Anal. Chem. 1991, 63, 1264-1270
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increase Nm,i.e., the column length required for full resolution by a factor approaching 5. Since the assumed a would still have led us to the same overall column length, the resulting chromatogram would have shown very unacceptable resolution of the mixture components. The conversion of f F to 1~ is thus crucially important in this case and the example shows us also that, when a narrow window offers the best option, the envelope around the window maximum demands careful definition. Second, it is clear that the column systems used here by no means represent the best choice in terms of substrate loading, operating temperature, and 80 forth since they provide poor efficiencies and excessively long retentions so that not only is the optimized column combination inconveniently long but analysis time is unacceptably protracted. However, their choice has allowed a clear demonstration of the fact that, in a serial system,when the more retentive column is at the front, the length of this column required is far less than when it is at the back. Moreover, the effect is not trivial; the lengths of the DA columns needed differ by over a factor of 2. In the present instance, the overlong retention time is of no concern since the objective was to demonstrate the potential of the GLC-GSC serial column technique and certain aspects of serial column operation. In practical terms, a much more lightly loaded GLC column would be desirable to provide much higher efficiency. Then, however, the resulting k 'would be dominated by the values for the GSC column, which are intrinsically much greater. A higher level of KOH doping of the DA would reduce k'but also the desirable selectivity while
the possibility of reducing the diameter of the GSC column further to reduce the amount of adsorbent is impractical. The logical answer is to operate such systems in a dual-temperature mode, rather than isothermally, with the GSC column held at higher temperature. Fortunately, the theory and procedures are exactly the same, although the identification of the best pair of temperatures adds to the amount of basic data and of the volume of calculation needed. Given the data, of course, the optimization procedure is again amenable to window analysis and, with suitable modification to the computer program, is no more complex than that described here. Registry No. Isopentane, 78-78-4; pent-1-ene, 109-67-1;npentane, 109-66-0;2-methylpentane, 107-83-5; 3-methylpentane, 96-14-0; hex-1-ene, 592-41-6; trans-2-hexene, 4050-45-7; cis-2hexene, 7688-21-3.
LITERATURE CITED (1) Jones, J. R.; Purrall, J. H. Anal. 0 . 1990, 62, 2300. 1884, 292, 197. (2) Purnell, J. H.: Williams, P. S. J . Chmrm-. (3) Pwnell, J. H.: Williams, P. S. J . chrometugr. 1885, 321, 249. (4) Purnell, J. H.; Williams, P. S. J . Chfomatu&T. 1885, 325, 1. (5) Purnell, J. H.; Rodrlquez, M.; Williams, P. S. J . Chrometogr. 1886,
358, 39. (6) Purnell, J. H.; Jones, J. R.; Wattan, M. H. J . Chrometcg. 1887, 399, 99. (7) Laub, R. J.: Purnell, J. H. J . Chrometogr. 1975, 112, 71. (8) hub, R. J.; Purnell, J. H.: Williams, P. S. J . chrometogr. 1877, 134, 249. (9) Laub, R. J.; Purnell. J. H. J . Chfomtogr. 1878, 161. 59. (10) Purnell, J. H. J . Chem. Soc. 1880. 1268.
RECEIVED for review December 17,1990. Accepted March 5, 1991.
Consecutive Gas Chromatograms from Parallel Columns Using a Single Injection and a Common Detector Pardeep K. Gupta and John G. Nikelly* Department of Pharmaceutics and Department of Chemistry, Philadelphia College of Pharmacy and Science, Philadelphia, Pennsylvania 19104
A method ol t w d i " l o n a l chromatography k described In whlch two consecutive chromatograms are obtained In a dngk run using two parallel capillary columns connected to a dngk dotector. The two fused dllca capillary columns, whlch have OV-1 and Carbowax 20 as the llquld phase, Mer In length, fllm thickness, Indde diameter, or combinations of these. It was lwnd that the resunlng ditferences In carrler vebclth, capactty factom, and retention times are wfflclent to create a gap between the chromatograms from each column. Depondlng on the number of components In the Injected sample and the range of thelr polarities and bolllng points, dbtlnc( chromatogram are obtained that may be used In determining the Identity of the components.
