Laplace plane analysis of the faradaic and non-faradaic impedance of the mercury electrode

Electroanalytical Chemistry and Interracial Electrochemistry

91

Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

LAPLACE PLANE ANALYSIS OF THE FARADAIC A N D NON-FARADAIC IMPEDANCE OF THE MERCURY ELECTRODE

K. D O B L H O F E R and A. A. PILLA

Electrochemistry Laboratory, ESB Incorporated, 19 West College Ave., Yardley, Pa. 19067 (U.S.A.) (Received 10th January, 1972)

INTRODUCTION

The mercury electrode has been extensively studied 1-10 particularly in the faradaic region (Hg/Hg22÷) by most of the modern relaxation techniques. These studies have still left unsolved the questions of double layer relaxation (in both the faradaic and non-faradaic potential regions) and of the possibility of reactant adsorption in the faradaic process. Of particular interest is a recent study 1° which utilizes results from both a.c. and pulse techniques to provide evidence of Hg 2÷ adsorption to explain previously observed anomalously high double layer capacitances while also generating anomalously low values for the exchange current density. The transient impedance technique 11,12 coupled with Laplace plane analysis 12'13 provides a relatively powerful approach for further elucidation of this system. This is so since frequencies as high as 108 rad s- ~ can be accurately studied utilizing digital Laplace transformation of time domain data obtained with an ultrafast potentiostat coupled with signal averaging techniques. As indicated elsewhere 11,14 this approach allows instrumental artefacts (e.g. finite rise of potentiostat, nonorthogonal analog phase sensitive detection) to be properly accounted for. In addition the use of both real and imaginary axis Laplace transformation provides two sets of relatively simple frequency functions (as compared to time domain functions) for system analysis. EXPERIMENTAL

The heart of the experimental apparatus is the Tacussel PIT 20-2X ultra-fastrise potentiostat which, when employed with a Monsanto 300A variable risetime pulse generator, allowed potential "steps" of clean (99~) risetimes of less than 200 ns to be applied. This provided an accurate first data point at 10-20 ns (i.e. along the risetime) for both the voltage input and current response, enabling the required accuracy for digital Laplace transformation up to 108 rad s-1 to be achieved. The electrolytic cell was specially constructed to provide for minimum inductance when employed with either a dropping or hanging mercury drop electrode. This was done by making the cell as short as possible at the expense of it being somewhat wider than average. In this way the working electrode lead was kept between 5 and 10 cm in length. A wide cell did not introduce error since it was found that inductance is an overwhelmingly greater problem at high frequencies then stray J. Electroanal. Chem., 39 (1972)

I,J

C3

'.,e

TRIG

I

OUTISTART

~IUtTlSEGMEFCT SIGNALGEN.

I~ REF

CLOCK

I STOP

1

NCL

]

•

•

A

R

W

FLT

M I POSED~ VOLTAGE

V(tl

POTE~iJTO I STAT

I SYNC

PULSEGENERATOR

TRIG OUT

V(ll -" TRIGI

GATE

• I(t~

• TRIG

DUALBEAM OSCL ILOSCOPE

Fig. 1. Exptl. set-up for Laplace plane impedance studies in the non-faradaic potential region. Detailed explanations are given in the text.

