Table 111.
Cysteic Acid Analyses of Commercial Wool Samples
Average values of at least three determinations Mg. Cysteic acid per Gram Wool ~ Dry _ ___ _ HighDirect Wool Samples photomvoltage Description etry Elution method 2 2 2 2 2 5 Kool top, unbleached 18 5 0 6 3 Wool top, peroxide bleached Australian wool, solvent 1 7 1 3 1 3 extracted only 17.0 15 8 15 5 Texas mohair, treatment unknown Plain weave fabric ( 3 2 / 2 ) , 11 .o 90 10 0 shrink-proofed by chlorination
SO.
1 2 3 4
3
amounts of 0, 2, 4, and 6 mg. of cysteic acid (Table 11). The observation by Schram et al. (4)that practically no cystcic acid is lost under the conditions of acid hydrolysis of proteins is confirmed. Table I11 shows the results obtained with five actual protein hydrolysates as compared with those obtained by Klaus Ziegler of the German Wool Research Institute, who analyzed samples of the same wool specimens, using the highvoltage technique (6). The results obtained by the two procedures described in this paper compare favorably with those obtained by the highvoltage method. As expected, the cysteic acid contents of the oxidized specimens 2 and 5 are much higher than those of untreated samples 1 and 3. CONCLUSIONS
The present investigation shows that cysteic acid can be completely separated from the other amino acids of a protein hydrolyzate by low-voltage paper elec-
trophoresis. Quantitatiyc determination is possible either b!. direct photometry or by colorimetry after elution. Applied to industrial wool svmples the method has shown that blenching or shrink-proofing treatments can increase the cysteic acid content of ivool fivefold and more. When a protein hydrolyzate is ready for analysis, a skilled technician can carry out the cysteic acid determination by the method here described within 5.5 hours following the elution procedure or 4.5 hours using direct scanning. T o increase accuracy, two or three strips should be used for each hydrolyzate. As two of the eight strips are required for construction of the standard curve, two or three different hydrolysates can be analyzed simultaneously within this period of time. This is hardly possible with paper chromatography or ion exchange methods. For research purposes the more accurate elution procedure is preferable to the faster method of direct scanning, while for certain industrial routine determinations of
cysteic acid the latter method would appear satisfactory. Low-voltage paper electrophoresis promises to become a particularly valuable tool in the control laboratories of the ~voolindustry. ACKNOWLEDGMENT
The author is much indebted to Helmut Zahn. Director of the German n 7 ~ 0Research 1 Institute a t Aachen, for making available the results of cysteic acid analyses carried out in his institute, and for supplying samples of the same wool specimens analyzed by his group. The Xnalytrol readings have been obtained through the kind cooperation of James E. Dusenberry of the Universitv of Arkansas School of Pharmacy. The technical assistance of Margaret Ashcraft is gratefully acknowledged. LITERATURE CITED
(1) Block, R. J., Durrum, E. L., Zweig, G., ‘‘Manual of Paper Chromatography and Paper Electrophoresis,” 2nd ed., p. 525, Academic Press, New York, 1958. (2) Giri, K. V., Radhakrishnan, A. X., Vaidyanathan, C. S., Nature 170, 1025 (1952). (3) Ryle, A. P., Sanger, F., Smith, L. F., Kitai, R., Biochem. J. 60, 541 (1955). (4) Schram, E., Moore, S., Bigxood, E. J., Ibid., 57, 33 (1954). (5) Wieland, T., Kawerau, E., Nature 168, 77 (1951). (6) Zuber, H., Ziegler, K., Zahn, H., 2. Naturforsch. 12b, 531 (1957). (7) Ibid.,p. 734. RECEIVEDfor review December 1, 1958. Accepted February 20, 1959. Work s u p ported by Grant A-721(ClO) from the National Institutes of Health. Public Health Service.
Gas and Liquid Elution Chromatography Quantitative Detector Evaluation H. W. JOHNSON,
Jr., and
F. H. STROSS
Shell Development Co., Emeryville, Calif.
b Quantitative methods for adequately evaluating detectors have not been available. This paper discusses desirable detector properties and proposes a specific evaluation procedure. A quantitative treatment of noise is developed, making possible a precise statistical definition for the limit of detection.
