Quantitative Interpretation of Semilogarithmic Gas Chromatographic Data R. L. Wade and S. P. Cram Department of Chemistry, Unirjersity of Florida, Gainesuille, Fla. 32601 Semilogarithmic chromatograms are shown to be useful in eliminating peak attenuation and for enhancing the display of small peak areas and shoulders. Furthermore, the detector output current is known at all times and is of analytical significance. The logarithmic ordinate is deceptive because the amount of effluent tailing appears to be greater than that displayed on a linear ordinate and the resolution and column efficiency appears to be less. Methods of calculating the resolution, column efficiency, and tailing factors are given by treating a Gaussian elution profile as a parabola in the semilog mode. Peak areas may be calculated from the area of a parabola by use of a floating-base line method or by choosing a fixed, arbitrary base line. The calculations are shown to give improved accuracy and precision over conventional methods. The errors associated with the instrumentation and interpretation of semilogarithmic chromatograms are discussed. Application of the relationships presented allows the analyst to use the semilogarithmic display mode exclusively. The techniques are applicable to all chromatographic methods which approach conditions of linear elution.
LOGARITHMIC AMPLIFIERS offer numerous advantages for the display of gas chromatographic data. They have not been widely used for this purpose because the quantitative interpretation of semilogarithmic chromatograms has not been previously described. A semilogarithmic chromatogram has a much greater dynamic range on a recorder display than a linear presentation and, therefore, does not require range switching or attenuation. This type of display results in a negligible loss of pertinent information when small peaks lie close to large peaks or when peaks elute too rapidly to permit manual attenuation. Furthermore, the detector current is shown at all times, and thus, the true column output before and after the elution of a peak may be measured accurately. The semilogarithmic chromatogram eliminates the necessity of making successive runs in order to keep all peaks on scale. Sampling errors and the time required for manipulation and interpretation of the gas chromatographic data are significantly reduced. Peaks of low concentration may be better observed by using the semilog display because the most sensitive part of the ordinate display is in the small current region. The sensitivity of the display decreases exponentially up to a full scale display, and in this manner, large concentration peaks are also kept on scale. The minimum detectable signal height with a linear electrometer is nominally 2% of full scale, whereas the minimum detectable signal height with a four-decade logarithmic electrometer, for example, is 0.01% of full scale. Thus, peaks up to ten thousand times smaller in height than the main peaks can be observed. The design of logarithmic electrometers has been described previously (1-3). Problems of excessive drift, calibration, and (1) R.A. Dewar and V. E. Maier, J. Chromatog., 15,461 (1964). (2) H. W. Moll, Pittsburgh Conf. on Anal. Chem. and Appl. Spectry., Pittsburgh, Pa., March 1-5, 1965. (3) R. D. Moeller and A. W. Hartz, Pittsburgh Conf. on Anal. Chem. and Appl. Spectry., Pittsburgh, Pa., Feb. 21-25, 1966.
