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results are not as such transferable to the case of the faradaic response. Even apart from this restriction to capacitance measurements, the results presented here deal with a somewhat idealized polarographic experiment, because we have assumed a rather simple form of the solution resistance; see Equation 2. The actual resistance in series with the double layer capacitance is usually larger than that assumed here, as it may include, e.g., the resistance of the polarographic capillary. Such additional time-independent series resistances can easily be identified, and their effect eliminated by instrumental iR compensation. If only this additional series resistance is compensated, there is no danger of circuit instability, Le., oscillatory behavior. The sampling error discussed here constitutes a systematic one, affecting data accuracy rather than precision. There are, of course, other sources of systematic error which affect the accuracy of capacitance measurements. Such errors are all due to the difference between an actual mercury droplet in a polarographic cell and the idealized, freely suspended and concentrically surrounded mercury sphere envisioned in most calculations. A most pernicious source of errors, affecting both precision and accuracy, results from the thin but not entirely reproducible film of solution which usually creeps between the mercury thread and the inner wall of the capillary, giving rise to the so-called “capillary response” (7-11). This effect, which ultimately limits the sensitivity of polarographic techniques (9) and which affects ac measurements mostly by causing the measured capacitance to vary with frequency, can be reduced but not completely eliminated by making the inner surface of the capillary water-repellent and/or by using capillary tips with special shapes (8, 9). A related effect is that of shielding of the top of the drop by the capillary (12) although model measurements (13) and calculations (14) tend to overemphasize it because the drop is somewhat elongated near its neck; see below. The position of the other electrode(s) and of the cell wall can also cause minor frequency dispersion. The mercury flow rate through the capillary is affected by the back-pressure from the curved drop surface. Since this back-pressure is directly proportional to interfacial tension, and the latter depends on the applied potential, the mercury flow rate and, hence, the drop area a t a fixed drop age vary somewhat with potential (15, 16). Also, the shape of the mercury droplet deviates from that of a perfect sphere, being somewhat elongated where it merges with the mercury thread inside the capillary (15). The extent of this elongation depends on interfacial tension, hence on potential. At potentials far from that of zero charge, these effects of flow rate and drop
elongation both tend to increase the surface area of the drop, and hence its capacitance C, while reducing the corresponding solution resistance R. When the admittance is sampled over, e.g., the last 20% of drop life, so that the resulting sampling error is less than 0.1 % , the resulting inaccuracy is considerably smaller than that introduced by the above-listed effects. The distortion resulting from the use of a network analyzer was studied in a recent paper by Sluyters-Rehbach et al. (17) which reached us after completion of the present study. Sluyters-Rehbach et al. report much larger sampling errors, and suggest that their results will also qualitatively apply to modern ac polarographic techniques using direct-reading lock-in amplifiers or Fourier transform methods. Apparently they reached their much less favorable conclusion because they compared the filtered output with the unfiltered one a t the same instant, instead of allowing for the signal delay in their detector. It appears that a shift of the comparison curves in their Figures 1 and 2 by the appropriate filter time delay will bring their results much more in line with ours. In summary, the in-phase and quadrature components of the admittance of a growing mercury drop electrode in an ideally polarizable solution have been shown to be sufficiently linear functions of time such that the average value over a sampling interval from tl to t 2 does not differ appreciably (less than 0.1%) from the instantaneous value a t t 3 = (tl + t 2 ) / 2 when t l I0.8t2. For more conventional measurements in which the instantaneous current is sampled, it is suggested that the sampling moment be adjusted for signal delay in the detector circuit. LITERATURE CITED (1) Kojima, H.; Fujiwara, S.Bull. Chem. SOC:.Jpn. 1971, 44, 2158. (2) Creason, S. C.; Smith, D. E. J . Electroanal. Chem. 1972, 36, Ai. (3) Creason, S.C.;Hayes, J. W.; Smith, D. E . J . Electroanal. Chem. 1973, 47, 9. (4) Seeling, P. F.; de Levie, R. Anal. Chem. 1980, 52,paper in this issue. (5) IikoviE, D. Collect. Czech. Chem. Commun. 1932, 4 , 480. (6) Smith, D. E. Crit. Rev. Anal. Chem. 1971, 2, 247. (7) Melik-Gaikazyan, V. I. Zh. Fiz. Khim. 1952, 26, 560. (8) Barker, G.C.; Jenkins, I. L. Ana/yst(London) 1952, 77, 685. (9) Barker, G. C. Anal. Chlm. Acta 1958, 18, 118. (10) Leikis, D. I.; Sevast’yanov, E. S.; Knots, L. L. Zh. Fir. Khim. 1964, 38, 1833. (11) de Levie, R. J. Elecboanal. Chem. 1965, 9 , 117. (12) Grahame, D. C. J , Am. Chem. SOC.1946, 68,301. (13) Gardner, A. W. “Polarography 1964”; Macmillan: London, 1966; p 187. (14) Newman, J. J. Electrochem. SOC. 1970, 117, 198. (15) Smith, G. S. Trans. Faraday SOC.1951. 47, 63. (16) Bresie, A. Acta Chem. Scand. 1956, 10, 943. (17) Siuyters-Rehbach, M.; Breukel, J. S. M. C.; Sluyters, J. H. J . Nectroanal. Chem. 1979, 102, 303.