G
chromatography (GLC) is widely used to analyze a variety of mixtures. Yevertheless, AS-LIQUID
1206
ANALYTICAL CHEMISTRY
its applicability could be extended by improving apparatus performance. Many attempts to improve the detector, the device which analyzes the gas stream emerging from a column, and several detector designs have been reported. Cnfortunately, there is no standard method of describing detectors quantitatively, and it is difficult to compare performance. The same problem will arise in liquid chromatography as suitable detectors are developed. This paper deals mainly with the
estimation of the smallest amount of sample that can ‘be determined reliably by a detector. In the past, detector sensitivity has often been used as a measure of this quantity. This is unwarranted because a detector with high sensitivity cannot necessarily detect very small samples. Sensitivity was defined for gas chromatography as
by Dimbat, Porter, and Stross ( I ) , who recognized its limitations by stating that the background noise should also be specified when describing detector performance. Unfortunately, sensitivity alone is frequently the only datum offered. The definition of sensitivity in some fields does measure the ability of a device to respond to a small input. For example, broadcast receiver sensitivity is usually defined as the minimum input required to give an output which is 20 db. (or some other factor) greater than noise output. Analogously, detector sensitivitj- could be defined as the minimum amount of sample which could produce a signal (peak area) tivice (or some other factor) as great as the noise. But there are four reasons why such a definition cannot be used directly. 1. Detector sensitivity is commonly defined by Equation 1, so another designation is necessary. 2. The subjective step of constructing a peak base under a peak to measure a peak area has no analogy in receiver output measurement. 3. Both noise and signal outputs have frequencies much higher than the time constant of the wattmeter used to measure receiver output. In chromatography, the frequency (by analogy, the reciprocal of the peak width) of the output is much lower than the time constant of the detector system. Thus, the wattmeter docs not distinguish between differences in noise frequency and desired output frequency in comparing thcir output, but a detector does. 4. For the reasons given in 3, the wattmeter is averaging a great many pcriods of output in its instantaneous reading n hile the detector system takes considerable time arid requires an integrator to measure one period (peak). This paper describes a procedure which accounts for these differences as follows: The new quantity is called limit of detection t o distinguish it from sensitivity; the definition of noise represents the construction of a peak base niathematically and, therefore, objectively; noise is measured a t various frequencies; and a number of noise periods are averaged and treated statistically. The procedure also includes the measurement of other detector parameters needed to provide an over-all picture of detector performance. DESIRABLE DETECTOR FEATURES
Several theoretically important features are desirable in a detector: Lowest possible effective detector volume. Detectors with large effective volumes distort sample peaks ( 2 ) . Constant sensitivity with varying sample concentration. Otherwise, neithrr peak area nor peak height will be proportional to amount of sample.
obtained a t zero flow rate. This is consistent with the purpose of a detector. Some flow must occur for a detector to monitor a column effluent. Integrator Zero. This is the line generated by the recorder pen at the position where the integrator gives a constant reading. I t is assumed for convenience that this line is below the lowest point of the detector trace. Interval Area. If two perpendiculars to the volume axis of a detector trace are designated i and i 1, the distance between them corresponding to A' in milliliters, the interval area of the interval i to i 1is designated A , and is the area enclosed by the perpendiculars, detector trace, and integrator zero (Figure 1). Any other reference line parallel to the volume axis of the chromatogram may be substituted for the integrator zero if it is always below the detector trace and is used for the entire evaluation. The arithmetic sign of the interval area is always positive, and the units are milliliters-millivolts. Soise Area. If four equally spaced perpendiculars to the volume axis of a detector trace are successively designated i - 1, i , i 1, and i 2 with the distance between adjacent perpendiculars equal to A p , the noise area of the interval from i to i 1 is designated A', and is equal to the interval area of the interval i to i 1 minus one half the sum of the interval areas for the intervals i - 1 to i and i 1 to i 2 (Figure 2). The sign of the noise area must be observed when performing arithmetic operations. Limit of Detection. Let n noise areas be determined from 3n interval areas of constant interval A p such that each interval area is used in only one calculation. If N, is the standard deviation of the noise areas, then the limit of detection is
be 'd'
VOLUME A X I S
Figure 1 .
Definition of interval area
V; = A ,
DETECTOR I-' TRACE
-
-
'/'A,,] lil
i-2
+
+
'JOLUME AXIS
,,
Figure 2.
