figure 6-4. figure 6-3. figure 6-2. figure 6-1

CHAPTER 6. POTENTIAL STEP METHODS, POLAROGRAPHY, AND PULSE VOLTAMMETRY

I. Overview of Step Experiments

i/. Types of Techniques

a) ChronoamperometryFIGURE 6-1. "Bard" Fig. 5.1.2 (p.137).

b) Sampled-current voltammetryFIGURE 6-2. "Bard" Fig. 5.1.3 (p.138).Basis for DC polarography and pulse polarographic methods.

c) Double potential step chronoamperometryFIGURE 6-3. "Bard" Fig. 5.1.4 (p.139).A reversal technique.

d) Chronocoulometry and Double Potential Step ChronocoulometryThe integral analogs of the corresponding chronoamperometric approaches - to record the integral of the current versus time.FIGURE 6-4. “Bard” Fig. 5.1.5 (p. 140).

ii/. Current-Potential Characteristics

a) Large-amplitude potential stepIf the potential is stepped to the mass-transfer-controlled region, the concentration of the electroactive species is nearly zero at the surface and the current is totally controlled by mass-transfer. For this case, electrode kinetics no longer influences the current and I is independent of E.

b) Small-amplitude potential changesIf the perturbation in potential is small in size (< 8 mV/n), and both redox forms of a couple are present, then current and potential are linked by the linearized I- relation.

While the small-amplitude perturbation can be made from an initial condition identical to that used for large-amplitude techniques, it is usual to combine the two experimentstogether. One can, for example, add a small-amplitude perturbation on top of a large-amplitude signal to provide more complete information about the chemical system.FIGURE 6-5. “Kissinger” Fig. 5.1 (p. 145).Under normal circumstances the large-amplitude signal is applied for a longer period of time and the small amplitude is added momentarily. Looking at this another way, we use the large-amplitude signal to establish a new surface concentration for the oxidized and reduced forms of a redox couple and then move away from this condition slightly by rapidapplication of a small potential. The large-amplitude technique therefore sets the initial condition for the small-amplitude technique.

FIGURE 6-5. “Kissinger” Fig. 5.1 (p. 145).This small-amplitude response can be considered to have been initiated at a condition defined by the concentration profile as it existed just prior to application of the small step. The time scale of the small-amplitude experiment is so much shorter than that for the large-amplitude signal that the later for practical purposes is not changing during the course of a given small-amplitude perturbation.

Small-Amplitude Controlled-Potential Voltammetry:Different waveforms have been used for the small-amplitude part of the excitation signal, e.g., sine waves, square waves, triangular waves, and sawtooth waves. In the early forms of these techniques the small-amplitude (so-called AC part) was simply summed with a slowly moving ramp (so-called DC part).FIGURE 6-6. “Kissinger” Fig. 5.2a (p. 147).

Consider the situation in which the DC current response would be sigmoidal in shape.FIGURE 6-6. “Kissinger” Fig. 5.2b (p. 147).The variation in small-amplitude current around the DC response will depend very much on the relation the DC excitation and the half-wave potential.FIGURE 6-6. “Kissinger” Fig. 5.2c (p. 147).

Prior to initiation of significant DC reduction current, the small-amplitude excitation signal does not result in any significant faradaic process. Well beyond the half-wave potential (on the limiting current plateau), the small-amplitude perturbation will again contribute very little due to the fact that we are already at a point where the surface concentration of the reactant is zero for all practical purposes. On the rising part of the “DC voltammogram” we anticipate a significant variation in the current due to the small-amplitude perturbation. The amplitude of this current response would be maximum at the point where the DC surface concentration is the greatest function of the applied potential (i.e., at the half-wave potential). As a result, when we plot the small-amplitude current response as a function of the DC applied potential we achieve a peak-shaped curve with a maximum value at E1/2. As with large-amplitude techniques, separation of faradaic from nonfaradaic events is a major experimental goal.

iii/. Diffusion-Controlled Currents at Microelectrodes

Microelectrodes: dimensions 20 m.Steady-state current,

Iss = (nFADC*)/r0

For a hemispherical microelectrode bounded by a planar mantle,Iss = 4nFDC*r0

Advantages:1. Very small current (pA to nA) Very small IR drop applicable to organic solvents and simpler instrumentation (three-electrode system not necessary).

2. Insignificant charging current.

3. Increased rate of mass transport rapid establishment of steady-state current in less than a microsecond (rather than in a millisecond or more) high-speed measurements possible.charging current + mass transport rate improved sign-to-noise ratio.

