Constant potential charging

A second approach to coulometry is to use a constant current in place of a constant potential (Figure 11.23). Controlled-current coulometry, also known as amperostatic coulometry or coulometric titrimetry, has two advantages over controlled-potential coulometry. First, using a constant current makes for a more rapid analysis since the current does not decrease over time. Thus, a typical analysis time for controlled-current coulometry is less than 10 min, as opposed to approximately 30-60 min for controlled-potential coulometry. Second, with a constant current the total charge is simply the product of current and time (equation 11.24). A method for integrating the current-time curve, therefore, is not necessary. 

Other acceptable charging methods that have been used are the two-level charging, modified constant potential, and constant potential methods. 

In the simplest case of one-dimensional steady flow in the x direction, there is a parallel between Eourier s law for heat flowrate and Ohm s law for charge flowrate (i.e., electrical current). Eor three-dimensional steady-state, potential and temperature distributions are both governed by Laplace s equation. The right-hand terms in Poisson s equation are (.Qy/e) = (volumetric charge density/permittivity) and (Qp // ) = (volumetric heat generation rate/thermal conductivity). The respective units of these terms are (V m ) and (K m ). Representations of isopotential and isothermal surfaces are known respectively as potential or temperature fields. Lines of constant potential gradient ( electric field lines ) normal to isopotential surfaces are similar to lines of constant temperature gradient ( lines of flow ) normal to... 

The simplest, and by far the most common, detection scheme is the measurement of the current at a constant potential. Such fixed-potential amperometric measurements have the advantage of being free of double-layer charging and surface-transient effects. As a result, extremely low detection limits—on the order of 1-100 pg (about 10 14 moles of analyte)—can be achieved, hi various situations, however, it may be desirable to change the potential during the detection (scan, pulse, etc.). 

For an ideally polarizable electrode, q has a unique value for a given set of conditions.1 For a nonpolarizable electrode, q does not have a unique value. It depends on the choice of the set of chemical potentials as independent variables1 and does not coincide with the physical charge residing at the interface. This can be easily understood if one considers that q measures the electric charge that must be supplied to the electrode as its surface area is increased by a unit at a constant potential." Clearly, with a nonpolarizable interface, only part of the charge exchanged between the phases remains localized at the interface to form the electrical double layer. 

In order to obtain the current consumed during the nucleated relaxation process under a constant potential, we assume that a stationary density of charge (<, ) will be stored in the polymer at the polarization potential E. The storage of these charges is controlled by both conformational relaxation (3r) and diffusion ( processes, so... 

In order to distinguish more clearly between effects induced by the varying potential and kinetic contributions, the continuous oxidation of the three Cj molecules was followed at a constant potential after the potential step. The corresponding faradaic and mass spectrometric (m/z = 44) current transients recorded after 3 minutes adsorption at 0.16 V and a subsequent potential step to 0.6 V (see Section 13.2) are reproduced in Figs. 13.5-13.7. In all cases, the faradaic current exhibits a small initial spike, which is associated with double-layer charging when stepping the electrode potential to 0.6 V. 

In most inorganic electrolytes at constant potential cr(m) = constant, giving for the instantaneous electrode charge... 

Controlled potential methods have been successfully applied to ion-selective electrodes. The term voltammetric ion-selective electrode (VISE) was suggested by Cammann [60], Senda and coworkers called electrodes placed under constant potential conditions amperometric ion-selective electrodes (AISE) [61, 62], Similarly to controlled current methods potentiostatic techniques help to overcome two major drawbacks of classic potentiometry. First, ISEs have a logarithmic response function, which makes them less sensitive to the small change in activity of the detected analyte. Second, an increased charge of the detected ions leads to the reduction of the response slope and, therefore, to the loss of sensitivity, especially in the case of large polyionic molecules. Due to the underlying response mechanism voltammetric ISEs yield a linear response function that is not as sensitive to the charge of the ion. 

Rate constants for the oxidation of the negatively charge high potential Fe/S protein from Chromatium Vinosum with PCu(II) do not exhibit any dependence on pH 5.0 - 8.5 which suggests that the His 87 site is being used in this case. 

A moment s thought shows that the minus sign is correct Increasing the capacity of a condenser at constant potential, for example, by decreasing the plate and hence the charge separation, must lower the energy of the system. 

Three concentrations of each redox couple that ranged over two orders of magnitude were examined as well as a solution containing only electrolyte. The details of these comprehensive experiments will be published elsewhere (22.) however, several pertinent features are described here. The kinetic currents were measured at constant potential. In order to eliminate mass transfer limitations to the current, a jet electrode configuration was utilized (42). The capacitance of the space charge layer (Csc) was measured at the same potentials simultaneously with the kinetic currents. 

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