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Optimization via Liquid Phase Mixtures in Capillary Gas Chromatography G. Takeoka, H. M. Richard’), Mehrzad Mehran2),and W. Jennings* Department of Food Science and Technology, University of California, Davis CA 95616, USA

Key Words: Binary phase mixtures Coupled capillary columns Velocity gradient Mixed liquid phases Optimization

Summary The use of sequentially coupled columns to achieve a binary liquid phase mixture has been simplified by the availability of zero dead volume fittings compatible with fused silica columns. The extent to which the velocity gradient through the coupled column affects the “apparent” liquid phase ratio can be determined by graphic interpolation; the length ratio of the coupled column segments can then be adjusted so that the “apparent” liquid phase ratio actually experienced by the solutes agrees with the targeted value. The f8Ct that the direction of flow through the coupled column affects the chromatographic dispersion suggests that accepted generalizations on flow optimization throughout the column may not be precisely correct.

1 Introduction The use of binary liquid phase mixtures to optimize separations has been the subject of several recent investigations (e.g. [1-5]). These efforts are based on two concepts first proposed by Maier and Karpathy [6]:1), that the distribution constant of a solute in a mixture of two liquid phases is the sum of the products of the distribution constant in each of these phases times the volume fraction of that phase, and 2), that the desired mixture could be obtained either by using a column containing the prescribed liquid phase mixture, or by coupling appropriate. lengths of columns containing one or the other of those phases. Laub and Purnell [ A then proposed that “window diagramming” be employed to establish the relative retentions of limiting solute pairs at any concentration of either liquid phase. lngraham eta/. [3] pointed out that a distinct advantagewas realized by coupling predetermined lengths of dissimilar columns to achieve the desired ratio of the two liquid phases:readily availablecolumns of specified quality could be used, obviating the usually onerous task of preparing a special column of unknown quality for each particular task. While various methods of coupling columns have been Permanent addresses: Ecole National Superieure des IndustriesAgricoles et Alimentaires, F-91305, Massy, France. 2, Drinking Water Research Laboratory, Florida International University, Miami, FLA 33199, USA.

0 1983 Dr. Alfred Huethig Publishers

suggested, the task has been greatly simplified by the introduction of a zero-deadvolumefitting suitable for fused silica capillary columns (Valco Instruments, Inc., Houston TX) ~51. While the velocity gradient through the column does cause complications, these are not insurmountable, as pointed out in the present paper. Once the separation is optimized, attention can be directed toward minimizing the analysis time. The method has particular utility for routine repetitive separations of mixtures that can be chromatographed under isothermal conditions.

2 Experimental Columns: Two columns were used for the initial separations: one was 30 m X 0.327 mm ID, containing a 0.25 pm film of DB-1(bonded, crosslinked polymethyl siloxane), and theotherwas30m X0.32mmID,coated witha0.25prnfilm of DB-1701 (bonded, crosslinked 7% phenyl, 7% cyanopropyl, polymethyl siloxane). Both were obtained from J&W Scientific, Rancho Cordova, CA. Gas Chromatography: A Hewlett Packard 5880, converted to capillary via an inlet splitter kit (J&W Scientific, Inc.) was used with flame ionization as the detection mode. Test Solution: Approximately equal quantities of the following solutes were mixed together and diluted with dichloromethane: ethyl hexanoate, ethyl octanoate, geranial,geraniol,limonene, linalylacetate, myrcene,neral, nonanol, octanal, octyl acetate, and terpinen-4-01,

3 Results and Discussion Figures 1 and 2 show chromatograms typical of the separations obtained on each of the two columns. On the DB-1column (Figure l ) ,ethyl hexanoate, octanal, and myrcene emerge as a single peak nonanol and terpinen-4-01, and geranial and linalyl acetate are but partially separated; analysistime at uoptis 25 minutes.On the DB-1701column (Figure 2), the analysis time is increasedto 57 minutes,and while the ethyl hexanoate, octanal, and myrcene are now resolved, ethyl octanoate and terpinen-4-01 elute as a single peak, as do nonanol and octyl acetate.

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Distribution constants were calculated from the relation= pk, and plotted as shown in Figure 3. In the lower ship section, the bottom portion of the figure is replotted with a five-fold vertical scale expansion to permit comparison of the four leading solutes. The window diagramming method of Laub and Purne//[7] as applied to these results is shown in Figure 4; two approximately equivalent windows are apparent, one at 25, and the other at 66, volume percent DB-1701.

