Constant Current Coulometric Titrator: Determination of Microgram and Submicrogram Quantities of Vanadium and Manganese L. B. Jaycox' and D. J. Curran* Department of Chemistry, University of Massachusetts, Amherst, Mass. 0 1002
A new coulometric titrator is described which is capable of routine determinations of sought-for-constituent in the ppb range. Both manual and automatic modes of operation are provided. Currents from 1 pA to 60 mA are available and the time of electrolysis can be controlled from 1 ps to 1000 8. The electrolysis cell is switched in or out of a galvanostatic circuit by a logic-operated analog switch. in the automatic mode, a comparator circuit is used to drive the switch and any end point detection system capable of providing a voltage signal to the comparator may be used with the titrator. Determinations of vanadium(V) and manganese(Vii) solutions were performed with eiectrogenerated Fe(li) using potentiometric end point detection to a preset and point potential. A new method of end point anticipation was used involving timing circuitry. Determinations of microgram amounts were made with precision and accuracy of a few ppt. Twenty-six nanograms of manganese were determined automatically with a precision and accuracy of 2 % . Coulometric titrations involving elapsed electrolysis times of tens of milliseconds are demonstrated.
Constant current coulometric titrations are an established technique and the number of titrants which can be generated continues to increase. The fundamentals of the method are well understood and can be found, for example, in Ref 1 . The quantity of interest in a coulometric titration is the number of Faradaic coulombs required to reach the end point, so the current-time integral must be obtained experimentally. The most common way of doing this is to rigorously control the current magnitude and accurately and precisely measure the time. Electric stopclocks have been popular for the latter purpose but their use generally requires that the electrolysis time be in the range of 100 to 1000 s, this being necessary but not sufficient to ensure a precision and accuracy in the time measurement of a few parts per thousand or better. Vorstenburg and Loffler ( 2 ) suggest that more precise timing of coulometric titrations could be achieved with a crystal oscillator timing circuit, but did not provide any data. Crystal oscillator timing circuits have been previously used as either a frequency device to directly drive a stopclock (3, 4 ) or as a timing signal which is stepped down and used to drive electronic or electromechanical timers (5-7). Counting circuits have been used in other ways. Pulses of known coulombic content have been applied to the cell and the number of pulses simply counted (8-13). I t is necessary to have several hundred or more counts in order to obtain the desired precision and the coulombs per count must be standardized. In other work the iR drop across a standard resistor in series with the cell has been measured and converted to frequency which is then shaped into pulses and counted with an elec-
tronic counter (14-16). This approach does not require an extremely constant current. Clem and Goldsworthy (17) have used a crystal oscillator and scaler circuits in conjunction with a galvanostat and Clem (18) points out the idea in a review. As yet, it does not seem that time as a measured variable in coulometric titrations has been exploited to the fullest. The availability of inexpensive digital circuits capable of generating, measuring, and controlling timing signals to a microsecond or better and the development of fast analog switches would indicate that the time variable ought to be measured and manipulated in the digital domain. Several advantages to coulometric titrimetry can be realized. Much shorter time intervals of electrolysis become possible. This implies that amounts of titrant smaller than those commonly encountered in the literature may be routinely generated. An ease of manipulation of timing is introduced which permits new approaches to the control of events during the course of the titration. A block diagram of the titrator is shown in Figure 1. Two operating modes are provided: manual and automatic. The dashed line indicates that the voltage comparator is not used in the manual mode. Any end point detection system may be used in the usual fashion of coulometric titrations. However, with this instrument, the operator preselects the length of time of electrolysis and when that time is reached, the cell current automatically ceases to flow. The instrument is now ready to add another increment of titrant and the operator, manually observing the end point detection system, dials in the time of electrolysis for the next increment of titrant. The total time of electrolysis required to reach the end point is accumulated in the readout of the timing module. The automatic mode of operation is based on titrating to a preselected end point signal. Any end point detection system which produces a dc voltage, or a signal which can be converted to a dc voltage, may be used.
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The Procter and Gamble Co., Winton Hill Technical Center, 6100 Center Hill Road, Cincinnati, Ohio 45224.
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Figure 1. Block diagram of coulometric titrator ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
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II voltage equal to, or corresponding to, the end point sig-
na! is set on the reference side of the voltage comparator and when the signal from the cell is equal to the reference, a change in the logic level output of the comparator circuit occurs which is used to turn off the cell current via the analog switch. The usual end point anticipation methods based on nonequilibrium conditions in the titration cell are applicable and additional anticipation is provided by circuits in the timing module. Coulometric titrations of solutions less concentrated than 0.1 ppm are rarely encountered in the literature. The reasons for this are primarily two: the concentration dependence of end point detection methods, and the prevalent iise of electric stopclocks. The works of Meites (14) and Cooke, Reilley, and Furman (19) clearly demonstrated that potentiometric end point detection is applicable to solutions down to a concentration of about 1 ppb. In both cases, titration to a preselected end point potential was used and Crrors of 5 to 10% were found a t this level. The same approach was used in this work and the chemical systems previously studied were used to evaluate instrument performance. Titration of vanadium(V) using electrogenerated iron(I1) with manual control of the titration was accomplished on samples containing as little as 105 ng of vanadiup11 in 50 ml of solution. Total titration electrolysis times as short as about 21 ms were achieved. Titrations of permanpanate with electrogenerated Fe(I1) were performed in the alltomatic mode on samples containing as little as about 50 q;of manganese with end point times as short as 0.5 s.