INTRODUCTION The method of identifying compounds based on their gas chromatographic retention times has been used from the very beginning of the technique. But because of the pcesibility that more than one compound may have the same or sufficiently
* Corresponding author. 0003-2700/91/0363-1264$02.50/0
similar retention index on a given liquid phase, a confiitory procedure is often necessary. Aside from the method of two-dimensional gas chromatography, i.e., confirming the identification by obtaining a second set of retention times on a dissimilar liquid phase (I,2))other techniques include using a selective detector, splitting the effluent into separate detectors, and others (3-5). The most definitive of these is GC/MS in which the retention data are combined with mass spectral fragmentation patterns and molecular ion masses (5). Retention on Two Columns. There is little likelihood that two compounds will have the same relative retention on columns of different liquid phases. For this reason, and because of its simplicity, this method, often referred to as two-dimensional chromatography, is the method of choice when better identification techniques such as GC/MS are not readily available. The two most widely used liquid phases in two-dimensional gas chromatography are poly(methylsi1oxane) (OV-1, SE-30) and poly(ethy1eneglycol) (Carbowax 20M). Not coincidentally, these phases are a t opposite ends of the polarity scale. In the simplest if not most common procedure of two-dimensional gas chromatography, the two chromatograms are obtained in separate runs, i.e., using one column a t a time. (Alternatively, the two chromatograms may be obtained at 0 1991 Amerlcen Chemical Society
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once if a dual-channel GC system is available.) Among the methods reported in the literature for obtaining
Table I. Effect of Film Thickness on Retention Time
two-dimensional chromatography are the use of two parallel
columns with common injector and separate detector of the same kind, usually a flame ionization detector (6, 7). Watts and Simonick have compiled a relative retention time list comprised of 110 common drugs of abuse and their metabolites for dual-column and dual nitrogen-phosphorus detectors (8). Characterization of drugs in terms of retention time and a relative detector response ratio has also been studied by using a dual-column nitrogen-phosphorus and flame ionization detection system (9,10). Another method to achieve multidimensional chromatography is where two capillary columns are arranged in series, such that the second column receives only selected fractions eluting from the first column (11-14). In the present work, we describe a two-column method of obtaining the two chromatograms consecutively in a single run, using a single detector. The two columns, which have dissimilar liquid phases and are connected in parallel, may be of unequal length, film thickness, or inside diameter or any combination of these. But all other conditions, i.e., inlet pressure and column temperature, are the same. The two chromatograms are thus separated with little or no overlap because the carrier velocities and the capacity factors are different. The degree of separation between the chromatograms would depend on among other variables the ratio of column lengths and film thicknesses of the two columns and can be calculated as described in the following section.
EXPERIMENTAL SECTION Effect of Column Length. As shown by Golay and others (15-17), the linear velocity, u, of a carrier flowing through an open tubular column depends directly on the pressure drop, Ap (the difference between inlet and outlet pressures across the length of the column), the inside radius, r,, the carrier viscosity, 7, and the column length, L, and is given by u = AprJ87L (1) The value of u is determined experimentallyby measuring the dead time of the column, t M , which is the elution time for an unretained component such as methane u =L/tM (2) Because Ap and are common to the two columns, it follows that u, and hence the differential in u between the two columns, depends only on r, and L. Given that commonly available columns have standard values of r, between 100 and 500 pm and given that practically any length of column can be selected as desired, it follows that almost any ratio of carrier velocities may bo obtained. For practical reasons, however, and particularly because of the decrease in theoretical plates that results when the value of u differs sharply from the optimum range, it is best to keep the velocity ratio to less than 4. Thus, for example, velocities of 15 and 50 cm/s for the two columns would be suitable, with little sacrifice in plate number. As discussed in the next subsection,the column of longer length and thus of lower carrier velocity is the one that may have a thicker film of liquid phase, thereby further increasing the retention times. It may be noted that the column with the thicker film would have an optimum carrier velocity lower than that for a thin film (18). Thus, operating the two columns at carrier velocities above and below the normal 25-30 cm/s may result in only minor degradation in plate height. This was tested experimentally. The columns in question were each 30 m long, had film thicknesses of 0.25 and 0.5 pm, and were operated at carrier velocities of 40 and 10 cm/s, respectively. The resulting plate heights were 0.6 and 0.4 mm, respectively. A disadvantage of using columns of unequal length is that the plate numbers will be different. Although this is not a serious side effect, it can nevertheless be avoided by using columns of equal length but extending one of the columns-the one with a thicker liquid-phase coating-with a suitable length of uncoated capillary tubing to provide a retention gap.
