apparently diffusion controlled with the free radical resulting as the sole product in the diffusion layer. Other electron transfer reactions, both oxidative and reductive, which exhibit two consecutive one-electron steps are under study using OTE and RSS. At fast scan rates, determination of spectra for transient intermediates will be informative to spectroscopists and also t o those interested in mechanism studies. For electrochemical investigations, spectral information will determine monitoring wavelengths for set-wavelength studies to allow determination of kinetic parameters of fast homogeneous reactions which follow charge transfer. The obvious extension of RSS investigations to photochemical, chemiluminescent, and biochemical phenomena will be undertaken shortly.
ACKNOWLEDGMENT
The authors gratefully acknowledge assistance in building the RSS by Herman Braun and Wayne Huhak. The assistance of T. Osa in the electrochemistry of methyl viologen is also appreciated.
RECEIVED for review September 4, 1968. Accepted December 12, 1968. Work was supported by grants from the Research Grant Branch of National Institute of Medical Science, NIHPHS (GM 14036) and National Science Foundation (GP6479). Portions of this work were presented at the Symposium o n the Synthetic and Mechanistic Aspects of Electroorganic Chemistry at Durham, N.C., on October 14-16, 1968, sponsored by Army Research Office.
A Piezoelectric Transducer for Determination of Metals at the Micromolar Level Jerry L. Jones1 and James P. Mieure2 Depurtment of’ Chemistry, Texas A&M University, College Station, Texas 77840
A conventional quartz piezoelectric crystal has been used for the detection of small mass changes caused by the electrodeposition of metals onto the gold electrode surfaces of the unit. Incorporation of the unit into a conventional oscillator circuit and measurement of the change in frequency of the unit due to the increase in mass allows highly sensitive indication of solution concentrations down to the micromolar level in the case of cadmium, nickel, indium, zinc, and lead. Analysis is essentially nondestructive and requires relatively little time. In the case of cadmium, analyses extended from 5.0 X lO-4M to 5.0 X 10-8M. AT-cut quartz crystals with fundamental frequencies of 1.65, 3.0, and 9.0 MHz were used as cathodes in a controlled potential electrodeposition circuit and changes in frequency were monitored with an electronic frequency counter and recorded on a strip-chart recorder after digital-to-analog conversion. Linear calibration curves were obtained over a wide concentration range. SEVERAL ELECTROANALYTICAL METHODS have been developed to extend the electrochemical determination of metals in solution into the micromolar concentration region. Prominent among these methods are ac polarography ( I ) , square wave polarography ( 2 , 3), fast scan polarography (4, and anodic stripping voltammetry ( 5 , 6). Descriptions of these procedures can be found in the references cited, and no discussion will be given here except to point out one limitation more or less common to all methods which utilize voltage scanning. This restriction results from the fact that the measurement step requires the monitoring of the current flowing between two ‘Present address, Department of Chemistry, Central Washington State College, Ellensburg, Wash. 98926 2Present address, The Monsanto Co., 1700 South Second Street, St. Louis, Mo. 63177 (I) W. F. Head, Anal. Chin?.Acta, 23, 297 (1960). (2) G. C. Barker and I. L. Jenkins, Analyst, 77,685 (1952). (3) G. C. Barker, Anal. Clzirn. Acta, 18, 118 (1958). (4) J. W. Ross, R. D. DeMars, and I. Shain, AXAL.CHEM.,28, 1768
(1956). ( 5 ) M . M. Nicholson, J. Amer. Chem. SOC.,79, 7 (1957).
(6) R. D. DeMars and I. Shain, ANAL.CHEM.,29, 1825 (1957). 484
ANALYTICAL CHEMISTRY
electrodes as a function of the changing voltage impressed between them. There are always, however, currents present other than the faradaic current due to the electrolysis of the electroactive species of interest. The most important of these is the charging current. As the concentration of the electroactive species decreases, the relative contribution of the charging current increases until finally it may completely obscure the electrolysis current. A method not relying strictly on current measurement would not be subject to this restriction. One electrochemical method which does not generally suffer the limitations imposed by the charging current is electrogravimetric analysis, or electrodeposition. Comprehensive treatments of the subject are available elsewhere ( 7 , 8). Electrogravimetric analysis is normally applicable to the estimation of metal concentrations greater than about 10-3 molar. In part, the lower concentration limit of conventional electrodeposition is imposed by the difficulties associated with the measurement of small mass changes on a n analytical balance. Even more significant is the fact that the time required for virtually complete deposition is a function ofthe current flowing. This time can become very long for dilute solutions in which currents will be relatively small. If these problems could be overcome, the utility of the method would be greatly increased. The present study was undertaken to investigate the very great sensitivity to mass of the piezoelectric effect in a n attempt t o extend electrogravimetry to lower concentrations without sacrificing time or accuracy. Mass Changes and the Piezoelectric Effect. When a piezoelectric crystal is inserted into a properly designed oscillator circuit, it controls the frequency of the oscillator over a very narrow range. The crystal actually undergoes simultaneous electromechanical oscillation at each of its vibrational modes, and the values of the oscillator components determine the ( 7 ) N. Tanaka, “Treatise on Analytical Chemistry,” Part 1, Vol. 4, I. M. Kolthoff and P. J. Elving, Eds., Interscience Publishers, Inc.,
New York, N.Y., 1963, Chapter 48. (8) J. J. Lingane, “Electroanalytical Chemistry,” Interscience Publishers, Inc., New York, N.Y., 1953, Chapter 12.