Definition of noise area
Constant response with either same weight or same number of moles of different substances. Otherwise, calibration with many substances is necessary. Unvarving sensitivitv a t different effluent flo~i.'rates is dlsirable but not essential. The ability to detect very small samples with good precision. This is probably the most important property. K'ew detectors are usually developed to improve this characteristic. The effective detector volume is evaluated by comparing the theoretical and actual width of peaks obtained from samples of small volume. The next three items simply require sensitivity measurements under various experimental conditions. The last property, the limit of detection, is determined by measuring the noise as intervals of area, averaging the intervals statistically, and converting the averaged area to a m i g h t of substance by dividing it by detector sensitivity a t the limiting concentration. The latter is estimated from effective detector volume and limit of detection. The limit of detection is thus determined from an implicit relation and requires a method of successive approximations unless sensitivity is linear ITith concentration. METHOD OF EVALUATION
Definitions. Detector Trace. This is the graphical record of detector output obtained by plotting detector outp u t against the volume of carrier gas t h a t has passed through the detector when either pure carrier gas or carrier gas containing a constant concentration of sample is flowing through the detector. The abscissa of the record produced by an automatic recorder is in time units and must be multiplied by the flow rate to obtain the volume units required for the detector trace. I t follons that a detector trace cannot
+
+
+
+
+
+
Peak Base. A straight line connecting the extremities of a sample peak from points corresponding to the passage of pure mobile phase through the detector. Peak Area. The area enclosed between a peak base and the chromatographic peak recorded as an isolated sample component passes through a detector. Recorder Sensitivity. The apparatus is assumed to include an attenuator of the voltage divider type ( I ) , considered a part of the recorder. At lonest attenuation the recorder sensitivity, C1, is defined as the nominal sensitivity of the recorder. For example, C1 for a I-mv. recorder with 20-cm. chart width would be 0.05 mv. per cm., and Ay for a signal which displaced the pen by half the chart n-idth would be 0.5 mv. VOL. 31, NO. 7, JULY 1959
1207
ACTUAL CHART. ZERO ADJUST
ZERO ADJUST
NOISE
SAMPLE PEAK
COMPONENT
WITHOUT NOISE
A
AC INT.
EQUIVALENT CHART.
n.
@8
ACI INT.
I N T E R V A L AREA AS D E F I N E D B
CORRECTION
1
ENTIRE D E F I h E D INTEGRATOR Z E R O MUST COIhCIDE LVITH L O U E S T S E C T I O N O F A C T U A L I N T E G R A T O R Z E R O
Figure 3.
Correcting interval area for zero adjustment Figure 4.
Any change in attenuation is counted against recorder sensitivity and output. The recorder above with attenuation set a t 10 times lowest level would have 81 = 0.5 mv. per cm., and Ay = 5 mv. for a half-chart signal. Any amplifiers or additional attenuators should be adjusted according to Section 6 of procedure and left that way. Some attenuators are calibrated in terms of amplification, which is the reciprocal of attenuation. If the apparatus lacks an attenuator, then whatever method of gain control is used must be calibrated and counted against recorder sensitivity as above. Fixed Variables. The following apparatus components and experimental conditions must remain unchanged throughout the evaluation and be specified in the evaluation report. APPARATUS.Pressure and flow controllers; detector temperature controller; power supply for detector; amplifiers; recorder model, sensitivity, and pen speed. CONDITIONS.Choice of carrier gas; detector temperature and pressure; temperature, voltage, frequency, and amperage of detecting element, as applicable. Apparatus Modifications. The minimum length of small-bore hypodermic tubing should be substituted for the usual chromatographic column throughout the evaluation. The apparatus must be supplied with a device for injecting, in essentially plug flow, small volumes of gas for gas chromatography or liquid for liquid chromatography. The gas or liquid is chosen to provide a different detector response than the pure mobile phase being used. The zero adjustment for recorder pen position must be calibrated in terms of millivolts of pen travel. Additional Apparatus. For gas 208
