ELECTROANALYTICAL CHEMISTRY AND INTERFACIAL ELECTROCHEMISTRY 133 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

APPLICATION OF THE METHOD OF TIME DOMAIN REFLECTOMETRY TO THE STUDY OF ELECTRODE PROCESSES. REPLY TO THE CRITIQUE OF SCHULDINER et al.

RICHARD PAYNE

Air Force Cambridge Research Laboratories, L. G. Hanscom Field, Bedford, Mass. 01730 (U.S.A.)

(Received September 13th, 1969)

In an earlier issue Schuldiner et aL 1 have presented a rather complete cri- tique of my earlier paper 2 describing an application of the methods of time domain reflectometry (TDR) to electrochemical problems. In so doing they appear to have been influenced not so much by principles of scientific objectivity as a desire to vindicate their own measurements. Their critique contains numerous misstatements of fact, errors of omission and instances of faulty logic, most of which however will be obvious to the informed reader. Furthermore, it is based in large measure on a complete misunderstanding of the measurements described and the analysis applied to the measurements. In order to place this discussion in proper perspective it should be noted that there is a basic disagreement between the experimental data given in my paper and similar measurements reported recently in several papers by Schuldiner and co-workers a- 5.

Schuldiner et al. 1 have pointed out quite correctly (but unnecessarily since it was stated explicitly in my paper) that the electrochemical measurements described were galvanostatic. My reasons for discarding the conventional TDR approach in favor of a galvanostatic measurement were clearly stated on page 9 of my paper and need not be repeated. Schuldiner et al. imply that the use of a current step rather than a voltage step, and superimposition of the incident and reflected pulses elimi- nates the advantages of the TDR technique, but this is not so. The principal advantage of the method in an electrochemical application is the superior high-frequency response of the sampling oscilloscope which at the time these measurements were made (1964-5) was (and still remains) considerably better than that of any conventional oscilloscope. The fact that the system was not used in a conventional TDR mode is quite irrelevant since the application was not conventional. The ability of TDR to determine the location of an impedance discontinuity on a transmission line is of no significance in electrochemical applications since the location of the discontinuity (i.e. the cell) is presumably already known! There is no particular advantage to be gained by deliberately isolating the incident and reflected pulse in time. Indeed attempts to do this by inserting long lengths of solid dielectric cable between the load and the probing point (as was done by O'Brien and Seto 6) inevitably lead to high frequency losses.

I should make it clear at this point that my paper was intended to be an introduction to TDR as a possible technique for studying the short time response of an electrode. The paper was not offered as a definitive study of the platinum/hydrogen

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electrode, a position to which it has been elevated by Schuldiner et al. The objective of the measurements as clearly stated was a study of relaxation phenomena in the double layer, evidence of which had previously been reported by Bockris and co- workers 7- 9 on the basis of audio frequency bridge measurements, and by Schuldiner and co-workers 4'5 using pulse methods. I expressed the opinion, which hardly seemed capable of contradiction, that these measurements stretch the experimental techniques up to and possibly beyond their useful limits. This is clearly so in the case of the bridge measurements which were made at frequencies at least two orders of magnitude below the region of interest. Similarly the most recent results published by Rosen et al. 5 show that their galvanostatic measurements give no useful information within the first 40 ns of polarization. Since by the very nature of measurements of this kind the experimental techniques are extended to their limit, the objections raised by Schul- diner et al. are difficult to understand.

As I stated in my paper (p. 9) the electrode capacitance was calculated as in conventional galvanostatic measurements from the current density divided by the slope of the voltage transient (assuming a simple series RC equivalent circuit). The potential measured was the total potential, i.e. the sum of the incident and reflected voltage pulses superimposed at the load. In conventional measurements in the micro- second or longer time range it is of course always the total potential which is measured since the propagation of the pulse through the connecting conductors is much faster than the time scale of the measurements. Schuldiner et al. have assumed incorrectly that I used the TDR equations given in Fig. 4 of my paper 2 to calculate the electrode impedance. As they point out, these equations apply to the reflection of a voltage step, and their application to galvanostatic measurements would have been a monumental error indeed. Fortunately this error was not made as a more careful reading of the paper would have shown.

