Size Effects in Electrocatalysis of Fuel Cell Reactions on Supported Metal Nanoparticles - Fuel Cell Catalysis: A Surface Science Approach - page 513

deposited as a thin film on the surface of the dried catalyst layer to stabilize it [Schmidt
et al., 1998a, 1999]. In the third case, there is no binder, and the catalyst is fixed on the
surface by adhesion [Park et al., 2001; Maillard et al., 2004b]. The electrodes thus pre-
pared may then be used for performing model studies in conventional three-electrode
cells with liquid electrolytes using various techniques: electrochemical, impedance
spectroscopy, FTIR, differential electrochemical mass spectroscopy (DEMS), and
others. This approach has been widely applied for the investigation of size effects
in fuel cell-related processes, including hydrogen electro-oxidation [Markovic and
Ross, 2000; Schmidt et al., 2001] and oxygen electroreduction [Gloaguen et al.,
1994; Kabbabi et al., 1994; Schmidt et al., 1998b; Paulus et al., 2001; Maillard
et al., 2002; Gasteiger et al., 2005] reactions, CO monolayer [Friedrich et al.,
2001; Park et al., 2002b; Arenz et al., 2005; Mayrhofer et al., 2005a; Maillard
et al., 2004b] and CO bulk [Arenz et al., 2005; Mayrhofer et al., 2005a; Schmidt
et al., 1999] electro-oxidation, and methanol electro-oxidation [Jusys and Behm,
2001; Park et al., 2002b].
Thin catalyst layers on a GC rotating disk electrode (RDE) or a rotating ring - disk
electrode (RRDE) serve for studies of ORR kinetics. In order to separate the kinetic
current j k from the measured current j, Schmidt and co-workers [Schmidt et al.,
1998b] corrected the latter for the influence of oxygen diffusion in the aqueous
electrolyte and in the polymer film using the following equation:

1

j ¼ 1 j k þ 1 j d þ 1 j f ¼ 1

1
BC O v 1 = 2 þ

L
nFC f D f j k þ

(15 : 10)

where B is the Levich constant, C O is the oxygen concentration in the electrolyte
solution, C f is the oxygen concentration in the Nafion w film, L is the film thickness,
D f is the diffusion coefficient of oxygen molecules in the film, v is the electrode
rotation rate, j d is the mass-transport-limiting current in the liquid electrolyte, and j f
is the limiting current in the polymer film, the other terms having their usual meaning.
Paulus and co-workers [Paulus et al., 2001] have shown that if the polymer film thick-
ness is reduced below about 0.1 mm, j f becomes significantly larger than j k and j d ; the
influence of the oxygen diffusion in the film on the measured current density is then
negligible, and the last term in (15.10) may be ignored.
Gloaguen and co-workers underlined the fact that it is also necessary to correct the
measured current for mass transport and ohmic losses within the catalytic layer
[Gloaguen et al., 1994]. They proposed a mathematical model for a fully flooded
catalytic layer comprising ionic and electronic conductors (no voids), taking into
account gas diffusion, ohmic drops, and interfacial kinetics within the CL. The so-
called “effectiveness factor” f, i.e., the ratio of the actual reaction rate to the rate expected
in the absence of mass and ion transport limitations, is a function of the roughness
factor g(the ratio of total catalyst area to geometric area), the exchange current density
j 0 , the diffusion coefficient D, the concentration of electroactive species, and the
overpotential. Figure 15.3 shows that f drops sharply with increasing exchange current
density and with decreasing product DC O . For oxygen in an aqueous electrolyte at
room temperature, DC O 10 211 mol cm 21 s 21 . Thus, the effectiveness factor of