The preponderance of evidence clearly indicates t h a t the exhaust hydrocarbon composition is dependent on the composition of the fuel. ACKNOWLEDGMENT
The authors thank the members of the Fuels and Lubricants Drpartment, Research Laboratories for their valuable criticism and advice. LITERATURE CITED
(1) Chandler, J. M., Cannon, W. A., Keer-
man, J. C., Rudolph, Arthur, J . A i r Pollution Control Assoc. 5 , 65 (1955).
IS.A., Rogers, L. H., Air Pollution Foundation (Los Angeles), Rept. 21 (October 1957). (3) Haagen-Smit, A. J., Fox, M. M., Ind. Ens. Chem. 48, 1484 (1956). (4) Hurn, R. W., Fifth Annual Anachem Conference, Association of Analytical Chemists, Dearborn, Mich., October 1957. (5) Mader, P. P., Chambers, L. A., First Technical Meeting, West Coast Section, Air Pollution Control Association, Los Angeles, Calif., March 1957. (6) Magill, P. L., Hutchison, D. H., Stormes, J. H., Proc. Second National Air Pollution Symposium, Stanford Research Institute: Menlo Park, Calif. (1952). ( 2 ) Faith, W. L., Renzetti,
(7) Martin, A. E., Smart, J., Nature 175, 422 (1955). (8) Richards, L. M., First Technical Meeting, West Coast Section, Air Pollution Control Association, Los Angeles, Calif.. March 1957. (9) Rounds, F. G., Bennett, P. A., Nebel, G. J., S . A . E. Trans. 6 3 , 591 (1955). (10) Tenny, H. & Harris, I., R. J., ANAL. CHEM.29, 317 (1957). (11) Twiss, S. B., Teague, D. M., Bozek, J. W.. Sink, M. V.. J . A i r Pollution Control Assoc. 5 , 71 (1955). RECEIVED for review January 24, 1958. Accepted October 13, 1958. Division of Petroleum Chemistry, 133rd Meeting, ACS, San Francisco, Calif., April 1958.
Gas-Liquid Chromatography Determination of Column Efficiency H. W. JOHNSON, Jr., and F. H. STROSS Shell Development
Co., Emeryville, Calif.
b Gas-liquid chromatography (GLC) can b e used to determine physical constants as well as for quantitative analyses. For the latter, only peak areas need be accurately known, but accurate determination of physical constants, such as partition and activity coefficients, requires that certain corrections b e applied to peak position and width for detector volume. Even in calculating column efficiency such corrections are important. The equations relating detector concentration to volume of carrier gas are derived for a model apparatus, which is shown to represent an actual gas-liquid chromatography apparatus with sufficient accuracy for this purpose. The necessary corrections for the detector volume within wide limits of retention volume, column efficiency, and detector volume can b e calculated by the use of graphs.
G
chromatography (GLC) is widely used to separate the components of chemical mixtures. The apparatus normally includes a detector and automatic recorder, so that the separated components are indicated on a chart as a series of peaks. 811 quantitative information must be obtained from the interpretation of these peaks. Each peak has three quantitatively useful parameters: peak height or area, peak position, and peak width. Peak height is a function of effluent concentration, sample identity, detector design, and other experimental variables (1,10). Peak height is not relatJed to separation. AS-LIQUID
Peak position and peak width both affect separation and their relationship is demonstrated in Figure 1. Gas-liquid chromatography is versatile because the peak position over wide ranges can be controlled by changing the liquid substrate (4-6, 8). However, with a n y given liquid substrate there will be materials with peak positions very close together and in such cases the peak width becomes very important. The actual peak width obtained on the chart determines the efficiency of the apparatus with the given column. However, such efficiency data are not sufficient. Chromatographers will be more interested in the performance of the partition column than in duplicating the entire apparatus. Even if there is interest in comparing apparatus, the actual peak width is of little value. It would be necessary to duplicate the column with the new apparatus under test, and it would still be difficult to decide if differences in peak widths were due to slight differences in the columns, or in the remainder of the apparatus. Gas-liquid chromatography is also used to determine physical constants (8, 9). Present uses are based on the linear relationship between peak position and the partition coefficient. However, peak width may also become important in the field of physical constant determination. The theoretical paper by van Deemter, Zuiderweg, and Klinkenberg (11) relates peak width to diffusivity and other kinetic quantities. Experimental evaluation and application of such a theory require accurate values for
A . U r r e s n l v e d !'ears
Figure 1. Relationship between peak position and peak width
the peak width due to the column alone. It would be desirable, therefore, to report the peak width due to the column independently from the peak width due to the remainder of the apparatus. This paper discusses the separation of peak ri-idth into column and noncolumn effects and the magnitude of errors that may arise when the entire peak width is attributed to the column alone. A comparison of the repeatability of peak n-idths with that of partition coefficients is made and a method for estimating column peak widths is described. PEAK WIDTH
Definition. Under ideal conditions. gas-liquid chromatography peaks a r e very close approximations t o normal distribution curves. These latter approach t h e base line asymptotically. VOL. 31, NO. 3, MARCH 1959
357
___----
" A ,iA \ Sample Volume 1) = 0 . 2 5 2
2 ) = 1.00 3) = 2.00
o
1
2
3
4
z '
Volume of C a r r i e r c a s P l u s Sample
Detector Volume
Figure 2.
