Gas Chromatography: of Air Peaks
An Experimental Study
RICHARD KIESELBACH Engineering Research laboratory, Engineering Department, E. 1. du Pont de Nemours & Co., Wilmingfon, Del. ,A series of air-peak plate-height measurements was made with Chromosorb and Microbead columns, extreme care being taken to eliminate errors introduced by factors external to the column packing. The data indicate the absence of a significant velocity-independent parameter in the plate-height equation and the presence of a masstransfer lag independent of partition coefficient.
is replete with conT f l i c t i n g evidence regarding the existence and magnitude of a velocityindependent mechanism contributing to the plate height of a gas chromatographic column. The subject was considered in detail by Giddings and Robison @),who concluded that the classical eddy diffusion concept was at least inadequate to explain available data. -1 brief study by the author (4) indicated that any observed velocity-independent parameter was an artifact arising from factors external to the column packing proper. The purpose of the present work is to confirm this observation by a more extended series of measurement on columns of different packing materials. It has been observed (3, 4) that any velocity-independent contribution to plate height will have its most severe effect upon the apparent plate height measured with a sample component not absorbed by the column packing-e.g., air in partition columns. This observation follows from the elementary van Deemter equation (1) H =A B/u Cu (1) HE LITERATURE
+
+
where only the C term contains factors related to the partition coefficient. The equation suggests that the plate height measured with air peaks should be lower than that obtained with partitioning solutes, because fewer mechanisms exist to broaden the peaks. The opposite is usually observed with ordinary equipment. The equation also indicates that air-peak plate height should approach constant value with increasing velocity. In practice, the air-peak plate height goes through a minimum with increasing velocity. The air-peak plate height can, indeed, be substantially lower than that of partitioning solutes ( 5 ) . Norem (9, in 1342
ANALYTICAL CHEMISTRY
column. Another Screen was installed at the column outlet, which vas reduced to 2 mm. to match the 2-mm. bore straight-through detector. The detector comprised a Fenwal G-112 thermistor mounted in the center of a straight 2-mm. bore in an aluminum block, and an additional thermistor in a cai.itJ- in the block for temperature compcniation, a> in conventional practice. The column was a 6-mm. bore, heavyn d l . straight glass tube, 1 meter long. The volume between inlet and outlet screens was tightly packed in every case by application of 150 lb. per sq. inch air pressure and vigorous tapping. The detector output was fed to a Sanborn recorder having an integral timing marker, a chart speed up to 100 mm. per second, and a frequency response flat to 50 c.p.s. nithin 3 db. A marker stylus was actuated simultaneously 11-ith electrical actuation of the sampling valve. The magnitude&of the residual mixing volumes and time constants of the system were determined as follows. The column n as replaced with a short capillary tube containing a wire, the wire size being adjusted to produce a pneumatic resistance equal to that of a packed column. A flow distributor was placed a t the detector inlet. A series of air peaks was measured a t outlet flow rates up to 10 cc. per second. Referring to Figure 1, tangents t o the peak inflection points were drann, their intersection being taken as true peak maximum. The apparent time constant, t, was measured from that intersection to a point on the tail of the peak a t 1,'e (0.37) times the height
a study of air peaks, assumed, but did not conclusively prove that the A term of Equation 1 was insignificant. Knox and McLaren (6) have shown that it is well under a particle diameter. The present work indicates that the A term is either nonexistent or of negligible magnitude a t normal carrier-gas velocities, and that a mass-transfer resistance exists even in the case of zero partition coefficient. EXPERIMENTAL TECHNIQUE
The extremes of care required to obtain meaningful plate-height data are not generally recognized. An insight into the magnitude of the problem can be gained by considering that a mixing volume-Le., a volume in which mixing can occur-of less than 0.1 cc. can produce a measurable skewing of an air peak and that a detector time constant of less than 0.1 second can introduce aimilar distortions in the recorded signal. Errors from these sources ere minimized in the present nork by use of the special equipment described below, and the residual irreducible errors \yere corrected mathematically. The gas-sampling valve employed was a specially designed multiport Spool valve with O-ring seals, having a total unpurged volume of about 0.001 cc. Its sample loop, constructed of 0.6-mm. bore capillary tubing, had a volume of 0.05 cc. The valve mas connected t o the column with a short, 0.6-mm., bore tube. A fine-mesh screen served as a flow distributor a t the junction to the
/ T 4 Figure 1. Measured air-peak parameters
Operational Detector Signal
u 0
0 Signal to 0 Recorder
i
Im v,-y
, 0
2
4
6 f.
8
1
0
, cc./sec.
