Linear current-potential relationship

In electroless deposition of a metal M, the current-potential relationships for the partial reaction may be written as linear functions ... 

Similar reasoning may hold if the electroactive species to be determined or studied otherwise can be adsorbed at the electrode surface. Also, in this case, the current—potential relationship is mathematically more complex and shapes and magnitudes (peak heights, limiting currents) of polarograms are more severely affected if the technique is faster (see also Sect. 6). As a consequence, calibration curves may become non-linear and even horizontal (i.e. the quantity monitored is independent of... 

Substitution of eqns. (209) into the linear rate equation (198a) leads to the general current—potential relationship... 

As is well known, the steady-state behavior of (spherical and disc) microelectrodes enables the generation of a unique current-potential relationship since the response is independent of the time or frequency variables [43]. This feature allows us to obtain identical I-E responses, independently of the electrochemical technique, when a voltammogram is generated by applying a linear sweep or a sequence of discrete potential steps, or a periodic potential. From the above, it can also be expected that the same behavior will be obtained under chronopotentiometric conditions when any current time function I(t) is applied, i.e., the steady-state I(t) —E curve (with E being the measured potential) will be identical to the voltammogram obtained under controlled potential-time conditions [44, 45]. 

With continuing increase in anode potential, the current-potential relationship deviates from the linear relationship. As the potential continues to increase, the increase in the current slows down until it reaches a maximum and then decreases to a minimum point, and finally increases to the limiting current plateau. This is a transition from kinetics of electrochemical reaction domain to mass transport domain. This region may have a very different shape depending on electrolytes, potential scan rate, and other factors. Details of this region are discussed elsewhere [7,8]. 

Consider the case of low overpotential, often referred to as the micropolarization region or the linear current-potential region. The exponential terms in Eq. 35E can be linearized, using the relationship exp X = 1 -t- X, which is valid for x 1. This yields a linear relationship between the current density and the overpotential, namely ... 

Linear sweep voltammetry delineates several regions in the current/potential relationships for the n-heptyl viologen... 

At high potentials where a linear current-voltage relationship is observed, Eq. (35) may be written as ... 

In the linear range of the current-potential relationship, the charge transfer is equivalent to a resistance called charge transfer resistance at the equilibrium potential,... 

Current-potential relationship, shown in Fig. 5.1, describes a redox system that departs shghtly (10-20 mV) from its equihbrium state. As shown in the figure, the relationship between the current and the apphed potential is nearly linear when measured close to the equihbrium potential. In this case, the overpotential in Butler-Volmer equation (3.28) is small and is equal to the inequahty ... 

The current-potential relationship of an electrochemical ceU provides the basis for voltammetric sensors. Amperometric sensors, that are also based on the current-potential relationship of the electrochemical cell, can be considered a subclass of voltammetric sensors. In amperometric sensors, a fixed potential is applied to the electrochemical cell, and a corresponding current, due to a reduction or oxidation reaction, is then obtained. This current can be used to quantify the species involved in the reaction. The key consideration of an amperometric sensor is that it operates at a fixed potential. However, a voltammetric sensor can operate in other modes such as linear cyclic voltammetric modes. Consequently, the respective current potential response for each mode will be different. 

In previous chapters only the linearized form of the current-potential relation has been used. The other terms of the Taylor series expansion were dropped. However, in reality, current-potential relationships show a considerable amount of curvature. The Taylor series expansion of the Butler-Volmer equation predicts that... 

One of the simplest electrochemical systems to analyse is that of a rapid reaction at its equilibrium, open circuit potential Eg h with no net current flowing. Under a.c. excitation (and in this and subsequent examples it is assumed that the excitation of potential of the working electrode is small, which means ideally less than 5 mV peak-to-peak) the net current is, of course, still zero, but the current-potential relationship is approximately linear rather than exponential. 

The shape of the curve depends on the same approximations holding true as before, i.e. the diffusion field is effectively planar, and Af is small enough (about 10/ mV or less) for the current—potential relationship to be linear. 

Amperometric sensors with the linear relationship of the current response have received great attention because of their high sensitivity, wide detection range, and short response time [5-9]. Amperometric sensors are based on the current-potential relationship of the electrochemical cell, in which a non-spontaneous reaction is driven by an external source of current. In amperometric sensors, the transduction mode works by operating the potential of the working electrode at a fixed value, relative to the reference electrode, and observing the current as a function of time. The applied potential assists to drive the electron... 

Figure 11.15 A large amplitude perturbation, here a potential sweep to a mass transport-controlled region, yields a nonlinear current-potential relationship. In contrast, a small amplitude perturbation, a few mV between and yields a linear relationship between current and potential.

When the sweep rate is very low, in the range of v = (0.1—5) mVs , measurement is conducted under quasi-steady-state conditions. The sweep rate plays no role in this case, except that it must be slow enough to ensure that the reaction is effectively at steady state along the course of the sweep. This type of measurement is widely used in corrosion and passivation studies, as we shall see, and also in the study of some fuel cell reactions in stirred solutions. Reversing the direction of the sweep should have no effect on the current-potential relationship, if the sweep is slow enough. Deviations occur sometimes as a result of slow formation and/or reduction of surface oxides or passive layers. Because the sweep rate is slow, the potential is often swept only in one direction, and the experiment is then referred to as linear sweep voltammetry (LSV). 

It is independent of potential and of the applied current density, but inversely proportional to the exchange current density, because the current-potential relationship is linear in this region (cf. Section 5.2.4). In this region the Wagner number is also inversely proportional to the heterogeneous rate constant of the metal deposition reaction. Thus, fast reactions have low value of the Wagner number and tend to lead to primary current distribution. This is a rather unique situation in electrochemistry, where poor catalytic activity (i.e., low specific rate constant) is an advantage. 

Due to the small amplitude of the superimposed voltage or current, the current-voltage relationship is linear and thus even charge-transfer reactions, which normally give rise to an exponential current-potential dependence (Chapter 4), appear as resistances, usually coupled with a capacitance. Thus any real ohmic resistance associated with the electrode will appear as a single point, while a charge transfer reaction (e.g. taking place at the tpb) will appear ideally as a semicircle, i.e. a combination of a resistor and capacitor connected in parallel (Fig. 5.29). 

Fig. 21.5. Levamisole-activated single-channel currents activated by 30 pM levamisole in a cell-attached patch and current voltage relationship. The rectangular current pulses were recorded at different patch potentials to determine the relationship between channel current and potential. The slope was linear with a conductance of 34 pS.

Electropolishing region does not occur in anhydrous organic solutions due to the lack of water which is required for the formation of oxide film. Figure 5, as an example, shows that in anhydrous HF-MeCN solution the current can increase with potential to a value of about 0.5 A/cm2 without showing a peak current. The relationship between current and potential is linear due to the rate limiting effect of resistance in solution and silicon substrate. 

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