The greater sensitivity of the present emission spectrochemical techniques compared with atomic absorption spectrophotometry is an important advantage in the measurement of serum chromium concentrations. Economy of sample size is similar to that achieved with gas-liquid chromatography, but in contrast t o the latter, sample preparation does not involve any extraction procedure, and there is only a minimum of handling of the oxidized sample. A further potential advantage of emission spectrochemical techniques is the capacity for simultaneous multielement analysis. Concurrently with chromium analyses, six other elements have been measured and these are listed in Table 111. Sensitivities are expressed as the quantity of element required for a 30% increase of line over background; in practice precision of analyses has permitted realistic detection limits lower than the tabulated figures. Optimization of analytical conditions for these elements has not been attempted. As an example of the economy in sample size which can be achieved with these techniques, only 10 pl of serum are required for the simultaneous determination of zinc, copper, and magnesium concentrations. Initial studies have been restricted to seven
elements only because of the lack of spectrographic facilities and the restricted number of photoelectric multipliers available for use in the direct-reading spectrometer. It is concluded that emission spectrochemical analysis with a static argon arc chamber as described by Gordon is a valuable technique for the quantitative measurement of chromium in biological samples. The inherent sensitivity of this technique is of particular importance for the determination of chromium in serum samples and other tissues in which the concentration of this element is only a few parts per billion. ACKNOWLEDGMENT
The invaluable advice of W. A. Gordon is gratefully acknowledged. Analyses were performed with the technical assistance of M. Jacobs. RECEIVED for review August 5 , 1970. Accepted October 26, 1970. This work was supported by USPHS Grant No. 1-R01-AM-12432 from NIAMD. ; partly supported by USPHS Grant No. R.R.-00069.
Mixed Carrier Gases in Chromatography-A Source of Error Raymond Annino, Joseph Franko,‘ and Harry Keller2 Research Center, The Foxboro Company, Foxboro, Mass.
Gas chromatography using mixed carrier gases has been evaluated for use as an on-line deviation analysis technique for process control. A serious experimental difficulty is uncovered. Briefly, it is shown that if a particular sample solute is also a component of the carrier gas stream, its elution peak area is not only determined by the difference between its concentration in the sample and in the carrier gas, but also by the identities and the concentrations of all other components of the sample. The origin of this effect is identified and a computer simulation of column behavior, based on the appropriate theoretical model, yields results consistent with those obtained experimentally. Although the observed effect severely limits the general use of chromatographic difference procedures, there are instances where mixed carrier gases provide an excellent solution to a problem. As an example, a method is proposed for the easy resolution of a difficult solute pair by including one of the two solutes in the carrier gas stream.
SUCCESSFUL OPERATION of industrial processes demands reliable means of control. This in turn requires sensing the magnitude of some particular property of the process and, when necessary, initiating a corrective action, the extent and duration of which depends on the sign and magnitude of the difference between the determined value of the property and some reference value. Therefore, if a gas chromatograph is to be used as the sensing element of a control system, there appears to be an advantage in using it in the differential, rather than the conventional mode. Reilley and his colleagues ( I ) in this country, and Zhukhovitskii ( 2 ) in the USSR, Present address, Iowa State University, Ames, Iowa.
* Present address, Northeastern University, Boston, Mass.
recognized this some time ago. They suggested that if a process sample, suitably diluted with helium, was chromatographed with a helium carrier gas containing fixed percentages of appropriately chosen reference materials, then the response to constituents common to the process stream and the carrier gas stream would appear as difference signals. The sign and magnitude of the difference signals would establish the deviation of the process stream from the desired concentration. Since the carrier gas contains components which can dissolve in the stationary phase or be adsorbed on an active surface in the column, a base line, elevated with respect to that which would be obtained in a conventional chromatogram, is observed. This corresponds to the plateau of the fully developed frontal chromatogram of the carrier. Either conventional elution or frontal gas chromatograms can be run on this plateau. This type of chromatography is known variously as Difference or Differential Chromatography, Vacancy, Shadow, or Mirror Chromatography and Plateau Elution Chromatography (1-5). There have, as yet, been few accounts of practical application of this form of difference chromatography; among these are the determination of small amounts of water in organic liquids, using water saturated helium carrier gas (6) and, more recently, the recommendation that the analysis of sulfur
(3) A. A. Zhukhovitskii, N. M. Turkeitaub, M. Gaier, M. N. Lagashkina, L. A. Malyasova, and G. P. Shlepuzhnikova,Zacod. Lab., 29, (1) 8 (1963). (4) J. R. Conder, in “Progress in Gas Chromatography,” J. H. Purnell, Ed., Interscience, New York, N.Y., 1968, pp 209-270. ( 5 ) Raymond
(1) C. N. Reilley, G. P. Hildebrand, and J. W. Ashley, Jr., ANAL. CHEM., 34, 1198 (1962).
(2) A. A. Zhukhovitskii, in “Gas Chromatography, 1964,” A. Goldup, Ed., Elsevier, New York, N.Y., 1965, pp 161-169.
Annino, “Plateau Elution Chromatography,” presented at the Pittsburgh Conference, Analytical Chemistry and Applied Spectroscopy, Cleveland, Ohio, March 1969. 37, (6) S. Ahuja, G . D. Chase, and J. G. Nikelly, ANAL.CHEM., 840 (1965).
