June, 19501 AIREY AND SMALES 287 Mercury Drop Control : Application to Derivative and Differential Polarography BY L. AIREY AND A. A. SMALES SYNoPsIs--Controlled disengagement of a mercury drop may be achieved either by the abrupt application of an electrical pulse to reduce the interfacial tension, or by a small lateral movement of the capillary, effectively “shearing” the drop from the mercury thread. The fundamentals of the two techniques are examined and it is concluded that the mechanical method possesses marked advantages. The modification of a standard Cambridge polarograph to permit operation either normally or as a bridge circuit for multiple electrode work, as required, is described and illustrated. The performance of the bridge circuit as used for both derivative and differential workipg is examined theoretically and practically.Illustrative examples of the utility of the two techniques are given. Possible future developments are briefly discussed and some observations on the Ilkovic equation are included. DURING the past few years several investigators1 p2 93 v4 15 have published details of bridge circuits incorporating two dropping-mercury electrodes. The general applicability of these methods, however, has been somewhat restricted by difficulties in the synchronisation of the drop rates. Heyrovskyl attempted to eliminate the objection by the use of streaming-jet mercury electrodes; these are fairly satisfactory in theory, but in practice are cumbersome. Rapidly dropping electrodes (approximately 1 sec.) have also been employed by the same author, with some success.Lingane,* in his review of polarographic development, comments that some means of synchronising the drop rates in these circuits would be a useful improvement in technique. Muller’ has observed that “knock off drops” have been made, but at present are in the category of laboratory toys. SevcW reports the use of electrical pulsing as a means of drop synchronisa- tion in his work on cathode ray polarography. This paper considers the problem of mercury drop control from three angles, vix. (a) fundamental principles governing the method, (b) the application of the technique to standard polarographic equipment, and ( c ) applications based upon nonstandard apparatus. FUNDAMENTALS OF DROP CONTROL Two general methods may be envisaged for inducing the disengagement of a pendant mercury drop from a capillary tube.Either the surface tension may be abruptly reduced to a value which renders the drop unstable, or the shape of the drop may be changed to such an extent that a condition of instability is attained. The primary process of severance from the capillary thread is the result of surface tension forces : gravitational action removes the drop from the vicinity of the capillary tube. The reduction in surface tension required288 AIREY AND SMALES : MERCURY DROP CONTROL: APPLICATION by the first method is obtained by a change of the electrical potential difference between the mercury and the solution: the distortion of the drop in the second method by a movement of the capillary tube.The two techniques are conveniently designated “electrostatic” and “electromechanical’ ’ respectively, and will be considered separately under those headings. ELECTROSTATIC CONTROL- The variation of the interfacial tension between a mercury drop and a salt solution theoretically provides a means of producing instability under any conditions. In practice, however, the extent to which the potential difference between the drop and the solution may be changed is determined largely by the presence and nature of the ions in solution. The mechanism of the process can be understood by reference to Fig. 1, which depicts the equivalent circuit of the cell assembly. If we assume an electrolyte of dilute hydrochloric acid, the passage of an electron current from B to A will charge C,; R, is practically infinite.The potential of C, will build up to a value of about 1 volt, and then reduction of hydrogen ions will commence; R, now has an appreciable finite value, which will vary somewhat as a diffusion gradient is produced. To obtain any further potential change across C,, the impressed current must be much increased because the shunting action of R, is dispropor- tionately increased with an increase of applied potential. [Vol. 75 c, C, R, R3 Fig. 1. C, Anode double layer capacitance C, R, Anode leakage resistance R, Cell electrolyte resistance R, Mercury drop leakage resistance R, Capillary thread resistance Simple equivalent circuit of polarographic cell Mercury drop double layer capacitance The presence of such a large steady current in a cell would be highly objectionable, as it causes changes in local concentration, hydrogen evolution and heating effects, particularly in R,.A practicable compromise is to discharge a condenser through the cell, giving a momentarily large current. A value of 0.1 microfarad at a potential of up to 250 volts has been found suitable when using a mercury pool. anode. If R, is increased by the use of an agar bridge, greater voltages would be needed, with attendant heating effects. Fig. 2 shows a series of instantaneous photomicrographs of a freely falling mercury drop. The salient fact is that during the last stages of its growth a drop assumes a pear shape, rupture occurs at the rapidly constricting neck and, after a few oscillations, a spherical shape is recovered within a few milliseconds. It is inferred that the elongated shape is an indispensable condition for detachment (assuming that reduction of interfacial tension nearly to zero is impossible).Hence, although a small abrupt change of potential during the last 10 per cent. or so of the life of a drop may be sufficient to detach it, the problem of detaching the drop is much more difficult during the early stages of growth. Not only must the change of interfacial tension be greater (k, a greater