•

OG

CAPILLARY

ULTRALOW RESS I TANCE

r-, t" >

m

©

©

LAPLACE PLANE ANALYSIS OF IMPEDANCE

93

capacitance. The cell was thermostatted to 25 _+0.1 °C. A mercury pool of approximately 50 cm 2 surface area served as auxiliary electrode. A thermostatted (25 _+0.1 °C) NCE reference electrode made contact to the cell via a NH4NO3 salt bridge. In addition, a platinum wire served as a high speed reference electrode 15, necessary to achieve highest speed and lowest noise in low level transient techniques. All d.c. potentials were monitored with a Tacussel Aries 10,000 digital electrometer and kept constant to + 20 #V. The experimental system used for studies in the non-faradaic potential region is shown in Fig. 1. The dropping mercury electrode, DME, was specially constructed to have a resistance of only 0.7f~. This was done by placing a constriction determining the mercury flow rate above the electrical contact point (see Fig. 1) enabling a relatively thick mercury column to be employed between this point and the fine, tapered thinwall capillary tip ~9. The DME was dewetted with dichlorodimethylsilane vapor and had a natural drop time of 20 s. In order to apply potential pulses at identical times during each drop life, the timing circuit illustrated in Fig. 1 was employed. A square wave generator synchronously activated the drop knocker and started the General Radio 1192 digital counter. At the end of the timing pulse (which could be set to any reasonable width--usually 6 s) a Tektronix 556 dual beam oscilloscope, used to display both current and voltage traces, was triggered. Synchronous with this, the Monsanto 300A pulse generator was triggered to activate the potentiostat and the digital counter was stopped. The delay feature on this generator was used to allow approximately 2 cm base line on the oscilloscope screen before the pulse display started, in order to determine accurately the start of each pulse. For each measurement 10 photographs at various sweep rates and vertical sensitivities of the oscilloscope were taken. The values read from the photographs were plotted and a smooth curve drawn. The data points taken from this smoothed curve were used as input for the digital Laplace transformation. Note that the first time point usually read was 10 ns, comparable to the time range used in time domain reflectometry 16. In order to compare the Laplace plane results thus obtained with those from classical a.c. impedance techniques a Tacussel PRG-3 a.c./d.e. polarograph was employed. This instrument utilizes phase sensitive detection with which both the in phase and 90 ° out of phase components of the impedance are readily obtainable. Capacitance values were obtained at 50 and 3000 Hz. The experimental approach used for studies in the faradaic potential region was somewhat different than that described above. This is so since it was found that at the very positive potentials near which mercury oxidation occurs the double layer capacitance was constant for hours indicating the absence of spurious adsorption. This allowed easy use of sampling and averaging techniques for data r~.cording; A hang~g mercury drop electrode was therefore employed. The electrode was prepared by sealing a piece of thin platinum wire in a fine soft glass tip and electrolyzing it for several hours in a 1 mM Hg22÷ solution in 1M HC104 to amalgamate the surface thus permitting a mercury drop to hang. It was found that a mercury drop which was hung on an improperly amalgamated platinum tip would not allow a stable equilibrium potential for Hg/Hg~ + to be achieved. The sampling and averaging technique used for data recording is schematized in Fig. 2. Since this technique requires a repetitive waveform it is necessary to assure that the repetition rate be low enough for the system to return to equilibrium before J. Electroanal. Chem., 39 (1972)

94

K. DOBLHOFER, A. A. PILLA

Fig. 2. Block diagram of exptl, system used for Laplace plane impedance studies in the faradaic potential region. P is the high-speed potentiostat. The box car detector consists of the scan delay generator, the gate, and the signal averager, SA.

the application of the next pulse. It was found that a repetition time 10 x longer than the pulse length was sufficient to allow this provided the pulse width was such that the system was well into diffusion control. The repetitive trigger source (see Fig. 2) was one time base of the Tektronix 556 oscilloscope which was also employed to verify that the proper pulse repetition rate had been chosen. The data were recorded with a Keithley-Brookdale Boxcar Detector (see Fig. 2) which consisted of a linear gate and a scan delay generator. This system essentially allows a moving gate to look at the signal to be recorded at much lower repetition rates than normal oscilloscope sampling. The gate width could be adjusted from 10 ns to 0.5 s. It scanned across that portion of the signal, and at a rate, determined by the scan delay generator. The linear gate was triggered synchronously with the pulse applied to the system via the potentiostat. Each repetitive trigger advanced the linear gate at a rate determined by the scan time chosen on the scan delay generator. Data were displayed at times usually between 50 and 1000 s on a Honeywell 530XY recorder. Voltage and current readings were made on the same Tektronix P6046 differential probe. For all experiments water was distilled four times, once from alkaline permanganate. Baker Analyzed Reagent 9652 HCIO 4 was used and a Hg 2+ stock solution was prepared by dissolving a weighed amount of HgO (Fisher Certified Reagent M174) in HC10 4 and reducing with mercury. Triply distilled mercury from Bethlehem Apparatus Co. Inc., Mellertown, Pa. was used. Cell and containers were cleaned with a mixture of HNO3 and H2SO 4. The solutions were deaerated with high-purity argon from Matheson Gas Products, East Rutherford, New Jersey. RESULTS AND DISCUSSION

