Experimental and theoretical correlations for the use of fundamental

Some Experimental and Theoretical Correlations for the Use of Fundamental Harmonic Alternating Current Polarography A. M. Bond Department of Inorganic Chemistry, Uniuersity of Melbourne, Parkville 3052, Victoria, Australia

In papers on direct current (dc) polarography, authors invariably state with reasons, whether the electrode process is diffusion controlled and reversible or if non-reversible, the degree of departure from reversibility, and much useful information is conveyed to the reader. Fundamentally, the reversibility or otherwise of an alternating current (ac) electrode rocess should be defined even more rigorously than or the dc electrode process if data from ac polarography are to be used satisfactorily in analytical and electroanalytical applications of the technique. Despite the considerable body of relatively simply used theory available, examples where authors describing an ac polarographic method for the determination of an electroactive species have attempted to assign the reversibility or otherwise of the ac electrode process, are extremely rare. As is shown in this paper this lack of endeavor to define the nature of ac electrode processes is an extreme hindrance to the advancement of ac polarography and to its wider acceptance as an electroanalytical method. This paper therefore describes some experimental and theoretical correlations which can be used to assign the different types of ac electrode rocesses, and considers the relative merits of the difgrent types of electrode processes in the analytical use of ac polarography, in an endeavor to encourage a systematic and logical approach to ac polarography as is the case with dc polarography.

P

THETECHNIQUE OF alternating current polarography has been in use for many years now. Unfortunately, however, the initial theoretical studies were inadequate in several aspects, and several misleading ideas arose. The earlier theoretical work has now been recognized as inadequate and more sophisticated theoretical treatments of ac polarography are now available which accurately describe the observed or experimental data (see Reference 1 for instance). However, several of the incorrect conclusions and statements made by earlier contributors to the field of ac polarography have not yet been completely eliminated from reviews and text books. Consequently, certain generalizations-e.g., ac polarography can be applied only to “reversible” electrode processes-have been somewhat slow to disappear and are still evident in current literature on ac polarography. Probably because of such confusion as to which is the correct theoretical treatment to use, the application of results of the sophisticated mathematical treatments of ac polarography have been markedly confined to specialists in the field. This has resulted in the unhappy situation where examples of workers using ac polarography as an electroanalytical or analytical tool, having attempted to rigorously classify an ac electrode process, or to provide any theoretical us. experimental parameters, are almost non-existent. By comparison, in almost any applied paper on dc polarography, the authors will invariably state for example, with reasons, whether the electrode process is diffusion controlled and reversible, or if nonreversible, the degree of departure from reversibility, and much useful information is conveyed to the reader. With ac polarography, ideally the same degree of sophistication should be used in reporting results, however, an ex-

tremely vague description of the ac wave, probably based on the understanding of the nature of the dc polarography, is usually the only information provided, and the reader is left to guess whether the ac wave for instance is in fact reversible. More often than not, it may be implied, without proof, and extremely misleadingly, that the ac wave is reversible, based on the earlier conclusion that ac polarography is sensitive or responsive only to reversible electrode pi ocesses. Theoretically and experimentally it has now been well established that ac polarography is responsive to all types of electrode processes, including quasi-reversible (1) and irreversible cases (2-4). The improved reporting of fundamental theoretical and experimental parameters in ac polarography is therefore extremely desirable, if the wider use of ac polarography in analytical and electroanalytical applications is to be encouraged in a sensible and rigorous fashion. To establish the reversibility of a dc electrode process, one would normally rigorously establish that several conditions hold. If the electrode process were to meet the criteria for reversibjlity, then the half-wave potential, E112,may be used to calculate thermodynamic parameters, such as equilibrium constants. If the electrode process were shown not to be reversible, then kinetic factors of the electrode process determine the observed E112values and corrections must be applied before they can be used for subsequent calculation of thermodynamic parameters. Fundamentally, the reversibility or otherwise of the ac electrode process should be defined even more rigorously than for the dc electrode process, if data from ac polarography are to be used satisfactorily in electroanalytical applications. The time scale for ac polarography is significantly different from that for dc polarography, which makes the present commonly accepted practice of treating the two methods jointly, rather than independently, extremely hazardous. In fact, it is possible that a reversible dc electrode process is nonreversible on the ac polarographic time scale. The mere appearance of an ac wave is therefore by no means a sufficient criterion for establishing unambiguously the reversibility or otherwise of the equivalent dc electrode process. The alternative approach of assuming characteristics of an ac electrode process from dc data is obviously even less reliable, and the practice should be strongly discouraged. As well as the readily apparent advantages in the theoretical sense of encouraging the reporting of the nature of ac electrodes from ac data, there are many practical reasons why this can be beneficial. Ac polarography has many basic and extremely useful advantages over dc polarography in analytical applications (5, 6). However, to utilize these advantages fully, it is necessary to be able to classify the nature of the electrode process. By way of example, in reporting the development of an ac polarographic method for the determination of an electroactive species, it is usually important to establish whether or not the ac electrode process is completely reversible. Alternatively, ac polarography may be advantageously used to measure Eliz in electroanalytical applications, such as the study of complex ions (7-11). For this, the

ANALYTICAL CHEMISTRY, VOL. 44, NO. 2, FEBRUARY 1972

315

nature of the ac electrode process again needs to be firmly established, although this was not recognized, in fact, by Gupta and Chatterjee (7,s)when they first proposed the use of ac polarography in the study of complex ions. In an endeavor to rectify the situation existing at present with respect to the use of ac polarography, and to eliminate from the literature, the future use of several commonly occurring misconceptions presently held by various people (and understandably so), the author of this paper would like to attempt to give an account of several simple experimental observations made with unsophisticated and conventional instrumentation which illustrate many of the theoretical concepts of ac polarography. In this manner it is hoped to show the technique can be utilized with little difficulty in a routine and similar way to dc polarography by even nonspecialists in the field of electrochemistry. It is also hoped to encourage the more frequent reporting of fundamental but simply obtained ac parameters of an ac electrode process which can be used to assess the nature of the electrode process and to establish its possible or potential use in analytical or electroanalytical applications. For convenience, the ac electrode processes are considered in four classes. The classes of electrode process to be discussed are summarized as follows: (a) Reversible ac electrode processes (b) Quasi-reversible ac electrode processes (i) Reversible dc charge transfer (ii) Quasi-reversible dc charge transfer (c) Irreversible ac electrode processes (d) Electrode processes with coupled chemical reactions. Having given an account of a systematic approach to ac polarography, which can be made with relatively simple instrumentation and theory, it then becomes convenient and logical to extend these ideas further, and embrace the cohsiderable number of additional complexities which are necessarily introduced when using more sophisticated forms of ac polarography. In this manner, it should be possible to understand how the limits of detection, accuracy, precision, convenience of measurement, etc., with conventional ac polarographic techniques, can be improved using more sophisticated forms of instrumentation, and how this instrumentation can most effectively be used. For instance, the introduction of phasesensitive ac polarography, three-electrode ac polarography, etc., requires a knowledge of the behavior of charging current, various phase-angle relationships, ohmic IR drop effects and other parameters. These phenomena, which are neglected or not even observable or measurable with simple instrumentation, assume an important role in the effective use of the newer ac polarographic methodology. This review, therefore, concludes with a discussion of some experimental and theoretical correlations relevant to the logical and systematic approach to ac polarography in its modern forms.

were recorded with Metrohm Polarecord E261, used in conjunction with Metrohm AC Modulator E393. The 10 mV voltage was chosen because it is common to most commercially available instruments, as is the frequency of 50 Hz, and the experimental arrangement was chosen to be representative of the type most frequently encountered. Ten mV is also a useful ac voltage in the analytical sense and is widely used because it provides a high sensitivity, without too much broadening of waves, as found with higher ac voltages. The reference electrode used was AglAgCl (5M NaCI) unless otherwise stated. Several measurements were made at extremely short controlled drop times of 0.16 sec. This drop time was obtained with Metrohm Polarographie Stand E354, and although such measurements are regarded as being outside those of standard ac polarography, they are given to conveniently illustrate several important aspects, and are therefor included in the section on conventional ac polarography. B. INSTRUMENTATION FOR PHASE-SENSITIVE, THREE-ELECTRODE AC POLAROGRAPHY. In the final section of the review, further experimental and theoretical correlations for use with phase-sensitive, three-electrode ac polarography are given. The PAR Electrochemistry System Model 170 (Princeton Applied Research Corporation, Princeton, N.J.) was used for this work. The reference electrode used was Ag/AgCl (5M NaCl), unless otherwise stated, and the third or auxiliary electrode was Tungsten. Controlled drop times were achieved with PAR Model 172 Drop Timer or Metrohm Polarographie Stand E354.

RESULTS AND DISCUSSION A. Experimental and Theoretical Correlations Obtainable with Conventional Instrumentation. (a) REVERSIBLE AC ELECTRODE PROCESSES.Rekersible ac waves, being defined as those controlled solely by diffusion, are relatively rare. The requirement for a reversible electrode process is that the heterogeneous rate constant for charge transfer, ks, should be extremely large. Fortunately, however, sufficient examples are available with large k, values, and these adequately fit the theory for the reversible ac wave. For the purposes of this paper, the theory for the reversible ac electrode process is taken from Reference ( I ) . The current produced by a fundamental harmonic reversible ac wave, Z(wr), is given by the expression

where A C,

= = w = Do = AE =

t

Eda = dc component of potential El,?' = reversible half-wave potential.