change of potential difference) but the reduction must be maintained for a longer time-sufficient, in fact, to allow the nearly spherical drop to extend to the required pear shape. In the presence of large con- centrations of hydrogen ion, e.g., in normal acids, it is frequently impossible to effect this without the simultaneous evolution of large amounts of hydrogen and disruptive heating of the capillary thread.In the practical utilisation of this method, it would be very desirable to be able to main- tain a constant drop time of about 3 seconds over the range 0 to -2 volts. If a time of free fall of 3 seconds at -2 volts is assumed, the drop rate at -0.6 volts would be about 6 seconds, and in acid solutions it would be quite impossible to disengage the drop after only 3 seconds of life. This applies with rather more force to the synchronisation of two approximately equal drops. Figs. 5 (a) and ( b ) respectively show the Ilkovic curves obtained at a freely falling drop and at a drop synchronised electrostatically to an external timing unit.The curves wereFig. 2. Instantaneous photomicrographs of a freely falling mercury drop Fig. 1. lnstantaneous photomicrographs of a mechanically disengaged dropFig. 3 (a). Pulsa,tor unit Fig. 7 (b) . Modified Cambridge polarographJune, 19501 TO DERIVATIVE AND DIFFERENTIAL POLAROGRAPHY 289 described on a cathode ray tube, using a modified version of the equipment designed by Randles,* and photographed in the usual way. It can be seen that some distortion of the curve is produced by the electrostatic control. The cause is rather uncertain, but is probably associated with convection stirring, which will be described later. In spite of this modification of shape, the reproducibility is good (the diagram shows a single curve only).In conclusion, it should be noted that the galvanometer in the circuit must be paralysed and protected from the current pulses. The most convenient method is to short-circuit the galvanometer with a relay operated slightly in advance of the one that injects the pulse. Some care is necessary in the disposition of the apparatus with respect to stray A.C. magnetic fields, or mechanical rectification of the induced alternating current may occur, and give rise to random fluctuations on the galvanometer. For cathode ray polarographic circuits, protection is unnecessary. ELECTROMECHANICAL CONTROL- Two possible motions of the capillary tube may be envisaged, vix., (a) vertical axial displacement, effectively “stretching” the drop, and (b) lateral movement, “shearing” the drop from the capillary thread.The primary requirement is that any such motion shall cause the minimum of stirring in the solution, and since effective disengagement is only produced by a rapid movement of the capillary tip, the shearing action is the only practicable method. Fig. 3 shows the apparatus by which this may be achieved. The upper end of the capillary tube (or tubes) is clamped rigidly to the armature of a small electromagnetic relay divested of its contacts. The relay is held open by adjustable springs, and a screw stop provides means for adjusting the travel of the armature. A small piece of thin sheet rubber, about 1/32-inch thick, is inserted into the gap to form a resilient buffer, and the adjusting screw is tightened until the rubber is lightly gripped.If the rubber buffer is omitted, it will be found that the working gap is only of the order of a few thousandths of an inch and, although initially the action may be quite satisfactory, such a small gap soon becomes wedged open by particles of almost impalpable dust. The electromagnet is “pulse” energised by the discharge of a 4-microfarad condenser. By tightening the adjusting screw of the relay armature, a condition is attained in which each discharge produces a very rapid lateral movement of the capillary tip of about 0-2 mm., followed by a highly damped oscillatory recovery. Under these conditions, which are not critical, mercury drops may be cleanly detached at any stage of their growth and under any conditions of polarisation or current flow. Fig.4 shows two typical instantaneous photomicrographs of the detachment of mercury drops at different stages in their lives. The rapidity of the process is apparent from the absence of any trace of the succeeding drop. The freedom from any marked distortion of the falling drop suggests that there is little turbulence produced by the movement. Fig. 3 (a) is a photograph of a pulsator, as it is convenient to name the unit, together with the Post Office type relay from which it was made. The real value of the latter as a starting-point lay in the facts that the yoke is made of high permeability iron showing low residual magnetism and that the “knife edge” method of supporting the armature is ideal for this purpose, permitting easy removal whenever desired.Other parts of the relay are discarded. Mainly for reasons of compactness, the 100-ohm latch-relay coil from a Siemens uniselector switch (standard Post Office equipment) was used. Included in Fig. 3 (b) is a simple control circuit. The only important requirement is that the discharge of the condenser through the pulsator coil shall be abrupt and unhindered by such features as poor contact or “bouncing” of the relay. The latter is very detrimental to the regularity of the galvanometer oscillations. The authors use as a timing control a small geared-down Klaxon split-phase (constant speed) motor to which has been fitted a pair of contacts and a cam. Closing of the contacts operates the relay which discharges a 4-microfarad condenser through the pulsator coil. Very little power is consumed in operating the contactor and the type of motive power for this is not of great importance.Electronic control of the relay by means of a multivibrator circuit has been successfully used and possesses the advantage of easy variation of drop