Photoactivity and electronic properties of graphene-like materials and TiO₂ composites using first-principles calculations

Abstract

Graphene-like materials (GLM) have attracted intense attention in the research on photocatalytic technology due to their superior properties. First-principles calculations based on DFT were used to explore the photoactivity and electronic properties of graphene-like materials and TiO₂ composites in this work. It was found that TiO₂/GLM composites might be demonstrated for high thermodynamic stability. The electronic properties of TiO₂/GLM, such as geometric structure, density of states, charge density, charge density difference and optical properties, were characterized. There were interactions between GLM sheets and TiO₂, which caused charge accumulation on the GLM surface and charge depletion on the other side of TiO₂ in the heterojunction. Electrons in the highest occupied molecular orbital (HOMO) consisted of the O2p orbital from TiO₂ could be directly excited or dispersed to the lowest unoccupied molecular orbital (LUMO) composed of the hybridized orbital from GLM and TiO₂ under irradiation. The produced well-separated electron–hole pairs induced an enhanced photocatalytic performance of TiO₂/GLM. The theoretical results pointed out the electron migration and transfer path at the interface, which might illustrate the mechanism of enhanced photocatalytic activity of TiO₂/GLM.

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1. Introduction

The efficient and cost-effective direct conversion of solar energy to chemical energy and solar fuels has been considered as one of the most perceptive strategies to solve the environmental and energy problems in the future.¹ Photocatalytical technology has been recognized as an effective means to environmental contaminant control and remediation.^2,3 Due to its chemical stability, low cost and strong oxidizing characteristics, TiO₂ has been widely used as a photocatalyst over the past several decades.^4,5 But unfortunately, TiO₂ can utilize no more than 5% of the total solar energy due to its wide band gap (3.0–3.2 eV), which limits its application in the industrial application of photocatalytic technology. Many strategies, such as doping with elements, surface modification and coupling with other semiconductors, have been made to improve its photocatalytic performance.

Owing to excellent conductivity, superior chemical stability and high specific surface area, graphene has attracted a great deal of attention in recent years,^6,7 which is valuable as a hot substrate that supports the heterogeneous growth of desired active guest materials.⁸ It seems that graphene can serve as a suitable candidate to be combined with TiO₂ and shows enhanced photocatalytic performance compared to bare TiO₂.⁹ Several reports have been devoted to the preparation of TiO₂ modified with graphene for the photodegradation of organic dyes.^10,11 For example, TiO₂/grapheme (hereinafter referred to TiO₂/G) composite produced by direct growth of (TiO₂)₃ nanocluster (hereinafter referred to TiO₂ cluster or TiO₂) on graphene oxide sheets showed a strong photocatalytic activity for the degradation of rhodamine B under UV irradiation.¹² The addition of graphene nanoplatelets to TiO₂ has been recently considered as a method to improve the photocatalytic efficiency of TiO₂ by favoring charge carrier separation.¹³ The conjugation of TiO₂ with graphene has been proved to be an effective approach to improve the photocatalytic properties of TiO₂.^7,9,14

There are various two-dimensional (2D) layered compounds with similar properties like graphene, which can be called graphene-like materials (hereinafter referred to GLM, including graphene), such as, graphitic carbon nitride, black phosphorus and transition metal dichalcogenides, might be used to combine with TiO₂ to enhance photocatalytic activity.¹⁴ Two-dimensional (2D) graphitic carbon nitride (g-C₃N₄) has attracted immense attention due to its unique electronic band structure, visible-light-responsiveness, high thermal and chemical stability, making it potentially suitable for solar energy conversion and environmental remediation.¹⁵ Despite the aforementioned benefits of g-C₃N₄ material and photocatalytic process, the photocatalytic efficiency is still low to make the system viable for practical applications owing to the high recombination rate of photogenerated charge carriers in the individual semiconductor.¹⁶ Sheet-like TiO₂/g-C₃N₄ heterojunctions exhibited excellent stability and good visible-light photocatalytic performance for photodegradation of rhodamine B.¹⁷ The enhanced photocatalytic activities of TiO₂/g-C₃N₄ photocatalysts could be primarily attributed to the formation of a hybrid structure in the contact interface between TiO₂ and g-C₃N₄, which greatly promoted the separation of photogenerated electron–hole charge carriers.¹⁸ The in situ growth of TiO₂ on the surface of g-C₃N₄ not only formed a TiO₂/g-C₃N₄ nanojunction with a more efficient interparticle electron transfer but also promoted further protonation, which increased the photocatalytic activities of TiO₂/g-C₃N₄.¹⁹ Molybdenum disulfide (MoS₂) has been commonly studied as a noble metal free low-cost and abundant cocatalyst which is comparative and even superior to noble metal cocatalyst for enhancing the photocatalytic H₂ evolution efficiency of the semiconductor.²⁰ Q. Xiang et al. reported a new composite material consisting of TiO₂ cluster grown in the presence of a layered MoS₂/graphene hybrid as a high-performance photocatalyst for H₂ evolution.²¹ Both MoS₂ and g-C₃N₄ played positive role for enhanced photocatalytic H₂ production activity of TiO₂.²² Moreover, black phosphorus (BP) is a layered semiconductor and has great potential applications in optical, electronic and nano-materials.^23,24

