A.J. Bard, L.R. Faulkner - Electrochemical methods - Fundamentals and Applications (794273), страница 73
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The most common manifestationis found in the diffusion-limited region of a voltammogram, where samples in successive cycles do not produce a plateau, as they do in polarography, but instead decline asthe depletion of electroactive species near the electrode becomes cumulatively greater.Thus the typical staircase voltammogram of a simple system is peak-shaped, rather thanwave-shaped.Staircase voltammetry has many features in common with the potential sweep methods described in Chapter 6. In most systems, the response in a staircase experiment withgood potential resolution (AE < 5 mV) is very similar to that from a linear sweep experiment with the same scan rate, especially if attention is given to the time in each periodwhen sampling is done (39, 40).
Thus one can often analyze results on the basis of the extensive theory available for linear sweep voltammetry and cyclic voltammetry (Chapters 6and 12).8In principle, one can suppress the charging current background by using the staircase method in place of a linear sweep. This can be true if the measurement is not demanding with respect to resolution or scan rate. For reasons discussed in the nextsection, т must be several times the cell time constant to eliminate charging current fromthe sample.
It is not always possible to meet that condition in staircase experiments because of the tradeoff between resolution and speed. There is no problem with a scan at100 mV/s having 5 mV resolution, because the sampling time would be 50 ms, which ismuch longer than the cell time constants of most systems of interest. On the other hand,a scan at 1 V/s with 1 mV resolution requires r = 1 ms, which is not long enough toallow charging current to decay fully in most practical situations.
Thus a charging current contribution would normally exist in the staircase experiment, and the relative advantage is muted. This reality and two drawbacks related to signal-to-noise (i.e., minimalfaradaic response at the sampling time and noise effects associated with sampling over anarrow time window) have limited the adoption of staircase voltammetry vis a vis linearsweep methods.73.2Normal Pulse Voltammetry(a) General Polarographic ContextSince tast measurements record the current only during a very small time period late in adrop's life, the faradaic current flow that occurs before the sampling period serves no useful purpose. Actually it works to the detriment of sensitivity because it depletes the regionnear the electrode of the substance being measured and necessarily reduces its flux to thesurface at the time of actual measurement.
Normal pulse polarography (NPP) was invented to eliminate this effect by forestalling electrolysis prior to the measurement period(6, 35, 41-44). Figure 7.3.5 is an outline of the way in which this goal is achieved with either a DME or an SMDE.8In fact, many instruments now generate "linear" scan waveforms as staircase functions with very small ( <0.2 mV) AE, because it is simpler to do so with digital control systems. When AE is reduced below thelevel of the noise on the waveform, the distinction between staircase and linear functions is lost.7.3 Pulse Voltammetry < 279• D r o p 1•- Drop 2 -- Drop 3 -(a)Pulsed electrolysis (1-100 ms)-Waiting period _" (500-5000 ms)"Currentsampled(b)(c)Figure 7.3.5 Samplingscheme for normal pulsepolarography. (a) Potentialprogram, (b) Current and(c) potential during a singledrop's lifetime.For most of the life of each mercury drop, the electrode is held at a base potential, Еъ, at which negligible electrolysis occurs.
After a fixed waiting period, т\measured from the birth of the drop, the potential is changed abruptly to value E fora period typically about 50 ms in duration. The potential pulse is ended by a returnto the base value, E^. The current is sampled at a time т near the end of the pulse,and a signal proportional to this sampled value is presented as a constant output to arecording system until the sample taken in the next drop lifetime replaces it. Thedrop is dislodged just after the pulse ends, then the whole cycle is repeated with successive drops, except that the step potential is made a few mV more extreme witheach additional cycle. The output is a plot of sampled current vs.
step potential E,and it takes the form shown in Figure 7.3.6a. A block diagram of the apparatus isshown in Figure 7.3.7.This experiment, first performed by Barker and Gardner (41), is immediately recognizable as a sampled-current voltammetric measurement exactly on the model describedin Sections 5.1, 5.4, and 5.5. Normal pulse voltammetry (NPV) is the more general namefor the method, which may also be applied at nonpolarographic electrodes, as discussed inSection 7.3.2(d).Since electrolysis during the waiting time is negligible, the initially uniform concentration distribution in solution is preserved until the pulse is applied.