I
I60
I80
Volume, V ( m u
^
L
Figure 3. Plot of Equation 1 1 V R = 185 r = 559
Theoretical noncolurnn peaks
The base of the theoretical curve is t h u s infinite, and actual curves approach t h e base line a t much too gradual a rate for a well defined base iyidth. This has been avoided by measuring the peak width a t half, or some other fraction, of the peak height (fa). Peak width has also been defined as the base line intercepted between the inflection tangents of the peak (If), as shown in Figure 1. This latter definition is used because of its simple relationship to other column quantities by
Ac is the peak width due to the column alone. The peak width due to a column and its associated apparatus is designated as At. The peak width due to the apparatus without the column is called the noncolumn peak width. Occasionally it is convenient to divide a peak width into ascending and descending peak widths. The ascending peak width is the base line intercepted between the ascending tangent and the projection of the peak maximum on the base line. The descending peak width is the remaining peak width. The units used for retention volume should be used for peak width. Regardless of the units, r mill then be dimensionless. Theoretical Considerations. Diffusion of sample in t h e gas phase is not confined t o t h e column section alone. Diffusion in other parts of a gas-liquid chromatography apparatus is especially pronounced in regions TI here relatively large holdup volumes exist. I n a ne11 designed apparatus, t h e only appreciable holdup volume occurs in t h e detector cell. T o develop a mathematical expression for the noncolumn diffusion, a n ideal gasliquid chromatography apparatus is used as a model. This consists of a gas-liquid chromatography column with incompressible mobile phase, plus a de-
358
2 2
ANALYTICAL CHEMISTRY
tector with cell volume Z in which perfect mixing occurs and through which all the column effluent passes. All other regions of the apparatus are assumed to have zero dead volume. The effect of operating such an apparatus without the column is also considered. CASE I. COLUMNREPLACEDB Y NOKDIFFUSISG,UNPACKEDTCBE OF ~ E G L I G I B L EYoLuhiE. A sample added to this apparatus enters the detector exactly as it left the sample injector. Applying a material balance to the plug flow case, the rate of change of amount of sample in the detector with respect to the volume must equal the inflow to the detector minus the outflow, or dx X dV'="z
as long as sample is being added to the detector, and dx
5
n = -Z -
(
-
S-cce
But x = 0 when V'
x=Zs
=
);
-
(T- _ -_I'R)2 - _1 _ _ 2 17R2 __
e
qo
4%5
(7)
r
4;
(3)
when pure carrier gas is being added to the detector. The general solution of Equation 2 is ! ;=z
Equation 6 for varying sample volumes. The shape of the noncolumn peaks changes from a relatively longer ascending to a longer descending peak width as the volume of sample is decreased. The peaks in Figure 2 are greatly magnified horizontally, as compared to the chart peaks obtained a t coninion chart speeds, and the peak is approximately symmetrical when the sample volume is equal to the detector volume. CASE 11. IDEAL COLUMN WITH SAhlPLE ADDEDTO FIR-TTHEORETICAL PLATE.For columns containing more than 100 theoretical plates, the normal distribution form of the relationship derived by Martin and Synge ( 7 ) may be used to predict the concpntration profile which leaves the column and therefore enters the detector:
Applying a material balance to the apparatus, there obtains
(4)
(8)
0, so
(
-
1 - e
);
The gcneral solution of this equation is (5)
The general solution of Equation 3 is
x
= c'e
T' Z
(6)
I n Equation 6 however, the relationship between 1' and 2: depends on the volume of sample added. From the structure of Equations 5 and 6, it is convenient to measure volumes in units of detector volumes ( V / Z ) rather than in milliliters. Figure 2 shows the plot of Equation 5 and three different plots of
- 2 1 . R % [ V - V R (1
+ $)I2
- -V2
dT'
By defining
+ c"e
(9 1
and setting V tains
=
0 ivhen IZ:
=
0 there ob-
j
Equation 11 is plotted in Figure 3 for = 185 ml., T = 559. and various val-
T7R
I .05
L
I
,
.IO
