column of 1-inch diameter, on the other hand, leads to Ro/r, > 100 or a coil diameter of 250 cm., a rather excessive value for practical work. Despite the simplicity of this criterion it should be kept in mind that the extra plate height, Equation 1, increases a t a spectacular rate (the fourth power) with increases in column diameter. With a given limit on this extra plate height, and other things (including particle diameter) being equal, the coil diameter
must be expanded with the square of column diameter. This criterion can be used to replace Equation 6, providing the lower limit on coil diameter has already been established for a given column. LITERATURE CITED
(1) Giddings, J. C., ANAL. CHEM.34,
1186 (1962). ( 2 ) Giddings, J. C., J . Chromatog. 3, 520 (1960).
(3) Giddings, J. C., Zbid., 16, 444 (1964). (4) Giddings, J. C., J . Gas Chromatog. 1 No. 4, 38 (1963).
J. CALVIN GIDDINQS Department of Chemistry University of Utah Salt Lake City, Utah
INVESTIGATION supported by Public Health Service Research Grant GM 10851-09 from the National Institutes of Health.
N e w Assay Value for Constant-Boiling Hydrochloric Acid SIR: The purpose of this correspondence is to call attention to a new value for the composition of constantboiling hydrochloric acid that we obtained in careful coulometric titrations on this acidimetric standard (1). The conditions needed to obtain reproducible compositions of the constant-boiling mixture were studied. With the usual equipment and procedure (2, 3) the distillation rate should be made slower than that normally recommended and should not exceed 2 ml. per minute. Two samples of constant-boiling mixture were carefully and independently prepared for coulometric analysis, a t pressures of 753.2 and 752.7 mm. Hg
(corrected), respectively. The coulometrically obtained composition values for these were, respectively, 179.952 and 179.941 air wt. grams of constantboiling distillate that contains 1 mole vacuum wt. of hydrochloric acid. These results are based on the latest value of the faraday, 96,487.0 coulombs per and are independent of equivalent (4, particular atomic weight values. Each of these results represents a concentration value that is 0.053% higher than would be given by presently accepted data (2, 3), interpolated for the particular pressure involved. It might be assumed that a similar discrepancy would be found a t other values of pressure.
LITERATURE CITED
(1) Eckfeldt, E. L., Shaffer, E. W., Jr., ANAL.CHEM.37, 1534 (1965). (2) Foulk, C. W., Hollingsworth, M., J . Am. Chem. Soe. 45, 1220 (1923). (3) Hillebrand, W. F., Lundell, G. E. F.,
Bright, H. A,, Hoffman, J. I.: “Applied Inorganic Analysis,” 2nd ed., p. 181, Wiley, New York, 1953. (4) Nat. Bur. Std. ( U . S.), Tech. News Bull. 47, 175 (1963).
EDGAR L. ECKFELDT E. W. SHAFFER, JR. Research and Development Center Leeds and Northrup Co. North Wales, Pa. NINTHConference on Analytical Chemistry in Nuclear Technology, Gatlinburg, Tenn., October 1965.
Evaluation of a Computer-Based Technique for Estimating the Limit of Detection of Chromatographic Detectors SIR: A previous paper (3) described the determination of the limit of detection of chromatographic detectors by a method that was objective and theoretically sound, but required collection of many data and a long calculation. Now, the use of automatic data recording and computing equipment, originally designed for interpreting chromatograms (2), has drastically reduced the labor involved and permitted a simple, quantitative evaluation of the method. Three flame ionization detectors have been tested, and an important implication of the theory confirmed: a detector can have markedly different limits of detection for peaks of different widths. The customary method of estimating detector noise as the maximum peak-to-peak random excursion of the base line was compared and found decidedly inferior. EXPERIMENTAL
Apparatus. Previously described data recording equipment (2) was attached t o the detector output. The data playback unit and computer ( 2 )
were also used, but an additional computer program was prepared to calculate the limit of detection. Procedure. The analysis of a small amount of reference compound (butane or hexane, depending on whether a gas or liquid sample injector was available) was recorded on magnetic tape ( 2 ) . For injectors with less than 2y0 accuracy, several analyses were made and the results averaged. The base line detector output was recorded on both magnetic tape and a strip chart for 35 minutes with the converter gain increased to 10 times its usual setting (2) to provide increased accuracy in measuring noise. A constant-voltage input to the converter was recorded to simulate a noiseless detector output. The reference compound analysis was interpreted as previously described (2) with the computer instructed to report the peak area in converter pulse units, to be consistent with the base line noise calculation. The base line tape was read with the interval setting (2, 3) a t 1.67 seconds. Each base line tape was read three times to indicate repeatability ( 2 ) . For comparison with the peak-to-peak
method, one of the strip chart base line recordings was divided into eight equal segments and the maximum peak-to peak excursion estimated in each. RESULTS AND DISCUSSION
Results. The noise estimates calculated for the “noiseless” input and one detector are shown in Table I and 11, respectively. The peak-to-peak measurements are also included in Table 11. The limits of detection for the three detectors are shown in Table 111.
