ANALYST, DECEMBER 1992, VOL. 117 The following article is a reprint of the original paper on square-wave polarography by Barker and Jenkins, published in The Analyst in 1952, volume 77, pages 685-695. Nov., 19521 SECTION 3 ELECTRICAL METHODS 685 Square-Wave Polarography BY G. C. BARKER AND I. L. JENKINS SUMMARY A method is described for eliminating the undesirable effect of the double-layer capacity current on the sensitivity of an A.C. polarograph. A square-wave voltage is used in place of the usual sinusoidal polarising voltage, and the amplitude of the A.C. component of the cell current is measured shortly before each sudden change in the applied voltage. Preliminary results suggest that the method is useful for the detection, at concentrations down to 2 X N, of ions that are reversibly reduced, and that the sensitivity of the method is not greatly influenced by the presence of large concentrations of ions that produce interfering waves on the ordinary polarogram.Brief mention is made of an extension of the method that permits the detection of certain metallic ions at concentrations RESUME On dCcrit une mbthode pour kliminer les mauvais effets d’un courant de capacitC A couche double sur la sensibilit6 d’un polarographe A courant alternatif. Au lieu de la tension polarisante sinusoldale qu ’on emploie d’habitude, on se sert d’une tension a ondes carrkes, et l’amplitude du constituant alternatif du courant de la cellule est mesurCe un peu avant chaque variation subite de la tension appliquCe. Les premiers rbsultats suggbrent qu’on peut appliquer cette mCthode pour la dktection de ces especes qui sont rCduites de faqon r6versible dans une concentration s’abaissant jusqu’8 2 x N, et que la sensibilite de la m6thode n’est gu&re influencbe par la prCsence de hautes concentrations de ces espCces q ui produisen t des ondes d’interfkrence sur le polarogramme ordinaire.On discute brihvement une extension de la mbthode, qui permet de d6couvrir la pdsence de certaines espkces m4talliques dans des concentrations s’abaissant jusqu’8 10-9 M . ZUSAMMENFASSUNG Ein Verfahren ist kurz beschrieben, das den unerwiinschten Einfluss des Kapazitatsstroms der elektrischen Doppelschicht auf die Empfind- lichkeit eines Wechselstrom-Polarographen vermeidet. Statt der gewohn- lichen sinusoidal-polarisierenden Spannung wird mit einer eckigen Wechsel- spannung gearbeitet, und die Wechselstrom-Amplitude des Zellenstroms wird kurz bevor jeder plotzlichen Veranderung der Spannung gemessen.Vorlaufige Ergebnisse lassen darauf schliessen, dass diese Methode brauchbar ist zum Nachweis von reversibel reduzierten Ionen bis zu einem Konzentra- tionsbereich von 2 x N herab; das gleichzeitige Vorhandensein grosser Konzentrationen von Ionen, die storende Stufen auf dem gewohnlichen Polarografim hervorrufen, hat nur geringen Einfluss auf die Empfindlichkeit der Methode. Es wird eine Erweiterung der Methode erwahnt, die den Nachweis gewisser Metallarten bei Konzentrationen bis zu 10-9 M herab ermoglicht. of 1 0 - 9 ~ . THE advantages of derivative polarography for the analysis of complex solutions are well known and in recent years several simple D.C.circuits have been described1’213’4 that permit the recording of derivative. polarograms with normal polarographic equipment. In effect, these circuits provide a current that is merely related to the theoretical slope of the normal polarogram, and minor experimental imperfections, such as small irregularities in the diffusion R1R2 ANALYST, DECEMBER 1992, VOL. 117 Reprinted from The Anufysr 1952. 77, 685 686 INTERNATIONAL CONGRESS ON ANALYTICAL CHEMISTRY [VOI. 77 system, tend to impair the definition of the recorded polarographic waves and to lower the sensitivity of the method. On theoretical grounds it might be expected that A.C. methods would give better resolving power, and this expectation, to some extent, is borne out by the work of Breyer, Gutman and Hac~bian.~+J These workers applied a small sinusoidal alter- nating voltage to the electrodes of the polarographic cell, in addition to the normal polarising voltage, and studied the variation of the amplitude of the resulting A.C.component of the cell current with the mean potential of the dropping-mercury electrode. Well-defined waves were observed with solutions containing ions tbat are readily reduced, and from all points of view, except perhaps sensitivity, this simple A.C. method appears to have considerable advantages over more conventional D.C. methods. The somewhat low sensitivity of the A.C. method results from a large and variable background current connected with the low A.C.impedance of the double-layer capacity of the dropping-mercury electrode. This capacity current obscures small polarographic waves. In this paper a preliminary account is given of a method for eliminating the capacity current. The method has been developed by one of us (G. C. B.) for studying the kinetics of rapid electrode reactions at a mercury surface, but its value for polarographic purposes has not been systematically studied. Such tests as have now been made show, however, that