Electrochemical reactivity and fractional conductance of nanowires

Electrochemistry Communications 11 (2009) 1764–1767

Contents lists available at ScienceDirect

Electrochemistry Communications journal homepage: www.elsevier.com/locate/elecom

Electrochemical reactivity and fractional conductance of nanowires E. Santos a,b, P. Quaino b,c, G. Soldano b, W. Schmickler b,* a

Facultad de Matemática, Astronomía y Física, IFFaMAF-CONICET Universidad Nacional de Córdoba, Córdoba, Argentina Institute of Theoretical Chemistry, Ulm University, D-89069 Ulm, Germany c PRELINE-Universidad Nacional del Litoral, Santa Fe, Argentina b

a r t i c l e

i n f o

Article history: Received 22 June 2009 Received in revised form 4 July 2009 Accepted 4 July 2009 Available online 9 July 2009 Keywords: Nanowire Electrocatalysis Fractional conductivity Hydrogen reaction

a b s t r a c t A theory for electrocatalysis devised in the authors’ group is combined with density functional theory to investigate the electrochemical reactivity of monoatomic nanowires towards hydrogen. On Cu and Au wires, hydrogen atoms are much more strongly adsorbed than on planar surfaces of the bulk metal, while on Ag adsorption is weak. These results explain recent observations of fractional conductances on electrochemical Cu and Au nanowires in the hydrogen evolution region. Free energy surfaces for the adsorption and discharge of the proton show low activation barriers of the order of 0.1 eV for Au and 0.5 eV for Cu. Thus, both Au and, most surprisingly, Cu wires promise to be good catalysts for hydrogen evolution. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Electrochemistry offers convenient and elegant techniques for the fabrication of monoatomic metallic nanowires [1,2]. The properties of these wires can be controlled by their electrochemical potential, a variable that is not available for wires in vacuum or in air. This makes electrochemical nanowires particularly versatile. In this work, we examine the electrochemical reactivity of monoatomic nanowires towards hydrogen, for two reasons: Firstly, these nanowires are excellent, well defined model systems to explore the relation between structure and catalytic properties. Secondly, two groups, Li et al. [3] and Kiguchi et al. [4,5] have found, that monoatomic wires of Au and Cu exhibit fractional conductances at potentials in the hydrogen evolution region, while at higher potentials the conductance was integral. In contrast, on Ag wires the conductance was always integral. Tentatively, this effect was ascribed to hydrogen adsorption on the Au and Cu wires, because in the vacuum hydrogen has indeed been shown to induce fractional conductances in gold nanowires [6,7]. However, hydrogen does not adsorb on bulk electrodes of Cu, Au, nor on Ag. Hence this explanation can only be true if the Cu and Au wires have a much greater affinity to hydrogen than the bulk electrodes. Here we apply a theory for electrocatalysis that we have recently proposed [8,9] in combinations with density functional theory (DFT) to the hydrogen reaction on nanowires. We shall show that, indeed, Cu and Au nanowires are much more reactive * Corresponding author. Tel.: +49 731 5031349; fax: +49 731 502 5409. E-mail address: [email protected] (W. Schmickler). 1388-2481/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.elecom.2009.07.012

to hydrogen than the bulk metals, while no major change is observed on Ag. 2. Results and discussions The investigation of the electrochemical reactivity requires extensive DFT calculations for the electronic properties of the monoatomic linear wires. Explicitly, we have considered the three coin metals and platinum; the latter metal was chosen for comparison, because a planar platinum surface adsorbs hydrogen well. All such calculations were performed using the DACAPO code [10]. The electron–ion interactions are accounted through ultrasoft pseudopotentials [11], an energy cutoff of 400 eV, was used in all calculations. Exchange and correlation interactions were treated with the generalized gradient approximation in the version of Perdew, Burke and Ernzerhof [12]. The Brillouin zone integration was performed using a 1  1  40 k-point Monkhorst–Pack grid [13] for the longest wires. Periodic boundary conditions were employed in the axis along the wire. The distance between the atoms in the wire was optimized in a linear configuration. In order to simulate the hydrogen adsorption on an infinite wire, the number of metal atoms were increased systematically until the change in the adsorption energy was less than 0.05 eV (Ag: 10 atoms, Cu and Pt: 9 atoms, Au: 8 atoms). Table 1 shows the equilibrium bond distances and the work functions of the wire; for comparison, the corresponding values for the bulk and for the (1 1 1) surfaces are also given. As expected, the interatomic spacing is shorter than in the bulk metals. The work functions are considerably larger in the wires, an effect that

