In our work, analytical measurements were made on Cd(I1) to in 0.2M KC1 over the concentration range of 1 x 5 x lO-7M. The measurement conditions were: N = 15 (the time of the f i s t sampling, T’, is 1040 psec), AE = 4 mV, T = 5 msec, and 4 ensemble averaging cycles per run. As shown in Table IV, the peak currents obtained were linearly dependent on concentration within experimental error over the entire range studied. All peak values were corrected for background currents. Figure 5 shows traces of raw and smoothed data for 1 X 10-6M Cd(I1). At this concentration, the signal-to-background ratio was about 1.5:l. A 7-point cubic-quartic smoothing function was used (14). It should be obvious that the analytical sensitivity can be extended below lOPM if larger N-values and ensemble averaging are used. Considering a practical limit of about 100
averaging cycles (15), the detection limit for our system appears to be about 5 x 10-*M. In order to minimize background current contributions at the lower concentrations, a larger value of 7 ’ could be used. But the signal-to-noise factor would suffer, and a larger number of averaging cycles would be required to achieve the same sensitivity. ACKNOWLEDGMENT.
The authors would like to thank J. E. Davis for his helpful suggestions in potentiostat design.
RECEIVED for review October 11, 1972. Accepted November 27, 1972. This work was supported by the National Science Foundation, Grant GP-21111.
Pulse Polarography in Process Analysis Determination of Ferric, Ferrous, and Cupric Ions E. P. Parry and D. P . Anderson1 North American Rockwell Science Center, Thousand Oaks, Cd$. 91360 A form of pulse polarography is described which can be used for automated analysis of process streams. The technique is rapid, has good sensitivity, and is not severely affected by small amounts of oxygen. Only one 50-millisecond pulse to the diffusion plateau for each species to be analyzed is all that is required for the analysis after suitable calibration. The choice of supporting electrolyte(s) is of great importance in the successful application of the technique. For determination of two different oxidation states of the same species (or where both oxidation states can be present), it is necessary thst the pulse polarographic wave be irreversible. The kinetic parameters are discussed. Pyrophosphate solution is shown to be a suitable medium for the simultaneous determination of ferric and ferrous ions and the pulse polarographic behavior of these ions, as well as cupric ion in this medium, is described in detail.
We have combined a sample handling system with a custom designed pulse polarograph and have successfully applied this system to the on-line analysis of the ferric, ferrous, and cupric ions in a copper etching bath used in microelectronics manufacture. The sample handling system and instrumentation will be described in future publications. It is the purpose of this paper to describe the principles which are required for application of pulse polarography to process analysis and to elucidate the details of the chemistry which underlie the pulse polarographic determination of ferric, ferrous, and cupric ions. It is shown that ferric and ferrous ions can be determined in a pyrophosphate supporting electrolyte a t p H of 8 containing Triton X-100. Although copper ion gives a wave in this medium, mutual interferences dictate that copper be determined in an acidified potassium sulfate solution.
THERECENT GROWING NEED for process analysis and process control has aroused interest in the application of new instrumentation and techniques for this purpose. The use of colorimetric analyzers and selective ion electrodes is well-known. Potentiometric and potentiometric titration analyzers as well as conductometric analyzers have also been used in monitoring process streams, but the possibility of using polarographic techniques has not received much attention. Pulse polarography, a polarographic technique described in some detail in previous publications ( I , 2), has several attractive features. It has good sensitivity, is not severely affected by small amounts of oxygen, and a reading can be made quickly as will be subsequently described. It also should be quite suitable for use with various solid electrodes, although the present application is with the dropping mercury electrode.