ions that are reversibly reduced are detectable at concentrations down to 2 x lo-' N or even less, and that this high sensitivity is largely maintained in the presence of large concentrations (10-2 M) of ions that produce interfering waves on the ordinary polarogram. GENERAL PRINCIPLES If a small alternating voltage is superimposed on the polarising voltage applied to the electrodes of a polarographic cell, the behaviour of the system as regards alternating com- ponents is almost exactly equivalent to that of the electrical circuit of Fig.1. In this circuit the condenser, C, is the double-layer capacity of the dropping-mercury electrode, G is a Fig. 1. Equivalent circuit of cell theoretical voltage generator of zero internal impedance, and the resistance, R, is a composite resistance made up from the output resistance of the experimental voltage generator, the resistance of the solution lying between the two electrodes of the cell and the resistance of the thread of mercury in the capillary used to form the mercury drops. If the solution contains a reducible species in addition to a large amount of an inert supporting electrolyte, the transfer of charge across the double-layer capacity, connected with periodic changes in the rate of the electrode reaction, is accurately represented by the resistance Re and the transmission line TL.The resistance Re is dependent on the reversibility of the electrode reaction, while the transmission line, which is the electrical equivalent of the diffusion system at the surface of the mercury drop, takes the form of a resistance of almost infinite length with distributed capacity along its length. The various circuit elements vary considerably in value throughout the drop cycle, and certain of them are dependent on such factors as the mean potential of the drop and the concentration of the reducible species in the solution. For polarographic purposes it is not particularly useful to consider the exact way in which these circuit elements vary, but the circuit as a whole is of value, as it is aperiodic and, there- fore, can be used to predict the variation of the A.C.component of the cell current with time when the generator voltage. is not sinusoidal in shape. I t is necessary to consider the behaviour of the circuit when the generator produces a square-wave voltage of the type shown in Fig. 2a, the time between successive voltage changes being much larger than the time-constant CR. If the concentration of the reducible ion is small, the voltage developed across the condenser C is not appreciably different in shape or in amplitude from the generator voltage.Then, without appreciable error, the A.C. component ofANALYST, DECEMBER 1992, VOL. 117 Reprinted from The Analyst 1952,77, 685. 687 the cell current can be regarded as the sum of two independent components, one (the capacity current) resulting from the application of the generator voltage to the series combination of R and C, and the other (the electrode-reaction current) from the application of the same voltage to the series combination of Re and TL. The variation of the capacity current with time is indicated in Fig. 2b, while Fig. 2c shows the concomitant changes in the electrode- reaction current for a reversible reaction. It will be noted that the electrode-reaction current never decays to zero in the interval between successive voltage changes owing to the length of the transmission line, but, in the same time interval, the capacity current decays ex- ponentially with time and falls to a negligibly small value some time before the next change of applied voltage.It is evident that an almost perfect separation of the two current com- ponents can be effected in these circumstances by measuring the amplitude of the A.C. component of the cell current just before each change of applied voltage. Nov., 19521 SECTION 3 : ELECTRICAL METHODS Fig. 2. Voltage and current wave-forms It might be thought from the foregoing remarks that, in the absence of an electrode reaction, the A.C. component of the cell current would always be negligibly small just before each change of applied voltage, as long as the time interval between voltage changes was made sufficiently large.A more detailed analysis of the system than that given above, however, shows that this may not be exactly true for the following reasons- (i) In ordinary polarography a small cell current, associated with the expansion of the drop surface and known as the residual current, is present. With a square-wave polarograph this current is modulated by the applied square-wave and hence contains an A.C. component that varies with time in much the same way as the applied square- wave voltage. At a given time after the start of growth of a drop, the amplitude of this additional current component is proportional to the differential double-layer capacity of the drop at that time. A compensating cell current that varies in the correct manner with the mean potential of the electrode can be produced by using a square-wave voltage with a very slight downward slope on its upper edge and a corresponding upward slope on its lower edge, as shown in Fig.2d (the slopes are exaggerated). If the slope is correctly chosen, this compensating current can be made to cancel out the residual current component at some predetermined time after the start of the growth of each drop. The small slope has a negligible effect on the electrode-reaction current. (ii) Although it is usual to regard the elecirical double-layer as a pure capacity, it is clear that this view is not quite correct if the solution contains traces of inorganic ions that are preferentially adsorbed in the double-layer and if this adsorption results R3R4 ANALYST, DECEMBER 1992, VOL.117 Reprinted from The Analyst 1952, 77, 685. 