ANALYTICAL CHEMISTRY
chromatography, small cylinders of carrier gas containing various concentrations of each sample component of interest must be prepared. This can be accomplished by breaking a weighed vial in a device such as the crusher of Porter, Deal, and Stross (S), flushing the vaporized sample into an evacuated cylinder, and pressuring to the desired level with carrier gas. It is also feasible to add metal balls to a cylinder with the sealed sample vial, fill the cylinder with pure carrier gas, and shake until the vial is crushed. In either case, one side of the vertically situated cylinder should be warmed for 24 hours to mix the contents by convection. For liquid chromatography it is only necessary to prepare solutions of the desired concentration of sample component in mobile phase. Preferably, the recorder should be equipped with an integrator. Otherwise a planimeter must be available. A direct-current amplifier with variable gain may be required to obtain sufficient amplification of the detector trace. PROCEDURE
1. Set attenuation sufficiently high so the detector trace is essentially a straight line. Add a very small sample in plug flow. Draw a line tangent to the descending side of the resulting peak a t the peak maximum. Construct the line through the peak maximum perpendicular to the volume axis. Measure the width of peak base intercepted between the perpendicular and tangent. Repeat six times, and report the average width, in milliliters, as the effective detector volume. Repeat the procedure a t several different flow rates, and record effective detector volume as a function of flow rate. The expected shape for such peaks and the interpretation of changes in effective detector volume as
OBSERVED PEAK
A AA
Influence of noise on peak area
a function of flow rate have been discussed ( 2 ) . Describe the peak shape if it is unusual. 2. Pass pure mobiIe phase through the system and observe the mean position of the pen. Then switch to mobile phase containing a constant concentration of a sample component of interest, maintaining the same flow rate. Adjust the attenuation to give a displacement of approximately one fourth the chart nidth. At lowest sample concentrations the detector trace will contain considerable noise, and the average displacement for several changes between carrier gas and sample stream will be needed t o obtain a valid sensitivity value. Calculate sensitivity by
s=Y C
(3)
Yormally only a few concentrations need be examined, because S will be nearly independent of concentration in the useful range of the detector. 3. Repeat 2 for each compound of interest for several concentrations up t o the maximum which can be tolerated by the detecting element or attenuated by the attenuator. The concentration CL must eventually be included, but this value is not determined until later. Determine the value of S a t CL and add to the curve when CLis known (paragraph 9). Plot sensitivity us. concentration curves for all the compounds on one graph. 4. Repeat 3 for one compound from 3, preferably the compound with highest sensitivity, a t different flow rates. Plot the set of sensitivity us. concentration curves, each curve applying t o a single flow rate, on a second graph. 5 . Select a compound from the graph prepared in 3. Use the value of S for the lou-est concentration available on the curve as a trial value of SL. 6. Pass pure mobile phase through the detector a t the selected flow rate. Adjust the amplification so that the detector trace wanders over approximately one third the width of the chart
= PEAK
t
NOISE
final recalculated value of Wa from 10 for pure mobile phase with that from 11 for sample mixture. Choose the higher Ws a t each Ap and plot us. Ap as the final Ws values. 13. Repeat the procedure of 5 through 12 for other flow rates or compounds of interest. Plot the Wa us, A. curves on the graph prepared in 12. 14. Repeat the procedure of 5 through 12 on different days and different times of day. Plot the resulting W6 us. Ap curves on a new graph and add the curve prepared initially in 12.
