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Impact of distributions and mixtures on the charge transfer properties of graphene nanoflakes† Hongqing Shi, Robert J. Rees, Manolo C. Per and Amanda S. Barnard* Many of the promising new applications of graphene nanoflakes are moderated by charge transfer reactions occurring between defects, such as edges, and the surrounding environment. In this context the sign and value of properties such as the ionization potential, electron affinity, electronegativity and chemical hardness can be useful indicators of the efficiency of graphene nanoflakes for different reactions, and can help identify new application areas. However, as samples of graphene nanoflakes cannot necessarily be perfectly monodispersed, it is necessary to predict these properties for polydispersed ensembles of flakes, and provide a statistical solution. In this study we use some simple statistical methods, in combination with electronic structure simulations, to predict the charge transfer properties of different types of
Received 17th October 2014, Accepted 9th December 2014
ensembles where restrictions have been placed on the diversity of the structures. By predicting quality
DOI: 10.1039/c4nr06123c
factors for a variety of cases, we find that there is a clear motivation for restricting the sizes and suppressing certain morphologies to increase the selectivity and efficiency of charge transfer reactions; even if
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samples cannot be completely purified.
1 Introduction In recent years electrically conductive1 graphene nanoflakes (nanographene) have emerged as a new tool in diverse fields such as electronics,2 energy,3–6 aeronautics,7 and sensing;8 and have facilitated the next generation of electronic, spintronic, optical and sensing devices.9 For example, adding graphene to composite films has been shown to simultaneously provide high transparency, good conductivity, and superior mechanical properties.10–14 In recent years a number of graphene-based electrochemical sensors have been developed, for applications in bioanalysis and environmental analysis.15–25 Commercialization of these technologies is also underway, as it is now possible to create low-cost samples of graphene nanoflakes, with a reasonably high degree of control.26 In the case of sensors, the efficiency, selectivity and sensitivity are moderated by a charge transfer reaction, which occurs between different defects, such as edges, and the surrounding molecules and/or environment. The direction and efficiency of charge transfer depend on whether the host nanographene acts as a donor or acceptor and so, in the case of
CSIRO Virtual Nanoscience Laboratory, 343 Royal Parade, Parkville, Victoria 3052, Australia. E-mail: [email protected]; Tel: +61-3-9662-7356 † Electronic supplementary information (ESI) available: Details of computational simulations and specific results. Comparison of the expectation values of quality factors for ensemble properties based on different statistical distributions. See DOI: 10.1039/c4nr06123c
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electron transfer, the sign and value of the ionization potential (the donation of an electron) and the electron affinity (the accepting of an electron) are ideal indicators. Other related indicators include the energy of the Fermi level and the fundamental electronic band gap; the chemical hardness which describes the preferred coordination of acids and bases;27 and the electronegativity,28 which is defined as the average between the absolute values of the ionization potential and the electron affinity.29 Although it is possible to measure these quantities,30 they have been little studied for nanographene, as producing monodispersed samples of nanographene is challenging. In such cases, when the property of each structure is independent, and varies depending on the size, shape and chemical composition at the edges, the presence of a distribution or a mixture of structures returns the average value of the properties for the sample as a whole. It is also possible to simulate the charge transfer properties of nanostructures, but we are still confronted with the challenge associated with the diversity of possible configurations. Previous works on chemical systems have shown that the values are unique to a given structure, and sensitive to isomeric variations.31,32 This can be captured in size- and shapedependent structure/property relationships, but these are strictly relevant only when samples are monodispersed. Structural polydispersivity is typical of nanographene samples, and so it is important that this diversity of structures is captured in any useful theoretical predictions. If we can predict the impact that different size and shape distributions have on properties,
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then we will have a better understanding of the importance of monodispersivity to performance, and make better decisions involving the synthesis and treatment of samples. In this study we use the electronic structure simulations to explore the size and shape dependence of the ionization potential, electron affinity, electronic band gap, Fermi level, electronegativity and chemical hardness of ensembles of reconstructed (clean) and hydrogen passivated graphene nanoflakes. We find that there are likely to be definite advantages to attempts to separate nanographene into more monodispersed samples. By predicting quality factors for a variety of cases, we find that there is a clear motivation for restricting the sizes and suppressing certain morphologies to increase the selectivity and efficiency of charge transfer reactions; even if samples cannot be completely purified. This suggests that the development of classes of nanographene products may be possible, and shows how manipulating the degree of mono/ poly-dispersivity can provide a new way of tuning fundamental properties.