1765

E. Santos et al. / Electrochemistry Communications 11 (2009) 1764–1767

vation of the number of d electrons. Thus, of the wires investigated only silver has a d band that lies well below the Fermi level. Since we are interested in the electrochemical situation, it is convenient to refer the free energy of adsorption of hydrogen to the standard hydrogen electrode (SHE), using the procedure described by Norskøv et al. [18]. On this scale, the value of DGad denotes the free energy that is needed (for positive values) or gained (for negative values) for the adsorption of a proton from an aqueous solution at pH 0 at the equilibrium potential for hydrogen evolution. Table 1 shows the corresponding values both for the nanowires and for the (1 1 1) surfaces. Within the accuracy of the calculations, our values for the surface are the same as those obtained by Norskøv et al. [18]. For the surfaces, the optimum adsorption site is always the threefold fcc hollow site, for the wire it is the bridge site between two adjacent atoms. Before turning to the adsorption on the wires, let us recapitulate our understanding of hydrogen adsorption on the surfaces, which is well explained by the d band model of Hammer and Norskøv [18,19]. On the surfaces of the three coin metals the d band lies well below the Fermi level. The hydrogen 1s orbital interacts with the d bands and is broadened into a density of states (DOS), which contains both a bonding and an antibonding part. Both lie below the Fermi level and are thus occupied, so that the d band does not contribute to the adsorption bond. Therefore only the sp bands, which are very broad on all these metals, contribute to the bonding. Because of Pauli repulsion, the overlap between the d band and the hydrogen orbital actually weakens the bond. Pauli repulsion increases with the radius of the d orbitals, which follows the column of the periodic table. Therefore, adsorption is most favorable on copper, and weakest on gold. In contrast, on a platinum surface the d band extends above the Fermi level. Therefore the antibonding part of the hydrogen DOS also extends above the Fermi level and is partially empty, so that the d band contributes to the bonding.

Table 1 Work function U, nearest neighbor distance dnn , and free energy DGad for hydrogen adsorption at SHE on nanowires and on fcc(1 1 1) surfaces of a few metals. Cu

Ag

Au

Pt

U [eV] (wire) U [eV] (1 1 1) surface

5.24 4.50

5.124 4.494

6.43 5.261

6.167 5.701

dnn =½Å (wire)

2.61

2.32

2.64

2.39

dnn =½Å (bulk)

2.88

2.59

2.93

2.83

DGad [eV] (wire) DGad [eV] (1 1 1) surface

0.31 0.10

0.18 0.34

0.51 0.41

0.33 0.25

we ascribe to the higher electronic density. These results confirm earlier findings for Au and Ag nanowires by Leiva et al. [14]. For the reactive properties of metal electrodes the position and the width of the d bands are important. This is both true for the adsorption of species [15] and for electrochemical electron transfer [16,17]. Because of the smaller number of neighbours, the d bands in all wires are much narrower than at surfaces, and show more pronounced peaks (see Fig. 1). Indeed, a detailed analysis shows that only the components along the wire are significantly broadened. In the three coin metals, the d bands in the bulk lie well below the Fermi level, so that they play no role in binding adsorbates like hydrogen. In the wire, they are significantly shifted to higher values, and for Cu and Au they end right at the Fermi level, making them similar to transition metals! Obviously, they cannot be shifted above the Fermi level because this would imply that the d bands are no longer completely filled, and the number of d electrons per atom must be conserved. This argument assumes that hybridization between d and sp electrons does not change; generally, this seems to hold [15]. For platinum, the center of the d band is also shifted to higher energies, but the part that lies above the Fermi level is practically unchanged, again because of the conser-

1.2

1.2

Ag

0.8

DOS [eV -1 ]

DOS [eV -1 ]

Cu

d band wire d band Cu(111)

0.4

0.0 -8

-6

-4

-2

0

0.8 d band wire d band Ag(111)

0.4

0.0 -10

2

-8

energy [eV]

-6

-4

-2

0

0

2

energy [eV]

0.8

d band wire

0.4

Pt

0.4

DOS [eV -1 ]

DOS [eV -1 ]

Au 0.6

d band Au(111)

0.2

0.0

d band wire d band Pt(111)

0.2

0.0 -8

-6

-4

-2

energy [eV]

0

2

-8

-6

-4

-2

energy [eV]

Fig. 1. d band densities of state of the wires and of the bulk metals; the Fermi level has been taken as the energy zero.

