Chemical Physics Letters 390 (2004) 440–444

www.elsevier.com/locate/cplett

Nano-scale effects in electrochemistry q

J. Meier a,*, J. Schiøtz b, P. Liu b,1, J.K. Nørskov b, U. Stimming a

a Department of Physics E19, Technical University Munich, James-Franck-Str. 1, D-85748 Garching, Germanyb Center for Atomic-scale Materials Physics, Department of Physics, Technical University of Denmark, DK-2800 Lyngby, Denmark

Received 18 December 2003; in final form 5 February 2004

Available online 6 May 2004

Abstract

We report combined scanning tunneling microscopy and electrochemical reactivity measurements on individual palladium

nanoparticles supported on a gold surface. It is shown that the catalytic activity towards electrochemical proton reduction is en-

hanced by more than two orders of magnitude as the diameter of the palladium particles parallel to the support surface decreases

from 200 to 6 nm. Density functional theory (DFT) calculations combined with molecular dynamics (MD) simulations have been

used to investigate the origin of the effect. It is concluded that the size effect is given by the thickness-variation of the support-

induced strain at the surface of the palladium nanoparticles.

� 2004 Elsevier B.V. All rights reserved.

Nano-scale effects in the catalytic properties of gold

particles are well known – chemically inert gold turns

catalytically active when the particle size is below 3–4nm [1,2]. The existence of such size effects offers a new

possibility to control reactivity by controlling the par-

ticle size. In this Letter, we will show that nano-scale

effects can also be found at the solid–liquid interface, i.e.

in electrochemistry for the example of hydrogen evolu-

tion on Pd nanoparticles. In addition, we provide a

quantitative explanation of the physical principle un-

derlying the observed effects. We show in a combinedSTM – electrochemistry experiment that the reactivity of

Pd particles for electrochemical proton reduction in-

creases by more than two orders of magnitude when the

number of Pd layers in the nanoparticles decreases from

10 to 2. We explain this behavior quantitatively on the

basis of a combination of density functional theory

(DFT) calculations of the variation in the hydrogen

chemisorption energy with the strain in the Pd particleand molecular dynamics (MD) simulations of the

qSupplementary data associated with this article can be found, in the

online version, at doi:10.1016/j.cplett.2004.03.149.* Corresponding author. Fax: +49-892-8912-536.

E-mail address: jhmeier@ph.tum.de (J. Meier).1 Present address: Department of Chemistry, Bldg. 555, Brookhaven

National Laboratory, Upton, NY 11973, USA.

0009-2614/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2004.03.149

thickness-dependence of the local strain at the Pd

particle surface.

In investigating nanoparticle behavior typically alarge number of particles are investigated in order to

obtain sufficiently high signals. Such measurements have

been performed using differently prepared surfaces with

a varying density of statistically arranged particles on

the surface. Although a rather small variation in particle

size can be achieved by different preparation methods

(e.g. vapor deposition, electrochemical deposition and

adsorption from colloidal solutions) usually a broadersize distribution results on the surface due to agglom-

eration [3–6]. For this reason, a novel technique was

developed to measure the properties of one single

structurally defined particle.

The all-in-situ method presented here consists of

generating a single supported nano particle on a non-

reactive substrate using a scanning tunneling microscope

(STM). The same instrument is then employed for thecharacterization of the particle structure. Subsequently,

the STM tip is retracted out of tunneling for the mea-

surement of the particle reactivity, see Fig. 1. All mea-

surements were preformed in 0.1 M sulfuric acid under

inertgas atmosphere (N2); for experimental details see

[7]. A special advantage lies in the favorable diffusion

conditions around a nano-sized particle. The spherical

(three dimensional) diffusion of the hydronium ions to

-400 -350 -300 -250 -200 -150 -100 -50 010-1

100

101

102

103

104

105

106

λ/ s

-1

Usample

/ mV vs. RHE

Fig. 3. Tafel plots of three different Pd particles on Au(1 1 1) in 0.1 M

H2SO4. s : Pd particle with 10 nm height and 200 nm diameter, N: Pd

particle with 2.5 nm height and 12 nm diameter, . : three Pd particles

with 0.5 nm height and 6 nm diameter, .: polycrystalline Pd from [12].

sample

Pd-particle

Pt/Ir-tip

Insulation of the tip

H2 2H + +2 e -

2H ++2 e - H210 nm

Fig. 1. Illustration of the proton reduction reactivity measurement.