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INSTRUMENTATION The instrument was designed as two modules: timing and analog. A brief description of their functions is presented in this section along with a discussion of the timing sequence diagram. Details of the electronics are found in the following section. T h e Timing Module. The purposes of this module are to generate, count, and display timing signals; to provide a logic level signal to operate the analog switch; and to generate signals for a timed mode of end point anticipation. Figure 2 shows a block diagram of the unit. Established digital circuit designs were used to produce timing signals via a crystal clock oscillator and scalers, and to provide counting and readout, The readout counter accumulates counts over the entire course of the experiment and therefore displays the total time of electrolysis. The logic counter and time selector network form a preset counter. Six, ten-position thumb wheel switches are used to preselect the time of electrolysis for an incremental addition of titrant or, in the automatic mode, the time during electrolysis at which the end point anticipation circuits begin to operate. Timing signals (1 MHz) from the clock are fed to a scaler network and the RANGE switch and then routed to the control section and the anticipation network. Signals passed through the control logic are continuously fed to the two counters, which are operated in parallel, until a signal from either the time selector network or the anticipation network causes the logic gates to close and a pulse to be fed to the analog switch to turn off the cell current. The Analog Module. A block diagram of the analog rnodule is shown in Figure 3 where, for clarity, the timing module and the cell are also shown. This module contains thc analog switch, the comparator, and the circuits required to produce the constant current. The analog switch is placed in the feedback loop of the constant current source and is in series with either the cell or the dummy re&tm, depending on the switch position. This configuration permits a dummy resistor to be used and feedback control 1062
ANALYTICAL CHEMISTRY, VOL. 48,
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Flgure 3. Block diagram of analog module
of the current is maintained whether or not the cell is in the circuit. The signal to the analog switch comes from the timing module. In manual operation, it is generated by either the STOP switch or by the TIME SELECTOR switches. In the automatic mode, the STOP switch, comparator and anticipation network are all capable of generating this signal. Thus, once a titration begins, the signal to the analog switch is never initiated by the operator in normal operation. Timing Sequence. An overall understanding of the instrument may be obtained from the timing sequence chart shown in Figure 4. Signals are drawn relative to each other on the time axis and signal labels refer to circuit components found in Figures 5 and 6. Signals above the dashed line illustrate the manual mode of operation. Timing pulses are continuously generated and fed to gate, G4. With G12 set HIGH by the time selector network, FF2 can be set HIGH with the START switch. When this happens, the analog switch is thrown, cell current is applied, and timing pulses are passed through G4 to the counters. Operation continues until the output of the time selector network drives G12 LOW. Gate G4 then closes, the analog switch is thrown to the dummy resistor, and current through the cell ceases. The accumulated time is displayed on the readout. Flip-flop 2 goes LOW to prevent any processes from occurring again until the PROCEED and START switches are thrown. Automatic operation is illustrated below the dashed line in Figure 4. Here, the output of G12 must be HIGH initially to produce a HIGH at the output of G9. The anticipation network output, 19, is the gated output of G9 and S6. When the output from I9 and FF2 are both HIGH, timing pulses may be counted and current applied to the cell. When a
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preselected time of electrolysis is reached, the output of G12 goes LOW and remains there. The output of G9 now goes HIGH for 5 s and LOW for 5 s. However, the first OFF period will be of variable duration but no longer than 10 s. Henceforth, until the end of the titration, current cannot be generated when G9 is LOW. When G9 is HIGH, the current can be controlled by the comparator output and can be either OFF or ON. Thus, the titrator automatically approaches the preset end point in an incremental manner. ELECTRONICS Timing Module. A schematic diagram of this module is shown in Figure 5 . The center of operations is the control logic and gate section which routes timing signals to their appropriate destinations and produces the logic signal to the analog switch. Front panel switches are used to control this section. Nand Gates G1-44, and inverters I10 and I12 are the control logic gates through which all main control signals pass. Gates G1 and G2 provide gating signals for manual and automatic operation, respectively. Their outputs are gated through OR gate, G3, which produces the primary on-off pulse for all subsequent circuits. Control of G4 by the OR gated output of G1 or G2 passes or blocks the selected scaler timing pulses to both the logic and readout counters. In manual operation, the outputs of flip-flop (FF2), G12, and switch S1B are HIGH and gate G1 opens G4. Similarly, in the automatic mode, G2 opens G4 when the outputs of FF2, 19, and S1G are HIGH. In manual operation, the output of FF2 is used as a stop signal but this function is assumed by G2 in the automatic mode. Inverter I12 inverts the timing pulses from G4 so they are synchronous with those from the scaler circuit. The output of I10 serves as a gating signal to the J input of FF2. Initially, the output from G3 is LOW which holds G4 closed. The inverted signal from I10 is therefore HIGH and primes FF2 to be set to the ONE state. Once FF2 is HIGH, it can only be set to the ZERO state by a reset pulse. The output G3 also provides the logic level control signal to the analog switch through jack J5. FUNCTION switch S1 turns on the power and selects manual (SlB) or automatic operation (SlC). The timing signal is scaled by decimal counters DC13-DC15 and the RANGE switch, S2A, selects the desired timing range. To begin a titration, the RESET, PROCEED, and START-
STOP switches are thrown in that order. The RESET switch, S5, resets the decade counters of the readout counter network, performs a segment test of the seven segment readout devices, and resets the time anticipation network. The PROCEED switch, S4, is used only to reset the decade counters in the logic circuit network. As the START switch is turned on, FF1 is set to the ONE state. The high output from Q, together with an initial HIGH from 110, are applied to the J input of FF2 which will then go HIGH on the next downclock from the oscillator (a maximum of 1 ms later). Flip-flop 2 cannot be set to the ZERO state because the K input is grounded. Gate 5 and I7 are a reset circuit for FF1 and FF2. In the manual mode, a transition to the LOW output state a t G12, routed through SlA, will set the flip-flops to the ZERO state. The STOP switch will also do this and is the only method by which FF1 and FF2 can be reset in the automatic mode. The STOP switch also opens the memory circuit via G I 1 and holds the count in the readout display. The anticipation network consists of decade counters DC16-DC19, flip-flops FF3-FF5, gates G6-Gl0, and inverters I8 and 19. Decade counter DC19 is tapped as a divide by 5 circuit and produces a pulse every 5 s which toggles FF3 to produce a square wave that is HIGH for 5 s and LOW for 5 s. The output of FF3 serves as the clock pulse for the D type flip-flops, FF4 and FF5, to sequentially pass on the logic condition of G7. Once FF5 goes HIGH and opens G8, the 10-s square wave is passed to G9 as a gating signal to open and close this gate every five seconds. When the time of electrolysis exceeds the preselected time a t which the anticipation network becomes operational, GI2 goes LOW, G7 goes HIGH, and G9 is under control of the square wave. The signal is passed on to G10 which together with I9 functions as an OR gate to pass either the signal from G9 or S6 to control the on-off condition of the titrator. The signal from switch S6 is the T T L compatible logic signal from the comparator circuit. The logic level of this signal depends on whether the input signal to the comparator is more positive than the comparator reference signal (logic output HIGH) or less positive (logic output LOW). Only one of the above conditions can exist during any particular titration and the comparator crossover point is approached from only one direction. To supply the same logic level to G10 regardless of the direction of approach to the ANALYTICAL CHEMISTRY, VOL. 48, NO. 7,