EXPERIMENTAL

Chemicals. All reagents used were of reagent grade purity. All solutions were degassed with either argon or nitrogen and thermostated at 25 "C, unless otherwise stated. Instrumentation. A. CONVENTIONAL AC POLARCGRAPHIC INSTRUMENTATION. Many sophisticated forms of instrumentation and methodology of ac polarography are available. However, to best achieve the objectives of this paper, all experimental work regarded as being conventional ac polarography, was recorded with an applied ac voltage of 10 mV, rms. at 50 Hz and with an electrode arrangement which does not compensate for Ohmic IR drop. These ac polarograms 316

=

electrode area concentration of electroactive species angular frequency diffusion coefficient of the electroactive species amplitude of applied alternating potential time

Other symbols are those used conventionally. At sufficiently low values of AE, it also can be shown that the shape of the ac reversible wave can be described by an expression

and that the peak potential of the ac wave, [Edolpeak= El,?'. In Equation 2, I, is the peak current corresponding to


Table I. Electrode Reactions Used to Experimentally Obtain Some Parameters Used to Assign a Reversible ac Electrode Process AE = 10 mV, frequency = 50 Hz Halfwidth, Supporting electrolytea mV Electrode reaction NaF, NaN03, NaClO4, KF, 9 3 i 3 Tl(1) e S Tl(0) HC104 U(V1) + e e U(V) NaCl, NaClO4, HC1, H C O , 94 =t4 NaN03 Cd(I1) 2e e Cd(0) NaF, NaCl, NaN03, NaC104, 48 i 3 HCl 49 + 3 Sn(I1) + 2e C Sn(0) HC1, HClOd, NaClO4 Pb(I1) 2e e Pb(0) NaF, NaCl, HCl, HClO4, NaClO4, 45 i 5

Figure 1. Undamped ac polarogram of bismuth (111) in hydrochloric acid

+

+

+ N~NO~ Cu(I1) + 2e e Cu(0) NaF. NaCIOa. NaNO, Bi(II1) + 3e C Bi(0) Ha,' (HC10; plus iow concn NaBr Nal, NaSCN) Sb(II1) + 3e Sb(0) 5M HCl, (HC104plus low concn NaBr, NaI, NaSCN) In(II1) + 3e C In(0) NaCl, NaBr, NaI, NaSCN (all at oH 2) Rh(II1) + 3e * Rh(0) 4M HClOa plus NaC1, NaBr c--

a

-,

6 7d

34 i 4 I

35 =t4

36 i 4

cosh(j/2) = 1, i.e., the peak faradaic alternating current at Edc = [Edo]peak = Eij2' and I is I(Ut). In essence Equation 2 is the ac equivalent of the extremely well known dc expression which applies to reversible dc electrode processes, (3) and in fact has the shape of the first derivative of Equation 3. Equation 3 is used extensively, in fact almost always, in dc polarography, however there are very few examples, if any, where Equation 2 is used in ac polarography, and yet this equation should provide a reasonably sensitive criterion for the presence of a reversible ac wave. Examination of Equation 2 shows that Edo at half the wave height is given by

or

where the two solutions arise from consideration of the two real solutions of the equation and correspond to the two equivalent parts of the symmetrical ac wave, where the current, but not the dc potential, is equal. Subtraction of Equation 4a from 4b to give the width of the ac wave at half its height gives Equation 5. ,-

( )::

1.52 2.303

I

50 i 3 34 i 4

1M concentration unless otherwise stated.

=

1

-0.05 0.05 V O J t vs. Ag/AgCI

-

At 25 "C, Equation 5 has a value of close to 90/n mV, and experimental measurement of the half-width provides a con-

A

Figure 2. Damped ac polarogram of bismuth (111) in hydrochloric acid

i

I

-0.05 0 . 0 5 v o l t vs. Ag/AgCI 913

venient check of the reversibility or otherwise of the ac electrode process. In actual fact, Equation 2 and therefore the result in Equation 5, is only approximate. However, it applies almost exactly for applied ac potentials of AE 6 81n mV (I). For AE values of 10 mV rms, as used in this work, very good agreement to the value 90jn would be expected for one-electron reversible electrode processes, and marginally higher values for two- and three-electron processes. Experimentally, reversible electrode processes listed in Table I were used to assess the acceptable range of half-wdiths which could be used to define a reversible electrode process, involving variable numbers of electrons. For n = 1, a half-width of (93 i 3) mV is considered to be acceptable to define a reversible ac electrode process with AE = 10 mV, rms, while for n = 2 and n = 3, the values would be (50 + 5) and (35 i 5) mV, respectively. Two points should be noted at this stage. First, these values of the half-width were obtained from relatively low concentrations of electroactive species (10-6 to 10-4M) to ensure that the ohmic IR drop is reduced to a minimum. At higher currents produced by higher concentrations, the IR drop can cause considerable "apparent" broadening of the wave and for this reason if theoretical studies are to be made with ac polarography without IR compensation, low concentrations are to be preferred. Second, the values obtained in this work were obtained on undamped ac polarograms, such as that for Bi(II1) in hydrochloric acid shown in Figure 1, and maximum currents were used. If, however, damping is to be employed, and scan rates of dc potential are sufficiently slow to minimize recorder distortion, polarograms of the type shown in Figure 2 can also be used to measure the half-width. In the presence of damping, averaged currents rather than maximum values, are most reliably used. The half-width is an extremely useful guide to the assignment of a reversible ac electrode process. However, since it is


317

Edc ‘0

Volt

vs

Ag

/ Ag Cl

I

\

1

-04

-0.8

0

-04

04

Figure 4. A test for reversibility of the ac electrode process Bi(II1) 3e e Bi(0) in 1M HCl

+

+

effectively only a two-point analysis of the ac wave, it is not entirely satisfactory. The complete wave can be analyzed using Equation 2. A graphical plot of

(6 8/n) :Rn

for a reversible

electrode process and for which AE mV ( I ) . Figure 3 shows such a plot for the reduction process TI(1) e e Tl(ama1gam) in 0.5M sodium perchlorate. A straight line of slope (118 f 2 ) mV is observed, in excellent agreement with the theoretical value of 118.2/n at 25 “C. If the IR drop is significant, which it can be at high concentrations, a curved plot is observed with a limiting slope close to the theoretical value at the most positive potentials, but with increasing departure at more negative potentials as the influence of the IR drop becomes more important. Figure 4 shows the same plot for the reduction Bi(II1) 3e e Bi(ama1gam) in 1M hydrochloric acid. A straight line of slope (42 f 2 ) mV is observed. Reversible electrode processes, where n = 2 such as reduction of Cd(II), Pb(II), and Sn(I1) to their respective amalgams in nitrate and perchlorate media, give straight lines for Equation 2 with slopes of (63 + 3 ) mV. The reversible ac electrode process is also characterized by several other features. The peak potential should be independent of concentration and drop time as should the shape of the wave. All reduction processes listed in Table I comply closely with this requisite. Absence of dependence of [Edolpeak and wave shape upon these variables is not in itself an extremely sensitive test for reversibility, but as will be shown later the shapes of quasi-reversible electrode processes in particular are often remarkably sensitive to changes in drop time and this feature can often readily distinguish a reversible from a quasi-reversible electrode process. Another requirement of [&]peak is that it should be equivalent to the dc half-wave potential Ell2. Measurement of is much more complex than [E&eakbecause the value cannot

+

318

04

08

Figure 3. A test for reversibility of the ac electrode process Tl(1) e eTl(0) in 0.5MNaC104

should be a straight line of slope 2 2.303-

0

+

be read directly from the graph. The diffusion current id has first to be defined in dc polarography and Elizis the potential at id/2. Measurement of id can be somewhat arbitrary unless a completely flat diffusion current region is obtained. Thus, although any one worker may be able to obtain reproducible Eli2 values, the absolute value of El,zwill always depend on the id value chosen which, in the usual case of a limiting or diffusion current which is not completely flat, and especially in the extreme cases of maxima or minima, depends on the judgment of the worker concerned. In ac polarography the value of [Edolpealt, on the other hand, is uniquely defined as being the potential at maximum current, and the result is obtained directly and unambiguously. However, for all reversible systems given in Table I, the difference between Ell2 and [Edelpeak was never found to be more than 5 mV. This agreement is considered satisfactory and within the limit of experimental error. Although it has been established that a requisite of a reversible electrode process is that the values of Eli2 and [Edclpeak should be equal, close or exact agreement of El/z and [Edolpeak can also be obtained for quasi-reversible or irreversible electrode processes. The mere equivalence of these two parameters does not define a reversible electrode process absolutely, although the literature contains many examples where this equivalence is given as evidence for a reversible electrode reaction. This feature of an ac polarogram needs to be coupled with considerably more evidence before any firm conclusions about reversibility can be reached. The correctness of part of Equation 1 concerning the current of a reversible ac electrode process and several important consequences in the analytical use can be shown simply in the following manner: For measurements made in this section, AE and o are constant. Thus it follows from Equation 1 that the maximum value of Z(wf), now called In, (occurring at a potential equal to [Edejpeak and for which cosh j / 2 = I), is proportional to n2CoDol i 2 for measurements made with the same capillary. Figure 5 shows that Ipis a linear function of concentration for all “!eversible” electrode processes examined. If higher


low scan rate of dc potential, to improve the ease of measurement, the limits of detection for Tl(1) (n = l), Cd(I1) ( n = 2) and In(II1) ( n = 3) were approximately 5 x lo-", 2 x 10-6M, and 1 X 10-6M, respectively. This difference is considered to be a direct consequence of the dependence of I p upon n2. It should also be noticed that I p is independent of k, for reversible electrode processes. This is particularly important because any variation in k, on the electrode process, resulting, for example, from the presence of an electrode process occurring at more positive potentials than the species being examined, or from slight alteration in supporting electrolyte, will not alter I,, providing of course that the change in ks is not a large decrease. As some electrode processes occurring at more positive potentials will alter k , , this lack of dependence of I , on k, is an essential factor in the simultaneous determination of two or more electroactive species. Similarly, a slight change in composition of electrolyte can alter k,, but for reversible ac electrode processes this will not alter Ip. By comparison, I p is dependent upon k, for quasi-reversible electroactive species, as shown later, and the analytical use of ac electrode processes, other than reversible ones, is extremely susceptible to interference. The absolute characterization of the nature of ac electrode processes is therefore strongly to be encouraged for analytical applications of ac polarography. The value of 1, is also proportional to the area of the mercury drop, A , as in Equation 1. The area in turn is proportional to the flow rate of mercury, rn, and drop time, t , used, both of these variables being dependent on mercury height. Figures 6 and 7, show, among other features, the marked dependence of I p on drop time by comparing ac polarograms of the same solution at the same mercury column height for reduction of Tl(1) in 5M NaCl at natural drop time, and a controlled, extremely short drop time of 0.32 sec. Very large differences in I p occur for the same mercury column height. Figure 7 also shows that if the drop time is controlled at a fixed value and the mercury column height is increased, Ip also increases for reversible electrode processes because A in-

L

E

Jr

2 4 6 CONCENTRATION

8

M

10

x 10'

Figure 5, Plots of peak height us. concentration for In(III), Cd(II), Pb(II), and TI(I) in lMNaCl

concentrations of depolarizer are used, curvature is found due to IR drop. The occurrence of significant IR drop is easily recognized because the half-width of the wave becomes larger and curvature of the I , us. Co plot can be correlated with departure of the half-width from the reversible value. A second significant feature of Figure 5 is the obvious dependence of I , on n. The diffusion coefficients of most inorganic species do not differ significantly and since I p varies , are further minimized. However, I , with D o 1 / 2differences varies as does n2, and in going from a one-electron reduction, e.g., Tl(1) or U(VI), to a three-electron reduction such as for In(III), the sensitivity (change in I , per unit concentration) increases markedly. This dependence of I p upon n 2 , according to Equation 1, means that for the same concentration and value of Do,the values of I, would be in the ratio 1:4:9 for reversible ac reduction processes involving one, two, and three electrons, respectively, and Figure 5 shows this to be qualitatively correct. One other important consequence of this dependence upon n2 is found in the limit of detection of various electroactive species. Using heavily damped ac polarograms recorded at

-&

-045

-d45

- 0 2 5 -065

-025

-065

-045

-0.25

I

Volt v s . Ag A g CI

Figure 6. Dependence of an ac electrode process on mercury column height when natural drop time is used. The electrode process considered is TI e s TI(0) in 5MNaCl

+

Right hand polarogram has a mercury column column height of 27 cm Center polarogram has a mercury column height of 51 cm Left hand polarogram has a mercury column height of 69 cm ANALYTICAL CHEMISTRY, VOL. 44, NO. 2 , FEBRUARY 1972

319

-065

-045

-0.25

-0.65

-945

- 0.25 -0.65

-025

-045 &I3 _. .