All time domain results in both the faradaic and non-faradaic potential regions were transformed into the frequency domain via digital computer programs published elsewhere ~2. In order to obtain maximum numerical accuracy the initial time points were cross-correlated from t = 0 to approximately 50 ns for the prevailing value of non-faradaic series resistance. In this way all phase errors up to the highest meaningful frequency (10 a rad s-1) were kept to a minimum. In addition, long time current data were extrapolated to i ~ 0 either via an exponential in the non-faradaic region or vs. 1/x/t in the faradaic region. In the latter, J. Electroanal. Chem., 39 (1972)

LAPLACE PLANE ANALYSIS OF IMPEDANCE

95

the longest time for which data were recorded was usually 100 ms and an extrapolation was performed to at least 50 s. This is to satisfy digital Laplace transformation which requires that the time function become zero or a constant at some time.

A. Ideally polarized potential region In the ideally polarized potential region, capacitance values were obtained at frequencies up to 108 rad s-1. over the potential range - 1.10 to + 0 . 3 0 V vs. N C E at 25 ° C. At each potential Laplace plane impedance results were analyzed according to it,t3 :

Z(s) = R e + 1/CdS

(1)

where Re is the series non-faradaic resistance and C d is the differential double layer capacitance. Both real, s = a and imaginary, s=jco, axis impedance values were examined. A typical plot for the real axis impedance is shown in Fig. 3 for the highest meaningful frequencies. Clearly the plot is linear up to nearly a = 10 s rad s - 1. In every case both real and imaginary axis results were identical to _+ 1%. Further, the capacitance value obtained at 50 and 3000 H z with the phase sensitive a.c./d.c, p o l a r o g r a p h were equally identical to the Laplace plane values. A c o m p a r i s o n of the double layer capacitance values obtained with b o t h Laplace plane and classical a.c. techniques is shown in Fig. 4. It can be seen that the results are essentially identical and that there a p p e a r s to be no ffeouency dispersion of the capacitance values over the frequency range 10-10 s tad s - 1. In addition the Ca values agree with those obtained by n u m e r o u s other authors 5'17'1s'5°. Z(a)/~

,~

34

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,

~

,

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,

'

0.4 -0.6 E / V vs. NCE

-018

'

-LO

Fig. 3. Typical high frequency impedance plot as obtained for pure double layer behavior in the ideally polarized potential region (-0.2 V, drop area = 0.0241 cmZ). Fig. 4. Differential capacitance as determined with a phase-sensitive a.c. polarograph at 50 Hz ( ) and the high frequency values obtained from Laplace plane analysis (O). ( - - - ) represents faradaic potential region (Eeq=0.356 V for 0.1 mM Hg] + ; 0.395 V for 2 mM Hg~+). Despite the a p p a r e n t reasonableness of the above results it is a p p r o p r i a t e to consider three m a j o r causes of frequency dispersion p r o p o s e d for the frequency range accessible to these experiments. These are g e o m e t r y effects 19 -22,34, dielectric relaxation 23 and diffuse double layer relaxation 24-33. Both g e o m e t r y effects and diffuse double layer relaxation can be described by essentially the same type of model. This