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
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PLATEAU ELUTION CHROMATOGRAM HELIUM SAMPLE
Figure 1. Development of normal elution (helium FRONTAL CHROMATOGRAM carrier: 100 ,d sample), frontal and plateau HYDROCARBON SAMPLE elution chromatograms of a mixture of air, propane, isobutane, and butane
i
Column: 20% w/w squalane on 100/120 mesh Chromosorb P; 6 ft X 0.085-inch i.d. Temperature, 20 “C
- 26 -
22-
G
I
34
-
30
a - 14 2
PROPANE SIGNAL
-
‘Ex
u
IO J
- 6
a z c3 v)
- 2
‘10 PROPANE IN
SAMPLE
\eTyr V
1.AIR 2. PROPANE 3 . ISOBUTANE 4 . BUTANE
NORMAL ELUTION CHROMATOGRAM
5 VI
+42
4
HYDROCARBON SAMPLE
operation which requires emphasis and elucidation if the method is to be more widely applied in practice. The problem is associated with the fact that the area of the so-called difference peaks (and the side of the base line on which they are seen) depends not only on the difference between the concentrations of the solute in the ?ample and in the carrier gas, but also on the identities and concentrations of all other components of the sample. This effect may be implicit in the development of finite concentration chromatography theory of recent years (9-17). However, to the best of our knowledge, except for this work and that of Helfferich and Klein (18), which appeared after the completion of the present investigation, it has never been clearly stated nor studied. EXPERIMENTAL
+2
/O/~PROPANE IN SAMPLE
-301
Figure 2. Elution of 10O-pl propane-helium samples from a column 6 ft X 0.085-inch i.d. of 20% w/w squalane on 100/120 mesh Chromosorb P. Carrier gas: 20% propylene-8Ox helium Bottom right, typical plateau elution chromatogram; sample propane-helium = 20:80 %. Left, dependence of propylene vacancy peak height on composition of 100-pl propanehelium sample. Upper right, dependence of propane peak height on composition of sample dioxide (7, 8) can be better performed with helium carrier gas containing a small amount of sulfur dioxide. The purpose of this paper is to call attention to a serious practical difficulty arising in this mode of chromatographic (7) R. K. Stevens, A. E. O’Keefe, J. D. Mulik, and K. J. Krost, “Gas Chromatography of Reactive Sulfur Gases in Air at the
Parts Per Billion Level. 11. Differential Response Chromatography,” presented at 157th National Meeting, ACS, Anal. Chem. Div., Minneapolis, Minn., April 14-18, 1969; Abstr. Papers, Anal. 56. (8) E. L. Obermiller and G. 0. Charlier, J . Chromatogr. Sci., 7, 580 (1969). 108
Apparatus and Procedure. The gas chromatograph was of conventional design using thermal conductivity detection and incorporating special switches to allow introduction inio the column of any one of several premixed carrier gases, either to conduct frontal analysis or to set up a carrier plateau upon which subsequent frontal or elution analyses could be run. Samples and mixed carrier gases were made up on the basis of partial pressure in large amounts from chromatographically pure components. Mixture compositions were checked by conventional elution gas chromatography using standard analyzed mixtures obtained from The Matheson Company as reference standards for calibration. The results of these analyses were found to be within i1 relative of the reference standards. A typical set of frontal, plateau elution, and conventional elution chromatograms obtained with the system is illustrated in Figure 1. RESULTS In its simplest form, plateau elution chromatography would involve a carrier stream comprising a nonretained gas (e.g., ~
(9) A. A. Zhukhovitskii, N. M. Turkeitaub, L. A. Malyasova, A. F. Shlyakhov, V. V. Naumova, and T. I. Pogrebnaya, Zavod. Lab., 29, 1162 (1963). (10) F. I. Stalkup and H. A. Deans, AZChE J.,9, 106 (1963). (11) F. I. Stalkup and R. Kobayashi, ibid., p 121. (12) D. L. Peterson and F. Helfferich, J. Phys. Chem., 69, 1283 (1965). (13) A. A. Zhukhovitskii, M. L. Sazonov, A. F. Shlyakhov, and A. I. Karymova, Zavod. Lab., 31, 1048 (1965). (14) K. T. Koonce, H. A. Deans, and R. Kobayashi, AZChEJ., 11, 259 (1965). (15) A. A. Zhukhovitskii, M. L. Sazonov, A. F. Shlyakhov, and V. P. Shvartsrnan, Zh. Fiz. Khim., 41,2640 (1967). (16) P. C. Mangelsdorf, Jr., ANAL,CHEM.,38, 1540 (1966). (17) J. R. Conder and J. H. Purnell, Trans, Faraday Soc., 64, 1505 (1968). (18) F. Helfferich and G. Klein, “Multicomponent Chromatography,” Marcel Dekker, Inc., New York, N. Y., 1970, pp 212-
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
213.