Table 1.
Interval, sec. 1.67 3.33 6.67 13.33
Apparent Noise Estimates for a Noiseless Input
Noise estimate, converter pulse units 0.56, 0.77, 0.80, 0.70, 0.61, 0.55, 0.74, 0.55 0.65,0.68,0.75, 0.66 0.97, 0.88 1.14
VOL. 37, NO. 12, NOVEMBER 1965
1581
Computer Calculations. Noise estimate is defined as the standard deviation, in converter pulse units, of a set of 50 noise areas (3) and is equal to N , ( 3 ) . The computer calculated four different sets of noise estimates, obtained by using the original 1.67second intervals, combining the original intervals in adjacent pairs to create 3.33-second intervals, and further repeating the pairing process to obtain 6.67- and 13.33-second intervals. The 35-minute recording provided sufficient data for eight successive noise estimates with 1.67-second intervals. Each pairing step halved the number of intervals and reduced the number of noise estimates proportionally. The limit of detection is calculated from the noise estimate by
where W6 = limit of detection, grams W = weight of reference compound, grams A = area of reference peak, converter output pulse units S = ratio of converter gain during recording of base line and reference peak tapes, dimensionless This equation is derived from Equation 2 in reference (3) by substituting n = 50 and the applicable chi-square value ( k ) estimated for 49 degrees of freedom. A / W has been substituted
Table II.
for SL because the units are then consistent with N , . Apparent Noise of System. The process of forming interval areas introduces a one-count uncertainty (9) and would result in Ni values of 1 or 0, and a noise estimate between 1 and 0, for a noiseless base line tape. The results in Table I correspond to an apparently noiseless base line tape for all interval sizes except the largest, demonstrating that a slight amount of noise is being introduced by the measuring equipment a t the 13.33-second interval. Converter gain must be set high enough to give noise estimates considerably greater than 1 in order to minimize the effect of this apparent noise. Interpretation of Experimental Data. I n Table 11, the seventh noise estimate is significantly higher than the other 1.67-second values. The tape for these data was recorded under programmed temperature conditions, and the seventh interval corresponds to the period of maximum column bleed. Since this method of noise measurement is very insensitive to slope (S), column bleeding is shown to increase noise as well as slope. The limit of detection data for the three detectors, as shown in Table 111, demonstrate significant differences in performance. The second detector is less than half as sensitive as the other two a t all interval sizes. The other two detectors are approximately equal in overall performance, with the third
Noise Estimates for a Flame Ionization Detector Corre-
s onding
peat-t o-peak noise, arbitrary units
~
Interval, sec.
Estimate No. 1 2 3 4 5 6 7 8 1 2 3 4 1 2 1
1.67
3.33
6.67 13.33
Table Ill.