mode at which the oscillator output stabilizes. Commercially available quartz crystals offer several advantages over other piezoelectric materials. Only quartz crystals were used in this study and all further discussion will be restricted t o these. Additional information on the general topic of piezoelectricity and its applications can be found in the definitive work by Cady (9). When an oscillator is being controlled by a crystal, any change in the fundamental frequency of the crystal will cause a corresponding shift in the oscillator frequency. One factor which can alter this fundamental frequency is a n increase or decrease in thickness of the crystal because the fundamental frequency varies inversely as the thickness. This is equivalent t o the statement that the frequency is dependent on the mass changes the crystal undergoes. Sauerbrey (10) has studied this phenomenon and presents t h e following equation t o describe the relationship between the change in mass of a crystal of fixed diameter and the crystal frequency: AM
=
-A,f. d
*
A
*
S/f
(1)
where A M represents the change in quartz mass, A,f is the corresponding frequency change, d is the density of quartz, A is the cross-sectional area of the crystal, s is the crystal thickness, and f is the frequency being monitored. As a n illustration with a 9-MHz crystal, assume d = 2.65 g cm-3, A = 1.45 cm*$and s = 0.184 mm; a n increase in mass of the quartz of 7.9 X 10-9 gram, distributed uniformly over the surface, would cause a frequency decrease of 1 Hz. Thus, a crystal can be used as a very sensitive transducer element to detect changes in the mass of the crystal, or, what is more important here, changes in the mass of a thin film on the surface of the crystal. Other researchers have taken advantage of this effect to enable them to detect and monitor small mass changes. Oberg and Lingensjo followed the evaporation of magnetic films onto crystals (11). Slutsky and Wade studied the absorption of argon and hexane onto a quartz crystal surface (12). King developed a sorption detector for gases which he used in a gas chromatograph (13). This same author later coated crystals with elastomers and studied the oxidation of the coatings by observing the resultant frequency changes (14). A preliminary report on the use of piezoelectric crystals to measure the mass changes produced by electrodeposition has recently been published (15). A more complete report is presented in this paper. EXPERIMENTAL
A controlled-potential electrodeposition circuit was used to supply the necessary current to the three-electrode system to maintain the proper electrolysis voltage. The electrode configuration, the oscillator circuit, and the measuring equipment have been described (15). The dual cathodes for electrodeposition were the two goldfilm electrodes of a quartz piezoelectric crystal. These vacuumdeposited films were about 0.0005 m m thick and were similar to the electrodes used by Reilley and others in electroanalytical studies (16). The crystals used in this study were obtained
(9) W. G. Cady, “Piezoelectricity” Dover Publication, Inc., New York, N.Y., 1964, Chapter 8. (10) G. Sauerbrey, Z. Physik, 155, 206 (1959). (11) P. Oberg and J. Lingensjo, Rev. Sci. Instrum.. 30, 1053 (1959). (12) L. J. Slutsky and W. H. Wade, J . Chem. Pliys., 36, 2688 (1962). (13) W. H. King, Jr., AKAL.CHEM.,36, 1735 (1964). (14) W. F. Fischer and W. H. King, Jr., ibid., 39, 1265 (1967). (15) J. P. Mieure and J. L. Jones, Tulanta, 16, 149 (1969). (16) A. Yildiz, P. T. Kissinger, and C . N. Reilley, ANAL.CHEM., 40, 1018 (1968).