II. Dropping Mercury Electrode (DME)

i/. Introduction

FIGURE 6-7. "Johnson" Fig. 1 (p. VI-3).The DME consists of a very fine bore (0.05-0.08 mm i.d.) glass capillary attached to a

mercury reservoir. A steady flow of droplets issues from the capillary at a rate of one drop every 3-5 seconds. Voltammetry at a DME is called polarography. At the slow rate of voltage scanning generally used in polarography (ca. 50-200 mV/min), the current measured on each drop can be considered to be under practically potentiostatic conditions (i.e., at constant potential).

FIGURE 6-8. “Skoog” Fig. 22-18 (p. 550).FIGURE 6-9. “Skoog” Fig. 22-19 (p. 551).

Advantages:1. Reproducible I-E curves obtained, since the surface of every mercury drop is fresh, clean,

practically unaffected by electrolysis at earlier drops (eliminates passivity or poisoning effects), and surface area of each is reproducible.

2. The high overpotential of hydrogen on mercury renders the electrode useful for electroactive species whose reduction potential is considerably more negative than the reversible potential of hydrogen discharge.

3. Mercury forms amalgams with many metals and thereby lowers their reduction potential.

Disadvantages:1. The anodic dissolution of mercury makes it impossible to study reaction at potentials more

positive than ca. + 0.4 V vs. SCE.2. Volatility of Hg limits its use at high temperature.3. Sensitivity is restricted by charging current caused by the growth of the drop.

Working Range: +0.3 to 2.8 V> +0.3 V, Hg dissolves and gives an anodic wave.< 1.2 V, visible H2 evolution occurs in 1 M HCl.At 2 V, usual supporting electrolyte of alkaline salts begins to discharge.

The most negative potentials may be attained in solutions in which a quaternary ammonium hydroxide is used as supporting electrolyte, e.g., the limit is 2.7 V with tetra-n-butyl-ammonium hydroxide.

ii/. Theory

a) Ilkovic Equation - Linear Diffusion to a Growing Dropping Electrode (Convective Diffusion to an Expanding Sphere)

The dropping electrode is assumed to behave as a plane electrode with an area equal to that of the surface of the drop, i.e., an area increasing with time.

When the drop grows, the concentration gradient is influenced by the rate of growth of the drop in the opposite direction to that caused by diffusion, i.e., by the decrease in thickness of the diffusion layer as the fixed amount of liquid inside the diffusion layer spreads out over the growing surface of the drop.Hence, the motion of the medium (convection) towards the drop

v = +dx/dtwill cause the concentration at a fixed distance for the growing surface to change with time in accordance with the steepness of the concentration gradient in the moving medium,

(C/t)convection = v(C/x)

The total change in concentration with time is given byC/t = (C/t)diffusion + (C/t)convection

C/t = D(2C/x2) - v(C/x)To determine v, consider a shell of incompressible liquid with inner radius r1, formed by the drop surface and an outer radius r2.

shell volume, Vs = (4/3)(r23 r1

3)Let r2 r1 = x and assume x << r1,

Vs = (4/3)[(r1 + x)3 r13] 4r1

2x = Ax

where A = area of the drop surfaceHence, dVs/dt = 0 = d(Ax)/dt = A(dx/dt) + x(dA/dt)i.e., v = dx/dt = (x/A)(dA/dt)

To determine A, consider the volume V of the drop at any instant during its growth,V = mt/ = (4/3)(r1

3)where m = flow rate of mercury

= density of mercuryr1 = [3mt/4]1/3

A = 4r12 = 4[3mt/4]2/3 = 0.85m2/3t2/3

On substituting,v = -(2/3)(x/t)

Hence, C/t = D(2C/x2) (2/3)(x/t)(C/x)Initial and boundary conditions:

at t = 0, x = 0;C = C*at t > 0, x = 0;C = Cs

where the value of Cs depends on the potential of the electrodeSolving,

(C/x)x=0 = (C* Cs)/[(3/7)(Dt)]1/2

I = nFAD(C* Cs)/[(3/7)(Dt)]1/2

Id = nFADC*/[(3/7)(Dt)]1/2

On substituting A = 0.85m2/3t2/3,

I = 0.732nFD1/2m2/3t1/6(C* Cs)

Id = 0.732nFD1/2m2/3t1/6C*

b) Diffusion CurrentFrom Ilkovic equation,

Id = 708nD1/2m2/3t1/6C*Units: D (cm2s1), m (mgs1), t (s), C (molcm3), Id (A).