initial k = 2 t p , min
4, Irm
k
0.1
2 10
0.5
k
initial k = 5 tR,min
5 25
6 22
12 52
Table 11. Comparison of Calculated Retention Times column
L,m df, r m u, cm/s tM, min t ~min~ tm, min tm, min
1
2
3
4
30 0.25 40 1.25 2.5 , (k = 1) 7.5 (k = 5) 13.5 (k = 10)
30 1.0 40 1.25 6.25 (k = 4) 26.25 (k = 20) 51.25 (k = 40)
30 + 30 0.25 20 5.0 10.0 (k = 1) 30.0 (k = 5) 55.0 (k = 10)
30 30 0.5 20 5.0 15.0 (k = 2) 55.0 (k = 10) 105 (k 20)
+
Using a retention gap instead of a longer length of column provides an additional advantage in that it increases the retention time of each peak emerging from the longer column equally. Thus, the second chromatogram (lower flow rate) is similar to the first chromatogram (higher flow rate). The quantitative effect of column length on retention time can be calculated by t R = L(1 + k ) / u (3) where t R is the retention time of the eluate and k is the corresponding capacity factor. If, for example, one column is twice as long as the other, the carrier velocity will be half and the retention 4 times longer. Effect of Film Thickness. As eq 3 shows, t R depends on k as well, albeit indirectly. As shown in eq 4, k is directly proportional to the partition coefficient, K , the inside radius, re and the liquid film thickness, df (18). k = 2Kdf/r, (4) Since in the present work all other variables except column length and film thickness are kept constant, the retention time will depend on dr according to the relationship t R = A + Bdf (5) where A and B are constants. Given that the range of film thicknesses generally available in capillary columnsis 0.1-1.0 pm, and considering that the optimum range of k is 1-10, it is possible to calculate the effect of film thickness on retention time and to select the appropriate values of dr for the two parallel columns. This calculation,Le., the effect of d f on t R when d other variables are constant, can be illustrated by letting dr = 0.1 and 0.5 pm and calculating the resulting t R for a compound eluting at k = 2 or 5. The results (Table I) show that, depending on the initial value of k, a 5-fold increase in film thickness results in a 3-4-fold increase in retention time. Comparison of Retention Times Resulting from Different Combinations of Column Length and Film Thickness. The combined effects of both liquid-phasethickness and column length were calculated by using a hypothetical three-component sample having initial k values of 1, 5, and 10. The purpose of the calculation is to determine what is the widest range of k values of sample componentsthat can be separated with little or no overlap of the chromatograms. Alternatively, the purpose of the calculation is to compare different combinationsof column length and film thickness to determine which combination is suitable for a given range of capacity factors. (In comparing columns, we have assumed that the three Components in question have the same partition coefficient on the two liquid phases. Put in another way, we have assumed that the two parallel columns have the same liquid phase.) Table I1 shows the calculated retention times for the three components on four combinations of column length and film thickness. Column 1, against which columns 2, 3, and 4 are compared, has a length of 30 m, and its film thickneas is 0.25 pm. The column temperature is set so that the capacity factors of three componenta
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of the sample are 1, 5, and 10. The carrier velocity is set at 40 cm/s, and the resulting chromatogramhas retention times of 2.5, 7.5, and 13.5 for the respective componenta of the sample. Columns 2-4 have either increased length or increased film thickness or both. Consequently, the retention times on these columns are longer than thw on column 1,although in some casea the two chromatograms overlap. Where there is no overlap, the retention times of the second chromatogram are in some cases, for practical purposes, too long. But if the sample components have a