Li-Functionalized Carbon Nanotubes for Hydrogen Storage

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Li-functionalized Carbon Nanotubes for Hydrogen Storage: Importance of Size Effects Ekaterina Anikina, Amitava Banerjee, Valery Beskachko, and Rajeev Ahuja ACS Appl. Nano Mater., Just Accepted Manuscript • DOI: 10.1021/acsanm.9b00406 • Publication Date (Web): 03 May 2019 Downloaded from http://pubs.acs.org on May 6, 2019

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ACS Applied Nano Materials

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

Materials Theory Division, Department of Physics and Astronomy, Uppsala University, Box -516, Sweden

‡ Institute

of Natural Sciences and Mathematics, South Ural State University, 76, Lenin prospekt, Chelyabinsk, Russia Materials Physics, Department of Materials and Engineering, Royal Institute of Technology (KTH), S-100 44 Stockholm, Sweden ⊥Applied

KEYWORDS: Carbon nanotubes, Hydrogen adsorption, Li-functionalization, DFT, Periodic boundary condition

ABSTRACT: We investigated Li-doped carbon nanotubes (CNTs) as a promising hydrogen storage media. Using computer modelling, 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 alter the adsorption energies of H2 molecules and cause the deformation of the carbon framework. Moreover, the size effects are not pronounced in 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 case of external adsorption on all considered nanotubes, doping with Li increases hydrogen adsorption energies of up to four H 2 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/H 2). In case of internal sorption on Lifunctionalized tubes, the generalized gradient approximation also gives hydrogen adsorption energies in the desired range of 200-600 meV/molecule. 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.

1.

Introduction

have also superior mechanical, unique electrical, and capillary features, having been drawing researcher’s attention for a long time4, 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 USA DOE specified target (6.5 wt %) for room temperature applications13. This happens because of insufficiently strong van der Waals interactions between H2 molecules and pure CNT surfaces in the case of physisorption14. Room-temperature reversible sorptiondesorption cycles can be obtained when the adsorption energy per one hydrogen molecule, 𝐸ads , falls in the range of 200-600 meV15, which is in between chemisorption and

Compact, safe, and efficient hydrogen storages remain one of the problems to solve on a way to eco-friendly 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 production1. 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)

1 ACS Paragon Plus Environment

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physisorption. Therefore, it is necessary to tune this 𝐸ads , which can be achieved by forming more active adsorption sites on CNT surface, for example, through metal atom decoration16-25. Previously, we showed that doping CNTs with Li-atom increases the adsorption energy of H2 molecule for single molecule adsorption, and the 𝐸ads of the hydrogen molecule adsorbed inside the nanotube is in the desirable range26. 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, while modelling extended structures without translation symmetry we can run in to issue, connected with periodic boundary conditions (PBC). 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 modelling 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.

Page 2 of 12

Computational Methods

Throughout this work we consider the armchair carbon nanotubes (pure and Li doped on internal and external surfaces, see Fig. 1) with indexes (𝑛, 𝑛), 𝑛 = 5, 7,9 and diameters 6.75, 9.46 Å, and 12.20 Å, respectively. Unit cells of these tubes contain 𝑛cell (𝑛) = 4𝑛 atoms. So, CNT fragments which are modeled with PBC, should consist of 𝑁calc atoms per simulation cell: 𝑁calc = 𝑁c ∙ 𝑛cell , 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 image29. Hence, the size of chosen models (with Li and H2 molecules) does not exceed two hundred atoms. In case of Li-functionalized CNTs hydrogen molecules were at the same side of a nanotube as Li atom. a)

c)

b)

d)

Fig. 1. Relaxed geometry and charge difference isosurfaces (0.0025e) of the complex CNT(5,5)@Li (𝑁c = 4): a) crosssection and b) side view of internally sorbed Li atom; c) crosssection and d) side view of externally sorbed Li atom. Carbon and Li atoms are represented as grey and green color balls. Yellow and cyan regions depict depletion and accumulation of charge density, respectively. All structure pictures were obtained using VESTA3 software package30

We have performed first-principles DFT based spinpolarized electronic structure calculations as implemented in the open source SIESTA suite31, 32. The local density


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approximation, LDA (Ceperley-Alder functional33) and the generalized gradient approximation, GGA (Perdew-BurkeErnzerhof 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, respectively35. 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 results36. 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 using only GGA and LDA approximation it is possible to find the similar trends, independent of a choice of approximation. All the pseudopotentials have been taken from the FHI pseudo database38. 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-zeta 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 Meshcutoff39 of 360 and 210 Ry for GGA and LDA calculations, respectively, and the 1x1x32 MonkhorstPack set of k-points have been considered to calculate adsorption energies within a numerical precision of ~ 7 meV. Before hydrogen sorption modelling 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 non-periodic directions we put not less than 100 Å. 3.