Schuldiner et al. refer in a general way to ill-defined reflections "from load parameters and discontinuities back toward the pulse generator . . .". There were no such ill-defmed reflections. The system was a properly designed, fully matched 50 transmission line. Minor, unavoidable but well-defined reactive reflections occurred at the oscilloscope terminals and the probe, the effects of which were described .The only other mismatched element in the circuit was the cell. Schuldiner et al. believe that it is necessary to match the impedance of the cell to that of the transmission line in order to avoid degradation of the pulse shape. However, the only impedance that will do this is a pure 50 f~ resistance, an obvious point which appears to cause Schul- diner et al. some difficulty. A case could be made for adjusting the resistive part of the cell impedance to 50 f~ by supplementing the cell resistance, but in practice this is undesirable in fast pulse work because it introduces unwanted inductance and capacitance. However it is really quite unnecessary to match the cell resistance to the characteristic impedance of the line in a properly designed system. This is because the source of the pulse degradation (if it occurs) is repeated reflection of the pulse between the load and the generator. However, this cannot happen if the generator impedance matches that of the line since the first reflection from the load is completely absorbed by the generator. The results shown in Figs. 1 and 2 were obtained with a Tektronix 545A oscilloscope with type CA preamplifier and a Hewlett Packard 214A generator. The generator was connected to the load by a 50 f~ coaxial cable and the voltage measured at the load using a Tektronix 6006 high impedance probe. The

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TIME-DOMAIN REFLECTOMETRY. REPLY 135

a

• . . . . . . i i i i . . . .

i !*i . . . . . . . . . . ~/

i

~ b

c

i

i

Fig. i. Oscillograms showing negligible effect of load resistance on pulse shape. Generator connected to load by GR874-R22A 50 fZ coaxial cable. Load : (a) 56 fl ~-~ W resistor, (b) open circuit, (c) 10 f~ ~-~ W resistor. Horizontal sweep rate 100 ns cm-1. Small reflection at ~ 50 ns in (b) and (c) is due to a small reactive mismatch in the generator.

overall rise-time of this system is ~ 15 ns. The source impedance of the 214A generator is an accurate 50 f2. The traces in Fig. 1 show that when the generator impedance is properly matched with a 50 fl line the rise-time and shape of the pulse measured at the load are essentially independent of the load resistance. This is as it should be since the reflection from the mismatched load is absorbed when it returns to the source. However, when the source impedance is deliberately mismatched (by inserting a resistance in the line at the generator terminal) multiple reflections occur providing the load is also a mismatch; the result as shown in Fig. 2 is degradation of the pulse shape of the kind mentioned by Schuldiner et al. When the load impedance matches that of the line the pulse shape is again preserved in spite of the mismatched source impedance because now the load absorbs all of the incident pulse and no multiple reflections are possible (Fig. 2a). When both the source and the load are mismatched, the pulse shape becomes rounded when the load is greater than 50 fl (Fig. 2b) and

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136 R. PAYNE

,,C" J

i

i.

F~

Fig. 2. Effect of source impedance on the pulse shape for various resistive loads. Source mismatched by inserting series resistor of 270 ~ at the generator terminal. Load : (a) 56 fl ~60 W resistor, (b) 270 f~ l~o W resistor, (c) and (d) 10 fl ~6o W resistor. Generator connected to load by 20 ns RG 58/U cable in (a), (b) and (c); 50 ns RG 8A/U cable in (d). Horizontal sweep rate 100 ns cm-1.

ove r shoo t and r inging occurs when the load is less than 50 f l (Fig. 2c). The or ig in of these effects is suggested by the stepwise appea rance of the leading and t ra i l ing edges of the pulse in Fig. 2b. Each step is 40 ns long, the t ime taken for the s ignal to pass

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down the line and return. If a short transmission line is used the individual steps are not resolved and the pulse rise becomes an apparently continuous curve. The trans- mission line behaves essentially as a resonant element the characteristic frequency of which depends on its length. However it should be stressed that when either the load or the generator (or both) impedances are accurately matched to the line no "oscillation" is possible and no degradation of the pulse shape occurs. The preceding argument of course applies only when the terminating impedances are purely resistive. If for example the load impedance contains some reactance, the pulse shape will be affected. A shunt capacitance will integrate the pulse causing effectively increased rise-time whereas a shunt inductance differentiates the pulse (Fig. 3). An LC com- bination produces oscillation at the resonant frequency which may or may not be damped according to whether the LC combination contains series resistance. Such problems can occur in electrochemical measurements if the cell contains appreciable residual inductance or capacitance. In my experiments such problems were not serious.