688 INTERNATIONAL CONGRESS ON ANALYTICAL CHEMISTRY [Vol. 77 in some change in the capacity of the double-layer. Consider, for example, a solution of a uni-univalent supporting electrolyte (potassium chloride) containing a small con- centration of a polyvalent cation (La***). In the vicinity of the electrocapillary maximum and at more negative potentials it is probable that the polyvalent cations are preferentially adsorbed in the double-layer, and the measurements made by Grahame' suggest that this adsorption may cause the double-layer capacity to be larger than it would othenvise be. After a sudden change of potential the double-layer may not immediately come to equilibrium with the remainder of the solution, and in the case when a square-wave voltage is applied to the cell, the number of polyvalent ions adsorbed in the double- layer may alternately increase and decrease throughout the time intervals between successive voltage changes.If these relatively slow changes in the composition of the double-layer influence the charge density at the surface, some current will flow either to or from the mercury surface. In this way it is conceivable that inorganic ions that are preferentially adsorbed may produce a small response on the polarogram even though they do not enter into electrode reactions in the usual meaning of the term. (iii) Finally, mention niust be made of the more serious effects of capillary-active organic materials.Such substances, if adsorbed on the surface of a mercury electrode, usually produce a large decrease in the double-layer capacity. If, further, the distribution of capillary-active material between the electrode and the solution is influenced by the electrode potential, the amount adsorbed tends alternately to increase and decrease in the intervals between successive changes of the applied square-wave voltage. The associated changes in the charge density of the double-layer, in turn, produce periodic variations in the cell current, and it can be shown that this additional A.C. component, under some circumstances, varies with time in much the same way as the electrode- reaction component for a reversible electrode reaction. The polarographic waves produced in this way can usually be distinguished by their abnormal shape.An un- charged species, for example, often produces a broad wave with sharp asymmetric peaks at the extremes of the potential range over which the species is adsorbed. Even if such waves do not interfere with the measurement of the heights of other waves, it is desirable that organic substances should be rigorously excluded from the solution, as adsorbed poisons may lower the sensitivity of the electrode for the detection of reducible species. The use of a maximum suppressor, therefore, is not admissable, but this matters little, as the magnitude of the electrode-reaction current for a reversible reaction is not directly dependent on the magnitude of the slowly changing component of the diffusion current, but is determined by the surface area of the electrode and the concentration and diffusion coefficients of the reacting species in the vicinity of the electrode - solution interface.These quantities are not sensibly affected by the occurrence of current maxima. Apart from their close approach to their theoretical shapes resulting from the use of an A.C. method, reversible polarographic waves observed with a square-wave polarograph are much the same as those observed on derivative polarograms plotted by other methods. The use of the square-wave method, however, leads to a large difference between the heights of reversible and irreversible waves. This is because the square-wave method makes possible the measurement of the current shortly (about 2 x second) after each change of applied voltage.If the electrode reaction is reversible, the measured peak-to-peak amplitude of the current may then be as much as 50 times larger than the correspoiiding current for a derivative polarograph using a D.C. circuit. Hence, to make the best use of the potentialities of the square-wave method, or indeed of any other A.C. method, the supporting electrolyte should be so chosen that the electrode reactions are as reversible as possible. For example, Breyer and Hacobians have found that the use of potassium cyanide as a supporting electrolyte greatly increases the size of manganese" and nickel" waves, owing to the formation of