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Figure 5. Schematic diagram of timing module Dl-D6, Shelly Incandescent Readout Device, Type 3015F; DC1-DC19, SN7490 Decade Counter: DD1-DD6, SN7442 Decimal Decoder-Driver: FFI, FF2, Heath J-K Flip-Flop Card, EU-800-CB; FF3. SN7472 J-K Flip-Flop; FF4, FF5, SN7474 Dual "D" Type Flip-Flop: G1-05, G11, Heath Nand Gate Card, EU-800JC: G6GlO. 19, SN7400 Quad 2-Input Nand Gate; 012, SN7430 Eight Input Nand Gate; 1,148, 110-113, SN7404 Hex Inverter; J l J 5 , Type55575 BNC bulkhead connector; L1-L6, SN7447 Quad Bistable Latch: OSC. Heath Oscillator Card, EU-800-KA; SI,4 pole, 3 position rotary wafer switch: 52, 2 pole, 4 position rotary waver switch: S3,DPDT-center neutral-telephone lever switch; S4. SPDT push button switch; S5, 2 gang SPDT push button micro-switch: S6, DPDT toggle switch: S7-S12, 1 pole, 10 position thumbwheel rotary switch: SSD1-SSD6. SN7447 Seven-Segment Decoder-Driver
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ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
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Figure 6. Electronic diagram of constant current source module ASW, Fairchild SH-3002 SPDT analog switch; B1, TR233, 4.2 V mercury cell: 82, TR234R, 5.6 V mercury cell; 63, HG42R, 1.35 V mercury cell; D1, lN53388, 5.1 V zener diode; J1-J13, Type 5575 BNC bulkhead connecter; OAl, OA2, Heath Operational Amplifier Card, EU-900-NA; OA3, TTL Driver, Heath Comparator/V-F Card, EU-800-HB; BY, 82, Heath Dual Booster OA Card, EU-900-CA; R1, 5K, 1 W, 0.5% trimmer pot; R2, 20K. 1 W. 0.5% trimmer pot; R3, R4, 500 R, 1 W, 0.5% trimmer pot; R5, IOOK, 1 W, 0.5% trimmer pot; R6. R51. R56, l K , 1%; R7, 1349, R57. 10K, 1 % ; R8. 1.000K; R9, 500.0 0;R10, 333.3 0;R11, 250.0 n; R12. 200.0 n; R13, 10.00K; R14, 5.000K; R15, 3.333K; R16. 2.500K; R17, 2.000K: R18, 1.666K; R19, 1.429K; R20, 1.250K; R21, 1.111K; R22, 100.OK; R23, 50.00K: R24, 33.33K; R25. 25.00K; R26, 20.00K; R27. 16.66K; R28, 14.29K: R29. 12.50K; R30, 11.11K; R31, 1.000M; R32, 500.OK; R33, 333.3K; R34, 250.OK; R35, 200.OK; R36. 166.6K; R37, 142.9K; R38, 125.OK; R39, 1ll.lK:R40. 10.00M; R41, 5.000M; R42, 3.333M; R43, 2.500M; R44, 2.00M; R45, 1.666M; R46, 1.429M; R47, 1.250M; R48, 1.111M; R50. R52, 100K, 1 %; R53, 100 R, 20 W, 3 % ; R54, R55, 15K, 5%; SI,9 pole, 4 position rotary wafer switch; S2, 4 gang SPST micro-switch; S3, DPST slide switch; S4-S8 1 pole, 10 position thumbwheel rotary switch; S9. SPST toggle switch. Resistors are 0.5 W. 0.3% as measured, unless otherwise noted
end point, inverting gate I8 is switched in or out of the circuit as needed by the DPDT switch, S6. The oscillator signal is scaled by decade counters, DC13-DC15 and the desired range is selected by switch S2A. The same timing pulses are counted by both counters. The logic counter consists of decade counters DC7-DC12, decimal decoder drivers DD1 -DD6, TIME SELECTOR switches S7-Sl2, inverters 11-116, and gate G12. The decimal outputs of the decoder drivers are connected to the corresponding position of one of the switches, S7-Sl2. The output of each switch is inverted and passed to gate G12. When the counter reaches the count set on the TIME SELECTOR switches, the output of G12 goes LOW and G1 closes to stop the counting process. As this sequence of events occurs, the readout counter is also operating. This network is comprised of decade counters DC1-DC6, quad bistable latches Ll-L6, seven segment decoder drivers SSD1-SSD6, seven segment readout units Dl-D6, and
switch S2B. Inverters I4 and I13 and gate G11 form a circuit which opens or closes the memory gates of the quad latches. When the titrator is on, the memory input is HIGH and passes the count from the decade counters to the decoder drivers. When a stop pulse is received, the memory input goes LOW to hold the count in the quad latches and to prevent the readout display from being altered. Switch S2B selects the proper decimal point for the readout display. Analog Module. A schematic diagram of the module is shown in Figure 6. The overall circuit design is based on established operational amplifier circuits. There are three main subsections: the voltage source and parallel resistor network, the constant current source and analog switch, and the comparator and TTL driver. Switch Sl, the RUNBAL switch, is the function switch for the module. The output and/or the input of each operational amplifier is controlled by this switch. In the RUN position (shown in ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
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the diagram) all of the circuits are connected for a titration. In each of the three balance positions (BAL), the associated OA is connected as a gain of ten amplifier with a grounded input resistor. The position of S1G selects the signal to appear at the VOLTMETER jacks, J 6 and 57, where it may be monitored. The voltage reference source is in a noninverting configuration (20) and is composed of OAl, booster amplifier B1, resistors R6 and R7, potentiometers R1 and R2, battery B3, switch S3, and wafers E and F of switch Sl. Potentiometer R3 is the balance control. Battery B3 is a 1.35 V mercury cell and the ratio of R7 to R1 is adjusted by the current calibration control (CUR CAL), R1, to bring the output voltage to about 10 V. Switch S3, labeled ANODICCATHODIC, reverses the polarity of B3 and therefore determines the direction of current through the cell. The output of the voltage source is applied across the parallel resistor network formed by resistors R8-R48 and thumbwheel switches S4-S8 (CURRENT SELECTOR). The value of each resistor was calculated so that currents from 1 pA to 59.999 mA could be directly dialed in 1 pA increments. Each resistor was hand selected from precision resistors so the precision and accuracy of lower microampere currents is considerably better than the precision with which the dials can be read. Further, in practice, the current through the dummy resistor can be monitored and R1 adjusted to make the current equal to the dial settings if any significant difference is observed. The total current from the parallel resistor network supplies a standard operational amplifier constant current source which has the cell in the feedback loop and the working electrode connected to vertual ground. The circuit consists of OA2, booster amplifier B2, wafers C and D of switch S1, resistors R56 and R57, potentiometer R4, the analog switch, jacks 58 and J 9 for the cell, jacks J10 and J l l for the dummy resistor, and jack 55 for the logic control signal to the analog switch. Potentiometer R4 is the balance pot used in connection with R56 and R57. The analog switch, a Fairchild SH-3002, is a SPDT MOSFET make-before-break type. The advantage of the latter feature for switching in the feedback loop is well known. Two other features of the switch are of interest: the ON resistance and the switching time. The ON resistance is a nonlinear function of the difference between the minimum voltage applied at either the normally open, or normally closed, or common switch contacts and the negative supply voltage to the switch. Battery B2 is placed in series with the minus 15V supply to bring the total to -20.6 V. According to the manufacturer’s data, these operating conditions produce a switch ON resistance of about 100 D (21). It is important to maintain both the switch and cell resistance as low as possible to avoid exceeding the 10-V compliance of the OA. The manufacturer’s recommended positive switch supply voltage is 11 V. A 4.2 V mercury cell, B1, was placed in series opposition to the positive 15 V supply. More recently, this arrangement has been replaced by a zener diode circuit. Switch S2 is the main power switch for the module. Switching times for the SH-3002 as listed by the manufacturer are ton= 120 ns and teff = 1.5 ws. The latter is a little slow for counting to the nearest microsecond. A nonstandard SH-3002 with a faster switching time was obtained. Performance of the titrator with commercially available SH-3002 switches might be somewhat poorer than that reported here. The comparator and TTL driver comprise the remainder of the circuit. The former consists of OA3, R5, R49-R52, and wafers A, B, H, and I of S1. A voltage divider across the 15 V supplies, R2, R54, and R55, is a variable reference 1066
ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
input circuit to the comparator. Potentiometer R2 (REF ADJ), produces a voltage range of +6.5 to -6.5 V. Jacks 512 and 513 are the comparator input (COMP INPUT). The TTL driver was available on the printed circuit card. I t did not seem desirable to bring the timing module 5 V supply into the analog module so power for the driver was supplied by the zener diode circuit of D1, R53, and S9. Power Supplies. A Philbrick Model PR-300 power supply (Teledyne-Philbrick, Dedham, Mass.) was used to supply f 1 5 V and a Lambda Model LH 121B-FM was used for the 5 V supply (Lambda Electronic Corp., Melville, N.Y.). High-frequency noise on the laboratory AC line was particularly troublesome and an isolation transformer was used to remove it (Del Electronics Type AD 1647). The transformer output was connected to a six-outlet power strip and the titrator and all auxiliary equipment was plugged into this strip. All signal grounds were connected in sequence and terminated a t the center tap of one of the power supply transformers. Chassis ground was carefully maintained separate from the signal ground system and the two joined at a single point. Construction. Complete wiring diagrams for individual printed circuit boards, pin number connections, and other details are available from the authors. Heath EU-800 and EU-900 series plug-in circuit boards (Heath Co., Benton Harbor, Mich.) and SN7400 series integrated circuits were used. The timing module was housed in a cowl-type Minibox, 12 X 6 X 7 in. (1 X w X h ) (Bud Radio, Willoughby, Ohio). External connections were made through BNC bulkhead connectors. Heath cards used in the timing module were: one EU-50-MC Dual Inline IC card, two EU-800-JC Nand Gate Cards, four EU-50-MD Blank PC Cards, one EU-800-CB J-K Flip-Flop Card, and one EU-800-KA Oscillator Card. The Dual Inline Card was modified to mount two additional integrated circuit sockets. One Blank PC Board was etched to receive two IC sockets which held SN7404 Hex Inverters. The three remaining PC boards were etched to mount two SN7490 decade counters, two SN7475 Quad Bistable Latches, and two SN7447 sevensegment decoder drivers. Heath boards were mounted horizontally in the module and pin connections were made with the Heath Permanent Patch Accessory, EU,-50-JA,which was mounted vertically. The entire logic counter was constructed on a 3.5 X 5 in. glass-epoxy board. Similarly, a board was constructed locally to hold the seven-segmentdisplay units. Integrated circuits for the time anticipation and scaler circuits were mounted on a 2.5 X 4 in. circuit board. The analog module was a two-piece Minibox, 12 X 7 X 4 in. ( 2 X w x h ) . Four Heath plug-in cards were used: two EU-900-NA Operational Amplifier Cards, one EU-900-CA Dual Booster OA Card, and one EU-800-HB Comparator/ V-F Card. The two OA cards were modified by removing the balance potentiometers from the circuit boards and mounting them on the front panel. The Comparator Card was modified by removal of the components of the voltageto-frequency converter since these proved to be a source of noise. Pin connections to these cards were also made with the Patch Accessory. The parallel resistor network was built on two 4.5 X 5 in. circuit boards. Decoupling capacitors were used throughout the construction between chassis and signal ground. EXPERIMENTAL Apparatus. Voltage measurements were made with either a Fluke Model 8300A-02 DVM (John Fluke Mfg. Co., Inc., Seattle, Wash.) or a Portametric PVB Potentiometer, Model 300 (Electro Scientific Industries, Portland, Ore.). Oscilloscope measurements were made with a Tektronix Type 564B Storage Oscilloscope
equipped with a type (2-12 camera, Type 3B3 Time Base, and either a Type 3A9 Differential Amplifier or a Type 3A6 Dual Beam Amplifier. A Heath Model 80A Voltage References Source was used. Cell temperature was controlled with a Tamson Model T 9 circulating constant temperature bath. The differential amplifier used to measure the cell emf in the automatic permanganate titrations was constructed on 'a Model 5001 OA Manifold (Teledyne-Philbrick, Dedham, Mass.). The circuit was designed according to Ref 22. The input stages were Nexus-Philbrick FET type OA's and the output stage was a Nexus-Philbrick Type SQ-loa general purpose OA. The overall circuit gain was one. Response linearity was checked using the VRS for input voltages from a few millivolts to several volts. Reagents. All chemicals used were reagent grade unless otherwise noted. Solutions were prepared from distilled water which had been redistilled from alkaline permanganate solution. Vanadium Solutions. A stock vanadium solution was prepared by dissolving 407 fig of vanadium pentoxide in 3 M H2S04. Supporting electrolyte was prepared by adding 100 ml of 0.5 M Fez(S0)4 to 500 ml of 3 M Hz(S0)4 to yield a solution 0.08 M in Fe2(S0)4 and 2.5 M in H2S04. Permanganate Solutions. A stock permanganate solution of approximately 0.1 N was prepared according to the procedure of Skoog and West (23). Working solutions for titrations were prepared by diluting approximately 0.5 ml of the 0.1 N stock solution to about 11. Supporting electrolyte was prepared from stock 0.5 M Fe2(S0)4 and 3 M H2S04. For samples in the nanogram region, a supporting electrolyte of lower iron concentration but higher acid concentration was used: 0.02 M in Fe2(S0)4 and 1.5 M in H2S04. Volume Delivery. Samples were added by one of two methods: larger volumes were added with calibrated 1, 5, or 10 ml, Class A transfer pipets; and volumes less than 1 ml were added with a micrometer driven microburet (Type S-3100, Roger Gilmont Instrumentation, Inc., Great Neck, N.Y.). Cell for the Vanadium Titrations. Titrations were carried out in a Pyrex weighing bottle, 65 mm high by 57 mm in diameter, fitted with a Teflon stopper with holes drilled in it to accept the electrodes and gas dispersion tube. The counter electrode of the generating electrode pair was isolated from the analytical solution by a 13-mm diameter filter tube sealed a t the end with an ultra fine porosity glass frit. The volume of the cell was 80 ml. Oxygen was removed with nitrogen gas. The titrant generation electrode pair were an approximately 1 cm square platinum flag generator electrode and a platinum spiral counter electrode of No. 22 gauge wire. A mercuryl mercurous sulfate reference electrode was constructed according to the method of Lingane (24). The experimentally measured potential of the electrode was 413 mV vs. SCE, or 659 mV vs. NHE (as calculated). The electrolyte in the bridge arm of this reference electrode was 3 M H2S04. The indicator electrode was a platinum flag nearly identical with the generator electrode. The assembled cell was placed in a water jacket through which 30 "C water from the bath circulated. A stirring bar and water were placed in the annular space of the jacket and a