-R,
frequency a t which measurements are most accurate, and we try to cluster our frequencies around it, perhaps, in a second measurement set. We have used this method for some time now and have built the switch in Figure 2 into our potentiostat. The only accurate components required are the capacitor Cs (an:y calibrated good-quality capacitor will do, or a decade) and a resistance decade box. A series of measurements takes about 30 min and reproducibility has been in the same range as the scatter reported above. T h e foregoing assumes t h a t there is (1) no frequency dispersion and (2) no Faradaic admittance. If frequency dispersion is found, due to distributed cell parameters, there is, in any case, no simple value of R, and one should perhaps then try to eliminate the dispersion by making the cell/electrode system as symmetrical as possible ( I ) . Faradaic components can often be removed simply by measuring a t a different potential-R, is usually (except with passivating layers) potential-independent; if C d l is the wanted quantity, a more complicated procedure such as that of Canagaratna and Kawhich could also be adapted for use with runathilaka (6), absolute values of impedances, could be used.
cdl
Figure 1. Equivalent cell circuit
Ac input
4P
1167
Anal. Chem. 1980, 52, 1167-1168
RE
.
Figure 2. Measuring setup: P, potentiostat with current-follower; CE,
counter electrode; RE, reference electrode; WE, working electrode; S, 3-pole, 2-position switch; C, calibrated Capacitor (or decade); R, resistance decade. Drop-knocking and timing circuitry for use with DME not shown
ACKNOWLEDGMENT
I thank my colleague Lars Kryger for generously allowing me time on his minicomputer during much of this work.
controls this timing, knocking off a drop, and obtaining a digital sample (average of 20 over one 5 0 - H ~cycle) of the rectified and filtered ac current signal a t a certain time; however, analog sample-and-hold plus timing circuitry does just as well. A typical run, a t 7 frequencies ranging from 800 to 6000 Hz, in 0.5 M Na2S04a t 0.00 V vs. Ag/AgCl electrode, produced 15 R, values ranging from 68.2 to 70.1 R , with mean 69.3 R, standard deviation 0.8%. The iteration procedure produced a new value of 69.2 R and the resulting C d l values a t the 7 frequencies showed a standard deviation of 0.8%. T h e program also outputs the frequency at which 45" phase-shift obtains, or where R, = 1/(27rJCdI). This is that
LITERATURE CITED (1) Britz, D. J . Electroanal. Chem. 1978, 88, 309-352. (2) Armstrong, R. D.; Race, W. P.; Thirsk, H. R. Electrochim. Acta 1968, 13, 215-239. (3) Britz, D.; Bauer, H. H. J . Sci. Instrum. 1967, 4 4 , 843-846. (4) Breyer, B.; Bauer. H. H. "Alternating Current Polarography and
Tensammetry"; Interscience: New York, 1963. (5) Britz. D.; Jackson, J. S.; Bauer. H. H. Chem. Instrum. 1971, 3 , 229-234. __. _. (6) Canagaratna, S. G.;Karunathilaka,S. A. G. R . J . Nectroanal. Chem. 1973, 48, 183-188.
RECEIVED for review December 10, 1979. Accepted March 3, 1980.
Determination of Subnanogram and Nanogram Amounts of Fluoride by Fluoride and Calomel Reference Electrodes Dan Deutsch* and Shahla Zarini Department of Dental Research, Dental School, Hebrew University
of Jerusalem, Jerusalem, Israel AnalaR reagent. A digital pH meter/millivolt meter MBK model A4031 is used to measure the electropotential. Standards. Fluoride standard solutions 0.0, 0.1, 0.5, 1.0, 2.0, and 10.0 ppm F- in 1 M acetate buffer IpH 5.3) are prepared according to the method described by Hallsworth, Weatherell, and Deutsch, 1976(2). Fluoride Determination. To determine the fluoride concentration of the sample solution, a 1-pL drop is placed at the center of the inverted fluoride electrode. The calomel reference electrode is then lowered t o 0.5 mm from the fluoride electrode surface, confining the sample solution drop between this surface and the surface of the ceramic frit junction. The electropotential of the solution is read after 2 min. This potential reflects the fluoride concentration of the solution. To avoid contamination by fluoride adsorbed to the surface of the electrode from a previous determination, the surfaces of both electrodes are rinsed between successive fluoride determinations with distilled water, to reach a potential 50 mV more positive than that obtained for the buffer blank (0.0 ppm F). The
In recent years extremely sensitive methods for determining subnanogram amounts of fluoride with the fluoride electrode have been developed (1-3). These methods involve the use of very small sample volumes placed between the ordinary fluoride electrode and a reference system specially constructed for this purpose. The present method dispenses with the need t o construct a reference electrode by employing the commercially available calomel electrode commonly used for p H measurements.