THEORY
Present address, Cutter Laboratories, Berkeley, Calif. (1) E. P. Parry and R. A. Osteryoung, ANAL. CHEM.,37, 1634 (1 965). (2) Zbid.,36, 1366 (1964). 458
ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
Pulse Polarography in Process Analysis. Normal and derivative pulse polarography have deen described (1). The normal mode has been used exclusively in this application and will be the only one described here. In the usual normal pulse polarographic application, potential pulses of gradually increasing amplitude are applied to a n electrode starting from a “rest” potential which is anodic of the electrode process of interest. The potential pulses applied t o the electrode are approximately 50 milliseconds duration, but the potential between pulses always returns to the “rest” potential. If the area of the electrode is changing ( e . g . , dropping mercury electrode), the pulses are always applied a t a fixed time in the life of the drop, so a constant electrode area can be maintained. Current values are measured before each pulse and toward the end of each pulse application, and the current difference is read out as a function of pulse amplitude. The curve obtained is very similar to a normal polarogram with the limiting current being proportional to the concentration of electroactive species in the solution. For process application, it is found most convenient to apply, from a potential well anodic
of the electrode process of interest, a single large potential pulse which reaches the diffusion plateau. The current difference, taken as before, is proportional to the concentration of reducible species. This current difference can be displayed digitally, and the concentration is thus obtained in 50 milliseconds with a single measurement. The total analysis would take longer than this because of the time required for sample handling and because of the frequent requirement for decreasing the oxygen content. Because a current difference is measured, the effect of a current from a more easily reduced component should be minimized. The desired analysis of the etching bath requires the determination of the concentration of iron in two different oxidation states. Most electroanalytical techniques, especially polarography, are highly suitable for such determinations. In normal polarography, it is well-known that the amount of oxidizable species present in the solution can be obtained by measurement of the anodic current. For a couple reduced reversibly, the cathodic current is measured from the diffusion plateau of the reduction wave to a line representing zero current (or residual current). The anodic current is measured in a similar manner on the diffusion plateau of the oxidation wave. Since in normal polarography the zero current axis is defined, the anodic current and cathodic current can be separated and the concentration of the oxidation states can be determined for a reversible couple. However, in normal pulse polarography, only a difference current is displayed so there is no zero current axis and the concentration of the two oxidation states cannot be determined if the system is reversible, since the half-wave potentials for the oxidation and reduction processes are the same. Therefore, some irreversibility must be present in the waves of the redox couple of interest in order to measure separately the oxidation and reduction waves. In Figure 1 is shown a hypothetical pulse polarographic wave with sufficient activation energy of the electron transfer step to separate the oxidation and reduction waves in the voltage axis. Under this irreversible condition, plateau B effectively establishes a zero current line such that stepping from B to C will give the concentration of the oxidized form, while stepping from B to A will give the concentration of the reduced form. Since the waves cannot be too drawn out in order to be used for analytical purpose, it would be desirable that the value of CY, the transfer coefficient, be approximately 0.5. In addition, the separation of the half-wave potentials of the two waves should be about 0.3 volt minimum in order to have a sufficient plateau at B. Under these conditions, the relation between the halfwave potentials of the two waves and the electrochemical rate constant ratio is calculated by the following consideration : The half-wave potential for the reduction step of an irreversible pulse polarographic wave is given by (3)
I
C
\ e
1
A
Figure 1. Polarographic behavior of irreversible redox couple
+
Since CYred aiOx = 1 ( 4 ) , Equation 2 can be subtracted from Equation 1 and simplified by assuming that Do, = Dred and all - CY = unity to give the expression (3)
where E, is the standard or reversible potential for the system, CYred is the transfer coefficient for the reduction reaction, k , is the heterogeneous electrochemical rate constant with reference to E , for the reduction, t is the time after pulse application a t which the current is read, Do,is the diffusion coefficient of the oxidized form, and the value of 2.303 RT/F at 25OC is 0.059. For the oxidation step, the corresponding equation would be
from which the approximate ratio of rate constants can be calculated for any half-wave potential separation. If n = 1 and a separation of 0.3 volt is taken, then k,,,,/k,,, &Z3.2 X 102. A larger separation than this could be more desirable, unless the wave of interest had interference from the wave of another ion or by mercury dissolution. Consideration of the above factors and other suggested requirements for the determination of two or more ions when present together in solution indicate that the following conditions are important. (1) If two different oxidation states of an ionic species are to be determined, the couple must be suitably irreversible. (2) All waves must be cathodic of mercury oxidation. (3) The waves must be sufficiently separated to allow for individual measurement. (4) The waves must be well-defined and it would be desirable that the limiting currents be proportional to the respective concentrations. ( 5 ) Ideally, there should be no interaction of a given ion on the other waves. If there is such interaction, it should be small and easily correctable. (6) No time-dependent homogeneous solution reactions should occur. If one or more supporting electrolyte solutions can be found such that these conditions are fulfilled, then by suitable choice of “rest” potential and potential pulse magnitude, the repeated measurements of concentration of each ion of interest can be quickly made, and with appropriate sample handling system, automation for continual measurement and subsequent control can thus be achieved. It is obvious that the fewer supporting electrolyte solutions required (i.e., the greater the number of ions which can be determined in one supporting electrolyte), the smaller the requirement on the sample handling system.
