Size Effects in Electrocatalysis of Fuel Cell Reactions on Supported Metal Nanoparticles - Fuel Cell Catalysis: A Surface Science Approach - page 515

Inspection of Fig. 15.3 reveals that while for j 0 0.1 nA cm 22 , the effectiveness
factor is expected to be close to 1, for a faster reaction with j 0 1 mAcm 22 , it will
drop to about 0.2. This is the case of internal diffusion limitation, well known in
heterogeneous catalysis, when the reagent concentration at the outer surface of the
catalyst grains is equal to its volume concentration, but drops sharply inside the
pores of the catalyst. In this context, it should be pointed out that when the pore
size is decreased below about 50 nm, the predominant mechanism of mass transport
is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient
being less than the Fick diffusion coefficient and dependent on the porosity and
pore structure. Moreover, the discrete distribution of the catalytic particles in the CL
may also affect the measured current owing to overlap of diffusion zones around
closely positioned particles [Antoine et al., 1998].
The above brief analysis underlines that the porous structure of the carbon substrate
and the presence of an ionomer impose limitations on the application of porous and
thin-layer RDEs to studies of the size effect. Unless measurements are carried out
at very low currents, corrections for mass transport and ohmic limitations within the
CL [Gloaguen et al., 1998; Antoine et al., 1998] must be performed, otherwise evalu-
ation of kinetic parameters may be erroneous. This is relevant for the ORR, and even
more so for the much faster HOR, especially if the measurements are performed at
high overpotentials and with relatively thick CLs. Impurities, which are often present
in technical carbons, must also be considered, given the high purity requirements in
electrocatalytic measurements in aqueous electrolytes at room temperature and for
samples with small surface area.
In order to overcome problems associated with the use of porous carbon materials, a
model approach was proposed based on the application of metal nanoparticles sup-
ported on flat nonporous substrates (Fig. 15.2d), such as highly oriented pyrolytic
graphite (HOPG) [Zoval et al., 1998; Savinova et al., 2000], GC [Tateishi et al.,
1991; Takasu et al., 1996; Cherstiouk et al., 2000, 2003a; Maillard et al., 2004a,
2005, 2007b], Au [Friedrich et al., 2000; Pronkin et al., 2001], or TiO 22x [Guerin
et al., 2006a, b; Hayden et al., 2007]. Pt, Pd, Pt-Ru, or Au nanoparticles with relatively
narrow size distributions were immobilized from colloidal solutions [Friedrich et al.,
2000; Pronkin et al., 2001], electrodeposited [Gloaguen et al., 1997; Zoval et al., 1998;
Liu and Penner, 2000; Maillard et al., 2007b], chemically deposited [Cherstiouk et al.,
2003a], vacuum-deposited [Takasu et al., 1989; Guerin et al., 2006b], etc. The rela-
tively simple structure of these model electrodes and the short time constants of
model electrochemical cells allow detailed in situ characterization and direct
observation of structural and size effects, for example in CO monolayer [Friedrich
et al., 2000; Cherstiouk et al., 2003a; Maillard et al., 2007b] and CO bulk [Guerin
et al., 2006b] electro-oxidation, and in the ORR [Takasu et al., 1996; Guerin et al.,
2006a], the MOR [Yahikozawa et al., 1991; Takasu et al., 2000], and the FOR
[Zhang et al., 1995]. Despite numerous advantages of model electrodes, it should
be mentioned that there is a disadvantage concerned with particle coalescence,
which is especially relevant to atomically flat substrates weakly interacting with
metal nanoparticles such as highly oriented pyrolytic graphite (HOPG) [Savinova