For normal polarographic measurements, a galvanometer with a long period (4 - 8 s) or recorder is used, which merely records small oscillations about the mean current

I = (Idt)/tmax

I = 0.627nFD1/2m2/3tmax1/6(C* Cs)

Id = 0.627nFD1/2m2/3tmax1/6C*

Comparing the instantaneous current Imax at the end of the drop life,

Id = (6/7)Imax = 607nD1/2m2/3tmax1/6C*

iii/. Effect of Mercury Column Height (h)Variation of Id with h occurs because of the dependence of m and T upon h.Since m hthen t 1/hThus, Id m2/3t1/6 h2/3h1/6 h1/2

Electrode reactions limited by mechanisms other than mass transport produce log(Id) vs. log(h) plots with slopes other than 0.5.

c) Charging Current (Residual Current)The charge on the double-layer is given by

Q = CiA(Ez E)where Ci = integral capacitance

A = electrode areaEz = potential relative to the point of zero charge

Charging Current, Ic = dQ/dt = Ci(Ez E)(dA/dt)Since A = 0.85m2/3t2/3,

dA/dt = 0.57m2/3t1/3

Ic = 0.00567Ci(Ez - E)m2/3t1/3

Average Charging Current is given by,

Ic = (Icdt)/(dt) = 0.0085Ci(Ez E)m2/3tmax1/3

Conclusions:1.This current typically is about the same magnitude as the average faradaic current for an electroactive substance present at 105 M levels. This charging current is the principle factor limits detection by normal polarography to concentration above 5 x 106 M.2.Since diffusion currents increase with time as t1/6, and charging current decreases as t1/3, measurement of the current late in the life of the drop gives a better sensitivity (or S/N ratio) than measurements of average currents.FIGURE 6-10. "Bard" Fig. 5.8.1 (p. 184).

3.Charging current is proportional to m2/3t1/3, which in turn proportional to h; but diffusion current is proportional to h½. Hence, S/N ratio in a diffusion current measurement (i.e., Id/Ic) actually degrades with increased column height, even though the signal itself (Id) increases.4.If Ci and tmax are not strongly varying functions of potential, Ic is linear with E, producing a highly sloping base line. Ic vanishes and changes sign at E = Ez.FIGURE 6-11. Charging current vs. potential.

iii/. Analytical Applications

a) Scope of Applications1. CationsTransition metals are most profitably determined, but some alkaline-earth and rare-earth ions also offer useful analytic curves.2. Anions- Halides, sulfides, selenides, and tellurides can be determined by means of anodic waves due to mercury-salt formation.- Oxygen containing anions, e.g., bromates, iodates, periodates, sulfites, and polythionates, can be determined by means of cathodic waves.3. Inorganic Moleculese.g., oxygen, hydrogen peroxide, elemental sulfur, some sulfur oxides, and oxides of nitrogen.4. Organic CompoundsUsually C-Cl, C-Br, C-I, N-N, N-O, S-O, C=C, and CC.

b) Detection LimitsDC Polarography - between 1 x 105 and 5 x 106 M.

iii/. Dissolved OxygenPolarographic measurements made in aqueous solutions exposed to the laboratory atmosphere will reveal two waves resulting from reduction of dissolved O2. The first wave for O2 with E½ 0.17 V corresponds to the reaction

O2 + 2H2O + 2e H2O2 + 2OH

The second wave with E½ 0.96 V results from the reactionO2 + 2H2O + 4e 4OH

If H2O2 is added to a solution free of dissolved O2, the polarographic wave has E½ 0.96 V. It is concluded that the reaction process for the second wave probably involves production of H2O2 as a short lived intermediate which is quickly reduced further to OH- (i.e., H2O2 + 2e 2OH).FIGURE 6-12. “Harris” Fig. 9, 17-17 (p. 390).The removal of dissolved oxygen from solutions before polarographic analysis is important. This can be accomplished quickly (ca. 5 - 10 min) by dispersion of O2-free N2 through the solution in the polarographic cell. During analysis, an atmosphere of N2 should be maintained over the solution to prevent the return of O2 to the solution. The N2 stream can be purified of residual O2 by bubbling through an acidic solution of Cr(II) or V(II) over amalgamated Zn.

c) MixturesGuides to obtain the highest possible accuracy in polarographic of mixtures:1. Values of component half wave potentials must be separated by a minimum of

approximately 150 mV if each wave is to be resolved.2. Maximum accuracy is achieved when the analyte concentrations of the mixture are

approximately the same.Separation of overlapping waves is frequently possible by a wise choice of solution pH,

supporting electrolyte, solvent, or masking agents.

iv/. Variations of the Conventional Polarographic Method

a) Tast Polarography (Sampled DC Polarography)The ratio of faradaic to charging current, and thus the sensitivity, can be optimized by

sampling the current at the instant just before the drop fall.FIGURE 6-10. "Bard" Fig. 5.8.1 (p. 184).FIGURE 6-13. "Bard" Fig. 5.8.2 (p. 185).FIGURE 6-14. “Skoog” Fig. 22-22 (p. 554).

