NOVEMBER, 1973 Vol. 98, No. 1172 Differential Electrolytic Potentiometry with Periodic Polarisation Part XXIII." The Effect of Bias and Distortion on Periodic Differential Electrolytic Potentiometry, the D.C. Output Produced and Time-biassed Differential Electrolytic Potentiometry in Oxidation - Reduction Titrationst BY E. BISHOP AND T. J. N. WEBBERI (Chemistry Department, University of Exeter, Stocker Road, Exeter, EX4 4QD) Any departure from the pure, symmetrical, bias-free input waveform ; external d.c. bias; internal d.c. offset, distortion, amplitude or mark-to-space (time) bias ; produces a deterioration in the periodic differential clectrolytic potentiometric titration curve. The peak potential is decreased, the peak becomes less sharp, the discrimination becomes worse, errors are introduced and the electrodes more quickly become deactivated when any bias or dis- tortion is present in the input current waveform, and this effect is manifest with 2 per cent.contamination of the waveform and destructive a t 5 per cent. A d.c. bias causes the peak to split into two peaks. At the same time, the electrodes produce a d.c. output; the symmetrical polarisation shows no d.c.-component in the output; and for d.c. offset and amplitude bias, this d.c. output is the same as for classical d.c. differential electrolytic potentiometry. With a time-biassed periodic input of any waveform, a d.c. output of unique properties is produced. This output has the same forms as the classical dlc. differential electrolytic potentiometric curves, but the end-points are sharper, the discrimination is better, the end-points are error- free with dichroniate and ceriuni(1V) titrants, the d.c.potential stabilises very quickly and remains di-ift-free, even for type I1 (b) curves, the high-quality end-point persists to very low concentrations, the electrodes retain their activity for a long time and the process is independent of frequency. Such titrations can be performed as fast as titrations with visual indicators. The positive errors in classical d.c. differential electrolytic potentiometric titrations with cerium(1V) , chromium(V1) and in zero-current potentiometric titrations with vanadium(V) are explained. No previous work on the use of biassed or asymmetrical waveforms has been discovered in a literature search; earlier work on periodic polarisation has been faulted because no effort seems to have been made to ensure purity and symmetry of waveform, or indeed to examine them, except for one attempt to block d.c.by means of a series capacitor in the generator output,l a device that gave very limited success.2 Both the Heathkit and Advance signal generators that were initially used in this ~ o r k ~ , ~ gave unsatisfactory results, which were traced to a d.c. offset in the former and low-frequency distortion in the latter. Addition of a series capacitor did not eliminate all of the d.c. offset, and had no influence on a badly shaped wave, other than to attenuate low frequencies. Moreover, the use of a transformer, even of the constant voltage saturable reactor type, to provide a 50-Hz signal, is productive of waveform distortion and harmonics because of the iron-cored inductance.These observa- tions led to a systematic quantitative examination of the effects of offset and waveform asymmetry on the precision, accuracy and discrimination of end-point location, and on the forms of the titration curves and the speed of electrode response. With a pure periodic waveform, there is no d.c. component in the output from the electrodes, just as there is no periodic component in the output from pure d.c. polarisation. With a biassed or offset waveform, both d.c. and periodic components will be present in the output. * For details of Part XXII of this series, see reference list, p. 776. t Presented a t the Second SAC Conference, Nottingham, 1968.5 Present address : Shell Research Limited, Woodstock Agricultural Research Centrc, Sittingbourne, @ SAC and the authors. Kent. 769770 BISHOP AND WEBBER : DIFFERENTIAL ELECTROLYTIC [Artahst, VOl. 98 Rough predictions of the form of the titration curve for single polarised electrodes veysus reference and zero-current indicator electrodes, and for pairs of polarised electrodes, were made (Fig. 1 in reference 3) on a basis of the titration analogue model,4 for