Volt v s . Ag/Ag CI

Figure 7. Dependence of an ac electrode process on mercury column height when a controlled drop time is used The same electrode process and conditions as for Figure 6 apply, except that drop time is fixed at 0.32 sec rather than using natural drop time

sec-I. With a k, value of this order, the dc electrode process is certainly close to reversible (12) and so the equivalence,

Table IT. Influence of Chloride on the Reduction of Bismuth(II1) Bismuth concentration = 2.53 X lO-'M in 0.5M perchloric acid, Data from Reference 13 Slope dc Rate constant plot of EdoUS. Chloride concn, M cm sec-1 log[(& - i ) / i ] , mV o.oO0o 0.023 40 0.0022 0.0062 0.018 0.060 0.180

0.030 0.079 0.21 0.20 0.20

23 23 23 21 20

creases. The dc id values vary with the square root of column height, if the mercury column height is varied with natural drop time frequency. The ac wave height, however, is virtually independent of column height under these conditions because A is constant. Figure 6 shows an ac polarogram of Tl(1) in 5M NaCl at 3 mercury column heights. The decrease in drop time as the column height increases can be seen; however ZP is virtually unaltered. (b) QUASI-REVERSIBLE AC ELECTRODEPROCESSES. (i) Reversible dc Charge Transfer. Quasi-reversibility of ac electrode processes is more common than complete reversibility. Quasi-reversible electrode processes are described in part, but not completely, by Equations 1 and 2 which apply to the reversible ac electrode process. Such electrode processes are not, however, completely diffusion controlled in the ac sense. The first type in which reversible dc charge transfer is observed, or very nearly so, is sometimes difficult to distinguish simply from the reversible electrode process. In fact, in analytical and electroanalytical applications with low frequency ac polarography (as used in this work) any distinction is quite slight. Theoretical considerations of the quasi-reversible electrode reaction ( I ) show that [Edclpeak varies with frequency, but approaches at low frequency and for k, 3 cm 320

Eli? =

El!?'

=

[J%olpeak

(7)

can apply for such systems, as is also the case with reversible ac electrode processes. However, the shape of an ac quasireversible wave will in general be slightly broader than that of the reversible electrode process, and even slight departures from the theoretical Nernstian slope (2.303RTlnF) of the linear dc plot of

€Go us. log

(y)

will be exhibited in the ac wave as broadening, although for this case, if the transfer coefficient, a , is close to 0.5, the shape will still be almost identical to the reversible case. For the purposes of this work, reversible dc charge transfer is considered to be applicable if the dc plot, Edo us. log

(y),

is linear with slope close to 2.303RTInF. If a

curved plot is observed, then dc charge transfer will be considered to be quasi-reversible and the corresponding ac quasi-reversible electrode process will be considered in part (ii) of this section. The important difference in distinguishing a quasi-reversible electrode process from a reversible one is the magnitude of Z(wt). The value of Z(wr) for the quasi-reversible electrode process is complex (1). However, it contains terms for k, and a and herein lies a major difference from the reversible case. It is also appreciably less in magnitude than for the reversible electrode process. A useful illustration of a quasi-reversible ac electrode process with reversible dc charge transfer can be seen in the reduction Bi(amalgam), in perchloric of bismuth(III), Bi(II1) + 3e acid in the presence of various concentrations of chloride. Table I1 gives some data obtained by Bauer and Elving (13). In the absence of chloride, the electrode process for Bi(II1) is irreversible by the usual dc criteria. However, with addition of as little as 2.2 x lO-3M chloride, or greater, the dc plot of


7

[CI'I M Figure 8. Dependence of I , upon the concentration of chloride for the electrode 3e e Bi(0). Data process Bi(II1) taken from Reference I 4

- 0.5

-10

0.0 I

I

Volt vs Ag A g C I

+

Figure 10. Quasi-reversible dc electrode processes for Sn(I1) in 0.8M NaF More positive wave is the oxidation electrode process Sn(I1) $ Sn(1V) 2e. More negative electrode process is the reduction Sn(I1) + 2e e Sn(0)

+

- 1.0

- 0.5 Volt

(F)

is consistent with what would be con-

sidered a reversible dc electrode process. The rate constant, however, increases with increasing chloride concentration. Data given by Bond and Waugh (14) on the dependence of the I , value as a function of chloride concentration are given in Figure 8. The I p value increases markedly with chloride ion concentrations up to about 0.1M and then becomes virtually independent of chloride concentration. At chloride concentrations below 0.1M, the electrode process has reversible dc charge transfer but the ac electrode process is quasi-reversible and I , increases as k , increases. Above 0.1M chloride, the value of k , is sufficiently high for the electrode process to be reversible even in the ac sense and I p becomes independent of k,. In concentrated chloride media the Bi(II1) electrode process attains k, values 3 1 cm sec-l (15, 16). Values of k , of this order are necessary for an ac electrode process to be diffusion controlled and hence completely reversible. By comparison, Delahay (12) has defined dc electrode processes as cm sec-l with being reversible if k , is greater than 2 x normal drop times. The difference between ac and dc polarography lies in the different time scales. (ii) Quasi-Recersible dc Charge Transfer. If k, lies between and 5 X cm sec-I, the dc electrode processes, 2 X may be defined as quasi-reversible(l2). For some quasireversible processes, plots of Edo us. log

')

( i d-

I

A g A g CI

Figure 11. The ac electrode processes for Sn(I1) in 0.8M NaF

Figure 9. Analysis of a quasi-reversible dc electrode process. Dashed line (- - -) shows reversible plot Edous. log

VS.

0.0

may be

curved. At the foot (i.e., more positive extreme) of the dc

wave, the plot can show Nernstian behavior (see Figure 9) and the wave exhibits reversible behavior at the more positive potentials. Reduction of tin(I1) in fluoride media (17) provides an excellent example of such a system. A dc polarogram of Sn(I1) in 0.8M N a F is given in Figure 10. Two quasireversible dc electrode processes are observed. The anodic (more positive) wave corresponds to the electrode process Sn(I1) e Sn(1V) 2e and the cathodic wave to Sn(I1) 2e a Sn(ama1gam). The heights of dc waves are independent of kinetics of the electrode process and id for both waves is the same except for sign. Furthermore, the shapes are almost identical. Figure 11 shows that, for this system the two ac electrode waves are obviously completely different ; the two quasi-reversible ac electrode processes have different values of k , and of CY and the shapes and heights of the waves therefore do not coincide. It should be noted that the readout of ac polarography with most instruments is such that no distinction is possible between anodic and cathodic waves and dc polarography is necessary to make the distinction. Because certain quasi-reversible dc waves exhibit Nernstian or reversible behavior at positive parts of the wave, it might be anticipated that some ac quasi-reversible waves would also exhibit similar behavior with equivalent equations. For the tin(I1) reduction wave in fluoride media, a plot of

+

+

has a limiting slope of (65 + 5) mV, corresponding to a reversible electrode process. The zinc(I1) electrode process,


321

Table 111. AC and DC Polarographic Parameters for Reduction of Zinc in Fluoride Media [Zn(II)] = 2 X 10-4M. Ionic strength of 1.0 maintained by sodium perchlorate. -El& volt

[NaFl, M

us.

0.00 0.16 0.24 0.40 0.56 0.80

-Em?, volt

AglAgCl

id,

0.9547 0.9636 0.9651 0.9731 0.9764 0.9821

ILA

os.

1.535 1.495 1.481 1.421 1.403 1.367

volt AglAgCl

-[Ede]peak,

AgIAgC1

cs.

0.9505 0.9611 0.9625 0.9705 0.9726 0.9780

ILA

0.9443 0.9508 0.9533 0.9610 0.9655 0.9716

0.975 0.785 0.690 0.585 0.520 0.440

~~

Table IV. AC and DC Polarographic Parameters for Reduction of Tin in Fluoride Media& Ionic strength = 1.0 maintained by sodium perchlorate.

-[Edolpesk [NaFl, M

Conventional

0.01 0.02 0.03 0.04 0.07 0.10 0.20 0.30

0.4868 0.5144 0.5386 0.5497 0.5703 0.5809 0.5996 0.6090

-Elin f

Rapid, = 0.16 sec

Rapid Conventional

0.5243 0.5488 0.5605 0.5698 0.5839 0.5943 0.6098 0.6172

0.4807 0.5053 0.5219 0.5322 0.5535 0.5678 0.5939 0.6076

t = 0.16 sec 0.5102 0.5422 0.5539 0.5672 0.5797 0.5900 0.6035 0.6110

-E, is? 0.4800 0.5048 0,5207 0,5308 0.5513 0.5658 0.5899 0.6043

(E114

- E d mV 32.2 32.8 32.8 33.4 33.6 35.5 36.4 36.6

Potentials measured relative to AglAgCl(5M NaC1).