Results & Discussions

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 𝐸bind = 𝐸frame + 𝐸H2 −𝐸frame+H2 ,

(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 hydrogen molecule attracts to the adsorbent, and the bigger 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 ext in considered cases, such as external (𝐸bind ) and internal (𝐸bind ) adsorption on pure CNT(5,5) and CNT(5,5)@Li with both approximation of exchange–correlation functional (GGA and LDA). Calculated 𝐸bind for CNT(5,5)@Li agrees with the previously reported similar complexes41-43. Table 1:Binding energy of single hydrogen molecule on in external (𝑬ext bind ) and internal (𝑬bind ) surfaces of CNT(5,5) and CNT(5,5)@Li, meV CNT(5,5)

CNT(5,5)@Li

ext 𝐸bind

𝑁c

ext 𝐸bind

in 𝐸bind

in 𝐸bind

GGA LDA GGA LDA GGA LDA GGA LDA 4

47

138

263

473

142

246

274

508

5

48

142

263

473

144

247

273

508

6

48

141

263

473

145

247

274

509

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 ext in 2, ∆𝐸L-G (∆𝐸L-G ) is the difference between LDA- and GGApredicted binding energy for external (internal) sorption; ext ext ∆𝐸GGA (∆𝐸LDA ) is the difference of GGA- (LDA-) predicted ext in 𝐸bind for Li-doped and pure CNT (similarly, ∆𝐸GGA and in in-ext in-ext ∆𝐸LDA for internal sorption); and ∆𝐸GGA (∆𝐸LDA ) is the in ext difference between GGA- (LDA-) predicted 𝐸bind and 𝐸bind . 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 ∆𝐸L-G significantly depends on the in curvature sign of the sorption surface (∆𝐸L-G is two times ext higher than ∆𝐸L-G ), whereas addition of Li atom changes the ∆𝐸L-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 ∆𝐸 in-ext value, which again strongly depends on the choice of the exchange-correlation approximation and the presence of Li-atom. Table 2: Differences in 𝑬bind, meV, induced by: I. choice of approximation LDA/GGA, II. Li-doping, III. sorption surface curvature sign

Page 4 of 12

Coulomb potential of Li+ ions (Fig. 1), since the Li atom, when adsorbed on CNT surface, donates almost all its valence electron to the tube29. Thus, for 𝑘 ≥ 5 we considered symmetrical starting configurations where the H2 molecules are located compactly near the Li adatom. a)

b)

I. LDA vs GGA CNT(5,5)

CNT(5,5)@Li

ext ∆𝐸L-G

91-94

ext ∆𝐸L-G

in ∆𝐸L-G

210

102-104

in ∆𝐸L-G

234-235

II. CNT(5,5)@Li vs CNT(5,5) ext ∆𝐸GGA

95-97

ext ∆𝐸LDA

105-108

in ∆𝐸GGA

10-11

in ∆𝐸LDA

35-36

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

III. Internal vs External CNT(5,5) in-ext ∆𝐸GGA

215-216

CNT(5,5)@Li in-ext ∆𝐸LDA

331-335

in-ext ∆𝐸GGA

129-132

in-ext ∆𝐸LDA

261-262

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 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 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

However, structural optimization of a few initial configurations for 𝑘 = 6 (as shown in SI) resulted in the spread of hydrogen onto the nanotube. So, some H2 molecules are no longer geometrically close to Li as shown in Fig. 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 centre of a square formed by four H2 molecules, while other two H2 molecules are located symmetrically in Li second neighbour’s sphere as shown in Fig. 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 (Fig. S2), where the Li atom is in the rhomb centre, 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 Fig. 2), turned out to be the most energetically favourable. 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, with consequent structural optimization at every step (the translation length was fixed). If the binding energy of the Li removed H2 molecule, 𝐸bind , is higher than the adsorption pure energy of H2 molecule on a pure CNT, 𝐸bind , we regarded


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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 H2 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:

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 comparison with the 𝐸bind of hydrogen molecules on pure CNT(5,5), which agrees with the previous results for CNT(8,0)@Li44, 45. a)

b)

c)

d)

e)

f)

𝐸bind = −𝐸𝑘 + 𝐸𝑘−1 + 𝐸H2 , (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 Fig. 3.

Fig. 3. Binding energies of H2 molecules externally adsorbed on CNT(5,5)@Li with Nc = 4 (grey 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)

Fig. 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 approximation. In particular, these approximations estimate the maximal size of Li-associated hydrogen complex, 𝑘max , pure pure Li based on the criterion 𝐸bind > 𝐸bind (𝐸bind is taken from Table 1 and represented as horizontal lines on Fig. 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 pure considerably less than 𝐸bind ). This fact can be explained by

Fig. 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 brackets. 𝑁c = 4

Thus, four CNT unit cells are sufficient for modelling sorption on the external surface of CNT(5,5) and nanotubes



with a bigger radius. Further increase of nanotube translation length does not change the results of 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 hydrogen cannot leave through the absent nanotubes edges or nanotube’s wall due to the high potential barrier46. 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 (Fig. 4ad) have similar total energies (with a minor difference of 17 meV). However, the energy of III (Fig. 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. Fig. 4a-d show a similar distribution of H2 molecules over lithium coordination spheres. The crosssection views (Fig. 4a,c) depict that six hydrogen molecules are arranged into two groups of three molecules, whereas the side views (Fig. 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.

