Quantitative Approach to the Use of Multicomponent Solvents in Gas-Liquid Chromatography R. J. Laub and J. H. Purnell' Department of Chemistry, University College of Swansea, Singleton Park, Swansea, Wales
A quantitative method for calculation of all important experimental parameters relating to the use of multicomponent solvents for complex mixture analyses in GLC is further developed. The method is based on a recently established general solution law. Complete resolution of a 30-component mixture is used as an example of the technique applied to binary solvents. So far as is known, this mixture has never been separated with a single solvent. It Is shown further that the method can be extended to ternary solvents with equal success. This indicates an even wider applicability of the general solution law. In conclusion, the method can be fully computerized.
analytical difficulty and so, since the majority of values of CY in the set will exceed this, the majority of solute pair calculations can be eliminated by inspection. Thus, it is necessary only to evaluate Equation 2 for all other solute pairs as a function of @'A, and plot these on a common graph. In our approach, we have recommended that cy 3 1 a t all times, that is, when plots of Equation 1 for any pair of solutes cross, the calculated ratio of retention is inverted. The resultant diagram is a series of approximate triangles rising from the @A axis, which constitute the "windows" within which complete (60) separation of all solutes can be achieved. Obviously, the optimum operating conditions ( a , 4 ~ correspond ) to the peak of the highest window. Further, the number of plates ( N )required for complete separation can be calculated ( 5 ) via:
T h a t mixed solvents might introduce a new dimension into selectivity in GLC analyses has been implicitly recognized since the inception of the technique. Indeed, in the earliest days, it was quite widely supposed that mixed solvents would eventually become the norm and single solvents, the exception. However, the anticipation that mixed liquids would exhibit complex and unpredictable interactions, and the recognition that an experimental search for appropriate mixtures and compositions was an enormously time-consuming process have combined to limit enthusiasm for this type of work. Not surprisingly, therefore, papers on this subject comprise little more than a fraction of 1%of the analytical GLC literature, while the actual use of mixed liquids is rare. We have shown in a recent series of papers (1-4) that, in fact, the solvent properties of liquid mixtures are quite simply related to those of the pure constituents. All published data relating to infinite dilution partition coefficients ( K R )have been shown to follow the general solution law:
Nreq= 36(a/a - 1)'
KR = 4 A K k ) -t @'SKk,
(1)
where 4 represents a volume fraction and K i a partition coefficient for a pure liquid. This observation removes both obstacles to progress in the use of mixed liquids in GLC, since relative retention ( a )values can obviously now be calculated from data for pure solvents. Thus, for solutes X and Y,
(3)
Thus, knowing the values of N attainable with the pure solvent columns, the required length of mixed-phase column can be calculated with fair precision. In the foregoing calculation, there is no need to identify the individual plots comprising the a/@'*diagram, nor the 100
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27 20
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31
We have developed this idea elsewhere ( 5 ) ,where examples of the initial success of the method were given. Briefly, for any n-component mixture to be analyzed, there are n ( h 1)/2 solute pairs, i.e., values of a. The degree of difficulty of the analysis is largely determined by the minimum value of a deriving from the whole set: if the capacity factor (k') is large for all components (say >lo), then a entirely determines the degree of difficulty. We restrict ourselves to this condition for our present purposes, since the effect of k' upon theoretical plate requirement can quite easily be ascertained from a well known equation ( 5 ) subsequent to the a-analysis. Any value of a > 1.5 represents only trivial
16
35
21
11
3
0.2
04
*
0.6
1.0
In
Figure 1. Plots of KR vs. @'A at 100 OC for the 30 components listed in Table I. Pure S is squalane and pure A is DNNP ANALYTICAL CHEMISTRY, VOL. 48, NO. 6, MAY 1976
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~
~~
Table I. Solute Partition Coefficients at 100 "C for Squalane (S),DNNP (A), and DPTC (B) No.
Name
3-Methyl-1-butene 1-Pentene 1,3-Pentadiene ( c u and trans) 4 4-Methyl-1-pentene 5 1-Hexene 6 3-Methyl-2-pentene (trans) 7 2-Methyl-1,3-pentadiene 8 Benzene 9 Cyclohexane 10 n-Heptane 11 2,4,4-Trimethyl-2-pentene 1 2 Methylcyclohexane 13 2,3,4-Trimethylpentane 14 Toluene 15 1-Octene 16 2,6-Dimethy173-heptene (cis and trans) 17 4-Vinyl-1-cyclohexene 18 Ethylbenzene 19 p-Xylene 20 1-Nonene 2 1 o-Xylene 22 n-Nonane 23 Isopropylbenzene 24 n-Propylbenzene 25 Ethoxybenzene 26 1,3,5-Trimethylbenzene 27 1-Decene 28 n-Decane 29 1,2,3-Trimethylbenzene 30 n-Butylbenzene 1 2 3
G ( B )
Kk(S)
G A )
11.0 13.8 14.9
8.9 10.4 18.1
...
