Separation Orthogonality in Temperature-Programmed

Since the potential peak capacity of a multidimensional chromatogram is the .... of DB225 (50% cyanopropylphenylmethylpolysiloxane; J&W Scientific, Fo...
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Anal. Chem. 1996, 68, 1486-1492

Separation Orthogonality in Temperature-Programmed Comprehensive Two-Dimensional Gas Chromatography C. J. Venkatramani,† Jingzhen Xu, and John B. Phillips*

Department of Chemistry and Biochemistry, Southern Illinois University, Carbondale, Illinois 62901-4409

In a comprehensive two-dimensional gas chromatograph, a thermal modulator serially couples two columns containing dissimilar stationary phases. The secondary column generates a series of high-speed secondary chromatograms from the sample stream formed by the chromatogram eluting from the primary column. This series of secondary chromatograms forms a two-dimensional gas chromatogram with peaks dispersed over a retention plane rather than along a line. The method is comprehensive because the entire primary column chromatogram is transmitted through the secondary column with fidelity. One might expect that a two-dimensional separation in which both dimensions are basically the same technique, gas chromatography, would be inefficient because the two dimensions would behave similarly, generating peaks whose retentions correlate across dimensions. Applying a temperature program to the two columns, however, can tune the separation to eliminate this inefficiency. The temperature program reduces the retentive power of the secondary column as a function of progress of the primary chromatogram such that the retention mechanism of the primary column is eliminated from the second dimension. Retention of a substance in the second dimension is then determined by the difference in its interaction with the two stationary phases. Retention times in the second dimension then fall within a fixed range, and the whole retention plane is accessible. In a properly tuned comprehensive two-dimensional chromatogram, retention times in the two dimensions are independent of each other, and the two-dimensional chromatogram is orthogonal. Orthogonality is important for two reasons. First, an orthogonal separation efficiently uses the separation space and so has either greater speed or peak capacity than nonorthogonal separations. Second, retention in the two dimensions of an orthogonal chromatogram is determined by two different and independent mechanisms and so provides two independent measures of molecular properties. Chromatographic techniques that separate mixtures in more than one dimension are potentially very powerful for the analysis of complex mixtures. Since the potential peak capacity of a multidimensional chromatogram is the arithmetic product of the peak capacities of the constituent dimensions, extremely large peak capacities can be obtained even if the constituent dimensions † Present address: Chemir/Polytech Laboratories, Inc., 2672 Metro Blvd., St. Louis, MO 63043.

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each have only modest peak capacities.1 A multidimensional separation actually generates this theoretically available peak capacity, however, only if the retention mechanisms in the constituent dimensions are independent of each other. Retention correlation across dimensions reduces the useful peak capacity to some fraction of that theoretically available. A high degree of retention correlation can reduce a multidimensional separation to what is, in effect, a one-dimensional separation with peaks distributed along a diagonal. An information theory analysis shows that the information content of a multidimensional system is the sum of the mean information content of each individual dimension minus the crossinformation.2 Minimizing cross-information, or synentropy, is important in multidimensional separations. If synentropy is large, much of the separation space is unoccupied or even completely inaccessible, and sample components tend to cluster along a diagonal. Generating inaccessible peak capacity wastes time and reduces the efficiency of the multidimensional separation. Minimizing synentropy maximizes the efficiency of information generation. An orthogonal multidimensional separation is one in which the constituent dimensions are uncorrelated and synentropy across dimensions is zero. In an orthogonal separation, the constituent dimensions operate independently, and the usable peak capacity equals the product of the constituent dimensions’ peak capacities. Hyphenated techniques, such as gas or liquid chromatography coupled to mass spectrometry or infrared spectroscopy, resemble multidimensional separations. Although the spectroscopic dimension does not physically separate chemical substances, it does disperse a signal along the spectroscopic axis. This signal is determined by the identity of substances and provides a separation in the technique’s data space. The data generated by a hyphenated technique often are presented in a planar form, with one independent dimension being a separation and the other a spectrum. It is commonly believed that coupled methods in hyphenated instruments can be made nearly independent of each other by combining methods that are as different as possible;1-3 GC/MS is then a good hyphenated instrument because mass spectrometry as an analytical method has little resemblance to gas chromatography. The chromatographic and spectroscopic dimensions provide different kinds of information and might be expected to be nearly orthogonal. However, having two dimensions operate (1) Giddings, J. C. In Multidimensional Chromatography: Techniques and Applications; Cortes, H. J., Ed.; Marcel Dekker: New York, 1990; pp 1-27. (2) Erni, F.; Frei, R. W. J. Chromatogr. 1978, 149, 561-569. (3) Bushley, M. M.; Jorgenson, J. W. Anal. Chem. 1990, 62, 978-984. 0003-2700/96/0368-1486$12.00/0

