Density Functional Theory Study of Oxygen Reduction Activity on

Article pubs.acs.org/JPCC

Density Functional Theory Study of Oxygen Reduction Activity on Ultrathin Platinum Nanotubes Ivana Matanović,*,†,‡ Paul R. C. Kent,§ Fernando H. Garzon,∥ and Neil J. Henson† †

Theoretical Division, Los Alamos National Laboratory, New Mexico 87545, United States R. Boškovíc Institute, Department of Physical Chemistry, Bijenička 54, 10000 Zagreb, Croatia § Center for Nanophase Material Sciences and Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ∥ Material Physics and Application Division, Los Alamos National Laboratory, New Mexico 87545, United States ‡

S Supporting Information *

ABSTRACT: The structure, stability, and catalytic activity of a number of single- and double-wall platinum (n,m) nanotubes ranging in diameter from 0.3 to 2.0 nm were studied using plane-wave based density functional theory in the gas phase and water environment. The change in the catalytic activity toward the oxygen reduction reaction (ORR) with the size and chirality of the nanotube was studied by calculating equilibrium adsorption potentials for ORR intermediates and by constructing free energy diagrams in the ORR dissociative mechanism network. In addition, the stability of the platinum nanotubes is investigated in terms of electrochemical dissolution potentials and by determining the most stable state of the material as a function of pH and potential, as represented in Pourbaix diagrams. Our results show that the catalytic activity and the stability toward electrochemical dissolution depend greatly on the diameter and chirality of the nanotube. On the basis of the estimated overpotentials for ORR, we conclude that smaller, approximately 0.5 nm in diameter single-wall platinum nanotubes consistently show a huge, up to 400 mV larger overpotential than platinum, indicating very poor catalytic activity toward ORR. This is the result of substantial structural changes induced by the adsorption of any chemical species on these tubes. Single-wall n = m platinum nanotubes with a diameter larger than 1 nm have smaller ORR overpotentials than bulk platinum for up to 180 mV and thus show improved catalytic activity relative to bulk. We also predict that these nanotubes can endure the highest cell potentials but dissolution potentials are still for 110 mV lower than for the bulk, indicating a possible corrosion problem.

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below a critical wire diameter were first predicted in moleculardynamics simulations by Gülseren et al. for Al and Pb.24 After the discovery of multishell helical gold nanowires,8 a number of theoretical papers discussed the structure of solid nanowires,14,15,25 and the variety of possible structures for singlewall metal nanotubes9,11 have been addressed. Using first principles calculations, Singer et al.16 investigated the structure of gold, Elizondo et al.21 of silver, and Konar et al.23 of platinum single-wall nanotubes. It was shown that in all three cases single wall tubes have tubular structures, like carbon nanotubes. Most of the previous work on ultrathin metal nanowires and nanotubes16−21,23 was inspired by the observation of quantized conductance which leads to the number of possible applications in nanoelectronics.26−28 However, besides their interesting electronic and transport properties, platinum nanotubes have potential applications in heterogeneous catalysis, as platinum is widely used as a catalyst for many important reactions. One of the most studied catalytic reactions is the oxygen reduction

INTRODUCTION Since the discovery of carbon nanotubes in 1991,1 onedimensional nanostructures have become one of the most popular subjects in material science due to their extraordinary thermal, mechanical, and electrical properties.2,3 Although there was some progress in the formation of nanotubes and nanowires composed of metal atoms before 2000,4−7 gold nanowires were the first to be synthesized in 2000 by Kondo et al.8,9 Gold nanowires were formed in an ultrahigh vacuum electron microscope using an electron beam thinning method, and both nanowires with helical multishell structures8 and single-wall gold nanotubes9 with diameter as small as 0.4 nm have been produced using this method. Subsequently, silver and platinum nanowires have been synthesized using the same technique in a vacuum.10,11 Silver nanotubes with diameters and helical periodicity similar to gold nanowires have also been reported in an ambient solution phase encapsulated in the pores of self-assembled organic nanotube arrays.12 A large number of theoretical studies have been performed on different metal nanotubes composed of gold,13−18 silver,10,19−21 and platinum22,23 atoms. Unusual noncrystalline structures of ultrathin unsupported metal nanowires that appear © 2012 American Chemical Society

Received: April 12, 2012 Revised: July 10, 2012 Published: July 13, 2012 16499

dx.doi.org/10.1021/jp3035456 | J. Phys. Chem. C 2012, 116, 16499−16510

The Journal of Physical Chemistry C

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optimum lattice constant a was determined for each tube by varying the Pt−Pt bond length and calculating the total energy of the tube. Hence, the optimal lattice constant was determined as a minimum on the total energy vs lattice parameter plot and was found to range from 2.62 Å for the (28,14) tube to 2.81 Å for the (4,2) tube. Consequently, minimum energy optimizations without symmetry restrictions were performed using the determined optimum lattice parameters. Calculations are carried out by using a periodically repeating supercell with a size of 23 Å × 23 Å × nLL for smaller tubes and 32 Å × 32 Å × nLL for bigger tubes where nL is the number of repeating unit cells of the tube with the length L. In that way, vacuum space was set to at least twice the nanotube diameter in order to avoid interactions between periodically repeated images. For n = m, L equals √3|a|, and for n = 2m, L equals |a| and in most cases nL was set to 2, generating approximately 10 Å long supercells. For chiral tubes, the repeating pattern differs depending on the chirality and nL was set accordingly. For the (5,3) tube, for example, L = 20.77 Å, while for the (5,4) tube L = 7.28 Å. All the calculations were performed using the spin polarized generalized gradient approximation (GGA) to density functional theory (DFT) with the Perdew−Wang (PW91)39−41 exchange-correlation functional. The PW91 functional was shown to perform reasonably well in the studies of ORR activity on the platinum (111) surface and for nanoparticles,42,43 and it was found to be superior in predicting the change in the overpotential for ORR upon alloying.43 The projector augmented wave method44,45 was used as implemented in the Vienna Ab initio Software Package (VASP)46−49 with a k-point Monkhorst−Pack50 mesh of the first Brillouin zone ranging between 1 × 1 × 4 and 1 × 1 × 21 depending on the length of the tube. The plane-wave basis cutoff energy was set to 400 eV. Methfessel−Paxton smearing51 of order 2 with a value of σ = 0.2 was used to aid convergence. We estimate that the energies are converged to within 0.001 eV per atom with these criteria and choice of overpotential. The chemical adsorption energies (Ead) are calculated using the energy of the nanotube with the adsorbate (ads) (Eads−tube), the energy of the pure nanotube without the adsorbate (Etube), and the energy of the adsorbate in the gas phase (Eads):