both unpassivated and passivated versions of each structure are included, making 50% of the ensemble H-terminated and 50% of the ensemble “clean”. This is not a random sample; it is a very deliberate sampling where all structures are unique. At this point it should be pointed out that it is difficult to preserve the exact geometric shape in each structure due to the constraints of the graphene lattice, and for our purposes it is important to preserve the right polygonal shape, rather than a particular size. It is not possible to make a structure of each shape with equivalent numbers of atoms, so we have included a range of sizes with each shape, and discuss the resulting trends in the predicted properties. Since we are also concerned with the properties of a diverse ensemble of possible structures, we have analysed the charge transfer property relationships statistically, using the expectation value μ (or ensemble average, which should not be confused with the term used to denote the atomic or molecular chemical potential in other publications), which defined as: μ¼
n X
pi xi
ð1Þ
pi ðxi μÞ2
ð2Þ
i¼1
2
Methodology
Since this study involves so many simulations, we have used the density functional tight-binding method with self-consistent charges (SCC-DFTB), which was implemented in the DFTB+ code,33 to perform the individual calculations.34,35 The SCC-DFTB is an approximate quantum chemical approach where the Kohn–Sham density functional is expanded to second order around a reference electron density. The reference density is obtained from self-consistent density functional calculations of weakly confined neutral atoms within the generalised gradient approximation (GGA). The confinement potential is optimised to anticipate the charge density and effective potential in molecules and solids. A minimal valence basis set is used to account explicitly for the two-centre tight-binding matrix elements within the DFT level. The double counting terms in the Coulomb and exchange–correlation potential, as well as the intra-nuclear repulsion are replaced by a universal short-range repulsive potential. All structures have been fully relaxed with a conjugate gradient methodology until forces on each atom were minimized to be less than 10−4 a.u. (i. e. ≈5 meV Å−1). In all the calculations, the “PBC” set of parameters is used to describe the contributions from diatomic interactions of carbon.36 This method has rigorously benchmarked for a variety of materials and applications,37–42 and has been shown to provide good and reliable results for nanographene in the past.43–46 Results are reproduced in the ESI.† The data set used in this study contains 622 graphene nanoflakes47 with an area between 0.21 nm2 and 54.18 nm2, and a range of different polygonal shapes terminated by zigzag (ZZ) and armchair edges (AC); as shown in Fig. 1 and 2. These include trigonal, hexagonal (Fig. 1) and rectangular flakes with different aspect ratios (α) defined by the number of rings n long the ZZ and AC directions (Fig. 2). Among the entire ensemble the AC and ZZ edges are equally represented, and
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and σ2 is the variance: σ2 ¼
n X i¼1
calculated by summing over the individual properties x of all structures i. The total number of structures for each set is n, and in each case pi is the probability of observation of i: ΔGi
pi ¼
ekB T n ΔGi P ekB T
ð3Þ
i¼1
where kB is Boltzmann’s constant, T is the temperature (taken at 750 K, which is consistent with the formation temperature during CVD synthesis), and the denominator is the canonical partition function. The change in the Gibbs free energy P ΔGi ¼ ðN j Ej Ei ðjÞÞ describes the thermodynamic stability, j as a function of the total energy, Ei ( j ), of particle i, containing j elements; Nj are the number of atoms of species j, and Ej is the energy of j in the reservoir. This can be define with respect to any chemical reservoir (temperature and/or supersaturation) that is required, but in this case we use carbon in a continuous graphene sheet (bulk-graphene), and hydrogen in a gas of H2. Larger structures and lower energy shapes have a higher probability of observation, and therefore contribute more to the properties of the ensemble. Smaller structures and higher energy flakes, such as the unpassivated structures, have a lower probability of observation, and naturally contribute less to the properties of the ensemble. As mentioned above, this study has focused on six properties (x) related to the transfer of electrons; the ionization potential (IP), the electron affinity (EA), the energy of the Fermi level (EF), and electronic band gap (Egap), the chemical hardness (η) and the Mulliken electronegativity (χ). With the
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Fig. 1 Schematic representing the edge-pure morphologies represented in the data set used in this study: (a) hexagons with exclusively ZZ edges, (b) hexagons with exclusively AC edges, (c) trigons with exclusively ZZ edges, and (c) trigons with exclusively AC edges. In each case sets containing a range of sizes are included, as described in ref. 43 and 44, along with unpassivated and passivated versions of each structure.
exception of EF, which is determined self-consistently during the DFTB structural optimization, these properties are defined adiabatically with respect to the total energy of the neutral structure E, and the corresponding anion E− and cation E+, such that: IPi ¼ Ei þ Ei ;
ð4Þ
EAi ¼ Ei Ei ;
ð5Þ
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Egap;i ¼ Ei þ þ Ei 2Ei ;
ð6Þ
1 ηi ¼ ðEi þ þ Ei 2Ei Þ; 2
ð7Þ
1 χ i ¼ ðEi þ Ei Þ: 2
ð8Þ
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Koster potentials, inputs and convergence criteria are applied to all structures; as has been done in this case. In the case of the ionization potential we calculated an ensemble average of 5.097 eV, with a standard deviation of 0.615 eV. In the case of the electron affinity the ensemble average was 3.891 eV, with a standard deviation of 0.632 eV; and the ensemble average of the Fermi energy was found to be −4.504 eV, with a standard deviation of 0.137 eV, and the ensemble average of the band gap was found to be 1.263 eV, with a standard deviation of 0.970 eV. The ensemble average of the chemical hardness was found to be 0.603 eV, with a standard deviation of 0.595 eV; and the electronegativity was found to have an ensemble average of 4.494 eV, with a standard deviation of 0.188 eV. Although these values are comparable to graphite and benzene, it is undoubtedly preferable to consider trends in these properties (rather than focussing on the absolute values), so that a certain amount of systematic error due to the choice of computational method can be eliminated. Fig. 2 Schematic representing the mixed-edge morphologies represented in the data set used in this study, defined by a rectangular n × m matrix, where 2 < n, m < 32. All (n, m) combinations are included, as described in ref. 45, along with unpassivated and passivated versions of each structure.