© 1996 American Chemical Society

on different principles does not guarantee that they are orthogonal. In GC/MS, for example, smaller molecules, which produce ions of low mass-to-charge ratio, also tend to be more volatile and so have low gas chromatographic retention. Both chromatographic retention and mass-to-charge ratio are correlated with molecule size and, thus, are correlated with each other. The hyphenated technique produces more information than either constituent instrument alone, but the technique is not orthogonal and does not make efficient use of the data space. Synentropy between the GC and MS dimensions is substantially greater than zero. Hyphenated techniques in general can be powerful in the right application, but they are usually not orthogonal. Planar chromatography is a practical implementation of a comprehensive two-dimensional separation in which both dimensions are chromatographic. It is a particularly convenient implementation because the second dimension separation occurs in parallel.4 Chemical strategies for creating an orthogonal separation in planar chromatography have been discussed by Guiochon et al.5 Conventional multidimensional gas chromatography using coupled columns (heart-cutting) is a multidimensional separation, but only a fraction of the primary column eluant is sampled into the secondary column for further separation.6 The rest of the sample is either discarded or subjected to only single-column separation. Although this technique provides high-resolution separation of target compounds from a complex mixture, it is not comprehensive. Most of the separation space is not recorded because the second dimension separation is not significantly faster than that in the first dimension. Unlike with hyphenated techniques, the second dimension does not increase the rate of information production. Peak capacity is at best equal to the sum of the peak capacities of the constituent dimensions. Gordon et al. extended the capability of multidimensional gas chromatography toward a total analysis of a complex tobacco essential oil by taking a sequential series of heart-cuts from a series of primary column chromatograms.7 Completing the analysis in reasonable time requires that relatively broad cuts be taken from the primary chromatogram. Much of the primary column resolution is lost, and the separation is not comprehensive. Wilkins et al. used a series of cold traps to store multiple cuts from one primary column chromatogram until they could be sequentially processed through a secondary column.8 The small number of traps available limits the resolution that can be obtained from the first dimension, and, again, the method is not comprehensive. In comprehensive two-dimensional gas chromatography, the second dimension separation is applied to the entire eluant stream emerging from the primary column. The technique is related to conventional coupled column chromatography in that both dimensions are gas chromatography, but it also resembles hyphenated methods and planar chromatography in that it generates com(4) Poole, C. F.; Poole, S. K. In Multidimensional Chromatography: Techniques and Applications; Cortes, H. J., Ed.; Marcel Dekker: New York, 1990; pp 29-73. (5) Zakaria, M.; Gonnord, M. F.; Guiochon, G. J. Chromatogr. 1983, 271, 127192. (6) Schomburg, G. LC-GC 1987, 5, 304. (7) Gordon, B. M.; Uhrig, M. S.; Borgerding, M. F.; Chung, H.; Coleman, W. M., II; Elder, J. F., Jr.; Giles, J. A.; Moore, D. S.; Rix, C. E.; White, E. L. J. Chromatogr. Sci. 1988, 26, 174-180. (8) Ragunathan, N.; Krock, K. A.; Wilkins, C. L. Anal. Chem. 1993, 65, 10121016.