second stirring bar was placed in the cell. Both stirring bars were driven by the same magnetic stirring motor. Cell for the Permanganate Titrations. A 100 mm length of 30 mm diameter Pyrex tubing, closed a t one end, was used. A 13 mm diameter Pyrex side arm, isolated by a very fine porosity glass frit, served as the isolated counter electrode chamber. A lid was constructed from Plexiglas with appropriate holes drilled in it. The same generating electrode pair as used in the vanadium work was used. The indicator electrode was a 12 in. length of No. 24 gauge, platinum-15% iridium wire, wound into a coil. A lead amalgamIlead sulfate reference electrode was constructed in the Lingane configuration. The lead amalgam was prepared according to the procedure of Parks ( 2 5 ) .Again, 3 M H2SO4 was used in the bridge arm of the electrode. The measured potential of the electrode was -546 mV vs. SCE or -300 mV as calculated vs. NHE. Vanadium Procedure. The electrodes and gas dispersion tube were placed in the cell containing about 50 ml of supporting electrolyte and nitrogen was bubbled for 10 min as the solution was stirred and brought to temperature equilibrium. Then the dispersion tube was pulled out of the solution and used to keep a nitrogen blanket over the solution. The end point potential was set on the potentiometer and the solution pretitrated to that potential, adding vanadium(V) if necessary. After completion of the pretitration, a vanadium(V) sample is added to the cell and an appropriate generation time is set on the TIME SELECTOR. A current is set in the CURRENT SELECTOR switches. The RESET, PROCEED, and START switches are set in that order. Current will
flow in the cell until the preselected time of electrolysis is reached. If more coulombs are required, a new time is set on the TIME SELECTOR, the PROCEED and START switches are set, and current again is applied to the cell. This process is continued until the solution potential has been returned to the end point potential. Near the end point, the tap key of the potentiometer is left closed but the solution is always titrated to the preset potential. The total elapsed time required to reach the end point is stored in the readout display. A new sample can be added to the solution, the titrator reset, and the next titration started. Permanganate Procedure. An initial shut-off time, corresponding to some fraction of the total electrolysis time, was set in the TIME SELECTOR. The desired generation current was set on the CURRENT SELECTOR and the end point potential was set on the reference input to the comparator using the REF ADJ control. Supporting electrolyte was added to the titration cell and the side arm was filled with the 3 M H2S04 to approximately the same level as the solution in the cell proper. The difference amplifier was connected to the reference and indicator electrodes and its output was connected to the comparator. Usually a drop or two of permanganate solution was added to the cell, and then pretitration started by setting the PROCEED, RESET, and START buttons in that order. The instrument will automatically pretitrate the solution. A permanganate sample is added to the cell and the titration sequence started by pushing the PROCEED, RESET, and START buttons. Titrant generation will continue until the preselected shut-off time is reached. The titration then continues to the end point under control of the anticipation circuit and the end point detection system. The elapsed electrolysis time for the completed titration is read from the readout display. Another sample may now be added.
RESULTS AND DISCUSSION One instrumental objective was to produce current pulses as short as 1 ms in duration with a precision and accuracy of a few parts per thousand in the elapsed time. With a highly accurate and stable clock producing 1-ws pulses, this is possible if the cell current-switching action is fast enough. Figure 7 shows several oscilloscope photographs of the switching action as measured differentially across a 50 0 f 0.05% resistor in series with the cell. In each case, the traces were stored and then photographed. The current pulses of 2.000 mA amplitude, as dialed on the CURRENT SELECTOR, were 200 ws in duration and were applied every millisecond. Part a of Figure 7 shows two such pulses. Little noise is evident and the transitions are very sharp. A closer look a t the leading and trailing edges is shown in parts b and c of Figure 7 . The horizontal time base in the latter cases is 500 ns/cm. A comparison of the traces in parts b and c with that in part a shows that the current applied to the cell is essentially fully on or fully off within a microsecond of the time the switching action begins. This performance was highly satisfactory. The noise present on the signal was also of interest since it would affect the accuracy of the current. The two major frequency components of the noise were 4 MHz from the crystal oscillator and 120 Hz from the power supplies. Figure 8 shows the noise signal as measured with the scope DC coupled and the DC component of the signal balanced out with the DC offset control of the T3A9 vertical amplifier. The upper trace is the 4 MHz component and the lower trace shows the 120 Hz component with the 4 MHz noise superimposed. The peak to peak noise voltage in the lower trace is about 1 mV. The experiment was done with 5.000 mA set on the CURRENT SELECTOR and the iR drop was measured differentially across a 199.7 R resistor in place of the cell. By centering the trace on a scope graticule line, removing the signal, and replacing it with the output of a potentiometer, 1000.2 mV were required to restore the scope trace to the same graticule line. The iR drop across the resistor as measured with the DVM was 1000.12 mV. The agreement between these two results is excellent. A measurement made about 10 h later yielded 1001.01 mV. ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
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ir drop across a precision resistor, mV
100.42 100.44 100.46
b
C
Flgure 7. Oscilloscope photos of
a current pulse train appliedto the
cell Horizontal scale: (a) 200 &s/cm: (b) 500 nslcm; (e) 500 ndcm. Verlical axis: (a-c) 20 mVlcm
Figure 8. Current noise Uppsr trace: 4 MHz component. horizontal scale, 500 "$/em: vefllcal scale. 1 mV/cm. Lower trace: 120 Hz component. horizontal scale, 5 mslcm: veflifa1 scale. 1 mV/cm
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ANALYTICAL CHEMISTRY. VOL.48, NO. 7, JUNE 1976
100.47 100.47
*
Av 100.48 0.03 mV Re1 error -0.02%
This stability requires an initial warmup of the current source for about 30 min. Further data on the precision and accuracy of the magnitude of the current were obtained by applying 10.000-s pulses, 10.047 mA in amplitude, across a 10 Q & 0.05% resistor (General Radio Type 500). The iR drop was measured with the DVM and the results are shown in Table I. The relative error is within the error of the resistor. The same precision was obtained a t 1 p A of current using a 100 kR type 500 resistor but accuracy here was limited by the 100 MQ input impedance of the DVM. Several objectives were realized by the use of the F E T input differential (instrumentation) amplifier in the detector circuit. The signal to the comparator is referenced to true ground rather than virtual ground and the signal noise is substantially reduced by the high CMRR of this circuit. The FET input stages provide very low current drain in the measurement, which may appear to be unnecessary since the electrodes have low resistance and the ionic strength of the solution is high, hut the concern is activation overpotential at the indicator electrode. Assuming small overpotential, the time constant for the decay of overpotential is fixed by the prevailing experimental conditions and is not subject to a large degree of control or manipulation in a titration experiment. However, if the current drain in the measurement is much smalIer than the exchange current of the potential determining couple in the region of the end point, the