IO
20
‘10 PROPANE IN SAMPLE 50 60 70 80 90 100
30 40
ISOBUTANE ISOBUTYLENE BUTANE
> 0
z a 0
9
+START
n
ISOBUTANE VACANCY
OF PROPANE VACANCY
12
-
14-
40
-
6
I
1
Figure 4. Variation of the vacancy signal as a function of partition ratio k‘ of injected sample material. Column (see Figure 2). Carrier gas: 20% propane-80Z helium. All samples 100 pl of undiluted material.
Yo PROPANE IN SAMPLE
Figure 3. Plateau elution of 100-pl propane-helium samples from column (see Figure 2). Carrier gas: 10% isobutane-90 % helium Upper diagrams show typical chromatograms. Lower diagrams show dependence of isobutane vacancy height and propane peak height on propane-helium sample composition
helium) and a retained gas. Injection of a sample of pure nonretained gas would then create a concentration “vacancy” of the retained material in the flowing stream and this “vacancy peak” would travel through the column, emerging at the correct retention time but being “negative.” It is this view which led t o the introduction of the term “vacancy” (3). In accord with this convention, in all discussion here, the term “vacancy” will be used to describe the chromatographic peak associated with the soluble components of the carrier gas mixture even though, as stated and illustrated below, the signal may be positive or negative depending on the circumstances. Effect of Sample Partition Coefficient on Area of Vacancy Peak. The results of experiments with a propylene-helium (20 :80 %) carrier gas stream and 100-p1 propane-helium sam-
ples are summarized in Figure 2 . As is seen (lower right), the positive propane peak is quite normally eluted and peak heights, over a reasonable range, are closely linearly proportional t o the propane concentration in the injected sample. In contrast, the propylene vacancy, which occurs at the retention time for propylene, varies in height very markedly with change in propane concentration in the injected sample. This is contrary to what would be expected since, in the simplest view, outlined above, the vacancy size should be dependent on sample size only and not on composition as long as no propylene occurred in the sample. The effect is so marked indeed, that above about 30 % propane, the propylene vacancies actually appear as positive peaks and a pure propane sample yielded a positive propylene peak large enough to be interpreted as indicating about 20% propylene in the propane.
The above findings establish clearly that the original simple postulate ( I , 2 ) is inadequate since no obviously simple relation exists between the vacancy peak height or area for the carrier gas component and its concentration in the sample unless other retained substances are absent from the sample. The results of a series of experiments with isobutane-helium (10:90z) carrier streams with, again, 100-pl propaqe-helium injected samples, are summarized in Figure 3. The variations of vacancy peak heights or area which occur with changes in the concentration of the sample solute (ie.,propane) are quite different in form from those shown in Figure 2 , since here the isobutane vacancy peaks are always negative and the peak areas increase continuously as the concentration of propane in the sample increases. Again, elution of the propane is normal, the fall off of linearity of peak height with propane concentration in the sample over a large concentration range is a detector problem. These observations indicate clearly that the changes in vacancy peak size are dependent not only on sample composition but also in some way on the partition coefficients of the sample solutes. That the above view is correct is established by the results of experiments summarized in Figure 4. These data are derived from the plateau elutions of a wide variety of sample types (100 pl, undiluted by helium) in a propane-helium (20:807J carrier gas stream. The partition ratio, k ‘ , for propane is about 1.8. As the k’ for the various sample materials which were used increases from 0 to 1.8, the size of the negative propane vacancy peak which is created by a fixed sample size, increases. In contrast, when k‘ for the sample material exceeds 1.8, the propane vacancy peaks are all positive and progressively then diminish in size as k’ for the sample material increases beyond 1.8. (The partition ratio expresses the equilibrium ratio of the amount of sample
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
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70
-
SAMPLE
100% ISOBUTANE
-
CARRIER GAS 20% PROPANE-
CARRIER GAS = 10% PROPANEBAL. HE
CARRIER GAS = 2.4% PROPANEBAL. HE
TIME I IO
20
30
40
50
Figure 7. Illustration of the shift in retention time of the vacancy peak for propane with change in its concentration in the carrier gas mixture. Sample components: air (l),ethane (2), propane (3), and isobutane (4).