3
Discussion of results
When we calculate the total energy of each nanographene in the entire ensemble, along with their corresponding anions and cations, the ensemble average and the standard deviation in each of the electronic properties can be predicted, and compared to a suitable reference system, such as bulk ( periodic) graphene. When Egap = 0, as it is for bulk graphene, then IP = EA = −EF; which is equal to 4.661 eV in the present case. This is in good agreement with the experimental value of 4.39 eV.48 However, given the small sizes of the structures in this ensemble (570% if the edges can be left unpassivated. In the cases of the different geometric categories, we can see that approximately isotropic shapes, and more specifically trigons, provide better resolution of these properties than an unrestricted/polydispersed sample, but exclusively hexagonal or square nanoflakes do not. Depending on the property of interest, it is better to have a mix of shapes than a distribution of hexagons or squares. And finally, we predict a variable
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response to quality when targeting ribbon-like structures and attempting to make them more monodispersed in size. Up to >87% improvement in the resolution of the Fermi level is predicted for ribbon-like flakes, accompanied by a simultaneous decrease in resolution of the χ and IP; and up to >220% improvement in the resolution of the EA of the 5–20 nm2 nanoflakes is also accompanied by a decrease in resolution of the χ. In almost all cases a trade-off is necessary; improving the quality of one property will likely degrade the quality of another. Before concluding, it is worthwhile pointing out that the results herein have used a Boltzmann distribution (as described above), and the distribution of samples grown using different methods and synthesis conditions may vary. Certainly many graphene nanoflakes are produced under kinetically driven conditions, and a variety of different distributions are possible (including the thermodynamic distribution used here). While there is no universal kinetic expression, as there is for thermodynamics, it is possible to apply any distribution to this type of study, and so to give some indication of the impact using different distributions the results for the Boltzmann distribution are compared to a frequency distribution and a Gaussian (normal) distribution in the ESI.†
4 Conclusions Perhaps the most important lesson from the results presented here is that the degree of polydispersivity in a sample of graphene nanoflakes provides opportunities for controlling properties. Rather than a hindrance, it represents another degree of freedom we can use to tailor samples to specific applications. Monodispersed samples are not always the best, and often a significant reduction in the quality (or resolution) of charge transfer properties can result from attempts to reduce the size-, shape- or structural distributions. This will be an important consideration when using size- or shape-control to red- or blue-shift properties, since the advantage will be lost if
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an increase in the property dispersion makes the shift unresolvable. In addition to this, based on the properties from an diverse ensemble of 622 unique graphene nanoflakes (calculated with electronic structure simulations), we may also draw a number of more specific conclusions. Deliberate attempts to homogeneously passivate the edges of graphene nanoflakes seems to have little impact on the charge transfer properties or the quality; and may be largely a waste of time and resources. In contrast, deliberate attempts to keep edges clear of passivation may be more useful than expected, with significant improvement in the resolution of the ionization potential, electron affinity, electronic band gap, Fermi level, electronegativity and chemical hardness, and measurable red- and blue-shifts between −0.244 eV and +0.942 eV. We also find that attention to the size-distributions of graphene nanoflakes (in relation to the mean size) may be worthwhile, even if no attempt were made to control any other structural features. In this study we have demonstrated how applying one aspect of structural control can impact the charge transfer properties of distributions and mixtures of graphene nanoflakes, and further work will reveal if more significant improvements can be expected if we control two or more parameters simultaneously. However, even if perfectly precise structural selectivity remains elusive during synthesis, the quality of samples can be still be enhanced if a subset of structures can be separated post-synthesis.
Acknowledgements Computational resources for this project have been supplied by the National Computational Infrastructure national facility under grant q27.
Notes and references 1 A. K. Geim and K. S. Novoselov, Nat. Mater., 2007, 183–191. 2 J. Du, S. Pei, L. Ma and H.-M. Cheng, Adv. Mater., 2014, 1958–1991. 3 M. D. Stoller, S. J. Park, Y. W. Zhu, J. H. An and R. S. Ruoff, Nano Lett., 2008, 3498–3502. 4 D. H. Wang, D. W. Choi, J. Li, Z. G. Yang, Z. M. Nie, R. Kou, D. H. Hu, C. M. Wang, L. V. Saraf, J. G. Zhang, I. A. Aksay and J. Liu, ACS Nano, 2009, 907–914. 5 E. Yoo, T. Okata, T. Akita, M. Kohyama, J. Nakamura and I. Honma, Nano Lett., 2009, 2255–2259. 6 J. L. Xie, C. X. Guo and C. M. Li, Energy Environ. Sci., 2014, 2559–2579. 7 V. Volman, Y. Zhu, A.-R. O. Raji, B. Genorio, W. Lu, C. Xiang, C. Kittrell and J. M. Tour, ACS Appl. Mater. Interfaces, 2014, 298–304. 8 Y. Shao, J. Wang, H. Wu, J. Liu, I. A. Aksay and Y. Lin, Electroanalysis, 2010, 1027–1036. 9 Y. H. Wu, T. Yu and Z. X. Shen, J. Appl. Phys., 2010, 071301.
This journal is © The Royal Society of Chemistry 2014
Paper
10 S. Watcharotone, D. A. Dikin, S. Stankovich, R. Piner, I. Jung, G. H. B. Dommett, G. Evmenenko, S. E. Wu, S. F. Chen, C. P. Liu, S. T. Nguyen and R. S. Ruoff, Nano Lett., 2007, 1888–1892. 11 G. Eda, G. Fanchini and M. Chhowalla, Nat. Nanotechnol., 2008, 270–274. 12 H. A. Becerril, J. Mao, Z. Liu, R. M. Stoltenberg, Z. Bao and Y. Chen, ACS Nano, 2008, 463–470. 13 X. Wang, L. J. Zhi and K. Mullen, Nano Lett., 2008, 323– 327. 14 K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, J. H. Ahn, P. Kim, J. Y. Choi and B. H. Hong, Nature, 2009, 706–710. 15 T. O. Wehling, K. S. Novoselov, S. V. Morozov, E. E. Vdovin, M. I. Katsnelson, A. K. Geim and A. I. Lichtenstein, Nano Lett., 2007, 8, 173–177. 16 J. T. Robinson, F. K. Perkins, E. S. Snow, Z. Wei and P. E. Sheehan, Nano Lett., 2008, 3137–3140. 17 C. S. Shan, H. F. Yang, J. F. Song, D. X. Han, A. Ivaska and L. Niu, Anal. Chem., 2009, 2378–2382. 18 M. Zhou, Y. M. Zhai and S. J. Dong, Anal. Chem., 2009, 5603–5613. 19 X. H. Kang, J. Wang, H. Wu, A. I. Aksay, J. Liu and Y. H. Lin, Biosens. Bioelectron., 2009, 901–905. 20 Y. Dan, Y. Lu, N. J. Kybert, Z. Luo and A. T. C. Johnson, Nano Lett., 2009, 1472–1475. 21 J. D. Fowler, M. J. Allen, V. C. Tung, Y. Yang, R. B. Kaner and B. H. Weiller, ACS Nano, 2009, 301–306. 22 V. Dua, S. P. Surwade, S. Ammu, S. R. Agnihotra, S. Jain, K. E. Roberts, S. Park, R. S. Ruoff and S. K. Manohar, Angew. Chem., Int. Ed., 2010, 2154–2157. 23 F. Yavari, Z. Chen, A. V. Thomas, W. Ren, H.-M. Cheng and N. Koratkar, Sci. Rep., 2011, 166. 24 W. Yuan, A. Liu, L. Huang, C. Li and G. Shi, Adv. Mater., 2013, 766–771. 25 L. K. Randeniya, H. Q. Shi, A. S. Barnard, J. Fang, P. J. Martin and K. Ostrikov, Small, 2013, 3993–3999. 26 J. Kim and J. S. Suh, ACS Nano, 2014, 4190–4196. 27 R. G. Pearson, Proc. Natl. Acad. Sci. U. S. A., 1986, 8440– 8441. 28 L. Pauling, J. Am. Chem. Soc., 1932, 3570–3582. 29 R. S. Mulliken, J. Chem. Phys., 1934, 782. 30 NIST Chemistry WebBook, NIST Standard Reference Database Number 69, ed. W. G. Mallard and P. J. Linstrom, National Institute of Standards and Technology, Gaithersburg, MD, 2001. 31 N. S. Hush and J. A. Pople, Trans. Faraday Soc., 1955, 600– 605. 32 R. S. Becker and W. E. Wentworth, J. Am. Chem. Soc., 1963, 2210. 33 B. Aradi, B. Hourahine and Th. Frauenheim, J. Phys. Chem. A, 2007, 5678–5684. 34 D. Porezag, Th. Frauenheim, Th. Köhler, G. Seifert and R. Kaschner, Phys. Rev. B: Condens. Matter, 1995, 12947. 35 Th. Frauenheim, G. Seifert, M. Elstner, Th. Niehaus, C. Köhler, M. Amkreutz, M. Sternberg, Z. Hajnal, A. Di Carlo and S. Suhai, J. Phys.: Condens. Matter, 2002, 3015.