As described above, there have been some experimental investigations on GLM layered nanomaterials, which improved the photocatalytic activity of TiO₂ during the past decades. However, the mechanism on enhanced photocatalytic activity of TiO₂/GLM has not been understood clearly. Meanwhile, there are few comprehensive theoretical studies reported on structural and electronic properties of the composites, which might resolve the photocatalytic mechanism of TiO₂/GLM.

Herein, first-principles calculations based on density functional theory (DFT) were used to explore the effect of GLM hybridization on the geometry structure and electronic properties of TiO₂ in this work. The hybridization of TiO₂ with GLM was proved to be susceptible thermodynamically. The theoretical investigation illustrated charge accumulated on the GLM surface and depleted on the side of TiO₂ cluster, indicating a probable charge migration or transference across the interface from GLM to TiO₂. The charge migration path and the well-separated electron–hole pairs could illustrate the mechanism of enhanced photocatalytic activity of TiO₂/GLM.

2. Model and computational details

In our work, all of the calculations were performed using the well tested Cambridge Serial Total Energy Package (CASTEP) code,^25,26 which employs planewave basis sets to treat valence electrons and norm-conserving pseudopotentials to approximate the potential field of ionic cores. We employed a generalized gradient approximation (GGA) method, the Perdew, Burke, Ernzerhof (PBE) exchange–correlation functional, and the ultrasoft pseudopotential in the calculations. The basis set cut-off energy was chosen at 340 eV, and we used a 5 × 5 × 1 Monkhorst–Pack k-point mesh for geometry optimization of the TiO₂ cluster and a 9 × 9 × 1 mesh to calculate its electronic properties. For the TiO₂ cluster hybridization with graphene or GLM, such as MoS₂, g-C₃N₄ and BP, Monkhorst–Pack special k-point was set to 4 × 4 × 1 and the k-point was set to 9 × 9 × 1 on the density of state for geometry optimization. Further increasing cutoff energy and k-points shows little difference in the calculation results. The convergence threshold for self-consistent iteration was set at 2 × 10⁻⁶ eV per atom.

S. A. Shevlin and S. M. Woodley have made a systematic study on (TiO₂)_n cluster by DFT calculation.²⁷ It indicated that (TiO₂)₃ nanocluster was a suitable structural model to explore its structure and electronic properties, which has been proved to be in good agreement with the experimental data. To reduce time-consuming calculations, a small stoichiometric TiO₂ cluster was employed in our study based on the above consideration, which was presented in Fig. 1. The optimized monolayer geometric structures of graphene, g-C₃N₄, MoS₂, and BP were presented in Fig. 2a–d, respectively. The g-C₃N₄ monolayer studied in this work was built on triazine rings with a hexagonal unit cell, in which all C atoms have three nearest neighbor N atoms, as shown in Fig. 2b.²⁸ The monolayer of MoS₂ is made up of hexagons with the Mo and S atoms located at alternating corners (Fig. 2c). Inside the monolayer of BP, each phosphorus atom is covalently bonded with three adjacent phosphorus atoms to form a puckered honeycomb structure,²⁹ as shown in Fig. 2d.

Fig. 1 Crystal structure of (TiO₂)₃ cluster. Gray and red balls represent Ti and O atom, respectively.