1766

E. Santos et al. / Electrochemistry Communications 11 (2009) 1764–1767

Fig. 2. Densities of states of the hydrogen 1s orbitals on gold and silver wires. On Au only the bonding orbital is occupied, on silver both the bonding (left) and the antibonding (right) orbitals.

These arguments immediately explain the large decrease of the adsorption energy for copper and gold wires. On both these wires, the d band extends right up to the Fermi level. Therefore, a part of the antibonding DOS of the hydrogen orbital now also extends above the Fermi level and is unfilled, so that the d band now contributes to the bonding. The effect is larger for gold than for copper, because gold, having the larger orbital radius, interacts more strongly with hydrogen than copper [18]. In contrast, on the silver wire the d band lies well below the Fermi level, and the antibonding part of the hydrogen DOS is filled, so that the d band still does not contribute to the bonding. This effect can be clearly observed in Fig. 2. For comparison, we also show the situation on silver, where the antibonding part is filled. To illustrate this point further, we have also calculated Wannier functions [20] from the occupied orbitals. In the case of silver, we found both a bonding and an antibonding orbital between the wire and the hydrogen atoms; on gold only the bonding orbital is occupied. So, on gold and copper wires hydrogen adsorption sets in at potentials well above the hydrogen evolution potential. Therefore the coverage with adsorbed hydrogen is high in the hydrogen evolution region. Thus, our calculations support the suggestion by Kiguchi et al. [4] that the fractional conductances observed on gold and copper wires are caused by hydrogen adsorption, and they also explain why this effect is not observed on silver. In addition they highlight the large difference in reactivity between wires and surfaces of Au and Cu.

2.6

2.6

-0.8 eV -0.4 eV 0.0 eV 0.4 eV 0.8 eV 1.2 eV

2.4 2.2

2.2

2.0

2.0

1.8

1.8

1.6

1.6

1.4

1.4

1.2

1.2

-1.0

-0.8

-0.6

-0.4

-0.2

-0.8 eV -0.4 eV 0.0 eV 0.4 eV 0.8 eV 1.2 eV

2.4

[Å]

[Å]

The energy of adsorption of hydrogen on the gold wire is of the same order of magnitude as on platinum surface. This suggest that the wire should be a good catalyst for hydrogen evolution. However, the adsorption energy is only a thermodynamic value; for the kinetics, the activation energy is important. For this purpose, we have calculated the free energy surface for the adsorption of a hydrogen atom on a Au wire using a method developed in our group [8,9]. Details of the method can be found in the cited literature. The resulting free energy surface for hydrogen adsorption is shown in Fig. 3. It is plotted as a function of the distance of the reactant from the center of the wire, and the solvent coordinate q. The latter is a concept familiar from the electron transfer theory of Marcus [21]. It takes account of the fact that solvation plays an important role in the transfer: the proton in the solution is strongly solvated, while the interaction of the adsorbed hydrogen with water is weak [22]. We have normalized the solvent coordinate such that it has the following meaning: When the configuration of the solvent is characterized by a coordinate q, it would be in equilibrium with a charge of q on the reactant. There are two minima on this surface; the one at the upper left, centered at q ¼ 1, corresponds to a solvated proton at a large distance from the wire. The second minimum is at q ¼ 0 and a distance of d ¼ 1:1 Å, and represents the adsorbed atom. The minimum for the adsorbate is deeper, since adsorption is exergonic. The two minima are separated by a ridge; the saddle point, which gives the energy of activation, has a height of about 0.1 eV, compared

0.0

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Fig. 3. Free energy surface for the adsorption of a proton on a Au (left) and on copper (right) wire, as a function of the separation from the center of the wire and of the solvent coordinate.