more limited range of capacity factors, e.g., k = 1-5 instead of k = 1-10, the resulting retention times from the two chromatograms have little or no overlap and are only moderately long. Chromatographic Instrument and Conditions. The gas chromatograph was a Perkin-Elmer Model 8500 with a flame ionization detector and Model GP-100 printer-plotter. Helium was the carrier gas, and it was passed through an in-line purifier to remove oxygen. The injection and detector temperatures were set at 240 and 200 O C , respectively. The column temperature, or the initial value in temperatureprogrammed runs, was usually determined by trial and error so that the earliest eluting component in the first of the consecutive chromatograms had a capacity factor of approximately 1. Columns. All columns were fused silica capillaries obtained from J&W Scientific (Folsom, CA) and in some cases from Alltech Associates ("Econocap" columns; Deerfield, IL). The inside diameters were 0.25 and 0.32 nm. Lengths were 15,30,45, and 60 m. Where needed, the column length was extended by linking (serially) sections of columns or by adding a section of uncoated deactivated capillary tubing (retention gap) at the front of the column. The columns were linked by using glass connectors, by pressing the square cut column ends into the conically shaped connector. The fused silica retention gap and the g k connectors were obtained from the Restek Corporation (Bellefonte PA). For each chromatographic run, the two columns were used in parallel and were connected to the injector via a twehole graphite ferrule, so that the two cross sections at the front end of the columns were closely aligned next to each other in the inlet. The back ends of the columns were connected to the detector via a glass three-way Y-connector and a 10-cm section of uncoated capillary tubing. Procedure. Dead times and carrier velocities were determined by methane injection. Sample injectionswere made with a 1O-pL Hamilton syringe fitted with a 7-cm needle. Usually 0.5 p L was injected in the split mode, with a splitting ratio of 751. The splitter was tumed off at 0.5 min after injection to conserve helium. Test Mixtures. Several test mixtures containing from five to nine componenta were used for evaluating the column systems as indicated in Figures 1-11. The mixtures were prepared by using equal volumes of 99% pure compounds of similar polarities or obtained from Alltech Associates. RESULTS AND DISCUSSION Columns of Equal Length and Different Diameter and Film Thickness. The two columns used in this case were 30-m X 0.32-mm4.d. X 0.25-pm OV-1 and 30-m X 0.25-mm-i.d. X 0.50-pm Carbowax. At an inlet pressure of 16 psi, the linear velocities of the carrier in the two columns were 42.7 and 25.8 cm/s, respectively; the velocity ratio, 1.63, is equal to the ratio of the diameters squared [(0.32/0.25)2]. The test sample used for this combination of columns was a seven-component mixture of substituted benzenes, and the resulting chromatogram and conditions are shown in Figure 1. There are 13 instead of 14 peaks because the 2 chlorotoluene isomers are coeluted as a single peak from the OV-1 column. The first five peaks and the seventh peak were eluted from the OV-1 column, and the remaining seven are from the Carbowax column. Although the separation time, 15 min, is satisfactory, there is no retention gap between the two chromatograms. In fact, there is an overlap between the last peak from OV-1 and the first peak from the Carbowax column. This is due to the high phase ratio (6 = 320) of the OV-1 column, resulting from the relatively large inside diameter, 0.32mm. This suggests that selecting a large-diameter column for the purpose of obtaining a higher carrier velocity may not
0
5
10
RETENTION TIME (MINUTES)
Figure 1. Separation of seven substituted benzenes. Columns: 3O-m X 0.32-mm X 0.25-pm OV-1 and 30-m X 0.25" X 0.5-pm Carbowax 20M. Cdumn temperature 70 O C (3 min) to 118 O C (4 OClmin); 118 O C (4 min).