Fig. 2 Crystal structures of monolayer graphene (a), g-C₃N₄ (b), MoS₂ (c) and black phosphorus (d). Dark gray, blue, yellow, aquamarine, pink balls represent C, N, and S, Mo and P atoms, respectively.

The geometry structures of TiO₂ cluster combined with graphene (a bare 4 × 4 monolayer sheet), g-C₃N₄ (a 3 × 3 monolayer sheet), MoS₂ (a 3 × 3 sandwich-like monolayer sheet) and BP (a bare 4 × 4 monolayer sheet) lattice parameters were (9.85 Å × 9.85 Å × 20.00 Å), (14.23 Å × 14.23 Å × 20.00 Å), (9.51 Å × 9.51 Å × 20.00 Å) and (12.72 Å × 9.72 Å × 20.00 Å), respectively. The thickness of vacuum layer was set as 20 Å to counteract stress. The distance from the adjacent Ti atom to the surface of GLM was set as 3 Å.

3. Results and discussion

3.1. Theoretical model of TiO₂ cluster combined with graphene

Graphene was taken as an example to combine with TiO₂ cluster to study the theoretical hybridization model of TiO₂/GLM. The atomic arrangement of TiO₂ cluster and the relative distance from the cluster to the graphene sheet were investigated to find out the suitable spatial position of TiO₂ cluster, which hybridized with graphene. In order to investigate the stability of the composite, the binding energy of TiO₂/G composite was calculated according to the eqn (1).

E_b = E_TiO2/G − E_TiO2 − E_G (1)

where E_b indicate the binding energy of TiO₂/G composite, E_TiO2 is the energy of TiO₂ cluster, E_G is the energy of graphene, and E_TiO2/G is the total energy of TiO₂/G. The negative value means that the hybridization process release heat, which implies that the hybridization process is energetically favourable on thermodynamics stability. The smaller the binding energy is, the easier the hybridization process can be achieved.

There are four types of TiO₂/G theoretical structure with different geometric location of TiO₂ cluster (Fig. 3) and the binding energies were listed blow each model. It could be seen that model A (Fig. 3a) was the most stable geometry as its binding energy was lowest. Since C and Ti atoms have a greater electronegativity difference than C and O atoms have, electrons transfer more easier from Ti to graphene, which contribute to a better thermodynamic stability of model A. Comparing with Ti₂ and Ti₃ atoms, the Ti₁ atom has a lower saturation of chemical bonds, which made model A stand out. As a result, a theoretical basis for the model of TiO₂/GLM has been done and details of electrons transfer in TiO₂/GLM will be discussed in the following chapters.

Fig. 3 The different theoretical structure of TiO₂/G with its binding energy.

3.2. Binding energies and geometric structures

Similarly, the binding energies of TiO₂/GLM composites were also calculated according to the eqn (2).

E_b = E_TiO2/GLM − E_TiO2 − E_GLM (2)

where E_b is the binding energy of the composite, E_TiO2 is the energy of TiO₂ cluster, E_GLM is the energy of GLM, and E_TiO2/GLM is the total energy of TiO₂ cluster hybridized with GLM. From stability perspective of TiO₂/GLM composites were in the order of TiO₂/g-C₃N₄(−7.67 eV) > TiO₂/BP(−1.33 eV) > TiO₂/MoS₂(−0.78 eV) = TiO₂/G(−0.78 eV). The theoretical result implied that the combination of TiO₂ cluster with GLM were all favourable, especially TiO₂/g-C₃N₄ composite.

Interaction occurred between TiO₂ cluster and GLM when they hybridized, which would make geometric structure of TiO₂ cluster change. Both bond lengths and bond angles were measured to characterize the effect of GLM hybridization on the structural variety of TiO₂ cluster. The bond lengths and the bond angles of TiO₂ cluster were respectively listed in Tables 1 and 2, which could be seen in the ESI.†