fast reactions and 50 per cent. of the particular bias. For example, if there is a d.c. component in the periodic waveform, then, with an oxidant titrant, for a single electrode the end-point will be displaced from the equivalence point by an amount proportional to the magnitude of the d.c.component, and the error will be positive if the d.c. polarisation is cathodic and negative if it is anodic. For paired electrodes, one electrode will be polarised cathodically and the other anodically, and a d.c. differential potential will exist between them. When observed in the sense anode minus cathode, there will be a periodic peak superimposed on the d.c. peak. The d.c. output will be the sum of the first and second differentials of the zero-current curve, and the periodic output will broaden, eventually splitting to give two peaks. EXPERIMENTAL Various forms of bias were introduced into the pure waveforms, as exemplified in Fig. I, either as an external or internal d.c. offset, or by waveform shaping to give amplitude or time bias. Amplitude bias and d.c.offset are the same for square waves, but not for sine or triangular waveforms. n n Apparatus,3 solutions and procedures2 have been described earlier. Symrnetrical square wave form Fig. 1. Biassing of pure waveforms. Initial pure square wave with: (a), external d.c. offset; ( b ) , a 2: 1 mark-to-space (time) bias; (c), a 2: 1 amplitude bias, which is identical with (a) for square wave forms but not for the other waveforms; and (d), sine wave with a 2: 1 amplitude bias D.C. OFFSET- A limited internal d.c. offset, up to 5 V, could be mixed into the waveform by adjustment of the reference level potentiometer, P9, in the waveform generat~r,~ but greater offset could not be produced in this way without introducing distortion into the output signal. Larger offsets were introduced externally by applying a d.c.potential from a battery and potentiometer across the “low” and “earth” connections (normally strapped together) on the waveform generator. After checking the equality of the duration of the half-cycles with the crystal clock, the amount of d.c. present was measured either directly on the oscilloscope, or by increasing the frequency and applying the signal to a d.c. meter. AMPLITUDE BIAS- As is evident from Fig. 1, the amplitude bias is the same as a d.c. offset for square waves, but not for sine and triangular waves. Limitation of facilities at the time prevented further examination of amplitude bias for sine and triangular waveforms. TIME HAS- Time bias can be obtained by adjustment of the potentiometers P3, P4 and P5 in the generator.3 For square waves, a perfectly symmetrical, pure signal was first obtained, the half-cycles being identical in amplitude and duration, and the selected amount of bias was introduced.The internal adjustments did not permit more than 5 2 0 per cent. relative variation. The crystal clock was then used to measure, the duration of each half-cycle accurately. For sine waves, the clock would not trigger at frequencies less than 14 Hz, and it u7as necessary to trace the shape of an individual cycle from the oscilloscope screen onNovember, 19731 POTENTIOMETRY WITH PERIODIC POLARISATION. PART XXIII 771 to translucent graph paper, and to cut out and weigh the area representing each half-cycle. This method obviously has poor accuracy; the average error determined by replication was less than 5 per cent.The titration cell was then set up,3 with the electrode configuration shown in Fig. 3 in reference 2, so that the d.c. and periodic potentials at each of the periodic electrodes could be measured with reference to a standard half-cell or a zero-current electrode, and the periodic and d.c. potential differences between the two periodic electrodes could also be measured. At the same time, d.c. differential electrolytic potentiometry and zero- current potentiometric potentials could also be monitored for comparison. RESULTS AND DISCUSSION EFFECT OF D.C. BIAS ON THE PERIODIC POTENTIAL CURVE- First, a system showing a modicum of charge-transfer overpotential was examined, the titration of iron(1I) with 0.1 M cerium(IV), with a gradually increasing d.c.offset. The results are shown in Fig. 2, and accord with prediction. These results should be compared with those in Fig. 3 and other figures in reference 2 that