EXPERIMENTAL Fluoride Electrode Assembly. The fluoride electrode assembly (Figure 1) consists of an Orion fluoride electrode, model 96-09 or 94-09, clamped in an inverted position, and a reference calomel electrode radiometer type K401, which is mounted above. The lower end of the calomel electrode is flat and contains at the center a ceramic frit junction, 0.75 mm in diameter. The reference filling solution consists of saturated KC1 solution prepared from 0003-2700/80/0352-1167$01.00/0
C
1980 American Chemical Society
1168
ANALYTICAL CHEMISTRY, VOL. 52, NO. 7, JUNE 1980
Table I. Precision of Measurement of the FConcentration in Standard Solution of Varying F- Concentration absolute precision of F- concn. amounta of F- measurement,b of the std. in the sample z rel. std. solution, ppm employed, ng dev., % 0.1 0.5 1.0 2.0 10.0
0.1 0.5 1.0 2.0 10.0
= 3.0 1.0 -4.0 i 2.0
= 3.5
a The volume of each sample was 1 pL. Twelve analyses were carried o u t on each standard solution,
that with the highest fluoride concentration and terminating with the lowest. Determination of L e a k R a t e . The leak rate of the calomel reference electrode is determined by the method of Hallsworth et al. (2). In the present system, it was found to be 0.018 pL/min. This corresponds to a 3.6% dilution of the sample during the period of fluoride determination.
RESULTS Reproducibility measurements were carried out on standard solutions containing 0.1,0.5, 1.0, 2.0, and 10.0 ppm F.Twelve electropotential measurements were carried out on each standard. T h e results (Table I) show that the precision of fluoride measurements a t the 0.1, 0.5, 1.0, 2.0, and 10.0 nanogram levels was 3%, 1.270, 470,2 % and 3.570, respectively. T h e response of the inverted electrode within the range of 0.1-10.0 ng F, followed a typical Nernstian response.
',_ _ _ - _ _ _ : c J- -L------, - _ _ _ _ _ _ - - - - --7 Figure 1. Fluoride electrode assembly. (a) Saturated calomel reference electrode (Radiometer K401j. (b) Ceramic frit junction. ( c j Electrode holder controlling the distance between the surface of the calomel electrode and the fluoride electrode (0.5 mmj. (d) Orion fluoride electrode. (e) Polypropylene cap, tightly fitted to the fluoride electrode, which collects into a conical flask the water used to rinse the electrode
calomel electrode is then raised and the distilled water removed by tissue paper. On completion of fluoride determination, the reference calomel electrode is placed in distilled water and the surface of the fluoride electrode is dried. When fluoride determination is resumed. the system is calibrated using the standard solutions, starting with
DISCUSSION T h e asset of this method is its precision and the ease with which this system can be assembled to measure subnanogram amounts of fluoride. I t dispenses with the need to construct a special reference system and requires no modification of the fluoride electrode itself. The precision of measurement of fluoride concentration is within the range of that achieved by other micro methods (1-3). T h e volume of 1-pL solution employed can be further reduced by half if smaller amounts of fluoride are to be determined. The system follows a Nernstian response over the range of 0.1-10.0 ng fluoride in 1-pL solution, which is comparable to the macro systems for fluoride determination. This method has been successfully used for determining fluoride concentration in mineralizing tissues. LITERATURE CITED ( 1 ) P. Venkateswarlu, Anal. Chem., 46, 878 (1974). (2) A . S.Hallsworth. J. A . Weatherell, and D. Deutsch. Anal. Chem., 48, 1660 (1976). (3) G. L. Vogel, L. C. Chow, and W. E. Brown, J . Dent. R e s . , Suppl. 6 , 56, 164 (1977).
RECEIVED for review July 9, 1979. Accepted November 11, 1979.