Figure 1. Schematic of a hypothetical comprehensive twodimensional gas chromatograph equivalent to a planar chromatograph.

prehensive data. One might expect comprehensive two-dimensional gas chromatography using coupled columns to be far from orthogonal, and thus inefficient, because the two dimensions are closely related. If significant synentropy exists in GC/MS, then GC/GC, especially that using columns which differ only a little in retention mechanisms, should be much worse. Volatility is the most important determinant of a substance’s retention; being a property of the substance, volatility remains constant through all the coupled columns. This expectation is incorrect.9-14 Varying the retentive power of the second dimension as a function of progress of the first dimension separation (by, for example, increasing the temperature of the secondary column) can eliminate any retention mechanism in common from the second dimension separation. The entire retention space is then accessible, allowing greater efficiency, which improves speed of separation or peak capacity or both. More subtle differences in sample properties, such as polarity and molecule shape, determine retention in the second dimension, making secondary column retention a measure of these molecular properties. THEORY Figure 1 shows the design of a hypothetical comprehensive two-dimensional gas chromatograph. Similar instrument designs have been discussed previously by Giddings.1 In this design, an array of stream switching valves sequentially transfers sample portions eluting from the primary column into an array of identical secondary columns for further separation. The head of each (9) Phillips, J. B.; Liu, Z. J. Chromatogr. Sci. 1991, 29, 227-231. (10) Phillips, J. B.; Liu, Z. U.S. Patent 5,135,549, 1992. (11) Phillips, J. B.; Liu, Z. U.S. Patent 5,196,039, 1993. (12) Phillips, J. B.; Venkatramani, C. J. J. Microcolumn Sep. 1993, 5, 511-516. (13) Liu, Z.; Sirimanne, S. R.; Patterson, D. G., Jr.; Needham, L. L.; Phillips, J. B. Anal. Chem. 1994, 66, 3086-3092. (14) Phillips, J. B.; Xu, J. J. Chromatogr. A 1995, 703, 327-334.

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Figure 2. Simulated comprehensive two-dimensional gas chromatogram showing the influence of temperature on sample retention.

secondary column connects to a carrier gas supply (not shown). The outlet of each secondary column connects to a corresponding detector in an array of detectors. The array of detectors generates a set of secondary chromatograms in parallel. If the number of secondary columns, stream switching valves, and detectors is substantially greater than the peak capacity of the primary column, then the set of secondary chromatograms forms a comprehensive two-dimensional chromatogram. This planar set of secondary chromatograms is equivalent in the form of the data to the data generated by a planar chromatography. The number of secondary chromatograms must be sufficient to preserve the primary column separation during passage through the second dimension of separation. Currently, building an instrument of this type is impractical, but the design is the most general way to build a true comprehensive two-dimensional gas chromatograph and is useful in explaining the orthogonality tuning process of comprehensive two-dimensional chromatography. Figure 2 illustrates several simulated two-dimensional gas chromatograms (shown as contour plots) that could be generated by the hypothetical instrument of Figure 1. Changing the operating conditions, especially the column temperatures, redistributes sample components over the retention plane. With both dimensions isothermal, sample components distribute about a diagonal as shown in Figure 2A. Since volatility, a property of the sample substance and not of the stationary phase, is the primary determinant of retention in gas chromatography, the two retention dimensions are correlated. The situation is analogous to planar chromatography operated such that there is little difference in the retention characteristics of the two separation axes. A substance strongly retained in the primary column is likely to be strongly retained in the secondary column, and a substance weakly retained in the primary column is likely to be 1488