show the results with pure, sym- metrical, bias-free waveforms. The presence of a very small (less than 2 per cent.) d.c. offset is sufficient to reduce the sharpness of the periodic potential curve under any given conditions. As the magnitude of the offset increases, the peak gradually broadens, until, at about 30 per cent. offset, it splits into two peaks. The presence of d.c. offset causes deactivation of the electrodes; not only is the relaxation following a concentration perturbation lengthened, but also, after some time, the initially bright and shiny electrodes assume a dull matt surface.With no d.c. offset, potentiometric and periodic end-points agree, but a deviation arises with d.c. offset and increases with increase in d.c. offset. A d.c. offset a d.c. component in the periodic output. I P oten t io me t r IC 1401 ejd-puin:; 120 in the periodic input produces Volume of cerium(lV) added/ml ---t Fig. 2. Variation of the peri- odic differential electrolytic potenti- ometric titration curve with increas- ing d.c. offset in the input signal. Expanded scale end-point region. Titration of 200 ml of 0-0125 M iron(I1) in 0.5 M sulphuric acid with 0.1 M cerium(1V). Sine wave, 3 Hz, r.1n.s. current density, 25 pA cm-2: (a), 2 per cent. d.c. offset; ( b ) , 5 per cent. d.c. offset; and (c), 40 per cent. d.c. offset Further titrations were then performed with periodic inputs containing an increasing time bias, and the deterioration in the periodic output was similar to that above with d.c.offset, although instrumental limitations at the time prevented examination of biasses above 20 per cent.772 BISHOP AND WEBBER : DIFFERENTIAL ELECTROLYTIC [Analyst, Vol. 98 Examination of the effect of offset and time bias was extended to reactions of type I1 (a) [titration of iron(I1) with dichromate] and type I1 (b) (titration of hydrazine with bromate). The results were again similar to those described above for d.c. offset in the titration of iron(I1) and cerium(1V). With increasing bias, the curves became less sharp, the discrimina- tion deteriorated and the periodic end-point deviated increasingly from the zero-current potentiometric end-point.Finally, the influence of d.c. offset on the electrodically fastest reactions, those of the titration of copper(1) with potassium bromate, was examined. The d.c. differential electrolytic potentiometric peak height is 600 mV at 1.0 p A cm-2, and a solution as near as possible to equivalence was prepared (platinum potential versus S.C.E. 520 mV) and a periodic signal of increasing d.c. offset applied to two electrodes; the amplitude of the square wave was maintained constant and the peak to peak output was measured on the oscilloscope. The results are shown in Table I, and indicate that for very fast charge-transfer processes an appreciable d.c. offset at fairly high frequency is necessary before significant reduction in the, probably already clipped, peak potential occurs, although eventually curve splitting into two peaks, as in Fig.2, occurs. TABLE I VARIATION OF PEAK POTENTIAL FOR AN ELECTRODICALLY FAST SYSTEM Applied signal: 10-Hz square wave; ballast resistance 5 x lo6 SZ; current density 10 pA cm-2 WITH INCREASING D.C. OFFSET +41 +42 +43 $48 $50 { 2:; -39 -38 -37 -32 -30 Applied signal/V . . Output signal/mV . . .. 275 275 275 270 200 170 It is therefore abundantly clear that any departure from pure, symmetrical, bias-free periodic waveforms,2 whether d.c. offset, amplitude or time bias, or distortion will cause a deterioration of the periodic output potential titration curve, and appreciable departures will seriously attenuate the precision and discrimination and introduce errors. THE D.C.OUTPUT COMPONENT FROM BIASSED OR OFFSET PERIODIC POLARISATION- By using a d.c. measuring device with a time constant that is long compared with the repetition frequency of the periodic polarising current, any d.c. component can be detected in the output. For an internal or external d.c. offset, the d.c. output produces a differential electrolytic potentiometric curve that is identical with a titration curve produced by classical d.c. differential electrolytic potentiometry at the same current density, but with the differences that in the former instance the electrode response is much faster and the electrodes retain their activity for a longer