J. Meier et al. / Chemical Physics Letters 390 (2004) 440–444 441

the surface dramatically enhances the diffusion-limited

current densities substantially relative to the case of a

flat surface. Assuming a hemispherically shaped nano-particle, the diffusion-limited current density can be

estimated to jlim ¼ 5.2 · 105 A/cm2 for steady state con-

ditions, r0 ¼ 2 nm, c0 ¼ 10�4 mol/cm3, and a diffusion

coefficient for protons D[Hþ]¼ 9.3 · 10�5cm2/s. Such a

high limiting current density guarantees that even at

considerable overpotentials, diffusion limitation is not

reached. Therefore it is possible to investigate fast in-

terfacial reactions in a broad potential range.Single palladium particles are produced as described

in [8]. In Fig. 2 images of typical tip-induced particles of

different sizes are given. All the particles are stable over

a period of several hours. In some cases particles showed

a variation of their morphology with time. This can

be correlated with the height of the voltage pulse at the

z-piezo during particle generation. This effect on the

structure of the particle is discussed elsewhere [8].The reactivity of a single palladium particle is inves-

tigated by reducing protons in solution at the nano-

particle to hydrogen. The evolved hydrogen is oxidized

at the STM tip, which is out of tunneling mode �10 nm

above the surface, see Fig. 1). Detection by the STM tip

is extremely spatially selective and is thus able to over-

Fig. 2. In-situ STM image of tip-induced palladium particles: (a) one particle

2.5 nm height. All images are 100� 100 nm2. All particles on Au(1 1 1) in 0.

come the sensitivity limitations due to the small surface

area (�10�13 cm2).

These kinetic measurements result in currents, which

correspond to the rate of proton reduction as a function

of the electrode potential. These currents are subse-quently expressed as a rate k, which is measured as the

integrated flux of charges ne� per time, t, and normal-

ized by the number of surface atoms, Ns:a:;estimated

from the STM images:

k ¼ ne�

Ns:a:t:

The measured rate at a given potential shows a pro-nounced effect of particle size, see Fig. 3. The general

trend is that the smaller the particle the higher the re-

activity. The rate change is more than two orders of

magnitude for a change in particle diameter parallel to

the surface from 6 to 200 nm. In addition, a change in

of 0.5 nm height; (b) particle of 1.4 nm height; (c) one larger particle of

1 M H2SO4. Itunnel ¼ 1 nA, UWE ¼ 400 mV, Utip ¼ 500 mV.

442 J. Meier et al. / Chemical Physics Letters 390 (2004) 440–444

slope is observed with decreasing particle size; this can

be explained by surfaces diffusion effects on the sub-

strate [9]. Enhancement effects by so-called positve

feedback can be neglected due to the typical shape of

STM tips. It was shown that the feedback effect athemispherical ultra micro electrodes (UME) is less

pronounced as compared with disk shaped UME

[10,11]. By varying the height we found that the tip

current changes at most by a factor of two, which is

small compared to the observed reactivity changes [7].

For comparison, data taken from the literature for a

flat polycrystalline Pd surface are included [12]. The

determination of the number of surface atoms is not asaccurate as in the case of STM images, but from the

experimental details given by the authors [12],

Ns:a: ¼ 2� 1015 cm�2 was estimated. This can be taken as

the lower limit of Ns:a:.