For TiO₂/G composite, the interaction between C and Ti were the electrostatic attraction, while C and O were the electrostatic repulsion. For this reason, it produced a series of changes. Both the bond numbered 1 (from 1.745 to 1.754 Å) and the bond numbered 2 (from 1.744 to 1.754 Å) have grown. The ∠O₅Ti₁O₆ increased from 108.49° to 110.58°, and ∠Ti₂O₁Ti₃ increased from 86.37° to 88.39°. The bond numbered 5 shorted from 2.076 to 2.037, and the bond numbered 6 shorted from 2.084 to 2.040. The ∠O₁Ti₂O₅ increased from 77.63° to 78.29°, and ∠O₁Ti₃O₆ increased from 77.43° to 78.42°, while ∠O₄Ti₃O₆ decreased from 124.86° to 122.64°. Above-mentioned bond length and angle changes of TiO₂ cluster in TiO₂/G system described the structural changes as a whole. Additionally, the TiO₂/MoS₂ system was very similar to the case of TiO₂/G and we also considered as one of the factors which caused the same binding energies between them. By contrast, geometric variations caused by the interaction of TiO₂ and g-C₃N₄ were very obvious. TiO₂ cluster overall structure has a certain extent variation which is a chain reaction in order to protect structural integrality. Meanwhile, the N atom which contains two C–N bonds of g-C₃N₄ monolayer shift upward clearly and g-C₃N₄ becomes irregularity. In the case of TiO₂/BP system, the TiO₂ cluster has C₂ symmetry and the interaction is mainly on one side of TiO₂ cluster: for bond length, bond numbered 2 > bond numbered 1, bond numbered 10 > bond numbered 9. For angles, the ∠O₅Ti₁O₆ decreased from 108.49° to 106.79°, ∠Ti₂O₁Ti₃ increased from 86.37° to 89.03°, ∠O₄Ti₃O₆ decreased from 124.86° to 118.68° and ∠O₁Ti₃O₆ increased from 77.43° to 82.31°.

In summary, there was electrostatic interaction between GLM sheet and TiO₂ cluster. The interaction between GLM and Ti was electrostatic attraction, while the interaction between GLM and O were electrostatic repulsion mainly. The electrostatic forces of TiO₂ cluster from graphene and MoS₂ sheet were relatively weak, while those from g-C₃N₄ and BP were much stronger. The reason might come from the electronegativity difference of various elements. The electronegativity of C (2.55) approached to Mo (2.16) and S (2.58), but it was between Ti (1.54) and O (3.44). In the same way, the electronegativity of N (3.04) approached to O (3.44) and the electronegativity of P (2.19) was closed to Ti (1.54). Therefore, the electrostatic interaction might not bring change to the geometry structure of graphene, MoS₂ and TiO₂ cluster. In contrast, larger electrostatic interaction brought change to the geometry structure of g-C₃N₄, BP and TiO₂ cluster, which might be correlated to the change of electronic properties.

3.3. Charge density and charge density difference analysis

In order to further explore how GLM affect the electronic properties and bonding character of the TiO₂/GLM composites, we calculated the electronic total charge density and difference charge density. The Fig. 4 exhibited the three-dimensional electron cloud and its potential distribution in TiO₂/GLM composites. The interface charge-redistribution could adjust the electrostatic potential distribution in those systems as a whole respectively. In the case of TiO₂/G composite (Fig. 4a), it was observed that the electron overlap between TiO₂ cluster and graphene was very weak. Similarly, the electron overlap of three other TiO₂/GLM composites were in the order of TiO₂/MoS₂ < TiO₂/BP < TiO₂/g-C₃N₄. All composites transient potential overlap was transition potential, which meant the reaction was spontaneous. That charge density of overlap increased signifies stronger covalent interaction and those calculation results agreed with the binding energy of TiO₂/GLM.

Fig. 4 The optimized geometric structures of TiO₂/GLM with charge density (set as the isovalue of 0.2 e Å⁻³) and potential. (a) TiO₂/G, (b) TiO₂/g-C₃N₄, (c) TiO₂/MoS₂, (d) TiO₂/BP.