period. Time biassing, however, produced results of greater benefit and considerable interest.TIME-BIASSED PERIODIC DIFFERENTIAL ELECTROLYTIC POTENTIOMETRY- The periodic component of the output from this biassed waveform showed the usual deterioration and error with increasing bias, but the d.c. component proved to have unique and valuable properties. The range of bias available at the time was too small to permit proper investigation of the effect of its magnitude, and so a 5 per cent. bias was selected for examination, and the d.c. current density arbitrarily assigned a value of 5 per cent. of the periodic r.m.s. current density for comparison purposes. Titrations at customary concentrations-With the time-biassed input, examples of each type of oxidation - reduction reaction were examined, and the precision, accuracy and dis- crimination were compared with those of d.c.and symmetrical periodic differential electrolytic potentiometry. Curves obtained at optimum or near optimum electrical conditions are shown in Fig. 3, on an expanded volume scale in the end-point region, for type I, I1 (a) and I1 ( b ) reactions. The titration curves were appreciably sharper, by a factor of about two, than the corresponding d.c. differential electrolytic potentiometric curves of equivalent peak height, with slopes in excess of 50 000 mVml-l, and also sharper than the symmetrical periodicNovember, 19731 POTENTIOMETRY WITH PERIODIC POLARISATION. PART XXIII 773 3 480 differential electrolytic potentiometric curves. The response of the electrodes to a concen- tration perturbation by an increment of titrant in the region of the equivalence point was extremely rapid and considerably faster than for the classical d.c.differential electrolytic potentiometry, by a factor in excess of ten; this result was confirmed by making potential measurements at 5-s intervals. The increase in response speed was most marked with the type I1 reactions, and is of great benefit. In the iron(I1) titration with cerium(1V) after the end-point, although the speed of response remained, potential drift still occurred, which is indicative of changing charge-transfer kinetic parameters ; it is possible that gold electrodes could be used with benefit in this titration. The titration curves were independent of the frequency used, over the range from 3 Hz to the upper limit of the generator (1200 Hz), and of the waveform used, whether it was square, sine or triangular.At frequencies below about 20 Hz, the mean periodic potential output traced a curve of the same form as the d.c. potential. However, it was again found that in titrations of iron(I1) with cerium(1V) or chromium(VI), the d.c. and periodic peaks failed to coincide. There was again a difference of about 0.01 ml in a 25-ml titration, the pure periodic output peak and the time-biassed d.c. output peak coinciding with the zero-current potentiometric inflection point, and coming before the classical d.c. differential electrolytic potentiometric peak obtained from other electrodes in the same titration. No such differences were found in any of the other titrations examined; all four end-points coincided.Titrations at lower concentrations-Many different titrations were satisfactorily performed with time-biassed differential electrolytic potentiometry at concentrations down to times those just discussed, but the particularly intractable titration of iron(I1) with cerium(1V) was chosen for extensive examination, together with classical d.c. differential electrolytic potentiometry and zero-current potentiometry. 5 x low3 and 5 x 1 0 - 4 ~ cerium(1V) are shown in Fig. 4. The results of these and other titrations are given in Table I1 for titrant concentrations in the region of l O V 4 ~ . The assigned current densities at 5 per cent. bias are again 5 per cent. of the r.m.s. Deriodic current density. Titrations with 5 x 320 280 240 200 160 > E .- + c n 4 120 -0 8D 40 - - - - - - - -.450 300 0 . L - (b 1 - 420 360 300 240 180 120 60 Volume of titrant added/ml- Fig. 3. Titration curve forms ob- tained by using time bias; end-point region on an expanded volume scale. Sine wave, 100 Hz, 5 per cent. mark-to- ‘space bias, resultant mean d.c. density 1.0 pA cm-a: (a), titration of 200 ml of 0.0125 M iron(I1) in 0.5 M sulphuric acid with 0.1 M cerium(1V); (b), titration of 200 ml of 0.0125 M iron(I1) in 0.5 M sulphuric acid with 0.016 67 M chromium- (VI) ; and (c) titration of 200 ml of 0.003 M hydrazine in 0.1 M potassium bromide and 2-5 M hydrochloric acid with 0.01667 M potassium bromate 300 >E 200 r- .