be the best way of obtaining a retention gap between the two chromatograms. It was apparent that a difference in carrier velocities through the parallel columns of equal length may also be obtained in prinicple by adding a flow restrictor at the end of one of the columns in place of a retention gap. This was tested by adding a 10- or 20-m section of 0.05-mm-i.d. fused silica capillary to one of the columns. But in practice this method did not work because it was difficult to attain a good seal to control helium leaks. Columns of Equal Length and Diameter and Different Film Thickness. The two columns used in one case were 30-m x 0.25-mm-i.d. X 0.25-pm OV-1 and 30-m X 0.25-mm4.d. X 0.5-pm Carbowax 20M. At an inlet pressure of 18 psi, the linear velocity through both columns was 34.3 cm/s. The test sample used here was a polar mixture of six components listed in Figure 2. The chromatogram and conditions are given in Figure 2, which shows a 3-min retention gap between the two columns and good resolution for both portions of the chromatogram. (There are 11 instead of 12 peaks because cyclohexanone and ethyl hexanoate are coeluted in the OV-1 column.) It should be noted that this sample and column combination, in which the carrier velocity in both columns is equal, has worked well. This is because of the relatively high polarities of the sample components. This was demonstrated when the less polar mixture of seven substituted benzenes was tested; the resulting retention gap between the two portions of the chromatogram was insufficient to distinguish the peaks from one column from those of the other. The same two-column system works well when a simpler five-component mixture was used as shown in Figure 3. There is a 1-min gap between the two portions of the chromatogram. The same five-component mixture was also separated on equal-length columns in which, however, the film thickness was interchanged. That is, the OV-1 column had a film thickness of 1.0 pm and the Carbowax 20M thickness wm 0.25
ANALYTICAL CHEMISTRY, VOL. .I
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o
q
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1
0
Flguro 2. Separatlon of SIX polar compounds. Columns: 30-m X 0.25-mm X 0.25-pm OV-1 and 3Om X 0 . 2 5 ” X 0.5-pm Carbowax 2 W . Cokmn temperawe 100 OC (4 mln) to 130 OC (15 OC/mIn); 130 OC (2 min).
20
15
10 RETENTIONTIME (MINUIESI
Figure 4. Separation of ftvecomponent mixture. Columns: 30-m X 0.32-mm X 0.25-pm Carbowax 20M and 3Om X 0.25” X 1.0-pm OV-1. Inlet pressure 17 psi; velocity 27 cm/s; column temperature 90 OC.
Table 111. Effect of Liquid-Phase Thickness on Retention Times (Minutes) and Retention Sequence 0.5-pm Carbowax, 0.25-pm OV-1 chlorobenzene p-xylene o-xylene 2-chlorotoluene decane
2.99 3.19 3.31 3.59 4.53
0.25-pm Carbowax, 1.0.” OV-1 decane p-xylene o-xylene chlorobenzene 2-chlorotoluene
Gap between the Two Chromatograms decane 5.56 chlorobenzene p-xylene 6.03 p-xylene o-xylene 6.93 o-xylene chlorobenzene 7.90 2-chlorotoluene 2-chlorotoluene 12.1 decane
-
I
P
0
5
10
15
R m N T l O N TlME (MINUTES)
Figure 9. Separation of fivecomponent mlxtwe. Columns: 30-m X 0 . 2 5 ” X 0.25-bm OV-1 and 3Om X 0 . 2 5 ” X 0.5-pm Carbowax 2OM. Inlet pressure 18 psl; vekclty 29 cm/s; column temperatue 85 OC.
pm. (The phases are reversed, and their thickness ratio is 4 rather than 2.) The resulting chromatogram in Figure 4 shows good and uniform resolution. Because the phases were reversed, the resulting retentions are reversed. For example, decane now is the 1st and 10th peak in the combined chromatograph, whereas before it was the 5th and 6th peak. The reversal of retention times is shown in Table 111. It may be noted that Figure 4 shows 12 rather than 10 peaks. The first two peaks are due to methane, which was injected with the sample to mark the carrier velocity. The relative size of the methane peaks shows the relative size of
2.66 3.80 4.43 4.90 6.29 6.82 7.17 8.86 10.9 15.3
the injection volumes entering the two columns. Injection volume is proportional to the flow rate or carrier velocity in each column. Columns of Different Length. As mentioned earlier, using columns of unequal length is one of the simplest and more convenient ways of obtaining a retention gap between the two portions of the chromatogram. If at the same time the liquid-phase thickness is also unequal, the resulting retention gap is quite large, as shown in Figure 5. In this case, the ratio of column lengths and carrier velocities is 1:3 and the retention gap for the five-component test sample is 8 min. But as Figure 5 demonstrates,using columna of unequal length and unequal liquid-phase thickness produces a sharp difference in resolution between the two columns. An alternative method is to keep the column lengths equal but decrease the carrier velocity and increase the retention time in one column by adding a length of uncoated capillary tubing (of the same inside diameter) as a retention gap. In this case, the two-column combination was 30-m X 0.25-mm X 0.25-pm OV-1 and 30-m x 0.25-mm x 0.25-pm Carbowax 20M plus 30-m fused silica tubing. When the inlet pressure
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f
!!!--
RETENTIONTIME lMlNLmSl
Flguro 5. Separation of five-component mixture columns: 10-m X 0 . 2 5 " X 0.25-pm Carbowax 20M and 3Om X 0 . 2 5 " X 1.0-pm
p
1 10
5
0
OV-1. Inlet pressure 12 psi: velocities 52 and 19.6 cm/s: column temperature 90 O C .