RECEIVED for review March 7 , 1980. Accepted May 5, 1980. Work supported by the Air Force Office of Scientific Research under Grant AFOSR 76-3027.
Modification of a Conventional Flame Photometric Detector for Increased Tin Response Walter A. Aue” and Christopher G. Flinn Department of Chemistry, Dalhousie Unversity, Halifax, Nova Scotia B3H 4J3, Canada
Ever since we reported the unusual response of a modified flame photometric detector (FPD) to organotin compounds ( I ) , it has been our interest to modify, in a simple way, a conventional FPD for maximum tin response. Besides simplicity of construction, it was also desirable to improve the detector in other ways. Its response to tin compounds is due to luminescence occurring on the surface of quartz and, most likely for this reason, suffers from two 0003-2700/80/0352-1537$01 .OO/O
drawbacks: the calibration curves deviate slightly from linearity in the upper region, and the detector can be contaminated by large amounts of phosphorus, tin, or germaniumcontaining substances. Since the detector responds to subpicogram amounts of tin compounds, a further increase in sensitivity was not sought. Surprisingly, however, a very simple modification of a commercial FPD brought about an increase in sensitivity in 0 1980 American
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LOG
Figure 1.
-10 GRAMS
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8
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INJECTED
Response of tetrapropyltin by two different mechanisms
Figure 2. Response of a quartz wool modified FPD to 100 fg of tetrapropyltin
addition to the other desired effects. The simple modification was to insert a loose plug of quartz wool right above the shielded flame. T o demonstrate the pronounced effect this produces, the regular quartz chimney of a Shimadzu FPD was replaced by a borosilicate tube of equal dimensions. This tube had slight indentations to hold a plug of quartz wool in place against
the detector gas flow. Other conditions were close to those described in our earlier paper (1). Figure 1 shows calibration curves of tetrapropyltin with and without the quartz wool inserted. Different emissions are observed under the two sets of conditions. With dark-adapted eyes it is easy to see them. Without quartz wool, tin compounds produce an elongated red glow (SnH band) right above the flame, surrounded by a grayish, diffused luminescence (sometimes attributed to SnO). When the quartz wool plug is in place, an intense blue glow appears at its lower end right above the flame. The emitter responsible for this continuum, which peaks a t 390 nm, is unknown. Figure 1 shows calibration curves for tetrapropyltin with and without quartz wool. The improvement brought about by using the surface luminescence as opposed to the gas phase emission (with perhaps a minor amount of surface luminescence present) is evident. Despite the apparent simplicity of a FPD modification that involves nothing more than the addition of some quartz wool, these results are better than those obtained with earlier models. These had given a slight deviation in the calibration curve, which now has vanished. Working with the quartz wool detector for some time, furthermore, demonstrated that it is less susceptible to contamination. The closeness of the flame to the quartz wool seems to dispose of certain impurities that would otherwise block its function. The detector is also more sensitive: the minimum detectable amount of tetrapropyltin is 4 X g, corresponding to 5 X mol (about 2 million atoms) tin/s. Figure 2 shows a typical chromatogram of 0.1 pg tetrapropyltin. Note that due to the surface effect, the peak is slightly broader than one would expect from the regular gas chromatographic dispersion. We did not attempt to modify other commerical FPDs by insertion of quartz wool. We do assume, however, that similar improvements in tin response would result.
LITERATURE CITED ( 1 ) Aue, W. A,: Flinn, C. G. J . Cbromatogr. 1977, 142, 145-154
RECEIVED for review July 9, 1979. Resubmitted March 18, 1980. Accepted March 18,1980. This research was supported by NRC Grant A9604 and by a grant from the Department of Fisheries and Oceans.
Use of an Automated, Stepping Differential Calorimeter for the Determination of Molecular Weight J. Zynger” and A. D. Kossoy Lilly Research Laboratories, Eli Lilly and Company, Indianapolis, Indiana 46206
A recent report ( I ) from this laboratory describes an automated, stepping differential calorimeter which is used to determine purity through the analysis of the thermogram generated by stepwise melting of a sample. Assuming ideal behavior between the components of the sample, the inverse of the fraction melted of the main component when plotted vs. the temperature should yield a straight line that is defined by the van’t Hoff equation (2):
where T , = instantaneous sample temperature, To= melting 0003-2700/80/0352-1538$01 .OO/O
point of the pure compound, R = gas constant, AHf = heat of fusion, F = fraction melted at T,,and X = mole fraction of impurity. In our laboratory, this technique has been used for over three years for about 3000 assays of mol 70 purity. Implicit in Equation 1 is the designation of two molecular weights which are incorporated into the mole fraction impurity term. Therefore, the data derived from the melting behavior of a mixture consisting of a known weight of a small amount of material of unknown molecular weight “impurity”, and a known weight of a relatively large amount of an appropriate host substance of known purity and molecular weight “main component” should yield the molecular weight of the unknown. Hence, by simply modifying the calculations in @ 1980 American Chemical Society