~~
FLAME m i z w o n DETECTOR
VllVllTlNG REED ELECTROMETER
OVAL CHANNEL SERVO
a T W O STAGE %’ NEEDLE
DIGIT41 WG ELECTROMETER
CoLUYN
IWJECTlON PORT
U
FLAME IONlZATlOli DETECTOR
RECORDER
U R E w u r w
V l L V E FLOW CONTROLLER
Figure 1. Schematic diagram of the chromatographic system with semilog and linear readout limited dynamic range have now been eliminated. Instrumentation is commercially available (4) which includes a calibrated full-scale display, an internal current standard for calibration of the electrometer, and a drift of less than O , S ~ o per hour. The analytical significance of displaying chromatographic data in the semilogarithmic mode has been pointed out, and the measurement errors have been discussed (5). Several instrument companies include a “log” attenuator display option on their digital integrators. Presently, however, these instruments do not give a true semilogarithmic chromatogram, as the recorder output from the integrator is a hybrid combination of a linear and a log display. Consequently, the “log” display is not calibrated, and quantitative interpretation of the analog display is not possible. This type of display is useful for indicating the relative peak heights and the retention times. The number of decades to be displayed on the ordinate must represent a compromise between the dynamic range required and the amount of data interpretation desired. If the analyst is interested in measuring the column efficiency, resolution, etc., as well as the peak area, then the display of four decades has been found to be the most applicable solution. If only the retention times are of interest and all samples are to include concentration ranges of the order of lo6:1, then a larger number of decades may be desirable. EXPERIMENTAL
The chromatographic system shown in Figure 1 was used to compare the outputs of a vibrating reed electrometer (Model 4010-1, Victoreen Instrument Co.) and a digital log electrometer (Model 4010-2, Victoreen Instrument Co.). A 20-ft, ‘/*-in. column packed with 5 % SE-30 (Varian Aerograph) on 80/100 mesh Chromosorb P (AW/DMCS) (Johns-Manville) was used for the separations reported. A 1 :1 sample splitter was constructed to give equal flow and (4) Victoreen Instrument Co., Cleveland, Ohio, Bulletin GC4000, 1965, p 8. (5) S. P. Cram, Pittsburgh Conf. on Anal. Chem. and Appl. Spectry., Cleveland, Ohio, March 3-8, 1968. VOL. 41, NO. 7, JUNE 1969
893
I
IO4
-1
loo
J W
4 m o -1 -1
LL 3
m
P W
9
w P
0
I-'
2
a
2 K
f
Y 8 t-o
J W
w 0
2 0
r
-I
-4.0
-3.0
-2.0
STANDARD
-IO
0
1.0
DEVIATION,
2.0
50
4.0
V
Figure 2. Comparison of linear and semilog Gaussian peaks normalized to the same peak height equal dead volume to each flame detector. The hydrogen and oxygen flow rates were 70 ml/min and 200 ml/min, respectively, and these flow rates were matched as closely as possible for each flame of the dual-flame detector. The carrier gas flow rate was nominally 50 ml/min. A f340 V polarizing voltage was applied to the flame detector (Model 4016-1, Victoreen Instrument Co.) from the digital log electrometer power supply. A positive input is required for the digital log electrometer, and thus the polarizing voltage on the second flame was -340 V. The digital log electrometer output was integrated by a six decade preset count scaler (Model 27104, Nuclear Chicago Corp.), and a digital integrator (Model 480 Varian Aerograph) was used to integrate the linear display. A dual-channel recorder (Model 7100B, Hewlett-Packard) was run in series with the electrometers for the analog display. RESULTS AND DISCUSSION
The model generally accepted for ideal chromatographic behavior is that of a Gaussian distribution of eluent with respect to time. The solution to Fick's second law for longitudinal diffusion may be given by Equation 1 1 -1 2 exp 2 ( ~ D t ) " ~ 4Dt
n
_=___
m
where n is the number of molecules/cm3,m is the total quantity of diffusing material, D is the diffusion coefficient, and 1 is the diffusion distance down the column at time t . This equation is a form of the normal error curve. However, when a logarithmic electrometer is employed, the electrometer output of this function will be described by the logarithm of Equation 1 n
logm 894
=
log
1 2(aDt)lI2 ~
ANALYTICAL CHEMISTRY
12 -9.2Dt
+
where Equation 2 is of the form y = a bxz which is a quadratic equation whose trace is parabolic. Thus, chromatographic peaks will appear as parabolas rather than as the nominal Gaussian distribution. Because there is no zero line with a semilog display, the problem of where to measure the peak widths arises for the calculation of the number of theoretical plates, the resolution, and the tailing factor. Furthermore, methods of integration such as planimetry, cutting and weighing, and triangulation are no longer valid. Peak Width Measurement. A Gaussian distribution is shown on both a linear and logarithmic ordinate in Figure 2. The peaks have been normalized to the same peak height for purposes of illustration. The method of extrapolating tangents through the inflection point corresponds to a 4a peak width at the base line where u represents the standard deviation from the mean or the peak quarter-width. This 46 peak width also can be determined by measuring the width of a Gaussian peak at 13.54% of the peak height, h. The same peak width, w , on the semilog trace will be found at 13.54% of the peak height, q , under conditions of ideal, linear-elution chromatography. Peak widths measured in this manner, therefore, should be identical with those measured with base line tangents on a linear display. A comparison of the results obtained for a mixture of n-pentane, 2-methylpentane, and n-hexane is given in Table I. The peaks were compared from chromatograms run simultaneously in the linear and semilog modes and at a chart recorder speed of 0.2 inch per second. The differences in the measured values of the peak widths are less than the experimental error of measuring peak widths by extrapolating tangents to the base line. Therefore, the semilog chromatogram may be interpreted with at least the same precision and accuracy in the peak width as by conventional method, and fewer steps are required in the measurement.