time. Figs. 5 (d) to (f) show the Ilkovic curves delineated as described above, using electro- mechanical control with variable timing. The curves were obtained with the optimum setting of the pulsator and by comparison with Fig. 5 ( c ) , the curve for a freely falling drop, The type of coil used is not very important.290 AIREY AND SMALES : MERCURY DROP CONTROL APPLICATION [Vol. 75 it wilI be seen that the stirring effect is quite negligible, and that the four curves are all congruent within the common portions.Figs. 5 (g) and (12) illustrate the effect of progressively increasing the movement of the capillary tip to 1 to 2 mm. Figs. 5 (i) and ( j ) are curves obtained from a thallium solution in the absence of maximum suppressor, with and without tY t Fig. 3 ( b ) . Pulsator (section) and control circuit A Adjusting screw B Armature - pole face gap. Sheet rubber insertion M Motor driven contactor C R Potentiometer 50,000 ohms w/w R, 20,000 ohms W Westinghouse rectifier, H 100 Paper condenser, 4 pF., 600 v. wkg. RELAY. P.O. type 10,000-ohm. coil, tungsten contacts drop control respectively. Three curves at corresponding potentials are shown in each figure. The experiments were carried out to ascertain wht':her the initial slight stirring during drop disengagement modified in any .way the stirrhg present during maximum production.The latter stirring is always very irregular, and the photographs from which the figures were prepared suggest that there is no marked effect. Fig. 6 shows some typical curves obtained on a Cambridge polarograph using a drop controlled as described. The regularity of the drop wave is quite satisfactory, and under conditions of constant rate of mercury flow, the variation of wave height with drop time is clearly seen. Reference will be made to this and similar experiments when the IlkovicJune, 19501 TO DERIVATIVE AND DIFFERENTIAL POLAROGRAPHY 29 1 I Fig. 5 (a). Free fall Fig. 5 (b). Electrostatic control I Fig. 5 (c). Free fall, t = 4 sec. 1 Fig. 5 (d). Electromechanical control, t = 3-5 sec.Fig. 5 (e). Electromechanical control, t = 2.5 sec. Fig. 5 (f) . Electromechanical control, t = 1.5 sec. .Fig. 5 (g) . Electromechanical control. Increased amplitude of capillary movement Fig. 5 (k) . Electromechanical control. Increased amplitude of capillary movement292 AIREY AND SMALES : MERCURY DROP CONTROL: APPLICATION equation is discussed, At the optimum settin,g of the pulsator, relatively large variations in the electrical energy in the condenser (f50 per “cent.) are practically without effect on the wave; an increase in capillary movement results in a slight increase in the step height antl in extreme cases to some “raggedness” of the wave top, as might be anticipated from the Ilkovic curve shown in Fig. 5 (h). It is estimated that an increase in capillary-tip displace- ment of 10 times produces approximately a 2 per cent.increase in wave height. Control to within 0.5 per cent. should be maintained with ease. [Vol. 75 9 Fig. 6 (i) . Electromechanical control. Three curves, (a) preceding maximum, (b) at maximum and (c) following maximum maximum Fig. 5 ( j ) . Free fall. Three curves, (a) preceding maximum, (b) a t maximum and (c) following The magnetic field of the pulsator will induce an oscillatory current in the electrodes and associated wiring. It is desirable that this should decay to zero before the drop is detached, or else partial mechanical rectification may occur, leading to the possibility of erratic fluctua- tions of the galvanometer. Precise data are not available, but this factor will probably set an upper limit to the speed of action (i.e., time between injection of pulse and disengagement of drop) of a pulsator, and it should be considered in any future designs.APPLICATIONS INVOLVING STANDARD POLAROGRAPHIC EQUIPMENT I t will be appreciated from the above that of the two methods of drop control, the electromechanical is much the more practicable. A limited success has been obtained in the use of the electrostatic method on the cathode ray polarograph, but continuation of this work is not envisaged. A single controlled capillary, used in conjunction with a conventional type of polarograph, may have limited advantages in so far as the product mitt is then independent of the applied potential. Furthermore, provided that a suitable capillary is chosen, the variation of t with capillary-active substances--e.g., proteins-may be obviated.The real value of the control scheme however, lies in the ease with which two capillaries may be accurately synchronised, and following from this, it is profitable by slight modifications and additions to extend the versatility of commercial polarographs. The circuit of the Cambridge polarograph is suitable for modification to bridge working. Fig. 7 (a) shows the electrical modifications madLe; Fig. 7 (b) shows the spatial arrangement of the additional components within the instrument. Apart from a pulsator, a controller, and a suitable stand for holding two capillaries, a large 2500-ohm potentiometer (standard electronic component) and a 2-volt accumulator are required.A change from normal working to bridge conditions is effected simply by the operation of the 6-circuit switch (standard Post Office equipment). On the latter setting, change from derivative to differential working is effected simply by moving the wander lead on the delay voltage potentiometer to the zero position. To compensate for variations in the e.m.f. of the 2-volt accumulator, a small variable resistance is included in this latter circuit. A 1-volt tap is taken from this network via a press-button switch to the wiping contact of the main drum potentiometer. With this set at 1 volt, any lack of equality in the two potentials will cause, on operation of the push- button, a deflection of the instrument galvanometer. Adjustments are made to the 50-ohm variable resistor in the delay