- + C + a -=f 100 a 80 a) 60 - 40 - -- I 1 .o 1- Volume of titrant addedhl- Fig. 4. Time bias d.c. differential electrolytic potentiometric curve forms in the expanded end-point region for lower titrant concentrations.Sine wave, 100 Hz, 5 per cent. mark-to-space bias. Titration of 200 ml of iron(I1) in 0-5 M sulphuric acid with cerium(1V) a t various concentrations and assigned current den- sities. Assigned (Celv]/ d.c. density/ mol 1-1 pA cm-8 CFeIII I Curve mol 1-1 6.25 x 10-3 5 x 10-2 1.0 (a) 6-25 x 10-4 5 x 10-3 0.25 6-25 x 10-5 5 x 10-4 . 0.10 (b) (4774 BISHOP AND WEBBER : DIFFERENTIAL ELECTROLYTIC [Analyst, Vol. 98 TABLE I1 TITRATIONS AT LOW TITRANT CONCENTRATION BY TIME-BIASSED DIFFERENTIAL ELECTROLYTIC POTENTIOMETRY . Current density/ Standard Reaction* pA cm-a Titrelml deviationlml 0.1 21.64, 21.59, 21.63, 21.60, 21.60, 21-58 0.02 0.1 23-11, 23.14, 23.12, 23.17, 23.10, 23.14 0.025 0.1 24.48, 24.53, 24.49, 24.47, 24.48, 24.52 0.02 (4 (b) (4 * (a) Titration of 200 ml of a 6.25 x with 5 x lo-* M cerium(1V).(b) Titration of 200 ml of a 1.25 x with 1.67 x M chromium(V1). (c) Titration of 200 ml of a 3 x 2.5 M hydrochloric acid with 1.67 x M solution of iron(I1) in 0.5 M sulphuric acid M solution of iron(I1) in 0.5 M sulphuric acid M solution of hydrazine in 0.1 M bromide plus M bromate. Even with titrant concentrations of 5 x M, the discrimination was still of the same order (about 0.15 per cent.) as the inherent volumetric error, but better than that for d.c. differential electrolytic potentiometry by a factor of about five and much better than that for pure symmetrical periodic polarisation (Fig. 5, reference 2). The response speed of the electrodes, judged by measurement of the time required to reach equilibrium, and the stability of the potentials showed a marked improvement over d.c.differential electrolytic potentio- metry at this concentration level. In Fig. 4, it can be seen that there is an increasing tendency towards type I1 ( a ) curves as the reactant concentrations decrease. This effect arises from the slowing down of the charge-transfer processes, particularly of cerium, on account of the decrease in the concentration terms in the charge-transfer equation and consequent increase in ria. Results for type I1 ( a ) and I1 (b) reactions are given in Table 11; the discrimination was of the same order as for the titration of iron(I1) with cerium(1V) and about twice as good as for d.c.differential electrolytic potentiometry. There was also a marked improvement in response speed and stability of the resultant potentials compared with d.c. differential electrolytic potentiometry. In order to investigate further the prevention of electrode fouling by time-biassed signals, titrations of iron(I1) with 5 x ~ O - * M cerium(1V) solution were performed by the classical d.c. differential electrolytic potentiometric method, and also with a balanced periodic signal of various frequencies of approximately the same r.m.s. current density, 20 p A cm-2, superimposed on the d.c. signal. This produces a synthetic amplitude biassed, but un- symmetrical, signal. There was no appreciable difference in electrode response speed after concentration changes, or any increase in the duration of electrode activity.The effect is similar to, but more deleterious than, that of d.c. offset signals. The special benefits of the time-biassed signal must therefore reside in its particular characteristic of equal anodic and cathodic current excursions of unequal duration. EXPLANATION OF THE SYSTEMATIC ERRORS IN D.C. DIFFERENTIAL ELECTROLYTIC POTENTIO- The systematic errors reported, but not recognised as such, at an early stage,5 occur in titrations of iron(I1) with cerium(IV), chromium(V1) and vanadium(V) , and are real errors as shown by the pipette dilution method2J in which the equivalence point region is traversed in very small increments with diluted titrant. The first peak occurs with symmetrical periodic polarisation and coincides with the d.c.output peak from time-biassed periodic polarisation, both of which coincide exactly with the zero-current