sulfate, which commonly occur with fluoride, caused any interference whatsoever in concentrations up to 0.1M, even in the presence of alkali metal ions. Procedure. The sample should contain 1 to 6 mg of fluorine in 15 ml for micro scale operation or 10 to 20 mg of fluorine in 35 ml if the larger cell is to be used. With 1.OM H N 0 8 or l.0M NaOH, adjust the pH to between 1 and 2. Add 2 or 3 drops of 50% polyethylene glycol 400 and enough NdF3 suspension to produce a noticeable turbidity. Introduce a magnetic stirring bar and stir, with the cell in the instrument illuminated with green incident light until readings are constant. Titrate with standard neodymium solution added in small increments, reading absorbance after each addition, until the absorbance readings reach a constant value. Plot absorbance as ordinate and volume of titrant as abscissa and extrapolate the lines to intersection.
lternating
RESULTS
The method was applied first to solutions of sodium fluoride containing from 1 to 20 mg of fluorine. The average absolute error was 0.09 mg. Finally, samples of p-fluorobenzoic acid and thenoyl trifluoroacetone were combusted by the Schoniger oxygen flask technique using 0.002M soaium hydroxide in the flask to collect the fluoride. The resulting solution was treated according to the above described procedure. For pfluorobenzoic acid: calcd F : 13.56; found: 13.63. For thenoyl trifluoroacetone: calcd F: 25.65 ; found: 25.58. These results compare favorably with the usual results of other titrimetric methods for fluorine.
RECEIVED for review May 24, 1967. Accepted August 25, 1967.
ith io
Ronald F . Evilia and A i James Diefenderfer Department of Chemistry, Lehigh University, Bethlehem, Pa. 18015
WITHINthe past few years several designs for phase-sensitive alternating current polarographs have been presented (1-5). A design using sharply tuned twin-T filters has been presented (1); however, operation at different frequencies is extremely difficult. An analog computation method has also been presented (2), but the large amount of circuit wiring necessary makes this method unattractive. Another approach to phase-sensitive ac polarography is the lock-in amplifier technique. This technique was recognized earlier (6)but no instrument making use of this alternative has appeared. We have obtained excellent results by incorporating a commercially available lock-in amplifier (Princeton Applied Research Model HR-8) into an operational amplifier instrument of standard design. This instrument, which was built with a minimum of external electronic wiring, equals or exceeds the specifications of earlier instruments (1-4). THEORY OF OPERATION
The amplifier components of the instrument are normal, and their operation was described previously (7-9). The lock-in amplifier serves as both the ac signal generator and the phase sensitive detector. Because the detector is locked-in to the signal generator, any drift of the signal is automatically
(I) E. R. Brown, T. G. McCord, D. E. Smith, and D. D. Deford, ANAL.CHEM., 38, 1119 (1966). (2) S. W. Hayes and C. N. Reilley, Zbid.,37, 1322 (1965). (3) T. Takakashi and E. Niki, Talanta, 1, 245 (1958). (4) D. E. Smith and W. H. Reinmuth, ANAL.CHEM.,32, 1892 ( 1960). (5) G. C.Bard, Anal. Chirn. Acta, lS, 118 (1958). (6) D. E. Smith, “Electroanalytical Chemistry,” A. J. Bard, ed., Vol. 1, Marcel Dekker, New York, 1966, p. 118. (7) D. D. Deford, Division of Analytical Chemistry, 133rd National Meeting, ACS, San Francisco, Calif., April 1958. (8) W. M. Schwarz and I. Shain, ANAL.CHEM., 35, 1770 (1963). (9) D. E. Smith, “Electroanalytical Chemistry,” A. J. Bard, ed., Vol. 1, Marcel Dekker, New York, 1966, pp. 102-108.