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weakly retained in the secondary column. Most of the retention plane is inaccessible, and the separation efficiency is poor because the method is far from orthogonal. Since the separations are isothermal, peak duration, shape, and intensity depend on retention in the two dimensions. Early-eluting peaks are sharp and intense, while later ones are broad and low. The real peak capacity of this system is a small fraction of its potential peak capacity. Large retention synentropy collapses the two-dimensional separation to little more than one dimension, which lies along the diagonal. The extent of scatter about the diagonal depends both on the degree of dissimilarity of the two stationary phases and on the range of substances present in the sample. The example presented in Figure 2A has a high degree of correlation to more clearly illustrate the operation of the method. A high degree of correlation such as this is realistic for many important sample mixtures. The chromatogram in Figure 2B is similar to that in Figure 2A, except that the temperature of the array of secondary columns is incremented from column to column. Alternatively, we could reduce the thickness of the stationary phase or increase the carrier gas linear velocity from column to column. The more volatile components eluting early from the primary column are sampled into low-temperature secondary columns, while less volatile components are sampled into higher temperature secondary columns. The progressive increase in secondary column temperature compensates for the progressive decrease in sample volatility. This rotates the diagonal in Figure 2A into a vertical in Figure 2B, as indicated by the arrows. Tuning the retentive power of the second dimension as a function of retention in the first dimension eliminates the influence of sample substance volatility on retention in the second dimension. The dashed rectangle delimits the accessible area of the retention plane. Figure 2C is another variation of the separation in Figure 2A. Here, the primary column is temperature programmed, while the secondary columns are all at the same temperature. This causes the diagonal in Figure 2A to curve downward. The dashed rectangle again delimits the accessible area. The temperature program sharpens later-eluting peaks so that all peaks have the same first dimension duration and the members of an homologous series elute at approximately equally spaced retention times. The chromatogram in Figure 2D would result from simultaneously programming the temperature of the primary column, as in Figure 2C, and incrementing the temperature of the secondary columns from column to column, as in Figure 2B. This confines the peaks within a smaller area, but within this area, peaks are well distributed and retention times in the two dimensions are independent of each other. The two-dimensional chromatogram in Figure 2D is orthogonal because retention in the second dimension is now independent of retention in the first dimension. Much of the original chromatographic plane of Figure 2A is now completely inaccessible. Efficiency is substantially improved because the inaccessible regions are clearly distinct from the occupied region and can be left unrecorded. The hypothetical instrument shown in Figure 1 and discussed above is a good way to explain how comprehensive twodimensional gas chromatography can be made orthogonal, but it is not practical. The method can be made practical by replacing the array of secondary columns with a single, very fast secondary column, as shown in Figure 3. Instead of generating the secondary chromatograms in parallel, the single fast secondary

Table 1. Symbols Used in the Two-Dimensional Chromatograms

Figure 3. Schematic of a comprehensive two-dimensional gas chromatograph with an on-column thermal desorption modulator interface. The secondary column generates a series of high-speed chromatograms throughout the period of the primary column separation.