potentiometric inflection i n cerium(1V) and chromium(V1) titrations, and these are followed after a voluiiie interval of 040.5 to 0.05 ml (depending on the degree of deactivation of the electrod2s) by the d.c. differential electrolytic potentiometric peak. In vanadium(V) titrations, the zero-current potentiometric inflection comes first, and d.c., symmetrical periodic, and time-biassed periodic d.c. peaks appear simultaneously after an interval that increases with the speed of the titration, i.e., with decreasing dwell time after the addition of an increment oi titrant. Each of the three errors has a different explnnation, none of which could be predicted by computer simulation with the program DEP 10.METRY WITH CERTAIN TITRANTS-Novzmber, 19731 POTENTIOMETRY WITH PERIODIC POLARISATION. PART XXIII 775 Ceriztm(IV)-On adding an increment of titrant immediately after the end-point, as indicated by the time-biassed differential electrolytic potentiometric output, the classical d.c. differential electrolytic potentiometric potential, E,, was observed at first to drift down- wards, but then drifted back upwards until EA became greater than it had been before the addition of the tiny increment of cerium(1V). This behaviour continued for several minute increments, equivalent to 0.0005 or 0-005 ml of the original titrant, after equivalence, so making it difficult to locate the end-point precisely.If the latter be taken as the point at which up-and-down drift of EA after addition of an increment changes to a down-and-up drift, then equivalence and end-points agree, but if the cessation of the drifting is awaited, a positive error of about 0.04 to 0.08 per cent. arises. This error is usually recorded because d.c. differential electrolytic potentiometry, like zero-current potentiometry, is essentially a pseudo-equilibrium technique, whereas the error-free, time-biassed periodic d.c. and the symmetrical periodic potential methods are highly dynamic. The d.c. differential electrolytic potentiometric behaviour is ascribed to a change in the nature of the anode surface when exposed to a minute excess of cerium(IV), leading to a decrease in k and a change in cc so that charge-transfer overpotential, q a , builds up.This process continues as the cerium(1V) concentration increases, the increase in q a being greater than the decrease in qc, until the charge-transfer rate parameters stabilise, and EA decreases as qc falls, but leaving a residual after equivalence. Even with freshly activated electrodes, charge-transfer overpotential is always manifest after the end-point in a cerium(1V) titration, as witness the titration curves for any of the methods. The drifting mentioned does not occur with the time-biassed periodic d.c. output peak, unless the titration is held just past equivalence for many hours; with long waiting periods, the time-biassed periodic d.c. outpeak peak can be persuaded to coincide with the classical d.c.differential electrolytic potentiometric peak, Normally, however, the periodic input current is comparatively large, and so the equilibration of the d.c. potential is very rapid, and the periodicity of the polarisation considerably delays the deactivation of the electrode. Chromiztm(1V)-With this titrant, the error arises from specific adsorption of chro- mium(V1) on the anode surface.6 This adsorption has been shown to be concentration- dependent and to occur at low dichromate concentrations. The adsorption therefore increases as the concentration of excess dichromate builds up after equivalence to the point of complete electrode coverage, and this point corresponds to the false, late d.c. differential electrolytic potentiometric end-point, The specific adsorption is encouraged by electrosorption on the anode, and the conditions at the anode surface represent a progressively more oxidising situation than mass transfer from the bulk of the solution would predict.Again, the accelerated potential equilibration of symmetrical periodic and time-biassed periodic polari- sation are antagonistic to the slow adsorption process, and the large r.m.s. current densities and the periodicity of the polarisation minimise the adsorption and its effect. Vanadium( V)-In this instance, classical d.c., symmetrical periodic, and time-biassed periodic d.c. output differential electrolytic