Faradaic to-capacitive current ratios

Faradaic-to-capacitive current ratios at an NEE and a conventional electrode with the same geometric area are related by equation (16.2.6) (86) ... 

The unique properties of microelectrodes such as low ohmic drop, high faradaic to capacitive current ratios, rapid achievement of steady-state currents, requirements of only two-electrode electrochemical cells, and small volume samples are exploited in many fields, including environmental, food, biomedical, and material science areas. ... 

Being typical/values for NEEs between 10 and 10, IpHc ratios at NEEs can be 2-3 orders of magnitude higher than for cmiventional electrodes with the same geometric area. Such an improvement in the faradaic to capacitive currents ratio explains why detection limits (DLs) at NEEs can be 2-3 order of magnitude lower... 

The behavior of array electrodes depends on the ratio of the diameter of the individual electrode to the spacing between electrode features. High diffusion current densities conditioned by radial flows and low values of ohmic potential drop are most prominent in the case of ultramicroelectrodes [13, 14]. By replacing a single macroelectrode by an array of ultramicroelectrodes, the current density can be increased by orders of magnitude as well as the ratio of faradaic to capacitive currents. 

In conclusion, microelectrodes possess unique electrochemical properties, namely, steady-state current response within short timescales, increased faradaic-to-capacitive ratio of the current intensity, independence of the ionic resistance from the distance between electrodes, and short time constants (fast response). 

On the other hand capacitive currents are also proportional to the electrode surface area. Thus the ratio of faradaic over capacitive current is not affected. Yet the time constant, RC, of the capacitive current is proportional to the radius, r, of the electrode since Ra(l/r) and Ca(r). Thus natural deconvolution occurs between capacitive and faradaic currents occurs when r is made smaller and smaller. 

The signal to noise ratio, that is the ratio of the Faradaic current (proportional to concentration) to the capacitive current is greatest at the end of the drop lifetime. Classical dc polarography records the mean current during the drop lifetime and thus does not record the maximum Faradaic current. Worse still, it includes an appreciable contribution from the capacitive current. This effectively limits the sensitivity of the classical dc technique to a limit of detection of about 5 X 10 mol dm -. ... 

As seen in previous sections, the response to a potential step is a pulse of current, which decreases with time as the electroactive species near the electrode surface is consumed and consists of a faradaic, /f, and a capacitive contribution, Iq. The advantage of most pulse techniques results from the measurement of the current flow near the end of the pulse when the faradaic current has decayed, often to a diffusion-limited value but when the capacitive current is insignificant. Pulse widths, tp, are adjusted to satisfy this condition and the additional condition that time has not been allowed for natural convection effects to influence the response. There is a greatly improved signal-to-noise ratio (sensitivity) compared to steady state techniques and in many cases, greater selectivity. Detection limits are of the order of 10 M. Furthermore, for analytical purposes, most current-voltage profiles from the pulse techniques are faster to interpret than those of dc voltammograms, because they are peak-shaped rather than the typical step curve of conventional voltammet-ric methods. 

The diagnostic ability of these forms of voltammetery are excellent, but their detection limits are poor, being limited to the 10 to lO M level, thus rendering them inappropriate for incorporation into chemical sensors. This rather poor limit of detection arises from the relative contributions to the total cell current of the faradaic and the capacitative currents. The capacitative current contribution is a linear function of sweep rate, whereas the faradaic current is a function of the square root of the sweep rate (for a reversible process). Thus, increasing the sweep rate in an attempt to produce larger faradaic currents inevitably causes a deterioration in the signal to noise ratio. An approximate expression can be used to evaluate the relative contribution of the capacitative (I c) and the peak faradaic currents (ip). Assuming typical values for the diffusion coefficient (10 cm s ), and the double layer capacitance (20 then... 

The advantage of amperometric measurements is that the faradaic currents are observed, at fixed electrode potentials. In these circumstances, capacitative currents no longer contribute to the overall cell current, and much lower detection limits are obtainable compared to linear sweep voltammetry. However, some of the newer variants of amperometry do involve pulsing the electrode potential to the active region measurements in these cases need to be made carefully to produce optimum signal to noise ratios. 

The simplest experimental arrangement may be used for concentration determinations in the range 10 M to 10 M. Below about 10 M, however, the ratio of faradaic current to the concentration-independent non-faradaic capacitance current, becomes progressively smaller until the latter predominates. All modern instrumental refinements, whose discussion is beyond the scope of this book, are aimed at improving this ratio. 

Note that this capacitance is linked to the electron transfer reaction and therefore has a faradaic origin and is not related to the double-layer charging process (this last capacitance corresponds to a pure capacitor see Sect. 6.4.1.5). In this sense, it has been called pseudo-capacitance [56]. The normalized current i/rCv is a ratio of capacitances since, from Eq. (6.161), y ev = (Icv/v)/(Qf F/RT)) = Ccv/Cf [48, 57],... 

As in all potentiostatic techniques, the double layer charging is a parallel process to the faradaic reaction that can substantially attenuate the photocurrent signal at short-time scale (see Section 5.3)" . This element introduces another important difference between fully spectroscopic and electrochemical techniques. Commercially available optical instrumentation can currently deliver time resolution of 50 fs or less for conventional techniques such as transient absorption. On the other hand, the resistance between the two reference electrodes commonly employed in electrochemical measurements at the liquid/liquid interfaces and the interfacial double layer capacitance provide time constants of the order of hundreds of microseconds. Consequently, direct information on the rate of heterogeneous electron injection from/to the excited state is not accessible from photocurrent measurements. These techniques do allow sensitive measurements of the ratio between electron injection and decay of the excited state under pho-tostationary conditions. Other approaches such as photopotential measurements, i.e. relative changes in the Fermi levels in both phases, can provide kinetic information in the nanosecond regime. 

The plateau seen in the CV trace is due to a high surface/volume ratio of the material within the film, generating a capacitive component of the current that superimposes on the Faradaic one. 

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