1 PolaroaraDh I Oscillator
Frequency
w n Converter
Recorder
Figure 1. Block diagram of electrodeposition and frequency measuring circuits from the International Crystal Co., Oklahoma City, Okla. These had fundamental frequencies of 1.65, 3.0, 9.0, and 15.0 MHz. Wire leads about 10 cm long were soldered to the existing spring clips on each crystal. The exposed ends of the wire leads, the clips, and the solder connections were coated with a n insulating nail polish lacquer. A photograph of a typical quartz crystal is shown in the paper by Fischer and King (14). Of the several cuts of quartz commercially available, AT-cut crystals, 1 to 1.5 cm in diameter and less than 1 m m thick, with a thickness-shear mode of vibration, were chosen because of their wide frequency spectrum and low temperature coefficient in the vicinity of room temperature. The fundamental frequency spectrum available for this quartz orientation covers the range from 0.8 to 33.0 MHz, and the temperature coefficient for frequency stability is less than one part per million at 25 “C. Each electrode with its associated crystal and wire leads was firmly mounted into a polystyrene disk which was large enough to cover the electrolysis cell. The electrode extended far enough below the disk so that it was immersed in the test solution when the disk was in place over the cell. Electrodeposition was carried out in a cylindrical borosilicate glass cell fabricated locally. The total volume of this cell was approximately 80 ml and its dimensions were 4.2 cm x 6.5 cm. A glass frit was built into the lower wall of the cell for deaerating with nitrogen. A magnetic stirrer and bar were used to provide reproducible convection with a stirring rate of 550 rpm. The frequency measuring circuit was based on a tuned gridtuned plate oscillator (17). By tuning the variable capacitor in the output tank circuit, it was possible to select the fundamental frequency or one of the harmonics for each crystal. The entire circuit diagram, in block form, is shown in Figure 1. A small, enclosed air blower was mounted so that its air flow was directed onto the crystal when the electrode assembly was in its raised position. This accelerated the drying process for the crystal and averaged out thermal gradients in the room air. All frequency measurements were made with this blower operating at room temperature. Reagents. Stock solutions of cadmium(II), nickel(II), copper(II), lead(II), indium(III), and zinc(I1) were prepared using reagent grade perchlorate salts (G. Frederick Smith Chemical Co.), whereas thallium(1) solutions were prepared using thallium nitrate (Fairmount Chemical Co.). With the exception of thallium, which was standardized by weighing, these stock solutions were standardized by titrating with reagent grade disodium (ethylenedinitri1o)tetraacetate dihydrate (EDTA) (J. T. Baker Chemical Co.) using procedures outlined by Welcher (18). After each metal ion solution was (17) “The Radio Amateur’s Handbook,” 30th Ed., American Radio Relay League, West Hartford, 1962, p 146. (18) F. J. Welcher, “The Analytical Uses of Ethylenediamine Tetraacetic Acid,” D. Van Nostrand Company, Inc., Princeton, N.J., 1958, pp 149, 161, 178, 189, 234, and 242. VOL. 41, NO. 3, MARCH 1969
485
Table I. Frequency Changes Observed after a 2-Min Deposition Using Various Cadmium Concentrations and a 3-MHz Crystal Operated at Different Frequencies Concentration, Frequency change, molarity Hertz 3.0 MHz 6.0 MHz 9.0 MHz 5.0 x 10-4 864 1730 860 1741 2.0 x 10-4 393 790 1181 390 787 1164 1.0 x 10-4 200 395 592 197 401 586 5.0 x 10-5 100 200 298 102 203 293 1.0 x 10-5 21 41 60 20 40 62 2.0 h 10-6 8 12 9 14 standardized, it was diluted to 1.00 X 10-ZM and stored in borosilicate glassware. Test samples were prepared by successive dilutions of these stock solutions. The nitrogen used t o deaerate the solutions before electrolysis was commercial prepurified grade. A stock solution of 1M NaC104 was prepared from reagent grade NaC104 (G. Frederick Smith Chemical Co.). The p H of this supporting electrolyte, after dilution t o 0.1M, was 6.4. A 0.1M potassium hydrogen phthalate buffer was adjusted to p H 4.1 by adding dilute sodium hydroxide. This was used in the indium determinations. The water used in all studies was deionized by passage through a mixed-bed ion-exchange column and was stored in a polyethylene container. Any other chemicals not specifically described were reagent grade. Procedure. The details of a typical determination at a given metal ion concentration follow. First, a 40.0-ml aliquot of the sample solution containing 0.1M sodium perchlorate and any necessary buffering solution was placed into the cell and covered with a plastic cap. Nitrogen gas was then bubbled through the solution with stirring for about 10 minutes. In the meantime the dry crystal was switched into the oscillator circuit and the initial frequency determined t o the nearest Hz. After the oxygen had been displaced from the analyte solution, the crystal was switched into the electrodeposition circuit and the appropriate voltage was applied. The electrode surfaces on the crystal were thoroughly wetted by dipping the mounted crystal into