Metalloporphyrin Catalysts of Oxygen Reduction - Fuel Cell Catalysis: A Surface Science Approach - page 640

amount of catalyst immobilized on the electrode by spontaneous adsorption (although
the amount of electroactive catalyst can be determined coulometrically). Nor is it
generally possible to vary the amount of the deposited catalyst. The alternative
(spin casting) is free of such limitations, but it may produce more morphologically
heterogeneous catalytic films owing to nonuniform precipitation of the catalyst
during the rapid evaporation of the solvent. The modified electrode is immersed in
a buffered air- (or O 2 -) saturated aqueous solution and its potential is scanned.
Rotating electrode voltammetry [Bard and Faulkner, 2001; Opekar and Beran,
1976], which is a forced convection/hydrodynamic method, allows one to quantify
k and n av as functions of the electrochemical potential by using an appropriate math-
ematical model to relate the observed catalytic currents to the rates of chemical reac-
tions and mass transport processes. A general description of electrochemical kinetics
at a chemically modified electrode was developed by Saveant and co-workers
[Andrieux and Saveant, 1992]. Their model takes into account the three processes
that can limit a catalytic current generated by a multilayer film of a catalyst on the sur-
face of an electrode: (i) the turnover frequency of the catalytic cycle; (ii) the rate of
reactant(s) transfer from the film - solution interface to the catalytic site(s); and (iii)
the rate of electron transfer from the electrode - film interface (or charge-compensatory
movement of counterions) to the catalytic site(s). In order to use rotating disk voltam-
metry to quantify the kinetics of the catalytic cycle, one must ensure that the last two
processes are not rate-determining, which can usually be achieved by controlling the
amount of catalyst deposited on the electrode (see below).
If the charge and reactant transfer within the film are much faster than the catalytic
turnover, and the catalytic current is proportional to the concentration of O 2 in the
catalytic film (i.e., the rate is first-order in O 2 and the catalyst is not even partially satu-
rated with O 2 ), the electrode kinetics is adequately described by the so-called
Koutecky - Levich equation (Fig. 18.7b) [Opekar and Beran, 1976]. This equation
is a solution of the convection - diffusion equation in the case of the current being lim-
ited by (i) mass transport of the reactant from the bulk solution to the electrode surface
(or, in the case of chemically modified electrodes, to the film - solution interface, since
reactant transport within the film is assumed not to be kinetically limiting) and (ii)
electrode reaction. To determine n av and k of the catalytic film by the Koutecky -
Levich equation, a series of linear sweep voltammograms is collected at different
rotational frequencies v of the modified electrode (Fig. 18.7b). Increasing the
rotational frequency increases the flux of O 2 and H þ to the electrode by decreasing
the thickness of a layer of the aqueous electrolyte that rotates with the electrode
(the stagnant layer [Opekar and Beran, 1976]). If the Koutecky - Levich equation is
applicable and the data quality is adequate, inverse catalytic currents i 1

cat are directly
proportional to the inverse square root of the rotational frequency v 21/2 ,
(Koutecky - Levich plot; Fig. 18.7b). The slope of the corresponding linear regression
line is 0.62FAD 2/3 n 21/6 n av [O 2 ] bulk where F is Faraday's constant, A is the geometric
area of the disk electrode, D is the diffusion coefficient of O 2 , n is the kinematic viscosity
of the electrolyte and [O 2 ] bulk is the concentration of O 2 in the bulk of electrolyte. Either
these parameters are taken from the literature or the factor 0.62FAD 2/3 n 21/6 [O 2 ] bulk is
measured experimentally by carrying out O 2 reduction under identical experimental