+

Zn(I1) 2e Zh (amalgam), which exhibits similar quasireversible behavior to that of Sn(I1) (18, 19), gives a similar limiting slope and this plot provides a means of defining an ac quasi-reversible electrode process with a reasonably high k , value. For dc quasi-reversible electrode processes not exhibiting a curved plot of

Edc

us. log

("

j)

with limiting

Nernstian slope, the equivalent ac plot is observed not to apply also. Theoretically, quasi-reversible electrode processes have [.!?do]pe&values quite close to Ellz( I ) . Whether the values are more positive or negative than El/; depends upon the values of k, and CY. Although intuitively it may seem strange to have [Edolpeak more positive than E,,; and therefore, of course, also more positive than &, this experimental observation is in agreement with theory. Results are given at various concentrations of sodium fluoride for zinc(I1) reduction in Table 111; R,z' was calculated from the dc polarograms from extrapolation of the limiting slope of the curved plot (given in Figure 9) of

For this set of data the shape of the ac waves remained essentially the same for all concentrations of fluoride, although ID decreases with increase in fluoride, and k, probably decreases slightly with increasing fluoride concentration. Table IV gives similar data for the Sn(I1) 2e 8 Sn(ama1gam) electrode process. The characteristics of this electrode process are described more fully elsewhere (17) but the quasi-reversible electrode process becomes considerably more irreversible on addition of fluoride as demonstrated by changes in tabulated values of (Ell4 - E3,4)derived from dc data. The polarographic characteristics of this system are also extremely dependent on drop time and results with a short controlled drop time of 0.16 sec are also included. For this and results system, [&]peak is always more negative than can be contrasted with those for zinc.

+

322

a

It should be noted, however, that these two quasi-reversible electrode processes are characterized by Values of [Edolpeak which are always in reasonable agreement with .!?I/z, and this distinguishes them from completely irreversible electrode processes as will be shown later. With examples such as for tin(I1) and zinc(II), the overvoltage is small and [Edo)peakis also close to El,;. Consideration of examples where the overvoltage is considerably higher can be given. In 1Mperchloric acid, the electrode process Bi(II1) -I- 3e

a Bi(ama1gdm)

has a k, value of 3.8 x 10-4 cm sec-l (16). The dc wave is reasonably well defined, but considerably drawn out, the value of (Eli4 - E3i4)being 64 mV. The ac wave is slightly asymmetrical with a half-width of 96 mV and obviously the elecis -0.004 volt us. trode process is not reversible. [&&e& AglAgCl compared with a dc value for El/z of 0.000 volt us. Ag AgCl. In lMHNOI the bismuth electrode process has a k3 value of (16). An extremely well defined ac wave is ob3.7 X served as shown in Figure 12 with a half-width of 64 mV. As in 1M perchloric acid, reduction is not reversible although an extremely symmetrical well-defined wave is observed which without mathematical analysis might be assumed to be reversible. Furthermore, [.!?&& is 0.048 volt us. AglAgC1, which is very close to the value for El/*of 0.050 volt US. Ag/AgC1. Obviously, agreement between [ E d c l p e a k and E1&annot be used to define a reversible electrode process. The shapes of the polarographic waves for quasi-reversible electrode processes have been shown to be extremely variable in the examples given and ac quasi-reversible electrode processes are typified by this feature. Any variation in k, or a can cause marked changes in ZP and shape. Consequently, drop time variations are often extremely significant, as are changes in electrolyte, in determining the shape and height of the ac wave to be observed. The vaiiation in the rate of the zinc(I1) electrode process with drop time has been considered in various media by the author (18,19) and this electrode process


I

9

U

e

H 015

-005

volt

VS.

A ~ / ACI~

Figure 12. An ac polarogram of bismuth(II1) in 1M HN03 provides a convenient illustration. Figure 13 shows analytical calibration curves of Z p us. concentration of Cu(I1) and Zn(I1) in 0.5M sodium perchlorate and 0.5M sodium fluoride. Copper(I1) and zinc(I1) both undergo reduction of the type M(I1)

+ 2e

M(ama1gam)

in both these media. The copper(I1) electrode process, however, approaches reversibility, but that for zinc is quasireversible. Two important features arise from Figure 13. First, the much greater sensitivity of the more reversible electrode process is obvious. Second, the value of Zp for copper(I1) is virtually the same in both perchlorate and fluoride media. However, for zinc, considerable differences in Zp occur between perchlorate and fluoride media. This latter behavior typifies a quasi-reversible electrode process and even slight changes in electrolyte can often markedly alter I,, as the value depends on k,. On the other hand, reversible ac electrode processes are independent of k,, and Zp does not usually change significantly even with considerable change in the nature of the electrolyte, unless the electrode process is altered substantially by complexation, for example. The only alteration in Zp which can arise with a reversible ac electrode and this process according to Equation 1 is a change in should be fairly small in most cases. The analytical use of quasi-reversible ac electrode processes can therefore be extremely unreliable. Measurement of Zp on an unknown solution and comparison with standards should normally be undertaken only if it has been previously established that the composition of the unknown is such that it will not alter k,, compared with the value obtained in the standards. Any complexing reagent, adsorbable species or other electroactive species present in the unknown, but not included in the standard, can potentially alter k , and lead to incorrect results. This feature, combined with the lower sensitivity of quasi-reversible electrode processes, makes it difficult to recommend use of anything but reversible ac electrode processes for analytical purposes, except in special circumstances or else when one is willing to employ the standard additions method to each sample. This also shows why the author considers it important for rigorous characterization of ac electrode processes to be included in papers reporting analytical applications of the technique. (c) IRREVERSIBLE ELECTRODE PROCESSES.The early inexact theory of ac polarography indicated that the magnitude of the ac polarographic wave is vanishingly small for irreversible

Figure 13. Plots of peak current us. concentration of zinc and copper in different media (0) Cu(I1) in O.5M NaCIO,, ( 0 ) Cu(I1) in 0.5 M NaF, ( X ) Zn(I1) in 0.5M NaClO,, (A) Zn(I1) in

0.5 M NaF

electrode processes. However, contrary to earlier beliefs, Timmer et al., (2, 3) and Smith and McCord ( 4 ) have now established by theory and experiment, that a finite, measurable ac polarographic wave is obtained with irreversible processes. Despite these results, the idea that ac measurements can be made on irreversible electrode processes has been slow to filter through to electrochemists, and exceedingly few examples of applications have appeared in the literature in which ac polarographic measurements have been made on irreversible electrode processes. Although quantitative differences are apparent between the theoretical treatments for the irreversible ac electrode processes, the theories are in agreement regarding the very important quantitative prediction that a measurable ac wave of magnitude and shape, which is independent of k,, will be observed with irreversible systems. The sole influence of IC, is to determine the position of the wave on the dc potential axis (4). The current magnitude, Z(wt), is a rather complex function. However, unlike the reversible case, it is proportional to a,the charge transfer coefficient. The peak potential is given approximately ( 4 ) by

where Q

=

1.907 (ur)1'2.

Since Elll =

4- anF RT In (1.34!21k:f1'2)

(9)

it follows that

This result indicates that the ac [Edoleesk value with irreversible systems is displaced cathodically by a substantial amount from the dc half-wave potential. This criterion characterizes an irreversible ac wave. Other features also characterize irreversible ac waves. The waves are extremely broad and are of very low sensitivity (Le., current per unit concentration) compared with those for reversible ac electrode processes.


323

r

0 0

2,5 5.0 [electroreducible species in 5 O/oWl x

75

ldu

2.5 K) 7.5 [electroreduci ble species in 5 O/O H=]x ld&l

Figure 15. Plots of id us. concentration for some electrode processes in 5 %hydrofluoric acid

Figure 14. Plots of I , VS. concentration for some electrode processes in 5 % hydrofluoricacid Woodson and Smith (20) have used the deviation of [E,&,ealt from Ell2 as a criterion of irreversibility of nondiffusion controlled ac waves. Bond and O’Donnell(21) have reported some extremely broad ac waves in aqueous hydrofluoric acid media, particularly for the electrode processes Bi(II1)

5Bi(0)

Mo(V1) e_ Mo(V) U(V1) e_ U(V) Plots of I , us. concentration are given in Figure 14 for the above three electrode processes with a controlled drop time of 0.16 sec in 5 % HF. For comparison, the reversible, or nearly reversible, electrode process in the same medium 2e

Cd(I1)

Cd(0)

is also plotted and the vast difference in sensitivity can be seen. Figure 15 shows the equivalent dc plot of id us. concentration, and it can be seen that the sensitivity of irreversible dc electrode processes is essentially the same as for the reversible cases. The value of id in dc polarography is given by the Ilkovic equation and id is independent of the kinetics of the electrode process, so that for totally irreversible electrode processes dc polarography would in general be preferred to ac polarography in analytical applications. In conclusion, it should be stressed that whenever a dc wave is observed, it has been the author’s experience that an ac wave will also be found even for totally irreversible electrode processes, if sufficiently high ac current sensitivities are used. The ac polarography of virtually any electrode process can therefore be studied. This feature of ac polarography is in fact well illustrated in a recent article by the author, where a number of extremely irreversible electrode processes were shown to give ac polarographic waves (22). The importance of irreversible electrode processes, as a possible source of interference in the analytical use of ac polarography, has also been discussed recently (23). Because of the low sensitivity of the ac polarographic method toward such electrode processes, there may be a tendency to neglect their presence. This work, particularly with respect to irreversibly reduced oxygen, shows a clear need to recognize their presence. (d) ELECTRODE PROCESSES WITH COUPLED CHEMICAL REACTIONS. In sections, (b) and (c) the departure from reversibility 324

of electrode processes has been considered in terms of slow charge transfer. However, kinetic effects introduced by coupled chemical reactions can be rather prevalent with certain types of systems, particularly with organic systems, and canexplain the departure from reversibility rather than slow charge transfer. Reference 24 provides an excellent example of some of the effects of coupled chemical reactions on electrode processes. Examination of the theory for electrode processes with coupled chemical reactions ( I ) shows that the effect on current amplitude and the shape of the wave are sufficiently similar to those of quasi-reversible charge transfer that one effect could easily be mistaken for the other. Unless one is prepared to proceed with measurement of frequency response, preferably the phase angle and other time consuming measurements and calculations, such as those undertaken by Huebert and Smith in their work on the polarographic behavior of cyclooctatetraene (24), then the reason for departure from reversibility may often be open to question. With most existing commercial instrumentation, the analytical chemist would probably find it far too time consuming, if not impossible, to undertake studies to determine the mechanism of electrode processes involving coupled chemical reactions, and in any case there is probably no real advantage to him in doing this. The peak current, being proportional to k, and a,and most characteristics of the electrode process being similar to the case where slow charge transfer is ratedetermining, means that analytical use of the electrode process is somewhat “chancy” unless the method of standard additions is used, or unless strict precautions are made to ensure that the standards and unknown solutions are prepared and maintained in exactly the same medium. As for the case where slow charge transfer gives rise to the quasi-reversible electrode process, the peak current is likely to be extremely sensitive to slight variations in the supporting electrolyte. For instance, if one were to attempt to determine an organic species undergoing an electrode process with a coupled chemical reaction in a nonaqueous solvent, then one would have to ensure that the most likely impurity, that of water, were completely absent for all standards and unknowns or remained at the same level in all solutions, as the electrode process is likely to be dependent on the water concentration. Although the more reversible the electrode process, the better the analytical method is likely to be, it is often necessary to use electrode processes showing departures from reversibility. It has been the author’s experience that if a nonrevers-