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Published on 18 December 2014. Downloaded by McMaster University on 19/12/2014 09:48:13.
Paper
36 C. Kohler and T. Frauenheim, Surf. Sci., 2006, 453–460. 37 J. Zheng, Y. Zhao and D. G. Truhlar, J. Chem. Theory Comput., 2007, 569–582. 38 N. M. Settergren, P. Bühlmann and E. A. Amin, Theochem, 2008, 68–73. 39 T. Schwabe and S. Grimme, Acc. Chem. Res., 2008, 569–579. 40 R. Liang, J. M. J. Swanson and G. A. Voth, J. Chem. Theory Comput., 2014, 451–462. 41 A. Zobelli, V. Ivanovskaya, P. Wagner, I. Suarez-Martinez, A. Yaya and C. P. Ewels, Phys. Status Solidi B, 2012, 276–282. 42 G. Zheng, M. Lundberg, J. Jakowski, T. Vreven, M. J. Frisch and K. Morokuma, Int. J. Quantum Chem., 2009, 1841–1854. 43 A. S. Barnard and I. K. Snook, Model. Simul. Mater. Sci. Eng., 2011, 054001. 44 H. Q. Shi, A. S. Barnard and I. K. Snook, Nanotechnology, 2012, 065707. 45 H. Q. Shi, A. S. Barnard and I. K. Snook, J. Mater. Chem., 2012, 18119–18123. 46 H. Q. Shi, A. S. Barnard and I. K. Snook, Nanoscale, 2012, 6761–6767. 47 A. Barnard, Graphene Structure Set. v1. CSIRO. Data Collection, 2014, DOI: 10.4225/08/541F61EC81EE3. 48 R. S. Mulliken, Phys. Rev., 1948, 730–738. 49 K. Kimura, S. Katsumata, Y. Achiba, T. Yamazaki and S. Iwata, Handbook of HeI Photoelectron Spectra of Fundamental Organic Molecules, Halsted, New York, 1981. 50 W. Schmidt, J. Chem. Phys., 1977, 828. 51 R. E. Honig, J. Chem. Phys., 1948, 105–112. 52 P. D. Burrow, J. A. Michejda and K. D. Jordan, J. Chem. Phys., 1987, 9–24. 53 H. M. Rosenstock, K. Draxl, B. W. Steiner and J. T. Herron, J. Phys. Chem. Ref. Data, 1977, 6(Suppl. 1).
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Nanoscale
54 J. C. Rienstra-Kiracofe, G. S. Tschumper and H. F. Schaefer III, Chem. Rev., 2002, 231–282. 55 J. Simons, Annu. Rev. Phys. Chem., 2011, 107–128. 56 R. V. Noorden, Nature, 2011, 14–16. 57 M. C. Hersam, Nat. Nanotechnol., 2008, 287–394. 58 K. Kamaras, M. E. Itkis, H. Hu, B. Zhao and R. C. Haddon, Science, 2003, 1501. 59 M. Zheng, A. Jagota, E. D. Semke, B. A. Diner, R. S. McLean, S. R. Lustig, R. E. Richardson and N. G. Tassi, Nat. Mater., 2003, 338–342. 60 M. Zheng, A. Jagota, M. S. Strano, A. P. Santos, P. Barone, S. G. Chou, B. A. Diner, M. S. Dresselhaus, R. S. Mclean, G. B. Onoa, G. G. Samsonidze, E. D. Semke, M. Usrey and D. J. Walls, Science, 2003, 1545–1548. 61 X. Tu, S. Manohr, A. Jagota and M. Zheng, Nature, 2009, 250–253. 62 R. Krupke, F. Hennrich, H. V. Löhneysen and M. M. Kappes, Science, 2003, 344–347. 63 Y. Miyata, T. Kawai, Y. Miyamoto, K. Yanagi, Y. Maniwa and H. Kataura, J. Phys. Chem. C, 2007, 9671–9677. 64 M. S. Arnold, A. A. Green, J. F. Hulvat, S. I. Stupp and M. C. Hersam, Nat. Nanotechnol., 2006, 60–65. 65 S. Ghosh, S. M. Bachilo and R. B. Weisman, Nat. Nanotechnol., 2010, 443–450. 66 P. C. Collins, M. S. Arnold and P. Avouris, Science, 2001, 706–709. 67 H. Liu, D. Nishide, T. Tanaka and H. Kataura, Nat. Commun., 2011, 309. 68 H. Liu, T. Tanak, Y. Urabe and H. Kataura, Nano Lett., 2013, 1996–2003. 69 S. Ghaffari, S. A. Chandorkar, S. Wang, E. J. Ng, C. H. Ahn, V. Hong, Y. Yan and T. W. Kenny, Sci. Rep., 2013, 3244.