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Equations for initially estimating the appropriate column lengths where the phase ratios of the two columns differ were presented by lngraham et a/. [3], but as originally presented, those equations suffered a misprint. The correct representations are:

and

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Figure 1 Chromatogram of the test mixture on 30 m X 0.327 mm column coated with a 0.25 pm film of DB-1. Helium carrier, ii = 30 cm/s; isothermal at 8OOC.

Examination of Figures 1 and 2indicates there should be no problem in maintaining partition ratios of at least k = 2.5for the limiting solutes; the window diagram indicates that the proper column length ratio should result in a relative retention a = 1.05 for the most limiting solutes. Application of the resolution equation nreq= 16 Rs2

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shows that some 31,000 theoretical plates would be required to separate this mixture underthese conditions, a goal readily attainable even with a short capillary column system.

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7500 Plots of solute distribution constants on (left ordinate) DB-I, and (right ordinate) DB-1701 at 8OOC. The four leading solutes are re-plotted with a five-fold vertical scale expansion on the

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Optimization via Liquid Phase Mixtures in Capillary GC velocity gradient operating through the column. Because the carrier gas velocity is lowerthan the average at the inlet end, and higher than the average at the outlet end, Ingraham eta/. [3] postulated that the solutes encountered (per unit of column length) more solubility sites at the inlet end, and fewer solubility sites at the outlet end, than would be expected. Hence the inlet end would contribute more (and the outlet end would contribute less) to the separation than would be predicted on the basis of length fractions alone.

Based on this information, a 6.8 m length of a DB-1 column, 0.262 mm ID with a0.25 pm film, was connected with a 15 m length of the DB-I701 column; Figure 5 shows the result when (top) the DB-1 end was connected to the inlet. While separation is essentially complete, the dispersion of the limiting solutes is not ideal; e.g. the relative retention of ethyl hexanoate and limonene could be larger, at the expense of the limonene-octanal separation. The analysis time was 36 min. Figure 5 (bottom) shows the chromatogram obtained when that same column was reversed, i.e. the DB-1701segment connected to the inlet. Dispersion of the ethyl hexanoate-limonene pair is adversely affected to a considerable degree.

The inter-relationships of the gradient and the accompanying gas density gradient have been the subject of considerable discussion (e.g. [8,9]), and it has been suggested that because of these inter-relationships, the carrier gas velocity is optimized throughout the column if it is optimized at one point (i.e.,at uopt).Thereasoning is that because the gas density is higher, diffusivity is lower in that portion of the column where the velocity is lower than optimum. Solutes spend more time per unit of column length, but more time is required for the mass transport (lateral diffusion) step; because the higher gas density inhibits band broadening due to longitudinal diffusion, the longer time can be tolerated. Similarly, during passagethrough the high velocity section of the column, less time is required for the lateral diffusion step because of the lower gas density, and because the solutes are moving at a faster rate, there is less time for longitudinal diffusion at this lower gas density. Both of the chromatograms in Figure 5 were obtained at an average linear carrier gas velocity of 30 to 32cm/s, which is at or very close to the optimum gas velocity for helium,

The fact that the chromatographic dispersion is altered as has been when a coupled column is reversed Previously discussed 1317 most Probably attributable to the

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calculated fora column of these average dimensions and a solute partition ratio of k = 2.8. It is interesting that it is in this region that the differences caused by column reversal are most apparent. The less-than-perfect dispersion indicates that, probably because of the velocity gradient complications, the “apparent” liquid phase mixture offered by the coupled column is not that defined by the window diagram. The composition of the “apparent” liquid phase mixture can be determined by comparing the relative retention exhibited by any two solutes with that indicated by the window diagram; it would be preferable to use a solute pair that undergoes a major change in relative retention with a minor change in liquid phase ratio. The relative retentions of the solute pair nonanol and ethyl octanoate are plotted by the line beginning at a = 1.15 (right hand ordinate), dropping to a point denoting ca. 48 volume percent DB-I701 on the abscissa, and then rising sharply to the upper left. At the desired “apparent” liquid phase ratio, the relative retention of this pair should be 1.05. Their relative retention, as determined from Figure 6, is actually 1.085. Hence the “apparent” liquid phase ratio is either 45.7, or 76.1 volume percent DB-1701, as these are the only points where the relative retentions of those two solutes are 1.085. Because the DB-I701 end was connected to the inlet, it seemed