Even though theelectrode is approximately spherical, it acts as a planar surface during the short time of280Chapter 7. Polarography and Pulse Voltammetry-0.4-0.8-0.6E(Vvs. SCE)(a)-0.4-0.8-0.6E{Vvs. SCE)(b)Figure 7.3.6 Polarograms at a DMEfor 10~5 M Cd 2 + in 0.01 M HC1. (a)Normal pulse mode, (b) Tast mode.the actual electrolysis (Section 5.2.2); therefore the sampled faradaic current on theplateau is(7.3.3)where (r - r') is time measured from the pulse rise.(b) Behavior at a DMEIn comparing this current to that measured in a tast experiment at a DME, it is useful torecall (from Section 7.1.2) that (7.3.1) can be rewritten as(*d)tast ~~7T 1 / 2 T 1 / 2(7.3.4)thus (42)('d)pulse('d)tast3^—г-41*(7.3.5)7.3 Pulse VoltammetryPotentialprogrammer281PulsesequencerCellPotentiostatDropknockerSample/HoldHEConverterRecorderFigure 7.3.7 Schematicexperimental arrangementfor normal pulsepolarography.for experiments in which the current-sampling times for both methods are equal to т.For the typical values of r = 4 s, and (r - r') = 50 ms, this ratio is about 6; thus theexpected increase in faradaic current is substantial.
Figure 7.3.6 is a comparison of results obtained by normal pulse and tast polarography at a DME for a solution of 10~5 MCd 2 + in 0.01 M HC1. The larger sampled currents obtained with the pulse method areobvious.For reasons discussed below, the charging current contributing to the sampled totalcurrent comes almost completely from the continuous expansion of the electrode's area atpotential E. It therefore is identical to that contributing to tast measurements at the samepotential (eq. 7.3.2), provided that т and m are the same for the two types of measurement.Thus, normal pulse polarography preserves entirely the sensitivity improvementsachieved in tast polarography by discrimination against the charging current.
In addition,the pulse method gains enhanced sensitivity through increased faradaic currents, by comparison to those observed in tast or conventional polarography. Detection limits are usually between 10~6 and 10" 7 M.Normal pulse polarography has been used widely as an analytical tool for the measurement of low-level concentrations of heavy metals and organics, particularly in environmental samples (6, 35, 43, 44, 45).
Section 7.3.6 deals specifically with its applicationto practical analysis.(c) Behavior at an SMDEOne of the important concepts behind the normal pulse method loses its significance witha static mercury drop electrode, because a continuous charging current, characteristic of aDME, does not exist at an SMDE.In electrochemical measurements, charging current arises when the electrode area,the electrode potential, or the interfacial capacitance varies with time.
Normally interfacial structure is either static or changes as quickly as the potential; hence there is rarely anappreciable contribution to charging current from a time dependence in capacitance perse. With the waveform shown in Figure 7.3.5, dE/dt is zero except on the edges of thesteps; therefore the charging current exists only in response to the potential change atthose edges, and it decays away exponentially according to the cell time constant RUC$(Section 1.2.4). After five cell time constants, the charging process is more than 99%complete, and charging current is usually negligible. Therefore, if т — r' is larger than5/?uQ, the sampled charging current will not include an appreciable contribution fromdE/dt.
In many media, the cell time constant at a DME or an SMDE is a few tens of microseconds to a few milliseconds (Section 5.9.1); hence this condition is easy to fulfillwithin normal operational conditions for NPP. Consequently, charging current in NPP is282 • Chapter 7. Polarography and Pulse Voltammetryalmost always based on changes in the area of the electrode and is proportional to dA/dt.At a DME, dA/dt is never zero, and the charging current contributes to the backgroundcurrent according to (7.3.2); but at an SMDE, dA/dt is always zero except in the few tensof milliseconds required to form the drop.We now see that when the current is actually sampled at an SMDE, charging currentfrom all sources is normally reduced to insignificance, and the background current comesfrom other faradaic processes, typically involving the electrode itself, the solvent, the supporting electrolyte, or impurities in solution, such as oxygen.Because the pulse width is relatively short, the sphericity of the SMDE does not normally manifest itself, and the faradaic current follows the Cottrell decay given as (7.3.3).The sampled signal in NPP at an SMDE is essentially the same as at a DME of the samemature electrode radius.There are three important operational advantages in performing NPP at an SMDE vs.a DME: (a) The complete elimination of the charging current produces generally lowerbackground currents and improved detection limits, (b) The elimination of the chargingcurrent also reduces the slope in the background current and consequently allows betterdefinition of wave heights, leading to improved precision, (c) It is much easier to employshort drop times (1 s or smaller) at an SMDE; hence one can record polarograms with atime saving of 75% or more, relative to performance at a DME.(d) Behavior at Nonpolarographic ElectrodesAn essential idea behind the normal pulse voltammetric method is the cyclic renewal ofthe diffusion layer.
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