reaction (ORR) in proton exchange fuel cells where the slow kinetics of the oxygen reduction decreases the electrical efficiency of the fuel cell.29 The chemical reactivity and the durability of the catalyst are known to greatly depend on the size and structure of the nanomaterial used in the fuel cell. The performance of platinum nanoparticles as ORR catalysts can, for example, be tuned by modifying their size and shape.30−34 Furthermore, shape-controlled synthetic pathways have recently shown great improvements in producing more complex nanostructures like nanobars, nanorods, and nanodendrites,35,36 all with the aim of improving the catalytic activity of the nanomaterial. Platinum nanotubes may offer better catalytic activity than the bulk due to their convex surface and their specific morphology. Additionally, when organized in arrays by use of a metal support or organic linkers similar to the case of silver nanotubes,12 these interesting one-dimensional nanostructures might provide an innovative way of increasing the active surface area, and thus reduce the catalyst cost. Although potential applications of platinum nanotubes in fuel cells have indeed been previously recognized22,23 and confirmed in experimental observations for 40 nm diameter platinum nanotubes37 and ultrathin acid-treated platinum nanowires,38 previous theoretical work only discussed the atomic structure, stability, and electronic structure of the platinum nanotubes in the gas phase.22,23 Thus, this work represents a pioneering work in this field by using density functional theory (DFT) to discuss possible application of ultrathin platinum nanotubes as catalysts for ORR and by investigating the influence of chirality and the diameter of the nanotubes on their catalytic activity.

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COMPUTATIONAL DETAILS (n,m) single-wall platinum nanotubes (SWPtNTs) were built by rolling up a one-atom-thick Pt(111) sheet to obtain a cylinder in an identical way to how a graphene sheet is rolled to form a carbon nanotube. Double-wall platinum nanotubes (DWPtNTs) were formed in an identical way by rolling two

ads Ead =

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Pt(111) sheets with a common axis. As described in Figure 1, (0,0) and (n,m) atoms define the rolling vector as

RESULTS AND DISCUSSION Structure and Stability. Platinum nanotubes thinner than 2 nm have been synthesized by Oshima et al.11 in an ultrahigh vacuum high resolution microscope using the electron-beam thinning method. By simulating the observed TEM images, it was concluded that the observed multishell structure corresponds to a nanotube in which the outer tube is formed from 13 and inner tube from 6 atomic rows (13−6) and the observed single-wall nanotube to the structure in which six atomic rows coil around the tube axis (6−0). Due to the poor resolution of the TEM images, the period and chirality of the

(1)

where a and b are the basis vectors of the 2D Pt(111) sheet. The diameter of an ideal nanotube can be calculated from its (n,m) indices as follows: d=

n2 + m2 − nm |a| /π

(3)

where nads is the number of chemical species adsorbed on the tube. The stability of platinum nanotubes at different pH's and potentials U was obtained by the approach developed by Nørskov et al. and described in detail in refs 52 and 53. Pourbaix diagrams were constructed by following the procedure by Hansen et al.54 Similar approaches were used in a number of previous works.43,55−58

Figure 1. Rolling of the 2D triangular network of platinum atoms (nonoptimized platinum nanotubes are shown). Basis vectors are denoted as a and b, and each tube is labeled by two integers (n,m) with a roll up vector R = na + mb.

R = na + m b

Eads − tube − (Etube(g) + nadsEads(g)) nads

(2)

We will consider three types of Pt nanotubes: achiral tubes for which n = 2m and n = m and chiral tubes with n ≠ m, ranging in diameter from 0.3 to 2.0 nm. To obtain the minimum energy structures of the studied tubes in the gas phase, first the 16500



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synthesized tubes were left undetermined. Although one previous theoretical study addressed this issue,23 the following discussion supplements this work by sampling a larger number of single-wall platinum nanotubes, showing increased diversity both in chirality and size. Furthermore, we address the stability of the platinum nanotubes in water and in the presence of a cell potential. The energy and structural parameters for the optimized structures are given for all the studied single-wall nanotubes in Tables 1 and 2, and the structures of some selected nanotubes Table 1. Various Physical Quantities of n = m and n = 2m Single-Wall Platinum Nanotubes Pt tube

diameter (theor.) (Å)

averg. width (Å)

E/atom (eV)

string tension (eV/Å)

(4,2) (4,4) (5,5) (6,3) (6,6) (7,7) (8,4) (8,8) (9,9) (10,5) (10,10) (11,11) (12,6) (12,12) (14,7) (13,13) (15,15) (16,8) (18,9) (18,18) (20,10) (22,11) (22,22) (24,12) (28,14)

3.10 3.56 4.33 4.47 5.18 5.94 5.90 6.75 7.58 7.29 8.40 9.24 8.72 10.05 10.15 10.88 12.56 11.57 13.02 14.99 14.46 15.91 18.47 17.36 20.24

3.26 3.66 4.40 4.54 5.17 5.93 5.48 6.52 7.33 6.33 8.16 8.97 8.34 9.75 9.63 10.51 12.12 11.05 12.80 14.60 13.80 15.23 17.81 16.64 19.42

−4.59 −4.66 −4.86 −4.93 −4.97 −5.05 −5.14 −5.15 −5.16 −5.21 −5.18 −5.19 −5.20 −5.21 −5.21 −5.22 −5.23 −5.22 −5.23 −5.23 −5.23 −5.23 −5.23 −5.24 −5.24

2.07 2.28 2.51 2.47 2.76 3.01 2.73 3.13 3.46 3.15 3.77 4.10 3.86 4.39 4.44 4.70 5.36 5.05 5.58 6.46 6.21 6.82 7.88 7.35 8.58

Figure 2. Cross section of the several n = m, n = 2m, and n ≠ m singlewall platinum nanotubes perpendicular to the tube axes. Relative sizes of the tubes are not represented faithfully.

Table 2. Various Physical Quantities of Chiral n ≠ m SingleWall Platinum Nanotubes Pt tube

diameter (theor.) (Å)

averg. width (Å)

E/atom (eV)

string tension (eV/Å)

(5,3) (5,4) (6,4) (6,5) (7,5) (8,6) (10,6) (10,8) (12,8) (12,10)

3.81 4.01 4.56 4.78 5.33 6.12 7.34 7.72 8.88 9.35

3.89 4.07 4.42 4.63 5.09 5.89 6.92 7.50 8.50 9.04

−4.80 −4.80 −4.97 −4.97 −5.05 −5.11 −5.16 −5.16 −5.19 −5.19

2.27 2.39 2.42 2.56 2.68 2.93 3.33 3.55 3.95 4.14

are shown in Figure 2. The stability of the tubes was examined by inspecting the energy per atom and the minimum string tension shown in Figure 3 as a function of the average width of the tubes after relaxation. String tension is commonly used to describe the stability of the tip-suspended wires14,16 and will be used here to describe the stability of platinum nanotubes in

Figure 3. Binding energy per atom and string tension (as defined in the text) of single-wall platinum nanotubes as a function of diameter.