S , .

l

b

i

Fig. 3. Effect of reactively mismatched load on pulse shape with properly matched generator and line. Load: (a) 0.001 pF disc capacitor, (b) 0.5 #H inductance, (c) parallel LC combination; C=0.001 #F, L=0.5 #H. Horizontal sweep rate 100 nscm 1.

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138 R. PAYNE

This does not however seem to be the case in the measurements reported by Schul- diner et al. They experienced ringing of the measured cell voltage which they were able to reduce by inserting a 200 f~ resistor between the probe and the cell. The resistor was supposed by them to match the low impedance of the cell with the high impedance of the probe. The resistor does not of course act as an impedance transformer but simply damps the oscillation ! The need to use such a device indicates a badly designed experiment.

The use of the sampling oscilloscope for electrode impedance studies is criticized by Schuldiner et al. because of the requirement for a repetitive pulse. They suggest correctly that reestablishment of equilibrium between pulses is an important condition which must be carefully checked. However, they claim incorrectly that this was not done in my work. This question was fully investigated, and as I state on page 10 "the results were normally independent of the repetition rate of the pulses." On page 11 of my paper I note that "for an electrode at the hydrogen potential, however, repetition rate effects were readily noticeable for the longer pulses. These effects were traceable to the (hydrogen) reaction, etc." A more careful reading of the paper could also have eliminated this point from contention. In connection with the question of pulse repetition rate they suggest that the time interval between each pulse (the OFF time), not the duty "cycle (ratio of ON to OFF time) of the pulse generator is the relevant criterion. However, if the pulse length is specified (as it was) the duty cycle gives the OFF time directly.

The 1 kHz repetition rate used in most of the measurements was selected arbitrarily for convenience although repetition rates all the way down to zero are feasible. As evidence of the visible effect of pulse repetition rate on the capacitance measurements Schuldiner et al. draw a comparison between the electrode polari- zation in Figs. 8 and 11 of my paper claiming that the polarization at 50 ns in Fig. 8 is about equal to that at 1 #s in Fig. 11. Since the current densities were similar in both measurements they suggest that the short pulse measurement must be incorrect due to repetition rate effects. In arriving at this conclusion they assume for their own purposes that the long time measurement was made using a single pulse, and therefore gives the correct impedance, whereas the short time measurement used repetitive pulses and therefore gives the wrong impedance. However, this was not the case. All the measurements reported were made with repetitive pulses using the sampling oscilloscope. This effectively disposes of their point, but in any case the logic of their argument is difficult to follow. Figures 8 and 11 of my paper showed different time segments of essentially the same curve (with slight differences of current density). Figure 8 showed the initial 50 ns where the current was mainly nonfaradaic, whereas Fig. 11 showed the time interval from 50 ns to 1 psec during which the current was largely due to oxidation of hydrogen. For this reason it is plainly absurd to compare the two curves in the manner of Schuldiner et al. The fact that they do so reveals a startling lack of objectivity.

Having thoroughly criticized the concept and execution of the experimental method, Schuldiner et al. next attempt to discredit the measurements on the grounds that the true electrode area was unknown and the solutions dirty. In support of their first point they quote a roughness factor of two in attempting to show that the capacitance value given in my paper (,-~ 20 #F/apparent cm / at the reversible hydrogen potential) is too low. However the true surface area of platinum depends, as is well

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known, on the method by which it is measured and, in the case of the hydrogen deposition method, on specific assumptions concerning the Pt-H stoichiometry. Furthermore, as Frumkinl 0 has remarked, the roughness also depends on the method of pretreatment of the electrode, and changes with time. Roughness factors as low as 1.311 and possibly below have been reported. The use of such a value would bring my capacitance value into agreement with that of Rosen et al. While this does not necessarily mean that it is correct, it nevertheless serves to illustrate the point. The reference to dirty solutions is of course a common criticism which is difficult to refute completely and is capable of being levelled at most electrochemical measurements. I can only repeat that reasonable purification of solutions by generally accepted methods was undertaken and that appropriate tests were made. The double layer capacity at a stationary mercury electrode seems an adequate test for the presence of traces of organic material irrespective of whether "adsorption and catalytic effects are quite different from those on platinum." Also it should be noted that Piersma et al. 4 used Teflon tubes sealed into their cell with polyethylene which is an arrange- ment hardly conducive to ultra pure conditions, although I would hesitate to dismiss their measurements on this score.. Similarly I do not believe their reference to "re- contamination due to atmospheric and other leaks into the system" to be of any importance in the measurements described in my paper. No difficulty was encountered in maintaining a smooth Pt electrode at the hydrogen potential with a minimal hydrogen gas flow.