Id() = nFADC*/[(3/7)(D)]1/2

= 708nD1/2m2/31/6C*where = a fixed time after the birth of a drop

The improvement in this method yield detection limits near 106 M.

III. Pulse Polarographic or Voltammetric Methods

One approach that minimizes the effect of charging current is pulse polarography. It takes advantage of the fact that, following a sudden change in applied potential, the capacitive current surge decays much more rapidly than does the faradaic current. In this technique, a single rectangular voltage pulse is applied to the electrode during the last portion of its life. In this way, the period at the beginning of the drop-life, when changes in charging current are greatest, is avoided. Moreover, the current is measured over a very short time, and appreciably later than the sudden change in voltage, so that the charging current has decreased more than the faradaic current has at the time the current is measured. The pulse is synchronized with the maximum growth of the mercury drop.

i/. Normal Pulse Polarography (NPP) and Normal Pulse Voltammetry (NPV)

Task polarography depletes the region near the electrode of the substance being measured and subsequently reduces its flux to the surface at the time of actual measurement. This is detrimental to sensitivity. NPP is designed to eliminate this effect by blocking electrolysis prior to the measured period.FIGURE 6-15. "Bard" Fig. 5.8.5 (p. 187).Although the electrode is approximately spherical, it acts as a planar surface during the short time of the actual electrolysis, and therefore the sampled faradaic current on the plateau is

Id = nFAD{C*/[D( - ')]½}where ( - ') is time measured from the pulse rise

In comparing this current to that measured in the task experiment,recall (Id)task = nFAD{C*/[(3/7)D ]½}Thus, (Id)NP/(Id)task = (3/7)½[/( - ')]½

For = 4 s, ( - ') = 50 ms,(Id)NP/(Id)task 6.

Hence, a larger sampled current is obtained with the pulse method.FIGURE 6-16. "Bard" Fig. 5.8.6 (p. 188).Detection Limit: 106 - 107 M.

Pulse polarography preserves entirely the sensitivity improvements achieved in task polarography by discrimination against the charging current. In addition, the pulse method gains enhanced sensitivity through the increased faradaic currents.

ii/. Differential Pulse Polarography (DPP) and Differential Pulse Voltammetry (DPV)

Obviously the name of the method is derived from its reliance on the differential current measurement.FIGURE 6-17. "Bard" Fig. 5.8.8 (p. 190) & Fig. 5.8.9 (p. 191).The overall response plotted is the difference in the two currents sampled, I. The plot of this difference (I) as a function of potential is peak-shaped.FIGURE 6-18. "Bard" Fig. 5.8.11 (p. 192).The underlying reason is easily understood qualitatively. Early in an experiment of O + ne R, when the base potential is much more positive than E', no faradaic current flows during the time before the pulse, and the change in potential manifested in the pulse is too small to stimulate the faradaic process. Thus I() - I(') is virtually zero, at least for the faradaic component. Late in the experiment, when the base potential is in the diffusion-limited-current region, O is reduced during the waiting period at the maximum possible rate. The pulse cannot increase the rate further, and hence the difference I() - I(') is again small. Only in the region of E' is an appreciable faradaicdifference current observed.

(I)max = nFAD{C*/[D( - ')]1/2}[(1 - )/(1 + )] (1)where = exp{(nF/RT)(E/2)}

The quotient (1 - )/(1 + ) decreases monotonically with diminishing E and it reaches zero for E = 0.

Emax = E½ - E/2

Since E is small, the potential of maximum current lies close to the polarographic half-wave potential E½.For small-amplitude differential pulse wave, the width of peak at half-height is given by,

W½ = 90.4/n mVFor large value of E, W½ E. Although it is apparent that the larger the value of E, the larger the value of (I)max. In practice, however, it is also obvious that increasing the pulse amplitude increases the width and decreases the resolution, which is undesirable.Detection Limit: ~108 M.

Sensitivity gain in the differential method does not come from enhanced faradaic response, but comes from a reduced charging current contribution. Since both current samples I() and I(') are taken under potentiostatic conditions, the charging currents appear only because dA/dt is never zero at the DME. From the equation derived for charging current at a DME, we express these contributions as

Ic() = 0.00567Ci(Ez E E)m2/31/3

Ic(') = 0.00567Ci(Ez - E)m2/3'1/3

Thus the contribution to the differential current isIc = Ic() Ic(') = 0.00567Cim2/3-1/3[(Ez E E) (/')1/3(Ez E)]where Ci has been taken as constant over the range from E to E + E.