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characterized with a global and at least one local minima, indicating that the structures that occur will depend sensitively on the synthesis conditions. All the other larger tubes (n > 6) relax to hollow structures composed of rows of Pt atoms along the tube axes shaped in irregular polygons with varying diameters even if the optimizations start from perfect cylindrical structures. The irregular polygons are staggered along the axes in the case of n = m and chiral tubes or aligned along the axes in the case of n = 2m (Figure 2). Relaxation of the bigger tubes is dominated by the tendency to form sections analogous to flat (111) surfaces, and optimized structures are characterized by more or less flat (111) areas interconnected with edges. The (8,8) tube, for example, is formed of quadrilaterals, the (11,11) tube of pentagons, and the (13,13) tube of hexagons of platinum atoms alternating along their axes. A large number of tubes are formed of alternating two or more different irregular polygons like in the case of the (12,12) tube whose structure is composed of alternating hexagons and pentagons along the tube axes. To understand this effect in more detail, we studied the energy of the Pt(111) monolayer as a function of an angle with which the monolayer is bent away from the plane. A one atom thick flat (111) sheet of Pt atoms, with the repeating pattern of approximately 20.0 Å in one direction and infinitely long in the perpendicular direction was bent from the plane in 5° increments to model the different extents of structural change observed in relaxed SWPtNTs. In this way, different zigzag configurations of a sheet of platinum atoms were created. After the optimal lattice parameter for each zigzag structure was determined, the structures were optimized. The calculated energy profile is shown in Figure 4. A monolayer of Pt atoms

contact with the bulk-like tips. The minimum string tension is defined as a work done in drawing the tube out of the tips and is given per unit wire length as f = (F − μN)/L. F is the total free energy defined as F = Etotal(tube) − NEatomic(Pt), μ is a chemical potential of the platinum in the bulk, and L is the length of the tube. The chemical potential of a bulk is calculated as μ = Ebulk − Eatomic and was found to be −5.53 eV for platinum. From the energy plot in Figure 3, it can be seen that the energy per atom of the SWPtNT converges to a constant value of approximately −5.24 eV. All the tubes with a diameter larger than 1 nm have an energy per atom close to this value, yet as was shown for gold nanotubes,8 it can be expected that, after a certain diameter, multishell structures would be more thermodynamically stable. Among the tubes with a diameter smaller than 1 nm, n = 2m tubes seem to have lower energy than other tubes of comparable diameter. However, the string tension plot in Figure 3 shows that only (6,3) and (8,4) tubes correspond to the minima on the string tension vs diameter plot and thus only these achiral tubes would show higher stability compared to the other nanotubes with similar diameter. Out of the smaller chiral tubes, only (6,4) and (5,3) tubes are characterized with favorable string tensions. As such, both (6,4) and (6,3) tubes with the calculated average diameters of 4.4 and 4.5 Å could correspond to the experimentally observed SWPtNT with a diameter of 4.8 Å.11 In previous computational work on the other hand, only the (6,4) tube was identified as corresponding to the experimentally observed single-wall tube with six row strands.23 On the basis of their experimental observations, Oshima et al. also indicated that the single-wall tube with five row strands could be formed stably, if the synthetic method had started from a 12−5 multishell tube.11 On the basis of the calculated string tension values, we can predict that in this case the (5,3) tube with an average diameter of 3.9 Å would be formed which agrees with the result of previous work.23 This tube was also identified as one of the “magic” structures of gold SWNTs16 and is referred to as the structure of the experimentally formed single-wall gold nanotube with a 4 Å diameter.9 The optimized structures of several tubes are shown in Figure 2 as a cut through the tube perpendicular to the axes of the tube. The hollowness of the tubes was inspected by examining the total charge density inside the tubes. The absence of charge inside the tube indicates the hollow structure. The (4,2) tube with a diameter of 3.26 Å is the smallest tube and the only nonhollow tube studied herein. Only relaxed achiral tubes with five strands (n = 5) retain their perfect cylindrical structure with a uniform diameter along the tube axes. The optimized structures of achiral tubes with six strands (n = 6) depend on the nature of the initial structures used for the relaxation. If the optimizations start from perfect cylindrical structures, tubes will retain their shape after relaxation (structures shown in Figure 2). However, if the symmetry of these structures is broken by randomly perturbing the initial atom positions by 0.05 Å, the (6,6) and (6,3) tubes deform into structures with energies of −4.98 and −4.99 eV per atom which are lower than the energies of the perfect cylindrical structures, −4.97 and −4.93 eV, respectively. The deformed structure of the (6,6) tube remains hollow but is now formed by consecutive irregular hexagons of platinum atoms along the tube axes. The (6,3) tube, on the other hand, collapses into a very stable nonhollow, bulk-like structure. This result indicates that the conformational space of achiral tubes with six strands is

Figure 4. Change in energy per atom of a Pt(111) sheet with the bending angle. For each sheet, only atoms in a repeating unit cell are shown.

has the lowest energy, i.e., −5.24 eV per atom, if it is bent ∼10° away from the plane, while the energy of the flat Pt(111) monolayer is −5.20 eV per atom. Interestingly, it was previously shown that the most stable atomic configuration of a chain of platinum atoms is a zigzag arrangement rather than a linear one.59 The minimum of the curve in Figure 4 is associated with the zigzag Pt(111) monolayer structure in which the angle between the two facets is around 160° and this approximately corresponds to the angle between the faces in the SWPtNTs with a diameter larger than 1 nm. As shown in Figure 3, the energy of SWPtNTs thus converges to the energy of the most stable zigzag structure of the Pt(111) monolayer and will not exceed it unless the tube collapses to a bulk or a multishell structure. 16502



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with the lowest energy was taken as a starting point for the final geometry optimization in the presence of water molecules. During each ab initio MD simulation, the initial perfect cylindrical structure of the (6,6) tube becomes severely deformed, the tube contracts (the average diameter of the tube decreases to 5.0 Å), and the final optimized structure contains some nonhollow regions along the tube axis. This feature of the smaller achiral tubes with six row strands was already identified in gas phase optimizations. As discussed previously, the optimization of the (6,6) tube results in a deformed structure if the optimization is started from a very deformed instead of a perfect cylindrical tube. However, in these calculations, it was difficult to quantify the deformations needed to trigger the conformational change from a perfect cylindrical to a deformed tube. From our ab initio MD simulations, it can be concluded that the thermal fluctuations of water around the tube can trigger this conformational change and that the (6,6) tube will likely preserve its hollow structure only in a vacuum. In contrast, the (13,13) tube is found to deform in a similar manner as during the gas phase optimization and preserves its hollow structure. Both optimizations in the gas phase and in water result in similar structures composed of irregular hexagons staggered along the tube axis. The (13,13) tube optimized in water has an average diameter of 10.51 Å, the same value as the structure optimized in the gas phase. We can thus conclude that the (13,13) tube will show similar behavior both in the aqueous and gas phase and will preserve its gas phase structure even in the solution. Moreover, we can expect that the stability of the bigger tubes would even increase with the presence of water molecules inside the tubes. For instance, our MD simulations show that the 13.66 Å long (13,13) tube can fit at least a dozen water molecules in its interior and they could additionally stabilize structures of SWPtNT with larger diameters. Corrosion. One of the most important issues when discussing the performance of any material as a catalyst is its durability. For instance, one of the major concerns in fuel cell applications is the resistance of the material to the corrosion, which can severely decrease its performance during a large number of operation cycles. One of the simplest ways to address the corrosion problem, i.e., the electrochemical dissolution of the material, is to study its surface cohesive energy as shown in the following equation:

The two double-wall structures studied in this work were the (6,6)@(13,13) and (5,5)@(12,12) tubes. The DWPtNTs were chosen in order to study the change in the catalytic activity of the corresponding single-wall nanotubes once they form the outer shell of a multiwall structure. Furthermore, these nanotubes could represent the experimentally observed 13−6 and predicted 12−5 multishell structures.11 As no other multishell structures were studied for comparison, one could easily argue that the experimentally observed multishell nanotube could have different chirality as well. However, due to the more demanding nature of the DFT computations needed to study the chemical reactivity of multishell structures, we were limited to a smaller number of structures. The optimized structure of the (6,6)@(13,13) tube is hollow with two distinct tubes, an inner (6,6) tube with an average diameter of 5.47 Å and an outer (13,13) tube with an average diameter of 10.75 Å. The obtained average diameter of the outer tube is larger than 9.8 Å which is the width of the multishell structure observed in the experiment.11 It is also slightly larger than the outer diameter of the corresponding structure obtained by Konar et al. which is calculated as 10.27 Å.23 During the optimization, the outer tube of the (6,6) @(13,13) tube deforms from the initial perfect cylindrical structure in a similar way to that for the (13,13) single-wall tube and, in the optimized structure, the outer tube is formed of alternating rows of Pt atoms in the form of pentagons. The inner tube preserves its cylindrical structure. The same is true for the (5,5)@(12,12) tube. During the optimization, the outer (12,12) tube deforms to a pentagonal shape having an average diameter of 9.93 Å, while the smaller (5,5) tube preserves its hollow structure and deforms only slightly from its starting cylindrical structure. The average diameter of the inner (5,5) tube in the optimized (5,5)@(12,12) structure is 4.63 Å. The diameter of the outer tube is again slightly larger than the values obtained for the corresponding DWPtNT by Konar et al.23 and Oshima et al.11 which are predicted as 9.55 and 9.3 Å, respectively. The energy per atom of both the (6,6)@(13,13) and (5,5)@(12,12) tubes is −5.44 eV. These energies are much lower than the energy per atom of any single-wall tube, which indicates the greater thermodynamic stability of double-wall tubes compared to the single-wall tubes. The higher stability of the double-wall tubes can be explained by the favorable interactions between the atoms of the outer and inner tubes which does not exist in the single-wall tubes. Stability in Water. To probe the stability of SWPtNTs in a water environment, we performed a number of ab initio MD simulations in water. As these calculations are very computationally demanding, only two tubes were studied. The (6,6) tube was chosen to represent tubes with a diameter less than 1 nm, and the (13,13) tube was chosen to represent tubes with a diameter larger than 1 nm. Simulations in water were performed in a box of a size 23 × 23 × 23.27 Å3 in the case of the (6,6) tube and 25 × 25 × 13.67 Å3 in the case of the (13,13) tube. The space around the tubes was filled with water in order to obtain the density of water around 1 g/cm3. This leads to a simulation box containing the tube and 100 water molecules in the case of a smaller tube and 212 water molecules in the case of a bigger tube. In the first step, around a dozen simulated annealing calculations were performed to probe the conformational space of the tubes. The starting temperature was set in the range between 650 and 350 K, with a final temperature of 50 K. The time step was set to 1 fs, and around 1200 MD steps were performed in each case. The geometry

M(s) → Mn +(aq) + ne−(aq)

(4)

If we assume that eq 4 can be divided in several steps: MN (s) → MN − 1 + M(g)

(5)

M(g) → Mn +(g) + ne−(g)

(6)

Mn +(g) + ne−(g) + H 2O → Mn +(aq) + ne−(aq)

(7)

and that all the steps other than the step MN (s) → MN − 1 + M(g)

(8)

involve the same energy change as for the bulk, then the energy change in eq 4 compared to the bulk will depend only on the energy change of the step in eq 8. N refers to the number of metal atoms in the model, and M refers to the lone metal atom. Thus, the dissolution potential of a platinum based nanomaterial relative to the bulk can be estimated using the relation 16503



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ΔU = ΔG /ne

(9)

15 out of 24 cases, the tube collapses from a hollow structure to a very stable bulk structure. This tendency, already identified in gas phase optimizations, explains the very low surface cohesive energy of the (6,3) tube of only 3.63 eV. The (6,4) and (6,6) tubes have surface cohesive energies that are 1.34 and 1.24 eV lower than that of a bulk platinum (6.50 eV). If we assume a Pt2+ concentration of ∼10−6 moldm−3, then the thermodynamic Pt/Pt2+ metal/metal-ion reversible potential would be ∼1.01 V (NHE)

where n is the number of exchanged electrons and ΔG is the change in free energy needed for eq 8. This model has been successfully applied to address the problem of corrosion in metal nanoparticles60 and alloys.43 However, the calculation of cohesive energy in nanotubes represents a more challenging problem because of the large number of nonequivalent atoms on the surface of the tube. Namely, in the case of crystal surfaces or well-defined polyhedra that are often used as models to study catalysis on metal nanoparticles,34,42,61,62 the number of surface atoms with nonequivalent coordination (vertexes, edges, facets) can easily be accounted for. Moreover, the number of nonequivalent sites will not change with the size of the particle as long as the nanoparticle preserves its shape. Although in the relaxed structures of SWPtNTs every platinum atom is coordinated with six atoms, it is difficult to identify atoms that have the same or at least similar chemical environments. Therefore, we assume that every atom in the repeating unit has a unique local environment and hence a different surface cohesive energy. To obtain the lowest surface cohesive energy and the lowest cell potential at which each of the studied tubes will start to dissolve, we calculated the surface cohesive energy of each atom in the repeating unit of the tube. This necessarily requires several optimization calculations of one tube. The surface cohesive energies of all the atoms for all the studied tubes are given in the Supporting Information, and only the lowest surface cohesive energy of each tube is reported in Table 3. The distribution of surface cohesive energies is very

reaction: MN(tube) → MN−1 + M

∼0.5 nm

∼1 nm

∼1 nm a

ΔE (eV)

ΔUcorr (V)

6.50 3.63 5.16 5.27 5.71 5.25 6.05 6.29 5.50 5.67

0.00 −1.44 −0.67 −0.62 −0.40 −0.63 −0.23 −0.11 −0.50 −0.42

(10)

E Pt/Pt2+ = 1.188 + 0.0295 log(c(Pt2 +))