symbol

compound name

symbol

compound name

P1 P2 P3 P4

n-decane n-dodecane n-tridecane n-tetradecane

OH1 OH2 OH3 OH4 OH5

1-heptanol 1-octanol 1-nonanol 1-decanol 1-undecanol

O1 O2 O3 O4

1-decene 1-dodecene 1-tridecene 1-tetradecene

A1 A2 A3 A4

benzaldehyde naphthalene ethyl phenyl acetate biphenyl

N1 N2

tert-butylbenzene durene

column generates them in series as sample portions elute from the primary column. The duration of each secondary chromatogram is less than the duration of bands emerging from the primary column. Temperature incrementing can be done by raising the temperature of the secondary column from chromatogram to chromatogram. With appropriately chosen column dimensions and stationary phase thicknesses, the secondary column operates at the same temperature as the primary column, and both columns can be placed in the same chromatographic oven. EXPERIMENTAL SECTION Instrumentation. An IBM dual-oven gas chromatograph equipped with a flame ionization detector was used. A thermal modulator connecting the two columns was mounted between the two ovens.15 The details of this modulator will be described elsewhere. A Macintosh IIci computer (Apple Computer, Cupertino, CA) equipped with an NB-MIO-16X interface card and LabVIEW 2 software (National Instruments, Austin, TX) was used for data acquisition. Spyglass Transform and Format software (Spyglass, Champaign, IL) were used to prepare two-dimensional plots. A 3 m long, 530 µm i.d., open tubular column with a 5 µm stationary phase film of SE30 (dimethylpolysiloxane; Alltech Associates, Deerfield, IL) was used as the primary column. A 5 m long, 250 µm i.d., open tubular column with a 0.25 µm stationary phase film of DB225 (50% cyanopropylphenylmethylpolysiloxane; J&W Scientific, Folsom, CA) was used as the secondary column. The injector was maintained at 280 °C. Hydrogen was used as the carrier gas at 2.5 mL/min. Carrier gas flowed directly from the primary column through the modulator into the secondary column. Samples and Reagents. A test mixture containing selected n-alkanes, n-alcohols, and an assortment of other moderately polar substances was obtained from various distributors and prepared in hexane solvent. RESULTS AND DISCUSSION The comprehensive two-dimensional gas chromatograms shown in Figures 4-7 verify the proposed theory. Table 1 lists the components of the mixture separated in these chromatograms. In Figure 4, both columns are isothermal at 95 and 160 °C in the primary and secondary ovens, respectively. Chromatographic (15) Liu, Z.; Phillips, J. B. J. Microcolumn Sep. 1989, 1, 249-256.

Figure 4. Comprehensive two-dimensional gas chromatogram of a test mixture with both the columns held isothermal at 95 °C for the primary column and 160 °C for the secondary. Compounds are listed in Table 1.

peaks tend to lie along the diagonal as they did in the hypothetical chromatogram of Figure 2A. The retention times of the sample components increase with increasing carbon atom number for members of each homologous series in both dimensions, and each series forms a nearly straight line of peaks across the plane. Differences in the relative slopes of the lines are due to differences in stationary phase interaction chemistries. Peaks in this twodimensional chromatogram are not well distributed over the retention plane, and the chromatogram clearly is not orthogonal. Incrementing the secondary column temperature as separation proceeds reduces the retention of lower volatility substances, converting the chromatogram into that of Figure 5. Better agreement with the hypothetical chromatogram in Figure 2B could have been obtained using a nonlinear temperature program, but that was impractical with the available instrument. Analytical Chemistry, Vol. 68, No. 9, May 1, 1996

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Figure 5. Comprehensive two-dimensional gas chromatogram of a test mixture with the primary column held isothermal at 95 °C as the secondary column is temperature programmed at an initial temperature of 130 °C and a program rate of 1.5 °C/min. Compounds are listed in Table 1.

In Figure 6, the primary column is temperature programmed, while the secondary column is held at constant temperature. Programming the primary column curves the diagonal of Figure 4 downward, in approximate agreement with the hypothetical chromatogram of Figure 2C. Simultaneously programming the temperature of the primary column and incrementing the temperature of the secondary column gives the chromatogram shown in Figure 7. In the first dimension, sample components separate according to their volatility, as expected for the nonpolar primary column. Incrementing the temperature of the secondary column as the primary column separation proceeds compensates for the progressive decrease in sample volatility, resulting in a nearly constant second dimension retention for members of each homologous series, independent of their position within the series. Alkanes, the least polar sample components of the test mixture, form a line of peaks at low retention in the moderately polar secondary column. The alcohol homologous series forms a second straight line of peaks with constant second dimension retention greater than that of the alkanes. Retention in the second dimension is no longer influenced at all by the volatility of a substance. Second dimension retention is independent of first dimension retention; therefore, the chromatogram is orthogonal. Independence of retention in the second dimension is a consequence of the relationship between retention and temperature in gas chromatography. In linear temperature-programmed gas chromatography, nonpolar solutes elute from a nonpolar stationary phase such that the difference between boiling point and elution temperature is almost a constant, ∆T(nonpolar). This 1490 Analytical Chemistry, Vol. 68, No. 9, May 1, 1996