1.67 3.33 6.67 13.33
1582
0.0027 0.0034 0.0059 0.0101
a
Noise estimate tape reading
1 2.27 2.71 2.62 2.27 2.45 2.66 5.04 2.29 4.49 6.21 4.80 7.02 10.06 12.10 19.86
2 2.15 2.28 2.05 2.24 2.76 2.46 5.29 2.89 5.73 5.58 4.23 9.90 13.96 11.70 23.04
3 2.02 2.35 2.31 2.02 3.13 3.03 5.31 2.55 4.41 5.77 5.89 7.71 9.23 13.51 24.45
13 14 11 27 17 16 24 13
Limit of Detection for Three Flame Ionization Detectors
0.0026 0.0038 0.0061 0.0091
0.0027 0.0038 0.0057 0.0106
ANALYTICAL CHEMISTRY
0.0079 0.0097 0.0189 0.0377
0.0080 0.0093 0.0206 0.0428
0.0088 0.0108 0.0189 0.0405
0.0022 0.0045 0.0088 0.0166
0.0022 0.0023 0.0050 0.0048 0.0101 0.0090 0.0182 0.0193
superior a t minimum interval size and the first a t the larger interval sizes. Thus, under the most favorable conditions, the third detector can detect approximately two nanograms with the prescribed (3) 50% accuracy. Comparison with Peak-to-Peak Method. The noise in electronic equipment is often specified as the maximum random fluctuation of the output, and is called peak-to-peak noise (4). This method of noise measurement has been proposed ( I ) and used (6) to specify the noise level of chromatographic detectors. The noise estimate defined in this paper appears preferable for several reasons. The measurement of peak-to-peak noise of a chromatographic base line is subjective. An analyst must decide what length of base line should be scanned, and to what extent fluctuations may be considered drift rather than noise. The treatment of one abnormally large fluctuation is not precisely defined. By contrast, each fluctuation receives the proper statistical consideration in the noise estimate. Table I11 shows that the limit of detection is a function of peak width, but the peak-to-peak method cannot be related t o peak width. In fact, no quantitative relationship between peakto-peak noise and the corresponding expected error in measuring a peak area has apparently been reported. The repeatability of peak-to-peak noise has never been demonstrated to be adequate for estimating detector noise, but one quantitative treatment of peak-to-peak detector noise contains statistical statements that might be misinterpreted. Phrases such as ‘[the analyst can choose peak-to-peak voltage values with as small an uncertainty as he chooses” (5) do not refer to the repeatability of the experimentally measured quantity, but only to the fact that multiplying the experimentally observed peak-to-peak noise by a sufficiently large coefficient mill give a product that exceeds all but a specified percentage of noise peaks ever produced by that detector. This multiplication does not affect relative repeatability of several peak-to-peak measurements on the same detector. The variation among the peak-to-peak values in Table I1 completely obscures the definitely noisier character of the seventh interval and far exceeds the variation among the noise estimates. Only this relative comparison of the two methods is possible because of the lack of a precise relationship between peak-to-peak noise and limit of detection. The variation in peak-to-peak values in Table I1 is typical for that technique, but an analyst might normally regard such variation as indicating an actual fluctuation in detector performance. In Table 11, however, the corresponding
noise estimates show that, except for the previously discussed seventh interval, the detector is remaining quite consistent in its ability to measure peak areas. When automatic data handling equipment is available, the noise estimate can be obtained more easily than the peakto-peak estimates. The same length of base line must be recorded with either procedure to provide the same sample size, and reading a magnetic tape a t the computer is faster than scrutinizing and making measurements on a chromatogram. Repeatability. The statistical basis for this procedure (3) permits a definite
LITERATURE CITED
prediction of repeatability. Interpolation in Table I of Reference (3) for the present case of 50 Ni in the noise estimate calculation indicates that 19 out of 20 noise estimates should have relative values within 0.596 to 0.891 and, therefore, should not vary more than ~ = 2 0 7from ~ their mean. The values in Tables I, 11, and I11 support this conclusion. A section of base line 1200 times as long as the minimum interval was used for a set of noise estimates to help ensure a representative sample. I n fact, the data of Table I1 illustrate how multiple noise estimates can be used to detect variations in base line noise.
(1) Dimbat, M., Porter, P. E., Stross, F. H., ANAL.CHEM.28, 290 (1956). ( 2 ) Johnson, H. W., Jr., Ibid., 35, 521
(1963).