20
RETENTIONTIME IMINUTES)
Figure 7. Separation of seven substituted benzenes. Columns: 30m X 0.25-mm X 0.25-pm OV-1 and 30-m X 0.25-mm X 0.50-pm Carbowax plus 30-m retention gap. Inlet pressure 20 psl; velocities 17.2 and 35.0 cm/s; column temperature 100 O C .
0
5
io
15
20
RETENTION TIME lMlNLmSl
I
sa
c,
0
5 RETENTlON TlME (MINUTES)
FIgwo 6. Separatbn of fivecomponent mixture. Columns: 3O-m X 0 . 2 5 " X 0.25-wm OV-1 and 3O-m X 0 . 2 5 " X 0.25-~unCarbe wax plus 30-m capiliaty tubing. Inlet pressure 20 psi; velocities 17.2 and 35.0 cm/s; column temperature 100 O C .
was 20 psi, the carrier velocities in the two columns were 35.0 and 17.2 cm/s, respectively. (The velocity ratio, 2:1, is equal to the ratio of column lengths or pressure drops.) The resulting chromatogram for the five-componenttest mixture is shown in Figure 6. Although the retention gap is smaller, the resolution is the same for both columns, as expected. When the above column system was used for the separation of the seven substituted benzenes, the retention gap was less than 1min. Therefore, the Carbowax column of 0.25-pm film thickness w a ~ replaced by a column of 0.5-pm film thickness. As the resulting chromatogram shows, Figure 7, there is a 3-min retention gap between the two portions of the chromatogram and the resolution is excellent.
Figure 8. Separation of polar test mixture. Columns and conditions as In Figure 8.
The same column system was also tested by using the six-component polar mixture, and the results are shown in Figure 8. The retention gap between the two portions of the chromatograms is approximately 7 min, and the resolution is very good, except for the coelution of two compounds on the OV-1 column as the second peak of the chromatogram. Columns of Equal Length,Diameter, and Thickness. In this case, the two columns differed only in that one was OV-1 and the other Carbowax 20M. All the other characteristics including carrier velocity and phase ratio were the same. Thus, any gap between the consecutive chromatograms would depend only on the difference in the partition coefficients of the componenta of the sample and the liquid phase. As shown in Figure 9, the five-component mixture is eluted with no overlap between the two portions of the chromatograms; the peaks of both portions of the chromatogram are similar in shape and thus indistinguishable from each other. If Figure 9 is compared with Figures 3 and 5 in which the same sample is chromatographed, the importance of having a dif-
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’0
. *
5
0
v1
R m N T l O N TlME (MINUTES)
Flgurr B. Separation of five-component mixture. The two columns
are identical except one is Carbowax and the other OV-1. Inlet pressure 18 psi; velocity 29.4 cm/s; column temperature 85 O C . s
Figwe 11. Separation of bbod alcohols. Columns: 3O-m X 0.25-mm X 0.25-pm OV-1 and 30-m X 0.25” X 0.50-pm Carbowax 30M plus 30-m retention gap. Inlet pressure 22 psi; velocities 40.0 and 10.0 cmls; column temperature 45 OC.