complex ions that are more readily reduced than the species existing in chloride solutions.The pH of the solution also is important with metallic species that are hydrolysed in neutral solution or that tend to form complex anions in alkaline solutions. In such circumstances the pH of the solution must be low if reversible polarographic waves are to be observed. It will be realised that the resistance R in the equivalent circuit of Fig. 1 should be made as small as possible in order to facilitate the elimination of the capacity current. This isANALYST, DECEMBER 1992, VOL. 117 Reprinted from The Analyst 1952, 77, 685. $! E 1 i Square wave R5 Filter , = Current detector Nov., 19521 generator 7- 2 - V SECTION 3 : ELECTRICAL METHODS A 689 J7J-L also desirable from the point of view of linearity of response, since the resistance R is wholly responsible for any non-linearity at high concentrations. It should be noted that non- linearity can always be minimised by using a voltage generator with a negative output resistance .So f a r mention has only been made of the AX. component of the cell current. This current, however, is accompanied by the normal diffusion current, which must be eliminated before measurements can be made of the amplitude of the cell current. Fortunately, the diffusion current changes quite slowly with time during the later part of the life of a drop, and during that time it is possible to effect a perfect separation of the required component with the aid of filters. Owing to the discontinuity in the diffusion current when the drop falls, the separation at that time is imperfect and consequently the measured value of the cell current is unreliable at the time of fall of the drop and during the early part of the drop life.Hence it is best to make the polarogram a record of the measured amplitude of the A.C. component of the cell current at a predetermined time in the later part of the life of the drop. A polarogram of this type has the additional advantage that it refers to a surface area that is practically constant throughout the recording of the polarogram. - - EXPERIMENTAL As stated above, the square-wave method for eliminating the capacity current has been developed specifically for the study of the kinetics of electrode reactions, and the associated electronic equipment is more elaborate in design than is necessary for polarography. A detailed description of the electronic circuits will not, therefore, be given here.A simplified block schematic diagram of the electronic equipment is shown in Fig. 3. A square-wave generator produces a square-wave voltage with a mark-to-space ratio of unity and a frequency of 225 cycles per second. A frequency intermediate between two harmonics of the A.C. power supply frequency is used to avoid spurious responses from harmonics of the power supply frequency. The square-wave voltage, after appropriate attenuation, is fed into the cell modulator circuit where it is combined with a slowly changing voltage supplied by the linear voltage-sweep generator. This generator controls the mean potential of the dropping-mercury electrode, and this potential can be made to change with time at various known positive or negative rates.,. H.F. current Modulator Output Cell selector unit I Fig. 3. Schematic diagram of electronic apparatus The combined polarising voltage appears at the output terminals of the cell modulator circuit. These are connected to the electrodes of the polarographic cell and the resulting cell current waveform is converted into a voltage waveform by passing it through a resistance in the anode circuit of one of the valves in the cell modulator circuit. Low-frequency com- ponents are removed from this voltage waveform by means of a high-pass filter and the resulting waveform, after some amplification, is passed to the input terminal of the current detector. This circuit monitors the amplitude of the waveform at a predetermined time after each change of applied voltage and produces a voltage that is proportional to theR6 ANALYST, DECEMBER 1992, VOL.117 Reprinted from The Analyst 1952, 77, 685. 690 INTERNATIONAL CONGRESS ON ANALYTICAL CHEMISTRY [Vol. 77 difference between the two values observed in each complete cycle of the square wave. This voltage is smoothed slightly to reduce fluctuations caused by valve noise and electrical interference and the smoothed voltage appears at the output terminals of the current detector. At the peak of a large polarographic wave the output voltage of the current detector circuit changes rapidly with time owing to the steady expansion of the drop, and it is difficult to get a pen recorder that will faithfully reproduce these rapid changes in voltage.For this and other reasons given earlier, the output voltage is passed to the output voltage selector unit. This unit contains a condenser which, at a predetermined time after the start of growth of each drop, is connected for a period of 2 x 10-* second to the output voltage of the preceding circuit, but which, at all other times, is completely isolated as regards leakage of charge. During