(11)

and compared to the bulk, the (6,4) and (6,6) tubes would thus dissolve at potentials as low as 0.34 and 0.39 V. Most of the larger tubes, namely, the (12,6), (12,12), and (13,13) tubes, have higher surface cohesive energies than the smaller tubes. The only exception is the chiral (12,8) tube with a surface cohesive energy of 5.25 eV which is comparable to those of the (6,4) and (6,6) tubes of 5.16 and 5.27 eV. The (12,12) and (13,13) tubes have the highest surface cohesive energies among all the tubes studied: 6.05 and 6.29 eV, respectively. This would correspond to the electrochemical dissolution potentials of 0.78 and 0.90 V which are still for 0.23 and 0.11 V lower, respectively, than the dissolution potential of the bulk platinum. It is also important to mention that removing any of the atoms in the bigger tubes does not appear to have a profound effect on the structure of these tubes. The structure changes only locally, in the vicinity of the defect site, but the tubes preserve their hollowness and original shape. As mentioned before for the (6,3) tube, the formation of defect sites severely influences the structure of all ∼0.5 nm diameter tubes and often leads to their collapse to the bulk or to the formation of nonhollow regions along the axes of the tube. The only two studied double-wall tubes also have surface cohesive energies lower than the bulk platinum. The lowest surface cohesive energy of the (6,6)@(13,13) tube is 5.50 eV, while that of the (5,5)@(12,12) tube is 5.67 eV. This would correspond to the dissolution potentials that are for 0.50 and 0.42 V lower than that of the bulk. The reason for such unexpectedly low dissolution potentials of two studied doublewall tubes can be found when analyzing the optimized structures of the tubes in the presence of defect sites. Namely, there is a small number of atoms that, if removed from the outer tube, induce the collapse of the inner tube to a more stable nonhollow structure which in turn reduces the energy change in eq 8. So far, we have discussed the structure and stability of various platinum nanotubes in a vacuum and in a water environment, and in the presence of applied potential. Our results indicate that the nanotubes with less than 1 nm diameter show more fluctuations in their structure and deform more easily into arrangements with bulk-like regions along the tube axes. This is especially true in a water environment or when applying a cell potential. Nanotubes with diameters greater than 1 nm have shown to be resistant to thermal fluctuations of water and endure the highest cell potentials. The highest dissolution potential was calculated for (13,13) SWPtNT (0.90 V), but this value is still for 0.11 V lower than that of the bulk, indicating that all the studied nanotubes would be more susceptible to electrochemical corrosion in the fuel cell than the metal catalyst. However, as the dissolution potentials clearly differ greatly with size and chirality, we cannot preclude the existence

Table 3. Calculated Surface Cohesive Energies and the Estimation of the Shift in the Electrochemical Dissolution Potential (ΔUcorr) Compared to Pt(111)a

Pt(111) (6,3) (6,4) (6,6) (12,6) (12,8) (12,12) (13,13) (6,6)@(13,13) (5,5)@(12,12)

Pt2 + + 2e− → Pt(s)

Nanotubes are grouped on the basis of their approximate diameters.

dependent on the size and the chirality of the tube, but they often span a range of up to 700 meV. For instance, in the case of the (13,13) tube, the lowest value of the surface cohesive energy is 6.29 eV, while the highest value is 6.97 eV. In some cases, it is possible to group atoms on the basis of similar surface cohesive energies, for instance, in the case of (6,3), (6,6), or (12,6) tubes. However, this is challenging for most of the studied tubes, which confirmed our assumption that every atom in the repeating unit plays a unique role in the structure and the stability of these nanostructures. All the smaller tubes with a diameter of ∼0.5 nm, namely, the (6,3), (6,4), and (6,6) tubes, have much lower surface cohesive energies than the bulk platinum (Table 3) and thus will dissolve at much lower potentials. The (6,3) tube becomes very unstable upon removal of certain atoms from the tube, and in 16504



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Table 4. Calculated Adsorption Energies (in eV) and the Shifts in the Equilibrium Adsorption Potential for Oxygena Relative to Pt(111) (in V) for Different Nanotubes and Monolayer (ML) Coverages on the fcc Site 0.25 ML diameter ∼0.5 nm

∼1 nm

∼1 nm a

Pt (6,3) (6,4) (6,6) (12,6) (12,8) (12,12) (13,13) (6,6)@(13,13) (5,5)@(12,12)

0.33 ML

0.5 ML

Ead

ΔUf

Ead

ΔUf

Ead

ΔUf

−4.42 −4.72 −4.70 −4.72 −4.29 −4.29 −4.18 −4.14 −4.05 −4.15

0.00 −0.15 −0.14 −0.15 +0.07 +0.07 +0.12 +0.14 +0.19 +0.14

−4.25 −4.52 −4.31 −4.41 −3.98 −4.03 −3.94 −3.90 −4.21 −3.94

0.00 −0.14 −0.03 −0.08 +0.14 +0.11 +0.16 +0.17 +0.02 +0.16

−4.07 −4.50 −4.44 −4.46 −3.96 −4.00 −3.97 −3.92 −4.06 −4.02

0.00 −0.22 −0.19 −0.20 +0.06 +0.04 +0.05 +0.08 +0.01 +0.03

ΔUf = ΔEad/ne, n = 2.

Namely, the oxygen prefers to adsorb on the fcc=hcp site with adsorption energies of −4.41 and −4.11 eV for the (6,6) and (13,13) SWPtNTs. Chemisorption on the atop site is the weakest, and the oxygen adsorption energies for the (6,6) and (13,13) SWPtNTs are −3.94 and −3.50 eV, respectively. The fcc site is further used as the preferred oxygen adsorption site for all other tubes, and the chemical adsorption energies were calculated for different coverages. The results are given in Table 4 and compared to the results for the extended Pt(111) surface. It was assumed that the change in the equilibrium adsorption potential for oxygen relative to the Pt(111) surface depends only on the change in the oxygen adsorption energy57 based on which we estimated the shifts in the oxygen adsorption potentials on different nanotubes relative to platinum. As seen in Table 4, the chemisorption energy of oxygen on different Pt nanotubes varies with coverage and chirality; however, all the tubes with a diameter of ∼0.5 nm consistently adsorb oxygen more strongly than the Pt(111) surface for all the coverages. For instance, the (6,3), (6,4), and (6,6) tubes have oxygen adsorption energies that are between 0.06 and 0.44 eV larger than on the Pt(111) surface. Larger (12,6), (12,8), (12,12), and (13,13) tubes on the other hand adsorb oxygen more weakly than Pt(111). Oxygen adsorption energies for these tubes are between 0.08 and 0.35 eV lower than on the Pt(111) surface, depending on the coverage. It is important to point out that, in the presence of oxygen, most of the smaller tubes get severely deformed, resulting in the formation of the bulk-like regions along the tube axes. These bulk-like structures in turn have greater stability than hollow structures, and this increases the change in energy related to the oxygen adsorption process. The lower thermodynamic stability of the hollow structures of the small tubes was discussed previously when studying the corrosion process and their structure in the aqueous phase. All of the larger tubes studied (∼1 nm in diameter) do not show substantial structural changes associated with the adsorption of oxygen. The chemisorption energies of oxygen on the two doublewall tubes studied in this work, (6,6)@(13,13) and (5,5) @(12,12) tubes, are similar or weaker than on Pt(111), depending on the coverage. For example, the (6,6)@(13,13) and (5,5)@(12,12) tubes bind oxygen for 0.38 and 0.28 eV weaker than Pt(111) for 0.25 monolayer (ML) coverage and for 0.02 and 0.06 eV weaker when the oxygen coverage is 0.5 ML. It was previously suggested that a surface that binds oxygen more weakly than Pt, by about 0.0−0.4 eV, should exhibit improved ORR activity over Pt.57,67 This would imply