60
SAMPLE PRESSURE (PSIA) IN I O O p L
Figure 5. Variation in the height of the vacancy signal for propane in indicated propane-helium streams as a function of amount of pure isobutane sample injected. Note all vacancies are positive under these conditions. Column as described in Figure 2
L* -
Chromatograms: A, carrier gas is 10% propane-90% helium; B , carrier gas is pure helium. Both chromatograms were obtained with a 6 foot X 0.085-inch i.d. column of 20% w/w bis(2-ethoxyethyl) sebacate on lOOjl20 Chromosorb P at
VACANCY (POSITIVE)
w
20 "C
>
PREDICTED LINE FOR
EXPERIMENTAL POINTS FOR 5 0 - 5 0 MIXTURE
I
E G
h
VACANCY CAUSED\
Figure 6. Variation of propane vacancy signal height with sample amount for elution of isobutane, of helium, and of 50-50 mixtures of these two, respectively. Column as described in Figure 2. Carrier gas: 20z propane-SOz helium component in the stationary phase to the amount in the mobile phase.) The dependence of propane vacancy peak height on the amount of sample injected (undiluted by helium), for a case where the k' of the sample material exceeds that for propane, 110
is shown in Figure 5, for several propane-helium carrier gas compositions. The vacancy peak height increases linearly with the amount of sample at all carrier gas compositions. When k' for the sample is less than that for propane, the negative propane vacancy peak is made more negative as the amount of sample is increased. The effect is again linearly related to sample amount. This i s illustrated in Figure 6 which shows plots of the effect on propane (k' = 1.8) vacancy size for sample injections of both pure isobutane (k' = 4) and pure helium (k' = 0) when different amounts of these are injected into a propane-helium (20 :80 %) stream. Shown also are the corresponding data obtained with isobutanehelium mixture (50:50z)as samples. These data points lie exactly on the arithmetic average line for the pure sample materials. These findings establish that the height (and hence also the sign) of the vacancy peak is defined, in the first instance, by the partition ratio of all sample components and, in the second instance, by the relative amounts of these components present in the sample. In the light of the above findings, it is difficult to visualize any readily applicable practical approach to the application of this form of deviation analysis to the quantitative study of complex mixtures since, minimally, solution of the relevant simultaneous equations would require use of (n - 1) samples of known composition in addition to the one of unknown composition, where n is the number of retained components. In an industrial process, n could be very large. Retention Time of Vacancy as a Function of Concentration. The chromatograms shown in Figure 7 illustrate something of the extent of the shift in retention time of a vacancy peak (here a positive peak) which can be achieved with a fixed sample size by varying the concentration of the corresponding
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
ISOBUTANE
STREAM SWITCH TO 10.5 % PROPANE BALANCE HELIUM.
- - - - - - - --
I
PROPANE
-7
10.5 % PROPANEBALANCE HELIUM.
TIME
FRONTAL ANALYSIS
TIME
+
Figure 9. Frontal and elution chromatograms obtained with column a s described in Figure 7
__P
Figure 8. Sorption and desorption frontal chromatograms obtained on 6-ft X 0.085-inch i.d. column as for Figure 7. Sequence of operation and stream compositions as indicated
soluble component in the carrier gas. This relatively large retention shift is a consequence of the several effects attending the use of high concentrations of the soluble carrier component and can be quantitatively accounted for by developed theory (10-23). As would then be expected, in the absence of any significant interdependence of partition coefficients, only imperceptible shifts of retention are noted for the highly dilute sample components which are not also components of the carrier stream. This aspect of the technique requires no theoretical elaboration here and is illustrated only to show an attractive aspect of the method, i.e., the added flexibility of choice of retention to facilitate separation. Frontal Analysis. A number of experimentally determined frontal chromatograms which exhibit curious peak shapes are shown in Figures 8 and 9. In the former, the initial base line corresponds to the plateau for a propane-helium (10.5:89.5%) stream. After some time, indicated on the diagram, a stream of propane-helium-ethane (10.5 :69.5 : 20.0 %) was substituted. Subsequently the new front emerged and eventually set up a new plateau level. This level was maintained for a while but, exactly at the retention time of propane, a fall to a new plateau level occurred. This then was maintained permanently. The hump produced was perfectly reproducible. A subsequent switch back to the original propane-helium stream caused a fall in plateau height which, initially, overshot the original base line and returned only to that level again, exactly at the retention time of propane. In this sequence a negative hump was produced and this, too, was perfectly reproducible. This behavior, that is, the production of positive and negative pulses depending on the relative mag(19) C. H. Bosanquet and G. D. Morgan, in “Vapor Phase Chromatography,” D. H. Desty, Ed., Butterworth, London, 1957, p 35. (20) C. H. Bosanquet, in “Gas Chromatography, 1958,” D. H. Desty, Ed., Butterworth, London, 1958, p 107. (21) P. C. Haarhoff and H. J. van der Linde, ANAL.CHEM.,37, 1742 (1965). (22) {bid., 38, 573 (1966). (23) G. Guiochon, L. Jacob, and P Valentin, J. Chim. Phys. Physicochim. Biol., 66, 1097 (1969).
B, helium stream and A , propanehelium (10.5 :89.5 %) stream replaced by propaneisobutane-helium (10.5 :20.0 :69.5 %) stream. C is elution of 100 p1 of pure isobutane sample in carrier mixture of propane-helium (10.5 : 89.5%) and D is elution of 100 pl of propaneisobutane-helium (10.5 :20.0 :69.5 %) sample in pure helium.