potentiometry all give the correct answer; it is the zero-current potentiometric inflection that is wrong. As an electrode kinetic study of the vanadium(V) - vanadium(1V) system has shown,6 the charge-transfer process is very slow; the exchange current is very small, and so relaxation of the zero-current potential after a concentration perturbation by the addition of an increment of titrant is very slow.It has been reported6 that the zero-current potential, even in heavily poised solutions equi- molar in the two oxidation states, takes an excessive time to reach equilibrium. If, as is commonly the practice with titrimetric reactions of reasonable Q values, “equilibrium” is interpreted as a drift of less than 1 mVmin-l, then the pseudo-equilibrium potential will lag behind the true equilibrium potential by a significant amount, especially in the equiva- lence point region where concentrations are low. The zero-current potentiometric curve therefore rises (or falls) prematurely and the inflection is early.That this fact has not previously been recorded is surprising; zero-current potentiometry has been accepted as the reference method in the titrimetric determination of vanadium for many decades. It can only be concluded that sufficiently pure vanadium and iron compounds have never pre- viously been matched to reveal this, admittedly small, systematic error. It has also been shown that vanadium species, predominantly vanadium(V), are adsorbed on electrodes,G and this adsorption aggravates the deviation explained above. That twin polarised electrodes give the correct answer arises from the enhanced rate of potential equilibration under the776 BISHOP AND WEBBER passage of current , and periodic polarisation further minimises adsorption and encourages the retention of electrode activity.CONCLUSIONS No previous examination of the various types of d.c. bias or of the form and accuracy of the titration curve has been reported, nor, with one exception,l has any effort been made to detect or eliminate d.c. bias. Any form of bias or distortion causes a deterioration in the periodic titration curve as well as introducing errors of end-point location, and, with d.c. offsets, marked electrode deactivation. For optimum results, the periodic waveform must be accurately shaped so as to remove all trace of offset, bias and distortion. There is then no d.c. component in the periodic output, but the presence of even traces of such deviations produces a d.c. output as well as. a periodic output. The most important result of this investigation is the discovery of the unique properties of time-biassing of the periodic signal. Such an input produces a d.c. differential titration curve that shows an improvement in precision and discrimination over both classical d.c. differential electrolytic potentiometry and symmetrical periodic differential electrolytic potentiometry. It retains the advantages of periodic differential electrolytic potentiometry in a great improvement in electrode response speed, stability of the electrode potentials and minimisation of electrode fouling and deactivation. The alternating anodisation and cathodisation of each electrode keeps it active, while the large over-all impressed current density accelerates the electrode response. Both of these factors are important, particularly in dilute solutions, in automatic operation and process control. Also, as with symmetrical periodic polarisation, the end-point is brought into agreement with the equivalence point. Errors that arise in d.c. differential electrolytic potentiometry with cerium(1V) and chromium(V1) titrations, and in zero-current potentiometry with vanadium(V) titrations, have been satisfactorily resolved from electrode kinetic studies. REFERENCES 1. 2. 3. 4. 5 . 6 . Doss, K. S. G., and Agarwal, H. P., Proc. Indian Acad. Sci., 1951, 34, 263. Bishop, E., and Webber, T. J. N., Analyst, 1973, 98, 712. -,- , Ibid., 1973, 98, 697. Bishop, E., in Shallis, P. W., Editor, “Proceedings of the SAC Conference, Nottingham, 1965,” W. Heffer & Sons Ltd., Cambridge, 1965, p. 416. Bishop, E., Analyst, 1958, 83, 212. Bishop, E., and Hitchcock, P. H., Ibid., 1973, 98, 563. NOTE-References 2, 3, 4 and 5 are to Parts XXII, XXI, XVII and 11, respectively, of this series. Received March 5th, 1973 Accepted A p d 12th, 1973