The interaction between the TiO₂ and GLM sheets implied a substantial charge transfer in the involved constituents. In order to explore the effect of GLM hybridization on the electron distribution of TiO₂ cluster and the interaction between TiO₂ and GLM, charge density difference was calculated. This could be visualized by three-dimensional charge density difference:

Δρ = ρ_TiO2/GLM − (ρ_TiO2 + ρ_GLM) (3)

where ρ_TiO2/GLM, ρ_TiO2 and ρ_GLM are the charge densities of the composite, TiO₂ cluster and GLM sheets, respectively. For comparison, the charge density difference of TiO₂/G, TiO₂/g-C₃N₄, TiO₂/MoS₂ and TiO₂/BP were presented in Fig. 5a–d, respectively. The orange color represented charge accumulation, while green color represented charge depletion. In the planar-averaged and 3D electron density difference plots of TiO₂/G (Fig. 5a), we found that charge accumulation occurred on the graphene surface and charge depletion happened on the other side of TiO₂ cluster. It was conclusive that the electron moved from the TiO₂ cluster to graphene. By analysing the principle and rule of TiO₂/G system's charge density difference, it would be suited to TiO₂/GLM, as well as explaining the charge distribution between the interfaces. Remarkably, the O₄ atom of TiO₂/BP system had some interaction with BP, it also explained the effects of BP to TiO₂ cluster on one side. As has been mentioned above, we concluded that the electron migrated from the TiO₂ cluster to GLM. In photocatalytic process, GLM sheets would work as electron acceptors and provide a conduction platform to transport electrons participating in the oxidation–reduction reactions during the photodegradation of contaminant. This theoretical study pointed out the electron migration and transfer path at the interface, which might demonstrate the mechanism of enhanced photocatalytic activity of TiO₂/GLM.

Fig. 5 The planar-averaged electron density difference as a function of position in the z-direction and the 3D charge density difference with an isovalue of 0.02 e Å⁻³. (a) TiO₂/G, (b) TiO₂/g-C₃N₄, (c) TiO₂/MoS₂, (d) TiO₂/BP.

3.4. Density of states, frontier molecular orbital and optical properties

To explore the electron distribution in different energy levels and the charge carrier migration path at the interface between TiO₂ cluster and GLM, the density of states of TiO₂ and TiO₂/GLM were calculated.

The plot of total density of states (TDOS) for TiO₂ cluster and the partial density of states (PDOS) on Ti, O atoms was presented in Fig. 6, in which both the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of TiO₂ cluster were presented. It could be seen that the upper of valence band (VB) was predominantly composed of O2p state, while the bottom of conduction band (CB) was mainly composed of Ti3d state. The calculated TiO₂ cluster energy gap with a value of 2.04 eV, which was similar to that of rutile TiO₂ we calculated, was lower than the experimental data (3.0–3.2 eV).³⁰ It might attribute to two main reasons: on the one hand, as the size effect the difference existed between a small cluster and the bulk matter. On the other hand, the well-known shortage that DFT underestimated the band gap due to the self-correlation error of electrons and inherent lack of derivative discontinuity.^31,32 HOMO was consisted of O2p_y state, whereas the LUMO was consisted by Ti3d_z² state, indicating that the O2p_y and Ti3d_z² states were the key-states of photogenerated electron transition in TiO₂ cluster. The electrons transit from O2p_y and Ti3d_z², leaving hole in the O2p_y orbit under light irradiation.

Fig. 6 The calculated TDOS and PDOS, and the side view of HOMO and LUMO with an isovalue of 0.02 e Å⁻³ of TiO₂ cluster.

For the TiO₂/G system (Fig. 7a), it was observed that the TDOS of TiO₂/G and PDOS of Ti, O and C atoms, in which HOMO and LUMO of TiO₂/G were also presented. From the perspective of DOS, the general shape of TDOS moved to lower energy state. Due to the hybridization of graphene, C2p orbit participated in both VB and CB. The upper of VB was predominantly composed of O2p, while the bottom of CB was mainly composed of C2p. And the electron from both VB and CB moved to the lower energy region. The above analysis showed that TiO₂ cluster tended to stabilize after combination with graphene. Interestingly, the HOMO was consisted of O2p_y state, whereas LUMO were dominated by 2p_z states of C and 3d_yz of Ti, indicating that the O2p_y, C2p_z and Ti3d_yz were key-states to the photo-generated carrier of TiO₂/G composite. Observably, the C2p_z and Ti3d_yz states have been hybridized and the CB shifted to lower energy region. So the electrons transit from O2p_y to LUMO leaving hole in the O2p_y orbit, which dispersed all over HOMO. The electron–hole pairs were easy to separate and difficult to recover so that graphene could enhance the photocatalytic activity of TiO₂.