activation overpotential is very small and the equilibrium electrode potential should be approached rapidly. Vanadium Titrations. Vanadium(V) was titrated with electrogenerated Fe(I1) according to the procedure of Furman, Reilley, and Cooke (26). The titrator was operated in the manual mode. The end point potential in all cases was 302.00 mV vs. the mercuryl mercurous sulfate reference electrode (961 mV vs. NHE) which corresponded to the inflection point of the experimental titration curve. Data and results for a number of determinations of the vanadium stock solution are presented in Table 11. The amount of vanadium found ranged from about 2.2 mg t o 2.2 wg and the concentration of the stock solution as calculated from these amount8 and the corresponding volumes taken is given in row 7 of Table 11. The agreement among the results is excellent and does not seem to depend on either the volume of stock solution taken or the length of time of electrolysis required to reach the end point. The error in this coulometric titration, as reported by Furman, Reilley, and Cooke for milligram amounts of vanadium, was 0.1 to 0.2% relative. Current densities in their work and ours are comparable. The average of all of the results in Table I1 for the concentration of the stock vanadium solution is 225.5 wglml and will be taken as the best value. The precision of each set of data is also excellent. The last two columns of Table I1 are of special interest from several points of view. The precision and accuracy of these results in the microgram region are better by about an order of magnitude than the results of the earlier workers (26). Since the electrochemistry
-
~~~
Table 11. Manual Titration of Vanadium(V) Stock Solution with Coulometrically Generated Ferrous Ion 6 6 6 6 No. of replicates 5 10.00= 20.00" 100.00" 1005 f 2 10005 1 3 Volume of stock solution taken, pl 0.4425 0.8852 4.432 44.38 443.4 Average end point time, s 9.649 9.649 9.646 9.649 Current, mA 9.649 2.255 4.510 226.0 22.58 Vanadium found, pg 2258 fO.1 fO.l fO.l fO.1 Re1 precision, % fO.0 225.5 225.5 225.8 224.9 225.7 Concn of stock solution found, pg/ml fO.0 fO.0 +0.13 -0.27 +0.09 Re1 difference fromb the overall av, % 0.045 4.43 0.452 0.090 Approximate concn of analysis solution, ppm 37.6 " Manufacturers specification for the microburet: accuracy 0.04%precision 4~0.004%relative to the full capacity of 250 pl. Average of all results = 225.5 pg/ml.
Table 111. Manual Titration of Diluted Vanadium(V) Stock Solution with Coulometrically Generated Ferrous Ion Solution A B B C C C No. of replicates 5 5 7 5 6 6 100.00~ 10 005 f 3 100.00" Vol of soln taken, pl 10 005 1 3 50.00" 10 005 f 3 4.321 0.04153 Av end point time, s 4.269 4.344 0.04256 0.02053 9.649 Current, mA 9.649 9.650 9.654 9.649 9.648 22.01 0.216~ 22.14 Vanadium found, pg 21.74 0.211~ 0.1046 f0.2 f1.2 f0.4 Re1 precision, % f0.2 A2.5 f1.5 220.0 216.8 221.3 211.6 Concn of diluted stock solution found, pglml 217.3 209.2 -2.4 -2.8 -1.9 Re1 error, % -3.6 -6.2 -7.2 4.3 Approx concn of analysis soln, ppb 362 4.2 367 369 2.1 " Specifications as in Table 11.
in both instances is similar in all aspects, this improvement is attributed to the unique features of the instrumentation presented here: reliable, fast solid-state switching, and digital timing circuits. These results also demonstrate that coulometric titrations with subsecond total electrolysis times are fully capable of very high precision and accuracy. This is of significance in terms of automatic coulometric titrations and will be examined in the section on permanganate titrations. The electrolysis solution volume was about 50 ml so the approximate changes in concentrations of the vanadium solutions actually used experimentally were 90 and 45 ppb for columns 5 and 6, respectively. These results prompted work on more dilute solutions. Three solutions were prepared by 1OO:l dilutions of the stock solution. Data and results are shown in Table 111. The precision of the results for the 10-ml samples is in agreement with that of Table 11. Precision for samples containing 0.1 to 0.2 pg of vanadium was fl to f 3 % relative and was limited by detector response. With the current used, it was necessary to generate titrant for a t least 100 pus to see a change in the detector response. This corresponds to equiv or 0.5 ng of vanadium and represents a change in concentration of about 10 parts per trillion. The relative error shown in row 8 of Table I11 is based on the overall average of the results in Table 11. Accepting the numbers a t face value, an error of -7% is tolerable for the 0.1-pg samples which correspond to determinations of 2 ppb solutions. However, it is probable that not all of the error is due to the coulometric method but rather that some vanadium is lost in the dilution and sample delivery processes. The end point times for the titration of the 0.1- and 0.2pg samples are worthy of comment. The results prove the feasibility of performing coulometric titrations with total electrolysis times of tens of milliseconds. Thus, shorter electrolysis times are a viable alternative to the use of smaller currents for the determination of very dilute solutions of sought-for constituent. However, the total time for
the titrations (after addition of sample) was typically several minutes. To generate an increment of titrant, the generator electrode must be shifted from the prevailing equilibrium potential of the system to the potential demanded by the current being passed. This requires that the double layer capacitance, for example, be charged. It might seem that these coulombs would be lost but they may be recovered by discharge of the double layer capacitance through the Faradaic reaction. It is necessary to allow sufficient time on open circuit (current OFF) for this to occur and a typical figure is 50 ms. Clearly, titration to a preset potential is a necessity for very dilute solutions. I t should be mentioned that other non-Faradaic processes may contribute to the background current and a net loss of coulombs may occur. Meites (27) has discussed these factors, and the double layer capacity, in terms of their effect on current efficiency. I t appears from our work that current pulses of constant amplitude and of very short pulse width can be used to generate very small known amounts of titrant provided that the equilibrium potential of the solution is the same at the end of the experiment as the beginning and that sufficient time elapses for the double layer capacitance to charge or discharge through the Faradaic reaction. Permanganate Titrations. Manganese(VI1) was titrated with electrogenerated Fe(11) according to the procedure of Cooke, Reilley, and Furman (28) except that the presence of Mn(I1) in the supporting electrolyte was not required and that the titrator was operated in the automatic mode. Because of potential instability and drift in the potential measurement, particularly with the more dilute solutions, a platinum, mercuryl mercurous sulfate indicator electrode pair was abandoned in favor of the platinum1 iridium alloy, lead amalgam1lead sulfate electrode pair recommended by these authors. A combination of the PqIr electrode with the mercuryl mercurous sulfate electrode produced considerable improvement but the performance was not as good as that achieved with the final arrangeANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
* 1069
Table IV. Automatic Coulometric Titration of Manganese(VI1) with Electrogenerated Ferrous Ion No. of replicates 7" 126 5c 7 6 9 8 10 100.OOd 10.OOd 10.OOd 5.00d 5001 f 4 1005 f 2 5001 h 4 Vol of stock soln taken, p1 5001 h 4 23.23 4.656 0.4594 47.18 0.4706 235.4 235.6 235.4 Av end point time, s 9.97 965.0 9649 96.90 963.4 963.2 963.4 Current, pA 963.2 0.0505 0.0264 0.5171 0.0514 25.82 5.176 25.82 Manganese found, pg 25.86 h1.3 h2.3 f0.6 hl.0 f0.2 10.2 h0.2 h0.3 Re1 precision, % 5.05 5.27 5.171 5.14 5.163 5.150 5.163 Concn stock soln found, pglml 5.171 1.4240 1.3640 1.3640 1.2590 1.1940 1.2550 1.2550 End point potential, v 1.2550 Titrations performed on the same day as the manual titrations. Titrations performed 2 weeks after the a Manual titrations. manual titrations. Specifications as in Table 11.