nitudes of the k’ for the stream components, clearly has affinities with what has been described earlier in the account of the plateau elution experiments. In Figure 9, B shows the switch from pure helium to a stream of propane-helium-isobutane (10.5 :69.5 :2073 which produces the expected two sharp steps. In A , the switch from an initial stream of propane-helium (10.5 :89.5 %) to the same propane-helium-isobutane stream as above is shown. Again, two steps are seen, although, since the propane concentration in both streams is the same, no propane step should, ideally, appear. Identical anomalous behavior is observed in the corresponding elution experiments, the chromatograms of which are also shown in Figure 9 (lower section). D is a conventional elution chromatogram in helium of 100 p1 of the quoted propane-helium-isobutane sample while C shows the plateau elution of a pure sample of isobutane in a carrier of propane-helium (10.5 :89.5 %). Since the sample contains no propane, a negative vacancy peak should appear in C . In contrast, a positive peak is observed. The elution and frontal anomalies are thus tied together by these experiments, which implies that the usual explanation offered for such anomalies in frontal analysis as are shown in Figures 8 and 9, Le., competitive sorption, displacement, etc. cannot explain the present findings since in the elution experiment the amount of isobutane in the column is much less than is the case in the frontal experiment. Further, the behavior exemplified in Figures 8 and 9 has evident association with the effects discussed earlier. DISCUSSION
The effect of finite vapor concentration in gas chromatography has been considered by a number of authors (9-23). However, their primary interest has been focused on the con-
ANALYTICAL CHEMISTRY, VOL. 43, NO, 1, JANUARY 1971
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111
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Figure 10. Computer simulation results. Plots of calculated ratios of partial pressure of component/total pressure against time in Frontal analysis. Original stream composition; inert carrier (k' = 0), 90%: component 1 (k' = 0.75), 10%. Switched stream composition; inert carrier, 70%: component 1,lOZ: component 2 (k' = 2.0), 20z. (b) . . Frontal analysis. Original stream composition; inert carrier, 100%. Switched stream composition; inert carrier, 7 0 z : component 1, IO % : component 2, io%. ( A Elution analvsis. Carrier gas: inert carrier. 90X : component 1.10 X . Sample, 100Z component 2. All curves shown &eredirectly drawn on an IBM 1620'ilotter. -Figure (h) represents &omato&amsconstructed from the data of Figures (u)-(c). Curve A corresponds to (a), curve B to (b), curve C to (c). Curve D is the conventional elution chromatogram of a sample of 50 :50 mixture of components1 and 2 with 100% inert carrier. The corresponding partial pressure ratio plots are not shown for the sake of brevity (a)
z
sequent band distortions and changes in retention volume which occur in either frontal or elution analysis, as a result of the several physical effects which accompany operation at high solute concentration. Little attention has been given to the impact of such studies on practical analytical application and for this reason the practical consequences established experimentally here have not been explicitly recognized. There are several possible reasons which might be postulated to account for the effects noted in this work, e.g., competitive sorption, 112
concentration dependence of partition coefficients, velocity changes at sorption boundaries, among others. However, it is the postulate of this work that while these may well be contributory, there is a more fundamental underlying problem. To elaborate this view let us first assume (a) no mutual interaction of solutes ; (b) concentration independent partition ratios; (c) ideal gas behavior; and (d)invariance of pressures throughout the system. The experimental consequences of operation at a finite
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
*
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Figure 11. Computer simulation results. Plots of calculated ratios of partial pressure of component/total pressure against time in frontal analyses (a) Original stream composition; inert carrier (k' = 0), 90%: component 2 (k' = 2.0), 10%. Switched stream composition; inert carrier, S O X , : component 2, 10%; component 1 ( k ' = 0.7% 40% (b) Original stream composition; inert carrier, 50%; component 2, 10%: component 1, 40%. Switched stream composition; inert carrier, 90 % : component 2,lO % Operation involved in (b) is reverse of (a). Combination corresponds to complete sorption-desorption frontal experiment. These data yield the computed chromatogram shown in (c). All curves shown were directly drawn by an IBM 1620 plotter
vapor concentration then, quite simply, can be attributed to the sample components having to adjust their contributions to the total gas volume in order to maintain constant total pressure in the gas phase. To illustrate this view, consider a binary carrier gas consisting of 90% inert gas and 10% of a soluble component A , of k' = 1.0, flowing at some fixed flow rate x ml/min, and in equilibrium with a liquid phase contained in a column. Then at some appropriate time, this carrier gas is diverted and another carrier mixture containing 80% inert gas, 10% of substance A and 10% of another soluble substance B, of k' = 2.0, is passed into the column. As the component B dissolves in the liquid phase, the flow of carrier mixture into the column increases to maintain the total pressure constant. Consequently, there is more of substance A entering the column per unit time than in the original situation where only inert gas and A were present. We can see that this is the case because, in the extreme situation that B had k' a , that is, was completely dissolved, the helium-
-
component A mixture remaining of the original gas packet has the composition 80:10%. Thus, extra A with respect to helium has been introduced. (It must be remembered that fixed inlet and outlet pressures are assumed; that is the rational view to take since it is standard practice.) If the capacity of the column remains constant, the excess quantity of A then breaks through as a positive peak at the retention time corresponding to k' = 1.0 and the signal remains anomalous until the column is equilibrated with B. The chromatograms shown in Figures 8 and 9 illustrate this effect and its converse, precisely. Since elution chromatography is the special case of frontal chromatography, corresponding to a momentary switching of the gas streams, the same phenomenon is expected to be evident in this mode also. Thus, as illustrated in Figure 9, the small positive hump evident in the frontal chromatograms has its elution counterpart, in accord with the present theory. In general then, during a separation (using either inert or
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
113
a simple plate model which was subject to the restraints (a)(6) previously listed. A detailed account is given in the appendix.
COMPUTER SIMULATION STUDIES a 0
5 W
Li P
W
v r 6 % W
z
n
INERT COMPONENT
k‘=O
( k‘10.75)
J W
f
2
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(~
COMPOYENT k ~3.0 3
-
m
?