a beaker of distilled water. Then the plastic cap covering the cell was removed and the entire moveable electrode assembly was lowered into place over the cell, thereby immersing the electrodes. Stirring and vigorous deaeration were continued throughout the deposition. At the end of the predetermined time interval, the electrode assembly was raised several inches above the cell. The electrodes were then rinsed thoroughly. A n absorbent tissue was used t o blot excess water from the bottom edge of the crystal. A blower, aimed at the crystal, was then turned o n to reduce the drying time t o about 20 seconds and to provide a moderating influence on fluctuations in the room temperature of 25 k 1 "C. As soon as the crystal was dry, it was again switched into the oscillator circuit and the frequency was recorded. The change in crystal frequency, Aji for a given deposition time interval, when plotted cs. the corresponding metal concentration, provided a calibration curve useful for the estimation of unknown concentrations. T o reproduce the original electrode surface conditions after a determination, the metal which had been deposited onto the gold cathode was dissolved by immersion in 1M nitric acid for a few seconds. The total time involved for a single determination in those cases where a 2-minute deposition time was used was about 15 minutes, including deaeration. Midway through the experimentation, absorption of metal ions into the cell walls and desorption of previously absorbed 486
ANALYTICAL CHEMISTRY
I
0
/
1.o 2 .o 3.0 4 .O CADMIUM CONCENTRATION ( ~ ~ 1 0 4 1
Figure 2. Calibration curves for cadmium using 2-rnin deposition intervals and a 3-MHz crystal operated at the fundamental and two harmonic frequencies ions caused significant changes in the actual cadmium concentration for very dilute solutions. In these cases, a cleansing procedure was used after each determination. A satisfactory method for removing this material consisted of three steps. First, the cell was washed with 0.1M HC1 and rinsed twice with distilled water. Then the compartment was washed with 0.1M alkaline EDTA and again rinsed twice. Finally, the wash and rinse treatment using the HC1 was repeated. The cell was then ready for the next determination. The frequency measurements were made with the crystals oscillating at the fundamental frequency or a harmonic. Unless otherwise noted, operation was at the fundamental frequency. RESULTS AND DISCUSSION
Determination of Cadmium. Cadmium was selected for preliminary study. A voltage of -0.90 V was optimum for the reproducible deposition of cadmium onto the gold electrodes of a crystal. The effect of stirring rate on the electroplating was examined and a rate of 550 rpm was chosen for all succeeding anaIytical studies. Cadmium metal was deposited onto a 3-MHz quartz crystal usingconcentrationsvaryingfrom5.0 X 10-4Mto2.0 X 10-6M. Two determinations were performed at each concentration and the average frequency change is presented as a function of concentration. The three curves in Figure 2 were obtained with the crystal oscillating at the fundamental frequency or at one of the first two harmonic frequencies. The individual experimental values for each determination are listed in Table I t o provide an indication of the good reproducibility of the method. The response in Afis larger by factors of 2 and 3 for operation at the first and second harmonics, respectively. This experimental observation supports Equation 1, which shows that for a given change in crystal mass, the corresponding Af should increase in direct proportion to the frequency being monitored. In addition to the direct proportionality between the fundamental crystal frequency and the frequency change observed for a given mass change, Equation 1 also indicates that any observed frequency change is inversely proportional to the initial crystal thickness. The fundamental frequency of the crystal is, in turn, related by a n inverse proportionality t o the thickness. Thus, the frequency change corresponding to a
400
,300 N I v W (3
Z
220c 0
> I L
1.o
0 10 100, CADMIUM CONCENTRATION ( M x l O
Figure 3. Calibration curves for cadmium using 2-min deposition intervals and 1.65,3.0-, and 9.0-MHz crystals given mass change on a crystal can be expected t o increase as the square of the fundamental frequency. In order to experimentally ascertain the influence of the fundamental frequency of the crystal o n mass sensitivity, two other crystals were used. The calibration curves for 2-min depositions onto crystals with fundamental frequencies of 1.65 and 9.0 MHz are compared to the response of the 3-MHz crystal in Figure 3. The data are shown on log-log axes so that all the points could be easily included. The responses of the crystals of higher frequency were greater than the response of the low frequency crystal by a factor slightly larger than the ratio of the squares of the respective frequencies. I n order for the sensitivity to be exactly proportional to the square of the fundamental frequency, all other variables would have to be identical for the crystals being compared. In particular the electrode areas would have to be equal, so that the same