ment. Potentials were very stable and the response was rapid. The role of surface oxide formation on electrodes used in potentiometric titrations is not clear but it is likely that the difference in behavior between the pure platinum and the PdIr electrodes is due in part to surface oxide effects. Also, Laitinen (29) has discussed the Fe(I1)-permanganate titration and points out strong evidence that the Mn(II1)-Mn(I1) couple plays a role in the reaction and may be potential determining near the equivalence point in the presence of excess permanganate. The fact that the equilibrium potential is attained more rapidly with the P( Ir electrode than with the pure platinum electrode indicates that the exchange current for the potential determining couple is higher on PqIr than it is on platinum. To see the experimental effect of using the Pd Ir electrode rather than the Pt electrode, a number of manual titrations were done on a point-by-point basis. The titration curves were normalized by plotting them in terms of fraction titrated. In general, the potential break is smaller with the alloy electrode than with the platinum electrode and the slope of the titration curve in the end point region is smaller with the alloy electrode. Neither of these results is expected for Nerstian behavior but the MnOd--Mn(II) couple is known to be irreversible. Analogous results were found by Athavale and coworkers in a comparison of PdRh electrodes with pure platinum electrodes (30). In this work, two methods of end point anticipation were used simultaneously. The first of these is well known and involved placing the indicator electrode :i a position in the cell where it was bathed with the solution coming from the generator electrode. The second method involved the timing circuits which automatically stopped the titration at a preset time of electrolysis and then allowed current to pass during every other 5 s time interval thereafter until the end point was reached. The initial shut-off times varied between 7 5 and 95% of the total electrolysis times. During the ON periods, the signal from the indicator electrode pair could turn the current ON or OFF. Despite these efforts, it was necessary to empirically choose the potential for the pretitration to avoid overshooting the end points. Mixing of the electrogenerated reagent with the bulk of solution is probably the single most troublesome problem in an automatic coulometric procedure. For higher concentrations, a less oxidizing potential would be chosen to lower the rate of change of potential and for lower concentrations, a potential closer to the equivalence point would be chosen, to produce a reasonable change in potential upon addition of sample. Furthermore, for titrations of samples containing less than a microgram of manganese, the Fe(II1) concentration of the supporting electrolyte was lowered. This has the effect of lowering the concentration of Fe(I1) required for a given electrode potential. Data and results for a number of determinations are shown in Table IV. Decomposition of the permanganate solutions was a problem and several pro1070
ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
cedures were developed to overcome this. The diluted permanganate solution could be stored for about 3 weeks if the storage bottle were covered with black plastic. If permanganate solutions were left in the microburet, manganese dioxide would form overnight a t the top of the glass plunger and at the tip of the buret stem. The glass portion of the microburet was covered with black plastic tubing to the point where the buret stem passed through the cell cover and the cell itself was also covered with black plastic. Finally, titrations were performed in subdued natural light or in the evening under artificial light. Since the concentration of this permanganate solution was not known exactly, a series of manual titrations (column 1 of Table IV) was run to establish it. The agreement among the results (row 7 ) is excellent and the precision for determinations of amQunts greater than 1 wg is f 2 to f 3 parts per thousand relative. For 26-ng samples the precision is f2.3% and the error is 2%. This amount of manganese added to the cell corresponded to a concentration change of 2.5 ppb. The error is about the same as the error in the delivery of the 5-wl sample. The problem of overshooting the end point is also more severe here as the preset potential is on the steepest part of the titration curve. Other situations illustrating the mixing problem can be found in the table. The least positive pretitration potential used corresponds to the fastest rate of generation of titrant. Selection of a preset end point potential of 1.3640 V produced a potential change of about 115 mV for samples containing 51 ng of manganese. Two sets of titrations were performed: one a t ten times the rate of titrant generation as the other. The relative error in the faster titration was four times that of the slower. The necessity of adjusting the end point potential and rate of titrant generation to achieve satisfactory results for different sample sizes is irksome but the results in Table I1 illustrate that the effort is worthwhile. Automatic titrations with subsecond total electrolysis time are entirely feasible. Data of very high precision and accuracy can be obtained and automatic titrations of very dilute solutions are possible. CONCLUSIONS While titration to a preset end point potential is an established procedure in the literature of coulometric titrations, it is informative to look a t it from the point of view of a null-type procedure. It is true that, upon addition of sample, the largest change in signal will occur if the null point coincides with the equivalence point of the titration, but this is not a necessary condition for the null point. In fact, the ability to shift the null point to a region where excess titrant exists can be an advantage in the determination of trace amounts since it will aid in forcing the titration reaction to completion, may shorten the time it takes the reaction to go to completion, and may improve the response
time for the electrode process in the case of potentiometric end point detection. In short, it should be possible to find an optimum compromise between the sensitivity at the null point and the kinetics of the various processes involved. This advantage of coulometric titrations in trace analysis does not seem to be fully recognized. Another advantage of the method in trace work is that it offers an optimal possibility to prevent loss of sought for constituent by adsorption on the walls of the vessel used for the determination. This is so because the ionic strength of the solution is very high corhpared with the concentration of sought for constituent and the adsorption sites may already be occupied. Furthermore, there is always some of the sought for constituent present prior to the addition of a sample. In view of the results presented it seems reasonable that in a fully automated constant current coulometric analyzer system, the number of samples handled per unit time would be limited primarily by the length of time required to change samples. It is possible that coulometric systems could be devised to handle well over a thousand samples in a 24-h period. Considerable simplification in plumbing might also occur since the supporting electrolyte could be premixed, no further reagents in solution are necessary, and a number of determinations can be made sequentially in the same supporting electrolyte. The present instrument is capable of generating a 10-ps current pulse containing pC of charge within an accuracy of 10% relative. The measurement of equiv of material is orders of magnitude beyond the capabilities of present end point detection systems. New approaches are needed. A report of our efforts using fluorescent indicators for coulometric acid-base titrations has been published (31).