J. Electroanal. Chem., 39 (1972)

96

K. DOBLHOFER, A. A. P1LLA

will lead to a distributed parameter approach wherein the spatial dependence of impedance elements must be taken into account. For a simplified model in which these elements are uniformly distributed and in series with Cd and R~ the following is obtained 34 for the real axis dispersion impedance, Zd:

Zd(a)

=

Re +

1/a coth (R 1C1 a)'- + C~ (R 1C1 aj'(C1/Rla)'-+ C a coth (R 1 C t a)'-

(2)

where R 1 and C1 represent the total distributed resistance and capacitance associated with the particular effect prevalent. For example they may represent solution creepage in the capillary or the diffuse double layer at the point of zero charge. Equation (2) has two limits which may be useful and relevant to this study. Thus at high enough frequencies (2) becomes: Z d (o) = Re + (R1/C1 a)'-

(3)

which indicates that 1/a ½behavior would be expected in the high frequency range contary to normal behavior which would have the frequency dependence given in eqn. (1). This limit is not relevant for this study since the expected frequency behavior is not observed (see Fig. 3). The second useful limit for (2) can be written for lower frequencies or when the distributed time constant (R 1C1) is low enough, which might occur when, for example, the thickness of the diffuse double layer is small, as expected in this study 35 for high supporting electrolyte concentration. Thus: R 1C d 1 Zd(a ) = R~ + - + Cd-JvC1 (Cd -[- C1) (7

(4)

This equation shows that, even though no apparent frequency dispersion may be observed, the results for R e and C d could be somewhat erroneous. Note that the frequency range in which 1/a behavior is observed can be relatively low to satisfy (4), but still be high enough for the system to exhibit normal behavior as shown in Fig. 3. Thus it can be seen that the absence of frequency dispersion does not necessarily mean that correct results are obtained for R~ and C d since, in the presence or absence of a faradaic reaction, the system will exhibit erroneous values for these quantities over the whole frequency range. In this study geometric effects have been adequately rendered negligible by preventing solution creepage with proper capillary dewetting and by minimizing shielding with fine, tapered thin-walled capillary tips. The effect of shielding was easily observed in this study because of the high frequency range employed. Blunt capillaries gave completely meaningless results even in the high supporting electrolyte concentration employed. An estimate of the maximum contribution to the total observed impedance from diffuse layer relaxation can be obtained by using the following25'26 : 2R T (At) 2 R~ ~- (nF)2 c i (2DoJ)'(5) and C~ ~-

RT(At):

(6)

where ci is the concentration of the ionic species (here predominantly C104 and H +), J. Electroanal. Chem., 39 (1972)

LAPLACE PLANEANALYSIS OF IMPEDANCE

97

At the difference between transport numbers in the bulk and interfacial region and the other quantities have their usual significance. Note that R~-ReCd/(Cd+C1) (see eqn. (4)) and C~_~C 1. Assuming reasonable values for the parameters (D = 10-5 cm 2 S-1, Ci = 10-3 mol cm-3, co = 1 0 7 S-l and At = 0.8) one obtains C s = 4 x 1 0 3 #F cm-2 and R~ = 10-5 flcm-2 both of which are such that their contribution to the observed response in this study is too small to be detected. It can therefore be concluded that diffuse layer effects contribute negligibly to the observed high frequency response of this system, as expected. The effect of water dipole relaxation has received considerable attention 36 which appears to indicate that the effect is negligible at frequencies attainable in previous work. However, in view of the fact that considerably higher frequencies are achieved with relatively high accuracy in this study it is useful to estimate a lower value for the relaxation time, %, of water dipoles in the electrical double layer. To do this it is convenient to use Debye's relaxation equation as given by Bockris et al. 23. This is (for the imaginary part only): 1 +(O)Zo)1-~ sin (fin~2) ACd = AeC' 1 + (~OVo)2- 2p + 2 (COzo)l- p sin (fl~z/2)