' 1 VOLUME AXIS
Figure 5. Peak added to detector trace of Figure 1
within a few minutes. The detector trace thus prepared should be a t least 75 times as long as the estimated maximum peak width of peaks that will be obtained during actual analysis of the compound selected in 5. During this time the trace may tend to drift off the chart. If so, restore it by the calibrated zero adjust. Record the adjustment on the chart in millivolts. Use this number to correct interval areas measured by an integrator or planimeter to obtain interval area as defined (Figure 3). 7 . Divide a portion of the trace into 75 segments equal to one half the peak width of the estimated narrowest peak that will be of interest in analyzing column effluents. For convenience, select this minimum as an aliquot of the estimated maximum from 6. Determine the interval areas and calculate the noise area of each set of three interval areas, not using any interval area in more than one calculation. Calculate the standard deviation, ATs, pf the 25 noise areas and calculate the limit of detection by Wa
=
5.29 N ,
(4)
using the trial value of S L from 5. 8. Repeat 7 with various Ap values, the highest being equal to the estimated maximum peak width. The number of Ap values needed depends on the variation of the limit of detection with AP. A periodic variation of Wa indicates that a periodic component is included in the detector trace, and its frequency may suggest that detector repairs or modifications are necessary. 9. Use the largest tentative value of Ws from the group calculated in 7 and 8, and divide it by the effective detector volume calculated in 1 and applicable a t the flow rate used, 6. Use this quotient as an estimate of CL. If possible, obtain the corresponding S L from the graph prepared in 3. Otherwise, obtain S L according to 2. Use this value of S E to recalculate the tentative Wa in 7 and 8. 10. Repeat the procedure of 9 using the largest of the values of mi8 most recently recalculated until the recalculation makes less than 5% further change in S L . 11. Prepare a mixture of the compound under test in the mobile phase a t concentration C L from 10. Repeat 6 through 10 using this mixture to prepare the detector trace. Use the value of SL estimated in 10 as the first trial value for 7. 12. At each A P value, compare the
DISCUSSION OF DEFINITIONS
Units. This paper assumes t h a t a potentiometer recorder is used, so the units for the vertical axis of the chromatogram will be millivolts. Milliamperes should be substituted for millivolts throughout if a galvanometer recorder is used. Interval Area and Noise Area. This section explains why noise is measured as a n area and how the definition of noise area corresponds closely to the subjective process of measuring a peak area. DETECTOR TRACE
VOLUME AXIS
'&'
1
Figure 6. Correction area peak of Figure 5
for
On a theoretical basis the amount of sample is invariably related to peak area, never to peak height. The latter may be used in elution chromatography to estimate sample amounts only when it bears a constant relationship to peak area, as, for example, a t a definite retention volume with a given column and sample component. Peak amplitude of noise has no definite relationship to sample peak (Figure 4). Although noise amplitude is greater in curve A , Figure 4, it is apparent that these extremely narrow peaks would have negligible effect on the area of the wider sample peak. The low amplitude, but larger area noise of curve B, Figure 4, would have much greater effect. Yoke area has been defined as a function of three interval areas. The interval area of any interval is equal to the interval areas of the smaller intervals into which it can be divided. Thus, noise areas for many interval sizes can be calculated from one set of interval areas. If a chromatographic peak were added to the detector trace of Figure 1 b e h e e n perpendiculars i and i 1, the resulting curve might appear as shown
+
in Figure 5. The peak area would normally be measured by constructing a peak base visually by reference to the detector trace in regions adjacent to the interval containing the peak. The measured peak area would be the algebraic sum of the true sample peak area plus errors caused by misplacement of the peak base because of noise distortion of the detector trace outside the interval i to i 1, and by distortion of the peak by noise. If the peak base of Figure 5 were drawn in on Figure I, then the area (positive or negative) enclosed by i, i 1, the detector trace and peak base (Figure 6) would be the exact correction to subtract from the peak area on Figure 5 to obtain true sample peak area. This situation can never arise in practice because both a peak and detector trace are never available for the same interval. I n addition, the peak base probably would not be drawn exactly the same each time, even for identical curves. Noise area is similar to the correction area of Figure 6, except that the subjective peak base construction is replaced by an arithmetic operation. This can be demonstrated by a second graphical interpretation of noise area. Let a horizontal line be placed between the perpendiculars i - 1 and i of Figure 2 so that the area of the rectangle formed by the horizontal line, integrator zero, and these perpendiculars is equal to the interval area of the interval i-1 to i. Let a horizontal line be similarly located between perpendiculars i 1and i 2. Then the noise area of the interval i to i 1 is equal to the area enclosed by the detector trace,, perpendiculars a t i and i 1, and a line joining the midpoints of the til-o horizontal lines (Figure 7). Segments of this area in which the detector trace forms the lower boundary are negative, and noise area is the algebraic sum of the segments. The line joining the mid-points is quite similar to a peak base and has the advantage of being exactly defined. It can be concluded that noise area for an interval Ap is a reasonable measure of the error which the detector trace would have introduced into the measurement of the area of a peak located in this interval. Many samples of noise area with interval Ap must be measured to provide data for a statistical
+
+
+
+
+
+
DETECTOR T
INTEGRATOR VOLUME AXIS
Figure 7.
Alternative
interpretation
of definition of noise area VOL. 31, NO. 7, JULY 1959
1209
Table 1.