Schuldiner et al. refer to the use of"dummy circuits" as a means of checking the correctness of the measured parameters, implying that no such checks were applied in my measurements. It is of course prudent to make such checks and this was in fact done routinely. An example was actually given in my paper (Fig. 5(c)) for a voltage pulse in the usual TDR mode, although the capacitor used (290 pF) was of somewhat lower value than the usual capacitance of the cell. The most compact capacitor comparable to the cell capacitance (~ 0.02 #F) was found, not surprisingly, to provide a rather poor comparison standard for nanosecond rise-time pulses because of residual inductance. The cell in fact provided a "purer" RC circuit than the dummy components. Nevertheless such components were measured in various con- figurations using voltage and current steps and shown to give correct values within the rated tolerance of the components. Indeed it would have been remarkable if this had not been the case.

Schuldiner et al. direct their final remarks toward the experimental results, their analysis and their interpretation. Unfortunately, however, they labor under the initial misapprehension that the electrode capacitance was calculated from the TDR equations given in Fig. 4 of my paper, which puts them at a considerable disadvantage. As I have already pointed out, the measurements reported were explicitly galvano- static and were analyzed appropriately. This fact immediately disposes of the major part of their argument. The initial assumption of a simple series RC equivalent circuit seemed fully justified in a study of the double layer. It was expected (incorrectly as it happened) that the hydrogen oxidation reaction would be too slow to interfere with the capacitance measurements at times less than 100 ns. I would agree of course that a full analysis of the electrode impedance in the presence of a substantial faradaic component would require a more complex (although still arbitrary) equivalent circuit. This was not however, as I have made clear, the object of the work. Extension of the

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140 R. PAYNE

equations for a more complicated equivalent circuit is a trivial problem. The galvanostatic potential-time transients for the measurements described

in my paper were generally linear in the time range 1-100 ns except at the reversible hydrogen potential where some curvature was observed at times longer than ~ 30 ns. The measurements were carefully analyzed to see whether the curvature could be attributed to variation of the iR drop caused by quite minor variations in the constant current. It could not. Furthermore, the curvature was shown to depend on the availability of hydrogen in the vicinity of the electrode. It was therefore reasonably attributed to the effect of the hydrogen oxidation reaction. Schuldiner et al. object to this conclusion on the grounds that it disagrees with their own recently published measurements s. They also find a curved galvanostatic potential transient for a Pt electrode in 1 M H2SO4 at the reversible hydrogen potential, which however they prefer to interpret as the effect of potential dependence of the double layer capacity rather than the hydrogen oxidation reaction. Unfortunately they do not present any evidence to support this conviction. The capacitance maximum at En=0.15 V in Fig. 4 of ref. 5 could actually be the residue of the hydrogen oxidation pseudocapacity peaks. Furthermore, examination of Fig. 3 of their paper suggests that the curvature of the potential transient in the time range 40-240 ns could also be accounted for by variation of the iR drop due to the effect of a 2 ~ variation of the current pulse top which is clearly visible. They do not consider this point. Their use of fixed external iR compensation in no way eliminates this problem.

Schuldiner et al. contend that the exchange current value for oxidation of adsorbed hydrogen of20A cm- 2 estimated from the measurements given in my paper is too high. I accept this as a possibility since the i0 value quoted was presented as no more than an estimate. They point out that an i0 of this magnitude requires that the faradaic current would have to be -,~ 30~ of the total current at t = 10 ns. This would mean that the double layer capacity values determined from the slope of the potential transient at 10 ns would be too high, a point which I would also accept. This appears to be the only valid point raised in their critique and it is a minor one.

Finally I would like to reconsider the possibility that observable dielectric (or other) relaxation processes occur within the double layer, and to discuss the so-called "perturbation time" described by Schuldiner and Presbrey 3 and by Piersma et al. 4. According to them the perturbation time is an interval varying from ,-~ 15 to 180 ns (depending on the solution) during which the potential of a platinum electrode remains constant under galvanostatic conditions. At least two independent explana- tions of this phenomenon were given, neither of which seems satisfactory. They first interpret the time independent potential in terms of the formula for the capacitance of a simple parallel plate condenser,