ANALYTICAL CHEMISTRY, VOL. 44, NO. 2. FEBRUARY 1972

w

:1000 hz

I

w :l 0 0 h z

-0 5

-0 4

- 0.6

v o l t vs. Ag/AgCI Figure 16. Variation of charging current with frequency AE

=

10 mV. Medium = 0.5M NaClO,

ible electrode process is to be used, then the best check that correct results are being obtained is to carefully ensure that the peak potentials and shapes of ac waves from unknown solutions are identical with the standards used for the determination. Any departure from this agreement is an excellent indication that interference to the analytical method is being encountered. B. Some Additional Experimental and Theoretical Correlations Obtainable with Phase-Sensitive and Three-Electrode ac Polarography. In Section A, some theoretical and experimental correlations that can be made with conventional ac polarographic instrumentation are given. A fixed applied ac voltage of 10 mV and a fixed frequency of 50 Hz were used, and no compensation for the ohmic IR drop was made, With more sophisticated instrumentation, variable frequency, variable applied ac voltage, compensation for ohmic IR drop, and measurement of phase angle, are generally possible. All of the principles mentioned previously are still entirely valid, but obviously additional parameters are now introduced. It is in fact the additional features of phasesensitive detection and three-electrode instrumentation which can lead to considerable improvement in the sensitivity, precision, and accuracy of the ac polarographic method. At the same time, of course, all the extra variables lead to additional complexities, and it is probably of even greater importance that a systematic and logical approach be applied when using sophisticated instrumentation, than is the case with the conventional forms. With this in mind, the extension to the application of phase-sensitive, three-electrode, variable frequency, and variable amplitude ac polarography is now considered, both in terms of experimental and theoretical correlations developed previously, and in terms of additional correlations possible with this form of instrumentation, particularly those directly relevant to the analytical applications. In the previous section, it was established and strongly recommended that analytical use of ac polarography is best confined to fast electrode processes. That section adequately covers the features of nonreversible electrode processes, from the analytical viewpoint, and it is considered that any further discussion on totally irreversible electrode processes, and electrode processes with coupled chemical reactions, while

being of considerable interest from mechanistic and other viewpoints, need not be considered further in this review. Hence, this segment of the review will be mainly confined to a discussion of features affecting the study and analytical use of fast electrode processes, particularly those exhibiting reversible behavior, or quasi-reversible behavior, with reversible dc charge transfer. (I) BACKGROUND OR CHARGING CURRENT IN AC POLAROGRAPHY. In order to understand the advantages and the use of phase-sensitive, three-electrode instrumentation in ac polarography, it is necessary to first introduce a discussion of the charging current, which has virtually been neglected in the first section. The total alternating current flowing during an experiment, consists of faradaic and capacitive components. The capacitive component results from the charging of the double layer, and gives rise to the background or charging current, while the faradaic component arises from the charge transfer. The magnitude of the charging current is primarily determined by the double layer, associated with a particular electrolyte, and is independent of the concentration of depolarizer, whereas the faradaic current is directly proportional to the concentration of depolarizer, for the classes of electrode process under consideration. Thus, although with high concentrations of depolarizer (e.g. 10-3M),the faradaic current is substantially higher than the charging current, at relatively dilute solutions (e.g., lO-5M or less) it can become far greater than the faradaic current and eventually, at sufficiently low concentrations, the faradaic current will be masked. With conventional ac polarographic equipment, the limit of detection has always been found by the author to be established by the charging current, and not by instrumental artifacts, such as noise. Furthermore, the precision of measurement at low concentrations decreases because of the presence of the charging current. In view of the above, the sensitivity, precision, and limit of detection of ac polarography is higher, the greater the ratio of faradaic to charging current, all other factors being equal. The relative dependence of the charging and faradaic currents on various parameters, therefore, needs to be established. (11) DEPENDENCE OF CHARGING CURRENT AND FARADAIC CURRENT ON FREQUENCY. (a) The Charging Current. Figure 16 shows the variation of the charging current with frequency in 0.5MNaC104. The considerable increase of charging or background current with frequency can be seen in this electrolyte, and this is a typical observation found with all electrolytes. The charging current actually increases directly with frequency, provided no ohmic IR drop or instrumental artifacts are present. (6) The Faradaic Current. (i) The Reversible ac Electrode Process. Figure 17 shows the variation of the faradaic current with frequency for the electrode process Cd(1I)

+ 2e e Cd(ama1gam)

in 5M HC1. According to Equation 1, Zp varies with the square root of frequency for a reversible electrode process and this relationship is closely obeyed for cadmium. That is, a plot of Zp us. u1/2is a straight line with intercept at the origin and an additional criterion of ac polarographic reversibility ( I ) is now introduced in this section. (ii) The Quasi-reversible ac Electrode Process with Reversible dc Charge Transfer. Very few ac electrode processes, used analytically, are likely to be as highly reversible as cadmium, in the ac sense, and this type of electrode process therefore cannot be considered typical. A much more com-


0

325

(a) Figure 17. Variation of faradaic current with frequency for the reversible ac electrode process Cd(I1) .eCd(0) in 5M HCI AE = 10 mV. Phaseaensitivereadout. (a) w = 20 Hz.(b) w = 100 Hz.(c) w = 200 Hz. [Cd] = 1 X 10-8M

1

1

-0.6 - 0 . 7

,A444

-06 -0.7 v o l t vs. Ag/AgCI Table V. Variation of [Edolpesk and Half-Width with Frequency, for the Copper(I1)-Copper(0) Quasi-Reversible AC Electrode Process in 1M NaNOp [Edolpeak

Frequency, Hz

V us. Ag/AgCl

Half-width, mV

10 100 200 500 600 800

0.075 0.076 0.078 0,080 0.081 0.082 0.083

48 53 56 63 67 68 71

lo00 a

Values from Reference 27, AE = 10 mV, [CUI= 1.00 X

M.

c 20 30 10

0

w 112

Figure 18. Variation of I, with frequency for the Cu(I1) e Cu(0) quasi-reversible ac electrode process in l M N a N 0 , AE

=

10 mV. [CUI

=

1 X 10-3M

monly occurring class of electrode process, in fact, will come under the category of ac quasi-reversible, with reversible dc charge transfer. Hence, this latter class of electrode process and its dependency on I p , need also to be considered in some detail. A good example to illustrate this type of ac electrode process is the reduction process of copper in nitrate media, Cu(I1)

+ 2.5

Cu(ama1gam)

Breyer et a/. (25) have studied the effect of supporting electrolyte on the polarographic reduction of copper. In various media, including nitrate, dc plots of Edrne us. log (id - i) , indicate the electrode process is close to reversible in i

the dc sense (25). Delahay and Adams (26),found that in 3M K N 0 3 , the height of the ac polarographic wave was proportional to the square root of frequency, for frequencies up to 326

about 100 Hz. Randles and Somerton (15) measured the rate constant in l M K N O l to be 4.5 X lo+ cm sec-I. From these observations, and discussion in Section A, it is apparent that in the dc sense, the electrode process of copper nitrate in nitrate media will be close to reversible. However, the rate constant is not sufficiently large for the ac electrode process to be completely reversible and diffusion controlled. The ac electrode process should therefore be quasi-reversible, with reversible dc charge transfer, and typical of those likely to be encountered most frequently. Assuming that the ac copper(I1) electrode process was in fact likely to be a typical example of an analytically usable ac electrode process, Bond and Canterford (27) undertook a comprehensive study of the ac polarography of copper in 1M N a N 0 3 with a wide variety of ac techniques, using the same instrumentation as in this review. In the remainder of the review, data will be drawn from this work on the copper(I1) electrode process in 1M N a N 0 3 to illustrate the various features of ac polarography with phase-sensitive, three-electrode instrumentation, in addition to considering the highly reversible cadmium electrode process. Figure 18 shows a plot of I p us. wl’z for copper in 1M NaN03. At low frequencies this plot approaches a straight line passing through the origin, and the faradaic current is proportional to ~ 1 ’ 2 . At higher frequencies, the proportionality to frequency becomes considerably less than ~ ~ A1 simple manner in which to explain this behavior is to consider the influence of frequency, as altering the time scale of the ac polarographic experiment. At low frequency, a fast electrode process can exhibit behavior approximating that of a reversible ac electrode process. Any increase in frequency of the po-


~

.

A E i lOmV

AE= 5 m V

.

.

-0 4

'

-ds

'

-

0.6

v o l t vs. Ag/AgCI AE-

I OmV

Figure 19. Charging current at low frequency Medium

=

mV.

=

0.5M NaCIO,. A E = 10 20 Hz. ( a ) No damping, scan rate = 20 mV/sec. (b) Damping (time constant of 3 sec), scan rate = 2 w

mV/sec larographic experiment, decreases the time scale, and eventually a frequency will be reached which does not allow the electrode process to even approach closely to diffusion controlled conditions. Thus at high frequencies, considerable departure from the w112 dependence of I p occurs, coincident with increasing departure from reversibility. In fact, for any ac electrode process, it has been the author's experience that if a sufficiently high frequency is used, even the fastest electrode processes will show some departure from reversibility, based on the criterion of departure from a linear I p us. w 1 I 2 plot or on any of the other criteria discussed in section A. It is worth noting at this stage that measurement of the half-width or the more rigorous treatment of a study of the shape of the ac wave, based on a plot of

as suggested in part A, would also have indicated the departure from reversibility at higher frequencies. Table V shows a summary of some data obtained for copper at variable frequency. At 1000 Hz the half-width of 71 mV is considerably greater than the 90/n mV expected for a reversible two-electron reduction process. As the frequency is decreased, the half-width can be seen to decrease also, until at frequencies between 10 and 100 Hz, the half-width approaches closely to the reversible value. It is interesting also to note that only a very small dependence of [Edolpeak on frequency is found in Table V, and that this value is almost the same as Elil, again illustrating that comparison of and [Edolpesk does not provide a very sensitive or satisfactory criterion for ac reversibility. (c) Relatiue Dependence o j Faradaic and Charging Currents on Frequency. From the above, it has been established that the charging current increases directly with w , and the faradaic current increases at a rate 6 w112. That is, the charging or background current increases faster with increasing frequency than does the faradaic current. Thus, although high frequency ac polarography would be expected to increase the sensitivity, by giving higher faradaic currents per unit concentration, the unfavorable ratio of frequency dependence of the charging and faradaic current outweighs this advantage and high frequency ac polarography, in itself, does not achieve improved sensitivity. It is because of this phenomenon that conventional ac polarography as considered in Section A is usually carried out at low frequency ranges, of about 50 to 100 Hz, rather than at high frequencies.