Confidence Intervals for N, as Function of Sample Size (1 = 0.95) (Nu =
Sample Size 4 16 25 51 101
Interval Extending to Zero k Interval 0.352 7.26 13 8 34 8 77 9
0 to 2.39 0 to 1.05 0 to 0.952 0 to 0.856 0 t o 0 805
0.707)
Minimum Interval jh
k’b
Interval
9.35 27.5 39.4 71.4 129.6
0.216 6.26 12 4 32 4 74 2
0.463 to 3 . 0 4 0.539 to 1.33 0 563 to 1.00 0 597 to 0 887 0 624 to 0 825
lar N . value. Kineteen out of 20 times the true N u value for N , = 0.707 will be within either set of limits given in Table 1. The right column gives a narrower range and is more informative. ilt sample size 25, the ratio of the upper and lower interval limits is 1.7. Thus, for this sample size, two detectors which give the same calculated N . value may actually differ in their noise levels by nearly a factor of two. Equation 10 gives a confidence interval for W,, the standard deviation of the entire population Wi. Because N iand, therefore, W , are assumed to be normally distributed, P( -1.96 Wu 5 W , 5 1.96 Wu)=O.95 (11)
correction applicable to any interval A’. LIMIT OF DETECTION
This section develops the statistical relationship betreen noise area and limit of detection. Individual noise areas are assumed to be independent samples from x normally distributed population. The assumption of normality is considered reasonable because each interval area is proportional to the average of the interval areas of many smaller intervals into which it could be divided. The central limit theorem states that the distribution of the average of several samples tends to become nornial as the number of samples being averaged increases, regardless of the distribution of the individual samples. The samples are considered independent because each interval area is used in only one noise a r m calculation. The calculated standard deviation of the group of experimental noise areas is designated N . and can be used to calculate a confidence interval for N u by use of the chi-square distribution
where j’ and k’ are defined implicitly by
The upper liniit of this interval, now given in milliliter-millivolts, can be divided by detector sensitivity to obtain the corresponding weight of a specific compound. But unless the applicable curve prepared in 3 of the procedure is flat, it is necessary to know the applicable concentration corresponding to a n amount of sample equal to the limit of detection. No definite relationship exists between these quantities in elution chromatography. A chromatographic peak ranges in concentration from zero to the peak maximum, and the peak maximum for a constant weight of sample will change with effective detector volume, retention volume, column efficiency, and method of sample injection. Two assumptions must be made to relate Wa to concentration. First, the maximum concentration for m y peak will not be greater than CI,, defined as TT’a divided by the effectilre detector volume. This is true for an\’ detector if perfect mixing occurs ($ and is a reasonable assumption for other detectors because of dilution by diffusion in the sample injector, connecting tulling, and column. It is also assumed that S L calculated at C L is applicable for all lower concentrations. A detector v, hich does not meet this assumption reasonably well is not useful quantitatively. When these assumptions are valid, w u =
T’aluw of j ’ and k’ are available in statistical tables. Ordinarily, values are selected to give the smallest interval possible. However, here it is the largest value of N , which will control 7T’a. The best interval under these conditions a t the 95% probability level is obtained \rhen j‘ = :md k’ = 12, nhere
Equation 5 then reduces to
12 10
ANALYTICAL CHEMISTRY
ST
N U
Combining Equations 8 and 9 P/
[5 0
;”I
1.v yidth. 8. Selection of interval widths to be used.
Sample size has been arbitrarily fixed to avoid reference to chi-square tables in the procedure. The procedure can be adapted to other sample sizes by
changing the values of n and k in Equation 2. The procedure requires some time to complete. Hon-ever, the design and development of a new detector is a time-consuming project, and evaluation time would be rather negligible by comparison. The procedure could also be used to improve existing detectors by measuring the effect of design changes. NOMENCLATURE
-4i
= peak area, sq. em. = interval area of the interval i
c
=
.i
+
to i 1, m1.-mv. concentration of sample in mobile phase, mg./ml. = recorder sensitivity, mv. per cm. of chart (see definitions) = reciprocal chart spwd, mine/ em. = flow rate a t exit of column, ml./min. corrected to column temperature and atmospheric pressure
C1 Cr C3
maximum concentration in detector when a sample of weight Wa passes through a chromatographic column, assumed to be Wa divided by effective detector volume, mg./ml. i = integer such that 0 < 1 < n f l j ' , k , k' = integration limits defined by Equations 6 and 7 L = statistical confidence level = noise area, m1.-mv. = standard deviation of set (Nil,
CL
=
= mean of set ( N i ) ,i = 1 to = true standard deviation
n P
n of
the population (assumed normal) from which set { X i } was obtained = number of N i in set ( N i ) = probability = fiducial probability = detector sensitivity defined by Equation 1, mv./(mg./ ml.)