(3) K . B. Oldham and E. P. Parry, ANAL.CHEM., 40,65 (1968).
(4) P. Delahay, “New Instrumental Methods in Electrochemistry,” Interscience, New York, N.Y., p 33. ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
459
E
V I
S.C.E.
Figure 2. Effect of pH on pulse polarographic wavecathodic scan Solution: 0.10M Na,Pz07,2 = 10-4M Fe3+. pH adjusted with NaOH or H2S04. Curve 1: pH 3; Curve 2: pH 4; Curve 3: pH 5; Curve 4: pH 6; Curve 5: pH 8; Curve 6: pH 10. Einitialfor Curves 1, 2,3, +0.1 volt; for Curve 4, - 0 volt; for Curves 5 and 6, -0.1 volt us. S.C.E
I
,
1 -E 1 -1.3 -0.9 -0.5 V o l t s vs S . C . E .
-0.3
-0.1
Figure 3. Cathodic and anodic scans for Fe3+at pH 8 without Triton X-100 EXPERIMENTAL
Apparatus. For most of the work described here a pulse polarograph built in this laboratory (2) was used. The process analyzer which will be described in more detail in a future publication consisted of an electronics package which controlled the application of potential pulses and the current read out, the sample handling system including the cell, and the master timer clock which controlled the operational sequencing. The electronics were built of TTL digital logic and allowed the repetitive application of a potential pulse of constant magnitude with accompanying current difference read out for each channel of data required. Because three ions were to be determined, the instrument used here had a three-channel capability. The “resting” or starting potential and the magnitude of the potential pulse applied were manually adjustable, separately, for each channel. These values were determined by the supporting electrolytes and the chemical conditions described below. Each channel of data was sequenced and controlled by the master control timer. The current difference value was held as a voltage on a capacitor until the next potential pulse was applied and was read out on a strip chart recorder. In the current application, each species was determined once every 8 minutes. The sampling handling system was made entirely of glass or Teflon (DuPont). A side stream of liquid was continually pumped from the bath and returned, and for each analysis a precise volume of this liquid was removed from this stream and added to the cell using a specially modified gas chromatographic value. Another similar valve was used to measure and add the supporting electrolyte(s). The contents of the cell were bubbled for 3 minutes before measurements were made. The valves used were pneumatic and pressurized nitrogen was used to transfer the liquids. All valves and transfer operations were controlled by the master control timer. The cell was made of glass and was thermostated by a water jacket. It had the usual openings for reference electrode, counter electrode, indicator electrode, nitrogen inlet, and reagent and sample inlet. In addition, it had a n outlet a t the bottom controlled by a pneumatic valve which would permit the cell contents to go through a mercury trap, then to drain after each analysis was completed. The indicator electrode was the usual dropping mercury electrode, using nitrogen pressure to maintain a constant head. 460
I
ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
Solution: 4.5 X 10-4M Fe3+,0.1M pyrophosphate, pH 8
The master control timer was a standard cam operated timer. Reagents. The reagents used were all reagent grade and were used without further purification. Procedure. For the automated analysis, a sample was withdrawn from the sample stream and added to the cell. The volume required was 5 to 10 microliters, and this volume was reproducible to i l z . Sulfuric acid (10 ml) was then added, the solution bubbled for 3 minutes and the potential pulse was applied to determine copper. Five milliliters of a pyrophosphate solution, adjusted to make the final solution 0.1M in pyrophosphate, p H b, and 0.002x in Triton X-100, was then added and ferric and ferrous ions were determined. The contents of the cell were dumped and the analysis was repeated. RESULTS AND DISCUSSION