(3) Johnson, H. W., Jr., Stross, F. H.,
Ibid., 31, 1206 (1959). (4) Williams, A. J., Jr., Tarpley, R. E., Clark, W. R., Trans. Am. I n s t . Elec. Engrs. 67, 47 (1948). (5) Young, I. G., “Gas Chromatography,”
H. J. Noebels, R. F. Wall, N. Brenner, eds., p. 75, Academic Press, New York, 1961. H. W. JOHNSON, JR. Shell Develo ment Co. Emeryville, 8alif. PITTSBURGH Conference on Analytical Chemistry and Applied Spectroscopy, Pittsburgh, Pa., March 1965.
An Improved Gradient for Ion Exchange Chromatography of Peptides on Dowex-1 SIR: Dowex-1 has proved to be a useful ion exchange resin for the separation of peptides. In earlier application of this resin to the separation of peptides (9), three different developers were used. The choice of a particular developer was dictated to a considerable degree by the charge of the peptides to be separated. I n each of the three developers, a rather abrupt change in p H occurred a t some point in the gradient which was produced by the addition of acetic acid to a starting buffer. Because of the abrupt change, some peptides were incompletely separated and had to be rechromatographed with a more gradual gradient. A more generally applicable developer has now been devised; it begins a t a higher pH in order to retard basic peptides and has a gradual, slightly sigmoid pH gradient. EXPERIMENTAL
Materials. The preparation of Dowex-1 has been described in detail (9). Five developers are needed. Four liters of aqueous pH 9.4 buffer require 60 ml. of N-ethylmorpholine, 80 ml. of a-picoline, 40 ml. of pyridine, and sufficient glacial acetic acid (about 0.5 ml.) to give a pH of 9.4. Buffers of pH 8.4 and 6.5 are made up identically except that the quantity of acetic acid is approximately 3 and 37 ml., respectively. I n addition, 0.5N and 2147 acetic acid are required. The source and quality of the reagents have been described (9). All of them except the acetic acid were distilled without fractionation before use. N-Ethylmorpholine is best preserved in the deep freeze after distillation, Procedure. The procedure has not been altered appreciably from that previously described in detail (9) except in the method of development, the size of the column, and the ninhydrin pro-
MIXER
A
HEATING BATH 2
I: 4
97.
MIXER
---
Tube Srre-Tyype
mm coils
mllmin
I ,034“ Polytlhyl8no
c.
c
COOLING
COIL
2;
Dummy
Dl SCA RD
Figure 1.
Revised system for ninhydrin analyses with Technicon AutoAnalyzer
cedure for detecting the position of zones. The use of smaller columns (0.6 X 60 em. instead of 1 X 100 em.) has been briefly outlined ( 3 ) . Prior to the pouring of the column, the regeneration of the resin (9) was completed with the pH 9.4 buffer described above, and the resin was suspended in it. The pouring of Dowex-1 columns can be troublesome because of the tendency of bubbles to be trapped or to form and grow. The following procedure usually resulted in a satisfactory column in the event that bubbles formed after a column was poured. The bottom of the tube was closed, a 1 X 35-em. extension was attached to the top of the chromatographic tube, buffer was added until the extension was about half full, and then the top of the extension was also closed. By carefully and repeatedly inverting the column and returning it to its normal position, the resin can eventually be suspended partially or completely in the supernatant buffer and then allowed
to resettle under gravity. If bubbles are present in the upper portion of the column, only this part need be suspended and resettled. After repeated use, the flow rate of a column a t a given pressure may decrease markedly. I t is usually simpler to suspend and resettle the column in the above way than to remove and repour the resin. The conditions of chromatography for two sizes of columns are listed in Table I. The columns differ by a factor of about 4 in volume and most quantities have been adjusted by about this ratio. The gradient was produced by a constant volume mixer of the indicated volume. The reservoir from which the various developers flow into the mixer should be attached directly to the mixer. If the changes were made manually, mixer and reservoir were filled initially with pH 9.4 buffer. After the indicated volume (Table I) had flowed through the column, p H 9.4 buffer in the reservoir was replaced VOL. 37, NO. 12, NOVEMBER 1965
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