voltage circuit until balance is attained. A precision of 1 per cent.is realisable, but the ultimate reference standard is the current milliameter on the instrument. Alternatively, for work of very high accuracy, the circuit could be standardised by the use of a Weston cell and an additional galvanometer.June, 19501 TO DERIVATIVE AND DIFFERENTIAL POLAROGRAPHY 293 No information on the circuits of other types of polarographs is accessible, but it is con- sidered that modifications such as the ones described should be quite practicable. For convenience and neatness, the circuit diagram of the Cambridge instrument is not identical with the wiring layout. Fig. 7 (a). P = standardising press switch Circuit diagram of modified polarograph Additional circuits shown dotted.Switches S1, S2, S3, S4 and S5 ganged on one frame. A Polarographic cell position-normal working B Polarographic cell positions-derivative and differential working DERIVATIVE POLAROGRAPHY- Following Heyrovsky, derivative polarography is defined as polarographic work involving the automatic production and delineation, with respect to the applied voltage, of curves representing the slopes of normal waves. In contrast , differential polarography involves the elimination or minimisation of unwanted waves or residual currents by automatic subtract ion. The simple circuit described by Heyrovsky,l while adequate to illustrate the principle of the method, is unsuitable for general analytical purposes. Reference to Fig. 8 (a) will show that there is a steady current through the galvanometer even when connections are not made to the electrodes.The actual difference in potential between the two dropping electrodes is thus equal to the IR drop across the galvanometer resistance. Since it is very desirable to include the galvanometer in an Ayrton shunt circuit, and the net resistance of this varies with the setting, the true voltage difference, which we may designate as hv, becomes a function of the shunt setting. To this may be added the facts that there is a permanent deflection of the galvanometer, also variable with the shunt position, and that other than the torsion head there is no means of adjusting the zero.294 In the circuit of Fig. 8 (b) these inconveniences are all avoided, although an additional source of e.m.f.is unfortunately necessary. The tapped resistance provides values of Ahv from 0 to 50 mv. in nominal increments of 10 mv. AIREY AND SMALES : MERCURY DROP CONTROL: APPLICATION [vol. 75 (4 (b) Fig. 8. (a) Heyrovsky derivative circuit, and (b) modification Making the assumptions of identical electrodes and equality of bridge arms, a simple theoretical analysis of the circuit performance may be made. Differentiating the fundamental equation12 we have- i E = E, - QT log - nF z D - i where- E = E i = i = i, = Q = % = applied potential half-wave potential number of electrons in reduction current flowing limiting current gas constant and, re-arranging, at the half-wave potential, i.e., where i = &,, we have- Let Av be the applied delay voltage and let 6v be the voltage drop across the galvanometer network in consequence of the current flowing.Approximating the central portion of a polarogram to a straight line, the following equations hold when 6v is a maximum nF ( h v - Sv) .. * * (1) a 3 = - ' :{ I - - 2QT -T) .. .. Applying the Kirchoff laws to the network, substituting and simplifying, we have- -Fig. 6. Normal polarograms, electromechanical drop control, of 0.001 M cadmium in solution containing 0.5 M potassium chloride + 0.01 per cent. of gelatin. S = 1/50 Curve . . . . A B C D E F t, sec. . . . . 3.90 3.05 2-50 1.93 1.50 1.00 Fig. 13. Normal and differential polarograms of 8 x 10-5 lead in solution containing 0-25 M potassium nitrate + 0.01 per cent. of gelatin. Curve A, simple polarogram; curve B, residual current; curve C , applied counter current; S = + curve D, differential polarogramFig.9 (b) Fig. 9 ( L ) Derivative polarograms of 0.001 A1 cadmium in solution containing 0.5 &I potassium chloride + 0-01 per cent. of gelatin. S = 1/10. For details see opposite pageJune, 19501 TO DERIVATIVE AND DIFFERENTIAL POLAROGRAPHY 295 The significant inferences to be drawn from this equation are as follows- (a) If other factors are constant, i, cc Av. Ignoring the second term in the denominator (it is shown below that it may be neglected) and if other factors are constant, ( b ) i, cc n. (c) Similarly, i, oc 2RI 2R1 + R' Since R is variable with shunt setting, the total sensitivity will thus be compounded of a shunt sensitivity and a network sensitivity.(d) If other factors are constant, i, is not strictly proportional to i,. If (d) is considered in more detail it will be seen that the magnitude of the error depends upon the product i, x R. Approximate proportionality exists between i,, the maximum bridge current, and iD, the cell diffusion current, but a graphical plot of i, x R against iB would show discontinuities because it is necessary to reduce the sensitivity (and thus the value of R) whenever full-scale deflection of the galvanometer is attained. The magnitude Fig. 9. chloride + 0.01 per cent. of gelatin. (a) Effect of variation of Av Derivative polarograms of 0.001 M cadmium in solution containing 0.5 M potassium S = 1/10. (Facing this page) Curve . . . . A B C D E F Av, mv... 0 9 18.2 27.2 36.4 46-3 Curve . . . . A B C D (b) Effect of resistance in anode lead (Av = 18.2 mv.) Resistance, ohms 0 1000 5000 15,000 (c) Effect of bridge asymmetry (Av = 18.2 mv.) Curve . . .. A B C D E F Rl = R, R, < R2 Rl > R2 R, = R, 51 = p2 Y J -. ZD, = ZD, ZD, = ZD, i D l > ZD, $0, < ZDs R l i ~ , = R$D, Conditions of the error may be calculated in the following manner. For a two-electron reduction, the ratio of i, to i, is, with'the circuit constants shown, approximately 0.2. At any given setting of the Ayrton shunt, the bridge current giving full-scale deflection, together with the total resistance R, may be measured or calculated. The corresponding value of i, is then obtained from the ratio above and, hence, for full-scale deflection conditions the magnitude of the error fact or, nF i, 4m 2 2R1R - ? 