For the usual operating conditions, (/')1/3 is very close to unity; hence the bracketed factor is approximately E:

Ic 0.00567Cim2/31/3E

For a negative scan, Ic is positive, and vice versa. A comparison shows that the capacitive contribution to differential pulse measurements differs from that in tast and normal pulse polarography by the factor E/(Ez - E). Over most regions of polarographic operation E is smaller than Ez - E by an order of magnitude or more.

Note also that the capacitive background in differential pulse polarography is flat, insofar as Ci is constant over a potential range. In contrast, normal pulse and tast measurements feature a sloping background because of the dependence on (Ez - E).

For an irreversible system, the peak will be shifted from E' toward more extreme potentials by an activation overpotential, and the peak width will be larger than for a reversible system, because the rising portion of an irreversible wave extends over a larger potential range. Since the maximum slope on the rising portion is smaller than in the corresponding reversible case, (I)max will be smaller than the value predicted by Equation (1).

For analytical purposes, the pulse heights used in DPV frequently exceed the limits imposed by the small-amplitude restriction. Large amplitude provides an increase in response which must be balanced against the loss in resolution and the increases in charging current, which ultimately limits the minimum detectable concentration. For most cases, a Ep of 50-100 mV is optimum.

iii/. Square-Wave Voltammetry (SWV)The excitation signal for SWV is illustrated below.FIGURE 6-19. “Harris” Fig. 17-18 (p. 393).A symmetrical pulse train (the total amplitude is 2ESW) is added to a staircase (the step height is E) with a period of . The response current is sampled at the end of both the forward and reverse half cycles (at 1 and 2 in the figure). A difference current is determined by subtracting the current measured on the reverse cycle from that measured on the forward cycle, i.e., difference in current, I, between regions 1 and 2 is recorded as a function of potential. Because the two currents have opposite signs, their difference is larger than either current alone.FIGURE 6-20. “Kissinger” Fig. 5.11 (p. 158).

Analytical response can be increased by using larger square wave amplitude, but, as in pulse voltammetry, increased amplitudes lead to broadening of the observed current peak.The step height has little effect on the height of the difference current peak. The individual forward and reverse currents, on the other hand, are markedly affected by the increase in step height.FIGURE 6-21. “Anal. Chem. 1977, 49, 1899-1903” Fig. 5 (p. 1901).The forward current increases when the step height is increased but the reverse current function also increases, becoming more negative. The magnitude of change for both currents is approximately the same, so the difference current remains relatively unchanged.

SWV is a very powerful technique. When a DME is used one can apply the entire excitation waveform to a single drop (allowing a delay time Td for the drop to grow to a predetermined size). In the previously described polarographic techniques as many as 1000 drops might be used in a typical experiment. The speed of SWV makes it possible to monitored dynamic processes. Besides being fast, the technique is somewhat more sensitive than the very popular differential pulse technique because both forward and reverse currents are measured in SWV, whereas only forwards are measured in DPV.Detection limit: 107~108 M.

FIGURE 6-1. Bard et al, Electrochemical Methods, 1st Ed.


FIGURE 6-5. Kissinger et al., Laboratory Techniques in Electroanalytical Chemistry.


FIGURE 6-7.

FIGURE 6-8. Skoog et al, Principles of Instrumental Analysis, 4th Ed.

FIGURE 6-9. Skoog et al, Principles of Instrumental Analysis, 4th Ed.

FIGURE 6-10. Bard, et al, Electrochemical Methods, 1st Ed.

FIGURE 6-11. Charging current versus potential.

Figure 17-17. Sampled current polarogram of 0.1 M KCl saturated with air and after bubbling N2 through to remove O2.

FIGURE 6-12. Harris, Quantitative Chemical Analysis, 6th Ed.

FIGURE 6-15.Bard, et al, Electrochemical Methods, 1st Ed.



FIGURE 6-18.Bard, et al, Electrochemical Methods, 1st Ed.

Figure 17-18. Waveform for square wave voltammetry. Typical parameters are pulse height (Ep) = 25 mV, step height (Es) = 10 mV, and pulse period (τ) = 5 ms. Current is measured in regions 1 and 2. Optimum values are Ep = 50/n mV and Es = 10/n mV, where n is the number of electrons in the half-reaction.

FIGURE 6-19. D. C. Harris, Quantitative Analysis, 6th Ed.


FIGURE 6-21.

figure 6-4. figure 6-3. figure 6-2. figure 6-1

Documents