(4) J. K. Taylor and S. W. Smith, J. Res. Natl. Bur. Stand., Sect. A, 63, 153 (1959). (5) V. V. Mironenkov and L. Sh. Malkin, Zavod. Lab., 35, 289 (1969). (6) J. A. Pike and G. C. Goode, Anal. Chim. Acta, 39, 1 (1967). (7) J. C. Quayle and F. A. Cooper, Analyst (London), 91, 355 (1966). (8) K. W. Kramer and R. B. Fischer, Anal. Chem., 26,415 (1954). (9) Y. Maekawa and L. Okasaki, Yakugaku Zasshi, 80, 1411 (1960). (10) M. Lindstrom and G. Sundholm. J. Chem. Educ., 49,847 (1972). (1 1) I. Slavicek and J. Soucek, Chem. Prum., 20, 334 (1970). (12) R. E. Karcher and H. L. Pardue. Clin. Chem. ( Winston-Salem, N.C.), 17, 214 (1971). (13) J. Loiselet and G. Srouji, SOC.Chlm. Bid. Bull., 50, 219 (1968). (14) L. Meites, Anal. Chern., 24, 1057 (1952). (15) J. S. Parsons, W. Seaman, and R. M. Amick. Anal. Chem., 27, 1754 (1955). (16) K. Jeffcoat and M. Akhtar, Analyst(London), 87, 455 (1962). (17) R . G. Clem and W. W. Goldsworthy, Anal. Chem.. 43, 918 (1971). (18) R. G. Clem, lnd. Res., 15, 50 (1973). (19) W. D. Cooke, C. N. Reilley, and N. H. Furman, Anal. Chem., 23, 1662 (1951). (20) Burr-Brown Research Corp., "Operational Amplifiers: Design and Applications", J. G. Graeme, G. E. Tobey, and L. P. Huelsman. Ed., McGrawHill, New York, N.Y., 1971, p 229. (21) Fairchild Semiconductor Corp., Mountain View, Calif., "Integrated Circuit Data Catalog", 1970, pp 5-34. (22) Philbrick Researches, "Application Manual for Computing Amplifiers", Nimrod Press Inc., Boston, 1966, p 82. (23) D. A. Skoog and D. M. West, "Fundamentals of Analytical Chemistry", Holt, Rinehart and Winston, New York, N.Y., 1963, p 435. (24) J. J. Lingane. "Electroanalvtical Chemistrv". 2nd ed, Interscience. New . York, N.i'., 1958, p 362. (25) W. G. Parks, J. Am. Chem. SOC., 53, 2045 (1931). (26) N. H. Furman, C. N. Reilley. and W. D. Cooke, Anal. Chern., 23, 1665 119511. (27) Meites, "Polarographic Techniques", 2nd ed, Interscience, New York, N.Y., 1965, pp 546-556. (28) W. D. Cooke, C. N. Reilley, and N. H. Furman, Anal. Chern., 24, 205 (1952). (29) H. A. Laitinen. "Chemical Analysis", McGraw-Hill, New York. N.Y., 1960, pp 332,368-372. (30) V. T. Athavale, R. G. Dhaneshwar, and D. A. Sarang, Talanta, 14, 1333 (1967). (31) L. E. Jaycox, G. E. Cadwgan, and D. J. Curran, Anal. Left, 6, 1061 (1973).
ACKNOWLEDGMENT The authors wish to thank C. E. Puleston of Fairchild Semiconductor Corp. for supplying the analog switch.
RECEIVEDfor review July 16, 1975. Accepted February 9, 1976. One of the authors (L.B.J.) expresses his appreciation of an NSF Traineeship for part of the work and the authors are grateful for partial support by the Research Council of the University of Massachusetts in the form of a Faculty Research Grant. Presented in part a t the 163rd National Meeting of the American Chemical Society, Boston, Mass., April 9-14, 1972, and at the 7th Materials Research Symposium, NBS. Taken in part from the Ph.D. thesis of L. B. Jaycox.
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i.
Response Time Curves of on-Selective Electrodes Ern6 Lindner, Klara Tbth, and Ern0 Pungor* lnstitute for General and Analytical Chemistry Technical Ur Iersity, Budapest, Hungary
The response characteristics of different types of ion-selective electrodes were investigated thoroughly for obtaining kinetic information for the electrode response. On the basis of response time data or supposed electrode mechanisms, the ion-selective electrodes have been divided into different groups. For the evaluation of the response time curves of electrodes, at which the rate-determining step is the diffusion of the appropriate ion in the electrode membrane phase (neutral carrier-, and covered surface electrodes), a dlff usion model has been used. The response characteristics of electrodes operating on ion-exchange equilibria (e.g., precipitate based electrodes etc.) have been interpreted with the help of a first-order kinetic equation. In addition to this, a so-called
multielectrode model has been worked out for the general interpretation of the electrode response if the rate determining sequence of the overall potential determining step is covered by a diffusion process through the adhering laminary layer at the electrode surface.
In order to understand the kinetics of ion-selective electrodes, the steps of the overall potential determining process are of fundamental importance. Since the thermodynamic treatment considers only the energetic conditions of the initial and the final states, the intermediate potential determining steps are irrelevant from the thermodynamic point of view. ANALYTICAL CHEMISTRY, VOL. 48, NO. 7, JUNE 1976
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