Figure 6. Comprehensive two-dimensional gas chromatogram of a test mixture with the primary column temperature programmed starting with an initial temperature of 40 °C at a rate of 1.5 °C/min and with the secondary column held isothermal at 160 °C. Compounds are listed in Table 1.

follows from the fact that selectivity of a nonpolar dimethylpolysiloxane column toward nonpolar solutes is primarily due to dispersion interactions resulting in vapor-pressure-based selectivity.16 A more polar homologous series may have a different value for this constant, ∆T(polar), because boiling point is influenced by nondispersive interactions between molecules in the pure liquid that are not present between solute molecules and the stationary phase. Within any one series, a solute’s elution temperature is linearly related to its boiling point, but the intercept of this relationship, ∆T, depends upon the polarity of the series. The elution temperatures of the members of a series determine the temperatures at which they enter the secondary column. If both columns are in the same oven, then primary column elution temperature becomes the temperature of the secondary column. Otherwise, a constant offset between primary and secondary column temperatures may exist. In either case, all members of a more polar series elute from the primary column at temperatures offset from the elution temperatures of the corresponding members of the n-alkane series by a constant amount, ∆T(polar) ∆T(nonpolar). Retention of a given homologous series in the secondary column depends on both this constant temperature offset and the strength of interaction with the secondary column stationary phase. The temperature offset has just been shown to be constant, and all members of a given polar homologous series would be expected to have the same specific nondispersive interaction with the secondary column stationary phase. Thus, (16) White, C. M.; Hackett, J.; Anderson, R. R. J. High Resolut. Chromatogr. 1992, 15, 105-120.

Figure 7. Comprehensive two-dimensional gas chromatogram of a test mixture with both primary and secondary columns temperature programmed. The initial temperatures for the primary and the secondary columns are 40 °C and 120 °C, repectively. Temperature program rates are the same for both columns, 1.5 °C/min. Compounds are listed in Table 1. The modulation period is 10 s.

second dimension retention of a more polar homologous series should be offset by a constant amount from that of the n-alkane series. Boiling point or volatility of members within the series has no affect on retention in the second dimension. Second dimension retention time is determined only by homologous series membership as defined by specific nondispersive interaction with the secondary column stationary phase. Members of a particular homologous series, then, all have approximately the same secondary retention time, as can be seen in Figure 7. Members of different homologous series with different specific nondispersive interactions have different retentions in the second dimension. Retention in the second dimension is now nearly independent of volatility. The small remaining correlation between retention in the first and second dimensions is due to variation in carrier gas linear velocity with temperature. This remaining correlation is potentially correctable. In the introduction, we defined an orthogonal multidimensional separation as being one in which synentropy, or cross-information, between dimensions is zero.2 Eliminating volatility as a factor influencing second dimension retention allows other, more subtle, molecular properties such as polarity to alone determine second dimension retention. The line of alcohol peaks is parallel to the line of alkane peaks but displaced from it by a constant amount. This constant difference in retention time is a measure of the difference in polarity between the alkanes and the alcohols, as defined by their interactions with the two particular stationary phases used. The volatility of members of either series is irrelevant in determining their second dimension retention.

Figure 8. Comprehensive two-dimensional gas chromatogram of a test mixture with both primary and secondary columns temperature programmed. The initial temperatures for the primary and the secondary columns are 40 °C and 120 °C, repectively. Temperature program rates are the same for both columns, 1.5 °C/min. Compounds are listed in Table 1. The modulation period is 2 s.