of a structure with corrosion properties superior to that of the bulk. Oxygen Reduction Activity. This section focuses on the chemisorption energies of atomic oxygen and a hydroxyl group on the platinum nanotubes and investigates how these energies change with chirality and diameter. Chemical adsorption is an important step in the catalytic process and will be related to the catalytic activity later in the section. Oxygen and hydroxyl species are of special importance when studying the ORR in fuel cells, as the chemisorption of these two species represents the most important steps in the 4e− oxygen reduction pathway.56 Due to the large size of the systems and the nonexistence of reliable models for the water-curved metal surface interface, the systems are further studied in the absence of water. Chemisorption Energy of Oxygen. On the extended Pt(111) surface, oxygen atoms prefer to adsorb on the high symmetry sites, such as fcc and hcp sites, while the adsorption on atop and bridge sites is much weaker. This was shown both in previous theoretical63,64 and experimental65,66 work. Metal clusters on the other hand show significantly different chemical activity than the bulk due to the number of undercoordinated metal atoms created by edges and vertices with very strong oxygen binding energies. For instance, in previous calculations involving Pt nanoparticles of different sizes, it was shown that oxygen adsorbs strongest on the bridge site at the edge of the (111) and (100) facets.34,42 In the case of the single-wall metal nanotubes, all surface Pt atoms have the same coordination number, i.e. six, but as their surface cohesive energies indicate, not all the surface atoms have the same chemical environment. Optimized Pt nanotubes are not characterized by the high symmetry of well-defined polyhedra that are often used as models to study catalysis on metal nanoparticles. It is not straightforward to identify or even classify different nonequivalent adsorption sites on the nanotubes and account for a difference in chemical activity of all the surface atoms. Thus, we decided to consider oxygen chemisorption with different coverages, assuming that the oxygen atoms have the same surface distribution as on the extended Pt(111) surface. This results in average chemisorption energies as opposite to a site specific adsorption energies which are, in our opinion, more informative and more likely to be representative of those observed experimentally. Several tubes were used to identify the most preferable site for oxygen adsorption, and it was shown that the oxygen atoms show very similar adsorption behavior as on the extended Pt(111) surface. 16505



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Table 5. Calculated Adsorption Energies (in eV) and the Shifts in the Equilibrium Adsorption Potential for Hydroxyla Relative to Pt(111) (in V) for Different Nanotubes and Monolayer (ML) Coverages on the Atop Site 0.25 ML diameter ∼0.5 nm

∼1 nm

∼1 nm a

Pt (6,3) (6,4) (6,6) (12,6) (12,8) (12,12) (13,13) (6,6)@(13,13) (5,5)@(12,12)

0.33 ML

0.5 ML

Ead

ΔUf

Ead

ΔUf

Ead

ΔUf

−2.88 −3.70 −3.60 −3.54 −2.92 −2.89 −2.89 −2.83 −3.07 −3.09

0.00 −0.82 −0.72 −0.66 −0.04 −0.01 −0.01 +0.05 −0.19 −0.21

−2.92 −3.47 −3.35 −3.54 −2.98 −2.98 −2.97 −2.87 −3.13 −3.23

0.00 −0.55 −0.43 −0.62 −0.06 −0.06 −0.05 +0.05 −0.21 −0.31

−3.09 −3.76 −3.69 −3.52 −2.73 −2.84 −2.91 −2.85 −3.20 −3.10

0.00 −0.67 −0.60 −0.43 +0.36 +0.25 +0.18 +0.24 −0.11 −0.01

ΔUf = ΔEad/ne, n = 1.

accompanied with the changes in the structure of the outer tube that in turn substantially influence the structure of the inner tube. This effect is, however, unexpected, as the adsorption energies of hydroxyl are in general less than those of oxygen. In many cases, for example, in the case of the (5,5) @(12,12) tube, the inner tube collapses to a rod structure at a hydroxyl coverage of 0.25 and 0.33 ML. These bulk-like structures are then more stable than the hollow structures, which increases the energy change associated with the adsorption of hydroxyl. Pourbaix Diagrams. Tables 4 and 5 are used to construct the Pourbaix diagrams of Pt nanotubes. Pourbaix diagrams have a great importance when assessing different applications of materials, as they provide information on the thermodynamically most stable state of the material for different conditions of potential and pH. Methods for calculating these diagrams using density functional theory are well developed52,53 and have been successfully applied on a number of metals,54 alloys,43,58 and metal nanoparticles.61 Gibbs free energy change for the adsorption of ORR intermediates on the surface of the material can be used to determine the corresponding equilibrium adsorption potentials at pH 0.52,53 For a Pt(111) surface and 0.33 ML, the Gibbs free energy changes for the reactions

higher ORR activity of both single-wall and double-wall nanotubes with ∼1 nm diameter. However, as will be discussed later, ORR activity also depends on the binding strength of other intermediates in the ORR, such as hydroxyl, and unfavorable binding of any intermediate will result in the decreased ORR activity. Chemisorption Energy of Hydroxyl. The most favorable adsorption site of hydroxyl on the extended Pt(111) surface is an atop site with a Pt−OH bond angle about 70° from the surface normal. We assumed that the atop site is the most favorable site for the adsorption of hydroxyl on the Pt nanotubes, as the nanotubes exhibited the same site adsorption trend for oxygen as the extended Pt(111) surface. Binding energies for hydroxyl were calculated for different coverages, and the results are given in Table 5. Similar to the case of oxygen adsorption, the equilibrium adsorption potentials52,53 for hydroxyl are given relative to the Pt(111) surface. Single-wall nanotubes show very similar adsorption trends toward hydroxyl as toward oxygen. Namely, smaller ∼0.5 nm diameter nanotubes bind hydroxyl more strongly than the extended Pt(111) surface. However, the change in binding energy is more pronounced. For example, the (6,3), (6,4), and (6,6) tubes bind hydroxyl between 0.43 and 0.82 eV stronger than the Pt(111) surface. Furthermore, adsorption of hydroxyl induces the same structural changes on smaller tubes as the adsorption of oxygen. In the presence of hydroxyl, the smaller tubes collapse from the hollow, tubular structures to more stable structures containing bulk-like regions along the tube axes. Larger (12,6), (12,8), (12,12), and (13,13) tubes adsorb hydroxyl very similarly to the flat Pt(111) surface. For example, the binding of hydroxyl on the (12,6), (12,8), and (12,12) tubes is between 0.06 and 0.01 eV stronger than on Pt(111), while it is 0.05 eV weaker on the (13,13) tube for 0.25 and 0.33 ML. The only exception is the 0.5 coverage in which the binding of hydroxyl on the ∼1 nm diameter tubes is much weaker than on Pt(111). This is probably due to the fact that the hydroxyl groups at this coverage cannot distribute as favorably on the curved surfaces as they can on the flat surface and the formation of hydrogen bonds between the adjacent hydroxyl groups is thus less effective. Compared to the extended Pt(111) surface, chemisorption energies of hydroxyl on the (6,6)@(13,13) and (5,5)@(12,12) tubes are significantly different than chemisorption energies of oxygen. Namely, both double-wall nanotubes bind hydroxyl more strongly than the Pt(111) surface. The adsorption of hydroxyl is, as compared to the adsorption of oxygen,