-0 4

-0 5

-

0.6

v o l t vs. Ag/AgCl Figure 20. Variation of charging current with applied ac voltage w =

200Hz. Medium

= 5MHCl

The use of extremely low frequencies, although theoretically having the most favorable ratio of faradaic to charging current, is not favored in analytical applications of ac polarography because of the relatively high noise level encountered. Figure 19 shows the charging current at 20 Hz. At this very low frequency, oscillations from the low frequency sinusoidal ac voltage, itself, can be seen with a fast response recorder as in Figure 19a. Figure 19b shows that even with a time constant of 3 sec on the recorder, considerable noise is present. The use of low frequency ac polarography, in say the 50 to 100 Hz range, as well as being advantageous on the grounds of having a more favorable faradaic to charging current ratio to high frequency ac polarography, also has the added advantage that ac electrode processes exhibiting quasi-reversible behavior, e.g. Cu(I1) in 1 M N a N 0 3 ,will be measured at closer to diffusion controlled or reversible conditions. In analytical applications of ac polarography, this feature is desirable, as discussed in section A. 111. DEPENDENCEOF THE CHARGINGAND FARADAIC CURRENTS ON THE AMPLITUDE OF THE APPLIED AC VOLTAGE. (i) Charging Current. Figure 20 shows the ac charging curreht in 5M HC1 at variable applied ac voltages, AE, over the range of 0.1 to 10 mV. An approximately linear relationship is evident. A considerable decrease in noise with increasing values of AEis also evident. (ii) Faradaic Current. Figure 21 shows the variation of faradaic current with AE for the reduction of cadmium(I1) in 5M HC1. In accordance with Equation 1, for a reversible ac electrode process, a linear relationship is evident. Figure 22 shows plots of I p us. AE for the quasi-reversible ac copper(I1) electrode process in 1M N a N 0 3 at variable frequency. Again, a linear relationship is evident. Table VI gives values of [Ede]pesk and the half-width for the copper(I1) electrode process, at variable values of A E and a. The half-width can be seen to be independent of AE for this quasi-reversible ac electrode process. This independence


327

Table VI. Variation of [&]peak and Half-Width with Applied AC Voltage, for the Copper(I1)-Copper(0) Quasi-Reversible AC Electrode Process in 1 M NaNOp Frequency (Hz) 500 lo00 100 [Edolpeak [Edolpeak [Edolpeak AE, mV V us. AglAgCl Half-width, mV V us. Ag/AgCI Half-width, mV V us. AgIAgCl Half-width, mV 0.5 0.081 54 0.081 63 0.086 71 1.o 0.081 53 0.080 63 0.084 71 5.0 0.078 53 0.082 63 0.085 71 10.0 0.076 53 0.080 63 0.083 71 a Values from Reference 27, [CUI = 1.00 X M.

V o l t vs. Ag/AgCI Figure 21. Variation of faradaic current with A E for the reversible ac electrode process Cd(I1) $ Cd(0) in 5 M HCI w =

100Ilz. Phase-sensitive readout. (a)AE

=

10 my. (b) AE = 5 mV. (c) AE

=

1 mV. [Cd]

=

1 X

10-3 M

601 40

1

7+

1

Q:

t cz H

0

2

4

6

8

10

A E mV Figure 22. Variation of I, with A E for the quasi-reversible Cu(I1) e Cu(0) ac electrode process in 1MNaN03 (a) w =

10 Hz. (6) w

=

100 Hz. (c) w = 500 Hz. [CUI = 1 X

10-3~

is also, of course, found for reversible ac electrode processes. From this it can be seen that changes in AE, provided A E is not too large, e.g., 3 about 10 mV, essentially have no other influence on the ac electrode process other than to increase the faradaic current in a linear fashion. (iii) Relatioe Dependence of Charging and Faradaic Currents on AE. From the above, it follows that the charging and faradaic currents show approximately the same dependence on AE. Hence, in principle, there should be no particular 328

analytical advantage in choosing any value of AE, However, the use of lower AE-values results in lower faradaic currents per unit concentration, and a consequent increase in instrument noise in detecting the same concentration. Therefore, the higher AE values are to be preferred in analytical applications of ac polarography, with all classes of fast electrode processes. The reason for the use of A E values of around 10 to 50 mV, in conventional ac polarographic instrumentation, as used in section A, can now be understood. IV. DEPENDENCE OF CHARGING AND FARADAIC CURRENTS ON PHASE ANGLE. In parts I to I11 of section B, the charging and faradaic currents have both been considered as a function of A E and w , and it has been shown why low frequency ac polarography at AE-values of around 10 mV are advantageous. This work, although important as background material and for other reasons, is applicable to all polarographic instrumentation and has not yet specifically introduced the real use and purpose of phase-sensitive, three-electrode ac polarography. The advantages of this form of polarographic instrumentation will now become evident when considering the various phase-angle relationships of the faradaic and charging currents to the applied ac voltage. ( i ) Theoretical Aspects of Phase-Sensitioe Detection.

In

any ac network, alternating currents possess a particular phase relationship to the input voltage, and the magnitude of the currents at different angles to this, are related by vector algebra. Hence, if the charging and faradaic currents possess a different phase angle relationship to each other, and circuitry is developed which enables measurement of ac current to be


(a)

V

I

I

'

* It IC-0

Figure 25. Comparison of measured charging current with phase sensitive and non phase-sensitive readout

I Figure 23. Phase relationships of charging and faradaic currents, relative to the applied ac voltage iF =

faradaic current ic = charging current

-0 5

-0 4

- 0.6

v o l t vs. Ag/AgCI Figure 24. Measurement of charging current as a function of the phase angle, relative to the applied ac voltage Medium

=

5 M HCI.

w = 200

Hz

made at selected phase-angles, relative to the input ac voltage, it follows that it should be possible to descriminate against the charging current, and at a particular phase-angle to measure pure faradaic currents only. (a). Phase-Angles of' Charging and Faradaic Currents. In ac polarography, the capacitive or charging current component is 90" out of phase with the input ac voltage, provided there are no effects due to the ohmic IR drop. The faradaic current, by comparison, exhibits a phase-angle relationship which depends upon the nature of the electrode process ( I ) . In particular, for a reversible ac electrode process, the faradaic current is 45" out of phase with the applied ac voltage. For quasi-reversible ac electrode processes, the phase-angle will be close to 45",with low frequency ac polarography, where the system approaches closest to diffusion controlled reversible ac conditions, but significant departures from this occur at high frequencies to give phase-angles less than 45". These phaseangle relationships for the faradaic current again assume that no ohmic IR drop effects are present. Figure 23 shows the

Medium = 0.5M NaCI04. A E = 10 mV. o = 100 Hz. (a) Non phase-sensitive (b) Phase-sensitive

phase relationships of the charging and faradaic currents graphically. From the above discussion, it follows that measurement of phase-angle provides an additional criterion for assigning the reversibility of an ac electrode process. However, the measurement of phase-angle, is usually too time consuming and a tedious process for the analytical chemist to undertake, with most existing commercial instrumentation, and the use of other criteria, as outlined previously, is recommended, on the basis of being experimentally simpler. (b). Discrimination against the Charging Current. From the previous discussion of phase-angles, it follows that if ac measurements can be made at 0" or 180°, relative to the applied ac voltage, then the charging current component will be zero and the measured signal will consist solely of .t.4?/2 of the faradaic current, for a reversible electrode process. Discrimination against the charging current is therefore achieved, using a phase-sensitive detector, which is capable of detecting only that component of the alternating current which is of a specific phase. The theoretical advantage of using phase-sensitive ac polarography, in preference to the conventional ac polarography, can therefore be appreciated. (ii) Experimental Aspects of Phase-Sensitive Detection. The discussion above concerns the completely idealized, or theoretical situation for phase-sensitive ac polarography, and assumes that no ohmic effects are present. In the remainder of this section, the more realistic, experimentally encountered situation will be examined. (a). The Charging Current. Figure 24 shows a series of measurements made of the charging current in 5M HC1, at particular phase-angles relative to the applied ac voltage at 200 Hz. The obvious dependence of the charging current on phase-angle can be seen. Figure 25 shows a comparison of the charging current found with phase-sensitive readout, compared with non phase-sensitive detection. The considerable discrimination against the charging current is obvious. However, it can also be noted in these figures that the theoretical or ideal situation where the charging current should be zero, with a phase-angle measurement, 4, of 0" is not obtained. This phenomenon basically arises from resistance effects as will be discussed later.


329

0

Ln c

m

0

0 b

N

0

0 N

N

0

0 W c

0

0 0 7

0

0

0

330

i

(b). The Faradaic Current. Figure 26 shows the measurement of the cadmium(I1) electrode process in 5M HCl at various values of 4, between 0' and 360'. The expected behavior of I , with $I is approximately observed. However, it can be seen in Figure 26, that when 4 is 135' or 315', the faradaic current is not zero, as would be expected from vector algebra for a reversible electrode process, 45' out of phase with the applied voltage. This apparent anomaly is again mainly a result of non-ideal behavior being incurred because of the influence of resistance. (c). The Influence of Resistance (IR Drop) Effects on Phase Relationships. The theoretical argument, that the charging and faradaic currents should be 90' and 45', respectively, out of phase with the applied ac voltage, was made assuming resistance effects (IR drop) are absent. In fact, resistance effects alter the phase relationships of both the charging and faradaic currents greatly. In part A it was also shown that the attainment of other theoretical-experimental correlations is also hindered by resistance effects, and resistance can be seen to be an extremely important area in ac polarography. It can be seen therefore, that if phase-sensitive ac polarography is to be used with maximum advantage and in a scientific or logical, rather than empirical manner, then IR drop effects need to be kept to a minimum, or even more preferably, eliminated. (d). Three-Electrode ac Polarography. In conventional two-electrode ac polarography, or two-electrode dc polarography for that matter, the current flows between the dropping mercury electrode, DME, and reference electrode, and if the IR drop is significant, distortion of polarographic waves occurs. In two-electrode dc polarography, the IR drop (for reduction processes) is observed as a negative shift in E I i z and a distorted wave shape. In two electrode ac polarography, the IR drop can give rise to a considerable number of phenomena. Amongst the more important ones are, a negaa decrease in I,, a distortion of wave shape tive shift in [Edelpesk, exhibited as broadening, and a change in phase-relationships. Most of these phenomena, except the last have been mentioned already in section A. To overcome the major sources of the ohmic loss, application of operational-amplifier circuitry, with a three-electrode configuration has been introduced. Detailed consideration of the three-electrode polarograph will not be given here, and the reader is referred to the literature (see references I , 28-40 for instance). The important point to note, however, is that although three-electrode ac instrumentation achieves a major degree of success in eliminating resistance effects, in so far as the effect of ohmic resistance is not reduced to zero, theoretical phase relationships are not exactly obtainable with most three-electrode instrumentation. Excellent discussions of the subject of uncompensated ohmic resistance have been given in several papers (28-30). Hence, although ac polarograms in Figures 25 and 26 were recorded with a three-electrode polarograph, nonideality can still be observed, due to uncompensated resistances, especially that from the DME ( I ) . With regard to the faradaic current, Figure 26 is deliberately presented with a high concentration of depolarizer, giving rise to large currents, and therefore pronounced IR drop effects. Figure 27, shows a comparison of a two-electrode and a three-electrode ac polarogram, again recorded with a high depolarizer concentration to emphasize resistance influences. Both these ac polarograms were recorded with 4 equal to O", and the considerable charging current present with the twoelectrode instrumentation, illustrates that the presence of resistance severely influences ac measurements. Furthermore,