thickness of metal would electrodeposit during a given time interval. I n practice, this is not generally the case, because optimum design of the crystal may require different electrode diameters for different frequencies. The overall short-term noise level for the fundamental frequency of each crystal, as observed by the digital frequency readout, was & 0.5 Hz for the 1.65-MHz and 3.0-MHz crystals and i 1.5 Hz for the 9-MHz crystal. The maximum long-term drift in frequency amounted to + 1 Hz in 30 min for the two crystals of lower frequency and i 2 Hz for the 9-HMz crystal. Both the noise and the drift reflect not only the instability of the crystal, but also that of the electronics and the readout device. Since the readout uncertainty of the frequency counter alone is + 1.0 Hz, it is apparent that the crystal and oscillator were quite stable. The previous discussion described the influence of crystal frequency on the sensitivity of concentration measurements. Another means of increasing the sensitivity of these measurements would be to increase the electrodeposition time interval. Two different estimates of the fraction of cadmium deposited during a 2-min interval gave a n average of about 1 %. One estimate was based upon average electrolysis current during deposition and the other upon the calculated mass change from a measured Af according t o Equation 1. Because only about 1 of the total cadmium in an aliquot was deposited in 2 min, increasing the deposition time should result in a considerable increase in the frequency change for a
Z W
30 100 W !Y LL
w-
2.0 4.0 6.0 8.0 10 Cd CONCENTRATION (Mx106)
: > ? [
Figure 4. Influence of cadmium concentration on frequency changes observed after 2-min, 2O-min, and 30-min depositions using a 3-MHz crystal operated a t 6 MHz given concentration and, hence, in the sensitivity of the method. Curves are presented in Figure 4 for a 3-MHz crystal oscillating at 6 MHz t o show the results of plating for 2, 20, and 30 min, respectively. Because the frequency can be determined to the nearest Hz with the frequency counter, cadmium determinations with an uncertainty of less than 10% at concentrations as low as 3.0 x 10-7M are shown to be possible on a 3-MHz crystal operated at 6 MHz when using 30 min deposition times. This lower limit of detection was decreased by a factor of 9/6 = 1.5 (see Equation 1) by operating the crystal at the next higher harmonic at 9 MHz. It was desired to test the previous prediction that greater sensitivity is obtainable on a crystal oscillating at its fundamental frequency than on a crystal of lower frequency operating on a harmonic. Figure 5 compares the data obtained with a 3-MHz crystal oscillating at 9 MHz to those obtained with a crystal of 9-MHz fundamental frequency. A 30-min deposition interval was used in each case. When the 9-MHz crystal is used, the lower useful concentration limit is decreased to less than 5.0 X 1O-*M cadmium before the 10% uncertainty limit is reached. At these very low cadmium concentrations and long deposition times, absorption of metal ions into the cell walls and desorption of previously absorbed ions caused large deviations. To eliminate desorption and allow absorption to occur at reproducible rates, the cell must be cleaned after each determination. Hence, the pretreatment described earlier was used in the collection of the data for Figure 5 and in all subsequent determinations at concentrations below 2.0 x 10-6M. I n an attempt to apply this method to even lower concentrations, this same 9-MHz crystal was made to oscillate at 18 MHz and was used to monitor electro-deposition for 3-hr intervals. The results are presented in Figure 6. The nonzero frequency intercept could be indicative of a metal contamiVOL. 41, NO. 3, MARCH 1969
487
300 h
N
I
v
W
9200 Q
r
0 t
2 100
3
2.0 4.0 6.0 8.0 10 Cd CONCENTRATION (Mxl 0’)
0
CT LL
0 Cd CONCENTRATION (M xl 06) Figure 5. Influence of cadmium concentration on frequency changes observed after 30-min depositions using a 3-MHz crystal operated at 9 M H z and a 9-MHz crystal operated at 9 M H z nant, not necessarily cadmium, and when extrapolated to the concentration axis corresponded t o 3 x IO-SM cadmium. Duplicate determinations at given concentrations differed by 15-20 Hz. Even when this crystal was immersed for 3 hrs in deionized water at zero applied voltage, the frequency after drying often differed from the original frequency by as much as 15 Hz. One possible explanation for this observation would be the irreproducible diffusion of water into and out of the quartz. Another plausible explanation seems to be the softening of the lacquer insulation o n the crystal edges and leads. As this lacquer slowly hardens during drying of the crystal, it can harden in a slightly different configuration than before softening and, by exerting a slightly different strain on the crystal, shift the frequency. Teflon would undoubtedly have been a more satisfactory insulating material because of its chemical inertness and resistence to swelling in water. A low molecular weight, Teflon-like, Table 11. Precision and Accuracy of Electrodeposition Method for Several Representative Cadmium Concentrations Concentration, Frequency change, Precision, Accuracy, molarity Hertz % % 5.0 x 10-4 530 0.42 0.42 528 527 532 4.0 x 10-5 164 1.2 2.1 164 168 164 1.7 1.7 25 5 5.0 x 249 252 259 4.1 3.4 117 5.0 x IO-’ 122 127 123 8.7 8.5 88 5.0 x IO-* 78 75 488