N
E
N
Tk’=5.0 4
a w Qa
0
0.000
TIME
+
Figure 12. Computer simulation results. Elution of a sample of composition: inert carrier ( k ‘ = 0), 20%: component 3 ( k ‘ = 3), 30%: component 4 (k’ = 5), 50%; using carrier gas of composition; inert carrier, 50%: component 1 ( k ’ = 0.75), 50% Curves for partial pressure of component/total pressure as a function of time for components 3 and 4 are shown in (a). Corresponding plots for inert carrier and for component 1 are shown in (b). Note correspondence of perturbations. (c) shows the resultant chromatogram. All curves shown were directly drawn by an IBM 1620 plotter.
mixed carrier gases), there are zones in the column where the solutes are concentrated and make a significant contribution to total pressure via their vapor pressures. Therefore, the partial pressure of the carrier gas must be reduced within these zones so that the total pressure is kept constant over that small region. A similar view has been expressed by Zhukhovitskii and his colleagues in their discussion of “Chromatography Without Carrier Gas” (9, 13, 15). The reduction in carrier gas pressure in a zone must also satisfy the equilibrium constant requirements of all components present in the zone. Thus, a concentration perturbation of all carrier components is produced under all peaks and must be satisfied in terms of the material balance of the entire column. Consequently, peak areas, which one expects to represent only the difference in concentration of solutes found in both sample and carrier gas, are drastically influenced by changes in the concentration of the other sample components. The adequacy of this explanation could, in principle, be demonstrated by theoretical calculational procedures but is much more graphically shown by comparing the type of results obtained in the laboratory experiments previously described with those obtained from a computer column simulation program based on the model outlined above. The mathematical basis of this program was developed from 114
The computer program was designed to accept as inputs the partition ratios (k’) of the various components, the carrier gas inlet and outlet pressures, the sample size, and the flow rate at the column exit. All computer outputs were directly plotted on an IBM 1620 plotter. All of the laboratory experiments described earlier, and others, could be simulated. Figure 10a shows the computer output plots of the ratio of individual component partial pressures to total pressure as a function of time for the simulated frontal analysis involving the switch from an initial stream of inert carrier (k’ = 0) and a component 1 of k’ = 0.75 (9O:lOx) to one containing inert carrier, component 1, and a component 2 of k’ = 2.0 (70 :10 :20 %). Note particularly the hump-shaped perturbation introduced in the plot for component 1, the concentration of which is, of course, unchanged by the switch, as evidenced by the return of the plot to the original level after the perturbation. It is interesting to note also that the return to the original level occurs precisely at the retention time for component 2. These observations correspond exactly to those seen in the laboratory experiment illustrated in Figure 8. This perturbation also is mirrored exactly in the plot for inert carrier. Figure 106 shows similar plots for a switch from a stream of pure inert carrier to one of inert carrier, component Again, the perturbation of 1, and component 2 (70 :10 :20 the partial pressure curve for component 1 is seen as a hump and this diagram is even more reminiscent of the first half of Figure 8. Again, of course, a balancing perturbation in the plot for inert carrier is seen. Figure 1Oc shows the same type of plots for simulated elution of a pure sample of component 2 in a carrier stream of inert carrier, component 1 (90 :10 Z). Again balancing perturbations are seen. Finally, Figure 10d illustrates the computer plotted chromatograms corresponding to the experiments illustrated in (a-c). Curve A corresponds to (a), curve B to (b) and curve C to (c). Included also in D is a conventional chromatogram computed for a sample of components 1 and 2 (50:50) eluted by pure helium. Figure 10d is to be compared directly with Figure 9, and it is clear that they are essentially identical. It is to be noted that the initial hump, such as seen for component 1 in Figure 8 and in Figure loa, is hidden in the combined two-component chromatogram of Figure 1Od. This is because the k‘ for component 2 exceeds component 1. Thus the breakthrough of component 2 obscures the return of component 1 to its final value. The correctness of this view can be established by computing curves for the reverse process illustrated in Figure 10, i.e., starting with a stream containing component 2 and switching to a stream containing, in addition, component 1. Figures l l a and I l b show computer derived partial pressure curves for this situation and Figure l l c , the composite chromatogram constructed from them. The hump for component 2 which appears in the partial pressure diagrams of I l a and I l b is now clearly visible in the composite chromatogram of Figure l l c . Further verification is found in the similarity of this chromatogram with one obtained experimentally for a similar experiment and shown in Figure 8. The above findings give substantial support to the model presented here and to the proposal that perturbations in the concentrations of all carrier components occur at times corresponding to the retention times of all components of both
ANALYTICAL CHEMISTRY, VOL. 43, NO, 1, JANUARY 1971
x).
12
-
10
-
8 6 -
4 2 -
-aII oO z a c3
4 b
2 2 -
a
,
6 b Ib k'
1'2
Id 1'6
ie io
;2
AA
,010
-;O .