Selection of Medium. For the determination of ferric, ferrous, and cupric ions in the etching bath, a supporting electrolyte was required which complied with most, if not all, of the requirements listed above. The etching bath, from which the sample is taken, is a concentrated ferric chlorideHCl solution and the copper etching reaction is a simple copper oxidation
Fe3+
+ Cu e Fez+ + Cuzf
(4)
By control of the etching bath composition, the quality and depth of etching can be controlled. Because the concentrations of Fe3+,Fez+, and C U ~are + relatively large in the used etchant, only a small sample ( 5 to 10 pl) of the sample used here was required for optimum polarographic determination. Because of this small sample size, the effect of the etchant components on the polarographic behavior can b e ignored. However, the precipitation of insoluble iron and copper salts must be prevented when this small volume of concentrated solution is added to the supporting electrolyte. Because of the requirement of irreversibility, the polarographic data which are in the literature cannot be used apriori to choose the right supporting electrolyte. The reversibility
of Fe3+Cathodic Wave Table I. Effect of Triton X-100 on E,,z 0.1MNa4P207, p H 8 ; 5 X 10-4MFe3+; 7 X 10-6MCu*+ [Triton] (x 1 0 - 4 7 3 Eiiz (V) 0 -0.870 2 -0.885 5.2 -0.915 9.2 -0.960 13.2 -1.025 - 1.080 15.2 -1.115 16.4
of the couple is generally not mentioned in the polarographic literature, particularly for separation of the cathodic and anodic steps. Additionally, unless heterogeneous rate constants are given or can be obtained for calculation, the polarographic data cannot be used alone because of the differences in the time of measurement for the two techniques. A number of solutions were tried as supporting electrolytes including tartrates, citrates, mannitol, EDTA (ethylenediaminetetraacetic acid), DTPA (diethylenetriaminepentaacetic acid), and triethanolamine at suitable pH values. Triethanolamine at first appeared attractive because of the good separation between the ferric and cupric reductions and the possibility of varying this separation by suitable choice of pH. In addition, most of the other conditions at first appeared to be met. The half-wave potential of iron is 0.58 volt more negative than that of copper in a solution 0.1M in NaOH and 0.03M in triethanolamine, so this medium is highly suitable for determining small amounts of copper in the presence of a large excess of iron. The very negative half-wave potential of the ferric reduction wave in this medium (- 1.05 volts c’s. SCE) strongly suggested that the ferric-ferrous couple would be irreversible. Surprisingly enough, however, the iron couple is reversible. The only report (5) in the literature on this system is very sketchy and does not discuss the Fe3+-Fe2+ reversibility. Calculation of K,/KR, the ratio of the dissociation constants of the complexes in the oxidized and reduced metal ion form, indicates that the ratio is approximately 10-z6. The remarkable stability of the ferric-triethanolamine complex is clear. The data also suggest that both the ferric and ferrous complexes contain the same number of triethanolamine ligands. Cursory examination of alkaline pyrophosphate and alkaline carbonate solutions suggested that these might make satisfactory supporting electrolytes. The use of pyrophosphate appeared to involve less complications; in addition, some detailed studies have been reported on the copper pyrophosphate system (6). For this reason, the behavior of the iron couple and cupric reduction in pyrophosphate media was investigated in some detail. Behavior of the Iron Couple in Pyrophosphate. The effect of pH on the pulse polarographic wave obtained in the reduction of FeaTin pyrophosphate medium is shown in Figure 2 . A single well-defined wave is obtained at pH of 3. With increasing pH, the wave shifts to more negative potentials and decreases in height, a new obviously irreversible wave forming at a much more negative potential. The magnitude of the final limiting current remains essentially constant throughout the total p H range.