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Impact of distributions and mixtures on the charge transfer properties of graphene nanoflakes† Hongqing Shi, Robert J. Rees, Manolo C. Per and Amanda S. Barnard* Many of the promising new applications of graphene nanoflakes are moderated by charge transfer reactions occurring between defects, such as edges, and the surrounding environment. In this context the sign and value of properties such as the ionization potential, electron affinity, electronegativity and chemical hardness can be useful indicators of the efficiency of graphene nanoflakes for different reactions, and can help identify new application areas. However, as samples of graphene nanoflakes cannot necessarily be perfectly monodispersed, it is necessary to predict these properties for polydispersed ensembles of flakes, and provide a statistical solution. In this study we use some simple statistical methods, in combination with electronic structure simulations, to predict the charge transfer properties of different types of
Received 17th October 2014, Accepted 9th December 2014
ensembles where restrictions have been placed on the diversity of the structures. By predicting quality
DOI: 10.1039/c4nr06123c
factors for a variety of cases, we find that there is a clear motivation for restricting the sizes and suppressing certain morphologies to increase the selectivity and efficiency of charge transfer reactions; even if
www.rsc.org/nanoscale
samples cannot be completely purified.
1 Introduction In recent years electrically conductive1 graphene nanoflakes (nanographene) have emerged as a new tool in diverse fields such as electronics,2 energy,3–6 aeronautics,7 and sensing;8 and have facilitated the next generation of electronic, spintronic, optical and sensing devices.9 For example, adding graphene to composite films has been shown to simultaneously provide high transparency, good conductivity, and superior mechanical properties.10–14 In recent years a number of graphene-based electrochemical sensors have been developed, for applications in bioanalysis and environmental analysis.15–25 Commercialization of these technologies is also underway, as it is now possible to create low-cost samples of graphene nanoflakes, with a reasonably high degree of control.26 In the case of sensors, the efficiency, selectivity and sensitivity are moderated by a charge transfer reaction, which occurs between different defects, such as edges, and the surrounding molecules and/or environment. The direction and efficiency of charge transfer depend on whether the host nanographene acts as a donor or acceptor and so, in the case of
CSIRO Virtual Nanoscience Laboratory, 343 Royal Parade, Parkville, Victoria 3052, Australia. E-mail: [email protected]; Tel: +61-3-9662-7356 † Electronic supplementary information (ESI) available: Details of computational simulations and specific results. Comparison of the expectation values of quality factors for ensemble properties based on different statistical distributions. See DOI: 10.1039/c4nr06123c
This journal is © The Royal Society of Chemistry 2014
electron transfer, the sign and value of the ionization potential (the donation of an electron) and the electron affinity (the accepting of an electron) are ideal indicators. Other related indicators include the energy of the Fermi level and the fundamental electronic band gap; the chemical hardness which describes the preferred coordination of acids and bases;27 and the electronegativity,28 which is defined as the average between the absolute values of the ionization potential and the electron affinity.29 Although it is possible to measure these quantities,30 they have been little studied for nanographene, as producing monodispersed samples of nanographene is challenging. In such cases, when the property of each structure is independent, and varies depending on the size, shape and chemical composition at the edges, the presence of a distribution or a mixture of structures returns the average value of the properties for the sample as a whole. It is also possible to simulate the charge transfer properties of nanostructures, but we are still confronted with the challenge associated with the diversity of possible configurations. Previous works on chemical systems have shown that the values are unique to a given structure, and sensitive to isomeric variations.31,32 This can be captured in size- and shapedependent structure/property relationships, but these are strictly relevant only when samples are monodispersed. Structural polydispersivity is typical of nanographene samples, and so it is important that this diversity of structures is captured in any useful theoretical predictions. If we can predict the impact that different size and shape distributions have on properties,
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then we will have a better understanding of the importance of monodispersivity to performance, and make better decisions involving the synthesis and treatment of samples. In this study we use the electronic structure simulations to explore the size and shape dependence of the ionization potential, electron affinity, electronic band gap, Fermi level, electronegativity and chemical hardness of ensembles of reconstructed (clean) and hydrogen passivated graphene nanoflakes. We find that there are likely to be definite advantages to attempts to separate nanographene into more monodispersed samples. By predicting quality factors for a variety of cases, we find that there is a clear motivation for restricting the sizes and suppressing certain morphologies to increase the selectivity and efficiency of charge transfer reactions; even if samples cannot be completely purified. This suggests that the development of classes of nanographene products may be possible, and shows how manipulating the degree of mono/ poly-dispersivity can provide a new way of tuning fundamental properties.