ANALYTICAL CHEMISTRY
Figure 6. Influence of cadmium concentration on frequency change observed after a 3-hr deposition using a 9-MHz crystal operated a t 18 M H z fluorotelomer from DuPont, Vydax 550, was tested as a n insulator. However, the temperature required to bake this dispersion onto the crystal was above the melting point of the solder used to fasten the leads to the crystal. The higher temperature needed to silver-solder leads to the crystals would have damaged the crystal, so the attempts to use a fluorocarbon were abandoned. A 15-MHz crystal was tested t o determine its value as an electrodeposition monitor. Whenever this crystal was wetted and dried, the oscillator output drifted at a rate of 30-40 H z in 5 min, and the frequency before wetting could not be reproduced for several hours. This rendered the crystal useless for precise analytical measurements. The erratic behavior of the 15-MHz crystal was viewed as an indication that crystals with fundamental frequencies above 15 MHz might similarly be restricted in usefulness for this application. In addition, these crystals would be so thin as to be impracticably fragile. (The thickness of the 15-MHz crystal was 0.1 mm.) Also, the technology involved in operatting higher frequency oscillators and transmitting the resultant signal to a measuring device becomes more complicated. As a result, no attempt was made to use crystals of higher frequency, and a fundamental frequency of 9 or 10 MHz is suggested as the largest practical value under the conditions of this study. The total span of cadmium concentrations which was determined by this method, using three crystals, was from 5.0 X 10-8M to 5.0 X lO-4M. By selecting the proper crystal frequency and plating time, utilizing the linear portion of one of the working curves for the determination of any cadmium ion concentration within these limits should be possible. When deciding on the proper crystal and deposition time for a given analysis, it is important to consider the uncertainty in determining the correct crystal frequency. Even with the relatively low-frequency 3-MHz crystal, each frequency measurement had a n uncertainly of 1 Hz after the frequency noise component was averaged out. Thus to approach a relative uncertainty of 1 with onfidence, the frequency change must be larger than 100 Hz. A study was undertaken to demonstrate the accuracy and precision which can be obtained at different cadmium concentration levels with this method. Four replicate determinations of five representative concentrations were performed. The results are summarized in Table 11. The precision is in terms of the relative standard deviation within each set of
determinations, and the accuracy is in terms of the relative standard deviation from the appropriate calibration curve. All of the experimental curves obtained, using the different crystals and the various electrodeposition time intervals, have the same general shape. At low metal concentrations, the frequency change due t o the cadmium plate is related linearly t o the initial cadmium concentration in the test solution. This behavior has a simple explanation. The mass of material deposited during a time interval is given by the integral of the instantaneous current :
s s idt
=
c[exp(-kt)]dt
=
c’[l - exp(-kkt’)]
(2)
where c, k, and c’ are constants and t ‘ represents the length of the time interval. Under these experimental conditions, each term in the final expression of Equation 2 is constant except c’, which is proportional to the initial metal concentration. Because this expression is directly proportional t o the mass of metal electro-deposited during the selected time interval, and this mass, in turn, is proportional t o the frequency change, the linear relationship between the frequency change and the initial metal concentrations is expected. The curvature which becomes apparent at higher concentrations can possibly be accounted for by two different explanations. Referring to Equation 1, in the calculation of the frequency change for a given mass change on a crystal surface, it was assumed that the mass change occurred uniformly over the crystal surface. Experimentally, the mass change is localized on the metallic electrodes. This in itself would not cause non-linear behavior as long as the deposited metal was spread evenly over the electrode. However, it is known that metallic deposits tend t o grow unevenly, particularly when the current density is increased, as is the case at higher concentrations. This irregular growth could cause deviation from linearity. The second explanation depends on the observation that the nature of the quartz crystal as a vibrator must change as the metal is deposited. The elastic, piezoelectric, and dielectric constants of a crystal will vary depending upon the mechanical load attached to it. I n this particular case, the vibrating body consists of the active quartz and the inactive electrodes, and