Figure 4. Effect of Triton X-100 on the Fe3+ pulse polarograph scan at pH 8 Solution: 0.1M Na4P20,,2 X 10-4M Fe3+, 0.0061z Triton X-100
-
The wave at pH 3 fulfills the usual requirements for reversibility. A cathodic pulse polarographic scan starting before the wave and an anodic scan starting on the wave gives scans of equal height and with about the same half-wave potential, an important criterion for reversibility (7). In addition, the usual log plot of E us. log(id-i)/i for the pulse polarographic wave gives a straight line with a reciprocal slope of 0.059. In pulse polarography irreversible waves do not have a straight line plot (3). The half-wave potential at pH 3 is -0.07 i 0.012 volt. The diffusion coefficient of the reducible cm2/sec, a value which, by comparison species is 4.6 x to other ions, would suggest a rather bulky ion. The small prewave at pH 8 involves Fe3+ reduction as can be shown by the anodic normal pulse polarographic scan with the rest potential of -0.6 V (Figure 3). The anodic wave with an E,,2of approximately -0.4 V is the oxidation of the Fez+ produced at -0.6 volt. A significant amount of Fez+ (about of total bulk concentration) is thus produced at this potential, which, therefore, does not allow a separation of the ferrous oxidation wave from the ferric reduction wave, even though the main reduction wave of Fe3+ has an E l i P of about -0.8 V, with a corresponding half-wave potential separation of 0.4 volt. Effect of Maximum Suppressors. A typical maximum suppressor, Triton X-100, causes a shift of the half-wave potential of the ferric reduction wave to more negative potenTriton X, the tials as shown in Table I. Above about small prewave and current inflection at about -0.44 in the Fe 3+ reduction wave are eliminated, allowing separation of the oxidation and reduction waves. Figure 4 shows the cathodic normal pulse scan for 2 x 10-4M Fe3+starting at a “rest” potential of -0.1 and an anodic normal pulse scan of the same solution starting at a “rest” potential of -0.7 V. The cathodic scan indicates no evidence of Fe3+ reduction until the beginning of the wave at approximately - 1.O volt, while the anodic scan confirms that Fez’ is not produced at -0.7 volt. However, if a potential of -1.4 volts is taken as the “rest” potential for an anodic normal pulse scan, a wave corresponding to the oxidation of ferrous ion is obtained with a half-wave potential of approximately -0.4 V DS. SCE.
( 5 ) G. Jessop, Nature, 158,59 (1946). (6) G. W. Higgins and P. E. Sturrock, ANAL.CHEM.,41, 633 (1969).
(7) K. B. Oldham and E. P. Parry, ANAL.CHEM., 42,229 (1970). ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
461
1
-1.7
I
-1.3
-0.9 t
-0.1
-0.5
Figure 5. Pulse polarographic trace of Cu2+ reduction in pyrophosphate, pH 8. 1.OM Na4P20i, 2 X 10-4M CU2f No Triton X-100 (b) 0.0061 Triton X-100 (0)
-0.50v
f
-E
Figure 6. Anodic scan showing effect of copper on the ferrous oxidation without Triton X-100
- - - - - - 2.5 X
- 2.5 x 1 0 - 4 ~ ~ e 2 ~ ; 2.5 X 1 . 0 - 4 M C ~ 2 +
Fez‘
centration of the ferrous ion a t least up to 8 x 10-4M. Concentrations of ferric ion at least equal to the concentration of ferrous ion have no effect. Without Triton X-100, cupric ion exhibits an unusual interference as described below. However, with Triton X-100 present, concentrations of copper(I1) ion a t least equal to that for ferrous ion do not interfere. The ferric reduction wave, using 1.3 x 10-3z Triton X-100, has a half-wave potential of -1.03 volts and the current is proportional to the concentration of ferric ion. In the presence of ferrous ion solution, a slight increase is found in the ferric wave. The increase is proportional to the ferrous concentration and is probably caused by some ferric impurity in the ferrous solution. However, no definite confirmation of this point has been obtained. As described below, the copper wave is drawn out and occurs after the ferric reduction. The foot of this extended copper wave, therefore, contributes significantly to the Fe3+limiting current, the amount of interference being proportional to the concentration of copper ion. Thus, a copper ion concentration 1/3 that of the ferric ion will increase the wave by about 20%. A correction for this rather significant interference, therefore, must be made in the ferric ion determination, and can be done if the concentration of copper ion in the solution is known. Fortunately, in the application described here which involves monitoring a copper etching bath, the ratio of ferric to cupric ions is always relatively large so the correction needed is quite small compared to the total ferric reduction wave height. Determination of Cu2+. The pulse polarogram of cupric ion reduction in a pyrophosphate medium is shown in Figure 5. Without Triton X-100, an unusual peak appears in the cathodic polarogram at a potential of approximately -0.35 volt. This