both unpassivated and passivated versions of each structure are included, making 50% of the ensemble H-terminated and 50% of the ensemble “clean”. This is not a random sample; it is a very deliberate sampling where all structures are unique. At this point it should be pointed out that it is difficult to preserve the exact geometric shape in each structure due to the constraints of the graphene lattice, and for our purposes it is important to preserve the right polygonal shape, rather than a particular size. It is not possible to make a structure of each shape with equivalent numbers of atoms, so we have included a range of sizes with each shape, and discuss the resulting trends in the predicted properties. Since we are also concerned with the properties of a diverse ensemble of possible structures, we have analysed the charge transfer property relationships statistically, using the expectation value μ (or ensemble average, which should not be confused with the term used to denote the atomic or molecular chemical potential in other publications), which defined as: μ¼
n X
pi xi
ð1Þ
pi ðxi μÞ2
ð2Þ
i¼1
2
Methodology
Since this study involves so many simulations, we have used the density functional tight-binding method with self-consistent charges (SCC-DFTB), which was implemented in the DFTB+ code,33 to perform the individual calculations.34,35 The SCC-DFTB is an approximate quantum chemical approach where the Kohn–Sham density functional is expanded to second order around a reference electron density. The reference density is obtained from self-consistent density functional calculations of weakly confined neutral atoms within the generalised gradient approximation (GGA). The confinement potential is optimised to anticipate the charge density and effective potential in molecules and solids. A minimal valence basis set is used to account explicitly for the two-centre tight-binding matrix elements within the DFT level. The double counting terms in the Coulomb and exchange–correlation potential, as well as the intra-nuclear repulsion are replaced by a universal short-range repulsive potential. All structures have been fully relaxed with a conjugate gradient methodology until forces on each atom were minimized to be less than 10−4 a.u. (i. e. ≈5 meV Å−1). In all the calculations, the “PBC” set of parameters is used to describe the contributions from diatomic interactions of carbon.36 This method has rigorously benchmarked for a variety of materials and applications,37–42 and has been shown to provide good and reliable results for nanographene in the past.43–46 Results are reproduced in the ESI.† The data set used in this study contains 622 graphene nanoflakes47 with an area between 0.21 nm2 and 54.18 nm2, and a range of different polygonal shapes terminated by zigzag (ZZ) and armchair edges (AC); as shown in Fig. 1 and 2. These include trigonal, hexagonal (Fig. 1) and rectangular flakes with different aspect ratios (α) defined by the number of rings n long the ZZ and AC directions (Fig. 2). Among the entire ensemble the AC and ZZ edges are equally represented, and
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and σ2 is the variance: σ2 ¼
n X i¼1
calculated by summing over the individual properties x of all structures i. The total number of structures for each set is n, and in each case pi is the probability of observation of i: ΔGi
pi ¼
ekB T n ΔGi P ekB T
ð3Þ
i¼1
where kB is Boltzmann’s constant, T is the temperature (taken at 750 K, which is consistent with the formation temperature during CVD synthesis), and the denominator is the canonical partition function. The change in the Gibbs free energy P ΔGi ¼ ðN j Ej Ei ðjÞÞ describes the thermodynamic stability, j as a function of the total energy, Ei ( j ), of particle i, containing j elements; Nj are the number of atoms of species j, and Ej is the energy of j in the reservoir. This can be define with respect to any chemical reservoir (temperature and/or supersaturation) that is required, but in this case we use carbon in a continuous graphene sheet (bulk-graphene), and hydrogen in a gas of H2. Larger structures and lower energy shapes have a higher probability of observation, and therefore contribute more to the properties of the ensemble. Smaller structures and higher energy flakes, such as the unpassivated structures, have a lower probability of observation, and naturally contribute less to the properties of the ensemble. As mentioned above, this study has focused on six properties (x) related to the transfer of electrons; the ionization potential (IP), the electron affinity (EA), the energy of the Fermi level (EF), and electronic band gap (Egap), the chemical hardness (η) and the Mulliken electronegativity (χ). With the
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Fig. 1 Schematic representing the edge-pure morphologies represented in the data set used in this study: (a) hexagons with exclusively ZZ edges, (b) hexagons with exclusively AC edges, (c) trigons with exclusively ZZ edges, and (c) trigons with exclusively AC edges. In each case sets containing a range of sizes are included, as described in ref. 43 and 44, along with unpassivated and passivated versions of each structure.
exception of EF, which is determined self-consistently during the DFTB structural optimization, these properties are defined adiabatically with respect to the total energy of the neutral structure E, and the corresponding anion E− and cation E+, such that: IPi ¼ Ei þ Ei ;
ð4Þ
EAi ¼ Ei Ei ;
ð5Þ
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Egap;i ¼ Ei þ þ Ei 2Ei ;
ð6Þ
1 ηi ¼ ðEi þ þ Ei 2Ei Þ; 2
ð7Þ
1 χ i ¼ ðEi þ Ei Þ: 2
ð8Þ
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Koster potentials, inputs and convergence criteria are applied to all structures; as has been done in this case. In the case of the ionization potential we calculated an ensemble average of 5.097 eV, with a standard deviation of 0.615 eV. In the case of the electron affinity the ensemble average was 3.891 eV, with a standard deviation of 0.632 eV; and the ensemble average of the Fermi energy was found to be −4.504 eV, with a standard deviation of 0.137 eV, and the ensemble average of the band gap was found to be 1.263 eV, with a standard deviation of 0.970 eV. The ensemble average of the chemical hardness was found to be 0.603 eV, with a standard deviation of 0.595 eV; and the electronegativity was found to have an ensemble average of 4.494 eV, with a standard deviation of 0.188 eV. Although these values are comparable to graphite and benzene, it is undoubtedly preferable to consider trends in these properties (rather than focussing on the absolute values), so that a certain amount of systematic error due to the choice of computational method can be eliminated. Fig. 2 Schematic representing the mixed-edge morphologies represented in the data set used in this study, defined by a rectangular n × m matrix, where 2 < n, m < 32. All (n, m) combinations are included, as described in ref. 45, along with unpassivated and passivated versions of each structure.
