with k = 3−4 by around 100 meV, as in the case of external sorption. And similar to the adsorption outside the tube, the adsorption energies do not considerably depend on the tube’s length. So the diameter of CNT(5,5) lies on the border separating narrow tubes with pronounced steric hindrances from wide tubes, where the parameters of internal sorption of the considered complexes are similar to external adsorption. These findings lead us to the conclusion that to correctly model the behavior of large adsorption complexes inside the narrow CNT with PBC, we need to consider quite extended fragments of a nanotube. LDA predictions of hydrogen Ebind in the case of external adsorption of Li-doped CNTs of all considered diameters exceed the lowest DOE requirement of 200 meV/H2. In these cases, theoretical estimations of hydrogen uptake (LiC6 coverage) are greater than 10 wt %, which is bigger than the DOE target by 1.5 times. Moreover, though adsorption energies of hydrogen inside considered nanotubes land within the desirable range for both GGA and LDA, steric hindrances could prevent the implantation of sufficient amount of H2 even inside wide CNTs (like in the case of CNT(5,5)). This could result in internal surface of these nanotubes (both pure and Li-doped) being unsuitable for practical applications.

(4)

where brackets stand for a round number. We obtained 12.2, 11.8, and 13.3 wt % for n = 5, 7, and 9, respectively. All these estimations exceed considerably the ultimate DOE target of 6.5 wt %. However, we got the size of hydrogen complex significantly influenced by Li atom (approximately three H2 molecules per Li) only in the case of isolated Li+3H2 complexes. Interactions of hydrogen molecules in the case of dense Li distribution on a CNT surface could drastically change the resulting hydrogen uptake. To obtain the precise values, further investigations are needed. Moreover, Figure 7b shows that the CNT(5,5) radius is a certain threshold, after which the behavior of an internally adsorbed isolated Li+H2 complex becomes similar to that externally adsorbed on a CNT. Indeed, for nanotubes (7,7) and (9,9) the difference between GGA/LDA predictions of Ebind (∼0.15 eV) and the influence of Li atom on hydrogen adsorption energies (∼0.1 eV for both GGA and LDA) are almost the same and close to the correspondent values in the case of external adsorption. With the rise of a nanotube’s diameter Ebind first significantly drops (from nanotube (5,5) to (7,7)) and then slowly decreases. For all considered nanotubes with a Li atom inside we obtained hydrogen adsorption energies in the needed range. As was mentioned above, steric hindrances prevent high hydrogen uptake inside CNT(5,5). And though for internal sorption of Li atoms on CNT(7,7) previous research29 showed that coverage close to LiC6 is possible (and we can expect the similar result for wider tube), we doubt that inside nanotubes we could obtain the same hydrogen uptakes as in the case of external sorption. However, further investigations are needed to clarify this question.

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4. CONCLUSIONS In this work we have observed the following behavior of CNT(n,n)@Li+kH2 complexes for the considered ranges of Nc, k, and n: (I) In the case of external sorption, binding energies of hydrogen molecules do not depend on the translational length (Nc) for any considered numbers of H2 molecules (k) in LDA and GGA. LDA predictions of ELi bind are quite optimistic, since five hydrogen molecules have binding energies in the desirable range (200−600 meV per molecule). Furthermore, the Li atom plays a significant role: in its presence, hydrogen molecules in complexes with k ≤ 4 have adsorption energies almost 100 meV higher than the Epure bind ≅ 140 meV. In GGA, the rise of Ebind also equals around 100 meV, compared to the Epure bind ≅ 50 meV. Therefore, for all considered k, the adsorption energies calculated in GGA are at least 50 meV outside of desirable range. With the rise of CNT diameter hydrogen adsorption energy slightly increases. (II) In the case of internal sorption on CNT(5,5) the situation changes drastically. The length of modeled CNT fragment affects the adsorption energies even for k > 2 in GGA and k > 3 in LDA. Moreover, Li+H2 complex causes noticeable cross-section deformation of the CNT model with Nc = 4. With the increase of the tube’s length, this hydrogen-induced deformation becomes less prominent (from eccentricity e ≅ 0.4 for Nc = 4 to e ≅ 0.2 for Nc = 6). In both approximations of the exchange−correlation potential, the influence of Li adatom on the hydrogen adsorption energies is insignificant. The

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsanm.9b00406.

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Figure S1 and Figure S2 for relaxed structures of CNT(5,5)@Li@6H2; Figure S3 for adsorption energies of hydrogen outside CNT(7,7)@Li and inside/outside CNT(9,9)@Li; Table S1 showing a comparison of GGA, DFT-D2, and LDA results for Ebind of hydrogen, adsorbed on CNT(7,7) and CNT(7,7)@Li (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Amitava Banerjee: 0000-0002-3548-133X Rajeev Ahuja: 0000-0003-1231-9994 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.B. and R.A. acknowledge respectively the Carl Tryggers Stiftelse for Vetenskaplig Forskning (CTS: Grant 18.04) and Swedish Research Council (VR Grant 2016-06014). E.A. is thankful for the Swedish Institute for providing a scholarship for her internship at Uppsala University. SUSU SSL is also 3028


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acknowledged for providing computing time (Tornado SUSU Supercomputer).

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