Electrocatalysis for Fuel Cells at Enzyme-Modified Electrodes - Fuel Cell Catalysis: A Surface Science Approach - page 600

orientation. Thus, the number of electrocatalytically active molecules is much higher
than for a monolayer of enzyme directly attached to an electrode, and the current will
be much greater, provided that there is efficient substrate transport in the hydrogel. The
redox hydrogel also serves to trap and stabilize enzymes on an electrode, translating
directly into technological applications. The enzyme may simply be sterically
enmeshed within the hydrogel, but can also be immobilized by electrostatic inter-
actions with the hydrogel or by covalent bonds. The net electrostatic charge on
most enzymes at pH 7 is negative, and the charge on redox hydrogels, in which the
backbone is generally neutral, is made positive by complexation with cationic com-
plexes or by quaternization. Additional covalent bonds may be created in a number
of ways. For instance, saccharide moieties on glycosylated enzymes such as laccase
(see Fig. 17.3) can be oxidized to aldehydes, which can then be reacted with primary
amines on the redox polymer to form Schiff bases.
In redox hydrogels, electron transport is accomplished by exchange between
neighboring flexible redox centers that come into sufficiently close proximity for
outer-sphere electron transfer through physical translation, and thus electron transport
should obey Fick's laws of diffusion. Application of a potential gradient leads to a flux
of electrons counter to the gradient, as the reduced form of the mediator is thermody-
namically more stable at lower potential. The sum of these effects is that electron
transport in redox mediators follows the well-known Nernst - Planck equation,
except that the migration term is somewhat complicated by the requirement that the
sum of the reduced mediator and oxidized mediator must be equal to the fixed total
mediator concentration. Thus, electron transport (both diffusion and migration,
assuming the Bose - Einstein relation) can be treated as proportional to mediator
concentration and an apparent diffusion coefficient D app .
Hydrogels typically have a low swelling ratio ( 2), which maintains a high
concentration of the redox complex. A redox polymer hydrogel with an Os content
of 10 wt% might contain up to 500 mM Os. A main disadvantage is that the redox
species themselves are physically bound and immobilized to the hydrogel network
leading to low values of the diffusion coefficient, typically in the range 10 28 to
10 29 cm 2 s 21 for Os complexes directly bound to a polyvinylimidazole backbone.
There are several possible solutions to this problem. The first is to increase the mobility
of the backbone by decreasing crosslinking. This approach has been demonstrated to
effectively increase electron diffusion, but at the expense of lower stability in the pre-
sence of shear. An alternative is to elongate the side chain attaching the complex to the
polymer backbone. This structural change enhances translational mobility of the redox
complex independent of backbone mobility. Mao and co-workers have demonstrated
that such a change can lead to diffusion coefficients in the 10 25 to 10 26 cm 2 s 21 range
[Mao et al., 2003], and the effect of increasing the tether length on the limiting rate of
electrocatalytic O 2 reduction by immobilized laccase is shown in Fig. 17.6b. Another
approach is to increase the mediator concentration, possibly by increasing the fraction
of backbone sites that are complexed, and D app has been shown (both theoretically and
experimentally) to increase linearly with mediator concentration [Mano et al., 2006].
Finally, the length scales over which electron transport takes place can be decreased by
preparation of thin catalyst films, and this need not decrease the amount of catalyst if