n-Pentane Sample No.
log
Linear
1 2
61 .O
60.0
62.2
61.8
Table I. Comparison of Measured Peak Widths Peak width, mm 2-Methyl-pentane Relative Relative error Log Linear error 1.7% 71 .O 71 .O 0.0% 0.6%
73.0
73.0
TIME
0.0%
n-Hexane Log
Linear
Relative error
75.5 76.0
78.0 75.5
3.2% 0.7%
, mln.
Figure 3. Comparison of resolution from linear and semilog electrometers Sample size 0.24 pl, Column temp, 150 “C Sample (a) n-pentane, (b) 2-methylpentme, (c) n-hexane, (4hexane isomer Chart speed 0.5 in./&
If the 0.13547 base line for the peak falls near or below a valley between peaks, the measured peak width will be too large because of the increased sensitivity of the semilogarithmic display in the region of peak overlap. This situation may arise for peaks which are shoulders on larger peaks, peaks eluting on the tail of a solvent peak, or incompletely resolved peaks. This is illustrated by the second peak in Figure 3. Inaccurate or infrequent calibration of the full-scale display will give incorrect peak heights, and, subsequently, the base line width will likewise be in error. The column efficiency and resolution of the separation for a Semilogarithmic chromatogram may be characterized by Equations 4 and 5, N ’= ):(61
(4)
and the results should agree with the values of N and R measured from chromatograms displayed on linear ordinates. Peak asymmetry will be more readily apparent with the semilog display because of the change in sensitivity along the y-axis. At the same time, the resolution and column aciency will appear to be markedly less on the semilog plot. This is shown in Figure 3 where a three-component mixture was run with the linear display. The hexane isomer, peak d, appears only on the log display. The two chromatograms were obtained simultaneously, and because R and N are functions of the column rather than the mode of display,
these functions must be identical. It should be noted that base line resolution is obtained between peaks a and b as noted on the linear display, whereas the semilog display indicates the true current at all times between the peaks. Furthermore, the resolution between peaks b and c is 1.7 even though this is not readily apparent from the semilog chromatogram, The asymmetry of peak a results from the slight tailing of the peak and is clearly shown on the semilog display. The tailing factor (6)for the G peak in Figure 4 is 70%, although it is not readily apparent from the linear trace. The benzaldehyde peak, however, would be expected to tail on a nonpolar column. The tailing factor of 15% for this peak may be calculated by using either mode of display. Although the tailing appears to be greater on a semilog display, it is not; the semilogarithmic chromatogram, however, is advantageous for characterizing small peaks in the tailing region. Peak Area Measurement. The most accurate and desirable method of measuring peak areas of semilogarithmic chromatograms is by digital integration. However, if voltage-tofrequency converters and data storage systems are not available, the peak area may be readily calculated from the formula for the area of a parabola
by either of two methods. (6) H.M.McNair and E. J. Bonelli, “Basic Gas Chromatography,” 1st Ed., Varian Aerograph, Walnut Creek, Calif., 1967, p 52. VOL. 41, NO. 7 , JUNE 1969
895
n-C6
IHJ.