ues of 2. The inflection tangents and peak nidths of these curves werp determined from Equation 11 by computation. The increased n-idening of the sample prak due to the volume, 2,is given in Table I for both curves of Figure 3 and somr of the corresponding data n hen r = 279.5 and 1118. Extension of Derived Equations to Actual Systems. PEAK KIDTH CORRECTION COEFFICIEXT.Table I shows that the At protiuccd by the model apparatus of the previous section is affected by the peak n-idth due to the column and a peak width due to the dead volunie of the detector. ;1factor, f,can be used to relate A' to At and Z by the equation 1 c = At - fZ
(12)
where
I ,
,
.I3
I
I
,
.20
I
/
,
1
, I , #
1
.30
,25
Detector Volume O b s e r v e d Peak Uid!h '
Figure 4.
by tlcfinition.
The table was constructed for particular values of V R ,2, and r. Hon ever, T'R and 2 always appear in forms reducible to I ' R / z and V / Z . Therefore the table is useful for all ratios of retention volume VR' and detcctor cell volume Z' such that
Equation I1 is c>quivalentto Equation 13 in reference ( 9 ) by Porter, Deal, and dtross but the niodrls and derivations are entirely different. I n ( 9 ) the equation is derived to estimate the effect of a perfect mixing sample chamber with volume B on retention volume. The sample injector of this report does not require this correction. On the other hand, the experimental chromatographic peaks of (9) were undoubtedly influenced by the detrctor cell volume, and the corrections described in this report would be applicable to their data. The quantity z/Z is the concentration of sample in the detector cell and is the quantity actually measured by differential-type detectors. z/poZ is the fractional concentration in the detector compared to the original sample concentration and is more convenient for plotting.
0
= (A' - A C ) / Z
, I ,
1
I
, j
, 35
40
z 5:
Correction factor for detector volume
Table I.
ITliere 2 = value tabulated in Table I corresponding to effective volume 2' in the actual detector. For example, the line Z = 3, in Table I would be used for a detector cell volume of 3 nil. and V 8 = 185 ml., or for a volume of 6 ml. a t V R= 370 ml. The table cannot be used for values of T not listed in Table I by any such procedure. However, when the correction, f, is plotted against Z/At, approximately the same curve is obtained for the three different values of T used in Table I. The plot is shown in Figure 4, which thus provides the correction factor, so that A' can be calculated from a knowledge of At and Z', the effective detector volume of the actual detector. This is not the same as the actual volume for bypass, diffusion, and convection-type detector cells, because only a fraction of the column effluent enters these types of cells. The effective drtector volume is also altered by any pressure change betn een the column exit and the detector chamber, because the effectiveness of the carrier gas in sn-eeping the detector is proportional to its volume rather than its neight. E~TIRIATION OF 2'. According to 1:quations 5 and 6, the peak n i d t h of the :r-cending portion of a noncolumn peak, o\presstd in appropriate units, should q u a l the plug f l o sample ~ volume, and only the descending portion should deIwnd on Z'. Experimental noncolumn pcxaks thus provide not only the information for estimating A?, hut also give a tlieck on the conformity of the actual apparatus to the ideal apparatus assumcd for t h t derivation..
Contribution of Detector Volume t o At
Calculated for V R = 185 mi.
0 1 2
x
5 7 9 11'
15 20 100
44 24 44 43 44 97 47 40 52 55 59 65
63 88 25 87 48 -18
0 19 0 73 3 5 8 11
39 64 01 63 15 24 21 24
0 023 0 044
0 190 0.365
0 105 0 140 0 172 0 215 0 252 0 305
0 0 0 0 1 1
678 806 890 969 015 062
31 31 32 33 35 37 40
30 61 24 16 -11
76 15 4J 77 47 29 54 14 1L38 os
0 0 1 4 6 8 12 15 22 107
31 94 86 11 46 85 47 99
84
63
0 0 0 0 0 0 0 0 0 0
032 062 091 141 185 224 271 317 370 720
0 310 0.470 0 620 0 822 0 923 0 983 1.039 1.066 1 142 1 076
22 12 22 51
0.39
0 044
0,390
2B, 78
4.66
0.187
0.932
35.11
13,09
0.342
1 091
VOL. 31, NO. 3, MARCH 1959
359
91
02
,04
.Ob
.03
D e t e c t o r C e l l Volume Retention Volume
5. Effect of detector retention volume
.