2% + R may be computed.Proceeding on these lines, it has been calculated that for the particular gahanometer and circuit constants employed, the error factor is -0.7 per cent. at a shunt setting of 1, rising to -3.5 per cent. at a sensitivity of 1/1000. As an example, if a comparison were being made at S = 1/5 (error factor = 3.0 per cent.) between two solutions which should give deflections of 100 (full scale) and 50 respectively, the actual values obtained would be 97 and 49-25, as the error factor for the second peak is only 1-5 per cent. The observed ratio would be 1.97 instead of 2.00, an err0.r of only 1.5 per cent. A similar error occurs for other ratios. Furthermore, since i, a iB/n, the error factor, which is proportional to i, x n, will be proportional to i, and independent of n.The validity of relation (a) is shown by the results in Table I. The departure from proportionality at greater values of Av than 25 mv. is due to the non-linearity of the polaro- gram over such extended ranges. The derivative curves are presented in Fig. 9 (a) as typical examples of the performance of the apparatus. The effect of bridge setting on the over-all sensitivity is demonstrated by the results of Table 11. The constancy of the results in the last column is satisfactory. Verification of (b)296 AIREY AND SMALES : MERCURY DROP CONTROL : APPLICATION TABLE 1 VERIFICATION OF THE RELATION iBa Av Data from experiments similar to Fig. 9 (a) [Vol. 75 hv, Peak height, b/Av mv.h 0 0 9 16-2 1-69 18.2 30-'7 1.69 27.2 44.10 1.62 36.4 85.1 1-61 46.3 64.2 1.39 I has not been attempted and, for the particular instrument employed, the error in (d) is not of sufficient practical importance to justify the extreme accuracy which would be necessary to verify its existence by experiment. TABLE I1 RELATION BETWEEN GALVANOMETER DEFLECTION AND SHUNT SENSITIVITY Derivative polarograms for solution of 0-001 M cadmium in 0.5 M potassium chloride; Av = 18-2 mv., R, = 2000 ohms FOR BRIDGE CIRCUIT Shunt sensitivity, Peak height, S h R h 2 R , + R -x - h S S 2R, I 61.5 336 1-084 308 334 46.2 253 1.064 316 336 32-2 185 1.047 322 337 21.7 127 1.032 326 336 1/6 1/20 16.3 96 1.024 326 333 1/30 11.0 66 1.018 330 335 The over-all validity of equation (3) is demonstrated by the results of Table 111.It may be noted that the simple equation derived by Heyrovskyl does not adequately represent the behaviour of a derivative bridge circuit. TABLE I11 $0 1/16 VERIFICATION OF EQUATION (3) Solution of 0.001 M cadmium in 0.5 A l potassium chloride; t = 3.05 sec. iB i B Av, .-obs. - theoret. i D , iB, S R, 2% T p amps. p amps. ohms ohms mv. ZD iD 6.98 1.09 1/10 185 4000 21OC. 18.2 0.16 0.18 The postulated condition of identical electrodes is very rarely attained in practice. If the two diffusion currents are iD, and iDn it may be shown that, providing equation (3) is still valid and may be re-written as- Rxi,, = ?32iDt, &, is preferred to i,,, since R, is a fixed resistance). Note, however, that R, + R2 + R replaces 2R, + R in the denominator, which implies a changed bridge sensitivity. The effect of extraneous resistance in the circuit is dependent upon its position. If, for example, the resistance is common to the two cells, as in an agar bridge, the peak is merely widened.Fig. 9 (b) illustrates this. The instrument measures di/dV, where V is the potential difference across the mercury surface, but delineates it with respect to E , the total appliedJune, 19501 TO DERIVATIVE AND DIFFERENTIAL POLAROGRAPHY 297 potential. If, however, the position of the resistance is such as to produce bridge asymmetry, as for example, a very high resistance capillary, the unbalanced voltage drop either assists or opposes Av, with a corresponding change of peak height. Since i, is proportional to Av, the magnitude of such errors may be estimated by expressing the potential difference across the extraneous resistance as a percentage of Av. Ideally, both capillaries should have zero resistance; the usual value of about 50 ohms produces but negligible errors except at high currents.THE TECHNIQUE OF DERIVATIVE POLAROGRAPHY- Since, as is mentioned above, identical rates of mercury flow in the two capillaries would be improbable, the primary requirement is that the condition expressed by the equation R,&, = R&,* (see above) be established. Fig. 9 (c) shows a number of derivative polarograms obtained under conditions when this equation was not satisfied, together with one designed to prove its validity. In the latter case the recovery of the original shape will be observed.It will be seen that the curves obtained may, to a first approximation, be regarded as com- pounded of a derivative curve and a positive or negative differential polarogram (dotted curve). For small deviations from exact balance, the peak height measured from the fore- foot of the curve will be the algebraic sum of a derivative peak proportional to the concentra- tion of reducible ion and half of a differential wave, also proportional to the ionic concentration. Hence, except for the verification of equation (4), balance to within 5 to 10 per cent. is adequate. Necessarily, any such setting must be maintained constant for a series of experiments. The method of balancing the bridge assumes a primary polarographic curve of ideal shape.The applied cell potential is adjusted to 0.3 to 0.4 volt more negative than the half- wave potential, i e . , both electrodes are operating under conditions of limiting diffusion, and the variable resistance arm of the bridge is adjusted until there is no galvanometer deflection. In general, this must be done as a separate initial procedure, using some ion such as cadmium or thallium, as the derivative method is only of value when dealing with waves which are but poorly defined. I 2 i 3 i P 4 I 5 J Fig. 10 (a). Normal polarograms of lead + cadmium in 0.25 M potassium Cadmium, (1) 1 0 - 4 M , (2) nitrate + 0.01 per cent. gelatin solution. S = 1/10. 