n-C7
n-C
c6n,cno
T I M E
Figure 4. Apparent increased tailing for polar compounds displayed in semilog readout mode Column: 5-ft, I/&. stainless steel with 5 % SE-30 on 60/80 mesh (AW/DMCS) Chromosorb W
A
T I M E , min
Figure 5. Arbitrary and floating base line methods of calculating peak areas for semilogarithmic chromatograms Sample: C5and C6saturated hydrocarbons
Table 11. Comparison of Relative Area Measurements for Semilogarithmic Gas Chromatographic Peaks Base line Base line at at 35% Peak No. Digital output of peak max 1Wl0A 1 2 3 4
2.89% 92.46 0.15 4.14
5 6
4.2% 90.2
3.5% 91.4 5.2
0.16
5.2 0.17
Total
0.20 100.00%
0.22 99.99%
896
ANALYTICAL CHEMISTRY
...
... ... ...
100.0%
If the relative peak areas of each component are to be measured for a sample which has a wide range of concentrations, then the peak width must be measured at the same per cent of maximum peak height for all peaks. The base width lines for peaks 1, 2, 4,5, and 6 in Figure 5 were drawn at 35% of the peak maximum in each case. This is an arbitrary number dictated by the height of the smallest peak in the mixture and by the resolution between peaks. The base width line must not be below a point on the curve where the peaks no longer follow the form of a parabola-Le., in the tailing and overlapping regions of the curve. This base width line then may be used to calculate the area of each peak from Equation 6. In no case should the linear distance from the base width line to the peak maximum be used as the parabola height. If the sample follows a pure Gaussian distribution on the column, exhibits no tailing, and has good resolution, the relative accuracy of measuring the peak area increases as the width is taken at smaller fractions of the peak height. If peak profiles such as those in Figure 5 are obtained, one arbitrary base line can be drawn for all peaks as long as it is significantly below the maximum of the smallest peak of interest. This method will give an accuracy of 1-2% which is as good as the height and width measurements themselves. Table I1 compares the results obtained by using a base width at 35% of each peak height and by using an arbitrary base line set at 10-10 A with the integrated digital data obtained. By setting the base line at 10-10 A, all peaks below this line are disregarded, and this is seen to represent an insignificant error in the analysis of the major components. If the base line had been set arbitrarily at 10-9 A, the peak area measurements likewise would have concerned only the 3 major components. In practice, small peaks such as peaks 3, 5, and 6 are often attenuated off-scale and consequently missed in manual calculation methods. Another justification for disregarding all peaks below 1O-lo A is the elimination of the problems of drawing parabolic tangents to the leading edge of peak 3 in
T I M E , rnin
Figure 6.
Application of semilogarithmic gas chromatography to rapid, multicomponent analyses
Sample: 0.50 pl. American Oil Co., ethyl grade gasoline Column temperature programmed from 50' to 250" at 20 "C/min order to be able to estimate its area. The largest error in the peak area calculations for the semilog display in Table I1 arises from the nonlogarithmic response of the 10-8-10-7 A decade. This introduces an appreciable error in the major component peaks by compressing the last decade and directly affects the accuracy of the relative peak areas. This electrometer error was found only in the last decade in the log diode pump and, therefore, does not affect the digital output. Fewer steps and less "eyeball accuracy" are required for the parabola measurements than in triangulation. The number of significant figures in the measurement of the peak height is determined by the location of the peak maxima in the decade. In the lower part of a decade, three significant figures may be reported, and for the chromatographer doing routine analyses with an accuracy of *1-2'%, this method of quantitation should suffice. Several integration methods are compared in Table I11 for mixtures similar in concentration to the chromatogram shown in Figure 3. The parabola area measurements show good agreement with the digital data and are consistently accurate. The peak area measurements using the 10-10 A base line will generally reflect any non-Gaussian behavior on the column and therefore give broader peaks, depending on the amplitude of a given peak. However, the peak widths measured at the same fraction--e.g., 35%-of the peak maximum for all peaks will reflect the same amount of non-Gaussian behavior for all of the peaks measured. The triangulation and peak height ratio data clearly indicate larger errors than those obtained from the semilog dis-