the time it is connected to the output voltage, the condenser charges up to the value of the output voltage at the time in question, and the voltage across the condenser, therefore, varies in a stepwise manner from drop to drop. By means of suitable electronic circuits the voltage across the condenser is made to control the movements of a pen recorder.In this way the output voltage at a definite time in the life of the drop is recorded. The necessary time delay (1.75 seconds) between the start of growth of a drop and the time at which the output voltage is recorded is procured by stimulating an electronic delay circuit each time a drop falls, use being made of the sudden increase in the internal resistance of the cell at that time to obtain a suitable stimulus. A high-frequency (18 Mc/s) alternating current is passed through the cell to detect the impedance change without affecting the behaviour of the system. The output voltage selector unit also includes a circuit that makes it possible to record a polarogram that is a record of the change in height of the derivative polarogram from one drop to the next, i e ., a second differential of the primary polarogram. A polarogram of this type, which we shall call a second-derivative polarogram, is useful for the separation of overlapping polarographic waves. Since the electrode-reaction component of the cell current frequently is quite small, the noise currents introduced by the cell modulator circuit may not always be unimportant. Two modulator circuits can be used with the present apparatus; one has a low output resistance of about 10ohms and a high noise level and, therefore, is most suitable for the study of solutions containing relatively high concentrations of reducible material. The other, which was used to record the polarograms reproduced in this paper, has an output resistance of about 30 ohms and a much smaller noise level, the noise voltages applied to the electrodes of the cell being of about the same amplitude as those appearing across a resistance of 500 ohms.With the latter circuit in use, the sensitivity of the instrument at the present time is not seriously affected by valve noise, although it is probable that this state of affairs may change as more experience is gained in the analysis of solutions containing minute amounts of reducible material. For polarographic purposes, the delay between each change in the applied voltage and the time at which the amplitude of the current is monitored is made a definite fraction of the time interval between successive voltage changes, namely, $ths of that time interval, this fraction being automatically fixed by electronic circuits that are not shown in the schematic diagram.A choice of three amplitudes for the applied square-wave voltage is available4, 12 or 35 millivolts peak-to-peak-and the small slope on the upper and lower edges of the waveform (for the elimination of the residual current component) is obtained by passing it through a condenser - resistance coupling of appropriate time-constant (of the order of 2 seconds) before injecting it into the cell modulator circuit. The polarographic cell requires no special mention as it is essentially the same as the usual type of polarographic cell with an internal mercury-pool anode. Some mention, however, must be made of the capillary design, although at the present’tirne it is not possible to reach any definite conclusions as to the best type of capillary.Various types of capillary have been used at different times, and it has been found that the normal type of polarographic capillary, with a uniform diameter of about 0.05 mm, gives quite satisfactory results at potentials more positive than about - 1.5 volts with respect to the saturated calomel electrode. At more negative potentials, there is a tendency for solution to enter the capillary at the time of fall of the drop, and this leads to a spurious and irregular response, as the surface of the thread of mercury then tends to follow the changes of cell voltage. These irregularities become more pronounced as the diameter of the capillary is increased, and recently anANALYST, DECEMBER 1992, VOL. 117 Reprinted from The Analyst 1952, 77, 685.691 attempt has been made to eliminate them by using a capillary that decreases rapidly in diameter towards the capillary orifice. Unfortunately, capillaries of this type with an orifice of the desired diameter (0.05 mm) cannot easily be made, and the only tapered capillary so far studied has an exceptiondy large orifice of diameter about 0.15 mm. The polaroeams reproduced in this paper were recorded with this capillary. Nov., 19621 SECTION 3 : ELECTRICAL METHODS 1. -I 5 --I 0 -0 5 0 0 Potential Y S S C.E.. volt5 Fig. 4. Derivative polarograms. Curves a, b, t and d , square-wave amplitude 35 mv, temperature 25" C. Curve e, square-wave amplitude 12 mv, temperature 70" C Curve a, M potassium chloride, p H e 8.5, without residual current compensation Curve b, M potassium chloride, pH h 8.5 Curve c, M potassium chloride, 10-6 M Pb", 10-6 M Cd" and 5 x 10" M Zn", pHC8 Curve d, as curve c, but