obviously the elastic constants of the two materials are different. Since they must vibrate as a unit, the average of the constants determines the frequency of vibration. These averages will approximate the constants of quartz as long as the metal films are very thin in relation to the quartz. As the electrodes become thicker by the deposition of metal, the instantaneous averages will deviate from the constants for quartz in a manner very difficult t o treat rigorously. Since the entire crystal unit will be less active, the response of the crystal frequency to a unit mass change will be proportionally less at heavy crystal loading. Other Metals. After we had thoroughly examined the feasibility of using these crystals for the electrogravimetric determination of submicromolar cadmium concentrations, attention was turned t o other metals to test the general applicability of the method. Nickel(II), indium(III), zinc(II), lead(II), copper (II), and thallium(1) were chosen for study. The experimentally determined optimum voltages, US. the SCE,for electrodeposition from the 0.1M NaCIOi supporting electrolyte were -0.75 V for nickel, -0.81 V for indium, -0.45 V for zinc, -0.75 V for lead, and -0.20 V for copper. Thallous ions could not be induced t o electrodeposit onto the gold electrodes even at - 1S O V cs. SCE. Copper deposited readily but could not be removed from the gold electrodes without also dissolving some of the gold. Thus the surface conditions could not be repro-
1000
h
N
I
v
W
’Q? 100 I 0 >-
2 9 e W 3 LL
10 1
10 CONCENTRATION &lx106)
100
Figure 7. Influence of concentrations of various metal ions on frequency changes observed after 2-min depositions using a S M H z crystal operated at 6 MHz duced from one determination t o the next and no useful working curves could be obtained. It was necessary t o buffer the indium solutions at pH 4.1 with the potassium hydrogen phthalate buffer t o obtain an approximately linear working curve. The experimental curves obtained from 2-min depositions onto the same 3-MHz crystal operated at 6 MHz for nickel, indium, zinc, and lead are shown in a log-log plot in Figure 7 . Similar curves were obtained using 20-min depositions and lower solution concentrations and these have not been shown. The total span of concentrations investigated for each metal on the 3-MHz crystal was 1.0 X lO-3M t o 1.0 X 10-6M for nickel, 1.0 x 10-4Mto 1.0 X 10-6Mfor indium, 2.0 X lO-4M t o 1.0 X 10-6M for zinc, and 5.0 X lO-4M t o 3.0 X lO-7M for lead. Other concentration ranges for these metals, as well as for cadmium, could probably be determined by using the proper combination of crystal frequency and deposition time interval. Figure 7 shows that the response of the crystal to deposition from a given analyte concentration is different for each metal. This is t o be expected, since the electrodeposition is dependent upon the diffusion coefficient for each ion; furthermore, the metal deposits would have different densities and elastic constants and could conceivably influence the frequency differently even if the same number of ions of two metals were deposited. In addition, the choice of plating voltage, the supporting electrolyte and its concentration, and the presence of surface active substances could possibly exert a measurable influence on the nature of the deposit and the magnitude of the mass change. Although these last variables were not examined in detail, they do point out that it is essential that any quantitative results be found using a calibration curve obtained under conditions which duplicate as nearly as possible those encountered with any real samples. Mixtures. The suitability of this new method t o the analysis of mixtures of metals in solution was investigated. Ideally, a suitable voltage could be found such that one metal of the mixture would deposit while the others remained in solution. However, under the conditions of this study, each metal plated to some degree at the optimum voltage for each of the other metals. As a result, in order to analyze a mixture of these metals, a Af at each voltage was sought and a system of VOL. 41, NO. 3, MARCH 1969
489
simultaneous equations, involving an experimentally determined sensitivity factor for each metal at each voltage, was used. The experimental value for each sensitivity factor was determined on a n aliquot of known concentration of each metal alone. By using 2-min plating times on a 3-MHz crystal, the four sensitivity factors for zinc and cadmium were determined for a concentration of 1.0 X lO-4M metal. Next, synthetic samples containing known concentrations of each metal were prepared, the frequency changes at -0.45 V and -0.90 V were determined, and the concentrations were calculated using two simultaneous equations. The calculated values did not compare well with the known concentrations, differing by 5 % for equal concentrations t o more than 50% when one species was present in tenfold excess. The process was repeated for a 20-min time interval, using 1.0 X 10-jM solutions t o determine the sensitivity factors. The results for a synthetic sample mixture were again in large error. The same procedure was followed for nickel and zinc mixtures, and again the experimentally determined concentrations differed from the known concentrations by more than 50%. The analyses of mixtures of zinc and either cadmium or nickel point out that under these conditions the A j values are not additive and that the individual ions cannot generally be resolved accurately by this method. One of the requirements for the application of this technique to the analysis of mixtures is that the contribution of each species to the total mass change during electrodeposition be independent of the other analytes present. Another way of viewing this stipulation is that only the mass transfer and .-
