Size Effects in Electrocatalysis of Fuel Cell Reactions on Supported Metal Nanoparticles - Fuel Cell Catalysis: A Surface Science Approach - page 507

parameter, the reader is referred to Nagaev [1992]; Vermaak et al. [1968]; Vermaak
and Kuhlmann-Wilsdorf [1968]; Gamarnik [1993]; and Henry [1998].
Along with size, interaction with the support may induce considerable changes in
the lattice parameter. For example, employing transmission electron microscopy
(TEM), Nepijko and co-workers found that the lattice constant of tantalum clusters
on a thin Al 2 O 3 film epitaxially grown on NiAl(110) decreased with decreasing cluster
size, with the greatest observed reduction being 4.5% for a cluster with a diameter of
1.25 nm [Nepijko et al., 1998], while for 1 nm Pt on NiAl(110) [Klimenkov et al.,
1997], a contraction of up to 10% was detected. Such strong deviations of the lattice
parameter from the bulk value may induce considerable changes in the reactivity of
the clusters.
15.2.3 Electronic Properties
The influence of cluster size on electronic properties has recently been the subject of
numerous studies by both theorists and experimentalists, so we will only touch briefly
upon this issue. More information can be found in the reviews [Nagaev, 1992; Henry,
1998, 2003; Binns, 2001; Pacchioni and Illas, 2003; Roduner, 2006]. From the stand-
point of electronic structure, metal clusters fall between isolated atoms with localized
atomic orbitals and the bulk metallic phase, where a continuous conduction band is
formed. For an isolated cluster, according to Kubo, splitting between electron levels
scales with the inverse number of atoms, so that at room temperature, for low sym-
metry systems, the inequality (15.4) should normally hold for metal particles compris-
ing more than 50 - 100 atoms [Kubo, 1962]. For smaller clusters, one may expect
quantization of electron levels and, upon reaching a critical size, a metal - insulator
transition. However, for high symmetry systems, quantum effects may be observed
at rather large characteristic sizes owing to degeneracy of the levels [Nagaev, 1992].
Until now, rigorous quantum chemical description of the electronic structure of tran-
sition metals has been an open problem. An opinion generally held is that the cluster
size strongly influences the electronic properties of metal particles comprising less
than 20 - 50 atoms, while larger clusters have the electronic properties of bulk
metals. Indeed, remarkable size effects have been demonstrated in the low dimension,
nonscalable interval both experimentally (e.g., by photoemission spectroscopy and
scanning tunneling spectroscopy) and computationally, and are widely discussed in
the literature [Henry, 1998, 2003; Binns, 2001; Pacchioni and Illas, 2003].
However, quantum chemical calculations performed by Nagaev strongly suggest
that size may influence the electronic properties of much larger particles in the
so-called weak quantization limit, when d k B T, resulting in a shift of the Fermi
level, variation of the density of states (DOS) at the Fermi level, and, in some
cases, the appearance of surface electronic states [Nagaev, 1992]. Various reasons
have been put forward to account for the size dependence of the Fermi level E F
[Grigorieva et al., 1987], including spatial quantization of the kinetic energy of elec-
trons stipulated by the size confinement—with a concomitant upshift of the Fermi
energy—and creation of a surface conduction band, lying below the volume
band—with a concomitant downshift of the Fermi level. Overall, both upshift and