(b)

I 1

Figure 28. Comparison of charging current as measured with and without additional curcuitry to eliminate most 1 0 p A ~ of the uncompensated resistance

-0 6

-0 7

v o l t vs. Ag/AgCI

-0 8

-0.6

-0.7

AE = 10 mV. w = 1000 Hz. Medium = 0.5 M NaCIOa. (a) With additional circuitry. (b) Without additional circuitry

-0.8

v o l t vs. Ag,/AgCI

Figure 27. Comparison of polarograms of 1 X 10eaMcadmium in 5 M HCI as recorded with a two-electrode and a threeelectrode AC polarograph AE

=

10 mV.

w =

(b>

200 Hz. (a) Three-electrode. (6) Two-electrode I

the desirability of using considerably lower depolarizer concentrations than lO+M, in conventional two-electrode ac polarography, if any theoretical-experimental correlations are to be undertaken, as stated in section A, can be understood by examination of Figure 27. Figures 25 and 26 were recorded with "normal" threeelectrode instrumentation, containing operational-amplifier circuitry and, to a good approximation, the only uncompensated resistance is the ohmic drop between the tip of the reference electrode and the summing point of the current measuring amplifier. That is, the uncompensated resistance basically encompasses the ohmic losses in the solution between the reference electrode, plus the resistance of the DME. Employment of a Luggin probe and/or a specially constructed low resistance DME (41) could be undertaken to decrease the resistance even further (28), although it is doubtful if an analytical chemist would find it worthwhile to undertake such procedures. Alternatively, or in addition, one can employ further 1R compensation circuitry. Such circuitry, which is available on the instrument used in this work (42), consists of a positive feedback network, which derives a signal from the measured current flow and feeds it back to the summing point of the current-measuring amplifier. This provides a means of overcompensating the three-electrode potentiostat. Too much positive feedback will result in instability (observed as oscillation of the summing amplifier), but the application of an amount of feedback, just under that required for instability, will compensate for the IR drop across the uncompensated resistance. Figure 28 shows a comparison of the charging current measured at 0", relative to the applied ac voltage, and at a frequency of 1000 Hz, both with and without the additional circuitry. The considerable decrease in charging current, as the IR drop is increasingly eliminated can be noted and theoretical expectations are approached. Figure 29 shows that, with this feed-back circuit, the expected zero value of the faradaic current at a phase-angle of 135" is now virtually obtained, even with concentrated solutions of depolarizer. Again, although such an operation leads to closer attainment of ideal operating conditions, where it should be possible to measure virtually purely faradaic currents at 0' relative to the applied ac voltage, it is doubtful whether the

+60

-0.65

-0.70

- 0 . 7 5 -0.60

-0.65

-0.70

-0.75

v o l t vs. Ag/AgCI Figure 29. Comparison of faradaic current for the Cd(1I) e Cd(0) electrode process as measured at a phase-angle of 135" with and without additional circuitry to eliminate most of the uncompensated resistance A E = 10mV. w = 1OOOHz. [Cd] = 1 X 10-3M. Medium = 5 M HCl. (a) Without additional circuitry. (b) With additional circuitry

analytical chemist, involved in routine work, would wish to proceed beyond the stage of using a standard phase-sensitive, three-electrode polarograph unless an extremely high resistance solvent is being used and/or high frequency ac polarography is necessary. Discussion can therefore return, at this stage, to a consideration of the standard form of instrumentation. (e). Optimum Conditions for Use of Phase-Sensitive, Three-Electrode AC Polarography. Since it has been established that considerable, but not complete, discrimination against background or charging current is possible, and readily achieved with phase-sensitive ac polarography, provided three-electrode instrumentation is used, it becomes evident from previous discussion that this instrumentation should provide a considerable improvement in performance over the type of instrumentation considered in section A. It is emphasized strongly that arguments on the optimum frequency and applied ac voltages given previously, still apply, because the charging current is not completely discriminated against. Hence, because the charging current increases at a greater rate with frequency than does the faradaic current, the use of low frequency ac polarography is still favored to the high frequencies with phase-sensitive instrumentation. The fact that ac electrode processes approach more closely to diffusion controlled conditions at low frequency, of course, still applies. Furthermore, the use of the higher AE-values, e.g. 10 mV, which give rise to higher faradaic currents per unit concentration, and less likelihood of noise problems than

ANALYTICAL CHEMISTRY, VOL. 44, NO. 2, F E B R U A R Y 1972

331

Figure 30. Comparison of phase-sensitiveand non phase-sensitive ac polarograms for the Cd(I1) e Cd(0) electrode process in 5M HCl [Cd] = 1 X 10-3M. A E = 10 mV. w = 100 Hz. Phase-sensitive. (b) Non phase-sensitive

(a)

-0.6

-0 7

-0 8

v o l t vs. Ag/AgCI

-0 6

volt

-0 8

-0 7

VS. Ag/AgCI

Table VII. Analytical Use of Copper(I1)-Copper(0) QuasiReversible ac Electrode Process with Phase-Sensitive, Three-Electrode Instrumentation Frequency, Hz [CUI, AE, mV 10 100 loo0 6

x 10-4

4

x 10-4

1 x 10-4 6 4

x 10-6 x

0.1

10 1.0 0.1 10 1.0

0.1

10-6

1 x 10-6 6 X

4

10 1.o 0.1 10 1.0

x 10-6

1 x 10-6

10

1.0 0.1 10

1.0 0.1 10 1 .o 0.1

10

1 .o

0.1 10 1.o 0.1

QD D ND QD D ND QD D ND QD ND ND QD ND ND D ND ND D ND ND ND ND ND ND ND ND

QD QD QD QD QD QD QD QD D QD QD D QD QD ND

QD QD ND QD D ND QD D ND D

ND ND

QD QD QD QD QD QD QD QD QD QD QD

QD QD D QD QD ND QD D ND D D ND ND ND ND

a Data taken from Reference 27. QD = quantitatively detectable with better than 2z reproducibility. D = detectable, but with less than 2z reproducibility. ND = not detectable.

low AE-values, e.g. 0.1 to 1 mV, are still recommended with phase-sensitive instrumentation. Table VI1 gives a summary, of a survey of the analytical determination of copper in 1M N a N 0 3 by phase-sensitive ac polarography a t various values of o and AE, all measurements being made a t a phase-angle of OD, relative to the ac voltage. This table illustrates clearly that optimum conditions are realized with w around 100 Hz, and A E of about 10 mV. (f). Comparison with Non Phase-Sensitive Instrumentation. The advantages of phase-sensitive, three-electrode methodology to instrumentation considered in section A can be listed as follows. 332

-0.5

D

- 0.6 -0.5 v o l t vs. Ag,/AgCI

0.6

-0.7

Figure 31. Comparison of phase-sensitive and non phase-sensitive ac polarograms for a 5 x 10-jM solution of cadmium in OSMNaCIO, (a) Phase-sensitive. (b) Non phase-sensitive. AE = 10 mV. w = 100 Hz

At high concentrations of depolarizer, ohmic IR effects give rise to considerable distortion with conventional instrumentation. Three-electrode instrumentation minimizes resistance effects. As a corollary to this, it follows that ac polarography in high resistance nonaqueous solvents, while not being possible with conventional instrumentation, is readily achieved with the three-electrode arrangement. This latter feature is obviously a considerable advantage which could be greatly exploited in future uses of ac polarography. The limit of detection is improved by the introduction of the phase-sensitive readout. Figure 30 shows a comparison of phase-sensitive and non phase-sensitive, but IR compensated, polarograms, of cadmium, at the 10-3M level. Obviously, both polarograms are well defined, and quantitatively usable a t this level, even though the presence of a significant charging current is apparent with the non phase-sensitive polarogram. Figure 31 shows phase-sensitive and non phase-sensitive polarograms at the 5 X lO-5M level. The contribution of the charging current is now quite significant and the phasesensitive polarogram is obviously considerably superior for use in analytical applications. Figure 32 shows comparative polarograms for copper at the 6 X 10-6M level in 1M NaN03. At this low concentration level, noise associated with measurement of low currents


(a Figure 32. Comparison of phase-sensitive and s for a 6 X 10-+M I

0.2

Y

0.1

0.Q

.

0.2

0.1

0.0

(a) Phase-sensitive.

mV. w

=

100 Hz

(b) Non phase-sensitive. A E = 10

v o l t vs. Ag/AgCI

Figure 33. Phase-sensitive ac polarogram of a 4 X 10-6M solution of cadmium in 0.5M NaC104 A E = 10 mV.

w =

100 Hz

I

-0 45

-0 55

-0.65

v o l t vs. Ag/AgCI

Figure 34. Noise associated with detection of low concentrations Solution is 8 X 10-7M cadmium in O.SMNaCIOa. Damping applied (time constant = 5 sec.). A E = 10 mV. w = 100 Hz

- 045 v o l t vs. Ag,/AgCl -0.55

’

-0’65

can become a problem, and a time constant (damping) of 1 sec has been applied to the recorder. It can be seen that at this concentration, unless phase-sensitive ac polarography is used, the charging current virtually masks the faradaic current. It can also be noted from Figure 32, that it is not the absolute limit of detection which is altered substantially by using the phase sensitive readout, but rather it is the precision and accuracy with which measurements can be made at low concentrations that is enhanced. It has been the author’s experience that the absolute limit of detection is improved by about 5 to 10 times that given with conventional instrumentation in section A. Figure 33 shows an ac polarogram of a 4 X 10-6A4cadmium solution. The wave is still extremely well defined at this concentration level. With phase-sensitive detection, this highly reversible electrode process enables cadmium to be determined down to the 5 X lo-’ to lO-7M level, although the reproducibility falls off markedly near the detection limit where noise becomes important in measuring low currents, as in Figure 34.