3
Discussion of results
When we calculate the total energy of each nanographene in the entire ensemble, along with their corresponding anions and cations, the ensemble average and the standard deviation in each of the electronic properties can be predicted, and compared to a suitable reference system, such as bulk ( periodic) graphene. When Egap = 0, as it is for bulk graphene, then IP = EA = −EF; which is equal to 4.661 eV in the present case. This is in good agreement with the experimental value of 4.39 eV.48 However, given the small sizes of the structures in this ensemble (570% if the edges can be left unpassivated. In the cases of the different geometric categories, we can see that approximately isotropic shapes, and more specifically trigons, provide better resolution of these properties than an unrestricted/polydispersed sample, but exclusively hexagonal or square nanoflakes do not. Depending on the property of interest, it is better to have a mix of shapes than a distribution of hexagons or squares. And finally, we predict a variable
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response to quality when targeting ribbon-like structures and attempting to make them more monodispersed in size. Up to >87% improvement in the resolution of the Fermi level is predicted for ribbon-like flakes, accompanied by a simultaneous decrease in resolution of the χ and IP; and up to >220% improvement in the resolution of the EA of the 5–20 nm2 nanoflakes is also accompanied by a decrease in resolution of the χ. In almost all cases a trade-off is necessary; improving the quality of one property will likely degrade the quality of another. Before concluding, it is worthwhile pointing out that the results herein have used a Boltzmann distribution (as described above), and the distribution of samples grown using different methods and synthesis conditions may vary. Certainly many graphene nanoflakes are produced under kinetically driven conditions, and a variety of different distributions are possible (including the thermodynamic distribution used here). While there is no universal kinetic expression, as there is for thermodynamics, it is possible to apply any distribution to this type of study, and so to give some indication of the impact using different distributions the results for the Boltzmann distribution are compared to a frequency distribution and a Gaussian (normal) distribution in the ESI.†
4 Conclusions Perhaps the most important lesson from the results presented here is that the degree of polydispersivity in a sample of graphene nanoflakes provides opportunities for controlling properties. Rather than a hindrance, it represents another degree of freedom we can use to tailor samples to specific applications. Monodispersed samples are not always the best, and often a significant reduction in the quality (or resolution) of charge transfer properties can result from attempts to reduce the size-, shape- or structural distributions. This will be an important consideration when using size- or shape-control to red- or blue-shift properties, since the advantage will be lost if
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an increase in the property dispersion makes the shift unresolvable. In addition to this, based on the properties from an diverse ensemble of 622 unique graphene nanoflakes (calculated with electronic structure simulations), we may also draw a number of more specific conclusions. Deliberate attempts to homogeneously passivate the edges of graphene nanoflakes seems to have little impact on the charge transfer properties or the quality; and may be largely a waste of time and resources. In contrast, deliberate attempts to keep edges clear of passivation may be more useful than expected, with significant improvement in the resolution of the ionization potential, electron affinity, electronic band gap, Fermi level, electronegativity and chemical hardness, and measurable red- and blue-shifts between −0.244 eV and +0.942 eV. We also find that attention to the size-distributions of graphene nanoflakes (in relation to the mean size) may be worthwhile, even if no attempt were made to control any other structural features. In this study we have demonstrated how applying one aspect of structural control can impact the charge transfer properties of distributions and mixtures of graphene nanoflakes, and further work will reveal if more significant improvements can be expected if we control two or more parameters simultaneously. However, even if perfectly precise structural selectivity remains elusive during synthesis, the quality of samples can be still be enhanced if a subset of structures can be separated post-synthesis.
Acknowledgements Computational resources for this project have been supplied by the National Computational Infrastructure national facility under grant q27.
Notes and references 1 A. K. Geim and K. S. Novoselov, Nat. Mater., 2007, 183–191. 2 J. Du, S. Pei, L. Ma and H.-M. Cheng, Adv. Mater., 2014, 1958–1991. 3 M. D. Stoller, S. J. Park, Y. W. Zhu, J. H. An and R. S. Ruoff, Nano Lett., 2008, 3498–3502. 4 D. H. Wang, D. W. Choi, J. Li, Z. G. Yang, Z. M. Nie, R. Kou, D. H. Hu, C. M. Wang, L. V. Saraf, J. G. Zhang, I. A. Aksay and J. Liu, ACS Nano, 2009, 907–914. 5 E. Yoo, T. Okata, T. Akita, M. Kohyama, J. Nakamura and I. Honma, Nano Lett., 2009, 2255–2259. 6 J. L. Xie, C. X. Guo and C. M. Li, Energy Environ. Sci., 2014, 2559–2579. 7 V. Volman, Y. Zhu, A.-R. O. Raji, B. Genorio, W. Lu, C. Xiang, C. Kittrell and J. M. Tour, ACS Appl. Mater. Interfaces, 2014, 298–304. 8 Y. Shao, J. Wang, H. Wu, J. Liu, I. A. Aksay and Y. Lin, Electroanalysis, 2010, 1027–1036. 9 Y. H. Wu, T. Yu and Z. X. Shen, J. Appl. Phys., 2010, 071301.
This journal is © The Royal Society of Chemistry 2014
Paper
10 S. Watcharotone, D. A. Dikin, S. Stankovich, R. Piner, I. Jung, G. H. B. Dommett, G. Evmenenko, S. E. Wu, S. F. Chen, C. P. Liu, S. T. Nguyen and R. S. Ruoff, Nano Lett., 2007, 1888–1892. 11 G. Eda, G. Fanchini and M. Chhowalla, Nat. Nanotechnol., 2008, 270–274. 12 H. A. Becerril, J. Mao, Z. Liu, R. M. Stoltenberg, Z. Bao and Y. Chen, ACS Nano, 2008, 463–470. 13 X. Wang, L. J. Zhi and K. Mullen, Nano Lett., 2008, 323– 327. 14 K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, J. H. Ahn, P. Kim, J. Y. Choi and B. H. Hong, Nature, 2009, 706–710. 15 T. O. Wehling, K. S. Novoselov, S. V. Morozov, E. E. Vdovin, M. I. Katsnelson, A. K. Geim and A. I. Lichtenstein, Nano Lett., 2007, 8, 173–177. 16 J. T. Robinson, F. K. Perkins, E. S. Snow, Z. Wei and P. E. Sheehan, Nano Lett., 2008, 3137–3140. 17 C. S. Shan, H. F. Yang, J. F. Song, D. X. Han, A. Ivaska and L. Niu, Anal. Chem., 2009, 2378–2382. 18 M. Zhou, Y. M. Zhai and S. J. Dong, Anal. Chem., 2009, 5603–5613. 19 X. H. Kang, J. Wang, H. Wu, A. I. Aksay, J. Liu and Y. H. Lin, Biosens. Bioelectron., 2009, 901–905. 20 Y. Dan, Y. Lu, N. J. Kybert, Z. Luo and A. T. C. Johnson, Nano Lett., 2009, 1472–1475. 21 J. D. Fowler, M. J. Allen, V. C. Tung, Y. Yang, R. B. Kaner and B. H. Weiller, ACS Nano, 2009, 301–306. 22 V. Dua, S. P. Surwade, S. Ammu, S. R. Agnihotra, S. Jain, K. E. Roberts, S. Park, R. S. Ruoff and S. K. Manohar, Angew. Chem., Int. Ed., 2010, 2154–2157. 23 F. Yavari, Z. Chen, A. V. Thomas, W. Ren, H.-M. Cheng and N. Koratkar, Sci. Rep., 2011, 166. 24 W. Yuan, A. Liu, L. Huang, C. Li and G. Shi, Adv. Mater., 2013, 766–771. 25 L. K. Randeniya, H. Q. Shi, A. S. Barnard, J. Fang, P. J. Martin and K. Ostrikov, Small, 2013, 3993–3999. 26 J. Kim and J. S. Suh, ACS Nano, 2014, 4190–4196. 27 R. G. Pearson, Proc. Natl. Acad. Sci. U. S. A., 1986, 8440– 8441. 28 L. Pauling, J. Am. Chem. Soc., 1932, 3570–3582. 29 R. S. Mulliken, J. Chem. Phys., 1934, 782. 30 NIST Chemistry WebBook, NIST Standard Reference Database Number 69, ed. W. G. Mallard and P. J. Linstrom, National Institute of Standards and Technology, Gaithersburg, MD, 2001. 31 N. S. Hush and J. A. Pople, Trans. Faraday Soc., 1955, 600– 605. 32 R. S. Becker and W. E. Wentworth, J. Am. Chem. Soc., 1963, 2210. 33 B. Aradi, B. Hourahine and Th. Frauenheim, J. Phys. Chem. A, 2007, 5678–5684. 34 D. Porezag, Th. Frauenheim, Th. Köhler, G. Seifert and R. Kaschner, Phys. Rev. B: Condens. Matter, 1995, 12947. 35 Th. Frauenheim, G. Seifert, M. Elstner, Th. Niehaus, C. Köhler, M. Amkreutz, M. Sternberg, Z. Hajnal, A. Di Carlo and S. Suhai, J. Phys.: Condens. Matter, 2002, 3015.