∗ + H 2O(g) → O* + H 2(g),

ΔGa

∗ + H 2O(g) → OH* + 1 2 H 2(g),

(12)

ΔG b

(13)

were calculated in previous work as ΔGa = 1.47 eV and ΔGb = 0.80 eV.43 These energies would correspond to equilibrium adsorption potentials of 0.74 and 0.80 V for oxygen and hydroxyl, respectively.43 If we assume that the Gibbs free energy change for the adsorption of ORR intermediates on the platinum nanotubes relative to platinum depends only on the change in the stability of the adsorbed intermediates, then the change in adsorption energies in Tables 4 and 5 can be used to calculate the change in equilibrium adsorption potentials for oxygen and hydroxyl on Pt nanotubes relative to platinum. For example, for the (13,13) tube, the adsorption energy of oxygen is 0.34 eV smaller than that on Pt(111), meaning that the Gibbs free energy change for reaction eq 12 will be increased for the same amount. This in turn increases the equilibrium adsorption potential for oxygen on a (13,13) tube 0.17 V relative to platinum. The same approach can be used for all the tubes and coverages studied and can accordingly be applied for the 16506



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begins to inhibit the ORR. The overpotential for ORR on Pt(111) can thus be estimated to be around 0.56 V.43 Smaller, ∼0.5 nm tubes can be excluded as possible ORR catalysts based on their Pourbaix diagrams. All smaller tubes, namely, the (6,3), (6,4), and (6,6) tubes, bind ORR intermediates too strongly and would thus show very poor ORR activity. As explained in the previous section, the Gibbs free energy change for the adsorption of oxygen, ΔGa, will be increased on average by 0.30 eV for ∼1 nm tubes relative to platinum, while the Gibbs free energy change for the adsorption of hydroxyl, ΔGb, will be reduced on average by −0.03 V (average values are calculated from Tables 4 and 5 for 0.33 ML coverage). Consequently, ΔG1(U) for larger Pt nanotubes will be, on average, decreased by −0.33 eV relative to Pt and ΔG2(U) will be increased by +0.03 eV. If ΔG1(U) = −0.68 + eU and ΔG2(U) = −0.80 + eU are taken as Pt reference values,43 the corresponding values for larger Pt nanotubes would, on average, be ΔG1(U) = −1.01 + eU and ΔG2(U) = −0.77 + eU. Hence, at cell potentials of 0.77 V, the proton and electron transfer step to the adsorbed hydroxyl to form water starts to be endergonic, resulting in an overpotential of approximately 0.46 V. This value is 100 mV smaller than that for the Pt(111) surface, implying that the ∼1 nm diameter Pt nanotubes might have higher ORR activity than platinum. This is clearly illustrated in Figure 6 which shows the difference in free

adsorption of hydroxyl. Once the equilibrium adsorption potential for the most stable form of the material at pH 0 is determined, its pH dependence is further governed with the simple kBT ln 10pH/e term (Nernst behavior). Figure 5 shows Pourbaix diagrams of (6,6) and (13,13) tubes which are taken as representatives for smaller, ∼0.5 nm in

Figure 5. Pourbaix diagram of platinum nanotubes compared to the bulk68,69 (black dashed lines). The regions of oxygen and hydroxide surface adsorptions are shown in blue and violet. The green and orange dashed lines show the highest solubility boundary for Pt nanotubes with diameters of 0.5 and 1 nm, respectively.

diameter, and larger, ∼1 nm in diameter, tubes. Black dashed lines correspond to the Pourbaix diagram of bulk platinum,68,69 while lack solid lines indicate the cell potentials of the reversible hydrogen and oxygen electrodes to show the stability range of water. The blue line denotes the (U,pH) conditions at which water starts to oxidize to form O* on the (6,6) and (13,13) tubes (the difference in the regions for the two tubes are indicated with the black arrow). The violet lines denote the area where the hydroxyl layer starts to form on the same two nanotubes. As can be seen from Figure 5, the smaller (6,6) tube has an extremely small stability region due to strong interactions with both oxygen and hydroxyl. On the other hand, the (13,13) tube has oxygen and hydroxyl adsorption regions very similar to that of the Pt(111) surface.43 One additional, very distinctive difference in Pourbaix diagrams of the two tubes are their solubility boundaries. As discussed earlier, the (6,6) tube will start to electrochemically dissolve at very low potentials, even lower than 0.4 V. The dissolution properties of the larger (13,13) tube are better than those of the smaller tubes but still not competitive with bulk platinum. Oxygen Reduction Activity. Tables 4 and 5 can be further used to estimate the change in the overpotential for oxygen reduction reaction on different nanotubes. Only two steps in the dissociative ORR mechanism involve positive changes in the Gibbs free energy.57 In the first step, the first proton and electron transfer occurs to adsorbed oxygen to form adsorbed hydroxyl, while in the second step the second proton and electron transfer occurs to the adsorbed hydroxyl to form water. The values of the Gibbs free energy changes at the different cell potentials associated with these two steps can be calculated from eqs 12 and 13 as ΔG1(U) = ΔGb − ΔGa + eU and ΔG2(U) = −ΔGb + eU. The highest value of these two quantities limits the oxygen reduction reaction and represents the rate limiting step. Accordingly, for the extended Pt(111) surface, ΔG1(U) and ΔG2(U) can be calculated as ΔG1(U) = −0.68 + eU and ΔG2(U) = −0.80 + eU.43 At a cell potential of 0.68 V, the proton and electron transfer step to adsorbed oxygen to form adsorbed hydroxyl starts to be endergonic and

Figure 6. Free energy diagrams for oxygen reduction over Pt(111) in black and ∼1 nm single-wall platinum nanotubes (in violet) based on the adsorption energies in ref 43, Table 4, and Table 5 (averaged values for all ∼1 nm nanotubes). The results are shown for 1/3 coverage of oxygen and hydroxyl at zero and cell potential of U = 0.77 V.

energy diagrams for oxygen reduction over Pt(111) (in black) and on ∼1 nm diameter single-wall platinum nanotubes (in violet) at cell potentials of 0 and 0.77 V. At cell potentials of 0.77 V, one of the steps in ORR on Pt nanotubes starts to be endergonic, while the rate limiting step on Pt(111) is already endergonic for 0.10 eV (ΔG1(0.77 V) = +0.10 eV). The value of overpotential estimated for larger platinum nanotubes is, as explained previously, calculated as an average value, and the exact values differ slightly between different tubes. For instance, the largest reduction of overpotential is for the (13,13) tube, namely, 180 mV. The reduction in overpotential for the (12,6), (12,8), and (12,12) tubes relative to platinum is calculated to be 70, 70, and 80 mV, respectively. Following the same approach, we can estimate the overpotential of the two studied double-wall tubes. Both the 16507



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∼1 nm in diameter, tube and forming the double-wall structure results in a decrease in both the stability of the outer nanotube toward the electrochemical dissolution and catalytic activity. This is due to the tendency of the smaller inner tubes to collapse into bulk-like structures, making ∼1 nm in diameter double-wall hollow structures worse candidates for ORR catalysts than ∼1 nm in diameter single-wall structures.