We find that the strong variation of the rate k cor-

relates strongly with the particle height, see Fig. 4. Al-

ternative explanations would be that k varies with the

number of low coordinated metal atoms at the surface.To test this possibility we use the STM experimental

data to estimate the number of low coordinated surface

atoms Nl:c:. With increasing ratio Nl:c:/Ns:a: the reactivity

should increase. There is a certain change of the rate

with particle size; however, this rate does not change

with Nl:c:/Ns:a: in any systematic manner. A major in-

fluence of the low coordinated surface atoms as active

sites can thus be ruled out.An understanding of the observed variation of the

reactivity with the number of layers in Pd particle re-

quires answers to two questions. First, we need to know

the surface structure of the small Pd particles. We will

make the reasonable assumption that Pd layers will be

0 5 10 40 4510-1

100

101

102

103

104

105

106

Pd(111), theory

~ Theory, pseudomorphic overlayer Theory, islands Experiment

r / s

-1

Number of Pd layers

Fig. 4. Semi-logarithmic plot of the relative reaction rate ~r vs. particleheight. Full circles are experimental data (UWE ¼ 200 mV). Open tri-

angles are theoretical predictions for pseudomorphic overlayers, ob-

tained from DFT calculations. Full squares are theoretical predictions

for islands, obtained by combining the DFT calculations with molec-

ular dynamics.

of the close packed (1 1 1) type when growing on top of

Au(1 1 1) [13], but the question remains what the Pd–Pd

distances are. There is a 4.8% mismatch between the

lattice constant of Au and Pd, and there is no detailed

understanding in the literature how this mismatch ishealed as a function of layer thickness for only a few Pd

layers. The other question is how the reactivity of the Pd

layer depends on layer thickness and on the local

structure. We answer the first question by performing

MD simulations of the equilibrium structure of Pd

overlayers on Au, and the second question by per-

forming DFT calculations of the hydrogen bonding to

Pd layers.The MD simulations were performed by placing cir-

cular Pd islands of varying diameter and thickness on an

Au(1 1 1) surface, and then minimize the energy with

respect to all atomic coordinates. The interactions be-

tween the atoms were described using the effective me-

dium theory (EMT) [14,15], which gives a realistic

description of both Au and Pd while allowing us to do

simulations with close to a million atoms. It is foundthat single-layer islands are pseudomorphic, while even

for two Pd layers it is energetically favorable to intro-

duce misfit dislocations in the interface. The misfit dis-

locations partially relieve the tensile strain.

Fig. 5 shows the simulation of a four-layer Pd island

with a radius of 6 nm. Three Shockley partial disloca-

tions appear in the interface, and partially relieve the

stress in the surface layer. It is clear that even for a four-layer island there are substantial variations in the local

strain at the Pd surface. We will show in the following

that this can explain the experimental observations

quantitatively.

The reactivity of the Pd clusters were studied using

DFT calculations, as described in the supporting online

material. We have calculated the adsorption energy of

hydrogen on pseudomorphic overlayers of Pd onAu(1 1 1). The hydrogen adsorption energy, EH, is clo-

sely related to the reactivity. The rate-limiting step in the

total hydrogen evolution reaction is commonly found to

be proton reduction [16]:

Hþe� þ �!k1 H� ð1Þ

The activation barrier for the process will then be

closely related to the stability of the final state relative tothe energy of the solvated proton. When the properties

of the surface changes only the stability of the final state,

EH, will change, and the change in the activation energy

of Eq. (1) will scale with EH. The reaction rate for Nlayers of Pd on Au(1 1 1) can then be expressed relative

to the rate on pure Pd(1 1 1) (corresponding to N ¼ 1)

as

~rN ¼ rNr1

� exp

�� dEHðNÞ

kBT

�; ð2Þ

2 The reaction on an extended surfaces Pd/Au(1 1 1) is may be not as

fast, because of slow hydrogen desorption [9].

Fig. 5. MD simulation of a Pd island on a Au(1 1 1) surface. The island is 4 layers thick, and 12 nm in diameter. Left: The structure of the interface.

Three partial dislocations (dark atoms) are seen, separating a region of perfect fcc stacking (white) from regions with a stacking fault in the interface

(light gray). Right: The strain in the surface of the island varies across the surface. Red atoms have a large average nearest-neighbor distance, blue

atoms have a smaller one and are thus less reactive (‘For interpretation of the references to colour in this figure legend, the reader is referred to the

web version of this article’).