;e
VACANCY CAUSED BY INJECTION OF PURE COMPONENT 2 (k'= 2.0)
OF SAMPLE COMPONENT
,002 1-2
AMPLE PRESSURE IN A FIXED SAMPLE VOLUME 3 4 5 6 7 8 9 IO I I 12
,002
18
20
PREDICTED LINE FOR 50-50 MIXTURE OF
7 (k'=o) z
F '1
COMPUTER COMPONENT EXPERIMENTAL POINTS
,010
'I I
AND l k I - 2 .O
Figure 13. Computer simulation results (a) Summary of calculated data for variation of size of vacancy signal for a carrier gas component with a k' = 5.0 diluted in inert carrier (20:
80%) which is caused by the injection of pure samples having various k' values (b) Summary of calculated data for dependence of vacancy peak height for carrier component of k' = 0.75 diluted in inert carrier (20:SOZ caused by the injection of varying amounts of pure samples having k' = 2.0 and zero, respectively. Shown also is arithmetic mean line and points for 50 5 0 sample mixture derived from computer simulated chromatograms
carrier and sample. Figure 12, again computer derived, establishes the validity of this view. It depicts in (a) and (6) the component partial pressure/total pressure ratios as a function of time in a plateau elution of a sample containing components 3 (k' = 3.0) and 4 (k' = 5.0) in a stream of inert carrier (k' = 0) and component 1 (k' = 0.75) in the proportions 50:50%. Perturbations in the curves for both inert carrier and component 1 occur at the k' for component 1 and also at those for Components 3 and 4 as well. In consequence, the size of the vacancy for component 1 shown in the computed chromatogram in Figure 12c is a complex function of the several variables. This accords with the experimental results. Figure 13 finally establishes without question that the model proposed identifies the essential origin of the anomalies uncovered. Figure 13a shows a plot of the computer-calculated size of vacancy peak created by plateau elution of pure samples, having a range of k', in a stream consisting of inert carrier and a component of k' = 5.0. This diagram is obviously identical in form with that constructed from the experimental data and illustrated in Figure 4. Figure 136 completes the evidence. It shows a plot of computer calculated vacancy peak heights for plateau elution of pure samples of k' = 0 and 2.0, respectively, in a stream consisting of inert carrier and a component of k' = 0.75. This combination corresponds qualitatively to that for the system used to provide the data employed in constructing Figure 6. Computer calculated values for vacancy peak height produced by plateau elution of 50 :50 samples of the components of k' = 0 and 2.0 fall exactly on the arithmetic average of the computed lines for the pure samples. The behavior shown is thus identically that illustrated in Figure 6. The remarkable agreement between the data derived through the model and the experimental information obtained
leaves little room for doubt that, despite the approximations involved, the main source of the response anomaly has been identified correctly as the natural requirement for material balance in a system of constant pressure gradient. The assumption of ideal gas behavior introduces little error as is shown by widespread gas chromatographic experience. The success of the present approach indicates that in the systems employed there can be little mutual interaction of solutes. It is a relatively simple matter to establish that the assumption of concentration independent partition ratios introduces little error; in fact, velocity variation due to concentration changes can be shown to be much more significant. Figure 14 shows the computer derived chromatograms for the vacancies, created by pure inert carrier samples, plateau eluted in carrier mixtures of: A , inert carrier 2 0 x , component 1 (k' = 0.75) 80 and B, inert carrier 80 %, component 1, 2 0 x . The results of numerous such computer experiments lead to the finding that retention times are well described by the equation
x
tr = to
+ tok'(1 - y )
where y = mole fraction of the soluble component of a binary
carrier gas t o = retention time of an unretained substance tr = retention time of the soluble component, which has a
partition ratio, k'. This equation is consistent with expressions derived in theoretical studies on the variation of flow rate due to sorption effects (10-12, 14, 17-23). A consequence of this effect is that in plateau elution, with a fixed amount of pure sample, the vacancy size dependence on
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
115
+
Lt..+a.f/
Figure 14. Computer column results
TIME
Plateau elution of pure inert carrier samples in carrier streams; A , inert carrier, 20%, component 1 ( k ’ = .75), 80%; E , inert carrier SO%,component 1, 20 %. Diagram illustrates substantial dependence of retention volume of the component 1 vacancy peak on carrier composition change due to consequent carrier velocity changes
the amount of soluble component in the carrier mixture is nonlinear. The corresponding laboratory experiments were not pursued in detail because of the complications introduced by nonlinearity of detector response at high solute concentrations in the inert carrier. However, Figure 5 contains implications supporting the above prediction. CONCLUSIONS
It has been demonstrated both experimentally and theoretically that the area or height of so-called ‘‘difference peaks” depends not only on any difference of concentration of the particular component in carrier gas and sample, but also on the identities and concentrations of all other components in the sample. Failure to take this into account leads to totally erroneous results, and analysts using doped carrier gases in differential chromatographic analysis should clearly be aware of this problem. For example, Ahuja et a/. (6),when using water saturated carrier gases, noted a positive peak for water when analyzing a water-free butanol sample and found also, in the analysis of acetone with a tritiated water saturated helium carrier gas, a perturbation of the water under both the acetone peak and at the water (vacancy) peak retention time. These effects are clearly accounted for in the present work, their analog being illustrated in Figure 12 here. Similarly, the use of sulfur dioxide doped carrier gases for the determination of sulfur dioxide (7, 8) will be useful only at levels of sulfur dioxide in the sample which are much above that in the carrier gas. Unless accurately calibrated under conditions of fixed sample composition, inaccurate results will be obtained. Other examples where unexpected vacancies have been noted have been attributed to impurity of the carrier gas (24). A correction scheme has been proposed (25) which involves subtracting the peak area of a purified sample from that ob(24) B. 0. Prescott and H. L. Wise, J. Gas Chromatogr., 4, 80 (1966). (25) G. Castello and G. D’Amato, J. Chromatogr., 32, 625 (1968).