(5,5)@(12,12) and (6,6)@(13,13) tubes show the increase in the ORR overpotential relative to platinum. Namely, the overpotential on the (5,5)@(12,12) tube was calculated to increase up to 180 mV and up to 80 mV on the (6,6)@(13,13) tube, indicating lower ORR activity of these tubes relative to both bulk platinum and SWPtNTs with a similar diameter. The reason for the increase in overpotential can be understood in terms of high adsorption energies for hydroxyl on the doublewall nanotubes. While the interactions with oxygen atoms are favorable, interactions with hydroxyl are too strong, resulting in surface poisoning with adsorbed hydroxyl. The lower ORR activity of the studied double-wall tubes is, however, unexpected, as it is more conceivable to think that multishell structures would be more effective as catalysts compared to single-wall tubes due to their larger stability. Improved ORR kinetics on platinum nanotubes with 40 nm diameter, for example, has been confirmed experimentally in the work of Chen et al.37 We should however note that the (5,5)@(12,12) and (6,6)@(13,13) tubes do not constitute a faithful representation of all possible multishell structures. Namely, previous work on gold nanotubes implied that multishell structures of gold might be helical in nature with the inner chain of gold atoms,14,15 and the same might hold for platinum as well. Further investigation of the structure and reactivity of platinum multishell structures is thus needed and will be the subject of future work. At this point, we have to stress that, although adsorption of oxygen and hydroxyl represent the most important steps in the 4e− ORR pathway, different mechanisms are also plausible that include the formation of OOH and generate hydrogen peroxide as an intermediate.56 We studied the adsorption of OOH on the (6,6) and (13,13) SWPtNTs as two representatives of 0.5 and 1 nm diameter nanotubes. In both cases, OOH was adsorbed on top−top (T−T) and top−bridge (T−B) sites with a coverage of 0.25 ML and the system is optimized. In all the final structures, most of the OOH is found in a dissociated form. Only on the (13,13) SWPtNT part of the OOH (around 0.10 ML coverage) is found in undissociated form characterized with a Pt1−O distance of 2.00 Å, Pt2−OH distance of 3.30 Å, O−O distance of 1.41 Å, and O−O−H angle of 103.30°. The observed behavior can be explained by the very unique surface morphology that characterizes all the ultrathin metal nanotubes and that was discussed in the first section of the paper. A complex network of “edge”-like sites connecting “flat”-like regions on the surface of the nanotubes forms a number of tilted two-metal sites, unfavorable for the adsorption of undissociated OOH. These results indicate that the formation of hydrogen peroxide on metal nanotubes might be partially suppressed and are in agreement with the experimental findings that the ORR mechanism on acid-treated platinum nanowires with 1.3 ± 0.4 nm diameters most closely follows the ideal 4e− process without peroxide formation.38 In conclusion, we have found that platinum nanotubes with diameters larger than 1 nm might be the best candidates for fuel cell applications, as they are characterized with ORR overpotentials similar or lower than that of the bulk platinum. This is again in agreement with the recent experimental work by C. Koenigsmann et al. where acid-treated platinum nanowires with a diameter of 1.3 ± 0.4 nm were shown to have lower ORR overpotentials than commercial nanoparticles.38 We predicted the best catalytic activity toward ORR for the (13,13) SWPtNT whose overpotential is for 180 mV lower compared to the bulk. Inserting a smaller, ∼0.5 nm in diameter, tube inside a larger,

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CONCLUSIONS We have calculated the relative stability of a large number of platinum (n,m) nanotubes ranging in diameter from 0.3 to 2.0 nm in the gas phase and in a water environment. Only relaxed achiral tubes with five strands are characterized with perfect cylindrical structures, whereas other single-wall platinum nanotubes are found to become distorted from the initial perfect cylindrical structure while remaining hollow. Our ab initio molecular dynamics simulations indicate that smaller tubes, of ∼0.5 nm in diameter, might preserve their hollow structures only in a vacuum as thermal fluctuations of water molecules induce the conformational change to more stable bulk-like structures. The larger, ∼1 nm diameter tube studied in molecular dynamics simulations shows similar behavior in both gas and aqueous phase and indicates that the tubes with diameter larger than 1 nm can preserve their gas phase structure upon solvation. We have also calculated the adsorption energies of intermediates in the oxygen reduction reaction (oxygen and hydroxyl) in the absence of water and used them to construct free energy diagrams for the oxygen reduction dissociative mechanism on different platinum nanotubes. On the basis of the estimated overpotentials for oxygen reduction reaction, we conclude that all smaller, ∼0.5 nm in diameter single-wall Pt nanotubes consistently show a large overpotential for oxygen reduction, indicating a very poor catalytic activity toward oxygen reduction reaction. The reason for such a behavior can be found in substantial structural changes induced by the adsorption of oxygen reduction reaction intermediates. Singlewall Pt nanotubes with a diameter larger than 1 nm have lower oxygen reduction overpotentials than bulk platinum for up to 180 mV and do not show significant structural fluctuations upon oxygen and hydroxyl adsorption. Thus, these materials might show promise as better oxygen reduction catalysts than bulk Pt. The stability of the platinum nanotubes toward corrosion is assessed in terms of electrochemical dissolution potentials. Tubes with n = m chirality and diameter larger than 1 nm have shown to be stable at higher cell potentials than the nanotubes with smaller diameter. However, even in the best case of the (13,13) tube, the dissolution potential is still for 110 mV lower than for the bulk platinum, indicating a possible corrosion problem and lower durability of these nanomaterials.

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ASSOCIATED CONTENT

S Supporting Information *

Figure showing the distribution of surface cohesive energies for nanotubes in Table 3. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 16508



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Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS I.M. thanks the LANL LDRD program for a postdoctoral fellowship, U.S. Department of Energy, Energy Efficiency and Renewable Energy for financial support. Part of the computational work was performed using computational resources of the NERSC, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0205CH11231, CNMS, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy and EMSL, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. I.M. also wants to acknowledge the support of MZOŠ project 098-0352851-2921. The authors also thank Christopher Taylor and Jan Rossmeisl for useful discussions. Los Alamos National Laboratory is operated by Los Alamos National Security, LLC for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. This paper has been designated LA-UR 12-01127.

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