I\ t----\ Triangular Genera t o r
Potential
MODE
-A C
_ _ _ _ -DC. - -- cy-1 c
Figure 1. Flow sheet-block ~~~r~~ of circuit showing modes of operation
compensated. The theory of lock-in amplifier operation has been presented previously (6, IO, 11). By using a lock-in amplifier as the phase-sensitive detector, one can examine either the in-phase or quadrature signal by simply switching from one mode to the other. By increasing the time constant (front panel switch) to several times the drop time, the drop oscillations are damped out at slow scan rates. In short, the lock-in amplifier approach is capable of performance equal to previously presented methods (1-4)9 but requires far less external electronic wiring.
(10) Instruction manual, Precision Lock-in Amplifier Model HR-8, Princeton Applied Research Gorp., Princeton, N. J., 1965. (1 1) “How the lock-in amplifier works,” Brower Laboratories, Inc.,
Westboro, Mass. V6b. 39, NO. 14, DECEMBER 1967
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+ C
EL
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2
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-8
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Figure 3. Reproducibility __*
EXPERIMENTAL
A block diagram of the instrument is presented in Figure 1 and the complete schematic diagram in Figure 2. The solidstate operational amplifier (No. 1 through 5) are Model SP656 (Philbrick Researches, Inc.), with the exception of the X-axis offset amplifier (No. 6) which is a Model P45ALU (Philbrick Researches, Inc.). Positive feedback is included for iR compensation as described by Brown et al. ( I ) . Provision is made for measurement of the uncompensated resistance of the cell by the method of Hayes and Reilley (2). All resistors are trimmed to +0.1 and are of carbon film composition with the exception of the 100M resistor which is &lox. The ramp circuit was modified so that 1 V was integrated (through a large resistance) instead of 10 mV through a small resistance and, hence, the output was less sensitive to noise picked up at the input. All chemicals used were reagent grade and were used without further purification. Singly distilled water was used throughout. The only temperature control was provided by the controlled environment of the room.
x
DISCUSSION
+
The system C d f Z 2e- S Cd(Hg) was used for all evaluations. Cadmium concentrations to approximately 5 X 10-*M could be evaluated with this instrument using a hanging drop mercury electrode with an overall accuracy of & 6 x . Inability to reproduce drop size and instrumental noise was the limiting factor. Future improvements in lock-in amplifiers could significantly lower the detection limit. For single electron reactions and for irreversible processes, the detection limits will be increased. The technique is of comparable sensitivity to previously reported methods (4,5). The alternating current increased linearly with increasing applied alternating voltage from 500 p V (pp) to 10 mV (pp). The reproductibility of the instrument is excellent, as shown
in Figure 3, which is three consecutive scans (after l/p-hour warm up) of a 1m M Cd+*in 1 M KC1 solution. These polarograms were recorded using a high RC time constant to damp out drop oscillation. The alternating current increased with the square root of frequency in a linear manner to approximately 150 Hz. A slight deviation from linearity was observed at low frequencies (1 to 5 Hz) caused by a drop in oscillator output. The separation of waves is comparable to similar techniques. Cd+2 and waves, which differ in peak potential by only 40 mV, could be separated. Second harmonic ac was done on the cadmium system by using a n external stable oscillator of exactly half the lock-in amplifier frequency. The second harmonic polarogram agreed in every respect with polarograms already in the Iiterature (6). No other systems were examined under second harmonic ac conditions. Figure 4 is a recording of both the in-phase and quadrature signals of a cadmium solution at 22 Hz. After correcting for capacitive current, it can be seen that the current heights are the same, hence a phase angle of 45 O is obtained. All the above observations are consistent with ac pohrographic theory and with previous data. The major advantage of this approach is that a research quality ac polarograph can be obtained with a minimum amount of electronic wiring and calibration. ACKNOWLEDGMENT
The authors thank Princeton Applied Research Corp. for the use of a lock-in amplifier. RECEIVED for review June 26, 1967. Accepted September 18,1967.
VOL. 39,
NO. 14,DECEMBER 1967
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