116
Figure 15. Chromatograms illustrating the improved resolution deriving from the use of mixed carrier gases Sample composition; 25 propylene, 10 propane, 0.1 % air, 64.9% helium. Carrier composition; A , 100% helium: B, 20% propyIene-SO% helium. Column: 6-ft X 0.085-inch i.d., 20% squalane on 100/120 Chromosorb P at 25 OC
tained before purification. In view of the complex nature of the relationship of vacancy size and sign to sample composition, it would appear that this procedure should be adopted with caution. Although the general use of mixed carrier gases for differential analysis may be in question, there are a number of areas where this technique provides an excellent solution to a problem. Its use for the adjustment of thermal conductivity of the carrier gas in the analysis of hydrogen (26) or other gases (27, 28) has been recommended. Also, since it was first suggested (29), a number of authors have used carrier gases containing some concentration of the stationary liquid phase to either maintain a constant level on the support or to block active sites. It is proposed here that there are some other aspects of the technique which have not been fully explored. For example, one can take good analytic advantage of the fact that the retention time of the vacancy can be changed by varying the concentration of the solute in the carrier gas. Since it allows selective adjustment of the retention time of one of the peaks of an unresolved pair, it obviates the need for a longer column with the consequent increase in analysis time (5). In Figure 15, the analysis of a propane/ propylene mixture is shown to be much improved by adjustment of propylene retention time by replacing pure helium with a propylene-helium carrier. Perhaps even more important, trace amounts of materials can be far better analyzed in the presence of large concentrations of interfering components by use of mixed carrier than by recourse to longer columns or the more usual two-column methods. Finally, mixed carrier (26) J. E. Purcell and L. S. Ettre, J. Gas Chromatogr., 3, 69 (1965). 37, 1572 (1965). (27) J. Jordan and B. B. Kebbekus, ANAL.CHEM., (28) B. B. Kebbekus, M. H. Barsky, R. T. Rossi, and J. Jordan, J . Amer. Chem. SOC.,88, 2398 (1966). (29) A. Kwantes and G. W. A. Rijnders, in “Gas Chromatography, 1958,” D. H. Desty, Ed., Butterworth, London, 1959.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 1, JANUARY 1971
gases with their attendant “vacancies” can also be used to good advantage to provide an internal timing standard for programming purposes (30). APPENDIX I
Equations Used for Column Simulation Program. Equations relating gaseous and dissolved components (Pdisa = KP,,,) and total pressure ( Z P t ,gas = Pct) are readily obtained for each plate and material balance equations for movement of each component through a plate are derived. The result is 2N 1 equations and 2 N 1 variables, where N is the total number of components. The program begins with the last plate, this plate being the only one for which a known amount of gas is removed per unit time. It calculates the new composition in this plate and the amount of gas which must be removed from the next plate to maintain constant pressure and to satisfy the other restraints. This procedure continues with each plate up to the first plate. A zero plate is provided to hold the sample; when it has been exhausted, it, too, is filled with carrier. Let Pi,& be the pressure of the jth component in the kth phase of the ith plate. Assume k = 1 to be gas and k = 2 to be liquid. Poijk is the present pressure; P’ijk is the new pressure. APi is the change in total pressure (quantity) between plates i and i 1. Thus it represents the amount of material transferred between these plates. Furthermore, let
+
+
+
It is assumed here that the composition of gas leaving the plate is the old composition. Plate zero is handled in a special fashion. While sample remains, the total amount remaining is simply reduced by APo until APo is greater than PTo. At this point an unknown amount of carrier is added to the sample plate to raise the pressure, PTo, up to APo which is the pressure demanded by the first plate. If the amount of added carrier is X,then the (APo/PTo)Potj term in Equation 3 will change to APo/(X PTo) (Pojt X‘CC,) subject to the restriction that APo = PTo X . After making these substitutions, Equation 3 becomes ( X is eliminated)
+ +
+
P’tjl
+
PJtj2
- POtjl - P o w = Pi-111 CCj
+
- P T d - Apt - PotJ1 (3a) PTi
+
There are now, for each plate, 2 n 1 unknowns. They are Pill and Pijz for each j and APi-l. There are also 2 n 1 equations. They are n equations like Equation 1, n equations like Equation 3 or 3a and Equation 2. The simple form of Equation 1 allows its immediate substitution into Equation 3 and 3a, thus reducing the work required to solve the system of equations. The results are, after dividing through by 1 K:
+
+
m = number of plates n = number of components K j = partition ratio for the jth component CC, = fraction of jth component in carrier SCj = fraction of jth component in sample PTi = total pressure in ith plate
(4)
Assuming equilibrium in each plate requires that: KjPijl = Pij2, 0 < i s m , O