C _ Q _ ~ E 4~d

They argue that the potential E could remain constant (i.e. during the perturbation time) if the increase (or decrease) of Q, the electrode charge, were compensated by a corresponding variation of the dielectric constant ~ or the thickness d of the double layer. For a 1 A cm- z pulse and a perturbation time of 100 ns, 0.1/zC cm- 2 of charge passes into the electrode during the perturbation time. For an arbitrarily selected value for Q of 10/~C cm -2, this represents 1~o of the total charge and would, as

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suggested by them 4, require a corresponding 1~o variation of e or d if E is to remain constant. However for Q = 1 #C cm- 2 the required variation in e would be 10~o and for Q = 0 it would be infinite. This interpretation also requires a dependence of the perturbation time on the current density which was not found. Irrespective of this point, the measurements reported are inconsistent with any reasonable model of dielectric relaxation. If such relaxation is observable within the experimentally accessible range of measurement it must result in an initially high rate of increase of polarization which should subsequently decrease with time to a value consistent with the equilibrium dielectric constant in the double layer. Schuldiner et al. on the con- trary find a low or zero d E / d t at short times. This could not possibly be explained by dielectric relaxation.

The second interpretation of the perturbation time offered by Schuldiner et al. proposes that the small slope of the potential transient during the perturbation time results from the occurrence of a fast faradaic process presumably involving an adsorbed species (e.g. specifically adsorbed anions). They evidently consider this argument complementary to the dielectric relaxation theory, but it is really quite independent. The most obvious weakness of this argument as propounded by Piersma et al. 4 is the fact that only ,-~0.1 #C cm -2 of charge passes during the perturbation period whereas the electrode is probably saturated with specifically adsorbed anions (e.g. I- ions) with a total charge in the region of 100 #C cm-2. If the adsorbed anion is indeed the electroactive species it is necessary to explain why only 0.1~ of the specifically adsorbed charge undergoes oxidation and why the same phenomenon is observed for a cathodic pulse.

An alternative explanation of these results is of course possible. The oscillo- graphic data shown in refs. 3 and 4 suggest that in reality the perturbation time is a period during which spurious transients associated with the pulse rise are decaying. This is shown clearly in Fig. 4 of ref. 3 and Fig. 4 of ref. 4. The occurrence of such transients effectively precludes any reasonable assessment of the behavior of the electrode potential during this period.

Irrespective of the true explanation of these results the following point can be made. Schuldiner et al. have proposed a radical interpretation of unusual results which is both ambiguous and basically inconsistent with the predicted behavior of the systems studied. In so doing they have failed to show that their measurements are anything but a trivial artifact of the experimental technique. Under the circum- stances therefore they need hardly be surprised if general acceptance of these ideas awaits a more objective approach.

SUMMARY

The critique by Schuldiner et al. 1 of a recent paper 2 on applications of time domain reflectometry in electrochemistry is answered. Specific points raised in the critique are analyzed, and attention is drawn to some anomalous results and their interpretation recently published by Schuldiner and co-workers 3- 5 for a platinum electrode in aqueous solutions.

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REFERENCES

1 S. SCHULDINrER, D. R. FL1NN, M. ROSEN AND C. H. PRESBREY, J. Electroanal. Chem., 24 (1970) 137. 2 R, PAYNE~ J. Electrodnal. Chem., 19 (1968) 1. 3 S. SCHUED1NER AND C. H. PRESBREY, J. Electrochem. Soc., 111 (1964) 457. 4 B. J. PIERSMA, S. SCHULDINER AND T. B. WARNER, J. Electrochem. Soc., 113 (1966) 1319. 5 M. ROSEN, D. R. FLINN AND S. SCHULDINER, J. Electrochem. Soc., 116 (1969) 1113. 6 R. N. O'BRIEN AND P. SETO, J. Electroanal. Chem., 18 (1968) 219. 7 J. O 'M. BOCKRIS, W. MERE, B. E. CONWA¥ AND L. YOUNG, J. Chem. Phys., 25 (1956) 776. 8 J. O'M. BOCKRIS AND B. E. CONWAY, J. Chem. Phys., 28 (1958) 707. 9 J. O'M. BOCKRIS, E. GILEADI AND K. MULLER, J. Chem. Phys., 44 (1966) 1445.

10 A. N. FRUMKIN in P. DEEAHAY (Ed.), Advances in Electrochemistry and Electrochemical Engineerino, Vol. 3, Interscience, New York, 1963, p. 287.

11 S. GILMAN, J. Phys. Chem., 68 (1964) 2098.

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