play. The difference between the values obtained with the decade scaler and the linear integrator is due to the fact that the flame detectors used could not be perfectly matched and therefore had different sensitivities. A small amount of fractionation in the splitter, and the estimation of the count rate minimum on the decade scaler between peaks also contributes to the difference obtained. Current calibration experiments show that the 10-8-10-7 decade was compressed, and because peak 2 falls in this region, an additional error was incorporated in the height, width, and the area measurement of this peak. The necessity of accurate calibration of all decades is emphasized for quantitative work. The application of the digital log electrometer is illustrated by a single run taken on a gasoline sample in Figure 6. This chromatogram is shown to illustrate the fact that all peaks are kept on scale without manual attenuation, the small peak areas are increased in size and allow area calculation, the total number of peaks in complex samples may be determined, the flame detector ion current is known at all times during the separation, and that the resolution is excellent although not immediately obvious. The latter point is a distinct advantage in locating shoulders on larger peaks. Work is presently in progress to explore the analytical potential of using a log-log display of chromatographic data. Log-log chromatograms offer the advantages of convenient storage of chromatograms on standard 16 X 11 in. paper by using an X-Y plotter for the readout. Peaks which normally elute very rapidly in the early part of the chromatogram are more spread out on the abscissa than on a linear
Table 111. Comparison of Integration Methods
Method Decade counter Parabola area, 10-9 A base Parabola area, 10-lO A base Integrator Triangulation Peak-height ratio Peak-height X retention time
Av %
n-Pentane Re1 u
27.9 27.9 28.1 28.9 27.9 34.3 32.7
0.13 0.26 0.04 0.56 1.04 0.44 0.38
2-Methyl-pentane Av % 36.3 36.2 25.7 36.9 37.8 35.3 35.7
Re1 u 0.10 0.50 0.0 0.29 2.19 0.22 0.19
Av
z
35.8 36.0 36.2 34.2 34.3 30.3 31.6
n-Hexane Re1 u 0.10 0.33 0.00 0.31 2.19 0.26 0.24
VOL. 41, NO. 7, JUNE 1969
897
display, very broad peaks with long retention times are compressed in width, and the distance between late peaks is decreased markedly. Any number of decades may be used on the abscissa and the retention time per decade may be Calibrated in any units of time so that very long or very short chromatograms all have the same standard format of display.
RECEIVED for review January 23, 1969. Accepted April 7, 1969. Research supported by the Petroleum Research Fund of the American Chemical Society Grant 1200-G3, The U. S. Department of the Interior as authorized under the Water Resources Research Act of 1964, Public Law 88-379, and the Graduate School of the University of Florida.
Cyanolysis and Spectrophotometric Estimation of Trithionate in Mixture with Thiosulfate and Tetrathionate D. P. Kelly, L. A. Chambers, and P. A. Trudinger Baas Becking Geobiological Lub., Bureau of Mineral Resources, P.O. Box 378, Canberra City, A.C.T. 2601, Australia Asensitive method for estimating trithionate is described, which gives a quantitative assay of trithionate in the presence of thiosulfate and tetrathionate. The conditions affecting cyanolysis of the three sulfur compounds were examined, including a brief examination of the catalysis of thiosulfate cyanolysis by cupric ions. The method could be extended to estimate trithionate in mixture with higher polythionates.