occurs in the cathodic scan starting at -0.1 volt and also in the anodic scan starting at -0.7 volt. It is similar to that found for the reduction of Fe3+except the peak for copper is much more pronounced. As shown in Figure 6, the peak caused by copper in the anodic scan interferes with the development of the ferrous oxidation wave, but does not appear to affect the wave height. However, the presence of Triton X-100 suppresses this peak in both the anodic and cathodic scans, thus preventing any interference by copper in the ferrous determination. It has been reported (6), that the first wave in the reduction of copper ion in alkaline (pH > 5) pyrophosphate medium is a kinetic wave wherein the charge transfer step is preceded by a slow dissociation reaction of a non-reducible copper pyrophosphate complex.
+
Because of the shift of the half-wave potential in the negative direction with increasing Triton X, the potential range over which the diffusion plateau is obtained is shortened. Thus, the amount of maximum suppressor used must be minimized consistent with the elimination of the premature ferric reduction. Determination of Fe3+and Fez+. A pyrophosphate medium a t p H 8 which contains approximately lop3 Triton X gives the necessary irreversibility for determination of both Fe 3T and Fez+. Stepping from a “rest” potential of -0.6 (or -0.7) volt to approximately -1.4 volts gives a signal for Fe3+ reduction and stepping from -0.6 (or -0.7) volt to approximately -0.2 volt will give a signal for Fe2+oxidation. The ferrous oxidation wave has a half-wave potential of -0.38 volt, and the current is strictly proportional to the con-
z
462
*
ANALYTICAL CHEMISTRY, VOL. 45, NO. 3 , MARCH 1973
ML? e ML
+L
(5)
where ML is the reducible species and L is the pyrophosphate ligand. The electron transfer step is said to be reversible. In order to have a significant amount of the reducible species in their study, these authors (6) used a ratio of pyrophosphate to copper generally of two and never more than 50. Ratios as high as used in the present work were never investigated. The interpretation of the present experimental observation of the pulse polarographic peak at -0.35 V which is eliminated by a maximum suppressor appears difficult to explain based on the hypothesis that the first wave is kinetically controlled. No attempt to explain our results in terms of the hypothesis of previous workers has therefore been made. One possible explanation involves the assumption that while adsorption of the species to be reduced is not important at low pyrophosphate/copper ratios, it becomes significant when the ratio becomes high. This would explain the effect of the Triton X-100 in eliminating the wave, although other ex-
planations are equally likely. Additional work is required to settle this point. The irreversible reduction of copper (11) ion in the pyrophosphate medium in the presence of approximately 1 0 - 3 x Triton X-100 gives a well-defined wave with a half-wave potential of about -1.57 V. The limiting current is proportional to the concentration of copper ions. However, in the presence of an equal concentration of ferrous ion, the limiting current is decreased by about 20z. The reason for this decrease is not understood. The presence of ferric ion causes an increase in the copper limiting current, perhaps because of incomplete separation of the ferric ion wave. An equimolar amount of Fe3+ion gives about a 10% increase in the copper ion limiting current. Thus, ferric ion interferes with the copper ion reduction wave, and copper ion interferes with the ferric ion reduction wave in the pyrophosphate medium. The quantitative determination of both ions in an unknown mixture, therefore, appeared only to be possible with a rather complex iterative procedure, if at all. To avoid this problem, at a minimum ncrease in sampling requirements, the copper first is deter-
mined in an acid sulfate supporting electrolyte, after which a suitable pyrophosphate aliquot is added and the ferric and ferrous ions are determined. The pH of the buffer increment added was adjusted to give a final pH value of 8 for the mixed solution. In a 0.1M potassium sulfate solution of pH -2 (to prevent hydrolysis of ferric ion), copper ion gives a well-defined reversible reduction wave with an El/2 of -0.028 volt. The presence of iron has no effect on this wave. Moreover, the presence of the final sulfate concentration was shown not to effect the determination of ferric and ferrous ions. Calibration curves for ferric, ferrous, and copper ions are all linear. By determining the concentration of copper ion independently, its contribution to the ferric reduction wave can be determined and a correction made. The reproducibility of the measurement of all three ions in the 10-'M conInvestigation of centration range was found to be * 5 % . other potential interferents was not made.