Page 6 of 12

longer tubes, we have purposely chosen configuration I as the same geometry for the corresponding complex predicted with GGA approximation. The CNT of configuration I (Fig. 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 0 deformation by using the following formula: 𝐸def = 𝐸tot − 0 𝐸tot , where 𝐸tot 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 centres as shown in Fig. 4a. Moreover, for 𝑁c = 4, this elliptic fitting of the tube cross-section is valid throughout the whole tube length (not only centred 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, corresponding 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 Fig. 5, which demonstrates that with higher 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.

Moreover, configurations I and II differ by the position of the Li atom with respect to the neighbouring 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


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

Fig. 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 Fig. 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 𝑚-th molecule 𝐸bind (𝑚) < 0). The corresponding H2 gravimetric density GDH could be estimated as 𝐺𝐷H = 𝑛

2×𝑊H ×(𝑚−1)

cell ×𝑊C ×𝑚+𝑊Li +2×𝑊H ×(𝑚−1)

2𝑚−2

= 122𝑚+1,

Fig. 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, pure the 𝐸bind exceeds 𝐸bind 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. a) 𝑛 = 5

(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 unfavourable 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, Fig. 6a indicates that the presence of the Li adatom does not substantially influence hydrogen adsorption as the 𝐸bind for 𝑘 = 1 − 3 pure (nearest neighbours of Li) exceeds 𝐸bind 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 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 – two times larger.

b) 𝑛 = 7

Fig. 6. Binding energies of H2 molecules internally adsorbed on: a) CNT(5,5)@Li and b) CNT(7,7)@Li complexes with Nc = 4 (grey 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)



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 case of a narrow nanotube (5,5). But 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 Fig. S3. Fig. 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 complexes47-49 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 (Fig. 7). For 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. a)

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Fig. 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 CNTs50. 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: 𝐺𝐷 =

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

(4)

where square parentheses stand for a round number. We obtained 12.2 wt %, 11.8 wt %, 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 (~ three H2 molecules per Li) only in case of isolated Li+3H2 complexes. Interactions of hydrogen molecules in 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, Fig. 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 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.

b)

Fig. 7. Dependence of hydrogen adsorption energy on CNT diameter in 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 Li-functionalized and pure CNTs, respectively

For all considered Li-functionalized nanotubes we obtained 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 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 case of external sorption.


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However, further investigations are needed to clarify this question. 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.

II.

III.

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 either LDA and Li GGA. LDA predictions of 𝐸bind 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 pure the 𝐸bind ≅ 140meV. In GGA, the rise of 𝐸bind also pure equals around 100 meV, compared to the 𝐸bind ≅ 50meV. 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. 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 for𝑁c = 6). In both approximations of the exchange-correlation potential, the influence of Li adatom on the hydrogen adsorption energies is insignificant. The adsorption energies of hydrogen molecules also depend on the nanotube’s curvature, e.g. the adsorption energies inside the pure CNT are much bigger than outside. The distinct differences in the external and internal adsorption on CNT(5,5) originate from the tube’s curvature. Modelling of internal adsorption on CNT(7,7) and CNT(9,9) confirmed this fact. In a pure wider tubes, 𝐸bind 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 case of external adsorption of Li-doped CNTs of all considered diameters exceed the lowest DOE requirement of 200 meV/molecule. In these cases, theoretical estimations of hydrogen uptake (LiC6 coverage) are greater than 10 wt %, which is bigger than 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 case of CNT(5,5)). This could result in internal surface of these nanotubes (both pure and Li-doped) being unsuitable for practical applications. ACKNOWLEDGMENT AB and RA would like to acknowledge respectively the Carl Tryggers Stiftelse for Vetenskaplig Forskning (CTS: 18.04), and Swedish Research Council (VR: 2016-06014). EA is thankful to the Swedish Institute for providing the scholarship for her internship at Uppsala University. SUSU SSL is also acknowledged for providing computing time (Tornado SUSU Supercomputer). Supporting Information: Fig. S1 and Fig. S2 for relaxed structures of CNT(5,5)@Li@6H2. Fig. S3 for adsorption energies of hydrogen outside CNT(7,7)@Li and inside/outside CNT(9,9)@Li Table S1 shows the comparison of GGA, DFT-D2 and LDA results for 𝐸bind of hydrogen, adsorbed on CNT(7,7) and CNT(7,7)@Li. AUTHOR INFORMATION Corresponding Author: *(AB) E-mail: [email protected]; amitava.banerjee@ physics.uu.se 



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Graphical Abstract (ToC)


Li-Functionalized Carbon Nanotubes for Hydrogen Storage

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