IN RECENT YEARS there has been a growing interest in the chemistry and biology of thiosulfate and the polythionic acids (1-3), and sensitive methods for the estimation of these compounds in mixtures have become increasingly desirable. Methods have been described for the titrimetric analysis of mixtures of thiosulfate, trithionate, and higher polythionates (4-6). We have found these methods to be relatively insensitive for the analysis of the small amounts of these materials frequently encountered in experiments on bacterial sulfur compound oxidation (7-9), and that values obtained for trithionate in mixtures were not always reliable. Sensitive colorimetric methods for estimating thiosulfate and tetra-, penta- and hexathionates have been described (10-16), but no similar consideration appears to have been given to the colorimetric determination of trithionate. We have devised a sensitive method for estimating trithionate in mixtures, based on the procedures of Koh et al. (10-13) and Sorbo (16). The method depends on the alkaline cyanolysis of thionates to yield thiocyanate which can be estimated colorimetrically. Tetrathionate, thiosulfate, and trithionate react with cyanide according to Equations 1, 2, and 3. (1) M. Goehring, Fortschr. Chem. Forsch., Bd2,444 (1952). (2) N. Kharasch, Ed., "Organic Sulphur Compounds," Vol. 1, Pergamon Press, 1961, Chapters 2 and 9. (3) P. A. Trudinger, Rev. Pure Appl. Chem., 17, 1 (1967). (4) R. R. Jay, ANAL.CHEM.,25, 288 (1953). (5) A. Kurtenacker, in "Handbuch der Anorganischen Chemie." R. Abegg, F. Auerbach, and I. Koppel, Eds., Vol. 4, part 1, 1st half, S. Hirzel, Leipzig, 1927. (6) R. L. Starkey, J. Gen. Physiol., 18, 325 (1935). (7) D. P. Kelly and P. J. Syrett, Biochem. J., 98, 537 (1966). (8) D. P. Kelly, Ausf. J . Sci., 31, 165 (1968). (9) P. A. Trudinger, Aust. J. Bid. Sci., 17,459, 738 (1964). (10) T. Koh, Bull. Chem. SOC.Japan, 38, 1510 (1965). (11) T. Koh and I. Iwasaki, ibid., 38, 2135 (1965). (12) T. Koh and I. Iwasaki, ibid., 39, 352 (1966). (13) T. Koh and I. Iwasaki, ibid., p 703. (14) 0. A. Nietzel and M. A. De Sesa, ANAL.CHEM.,27, 1839 (1955). (15) N. H. Schoon, Acta. Chem. Scand., 13, 525 (1959). (16) B. Sorbo, Biochim. Biophys. Acta, 23, 412 (1957). 898
ANALYTICAL CHEMISTRY
The present method depends on the fact that Reaction 1 occurs spontaneously at low temperatures, Reaction 2 occurs at low temperature in the presence of cupric ions, while Reaction 3 takes place only at high temperatures. The factors affecting the reaction of thiosulfate, trithionate, and tetrathionate under our assay conditions are described. EXPERIMENTAL
Assay procedure for a mixture of thiosulfate, trithionate, and tetrathionate. Three replicate reaction mixtures were prepared in 25-ml volumetric flasks. The sample to be analyzed (containing up to 8 pmoles total thionate) was added to 4 ml of NaH,P04-NaOH buffer (ZO), pH 7.4, and water added to give a total volume of 10 ml. The replicates were separately treated as follows. I. The mixture was cooled to 5 "C; 5 ml of 0.1M KCN was added and mixed rapidly, thereby, giving 0.033M cyanide and raising the pH to pH 9.65. The mixture was maintained at 5 "C for 20 min. 11. A replicate mixture was cooled to 5 "C and 5 ml of 0.1M KCN added. After maintaining at 5 "C for 10 min 1.5 ml of 0.1M CuS04 was added with rapid mixing, thereby lowering the pH to pH 7.35 and giving a concentration of 0.0091M C U ~ + .The mixture was maintained at 5 "C for 10-15 min. 111. A third replicate was mixed with 5 ml of 0.1M KCN and heated in a boiling water bath for 45 min, then cooled to 5 "C and 1.5 ml of 0.1M CuSOi rapidly mixed. The mixture was maintained at 5 "C for 10-15 min. Finally, 3 ml of 1.5M ferric nitrate in 4N HCIOl was added to each replicate with continuous agitation; the flask contents were warmed to room temperature with constant shaking to redissolve any precipitate, then made up to 25 ml with distilled water. The ferric thiocyanate color which developed was read at once at 460 mp in IO-mm round cuvettes in a Coleman Junior spectrophotometer. Samples and thiocyanate standards were read against a sulfur-free reagent blank prepared as in treatment I. Thiocyanate standards were prepared in the same mixture and gave optical density readings deviating only