1-3 x lo-* M lead M , (3) 10-2M, (4) 10-1 M and (5) 1 M In other respects, the operation of the polarograph is similar to normal working. The slow recording speed must be employed, particularly when working at S = 1 owing to the sharpness of the peak.Additional damping may be secured by the use of the appropriate control, but a reduction in bridge sensitivity is simultaneously effected. Provided that the bridge resistances are all known and approximately constant, it is apparently (see Table 11) satisfactory to calculate the over-all sensitivity and make a correction table for the Ayrton shunt. Alternatively, calibration at each setting is feasible, although time-consuming. Illustrative examples of the possibilities of derivative methods are provided by Figs. 10 and 11. Fig. 10 (a) shows the ordinary polarograms of solutions of lead and cadmium in which the ratio of lead to cadmium was vaned from approximately 1/1 to l/l@.Figs. 10 (b) and (c) are the corresponding derivative polarograms, the experiment having been designed298 AIREY AND SMALES : MERCURY DROP CONTROL APPLICATION Fol. 76 to ascertain the point at which the simple proportionality between peak height and con- centration is vitiated by interference from the cadTmium peak. It will be seen that significant interference, due to a constant contribution from the fore-foot of the cadmium peak, only appears in the last example. Even under these conditions, an approximate correction for the 2 A ni Fig. 10 (b). Derivative polarograms of lead + cadmium in 0.25 M potassium nitrate + 0.01 per cent. gelatin solution. Av = 18.2 mv., S = 8 1 Cd = 104M Pb = 1.3 x M Pb = 3.9 x 104M 2 3 Cd = 104M Cd = 10-sM (A) Pb = 1.3 x 10-*M (A) Pb = 1.3 X lo-* M (B) Pb = 2.6 x 10-4 M (B) Pb = 2.6 X lO-"M ha/hb = 2.00 ha/hb = 2.00 A n I a 8 ~ 3 A 1 0 ?" Fig.10 (c). Derivative polarograms oE lead + cadmium in 0-25 M potassium nitrate + 0-01 per cent. gelatin solution. Av = 18.2 mv., S = 8 1 2 3 (A) Pb = 1.3 x lo-* M (A) Pb = 1.3 x M (A) Pb = 1.3 x lO4M (B) Pb = 2.6 X lO-4M (B) Pb = 2.13 x 10-4 M (B) Pb = 2.6 x 10-4 M Cd = 10-aM Cd = 10-IM C d = l M ha/hb = 1.99 ha/hb = 2.02 ha/hb = 1.88 interference could be obtained by making a 'blank measurement on a lead-free cadmium solution of equal concentration, Le., by subtracting the height of the cadmium peak fore-foot at the lead half-wave potential. Figs. 11 (a) and (b) respectively show the normal and derivative polarograms of lead in admixture with increasing amounts of thallium.The half-wave potentials of the two waves differ by 0.08 volt.June, 19501 TO DERIVATIVE AND DIFFERENTIAL POLAROGRAPHY 299 No consideration has been given to the use of the derivative curve for qualitative purposes. Corrections for delay voltage, net bridge resistance, cell resistance and other factors might be of importance. 2 I 4 Fig. 11 (u). Normal polarograms of lead + thallium in 0.25 M potassium nitrate + 0.01 per cent. gelatin. Thallium, (1) nil, (2) 0-5 x M , (3) 2 x M , (4) 5 x Mand ( 5 ) 20 x M S = 1/15. 2.7 x lO-4M lead I 2 3 4 Fig. 11 (b). Derivative polarograms of lead + thallium in 0.25 M potassium Mand (5) 20 x 10-4 M nitrate + 0.01 per cent. gelatin. Thallium, (1) nil, (2) 0-5 x lo-* M , (3) 20 x Av = 18.2 mv., S = i.M , (4) 5 x 2.7 x lo4 M lead DIFFERENTIAL POLAROGRAPHY- With the omission, for simplicity, of the resistances rl and r2, the circuit of Semerano and Riccoboni2 has been adopted (Fig. 12). A simple theoretical analysis is possible on the following considerations. Assuming a symmetrical bridge with identical electrodes, let a limiting current of i, flow in one cell and a current of i, + it, in the other. It is required to measure i t , and eliminate i,. If attention is focussed on the horizontal portions of the waves, the relation between cell current and voltage is expressed by di/dE = 0. With this condition, a simple application of the Kirchoff laws gives .. (5) * . .. .. R2 2R, + R i, = it, The over-all sensitivity of the bridge plus galvanometer circuit can, therefore, never exceed 50 per cent.of the sensitivity of the galvanometer alone at a comparable setting. The validity300 of the equation is shown by the results given in Table IV. requires, as before, that R1iDt = R2iDe, and the equation assumes the form AIREY AND SMALES : MERCURY DROP CONTROL : APPLICATION [Vol. 75 Inequality in the electrocies . . . . .. i, = i ' D R2 - R1+ R2 -+ R ' * TABLE 1.V VERIFICATION OF EQUATION (5) Solution of 0.001 M thallium in 0.25 M potassium nitrate; S = 1/15] t = 3.05 sec. iD. iB, R, is - R, p amps. p amps. ohms ohms i D 2R, + R 2.64 1.29 2000 127 0.487 0-484 THE TECHNIQUE OF DIFFERENTIAL POLAROGRAPHY- As for derivative work, the balancing of the bridge is the most important requirement.The purpose of the differential method is to reimove unwanted currents, whether residual or otherwise. If it is known that after such removal an ideally or nearly ideally shaped polarogram should be obtained, the procedure is merely to adjust the variable resistance bridge arm until such a shape is obtained. If, however, as in an irreversible electrode process, a distorted wave is expected, it is desirable to balance the bridge initially with e.g., a cadmium or thallium solution. As two electrodes dropping into two solutions of possibly different concentrations are now concerned, the number of variables is increased. For theoretically perfect compensation, the requirement that R,i, = R2i, must be satisfied for both the reduction and condenser currents.Ideally, therefore, the bridge should be balanced with the same cadmium or thallium solution in both cells, the