I0
.08,
.I2
2/ ’
VR‘
volume
on
observed
Detector Cell Volume Retention V o l u m e
Figure 6. symmetry
The length of base line intercepted by a tangent drawn from any point on the descending curves of Figure 2 and by the projection of the point of tangency on the base line, is equal to 2‘. It is more convenient to draw the tangent which intersects the curve a t V = 0 and this tangent is shown in Figure 2. Other Theoretical Considerations Affecting Experimental Design. T h e model gas - liquid chromatography column used in t h e Case I1 derivation had the sample added t o t h e first theoretical plate. This cannot be achieyed in a n actual column, and larger samples might contribute t o peak widening and invalidate peak measurements. Fortunately, van Deemter and coworkers (11)have shown by analysis of theoretical equations that a sample volume will not contribute measurably to peak width if
If the sample is not added in plug flow, but rather flushed out of a bypass chamber of volume equal to the plug flow volume, the sample will enter the column in a much larger volume of gas and have a greater effect on peak width. The effect of sample volume for both plug flow and a bypass chamber was treated by Porter, Deal, and Stross (9). They were interested in retention volumes rather than peak widths; however, two of their figures can be used to estimate quantitatively the difference in effect of the same volume of sample with either plug flow or a bypass chamber. Both types of curves are given for V R = 300 and r = 2000, and the peak widths were eonstructed and measured in the usual manner. For a volume of 10 ml., plug flow peak width corresponds to li00 plates, while a 10-ml. bypass chamber with perfect mixing gives 1100 plates. Consequently, a sample injector for peak width experiments should preferably add the sample in plug flow. Corrections for Nonideality of Apparatus. RETENTIONVoLuim CORRECTIONS. For convenience, t h e corrections are divided into two 360
0
ANALYTICAL CHEMISTRY
Effect
parts. Correction 1 accounts for t h e voIume of t h e apparatus from t h e point of sample injection to the detector, b u t excluding the column. Correction 2 accounts for the error in retention volume caused by perfect mixing in the detector. V., is the sum of corrections 1 and 2. Correction 1. This is due to volumes which were ignored in the theoretical model and is estimated by nonconformity of actual noncolumn peaks to the curves of Figure 2 . This is discussed under Discussion of Results. Correction 1 should be a constant for any given apparatus, regardless of the column being used. Correction 2. Figure 3 shows that the detector cell volume influences peak position. By Equation 13, the figure can be used with other values of 2’and VR’ but the curves should be changed for different values of r. The increase in retention volume is not a linear function of the detector cell volume. The most convenient method for estimating the correction is from a plot such as Figure 5. Here the fraction of the measured retention volume which is due to noncolumn effects is plotted as ordinate us. the retention volume measured in units of effective detector volume. The curves in Figure 5 are based on computation of peak maxima from Equation 11. Correction 2, and therefore, V., varies m-ith retention volume and column efficiency. I n the derivation of the equation, V i = Vz
+ VLH
(15)
only the column was considered. Accordingly, both V i and V i should be corrected for Val but two different values of V . would be involved because of differences in retention volumes. Failure to take this into account could lead to inaccurate partition coefficients if the effective detector volume were large. PRESSURE DROPCORRECTION.The pressure drop correction of James and Martin (6) need not be applied when calculating T by Equation l, because the correction would appear in both num-
of
detector
’ vR’
volume
on
peak
erator and denominator. However, the pressure relationship between A‘ and 2’must be considered. The peak width, A‘, was obtained with considerable pressure drop in the column, while the estimate of 2‘ was obtained with essentially none. 2’ needs no pressure correction, but it is necessary to decide if pressure corrections must be applied to A‘. The effluent stream which entered the detector was accurately expressed by Equation 7 for the theoretical model, but this is not true for a n actual apparatus because Equation 7 does not alloly for pressure drop in the column. Kevertheless, Equation 11 does show how a detector cell affects the shape of a peak which enters the cell. By reversing this process, Equation 11 can provide an estimate of the peak width of the uncorrected peak which entered the detector. Therefore, A‘ must be estimated from A‘ before applying any pressure drop correction. After A’ has been estimated, the pressure drop correction can be applied to obtain a corrected A”, but this is not necessary to calculate T, provided V R is not corrected for pressure drop either. ASYMMETRY CORRECTION.I n the derivation of Equation 7, the value of H was assumed to be constant ( 7 ) . Accordingly, the symmetry of a chromatographic peak is often used as a measure of absorption isotherm linearity (9). Figure 3 s h o w that the detector volume can cause considerable asymmetry. 3Iuch of this occurs in the tail and can be eliminated by considering only the ascending and descending peak widths, but even here the descending peak width increases faster than the ascending with increasing detector volume. The effect must be corrected for before evaluating peak symmetry as a criterion for constant H . Curves providing this correction are given in Figure 6. The plot is made in units which permit application to wide ranges of values for VR’and 2’. Different curves are obtained for different values of T . The curves were determined by computation from Equation 11.