Figure 2. Graphical measurement of residual mixing volLme
of the intersection. This quantity 5 5 3 s recorded in units of both time and, from the measured carrier-gas floiv rate, volume. A plot of the data in units of volume against flow rate, Figure 2, produces a curve having a straight portion, which can be extrapolated to the total effective mising volume at zero flow rate. (The upward bend of the curve a t lon flow rates reflects longitudinal diffusion, which can be neglected for the purpose of this measurement.) The volume so measured indicates that the sample loop of the sampling valve is the only significant volume in the system, 0.05 cc. A plot of t in seconds against reciprocal f l o ~rate, Figure 3, produces a straight line which (an be extrapolated to the value of the detector time constant, I, a t infinite flow rate (l(fo = 0). The observed time constant of 0.07 second \\as compensated electrically by the adjustable ferdback amplifier shown in Figure 4. The effect of this amplifier is to pro\ ide increased gain a t the higher frequenvies a t which the thermistor response ic,falling. To ensure proper compensatio1 , the feedback adjustment was made to produce 3 symmetrical air peak at a carrier-gas flow rate well in excess of any to he wed during column tests. -4fter introduction of the compensating amplifier, the above series of airpeak measurements !\ as repeated. The residual time constartt was 0.01 second, representing uncompensated secondorder time constants in the system. Column5 was tested a t room temperature (ca. 25" C.) using helium carrier gas. Inlet pressure iras measured with Heise pressure gauges. Outlet volumetric flow rate was measured with 3 soap-bubble flow me1 er. Each column was first calibrated as a flow meter to evaluate the constant term Ka in the relation (3)
CORRECTIONS AND COMPUTATIONS
The small residual errors arising from the sample volume, and longitudinal diffusion in connecting tubes, uncompensated time constants were corrected in the following manner. The elution times, Va, of air peaks with no column were recorded as a function of outlet flow rate, fo, and fitted to the following empirical equation:
tta
=
0.201 ~
S O
I /f,,
sec / c c
Figure 3. Graphical measurement of defector time constant
Table 1.
at'
Chromosorb, Siliclad +27n Dow-Corning 200 Chromosorb, Siliclad + 5 % Dow-Corning 200 Chromosorb, Siliclad + 10yo Dow-Corning 200 Microbeads, dry
+ 0.008
(4)
0.0179
= -2-
+ 0.009
(5)
where f, is the pressure-corrected flow rate a t the sampling-valve inlet. The data fit Equations 3, 4, and 5 with a standard error of 0.012, 0.008, and 0.006 second, respectively. These equations are purely empirical. No iatisfactory explanation for the quadratic relation of Equation 5 has been found. Since the column inlet pressure could be measured with a higher degree of precision ( + 1%) than could the outlet flow rate, j o ,the value of j o for each column data point was computed from the measured pressure and Equation 2.
Derived Equation Coefficients
K (sq.
Column packing (100-120 mesh) Chromosorb, dry Chromosorb, dry Chromosorb, Siliclada-
pf
The asymmetrical portion of the peak width, at', was taken as the difference between leading and trailing widths, and the data fitted to the equation si
Referring to Figure 1,the symmetrical portion of the peak width, Pw,was taken as twice the distance from the leading
O"
tangent to peak center. These data were fitted to the equation
(3)
treated
This and all subsequent computations were performed wil,h an automatic digital computer, by least squares. A series of air-peak measurements was then made, recording inlet pressure, elution time to the intersection of the tangents to the inflection points of a peak, and peak width a t the baseline intercepts of those ta.igents.
IT
b Figure 4. Time constant-corn penso ting amplifier
c,
cm. /
(3 x
Correla-
Std.
104 1.58 0.95
tion coeff. -0.19 -0.23
error, cm . 0.003 0.003
0.60
1.51
-0.16
0.006
0.125
0.62
1.24
-0.17
0 005
1070
0.116
0.57
1.07
-0.13
0.003
1027 1197
0.108 0.053
0.57 0.61
1.24 0.47
-0.16 -0.15
0.006 0.002
atm. 1044 1041
a (sq. cm.) 0.126 0.130
0.63 0.62
1001
0.119
988
sec.)
Y
Clay-Adams Inc.
VOL. 35, NO. 10, SEPTEMBER 1963
1343
These values were then used to compute the appropriate values of Val t',,,, and at' for correction purposrs, by use of Equations 3, 4, and 5. The true value of air elution time, t,, was taken as tdoorr.)
=
lo
- t'n
(6)
The corrected values of t. were then used to compute the value of K in the relation (3)
Table II.
Coluriiii packing (100-120 mesh)
Chromosorb, dry
Chromosorb, dry
A ~ atm. ,
0
ANALYTICAL CHEMISTRY
(7)
K 2L- P(P
+ 2)
It was empirically observed that, while symmetrical peak width adds geometrically, the asymmetrical portion of peak width adds arithmetically. Thus, corrected peak width was taken as indicated in Equation 9, below, using the corrections computed from Equations 4 and 5 .