Table IV. Comparison of Plate Heights (Millimeters) in Single and Parallel Columns single columns
parallel columns
0
ov-1 df = 0.25 pm u = 30 cm/s 0.35 0.36 0.40
carbowax df = 0.5 fim u = 30 cm/s 0.60 0.51 0.55
5
10
20
15
RETENTION TlME (MINUTES1
Flgure 10. Separation of five-component mixture. Columns: 30-m X 0.25-mm X 0.25-pm OV-1 and 30-m X 0.25” X 0.50-pm Carbowax 20M plus 30-m retention gap. Inlet pressure 30 psi; velocities 50.0
and 25.0 cm/s; column temperature 85
OC.
ferent liquid-phase thickness, or different column length, or both, is apparent. This is demonstrated in Figure 10 in which the two columns differ in both liquid-phase thickness and length (retention gap). In many ways, this approaches the ideal separation. There is a good retention gap between the two portions of the chromatogram, and all the peaks have approximately the same plate number. Analysis of Blood Alcohols. In order to test the twocolumn system with a ‘real world” sample, a five-component
df = 0.25 pm u = 40 cm/s 0.35 0.30 0.49 df = 0.5 pm u = 20 cm/s 0.34 0.33 0.31
mixture of blood alcohols and their metabolites was prepared in hexane as the solvent. The resulting separation, Figure 11, shows a complete separation gap between the two chromatograms, including the solvent peak, which owing to ita completely nonpolar nature elutes last in the first chromatogram and first in the second chromatogram. Comparison of Column Efficiencies. Because the two parallel columns in every case are operating at different carrier velocities, the common inlet pressure was adjusted so that the carrier velocity in one column is above and the other is below the optimum. For this reason, and also because the film thicknesses are different in the two columns, there is some question as to whether there is significant degradation in plate height compared to that obtained when each column is operated separately at optimum carrier velocity. Plate height measurements were made with each column operating singly a t 30 cm/s (optimum) and also when connected in parallel where one column was operating at 40 cm/s and the other at 20 cm/s. The results for a three-component mixture, tetradecane, 1-octanol,and 5-nonanone, are shown in Table IV. Under the conditions used in this test (0.2-mL injection, 501 splitting), there is little change in plate height
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between single and parallel columns. (The higher efficiency observed when the Carbowax column is operating in parallel may be the result of two factors: (a) owing to the lower flow rate, only one-third of the total injected sample is channeled through this column, and (b) the lower carrier velocity of 20 cm/s is near the optimum level for 0.5pm liquid film thickness.)
CONCLUSIONS There are a number of ways in which the difference in carrier velocities and capacity factors between two parallel capillary columns of dissimilar liquid phase may be set 80 that the resulting chromatograms do not overlap. Simply using two columna of unequal length or unequal inside diameter or both is not as satisfactory as using columns of unequal liquid-phase thickness and adding a retention gap to the column with the thicker liquid phase. Samples containing several components of low polarity can be satisfactorily resolved on the two-column system if the low thickness phase is the polar column (Carbowax 20M). The reverse holds for high polarity samples. Samples of intermediate polarity and narrow polarity range, or containing fewer components, can be satisfactorily resolved on either system.
(3) WtSCh. W. TwOdknsnsknel T e c h n i q ~ .R M t I n Cepillarv Qas Clwometopaphy; Huethb Betlag: Heidelberg. Germany, 1981;pp 3-56. (4) Mdven. U. F.; Cooper, W. J.; W a n . M.; Maz. R. J . &$I Res. chromaw.1984, 7,639-40. (5) Jennlngs, W. G.; Shlbamoto, T. OuelldpbrveAna!~sl6of Flew and Frawnce VdenVes by &I? Capby c)vcwnatOgaphy;Academlc Press: New York, 1980,chepter I. (6) TSI, M. Y.; CatherlM. C. Ckh. chem. 1989, 35, 1989-1991. (7) Tsal, M. Y.; Oliphant, C.; Josephson, M. W. J . Cfiromatogr. 1985, 347,l-10. (8) Watts, V. W.; Simonlck, R. F. J . Ana/. Toxlc4. 1088, 10, 198-204. (9) Perrigo, B. J.; Peel, H. W.; Ballantyne, D. J. J. chrometog. 1985, 341.81-88. (10) Baker, J. K. Anal. Chem. 1977. 49, 906-910. (11) Dulnker, J. C.; Schulr, D. E.; Petrlck, 0. Anal. Chem. 1988. 60, 478-482. (12) Schulte, E.; Malisch, R. Fresenius' Z . Anal. Chem. 1989, 311, 545-555. (13) Sefe, S.;Bandlera. S.; Sawyer, T.; Robertwon. L.; Sage, L.; Parkinson, A.; Thomas, P. E.; Ryan, D. E.; Reik, L. M.; Levkr, W.; Denomme, M. A.; Flgb, T. EHP. EnvLon. Heellh Perspect. 1985,60,47-56. ( 14) Leece, B.; Denomme, M. A.; Towner, R.; Angela, Ll S. M.; Sage, S. J . T o x h l . &&on. Health 1965, 16, 379-388. (15) M y . M. J. E., In Gas " I t O g * e p h y ; Coates. V. J., Noebels, H. J., Gerguson, I. S., E a . ; Academic Press: New York, 1958; pp 1-13. (16) Hlnshaw, J. LC-GC 1989, 7,237-240. (17) Enre, Leslle Open Tubhr cduvnns I n Ges Chromatography; Plenum Press: New York, 1965;Chapter 2. (18) Jennlng, W. G. Ana&tkal Gas chrometogrephy; Academlc Press: New York, 1980;Chapter 6.