at pH 3 Curve e, as curve d , but temperature raised to 70°C So far only the behaviour of potassium chloride as a supporting electrolyte has been studied. Conductivity water, prepared by redistilling distilled water in a quartz still, has been used for the recrystallisation of potassium chloride of analytical reagent purity and for the preparation of solutions.To remove any traces of capillary-active material, the solution of the supporting electrolyte was passed through a column of purified adsorbent charcoal before admitting it to the cell. This generally resulted in a slight rise in the pH of the solution, which was subsequently corrected, if necessary, by the addition of small amounts of acid to the solution in the cell.Dissolved air was expelled from the solution in the cell by bubbling nitrogen through it for some time before recording a polarogram. However, owing to the diffusion of air through the ungreased joints of the cell, it is probable that the oxygen R7R8 ANALYST, DECEMBER 1992, VOL. 117 Reprinted from The Analyst 1952, 77, 685. 692 INTERNATIONAL CONGRESS ON ANALYTICAL CHEMISTRY [Vol. 77 concentration in the solution did not in any experiment fall below 2 x lo-* M. In this connection it should be noted that traces of oxygen in the solution are less objectionable than traces of organic matter from tap-grease. Solutions containing small amounts of reducible electrolytes were prepared by adding small volumes of concentrated solutions of the electrolytes in question to the solution in the cell.This somewhat rough procedure was considered adequate for the purpose of the experiments. RESULTS The results presented in this section are exploratory in character and a more detailed investigation of the performance of the polarograph is contemplated. The potential scales attached to the polarograms reproduced in Figs. 4, 5 and 6 may be slightly inaccurate, as a ;K i______j 0 0 -05 -10 -Is Potentlrl II 5 C.E . volts Fig. 5. Derivative polarograms. Square- Curve a, 1l.I potassium chloride, pH fi 8-5 Curve b, A2 potassium chloride, 2 x A2 Cu", 2 x M Pb", 2 x 1O-hAf In"', 2 x -42 T1' and 2 x lo-' d2 Zn", p H e 6 wave amplitude 12 mv, temperature 25" C i\i Cd".4 x Curve c, as curve b, but at pH 3 Curve d . as curve c, esccpt that concmtra- tion of copper altered to 2 x 10-%M Cu" Curve e , as curve c, 10-2471 Cu" potentials were not automatically recorded on the polarograrns and had to be superimposed later from a knowledge of the potentials associated with certain characteristic features of the polarograms. The polarograms shown in Fig. 4 are typical of tlie results for a solution containing small traces of reducible material. The amplitude of tlie applied square-wave was 35 millivolts peak-to-peak, except for Fig. 4e, when the 12-millivolt square-wave was used. The beneficialANALYST, DECEMBER 1992, VOL. 117 Reprinted from The Analyst 1952,77,685. Nov., 19521 SECTION 3 : ELECTRICAL METHODS 693 effect of the residual current compensating circuit is clearly shown by the difference between Fig.4a and Fig. 4b. It must be noted, however, that the variation in the real residual current component with the mean potential of the dropping-mercury electrode is smaller than Fig. 4a would suggest, owing to the fact that the cell modulator circuit introduces an additional current component that varies with the mean potential of the dropping-mercury electrode in the same way as the residual current. The compensation circuit, however, eliminates both components. 70.2 -0.4 - 0 6 Potential vs S.C.E.. volts Fig. 6. Polarograms. Square-wave ampli- tude 4 mv, temperature 25" C. Solutions con- taining M potassium chloride, 2 x lovs M Cu". 2 x M Pb", 2 x M In"', 2 x M Cd" and 4 x 10-5 M T1' ; pH 2 Curve a, derivative polarogram; curve b, second derivative polarogram After eliminating the residual current some signs of small waves due to irreversible processes can be detected; these arise from the presence of traces of dissolved oxygen and other impurities in the solution of the supporting electrolyte.On adding small traces of Pb" M), Cd" M ) and Zn" (5 x M ) to the slightly alkaline solution, the zinc and lead waves are quite small (Fig. 4c), owing to the formation of plumbate and zincate ions. The cadmiumn wave is clearly seen and its height can be measured with an accuracy of about 2 per cent. It will be seen that the background response is exactly the same as that for the supporting electrolyte alone. However, on adding sufficient nitric acid to lower the pH of the solution to 3, there is a noticeable change in the background current (Fig.a), due perhaps to the presence of impurities in the acid, to the effect of pH on the kinetics of some irreversible reaction or to the preferential adsorption of polyvalent ions in the double layer. The change in the pH of the solution greatly increases the heights of the zincn and lead" waves, but the zincU wave in acid solution is still relatively much smaller than the leadxx or cadmium" waves, owing to irreversibility in the Zn" + Zn(Hg) reaction. Fig. 5 gives some indication of the resolving power of the polarograph with solutions containing somewhat larger concentrations of Cu", Pb'., Cd**, In***, T1' and. Zn". The square-wave amplitude in all these examples was 12 millivolts and the sensitivity of the pen recorder was reduced by a factor of five.The zero level, it will be noted, is practically constant over a considerable range of potential (Fig. 5 4 . In almost neutral solution the sharp In"' (2 x 10dM) wave disappears completely, owing, no doubt, to hydrolysis of the This difference becomes less marked as the temperature increases (Fig. 4c). R9R10 ANALYST, DECEMBER 1992, VOL. 117 Reprinted from The Analyst 1952, 77, 685. 