23.3 29.8 37.3
18.7 24.7 31.3
...
39.6 41.2 55.9 67.2 76.4
43.5 58.6 44.7 49.0 58.2
...
90.0 106 108 123 147
70.2 73.3 138 96.4 110
187 200 221 265 271 301 323 372 416 501 557 630 725 830
178 254 276 200 332 202 368 462 745 575 419 414 882 980
... ...
...
...
...
. . ..
... ...
Figure 2. Window diagram for compounds and data of Figure 1. Best window (optimum 4~ value for separation) occurs at 4~ = 0.0807
...
...
... ... ... ...
576 274 737
... ... ... ... ...
568 516
... ...
two pairs whose data constitute the window peak. However, the precise sequence of elution can be evaluated, if desired, because $A is fixed a t the optimum value. This paper extends our earlier work ( 5 ) by, first, showing the further application of the method with an example of a complete separation of a 30-component mixture which, from our analysis of published retention data, cannot be resolved with any pure liquid phase so far employed; and, second, showing that our theory can be extended to stationary phases composed of three or more components.
EXPERIMENTAL All chromatograms were run on a Perkin-Elmer model F-11 gas chromatograph at 100 "C. Eighth-inch 0.d. stainless steel tubing and Chromosorb G(AW-DMCS treated) supports were used throughout. The stationary phases, squalane, di-n-nonyl phthalate (DNNP), and di-n-propyl tetrachlorophthalate (DPTC) were reagent grade and were used as received. The densities of these phases, methods of packing preparation, and solute partition coefficients have previously been reported elsewhere (3, 5-9). A 100/ 120-mesh support and 3.5 wt % liquid loadings were used for the 30-component mixture analysis, and 60/80-mesh support and 7 wt % liquid loadings were employed for the 5-component mixture studies.
RESULTS Figure 1 shows a plot of K& and K&s, data for the 30 hydrocarbons listed in Table I. The data relate to elution a t 100 "C from di-n-nonyl phthalate (DNNP) (A) and squalane (S), and are taken from published work (5-9). We have presumed the applicability of Equation 1 and connected the appropriate values of Kk with straight lines. We see that not only are there several solute pairs having a very close to 1 for each pure solvent (Le., are extremely difficult to separate), but there are 17 values of $A a t which some pair or another also has this value. This observation immediately underlines the difficulty of a purely experimental search for the optimum value of $A. 13t14
I
360
1
300
240
180 Time.mins
120
60
Flgure 3. Chromatogram of 30 components listed in Table I with: (a)pure squalane; ( b ) pure DNNP: ( c ) squalane
(d)mechanically-mixed squalane 4- DNNP (dA= 0.0807). All columns 36 ft long 800
ANALYTICAL CHEMISTRY, VOL. 48, NO. 6, MAY 1976
0
+ DNNP
($A
= 0.0807); and
la) S q u a l a n e i D N N P
8 19
’20
0
0.2
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@A
06
(b) Squalane t DPTC
(c) D N N P
02
+
I
I
DPTC
06
0 4
1.0
08
I
10
OA
Figure 4. Plots of KR vs. @ A for components 19, 20, 21, 27, and 28 in Table I. ( a )squalane and DNNP; (b) squalane and DPTC; ( c ) DNNP and DPTC. All at 100 OC
Figure 2 shows the window diagram for the full mixture, where we find 18 windows varying in height from as little as a = 1.01 to a = 1.06. The difficult nature of an experimental search now becomes clear: only one window is higher than that at pure S (+A = 0), Le., all 17 other compositions would offer less analytical selectivity than does pure S. Thus, for this system there is a unique solution for this solvent pair. Since the best value of a pertaining is 1.06, we require close to 11 500 plates for the complete separation. Our test columns of S yielded around 315 plates per foot and so a 36-ft long column of @A = 0.0807 is indicated, if k’ is made large. Figure 3 illustrates four chromatograms obtained in comparable conditions. ( a ) and ( b ) show those obtained with pure squalane and pure DNNP, respectively. ( c ) shows the “first time” chromatogram obtained with the calculated column in which A and S had been mixed prior to coating the support. ( d ) shows the chromatogram obtained with the calculated column packing made by mixing support A with support S in the correct proportions. Clearly, the calculation has been totally successful. But further, each peak appears precisely a t the point demanded by reading up Figure 1 at +A = 0.0807. Thus, our assumption that Equation 1 applied has been precisely confirmed. It is eminently clear that the chromatograms in Figure 3 ( c ) and ( d ) are identical. We have elsewhere (1, 3 ) elaborated a theory of independent solvent action to account for Equation 1, for which, incidentally, no basis has yet been found in conventional theory. I t is a necessary conclusion of this theory that combined solvents and combined pack-
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Time, m,n5
Chromatograms for the 5 components of Figure 4 with: ( a ) pure squalane; (b) pure DNNP; and (c)pure DPTC Figure 5.