(7)

where A C d is the change in capacitance from the high frequency value; Ae = e s - e ~ where e~ is the permittivity at co ~ z~ 1 and ~ that at co~ zo 1 ; C' is the capacitance at e = 1 and fl describes the distribution of relaxation times (0 ~< fl ~< 1). Assuming AeC' to be 10 #F cm-2 (CJ~ ref. 36), an uncertainty in the determined capacitance at co= 107 of ~___1 #F cm- 2 and no distribution of relaxation times one can estimate a maximum relaxation time of 2 x 10-s s, somewhat shorter than the estimate given by previous workers 23'36. A longer relaxation time would have been noticeable. B. Faradaic potential region It has been shown elsewhere av that the general lower frequency behavior for an electrochemical system, even in the presence of specific adsorption, is linearity of impedance vs. 1/a ~ with a slope proportional to the diffusion coefficient, D, and extrapolation of this region to a true charge transfer resistance, Rt, provided that it can be ascertained that Cd has been eliminated from the response, as will be shown below. Therefore it was decided that an overall plot of this type would be useful as a preliminary diagnosis. In addition since linearity is important to achieve correct results, 3-4 mV anodic and cathodic perturbations about the equilibrium potential were applied. The system was studied at concentrations of 0.1-2 m M Hg~ +. The results shown in Fig. 5 illustrate typical behavior for oxidation and reduction. Clearly each plot initially appears reasonable. There is a substantial frequency range over which linearity in 1/a ~ is obeyed for voltage pulses in each direction. The slopes of each curve in this region however, are substantially different, leading to different values for D and R t in each case (see below). It was therefore concluded at this point that the amplitude of the voltage pulses exceeded significantly the range for which linearized behavior could be expected. This means that, even though reasonable frequency (and therefore time) behavior can be observed, proper precautions must be taken to assure that the system is indeed behaving linearly. It is conceivable that previous evaluations of this system, particularly in the time domain, did not take this point sufficiently into account. J. Electroanal.Chem.,39 (1972)

98

K. D O B L H O F E R , A.A. P1LLA

Z((;)~

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5?

! /////

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5.1

.'/ //

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S.t

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5.5

O.O2

0.~

I O.O6

I o.O8

i 0.10

i i 012 0.14 0-- V 2 / S I/'2

54 1070" - ~ s

Fig. 5. Overall impedance plots. R E D is obtained from a negative pulse of 3.5 mV, OXID from an identical positive pulse, Z + is calcd, from the linearization procedure outlined in the text. For 0.2 m M Hg22+, drop area = 0.0308 cm 2. Fig. 6. High frequency impedance plot in the faradaic region. The dashed line has C d as slope and R, as intercept (0.2 m M Hg 2+, drop area =0.0308 cm2).

In order to approach linear conditions more closely, from a consideration of the Taylor expansion of generalized expressions for the faradaic and charging current 37'39, it was determined that it is possible to eliminate second order (non-linear) effects from the response by an algebraic subtraction of the negative from the positive pulse, i.e., addition of the absolute values of both the experimental voltage and current (see also ref. 38). In order to illustrate this for the specific case of non-linear response in the faradaic current, consider the classical electrochemical rate equation:

where CR(0, t) and Co(0, t) are the time (frequency) dependent concentrations of the reduced and oxidized species respectively at the electrode surface, CRand Co their bulk concentrations, and the other symbols have their usual meaning. The Taylor expansion of (8) retaining first and second order terms results in 4° : nF ~zqF -~)nF l (nFq~ 2 i io = ACR-AC o + ~-~r/ + A C R R ~ q + A c o ( 1 ~ r/-- ~ k• ~ / , ( 2 a - 1 ) (9)

where

Ac. = (c.(O, t)--CR)/ ¢.