LITERATURE CITED (1) Schombwg, 0.;Husmann, H. ClwometoqepMe 1975,8 , 36. (2) Jennlngs, W. (3. Ana&?!caI Gas chrometobxephy; Academic Press: New York, 1980:Chapter 1.
RECEIVED for review January 7,1991. Accepted March 28, 1991.
Confidence Limits for the Abscissa of Intersection of Two Least-Squares Lines Such as Linear Segmented Titration Curves Kenneth N. Carter, Jr.,* Dan M. Scott,' Jon K. Salmon, and Gregory S. Zarcone Division of Science, Northeast Missouri State University, Kirksville, Missouri 63501
The confidence limits for the abscissa of the Intersection of two Ieadsquarw lines, such as linear segmented tltratlon curves, are cakuiated by udng a rknple method, based on the Interuction of confidence bands, that always overedlmates the wldth of the confidence Interval, and by'udng a more accurate computatlonally Intenrlve method based on Integratlon of the transformed bivariate normal distribution (Le.,Creasy's method). Numerical results obtalned by a p plying the forogolng methods to experhntai and simulated data are compared wlth thoro obtained by Fkller's theorem and H o r d o r propagation of variance as previously applied in the primary chemical Mrature. A dkcrepancy k resolved by correcting the poollng of varlance In the prior work. Rebtlonrhlpr between the various methods are shown. Fldkr's method, wlth proper pooling, gives reliable results unless the data are very noisy, whereas Creasy's method glves finlte inciuslve confldence intervals even when Fkiier's method falls.
INTRODUCTION For many analytical methods, including conductometric, amprometric, and spectrophotometric titrations and the Gran
* To whom corres ondence should be addressed.
De artment o f Industrial Engineering, University of Nebrasia-Lincoln, Lincoln, NE 68588.0518. 0003-2700/91/0383-1270$02.50/0
plot method for potentiometric titrations, the titration curve consists (essentially) of two joined lines, the changeover point being the endpoint. This end point is estimated by the abscissa of intersection of the least-squares straight lines that are fit to the experimental points for each segment. We will aasume that the assignment of each point to one line segment or the other is known, and that the abscissa of intersection will therefore lie between the largest x value of one set and the smallest x value of the other. (We will later examine this very big assumption.) At the point of intersection, the two lines y1 = al + blx and yz = a2 + b2x have the same ordinate, from which it follows that the abscissa of intersection, henceforth denoted by uppercase X,is given by
Random errors in the points produce uncertainty in the slopes and intercepts of the lines and therefore in the point of intersection. The uncertainty of the end point can be expressed as a confidence interval for the abscissa of intersection. The probability that a confidence interval contains the true value is equal to the confidence level (e.g., 95%) chosen. Our initial cursory search of the literature via the DIALOG Chemical Abstracts database in the mid 1980s did not reveal any published methods. Our first approach, based on intersecting confidence bands about each line, gave intervals that were clearly too wide, but 0 1991 American Chemical Soclety