(8)
uu,L ' I I I . / B ~ ~ .
8,om.
5.0 12.6 21.2 32.3 42.6 70.3 97.8 130.7
0.178 0.077 0.048 0.031 0.034 0.030 0.033 0.033
11.8 16 4 19.2 26.4 32.5 36.1
6.4 13.0 19.7 32 3 41.7 71.2 102.6 123.9
0.137 0.069 0.051 0.035 0.030 0.023 0,023 0.021
18.3 2.5 430.5 35.6 40.7
39.5 68.4 94.4 124.6 159.6
0 036 0.033 0.032 0.034 0.032
4.4 8.3 11.9 15.6 18.4 24.7
0.163 0.073 0.048 0.038 0.032 0.028 0.028 0.029 0.031 0.166 0.115 0.070 0.044 0.032 0.024 0.026 0.029 0.026 0.129 0.073 0.048 0.036 0.032 0.030 0.031 0.032 0.032 0.034 0.125 0.072 0.039 0.027 0.023 0.018 0.016 0.01i 0.016 0.01s
,ti,cin./Bec.
4.1 X- .- . 6
1.25 1.68 2.03 2.80 3.44 4.10
12.4 16.4 19.5 26.3 31.7 37.2
0.50 0.87 1.19
5.1
3.46 4.09 4.74
1344
uo =
x.5
n
1 98
Microbeads, dry
+
P,"4PL-L43
p z + 3p
and t, for each data point then was computed from Equation 7 and the measured inlet pressure. Carrier-gas outlet velocity was also computed from the relation (3)
0.40
2 R:i
Chromosorb, Siliclad + l o % Dow-Corning 200
3g 4L
Corrected Experimental Data
2.00 2.83 3.55 3.98
Chromosorb, Siliclad +5% Ihw-Corning 200
=
The corrected data were then used to c_ompute pressure-average plate height, I I , and the results fitted to the equation
1 69
Chromosorb, Siliclad +2y0 Dow-Corning 200
a
8.8 ~
~~
~
0.53 0.80 1.29 1.79 2.72 3.44 4.09 4.81
5.5 8.4 13.1 17.8 26.2 32.4 38.0 44.1
5.4 12.3 20.5 30.7 40.2 65.5 92.6 124.8 165 4 4.9 7.1 12.1 22.8 36.2 68.8 99.9 133.3 175.3
0.48 0.82 1.25 1.69 1.99 2.76 3.45 4.12 4.78 5.53 0.46 0.77 1.26 1.78 2.00 2.80 3.47 4.16 4.59 5.50
4.9 8.1 12.3 16.2 18.9 25.4 31.2 36.7 42.1 48.1 5.5 9.0 14.3 19.9 22.1 30.1 36 6 43.3 50.1 55 8
6.1 11.8 20.9 32.1 40.9 67.3 96.5 129.3 166.2 213.9 6.8 12.7 24.5 40.4 47.9 80.3 113.6 153.6 201.3 246. i
0.45 0.87 1.27 1 69 2.02 2.78 .? - . 44 -4.12 4.87
n- . 28 _.
xn n35.4 41.2 4-. 1-
in which diffusivity of air int,o helium, D,, was taken as 0.71 sq. cm./second (3). A very high correlation coefficient (0.8 to 0.9) was obtained between the A and the y and C terms, and the values of those terms for duplicate experiments showed relatively large random variations. On the assumption that the observed A term represented a mathematical residual of no real significance, the data were recomputed, using only the last two terms of Equation 10. -4s shown in Table I, a good fit to the data was obtained. The magnitude of the standard error was of the same order as the values of A previously computed, while the random variations previously observed were reduced. Consequently, it is clear that the data do not justify an A term. RESULTS AND DISCUSSION
The complete, corrected data are presented in Table 11, for the benefit of those who may Wish to apply another mathematical treatment. The present discussion will deal only with the constants derived as described above, presented in Table I. In general, the data speak for themselves. The low values of correlation coefficient between computed equation constants and the low standard error show an excellent fit of the data to Equation 10, less the -4 term. The value of K , a measure of the tightness of the packing, shows a reasonable 8% spread for the Chromosorb (JohnsManville Corp.) packings. The value of a, a measure of the cross-sectional packing porosity (including particle pores) shows a comparable spread for the dry Chromosorb packings, with an espected decrease with liquid loading. The difference in these constants between Chromosorb and 1Iicrobeads (Microbeads, Inc.) is as expected, considering the superior packing characteristics of the nearly spherical glass beads. The reproducibility of the value of y (0.60 i 0.03) is remarkable, especially as between the Chromosorb and Micro-
bead packings. It seems to leave little doubt as to thc validity of this measurement. The value of C, the mass transfer coefficient, is not nearly so reproducible, as is to be expected from the difficulties of measurement at the higher velocities. h-evertheless, the data lend strong support to tile existence of a mass-transfer resistance from velocity distribution. The lorn value
of C for the nonporous Microbead particles provides additional weight to this argument. LITERATURE C I T E D
(1) Deemter, J. J. van, Zuiderweg, F. J., Klinkenberg, A., Chem. Eny. Sci. 5, 271 (1956). ( 2 ) Giddings, J. C., Robinson, R. A,, ANAL.CHEM.34, 885 (1962).