Nanoscale
View Article Online
Published on 18 December 2014. Downloaded by McMaster University on 19/12/2014 09:48:13.
Paper
36 C. Kohler and T. Frauenheim, Surf. Sci., 2006, 453–460. 37 J. Zheng, Y. Zhao and D. G. Truhlar, J. Chem. Theory Comput., 2007, 569–582. 38 N. M. Settergren, P. Bühlmann and E. A. Amin, Theochem, 2008, 68–73. 39 T. Schwabe and S. Grimme, Acc. Chem. Res., 2008, 569–579. 40 R. Liang, J. M. J. Swanson and G. A. Voth, J. Chem. Theory Comput., 2014, 451–462. 41 A. Zobelli, V. Ivanovskaya, P. Wagner, I. Suarez-Martinez, A. Yaya and C. P. Ewels, Phys. Status Solidi B, 2012, 276–282. 42 G. Zheng, M. Lundberg, J. Jakowski, T. Vreven, M. J. Frisch and K. Morokuma, Int. J. Quantum Chem., 2009, 1841–1854. 43 A. S. Barnard and I. K. Snook, Model. Simul. Mater. Sci. Eng., 2011, 054001. 44 H. Q. Shi, A. S. Barnard and I. K. Snook, Nanotechnology, 2012, 065707. 45 H. Q. Shi, A. S. Barnard and I. K. Snook, J. Mater. Chem., 2012, 18119–18123. 46 H. Q. Shi, A. S. Barnard and I. K. Snook, Nanoscale, 2012, 6761–6767. 47 A. Barnard, Graphene Structure Set. v1. CSIRO. Data Collection, 2014, DOI: 10.4225/08/541F61EC81EE3. 48 R. S. Mulliken, Phys. Rev., 1948, 730–738. 49 K. Kimura, S. Katsumata, Y. Achiba, T. Yamazaki and S. Iwata, Handbook of HeI Photoelectron Spectra of Fundamental Organic Molecules, Halsted, New York, 1981. 50 W. Schmidt, J. Chem. Phys., 1977, 828. 51 R. E. Honig, J. Chem. Phys., 1948, 105–112. 52 P. D. Burrow, J. A. Michejda and K. D. Jordan, J. Chem. Phys., 1987, 9–24. 53 H. M. Rosenstock, K. Draxl, B. W. Steiner and J. T. Herron, J. Phys. Chem. Ref. Data, 1977, 6(Suppl. 1).
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Nanoscale
54 J. C. Rienstra-Kiracofe, G. S. Tschumper and H. F. Schaefer III, Chem. Rev., 2002, 231–282. 55 J. Simons, Annu. Rev. Phys. Chem., 2011, 107–128. 56 R. V. Noorden, Nature, 2011, 14–16. 57 M. C. Hersam, Nat. Nanotechnol., 2008, 287–394. 58 K. Kamaras, M. E. Itkis, H. Hu, B. Zhao and R. C. Haddon, Science, 2003, 1501. 59 M. Zheng, A. Jagota, E. D. Semke, B. A. Diner, R. S. McLean, S. R. Lustig, R. E. Richardson and N. G. Tassi, Nat. Mater., 2003, 338–342. 60 M. Zheng, A. Jagota, M. S. Strano, A. P. Santos, P. Barone, S. G. Chou, B. A. Diner, M. S. Dresselhaus, R. S. Mclean, G. B. Onoa, G. G. Samsonidze, E. D. Semke, M. Usrey and D. J. Walls, Science, 2003, 1545–1548. 61 X. Tu, S. Manohr, A. Jagota and M. Zheng, Nature, 2009, 250–253. 62 R. Krupke, F. Hennrich, H. V. Löhneysen and M. M. Kappes, Science, 2003, 344–347. 63 Y. Miyata, T. Kawai, Y. Miyamoto, K. Yanagi, Y. Maniwa and H. Kataura, J. Phys. Chem. C, 2007, 9671–9677. 64 M. S. Arnold, A. A. Green, J. F. Hulvat, S. I. Stupp and M. C. Hersam, Nat. Nanotechnol., 2006, 60–65. 65 S. Ghosh, S. M. Bachilo and R. B. Weisman, Nat. Nanotechnol., 2010, 443–450. 66 P. C. Collins, M. S. Arnold and P. Avouris, Science, 2001, 706–709. 67 H. Liu, D. Nishide, T. Tanaka and H. Kataura, Nat. Commun., 2011, 309. 68 H. Liu, T. Tanak, Y. Urabe and H. Kataura, Nano Lett., 2013, 1996–2003. 69 S. Ghaffari, S. A. Chandorkar, S. Wang, E. J. Ng, C. H. Ahn, V. Hong, Y. Yan and T. W. Kenny, Sci. Rep., 2013, 3244.
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