APPARATUS
Apparatus was conventional except for the sample injector. Columns. Three different columns mere used, varying only in length of column and mesh size of the solid support. Each was prepared from '/d-inch copper tubing which was coiled after packing. The packings mere prepared by adding 40.0 grams of diisodecyl phthalate in approximately 100 ml. of petroleum ether t o 100 grams of ground, waterscreened insulating brick (Johns-Manville C-22). The petroleum ether was removed by heating on a steam bath for 30 minutes longer than required to remove stickiness. It was necessary to stir a t first to prevent spattering. The resulting solid x a s free flowing and easily poured into the columns. The columns (Table 11) were agitated for 1 or 2 minutes with a small massagetype vibrator until packing compression ceased. Carrier Gas. Helium was used as carrier gas. Fine pressure regulation was provided by a Nullmatic pressure controller (hioore Products Co.). Detector System. The detector consisted of a brass block containing two Gow-Mac G-49 coiled mire elements (Cow-Mac Instrument Co.) with bypass flow arrangement (3). A current of 75 ma. per element was provided by a 12-volt storage battery, which was not charged during operation. An accurate potentiometer across a fixed resistance in the bridge was used to set the bridge current reproducibly in spite of variations in battery voltage. ,4 chart speed of 24 inches per hour was used except in some of the noncolumn experiments. Sample Injector. This sample injector added sample volumes of 0.1 t o 2.0 ml. n i t h a maximum relative standard deviation of approximately 1%. The weight of sample added could be decreased to any desired level by diluting with carrier gas The maximum concentration was limited to that which gave a partial pressure of sample equal t o the vapor
I I
Table
II.
Length
Description Columns
Mesh Size
of
Partition
wt.
of Impreg-
of nated of PackPacking, Col- ing, Solid umn Ft. Support Grams A 6.0 30-80 21.2 B 3.0 30-80 11.0 C 6.0 304O 21.0
Kt. of Liquid, Grams 6.06 3 14 6.00
pressure of the sample a t injection temperature; otherwise condensation could occur. The operation of the injector was complex compared to injection with a bypass injector (3) or hypodermic syringe, but had several advantages: It permitted repeated analysis of a solute containing a knoxn and constant sample concentration; it permitted dilution of the sample with any desired quantity of carrier gas; the sample was added in plug flow; when repeated analyses of the same sample were needed, time was saved, because only one weighing was necessary; and there was no lower limit on the concentration of sample. The sample injector consisted of two parts as shovn in Figure 7 and described below. XAGKETIC CRUSHER. The sample chamber had a free volume of 10 ml. and was designed to hold sealed ampoules which could be crushed after closing the chamber. The crusher and its associated diaphragm va!ves D , E, F , and G have been described ( 3 ) . ~IASOJIETER ASSEMBLY.This consists of two burets and a pipet connected by appropriate valring to a mercury reservoir so the mercury levels in each can be adjusted. One buret, called the pressure buret, PB, adjusts the pressure in the assembly. The sample is drawn from the magnetic crusher, and stored in the volume pipet, VP, and volume buret, VB. Specifications were as follows: Valve A is a 3-rray selector valve with bottom outlet.
..A
Flov M e t e r Atm.
Pressure
4 Compressed
#. "q I II
+++ JL \'ach,um JL II H
" He:.um f r o m Ref Ce.1
M
D v