unknown solution should be placed in cell 2 and the concentration of a solution containing the ion giving the unwanted wave should be adjusted until balance is again attained. Practically, this would be tedious, and no noticeable error results if the final accurate balancing is done by the variable bridge resistance. . i3 . '4 Fig. 12 Differential circuit of Semerano and Raccoboni The relatively high temperature coefficient of the diffusion current (2 per cent. per O C.) necessitates temperature equality, if not temperature constancy, in the two cells, and a thermostat is almost indispensable. As yet, insufficient evidence has been accumulated to.decide whether the two electrodes must be operated on one pulsator or whether two pulsators, each carrying one capillary and operated simultaneously, are satisfactory. The latter scheme is advantageous in that the standard Cambridge thermostat and dropping electrode stand are immediately adaptable. In the case of the derivative method, the separation of the two electrodes should be a minimum and the question does not arise.June, 19501 TO DERIVATIVE AND DIFFERENTIAL POLAROGRAPHY 301 Perfect compensation of two waves at aZZ voltages requires, apart from the conditions already discussed, that they have identical apparent half-wave potentials and shapes. Any differences in these quantities, caused by the inequality of calomel half-cells or cell resistances, will be observed by the galvanometer both in magnitude and sign, giving rise to minor derivative effects superimposed on the differential.The resistances r1 and y2 (Fig. 12) are Fig. 14 ( a ) . Normal polarograms of zinc + cadmium in 0.5 M ammonium M (1) Cadmium, nil; S = l j 5 . (3) Cadmium, chloride + 0.5 M ammonium hydroxide -+ 0-01 per cent. gelatin solution. zinc , 8 x (2) Cadmium, 8 x lo4 M ; S = 1/30. 2 x 10-3 M ; s = 1/20 designed to minimise such phenomena. However, within the ratio limit of 10/1 discussed below, the effects are small and the two compensating resistances may be discarded. As shown by the former example, nearly perfect elimination of the residual current over the whole working voltage range may be achieved. This is an attribute not possessed by the counter-current method of Ilkovic and Semerano, and more than compensates for the 50 per cent.loss in sensitivity. Fig. 14 illustrates the minimisation of a large cadmium wave preceding a zinc wave. The polarogram of Fig. 14 (6, 3) is anomalous. Fig. 14 (c) presents three consecutive repeats carried out several hours later (a somewhat smaller mercury flow rate, in consequence of a The utility of the differential technique is shown by Figs. 13 and 14. 2 3 Fig. 14 (b). Differential polarograms of zinc + cadmium in 0.5 M ammonium S = Q. chloride + 0-5 M ammonium hydroxide + 0.01 per cent. gelatin solution. 8 x 10-5M zinc Cadmium, (1) nil, (2) 8 x M and (3) 2 X 10-aM302 AIREY AND SMALES MERCURY DROP CONTROL: APPLICATION [Vol. 75 reduced head, was employed).The regularity of the galvanometer oscillations in each case is good: from the known cadmium to zinc ratio of 25/1, it will be seen that the average reduction current associated with each drop is constant to well within 0.1 per cent. It must be emphasised, however, that such regularity can only be obtained if the pulsator receives electrical excitations of constant energy and duration. As was briefly noted earlier, the phenomenon known as “relay bouncing” is particularly objectionable. On the first closure of the contacts, the condenser is partially disch.arged and the drop is probably detached. The second closure completes the discharge, causing a further shock to the capillary, which results in a slight irregular stirring and corresponding variations in the reduction current. Normally, such effects would be almost indiscernible, but the differential method magnifies Fig.14 (c). Differential polarograms of zinc + cadmium in 0-5 M ammonium S = 8. chloride + 0.5 M ammonium hydroxide + 0.01 per cent. gelatin solution. 8 :< M zinc + 2 x M cadmium them to such an extent that they may produce: a “raggedness” of the wave which almost obscures it. With reasonably careful working it is possible to carry out estimations on solutions in which the ratio of the unwanted to the desired wave is 100/1. By comparison, the simple compensation procedure of Lingane and Kerlinger9 is applicable in favourable cases up to a limit of 50/1. However, it is considered that above a ratio of 10/1 the use of automatic controlled potential electrolysis at a mercury cathode is a much more effective method of dealing with large preceding waves.The special merit of the differential method is that, unlike that of Lingane and Kerlinger, it is possible to compensate waves of any shape, such as those frequently obtained in the reduction of organic compounds. APPLICATIONS INVOLVING NON-STANDARD EQUIPMENT MULTI-TIP ELECTRODES- McGilvery, Hawkins and ThodelO have described multi-tip electrodes as a means of increasing sensitivity. Simultaneously, there occurs a proportionate increase in the condenser current, but it is claimed that the natural asynchronism of dropping rates materially reduces what would otherwise be an enhanced drop wave. Bricker and Funnanll have criticised this latter statement, claiming that an irregular wave-top results. A five-tip electrode has been made (unfortunately of a very rapid drop rate) and the drops have been shown to be capable of synchronisation by means of a pulsator. Work is in abeyance owing to the difficulty of obtaining a suitable size of capil1ar:y tubing, but there appears to be noreason why this type of electrode should not prove very profitable if the residual current iseliminated by means of a differential circuit.COMBINATIONS OF DERIVATIVE AND DIFFERENTIAL METHODS- The practicability of the separation of two waves by derivative methods depends upon the difference of half-wave potentials and the