electron transfer processes must control the plating reactions. Without this limitation o n the nature of the control, thermodynamic considerations could possibly make a given site energetically more favorable for the deposition of one metal than for another. Evidently such is the case under these experimental conditions, so that the frequency changes due to electroplating from mixtures are not the simple sums of the frequency changes determined for each metal separately. Jones and Lingane successfully used electrogravimetric separations in the determination of copper, bismuth, lead, and tin ions in a sample (19). Controlled potential deposition was used to plate one metal at a time from 0.25M sodium tartrate onto a platinum working electrode. The weight changes were observed by weighing the electrode periodically. The lowest metal concentration determined was greater than lO-3M because of the limitations of conventional electrodeposition previously discussed. An effort was made in the present investigation to obtain quartz crystals with platinum electrodes so that the experimental conditions of Lingane and Jones (19) could be essentially duplicated in this laboratory and applied to much more dilute mixtures using the new method described herein. However, platinum-surfaced crystals could not be secured at a reasonable cost and the attempt was abandoned. RECEIVED for review October 7, 1968. Accepted December 23, 1968. We thank Phillips Petroleum Co. for a fellowship t o J.P.M. (19) J. J. Lingane and S . L. Jones, ANAL.CHEM.,23, 1798 (1951).
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A Kinetic and Spectrophotometric Study of the Formation and Reduction of a Phosphorus-Bismuth Dimeric Heteropolymolybdate H. D. Goldman and L. G . Hargisl Department of Chemistry, Louisiana State Uniuersity in New Orleans, New Orleans, La. 70122
A spectrophotometric procedure has been used to determine the composition of a unique, mixed bismuthphosphorus, dimeric heteropolymolybdate. A stoichiometry study indicated that the Mo:P:Bi ratio in the complex was 18:l:l. The complex was more stable in perchloric acid solutions than 12-molybdophosphoric acid but it was reduced considerably more easily to a heteropoly blue. The experimental rate law i s in good agreement with a mechanism involving an equilibrium step forming the heteropoly acid followed by a reduction step. The initial reduction of the complex by ascorbic acid apparently proceeded by a 2-electron, acid independent step. THERE HAVE BEEN several reports in the literature of bismuth affecting the reduction of 12-molybdophosphoric acid t o the corresponding hereropoly blue. The first report arose from some interference studies on a spectrophotometric method for phosphate ( I ) . Campbell and Mellon later developed a spectrophotometric method for bismuth based on an enhancement of the'blue hue produced on reduction of 12-molybdophosphoric acid in the presence of bismuth (2). However, their 'To whom all correspondence should be addressed. ( I ) D. F. Boltz and M. G. Mellon, ANAL.CHEM., 20,749 (1948). (2) R. H. Campbell and M. G. Mellon, ibid., 32, 54 (1960). 490
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preliminary investigations concerning the nature of the effect were inconclusive and they were unable to determine if the effect was catalytic or the result of complex formation involving bismuth. Recently it was shown for the first time, by means of a spectrophotometric study, that a discrete phosphorus-bismuth heteropolymolybdate can be formed in solution which reduces considerably more rapidly than 12-molybdophosphoric acid (3). This great difference in the rate of reduction, coupled with the fact that it was not previously known that a mixed heteropoly was formed, has contributed t o a false belief that the bismuth may have been acting catalytically in the reduction of 12-molybdophosphoric acid. A quantitative description of the steps leading to the formation of heteropolymolybdates requires knowledge of the principal equilibria of the isopolymolybdates in acid solution. Numerous studies of these equilibria have been made ( 4 4 but general agreement is still lacking, especially for systems at (3) L. G. Hargis, Anal. Lttrs., 1, 799 (1968). (4)I. Lindqvist, Ark. Kemi, 2, 325, 349 (1950). ( 5 ) 1. Lindqvist, Acta Chem. Scand., 5, 568 (1951). (6) Y. Sasaki, I. Lindqvist, and L. G. Sillen, J. Inorg. Nucl. Chem., 9, 93 (1959). (7) P. Souchay, Bull. SOC.Chim. Fr., 1947, 914. (8) F. Chauveau, P. Souchay, and R. Schaal, ibid., 1959, 1190.