Figure 6. Window diagrams for the 5 components of Figure 4 for: ( a ) squaiane and DNNP; (b) squalane and DPTC; and (c) DNNP and
DPTC
ANALYTICAL CHEMISTRY, VOL. 48, NO. 6, MAY 1976
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1
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120
60
90
30
I 0
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Flgure 7. Chromatograms of the 5-component mixture of Figure 4 with: (a) squalane DNNP = 0.1648); (b)mechanically-mixed squalane DNNP (4A = 0.1648); (c) squalane DPTC ( 4 ~ = 0.0522); (d) mechanically-mixedsqualane DPTC (& = 0.0522)
+
+
+
+
ings would produce identical GLC results. Hence, the identity of Figure 3 (c) and ( d ) adds confirmation to our theoretical proposals. It is self-evidently a very simple matter to computerize the procedures described above. Figure 2 was, in fact, produced by hand calculation, but we have since confirmed it by use of a computer program we have devised. We are currently extending this to allow for direct drawing of window diagrams and hope to describe the results on a future occasion. The volume of evidence for the generality of Equation 1 and the success of our analytical application of this solution law is now very considerable. This prompts the query as to whether or not Equation 1 can be extended to ternary and higher solvent mixtures. In what follows, we show that this is very likely to be the case.
20/19
1.05 l .
“‘0
Ql
l
0
N
l-3 0.50
1.0
KR = E 4 K L
(4)
and further, mechanical and intimate mixtures operate identically. In concluding, it is worth noting that the optimum (Y achieved is 1.11,exactly as for the binary mixtures. We hope to return to this feature in future work.
DISCUSSION It seems clear that we have developed a highly successful approach to the handling of the analysis of very complex mixtures with multicomponent solvent systems in GLC. Furthermore, the fundamental ideas underlying it receive continuing confirmation and must affect developments in the area of solution theory. Since we have shown elsewhere that our general law applies equally to noninteracting solu0
28121
21120
0.50
0
For this study we selected the five solutes (19, 20, 21, 27, 28) of Table I that consistently offered the greatest analytical difficulty. Figure 4 shows plots of K i ( s )and vs. 4~ for the five solutes with each of the three pairs of solvents. Again we have assumed Equation 1 in drawing the straight lines. Figure 5 shows chromatograms of the five-component mixture obtained with each solvent separately; as Figure 4 would demand, each shows only four peaks. Figure 6 shows the window diagrams for each solvent pair, and we see that the best a attainable is ( a ) 1.11, ( b ) 1.11,and ( c ) 1.07. The chromatograms for the two best windows are shown in Figure 7 , where, again, mechanically-mixed packings are seen to be equivalent to intimately-mixed packings. It is clearly not possible to produce a single window diagram for a ternary solvent. Hence, here we have calculated a series of 12 which cover the spectrum of compositions satisfactorily. These are illustrated in Figure 8, from which we see that the best windows occur in ( b ) , ( e ) , and ( d ) . That indicated in (c) is marginally the best, but the differences are trivial. From these we have calculated the optimum columns and Figure 9 shows the success of the technique with columns made up with pre-mixed solvents. Further, the elution order and times are exactly those calculable via an extended Equation 1. Finally, Figure 10 shows the same systems chromatographed with mixed packings rather than with mixed solvents, and, once more, there is total identity with Figure 9. It is clear that this analytical application supports our solution model, since we may now write:
\ 20119
(e) 20119
10 0 - 0
0-0
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0.50
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%N N P/ D N NP + D PTC)
: : : p - / o
1.05
1.00 0
20119
0.50
1---------1 28/27
0 1.0- 0
10
Figure 8. Window diagrams for the 5 components of Figure 4 for ternary solvent mixtures. In each, squalane is held constant while DNNP and DPTC are varied over the indicated ranges