Fig. 7 The calculated TDOSs and PDOS, and the side view of HOMO and LUMO with an isovalue of 0.02 e Å⁻³. (a) TiO₂/G, (b) TiO₂/g-C₃N₄, (c) TiO₂/MoS₂, (d) TiO₂/BP. Orange and green isosurfaces represent LUMO and HOMO in the space with respect to isolated TiO₂/GLM.

Because of the interaction and redistribution, TDOS shape of TiO₂/g-C₃N₄ (Fig. 7b), TiO₂/MoS₂ (Fig. 7c) and TiO₂/BP (Fig. 7d) showed the characteristic features of significant changes. The O2p and Ti3d states of the three systems shifted slightly to lower energy levels. It was found that GLM could affect CB ingredient but BP could affect VB ingredient as well. Intuitively, we analyzed the HOMO–LUMO orbit of TiO₂/g-C₃N₄, TiO₂/MoS₂ and TiO₂/BP, respectively. For the TiO₂/g-C₃N₄ system, HOMO was consisted of O2p_x state and LUMO was hybridized from 2p_z state of C and 2p_z state of N. There was no doubt that 2p orbit had the lower energy than the 3d orbit so that photo-generated carriers transfer easier. In the case of TiO₂/MoS₂ system, O2p_y orbit constituted HOMO and Mo4d_z² orbit constituted LUMO. It was conceivable that photo-excited electrons were difficult to recover and those hole-rich O atoms were active sites for oxidation. The P3p_z state forms HOMO, LUMO was formed by P3p_y state and O2p_y state at TiO₂/BP system. Because the HOMO and LUMO diffused all around TiO₂/BP system, the mobility of electrons increased substantially. To further verify the photocatalytic of TiO₂/GLM systems, optical properties should be investigated.

The optical property of semiconductor photocatalyst is one of the key factors in determining photocatalytic properties. The UV-visible absorption spectra of TiO₂ cluster and TiO₂/GLM were calculated to characterize optical properties, as shown in Fig. 8. The photoelectric response and absorption intensity of TiO₂ cluster have been changed after incorporation with GLM. Not only the TiO₂/GLM systems gave rise to obvious red-shift of absorption edge but also the absorption intensity in the visible region improved greatly. Thus, it was concluded that coupling TiO₂ cluster on the GLM would enhance the absorption in the UV-vis region and modify the absorption edge. Meanwhile, it improved the photocatalytic activity of TiO₂ and likely to demonstrate excellent photocatalytic performance under vis-light irradiation.

Fig. 8 Calculated absorption spectra of TiO₂ cluster and TiO₂/GLM.

In summary, interaction between GLM and TiO₂ cluster caused electrons diffuse to lower energy region, which could explain why the TiO₂/GLM composites became stable. HOMO and LUMO of TiO₂ cluster could be changed by GLM to the benefit of photoactivity. This character could yield well-separated electron–hole pairs, and red-shift of absorption edge, absorption range extending and absorption intensity of TiO₂/GLM increasing, which induced the enhanced photocatalytic performance of TiO₂/GLM.

4. Conclusions

First-principles calculation based on DFT was used to explore the photoactivity and electronic properties of TiO₂/GLM composites in this work. The electronic properties and geometric structures of TiO₂/GLM systems were calculated to expound the interface interaction and account for the photocatalytic mechanism. It was found that TiO₂/GLM composites might be demonstrated for high thermodynamical stability. The interaction of GLM and TiO₂ caused charge accumulation on the GLM surface and charge depletion on the other side of TiO₂. Therefore, not only was the charge transport path indicated, but also the photo-electron transition tracks were changed. We discussed the cause of photocatalytic performance enhancements from two aspects: on the one hand, the hybridization of GLM brought HOMO and LUMO of TiO₂ cluster to the benefit changing of photoactivity. On the other hand, the absorption edge of TiO₂/GLM systems occur red-shift and its absorption intensity aggrandize. This work can provide theoretical basis for the feasibility of experiment and the TiO₂/GLM systems could be promising for photocatalytic applications.

Acknowledgements

This work has been supported by The National Natural Science Foundation of China (Grant No. 41573103, 41340037) and the scientific research program of Shandong Province (2013G0021701, 2014GGH217001) P. R. China.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra12980c

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