Biomedical Engineering Reference
In-Depth Information
Figure 4. Sketch of the structure of the double layer showing the compact layer
(gray) and the diffuse layer (white). (a) Electrostatic potential versus distance from
the surface. In the diffuse layer, the potential decays exponentially with distance;
the dependence can be more complicated in the compact layer. Because redox
molecules must penetrate into the diffuse layer to undergo electron transfer, a frac-
tion of the driving potential, labeled 'I cor , does not contribute to assisting the elec-
tron transfer reaction. (b) Distribution of counterions and coions at the surface. In
the diffuse layer, excess counterions and a dearth of coions contribute comparably
to the net charge of the double layer. The compact layer consists predominantly of
excess counterions.
tial correlations between ions, adsorption of ions to the surface and
so forth can all play important roles. Different levels of sophistica-
tion are required to capture the salient features of different experi-
ments, but in general our ability to describe the compact layer re-
mains limited.
Because the value of O d is comparable to or greater than the
thickness of the compact layer, however, the value of O d provides a
good first estimate of the range of electrostatic interactions in solu-
tion. Does the existence of a double layer with characteristic size
O d influence electrochemical experiments? It does, in at least two
different ways. First, we implicitly assumed in Section II.1 that the
full electrostatic potential imposed between an electrode and bulk
solution is available for driving redox processes at the electrode
surface. To undergo electron transfer, redox molecules must, how-
ever, approach within a distance from the electrode that roughly
coincides with the extent of the compact layer. The fraction of the
potential appearing across the diffuse part of the double layer (la-
beled 'I cor in Fig. 4a ) is then waste d during the approach of the
molecule to the surface, and only a fraction of the potential differ-
ence is available for driving the electrochemical reaction. To add
 
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