E. Santos et al. / Electrochemistry Communications 11 (2009) 1764–1767

with a value of about 0.7 eV obtained with the same method for the planar gold surface [9]. This indicates that the reaction is very fast. The high rate is caused both by the favorable position of the d band and its strong interaction with hydrogen. Copper nanowires also look promising as catalysts, since the d band ends right at the Fermi level. However, the valence orbitals of copper are much tighter than those of gold, and hence the interaction is weaker. In the critical region near the saddle point, it is by about a factor of two smaller than on gold. The resulting free energy surface is also shown in Fig. 3. The energy of activation is about 0.5 eV and hence by about 0.2 eV lower than for the Cu(1 1 1) surface. At room temperature, this corresponds to an increase in the reaction rate by more than three orders of magnitude, placing the copper wire in the range expensive transition metal catalysts like Ir and Rh. The lowering of the energy of activation for hydrogen adsorption on these two wires is mainly caused by the decrease in the adsorption free energy, as can be seen from the following argument. In electrochemical, kinetics, a decrease dðDGÞ of the reaction free energy entails a proportional decrease of the energy of activation: dðEact Þ ¼ adðDGÞ, where the transfer coefficient a is of the order of 1=2. A look at Table 1 shows, that on the basis of this argument we would indeed expect a lowering of the activation energy by about 0.5 eV for gold and by about 0.2 eV for copper. Our results for gold are in line with the general finding, that gold nanostructures show a strongly enhanced reactivity [23–27]. Within the geometry of nanowires this can be well explained by the shift of the work function and concomitant shift of the d band towards the Fermi level. For copper, to the best of our knowledge, no such effect has been reported before. Acknowledgements Financial supports by the Deutsche Forschungsgemeinschaft (Schm 344/34-1,2 and Sa 1770/1-1,2), by the European Union un-

1767

der COST and ELCAT, and by an exchange agreement between the BMBF and CONICET are gratefully acknowledged. E.S., P.Q. and W.S. thank CONICET for continued support. References [1] C.Z. Li, A. Bogozi, W. Huang, J.J. Tao, Nanotechnology 10 (1999) 221. [2] H.X. He, S. Boussaad, B.Q. Xu, C.Z. Li, N.J. Tao, J. Electroanal. Chem. 522 (2002) 167. [3] C. Shu, C.Z. Li, H.X. He, A. Bogozim, J.S. Bunch, N.J. Tao, Phys. Rev. Lett. 84 (2000) 5197. [4] M. Kiguchi, T. Konishi, K. Hasegawa, S. Shidira, K. Murakoshi, Phys. Rev. B 77 (2008) 245421. [5] M. Kiguchi, T. Konishi, S. Miura, K. Murakoshi, Nanotechnology 18 (2007) 424011. [6] Sz. Czonka, A. Halbritter, G. Mihalny, E. Jurdik, O. Shklyarevskii, S. Speller, H. van Kempen, Phys. Rev. Lett. 90 (2003) 116803. [7] Sz. Czonka, A. Halbritter, G. Mihalny, Phys. Rev. B 73 (2006) 075405. [8] E. Santos, A. Lundin, K. Pötting, P. Quaino, W. Schmickler, J. Solid State Electrochem. 13 (2009) 1101. [9] E. Santos, A. Lundin, K. Pötting, P. Quaino, W. Schmickler, Phys. Rev. B 79 (2009) 235436. [10] B. Hammer, L.B. Hansen, J.K. Nørskov, Phys. Rev. B 59 (1999) 7413. [11] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [12] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [13] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [14] E. Leiva, P. Vélez, C. Sanchez, W. Schmickler, Phys. Rev. B 74 (2006) 035422. [15] B. Hammer, J.K. Nørskov, Adv. Catal. 45 (2000) 71. [16] E. Santos, W. Schmickler, Angew. Chem. Int. Ed. 46 (2007) 8262. [17] E. Santos, W. Schmickler, Chem. Phys. Chem. 7 (2006) 2282. [18] J.K. Norskøv, T. Bligaard, A. Logadottir, J.R. Kitchin, J.G. Chen, S. Pandelov, U. Stimming, J. Electrochem. Soc. 152 (2005) J23 (1985) 138. [19] B. Hammer, J.K. Nørskov, Nature 376 (1995) 238. [20] Thygesen, Hansen, Jacobsen, Phys. Rev. Lett. 94 (2005) 026405. [21] R.A. Marcus, J. Chem. Phys. 24 (1956) 966. [22] Y. Gohda, S. Schnur, A. Groß, Faraday Discuss. 140 (2009) 233. [23] M. Valden, X. Lai, D.W. Goodman, Science 281 (1998) 1647. [24] H.J. Zhai, B. Kiran, L.S. Wang, J. Chem. Phys. 121 (2004) 8231. [25] S.R. Bahn, N. Lopez, J.K. Nørskov, K.W. Jacobsen, Phys. Rev. B 66 (2002) 081405(R). [26] R.N. Barnett, H. Hakkinen, A.G. Scherbakov, U. Landman, Nano Lett. 4 (2004) 1845. [27] A. Corma, M. Boronat, S. Gonzales, F. Illas, Chem. Commun. 4 (2007) 3371.