probable that the latter value was correct, owing to the reasons detailed above. The results of removing short segments of the (DB-1701) inlet end are shown by the insets in Figure 6; the chromatogram at the upper right shows the initial separation, where a = 1.085 for nonanolethyl octanoate. As short sections (ca.2 m each) of the inlet segment were successively removed, the relative retention of this pair shifted to 1.073, to 1.061, to (bottom inset) 1.05. At this point, the “apparent” liquid phase mixture is the same as the targeted one. Figure7shows the chromatogram on this coupled column, which consisted of 6.8 m of DB-I plus 7.3 m of DB-1701 (inlet end), using hydrogen carrier gas. Because the dispersion is now optimized, separation is greater than required and some resolution can be sacrificed in the interest of shorter analysis times. Normally three routes can be employed toward this end: higher temperatures, higher-than-optimum carrier gas velocities, or shorter columns.The first is not possible in this case, as a temperature change would cause a shift in distribution constants and relative retentions, on which this whole scheme was based. The optimum practical gas velocity (OPGV) for our most limiting solutes (which exhibit an average k = 2.8) is 88 cmls with hydrogen carrier, and, as indicated in Figure 8, the loss in platesls at even higher

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Figure 6 Method of adjusting the “apparent” liquid phase ratio by successively removing short segments from the inlet end of the coupled column. Insets show partial chromatograms of 6.8 m DB-1 plus (upper right) 15 m DB-1701; 10.6 m DB-1701 (center right); 8.4 m DB-1701 (bottom right); and 7.3 m DB-1701 (bottom left). Journal of High Resolution Chromatography& Chromatography Communications

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TIME IN MINUTES

Chromatogramof the test mixture on the coupled column described in Figure 7, ii = 93 cm/s.

Figure 7 Chromatogram of the test mixture on the coupled column composed of a 6.8 m X 0.262 mm DB-1 segment plus 7.3 m X 0.32 mm DB-1701 segment (inlet end). Hydrogen carrier at ii = 40 cm/s; isothermal at 8OOC.

velocities is not serious. Figure 9 illustrates the separation on this same column a t u = 93cmIs; analysis time has been reduced from 17 to 7 min, and in Figure 10, the analysis time is reduced to 4.9 min at a carrier gas velocity of U = 132 c m k . In this latter case, the chart speed was stepprogrammed, producing a non-linear time scale. Figure 11 shows the result of using shorter column segments. The column consisted of 2.9 m of DB-1701 plus 3.1 m of DB-1, and was operated at an average linear carrier gas velocity of 94 cm/s; analysis time was 2.9 min.

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Acknowledgments The computer programs employed in this study were written by D. F. Ingrabam, present address Phillip Morris Research Center, PO Box 26583, Richmond VA 23261, as a portion of his thesis endeavors [lo].



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Figure 10 Chromatogramof the test mixture on the column described in Figure 7, ii = 132 cm/s. The chart speed was programmedas indicated.

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Figure 11 Chromatogramof the test mixture on a coupled column composed of a 2.9 m X 0.32 mm DB-1701 segment (inlet end) plus a 3.1 m X 0.262 mm DB-1 segment; ii = 94 cmls; isothermal at 8OOC.

References J. Krupcik, G. Guiochon, and J. M. Schmitter, J. Chromatogr.

213 (1981)189. J. Krupcik, J. Mocak, A. Simova, J. Garaj, and G. Guiochon, J. Chromatogr. 238 (1982)1.

D.F. Ingraham, C. F. Shoemaker, and W. Jennings, J. Chromatogr. 239 (1 982)39. R. C. Kong, M. L. Lee, Y. Tominaga, R. Pratap, M. Iwao, R. W. Castle, and S. A. Wise, J. Chromatogr. Sci. 20 (1982)

502. W. Jennings, paper presented at the symposium “Capillary Chromatography 1982”, Tarrytown, New York, October 4-6,

1982. Journal of High Resolution Chromatography & Chromatography Communications

H. J. Maier and 0. C. Karpathy, J. Chromatogr. 8 (1962)308. R. J. Laub and J. H. Purnell, Anal. Chem. 48 (1976)799. J. C. Giddings, Anal. Chem. 36 (1964)741.

J. C. Sternberg, Anal. Chem. 36 (1964)921. D. F. Ingraham, “Theoretical and Practical Considerations of Some Aspects of Gas Chromatographic Optimization” (1981).Thesis submitted in partial satisfaction of the requirements for the Ph. D. degree in Agricultural and Environmental Chemistry, University of California, Davis.

MS received: December 20,1982 Accepted by REK

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