(10)

ac o

(11)

and =

(Co(0 , t)-- Co)/Co

and the other terms have their usual significance. It can be seen that if (9) corresponds to a positive voltage pulse then the subtraction of the response to an identical negative pulse, remembering that the relative concentration gradients (10) and (11) change signs, as well as q, results in: (i + - i - )/io = Ac~ - A c R - A c ~ + A c o + ( n F / R T)(r I + - ~l- )

(12)

where the superscripts + and - refer to the response to a positive and negative going J. Electroanal. Chem., 39 (1972)

99

LAPLACE PLANE ANALYSIS OF IMPEDANCE

perturbation respectively. Use of (12) should result in more meaningful impedance data. The resulting impedance values, Z +- are shown in Fig. 5. A test of the validity of this approach is the fact that identical diffusion coefficients were obtained for all Hg 2+ concentrations studied. This was not achieved without employing the linearization procedure outlined above. All analyses described below were carried out using impedance results obtained in this manner. In order to evaluate these impedance data more fully, the high frequency behavior of the system was examined. For this, eqn. (1) was employed since it has already been shown 11,13,48 t~hat the high frequency limit should reduce to simple RC series behavior. A typical plot is shown in Fig. 6. It can be seen that there is a wide frequency range over which linearity is achieved. The values obtained for the differential capacitance from these initial slopes were between 30 and 38 #F cm- 2 for the concentration range 0.1-2 mM Hg~ +. The above procedure allows two parameters for the system, Re and Cd, to be obtained. To analyze the system further it is necessary to choose one of the diagnostic plots described elsewhere 37 for a variety of systems with and without specific adsorption. The simplest is that obtained from Randles-Ershler ~1 behavior which is given here in real axis notation as : Z(o) --- Re+ [Cdo- + 1 / ( g t + K / a ~ ) ]

-1

(13)

in which the charge transfer resistance, Rt, is related to the exchange current, io, by : (14)

R t -- ( R T / A n F ) ( 1 / i o )

and K is related to the diffusion coefficient, D, of the electroactive species by : (15)

K = RT/n2F2AcoDo

where A is the electrode area in (14) and (15). This set of equations describes the aperiodic equivalent circuit shown in Fig. 7, in which it can be seen that the electrochemical system is represented by four parameters representing both the faradaic and non-faradaic portions of the impedance. Cd

II

Rt

Fig. 7. Aperiodic Randles-Ershler equiv, circuit. Zo is diffusion impedance (see text for further details).

If Re and C d a r e known from high frequency studies then the following diagnosis can be used to determine if only R t and K are needed to describe the system further. From (13) it follows that: J. Electroanal. Chem., 39 (1972)

100

K. DOBLHOFER, A. A. PILLA

W(a) = [ Y (a)-Cda] -1 = Rt + K /.,/a

(16)

where Y (a) = 1/(Z (a)- Re). The quantity W(a) is calculated knowing Z (a), Re and Cd and plotted vs. a-~, whereby a straight line should result if Randles-Ershler behavior is prevalent. A typical plot is shown in Fig. 8 where it can be seen that there is linearity (within experimental error) over more than 4 orders of magnitude in frequency, up to l0 s rad s-1. 6O0

w(o-)/~

400

30O

200

100

2

4

6

8

I0

102

12

14

6~lla/s 112

Fig. 8. Diagnostic plot for Randles-Ershler behavior. The quantity W is defined in eqn. (12).

For concentrations of Hg~ + less than 1 m M the W(a) plot was linear with the values of R e and Cd obtained directly from the high frequency analysis. However, for 1-2 m M solutions these plots exhibited a small deviation from linearity at the highest frequencies. It was found that this was due to a value of Cd up to 7 ~ too high as extracted from the high frequency data (see Fig. 6). Such an error is easily explained by the fact that at high concentrations of the electroactive species the faradaic impedance is relatively low even at the highest frequencies. Lowering the values of Cd obtained from the initial slopes by 4~o at 1 m M Hg~ + and 7~o at 2 m M Hg~ + led to a perfectly straight W plot and therefore to a more accurate value of Cd. Utilizing the above analysis the results shown in Table 1 were obtained. The final error associated with these results is as follows: D (and Re) are estimated to be correct to within + 1~ , Cd to + 3 ~ , and as can be seen from Table 1, io has the highest uncertainty (attaining ___50~o) because Rt tends to be masked by Re. A measurable exchange current exists, however, at all potentials. Knowing an estimate of io at various Hg~ + concentrations, it is possible to give an estimate of the rate content. The apparent standard rate constant s 1 ka is found to TABLE 1