ratio of the concentrations. Instances may arise in which a separation is feasible when the two substances are present in equal amounts,June, 19501 TO DERIVATIVE AND DIFFERENTIAL POLAROGRAPHY 303 but not when present in a ratio of, for example, 1/10.Theoretically it should be possible to set up two derivative bridge circuits, one operating on the second reducible substance only. By means of a galvanometer having independent differential windings, automatic subtraction of the two derivative curves should be feasible. Numerous other combinations might be advanced; in particular it should be possible to gain the desired results with only three synchronised mercury drops, but as yet no satisfactory circuits have been designed. CATHODE RAY POLAROGRAPHY- The apparatus devised by Randless has been elaborated to permit differential operation. As an example of the performance, one part of zinc in 104 parts of cadmium may be detected- with certainty.The work is as yet in a preliminary stage and will be reported fully in a subsequent paper. MISCELLANEOUS OBSERVATIONS The Ilkovic curves of Fig. 5 show that, with proper adjustment of operation, the pulsator has no directly discernable effect on the diffusion current. It thus becomes possible to separate the variables m and t in the Ilkovic equation. The results of Table V show that the relation i a d is followed to within less than rt2 per cent. over a 2 to 1 range in flow rates. TABLE V VERIFICATION OF RELATION i, a mt Solution of cadmium in 0.5 M potassium chloride; t = 3.05 sec. h 64.0 49.6 44.0 36.7 32.9 A m, m) mg./sec. 1.41 42.9 1.278 42.0 1.066 42-4 0-831 41.5 0-706 41.5 . 42.1 + 1.9% - 1.4% Table VI shows results verifying the relation i a t i to within approximately k2.6 per cent.However, the Ilkovic curves of Fig. 5 do not exactly fit a one-sixth power law, the TABLE VI Series 1 Series 2 VERIFICATION OF RELATION i, cc t* Data from experiments similar to Fig. 6 k 43.3 41.1 39-7 37.8 35.4 33.4 43.0 42.6 40.7 37.5 37.0 32.0 t, sec. 3.9 3.06 2.60 1.93 1.60 1.00 3.9 3-66 3-05 2-15 1.68 0.75 12 t4 34-6 34.1 34.0 34.0 33-1 33.4 - mean 334 + 2.1% - 2.4% 34.3 34.3 33.8 33.0 34.3 33-6 mean 33.9 + 1.2% - 2.7% slope of the initial portions being too low. This could be qualitatively explained by the postulate that during the life of a drop there is some small accumulation (by convection and, possibly, mercury vortex action) of the depleted solution from the diffusion layer around the neck of the mercury drop.This would not be entirely removed by the falling drop,304 AIREY AND SMALES [Vol. 75 and the new drop would therefore grow through a portion of solution of concentration some- what lower than that in the bulk of the electrolyte. With increase of drop size the diffusion conditions would become those required by the Ilkovic equation. Some substantiation of this hypothesis is provided by results obtained on the cathode ray polarograph. With this instrument a polarogram is observed during the life of a drop; one such polarogram may be observed or the process may be repetitive, depending on the particular drop frequency employed. In several cases examined, single polarograms appear to be a few per cent. larger than those obtained when there has been a preceding wave.It would be of interest to examine a reduction process in which the product of the reaction remains in solution and is more dense than the bulk of the electrolyte. A small distortion of the Ilkovic equation such as is considered would not markedly affect the one-sixth power law as determined by an integration of the curve, i.e., a mean current measurement by a galvanometer. There is a suggestion of a drift in the results of Table VI, but the order of accuracy is insufficient for unequivocal deductions. DESIGN OF CAPILLARIES- Composite capillary tubes consisting of a 10-cm. length of 0.05-mm. bore tubing plus a l-cm. tip of 0-l-mm. bore, are employed with the pulsators. The free-drop time may be as great as 15 seconds, but the drop time is easily controlled to the convenient value of 3 seconds. The relatively large bore of the tip makes such capillaries much less liable to clogging, which for protein-like substances may be a decided advantage. ADDENIIUM Since the submission of this work for publication, a paper by L6v6quels has appeared. Mention is made of experiments on electromechanical drop-control, using a somewhat similar scheme to that described, and failure to devise a useful technique was reported. From an examination of the circuit diagram it would appear that the lack of success was probably due to the stirring effects arising from the cessation of the magnet-energising current after the relatively long time of energisation of the driving magnet. Acknowledgment is made to the Director, Atomic Energy Research Establishment, Ministry of Supply, for permission to publish this work. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. REFEREXES Heyrovsky, J., Anal. Chim. Acta, 1948, 2, 536; Analyst, 1947, 72, 229. Semerano, G., and Riccoboni, L., Gazz. Chim. Ital., 1942, 72, 297. Kanewskii, E. A,, J . Appl. Chem. (U.S.S.R.), 1944, 17, 514. Matheson, L. A., Nichols, N., et al., Anal. Chim. Acta, 1948, 2, 541. Sevcik, A., Cold. Czech. Chem. Commun., 1948, 13, 349. Lingane, J. J., Anal. Chem., 1949, 21, 57. Muller, 0. H., Chem, Eng. News, 1949, 27, 847. Randles, J. E. B., Trans. Farad. Soc., 1948, 44, 322. Lingane, J. J., and Kerlinger, H., I n d . Eng. Chem., Anal. Ed., 1940, 12, 750. McGilvery, J., Hawkins, R. C., and Thode, H. G., Cunad. J . Ras., 1947, 25, B 132. Bricker. C. E.. and Furman. N. H.. Anal. Ch.em.. 1948. 20. 1123. Kolthoff, I. M., and Lingane, J. J.-, “Polarography,” Interscience Publishers, Inc., New York, L6v$que, M. P., “Differential Polarography with a Single Dropping Electrode,” J . Chim. Phys., 1946, p. 144. 1949, 46, 480. ATOMIC ENERGY RESEARCH ESTABLISHMENT HARWELL, BERKS. October, 1949