SL
= value of S a t concentration
1'
= volume of carrier gas passed
W
=
W,
= )\eight of sample coniponent
W6
=
CL
through detector, ml.
n eight of sample component, mg.
corresponding to N , , mg. limit of detection defined by Equation 2, mg. AP = distance between adjacent perpendiculars in ddinitions of interval area and noise area, ml. Ay = change in recorder output, millivolts (see definitions: recorder sensitivity) f ( ~ )= ~ a variate, x2, distributed by chi-square distribntion LITERATURE CITED
( 1 ) Dimbat, Martin, Porter, P. E., Stross, F. H.. H., ANAL.CHEM.28. 28, 290 11956). (1956). (2) Johnson, H. W.,Jr.; Jr., Strok, Strose, F . H.. Ibzd., 31, 357 (1959). (3) Porter, P. E., Deal, C. H., Stross, F. H., J . A m . Chem. SOC.78, 2909 (1956). (1956): RECEIVEDfor review August 26, 1058. Accepted I I a r c h 16, 1059.
Gas Chromatography Effect of Sample Size on Height of Equivalent Theoretical Plate and Retention Volume R. M. BETHEA and M O R T O N SMUTZ Chemical Engineering Department, Iowa State College, Ames, Iowa
b This research was conducted to determine the importance of sample size on the performance of gas chromatography columns a t low flow rates. The minimum value of HETP was found when a 4- to 7-pI. liquid sample was used for an alcohol test mixture in a dibutyl phthalate column. Minimum HETP values for the same mixture in a dibutyl sebacate column occurred a t a sample size of 10 to 12 pi. and also when an ester test mixture was used on the same two columns. Minimum values of retention time with sample size were obtained for all systems tested. Optimum values of sample size exist for some feed systems in certain substrates at low flow rates. This may aid other research workers in obtaining maximum resolution of mixtures.
T
best liquid sainple size for gasliquid partition chromatographic analysis in columns having an internal diameter of 2.5 to 7.6 mm. has been HE
determined by several investigators (10, 12) to be between 0.03 and 0.07 ml. and not over 0.10 ml. One of the most widely used methods of sample injection is with a microsyringe through B self-sealing rubber serum bottle cap. Lichtenfels et al. (9) have developed a micropipet for reproducibly injecting liquid samples in the range of 0.005 to 0.02 ml. Haskin et al. (?) have used the syringe method to reproduce peak heights within the rang" of zk0.5 to zk4.4% for known azeotropic. mixtures. The vaporized sample may reach the column in one of two ways, according to Keulemans (S),which represent two definable extremes: plug flow, defined as occurring when the sample reaches the column undiluted followed by tht, carrier gas at a sharp interface, and rxponential flow, defined as occurring when the sample and the carrier ga. are mixed before reaching the column. He stated two disadvantages to the syringe method. The first is that plug flow is not approached unless the syringe
tip is level 111th the top of the column packing, so that the sample may dissolve immediately in the partitioning agent. Many chromatographic systems use a sample bypass such as that reported by Davis and McCrea (1) for reproducibly injecting samples in approximately plug flow and thus avoiding this objection. The result of exponential flow is a superposition of a number of chromatograms whose time origins vary over the time required for the sample to be injected. Pollard and Hardy ( 3 ) have indicated that the column efficiency as measured by the number of theoretical plates is constant within = t l % for injection times up to 10 seconds. Keulemans' other objection to syringe injection is that the absolute size of the sample is subject to :I systematic error caused by expansion of the liquid in the needle or by creeping of the liquid. This error should be constant for a given sample injection system. Recently. Eggertsen and Groennings ($) have used the syringe injection VOL. 31, N O 7,JULY 1959
1211