694 IXTERNATIONAL CONGRESS ON ANALYTICAL CHEMISTRY [Vol. 77 ions (Figs. 6b and c). The Zn" (2 x lO-'M) and Cu' (2 x M ) waves are also somewhat smaller in the almost neutral solution than in acid solution. The cause of the small wave that overlaps the negative branch of the zinc wave in both neutral and acid solutions is not known.The Pb'* (2 x 10-6M), T1' (4 x lO"M) and Cd" (2 x 10-6M) waves are quite unaffected by the change in the pH of the solution. Figs. 5d and e are particularly interesting, as they show that the sensitivity of the instrument is not appreciably affected by the addition of relatively large amounts (2 x 104M and 10-%M) of interfering copperu ions to the solution. If the shapes of reversible waves such as the Cd", Pb", In"' and T1' waves are examined, it is found that they agree exactly with the theoretical shapes if due account is taken of the effect of the square-wave amplitude on the width of a wave. If two such waves overlap to some extent, the individual waves can often be resolved by virtue of the fact that their shapes are known.For example, it would not be particularly difficult to estimate the heights of the Cd", In"', T1' and Pb" waves on the polarogram shown in Fig. 6a. However, this separation is facilitated by recording a second-derivative polarogram, such as the one shown in Fig. 6b. On this type of polarogram each species produces a wave that has zero amplitude at the half-wave potential and shows positive and negative maxima at the p i n t s of inflection of the derivative polarogram. The heights of the maxima can be used to estimate concentrations if the rate of change of the mean potential of the dropping-mercury electrode is known. It sometimes happens that although two waves on the derivative polarogram may overlap to such an extent that the height of the interfering wave at the half-wave potential for either of the species is not negligibly small, one of the maxima for either of the species on the second derivative polarogram may be quite unaffected by the presence of the wave produced by the second species.For example, one of the cadmiumn maxima on the polarogram shown in Fig. 6b is unaffected by the indiumm wave, and its height, therefore, could be used to estimate the concentration of cadmiumn in the solution. Similarly one of the indium'" maxima could be used to estimate the indiumxn concentration. DISCUSSION OF RESULTS The results given in the preceding section need little discussion as they merely illustrate the general principles of square-wave polarography that were outlined earlier. It is fair to conclude that, without any major change in experimental technique, a square-wave polarograph is capable of detecting waves produced by reversibly reduced ions at con- centrations of the order of 2 x lO-'N, and that concentrations greater than 2 x .%- can be estimated with the accuracy usually attained in polarographic studies.Further, if care is taken in the design of the electronic equipment there is no real reason why concentra- tions above 2 x N should not be estimated with an accuracy approaching 0-5 per cent., as an accurate pen recorder permits wave heights to be measured with an accuracy of 0.2 per cent. or better. A high accuracy is inherent in the method because the response at any time is not subject to the uncertainties in the diffusion system that limit the accuracy of con- ventional polarographic techniques. Convection currents in the solution surrounding the mercury drop have no effect on the shape or size of reversible waves and, in fact, polarograms can be recorded with gently stirred solutions, provided that the stirring process does not introduce high-frequency alternating components into the cell current. One of the most valuable features of the square-wave polarograph appears to be its ability to detect reversible waves in the presence of species that produce interfering waves on the ordinary polarogram and also interfere, to some extent, with the simpler methods for recording derivative polarograms.It would appear entirely feasible, for example, to estimate traces of impurities in brass or copper with the aid of the square-wave polarograph without previously eliminating the interfering copper ions.As regards any further improvement in sensitivity, it is believed that the useful con- centration range of the present instrument might be extended to lower values by a factor of 10 or more by paying more attention to the purity of chemicals, to the noise level of the electronic circuits and to the design of the capillary. The experimental technique would then become somewhat specialised and it may be doubted whether it would be acceptable for analytical purposes. Indeed, there is some doubt in the authors' minds as to whether there is any real need for higher sensitivity. If there were, one might mention a recent development that can lead to a large increase in sensitivity for the detection of many of theANALYST, DECEMBER 1992. VOL.117 Reprinted from The Atzalysr 1952. 