RECEIVED for review August 2, 1972. Accepted November 27, 1972.
Bipolar Current Method for Determination of Solution Resistance P. H. Daum and D. F. Nelson Northern Illinois University, DeKalb, Ill. 60115
A bipolar method for measurement of solution resistance has been developed which involves the successive application of constant current pulses of equal magnitude, but of opposite sign, to a conductance cell, and integration of the resultant cell voltage to determine the area of the voltage-time curve. I t is shown that this area is directly proportional to the solution resistance, independent of the magnitude of the series cell capacitance C,, and essentially independent of the parallel capacitance C, over a wide range of values. The design and construction of the instrument, which features a solid state MOS-LSI memory for the rapid accumulation of data points, is detailed. Application of the instrument is illustrated with studies of low resistance KCI solutions and with kinetic studies of the acetyl chloride ethanolysis reaction. THERE HAS BEEN a good deal of interest generated recently in extending the available range of conductance instrumentation to include measurements in experimental situations which are usually avoided. These include the rapid precise measurement of solutions with high resistances, as in the study of solvolysis reactions in nonaqueous solvents and the measurement of solutions with extremely low resistances as those encountered in the study of the characteristics of fused salt systems. Classically, the approach to the measurement of conductance in systems such as these has been to experimentally adjust the parameters of the system such as the cell constant so that the measured conductance falls within the linear operating region of normal conductance instrumentation. However, this has proved not to be a practical approach for many applications because of stringent design considerations of size, electrode placement, and so forth, which must be placed on conductivity detectors for other reasons. This has prevented the use of conductivity detectors
in a number of systems for which conductance measurement is uniquely applicable. A good example of this is the potential usefulness of conductivity detectors in i,on-exchange chromatography. The requirements of such a detector necessitate close placement of the electrodes to limit the dead volume of the detector so that the sensitivities are high. This requirement means that the cell constants in such systems are going to be rather large and, consequently, the measured resistances very low in many circumstances, and changes representing elution of solute even smaller. Using conventional instrumentation, the dependency of measured conductivity with concentration will be nonlinear for many situations, because normal apparatus is not designed to measure systems which have resistances which are less than 1 Kohm. Thus, what is potentially a sensitive and generally applicable detector has not enjoyed wide use for quantitative work. There are a good number of problems associated with making measurements on solutions which have either extremely high or low resistances. The problems arise from the unfortunate fact that conductance cells cannot be modeled as a simple resistance; associated with that resistance are series and parallel capacitances, contact and lead resistance, and a faradaic impedance. These factors cause the observed solution resistance to be frequency dependent and the errors caused by the existence of these extraneous factors become increasingly important when the solution resistance is either very high or very low. The origin of these undesirable effects is due to the complicated nature of electrochemical systems in general, and can best be understood with reference to Figure l a . This figure depicts a reasonably complete model of conductance cell, ANALYTICAL CHEMISTRY, VOL. 45, NO. 3, MARCH 1973
463
