Semi-infinite planar diffusion

The geometry shown here corresponds to a semi-infinite planar diffusion. Other geometries (e.g., radial geometries) typical for microsensors can be used. The enzyme-containing layer is usually a hydrogel, whose optimum thickness depends on the enzymatic reaction, on the operating pH, and on the activity of the enzyme (i.e., on the Km). Enzymes can be used with nearly any transduction principle, that is, thermal, electrochemical, or optical sensors. They are not, however, generally suitable for mass sensors, for several reasons. The most fundamental one is the fact... 

The concentration profiles for semi-infinite planar diffusion are shown in Fig. 7.1a. The difference between the exact solution (7.17) and the approximate one (7.14) is only 11%. 

Electrode geometry — Figure 3. Concentration profiles at an array of inlaid disks at different time in response to an electrochemical perturbation. a Semi-infinite planar diffusion at short times b hemispherical diffusion at intermediate times c semi-infinite linear diffusion due to overlap of concentration profiles at long times... 

In general, the frequency dependence of the dif-fusional impedance and the geometry of diffusion are correlated. The (ice)-1/2 frequency dependence corresponds to the semi-infinite planar diffusion such a frequency dependence is valid only if the characteristic length, (D/ce)1/2 of diffusion is much shorter than any size of the electrode or the thickness of the electrolyte layer from which diffusion proceeds. Otherwise spherical, or bounded diffusion with different frequency dependence is observed. 

In linear scan voltammetry (LSV) the peak current of fast and reversible electrode reactions controlled by semi-infinite planar diffusion is given by the following equation [i] ... 

From these expressions it can be deduced that, in contrast to cyclic voltammet-ric responses for solution systems with semi-infinite planar diffusion, for redox processes for confined or thin layer systems close to the electrode or adsorbed molecules at the electrode surface, the peak current expression becomes linear with respect to the scan rate (Eqs. II.1.13a and II.1.13b). 

As shown in both the experimental and theoretical transients, the currents first increase as a result of the formation ofmercury drops and their growth controlled by radial diffusion, decaying at longer times due to the onset of semi-infinite planar diffusion. The diffusion coefficients may be obtained either from i versus plots... 

Peak potential (in voltammetry) — It is the potential at which the maximum current appears in -> linear scan voltammetry (LSV) and several other techniques peak height). It is one of diagnostic criteria for the estimation of electrode kinetics. If the reaction is simple, fast, and - reversible the peak potential is independent of the scan rate, or frequency, or pulse duration. The condition is that the electrode reaction is not complicated by the -> adsorption, the -> amalgam formation, the precipitation of solid phase, the gas evolution, or the coupled chemical reactions. In LSV and cyclic voltammetry (CV) of a simple, reversible, semi-infinite planar diffusion-controlled reaction Oxaq h- e Redaq the cathodic and anodic peak potentials are p,c = ... 

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