FUTURE DEVELOPMENTS, OTHER CONSIDERATIONS AND CONCLUSIONS Future developments in ac polarography, in the analytical context, could well and, in the author’s opinion, most profitably proceed along the lines of using and applying existing instrumentation to the laboratory situation, particularly toward routine analysis. There is still a considerable storehouse of ac polarographic methodology available in the literature, with numerous apparent advantages over existing commercial and commonly used instrumentation. The practical advantages, limitations, and real performance of instrumentation can only be assessed in the analytical laboratory when given over to the general use of the analytical chemist, and this has yet to be done in many instances. It is not feasible in this review to discuss the almost limitless variations of ac methodology, and to see which ones might best find their way into routine use in analytical laboratories. However, this author would like to suggest that the short drop time technique of “rapid ac polarography” discussed in part in section A, could profitably receive more attention in the f u ture, than presently accorded. In a recent paper, Zatka (43) states “the dropping mercury electrode with artificial drop time control, described by Wolf, has been recommended for use in alternating current polarography by the producer of the ac polarographic adaptor, but the first papers describing its use did not appear before 1969.” It can be seen that a technique made available in a commercial instrument as early as 1960 (Metrohm, Switzerland) was not applied to the laboratory situation till 1969. This serves as a not too uncommon instance, where it has obviously taken considerable time for a new ac polarographic method, which has been shown to be markedly superior to conventional ac polarography (44), to be used even in an applied sense, much less accepted and established as a reliable routine method, as a recent paper by the author shows it could be (45). In fact, even at this stage of time, the rapid ac polarographic method has almost exclusively been confined to non phase-sensitive instrumentation (45). Figure 35 shows a comparison of a phase-sensitive and a non phase-sensitive rapid ac polarogram. As indicated in Reference 45,exactly the same philosophy can be applied to controlled drop time, rapid ac polarography as to conventional ac polarography. Thus the rapid ac polarographic method should be usable with phase-sensitive readout, as in Figure 35, to make the technique even more valuable. Another aspect of controlled drop time ac polarography which could become attractive, is current-sampled or Tast ac polarography. Figure 36 shows a comparison of a controlled drop time ac polarogram, with and without current sampling. If the drop time is shortened from the 5 sec of Figure 36 to the 0.5 to 0.1 sec region as in Figure 37, essentially a rapid phasesensitive, current sampled ac polarographic method is arrived at, in which readily readable smooth curves are obtained.


333

T Figure 35. Comparison of rapid ac phase-sensitive and non phase-sensitive polarography Solution is 10-3M cadmium in 5 M HCI. AE = 10 mV. w = 100 Hz. (a) Non phase-sensitive. (b)Phase-sensitive

,

I

-0.7

-0 6

-0 6

-0 8

volt

-0 8

-0 7

VS.

Ag/AgCI

,

i

-0 7

-0 6

-0 8

v o l t vs. A ~ J A Q C I

There are obviously many other important areas of the subject not discussed a t all, such as second harmonic ac polarography ( I , 5 ) and Tensammetry (46), not to specifically mention the many other areas of application necessarily neglected by concentrating on analytical aspects of fast Faradaic Electrode processes, as was done in the main in this work. The author, hopes by way of this review, to convey a philosophy of applying a systematic approach to the subject. This philosophy, that of applying a completely systematic and logical approach to the subject based on carefully considering theoretical and experimental correlations, applies to all aspects and can lead to the two conclusions presented in the following and final two paragraphs of this review.

Figure 36. Comparison of controlled drop time ac polarography and current-sampled or Tast ac polarography (a) Tast ac polarography with controlled drop time of 5 sec. ( b ) Controlled drop time ac polarography, drop time = 5 sec. A E 10 mV. w = 100 Hz. Solution is 10VM cadmium in 5M HCI

This form of readout could be quite attractive in analytical applications of ac polarography, because of the extremely fast scan rates of potential permitted by the short controlled drop time, giving rise to considerable time saving (45),now coupled with a particularly convenient form of phase-sensitive readout. Finally, it is obvious that this is by no means a comprehensive review of ac polarography, nor was it intended to be.

t

CONCLUSIONS

With a systematic approach, as described in this paper, it is possible to utilize all the advantages of ac polarography over dc polarography (5, 6) to their fullest. For instance, having established the reversibility of an ac electrode process, the improved sensitivity, limit of detection, and resolution and other aspects make the ac method of analysis considerably superior to that of conventional dc polarography, and it would certainly be the preferred technique. In electroanalytical application, ac polarography can often readily reveal subtleties of electrode processes not easily seen with dc polarography. In all cases the technique can be expected to be complementary to dc polarography, and even if it does

i

-0.6 -0.7 -0.8

v o l t vs. Ag/AgCI Figure 37. Use of short, controlled drop time, Tast ac polarography to obtain smooth ac polarograms (a) Drop

time

=

2 sec. (b) Drop time

=

5 sec. (c) Drop time

A € = 10 mV. w = 100 Hz. Solution is 10-3M cadmium in

334

-0 8

v o l t vs. Ag/AgCI

v o l t vs. Ag/AgCI

-0 6

-0 7


=

0.5 sec

5M HCI

not provide new information, it can be used to confirm conclusions drawn from dc work. In the author’s opinion, the key to using the ac method hinges on a systematic approach similar to that used in dc polarography. In fact, if this is done and the theory continues to advance as it is presently, then it seems reasonable to speculate that a point in time will be reached in the not too distant future, where one could carry out the ac polarography of systems and assign all electrode characteristics without any resort to dc polarography. ACKNOWLEDGMENT The author acknowledges the assistance of D. E. Smith in kindly agreeing to read this manuscript prior to submission for publication and for providing helpful comments. (1) D. E. Smith in “Electroanalytical Chemistry,” A. J. Bard, Ed., Marcel Dekker, New York, N.Y., Vol. 1, Chap. 1, 1966. (2) B. Timmer, M. Sluyters-Rehbach, and J. H. Sluyters, J. Electroanal. Chem., 14, 169 (1967). (3) Ibid., p 181. (4) D. E. Smith and T. G. McCord, ANAL.CHEM., 40,474 (1968). ( 5 ) B. Breyer and H. H. Bauer, “Alternating Current Polarography and Tensammetry,” P. J. Elving and I. M. Kolthoff, Ed., Interscience, New York/London, 1963. (6) H. Schmidt and M. Von Stackelberg, “Modern Polarographic Methods,” Academic Press, New York, N.Y., 1963. (7) S. L. Gupta and M. K. Chatterjee, J. Electroanal. Chem., 14, 198 (1964). (8) S. L. Gupta and M. K. Chatterjee, Reu. Polarog., 14,198 (1967). (9) A. M. Bond, J . Electroanal. Chem., 20, 223 (1969); 23, 277 (1969). (10) A. M. Bond, J. Phys. Chem., 74,331 (1970). (11) A. M. Bond, J . Electrochem. Soc., 117,1145 (1970). (12) P. J. Delahay, J. Amer. Chem. SOC.,75, 1430 (1953). (13) H. H. Bauer and P. J. Elving, Electrochim. Acta, 2, 240 (1960). (14) A. M. Bond and A. B. Waugh, ibid., 15, 1471 (1970). (15) J. E. B. Randles and K. W. Somerton, Trans. Faraday Soc., 48, 951 (1952). (16) A. A. Moussa and H. M. Sammour, J. Chem. Soc., 1960, 2151. (17) A. M. Bond and R. J. Taylor, J. Electroanal. Chem., 28, 209 (1970). (18) A. M. Bond, ibid., 20, 109(1969).

(19) Ibid., 28, 433 (1970). (20) A. L. Woodson and D. E. Smith, ANAL.CHEM., 42,242 (1970). (21) A. M. Bond and T. A. O’Donnell, ibid., 41,1801 (1969). (22) A. M. Bond, J. Phys. Chem., 75, 2640(1971). (23) A. M. Bond and J. H. Canterford, ANAL.CHEM.,43, 228 (1971). (24) B. J. Huebert and D. E. Smith, J. Electroanal. Chem., 31, 333 (1971). (25) B. Breyer, F. Gutman, and S. Hacobian, Aust. J. Sei. Res., Ser. A , 4 595 (1952). (26) P. Delahav and T. J. Adams, J . Amer. Chem. Soc.. 74. 5740 ‘ (1952): (27) A. M. Bond and D. R. Canterford, unpublished work, University of Melbourne, Australia, 1971. (28) G. L. Booman and W. B. Holbrook, ANAL.CHEM.,35, 1793 (1963). (29) W. B. Schaap and P. S. McKinney, ibid., 36, 29 (1964). (30) D. E. Smith, ibid., 35, 1811 (1963). (31) D. E. Walker, R. N. Adams, and J. R. Alden, ibid., 33, 308 (1961). (32) W. L. Underkoffler and I. Shain, ibid., 35, 1778 (1963); 37, 218 (1965). (33) G. L. Booman, ibid., 29, 213 (1957). (34) M. T. Kelley, D. J. Fisher, and H. C. Jones, ibid., 31, 1475 (1959); 32, 1262 (1960). (35) E. R. Brown, D. E. Smith, and G. L. Booman, ibid., 40, 1411 (1968) and references cited therein. (36) E. R. Brown, H. L. Hung, T. G. McCord, and D. E. Smith, ibid., p 1424. (37) R. Bezman and P. S. McKinney, ibid., 41, 1560 (1969) and references cited therein. (38) F. M. Hawkridge and H. H. Bauer, ibid., 43, 768 (1971). (39) W. E. Thomas, Jr., and W. B. Schaap, ibid., 41, 136 (1969). (40) H. C. Jones, W. L. Belew, R. M. Stelzner, T. R. Mueller, and D. J. Fisher, ibid., p 772. (41) G. Jessop, British Pat, 640,768 (1950). (42) Instruction Manual for PAR Electrochemistry System Model 170, Princeton Applied Research Corporation, Princeton, N.J., (1970) p. IV-6. (43) A. Zatka, J. Electroanal. Chem., 27, 164 (1970). (44) Instructions for use of AC-Modulator E393, Metrohm AG, Herisau, Switzerland. (45) A. M. Bond, J. Electrochem. SOC.,118, 1588 (1971). (46) H. Jehring, J. Electroanal. Chem., 21, 77 (1969). RECEIVED for review April 8, 1971. Accepted August 16, 1971.


335

Experimental and theoretical correlations for the use of fundamental

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