co/mM

Cd/#F cm-2

io/A cm 2

105 D/cm 2 s-1

0.1 0.2 0A 1.0 2.0

32±1 33±1 32±2 34±2 35±3

1.0±0.2 1.5±0.4 3.0±1.0 4.0±2.0 7.0±3.0

0.94 0.95 0.92 0.93 0.96

J. Electroanal. Chem., 39 (1972)

LAPLACE PLANE ANALYSIS OF IMPEDANCE

101

be ka =0.02 cm s-1 using e =0.5. Since ~)2 is still positive at potentials very near the onset of the faradaic process 18, it is interesting to consider the significance of the static double layer correction which can be calculated using the classical Frumkin relation : ko = ka exp [ - ( ~ n - z ) F

~a2/RT ]

(17)

The calculation results in kS=0.036 cm s- ~ using a value of + 15 mV for ~b2(see ref. 18), which shows that there is indeed a non-negligible correction. The strong specific adsorption of ClOg certainly has a rate-increasing effect upon the process. In fact, in the absence of any specific adsorption, the apparent (experimental) rate constant would have been lower by an order of magnitude because qb 2 would have been expected to have a value of +75 mV (see p. 315 of ref. 35), i.e. considerably more positive. These results allow the conclusion that the Hg/Hg22+ system, while very rapid, still follows the straightforward Randles-Ershler scheme. There was no necessity to introduce more than four parameters to obtain an entirely self-consistent set of results. There is certainly no evidence for specific adsorption of Hg~ + despite the fact ,that there are two conceivable reasons for suspecting this. Super-equivalent specific adsorption of ClOg would render d~2 negative leading to increased Hg~ + concentration at the interface. Of course, strong specific adsorption of ClOg has been determined in this system by several workers 18''~z. However, Payne ~8 has shown that at high positive electrode charges ~ z is still positive, i.e. there is no super-equivalent ClO4 adsorption. This results in repulsion of Hg~ ÷ and therefore less probability of its specific adsorption. There is some evidence 43 that Hg22÷ is complexed to a small extent with ClOg. However, the high electric field at the interface would be expected to favor dissociation 43-47. It is concluded, therefore, that significant specific adsorption of Hg~ + would not be expected, as confirmed by this study. SUMMARY

The mercury electrode has been studied in both the ideally polarized and faradaic regions of potential using the transient impedance technique coupled with Laplace plane analysis. Both real and imaginary axis impedance values were obtained at frequencies up to 108 rad s-1 using an ultra-fast potentiostat coupled with signal averaging techniques. Results in the ideally polarized region of potentials showed no frequency dispersion. Results in the faradaic potential region showed that Hg/Hg 2+ follows the straightforward Randles-Ershler scheme. Self consistent results were obtained only after using a linearization procedure involving addition of the absolute values of the experimental voltage s and currents for cathodic and anodic perturbations. No evidence for specific adsorption of Hg 2+ was obtained nor any unusual double layer capacitance in the presence of the faradaic process.

REFERENCES 1 2 3 4

H. H. H. H.

Gerischer and K. Staubach, Z. Phys. Chem. (FrankJurt), 6 (1956) 118. Gerischer and M. Krause, Z. Phys. Chem. (Frankfi~rt), 14 (1958) 184. Matsuda, S. Oka and P. Delahay, J. Amer. Chem. Soc., 81 (1959) 5077. Imai and P. Delahay, J. Phys. Chem., 66 (1962) 1108.

J. Electroanal. Chem., 39 (1972)

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