J. Meier et al. / Chemical Physics Letters 390 (2004) 440–444 443

where dEHðNÞ ¼ EHðNÞ � EHð1Þ is the difference in

hydrogen adsorption energy on the N layer thick over-

layer and on Pd(1 1 1).

We have calculated dEHðNÞ, for N ¼ 1–3, and theresults are shown as ~rN in Fig. 4.

Clearly the overall enhancement of the rate relative to

pure Pd(1 1 1) for 1–3 layer thick islands is well de-

scribed by the calculation, but it is also clear that the

calculated variation with layer thickness in the range 1–3

is much too weak. The reason is of course that in the

DFT calculations we have assumed the Pd overlayers to

be pseudomorphic, while the MD simulation showedthat this is only true for N ¼ 1.

The weak dependence of dEHðNÞ on the number of

layers for pseudomorphic overlayers shows that the

main effect of growing Pd layers on Au(1 1 1) is to in-

troduce a strain in the Pd surface. Such strain has been

shown in other cases to induce a strong effect in the

reactivity [17]. Effects due to interactions with the Au

substrate or quantum size effects perpendicular to thelayer are present, but are of smaller significance. We can

exploit this in a model, which combines the DFT results

with the MD simulations of local strain at the surface of

Pd islands on Au(1 1 1). Since the reactivity depends

primarily on the Pd–Pd bond stretch, we use the MD

simulation results to make histograms for the average

nearest-neighbor distance of the Pd atoms, see the inset

in Fig. 5. As the strain field of the dislocations is highlyanisotropic (the stress is mainly relieved in the direction

perpendicular to the dislocation line), the histograms

were made using the average of the distances to the six

nearest-neighbor surface atoms. It is thus not the usual

pair-distribution function. The histogram in Fig. 5

shows that even with four layers of Pd atoms, the bonds

are significantly stretched compared to bulk Pd.

For each surface atom, we now exploit the fact that

the activation energy depends linearly on the average

nearest-neighbor distance within a relatively narrow

interval [17]. The activation energy is then interpolatedfrom the values obtained from the DFT calculation of a

Pd surface and of a single monolayer of Pd on Au. The

reaction rate can then finally be found by averaging over

the surface atoms. In this way relative reaction rates can

be obtained from the MD simulation without fitting to

experimental data. The results are included in Fig. 4. All

data points were obtained using Pd islands with a di-

ameter of 12 nm, except for the thickest island (10 lay-ers), where an additional calculation were done with a

24 nm island.

The agreement between the measured results and the

‘ab initio’ calculations strongly suggest that the strong

variations in the reactivity with the number of Pd layers

supported on a gold substrate are given by the variations

in the surface strain with particle thickness. The com-

bination of detailed experimental results and theory thusallows for the establishment of a clear physical picture

of a nano-scale effect in electro-catalysis 2. The effect

should be quite general. Any case of metallic nano-

particles grown on a substrate with a lattice mismatch

should give rise to variations in the surface strain with

particle thickness, and since the strain effects in reac-

tivity have been shown not to be confined to hydrogen

adsorption, but to apply quite generally to adsorptionenergies and activation energies for surface reactions

[17], the effects should be found for a number of reac-

tions in heterogeneous catalysis and electro-catalysis.

The present work thus points to an important method

444 J. Meier et al. / Chemical Physics Letters 390 (2004) 440–444

for a systematic ‘design’ of nano-catalysts with a con-

trolled reactivity.

Acknowledgements

This work was funded in parts by the Deutsche

Forschungsgemeinschaft (DFG), Germany, under

Grant Sti 74/6-3 and U.S Army Research Office (ARO),

USA, under Grant DAAD 19-02-1-0311. Center for

Atomic-scale Materials Physics is sponsored by the

Danish National Research Foundation. This work was

financed in part by EU Grant APOLLON (ContractNo. ENK5-CT-2001-00572) and the Danish Center for

Scientific Computing.

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