(3) Kieselbach, R., Ibid., 33, 23 (1961). (4)Ibi& P. go& ( 5 ) Kieselbach, R., “Gaa Chromatography,” N. Brenner, J. E. Callen, M. D. Weiss, eds., p. 139, Academic Press,
New Yorlr, 1962. (6) Knox, J. H., McLaren, L., ANAL. CHEM.35, 449 (19G3). (7) D.~ j 4 9 4o (lYG2).
‘.
RECEIVEDfor review May 21, 1963. Accepted July 12, 1963.
lonizatiorr Cross-Section Detector as a Reference Standard in Quantitative Analysis by Gas Chromatography P. G. SIMMONDS
and J. E. LOVELOCK
Lipid Research Center, Baylor University College o f Medicine, Houston, Texas
b The small volume ionization cross-section detector, although less sensitive than other ionization detectors, is absolute and therefore valuable in establishing new quantitative analysis by gas chromatography. This paper reports a preliminary exercise with this detector in the general problem of steroid analysis by gas chromatography. The results confirm the utility of empirical practices for column preparation.
T
of analysis by gas chromatography is sometimes hazarded by the loss of a substance between its injection onto the column and its arrival at the detector. This may be due to thermal decomposition, or to either temporary or permanent adsorption upon the surfaces of the apparatus. This problem is most f-equently encountered with relatively involatile polar substances for these require the use of high temperatures arLd lightly coated columns for their seprtration in reasonable times and the us(?of small sample loads. The development o ’ an accurate gas chromatographic mett od requires some means of comparing the quantity injected with that emerging from the chromatograph column. It is possible, although laborious, to do this by the direct collection and measurement of an eluted component by a static method such as weighing or r:tdioactive counting. Alternatively. given an absolute detector, the quantity of any eluted component can be directly calculated knowing only the relevant molecular properties and the physical conditions of the measurement. The ionization cross-section detector is absolute in this sense and in its reccbntly developed, HE ACCURACY
small-volume form is well suited to the needs of gas chromatography (6). A remarkable development in gas chromatography techniques is the analysis of steroids made possible by the methods of Homing and his colleagues ( 2 ) . The possibility of thermal decomposition or loss by other causes with these complex substances and a t the high temperatures of the analysis has been recognized (3). With the steroids, the small sample loads which must be used and the severe conditions of the chromatographic separation make evaluation of the accuracy a formidable problem. This paper reports experiments using a small-volume ionization cross-section detector to measure precisely the recovery of steroids after their passage through a gas chromatography apparatus. Its purpose is to draw attention to the value of this detector in such applications rather than to provide conclusive technical details on the methods of analysis of steroids by gas chromatography. Nevertheless, it con-
Figure 1. Small volume cross-section detector
ionization
firms that with the proper techniques the errors due to the loss of components are for must of the steroids acceptablv small. EXP€RIMENTAL
Apparatus. A modified Chromalab instrument (Glowall Corp., Glenside, Pa.) was used as the basic gas chromatographic unit. The detector oven was redesigned t o accommodate the cross-section detector and the signal from the detector was amplified by a Cary Model 31 vibrating reed electrometer. Output from this electrometer was connected directly to a POtentiometric recorder. The detector design and details of its construction are illustrated in Figure 1. The source is of thin stainless steel coated with a thin film of titanium or zirconium containing occluded tritium and may serve both as the radioactive source and as the chamber electrodes. The quantity of tritium was between 100 and 200 me. Two 6-ft., 3.4-mm. i.d. glass coiled columns were used. Column 1 was packed with 1% SE-30 gum rubber on Gas-Chrom P, 100 to 120 mesh (dpplied Science Corp.); Column 2 was packed with 1% fluoroalkyl silicone polymer (QF-1) on 60- to 80-mesh Gas-Chrom P. The columns and column materials mere prepared and packed according to a well established technique (4, 7 ) . The carefully prepared columns were conditioned a t 240’ C. for 48 hours in an atmosphere of argon. No further precautions were taken initially with the SE-30 column ( S o . 1) and it was used experimentally to observe minor relative losses of steroids under variable column conditions. Subsequently, this column R as treated with hexamethyldisilazane, this treatment being generally recognized as reducing the active sites. The QI71 column wasalso deactivated with hexamethyldisilazane. Uniform sample inV O L . 35,
NO. 10,
SEPTEMBER 1963
* 1345