802
ANALYTICAL CHEMISTRY, VOL. 48, NO. 6, MAY 1976
T
inn
150
120
90
6C
15
Tim. m , n 5
I
100
I
150
120
90 Timc.mins
60
30
Figure 10. Chromatograms of the 5 components of Figure 4 at window compositions indicated in Figure 8 using mechanically-mixed packings
0
Figure 9. Chromatograms of the 5 components of Figure 4 at the three best column compositions indicated in Figure 8: ( a ) 4 s = 0.9200, I#JDNNP = 0.0388,~ D P T C= 0.0412; (b)4 s = 0.9000, #JDNNP = 0.0715, ~ D P T C= 0.0285;( c ) 4 s = 0.8800,4 ~ ~ j = - p0.1038, ~ D P T C= 0.0162
tions, e.g., alkane/alkane/alkane as well as to supposedly interacting systems, e.g., electron donor/electron acceptor/ base solvent, it seems that ideas on weak molecular complexing also need re-examination. From the analytical point of view, new horizons are quite clearly presented. Very complex analyses may now be contemplated on a single column-single run basis. In addition, this new method makes it possible to state precisely what is required in terms of column length and performance. The widespread adoption of our method, however, has certain implications. In particular, its use demands that, in future, data be reported as partition coefficients, specific retention volumes (and densities), or as retentions relative to some simple and easily available standard solute. Reporting of data in the form of one or another of the several retention indices will clearly be of little value to those interested in multisolvent work, since, a t worst, the data will be useless and, a t best, will demand much arithmetic revision. Finally, since, as we have shown, mixed packings work as well as mixed solvents, it should be possible to attack a
wide range of problems with a stock of a dozen or so prepared packings, which will only require mixing in the correct proportions. We hope, in fact, soon to report on an approach to developing a computerized library storage of GC data, such that the analyst need eventually only tell the computer which compounds he wishes to separate; the computer will then respond with the exact composition of stationary phases necessary, the length of column needed, the temperature, and the order of elution of the components.
LITERATURE CITED (1) J. H. Purnell and J. M. Vargas de Andrade, J. Am. Chem. SOC.,97, 3585 (1975). (2) J. H. Purnell and J. M. Vargas de Andrade, J. Am. Chem. SOC.,97, 3590, 11R75) . - . _,. ~
. . isi
(7) (8)
(9)
R. J. Laub and J. H. Purnell, J. Am. Chem. SOC.,98, 30 (1976). R . J. Laub and J. H. Purnell, J. Am. Chem. SOC.,98, 35 (1976). R. J. Laub and J. H. Purnell, J. Chromatogr.. 112, 71 (1975). R. J. Laub and J. H. Purnell, paper presented at 10th International Advances in Chromatography Symposium, Munich, Germany, 1975. H. Miyake, M. Mitooka, and T. Matsumoto, Bull. Chem. SOC.Jpn, 38, 62 (1965). M. Mitooka, Jpn Anal., 21, 189 (1972). S.H. Langer and J. H. Purnell, J. Phys. Chem., 70, 904 (1966).
RECEIVEDfor review November 17, 1975. Accepted January 16, 1976. R.J.L. acknowledges the Foxboro Company for financial support.
Determination of Trace Hazardous Organic Vapor Pollutants in Ambient Atmospheres by Gas Chromatography/Mass Spectrometry/Computer E. D. Pellizzari," J. E. Bunch, R. E. Berkley,
and J. McRae
Chemistry and Life Sciences Division, Research Triangle Institute, P.O. Box
Tenax GC cartridges were used to collect organic vapors in the ambient air of Houston, Tex., the Los Angeles, Calif. Basin, and the Raleigh, N.C. area. The vapors were thermally desorbed and analyzed by a capillary gas-liquid chromatograph coupled to a mass spectrometer. An on-line computer recorded data on magnetic tape and generated
72794, Research Triangle Park, N.C. 27709
normalized mass spectra and mass fragmentograms. The ubiquitous background of hydrocarbons from automobile exhaust were substantially resolved from each other, and 21 halogenated hydrocarbons were detected, including the carcinogens vinyl chloride and trichloroethylene, as well as numerous oxygen, sulfur, nitrogen, and silicon compounds. ANALYTICAL CHEMISTRY, VOL. 48, NO. 6, MAY 1976
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