77. 685. R l l Nov., 19521 SECTION 3 : ELECTRICAL METHODS 695 species that form metallic amalgams. Briefly, this involves the use of a single mercury h o p in place of the dropping-mercury electrode, and a special cell is used that permits the circulation of the solution past the surface of the drop, the circulation system being such that the diffusion system in the vicinity of the drop can be reproduced. At the start of an experiment the drop electrode is polarised to as negative a potential as is possible without depositing the cations of the supporting electrolyte and is held at this potential for a suitable time. Metallic impurities in the solution then tend to be concentrated in the drop and, after 15 minutes have elapsed, the concentrations of the electro-deposited ions in the drop may well exceed their concentrations in the solution by a factor of a hundred or more.After a suitable amount of concentration has been effected, the circulation of the solution is stopped and a derivative polarogram is recorded with a relatively rapid rate of change of the mean potential of the drop. If the conditions under which the experiment is carried out are correctly chosen, the heights of the waves observed on the polarogram are determined by the concentrations of the various metallic ions in the drop at the start of the polarogram, and these concentra- tions consequently can be determined from the measured wave heights. If the system is calibrated in some way, the concentrations in the drop can be used to estimate the original concentrations of the various ions in the solution. The accuracy of the method is probably not better than 6 to 10 per cent., but the method is of interest a s it is readily applicable to the estimation of concentrations as small as lO-9M and, if pressed to its limit, one might expect the smallest amount of a single species that could be detected to be of the order of 10-11 moles.The method has been found useful for studying the purity of the supporting electrolyte. Finally, some mention should be made of the instrumental complexity of a square-wave polarograph. I t is likely that the operator of the instrument will have only an imperfect understanding of the operation of the electronic circuits, and therefore it seems essential that the electronic circuits should be as automatic in operation as possible and that their operational characteristics should be clearly defined.The onus for obtaining accurate results should thus be transferred from the operator of the instrument to its designer, and it is clear that this can be achieved if full use is made of modem electronic techniques. The instrument then should be no more difficult to operate than conventional polarographic equipment. It is estimated that 15 to 20 electronic valves and their associated components are needed to produce a reliable instrument of this character. The authors are indebted to the Director, A . E . R . E . , for permission to publish this paper. 1. 2. 3. 4. 5. 6. 7 . 8. REFERENCES Hey-rovskl, J., Chem. Listy, 1946, 40, 222; Analyst, 1947, 72, 229; Chem. Listy, 1949, 43, 149. Vogel, J., and Riha, J., J . Chim. Phys., 1950, 47, 5. Airey, L., and Smales, A. A., Analyst, 1950, 75, 287. Leveque, M. P., and Roth, F., J . Chim. Ph-ys., 1949, 46, 480; 1950, 47, 623. Breyer, B., and Gutman, F., Aust. J . Sci. Res., 1950, 3, 558. Breyer, B., Gutman, F., and Hacobian, S., Ibid., 1950, 3, 567. Grahame, D. C., J. Electrochem. Soc., 1951, 98, 343. Breyer, B., and Hacobian, S., Aust. J . Sci. Res., 1951, 4, 604. ATOMIC ENERGY RESEARCH ESTABLISHMENT HARWELL, DIDCOT, BERKS. April 24th, 1952 DISCUSSION MRS. B. LAMB (London) asked what recorder was used. DR. A. J. LINDSEY (Rickmansworth) (Chairman) said that the sensitivity of this instrument appeared to be much greater than was customary, and that a lower sensitivity would have been better for most analysts. DR. BARKER replied that the sensitivity of a square-wave polarograph could easily be reduced by appropriately decreasing the voltage gain of the amplifier that preceded the current detector. Concentra- tions of reducible ions up to about 2 x lo-* N could then be studied. As the output voltage of an instrument of the type outlined in the present paper changed only slowly with time, the simplest type of pen recorder could be used to record a polarogram. They had generally used a high-speed recorder manufactured by the Brown Instrument Co., as high-accuracy recordings were needed for their kinetic experiments. He asked if the instrument could be adjusted to a lower sensitivity.