Because the two dimensions contain two different and independent types of information, volatility in the first dimension and polarity in the second dimension, the two-dimensional chromatogram must have zero synentropy and must be orthogonal. The above argument can be generalized to include other retention mechanisms. Whatever chemistry determines retention in the first dimension becomes irrelevant in determining retention in the second dimension of a properly tuned comprehensive twodimensional gas chromatogram. Retention in the two dimensions may not have such clear labels as volatility and polarity, but they can be independent, and the chromatogram can be orthogonal. In a properly tuned comprehensive two-dimensional gas chromatogram, the members of an homologous series elute at a nearly constant second dimension retention time. This isochronic elution is valuable because it separates sample components on the basis of their chemical class, independent of molecular size or volatility. Measures of second dimension retention provide a type of functional group analysis. Much of the recorded retention plane in Figure 7 is vacant and carries no information. Sample components actually emerge only during the 2 s interval between 5.5 and 7.5 s. Since there is no need to record vacant areas of the retention plane, we can improve the efficiency of the separation by increasing the frequency of secondary chromatogram generation, which decreases the modulation period. The chromatogram in Figure 8 was recorded with a second dimension modulation period of 2 s. Sample components now occupy the entire recorded retention plane. Analytical Chemistry, Vol. 68, No. 9, May 1, 1996

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Increasing the frequency of secondary chromatogram generation can either improve the fidelity with which the first dimension separation is transmitted through the secondary column or increase the speed of the first dimension separation. Improving first dimension fidelity increases peak capacity because it allows peaks more closely spaced in the first dimension to be seen as distinctly separate. Once the modulation frequency is sufficient to preserve first dimension peak shapes, further increases in frequency do not increase peak capacity but only improve the precision of peak shape observation. Most of the retention plane in Figure 8 is accessible to chromatographic peaks because the two dimensions are orthogonal, the modulation period was selected to match the retention range of the sample being separated, and the sample contains a wide variety of substances. Being able to generate a set of multidimensional data in which the entire space is accessible is a good indication of orthogonality, but every separation done with the method does not have to demonstrate this accessibility for the method to be considered orthogonal. For example, if the four substances of lowest volatility and polarity (P3, P4, O3, O4) are removed from the test sample, then the lower left quadrant of the chromatogram in Figure 8 would be unoccupied, and the chromatogram would not appear to be as well distributed over the retention space. Changing the sample, however, does not change the method. To properly test a method’s orthogonality, the test sample itself must contain substances distributed over the whole range of properties relevant to the method. The sample used for Figures 4-8 was specifically chosen to contain substances over the range of volatilities relevant to the first dimension and polarities relevant to the second dimension of the comprehensive two-dimensional column set. Experimentally determined measures of orthogonality have been proposed.17,18 These are useful for comparing the efficiency of particular multidimensional methods for separation of a particular sample but do not directly address the orthogonality of the methods independent of sample. Giddings has recently introduced the concept of the dimensionality of a mixture.19 Inherent in this concept are two distinct spaces: a data space, which is defined by a multidimensional separation method, and a chemical properties space, which is defined by a particular mixture. The data space is determined by the characteristics of the separation method, while a chemical properties space is determined by the components present in the mixture. The two properties of the two spaces can and should be considered independently. A two-dimensional separation method is, thus, orthogonal if the two axes of the separation space (17) Liu, Z.; Patterson, D. G.; Lee, M. L. Anal. Chem. 1995, 67, 3840-3845. (18) Slonecker, P. J.; Li, X.; Dorsey, J. G. Federation of Analytical Chemistry and Spectroscopy Society 22nd annual meeting, Oct 17, 1995; Abstract 393. (19) Giddings, J. C. J. Chromatogr. A 1995, 703, 3-15.

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correspond to two independent chemical properties. The method is useful for a particular mixture if the same two chemical properties are significant in distinguishing components of the mixture from each other. A properly tuned comprehensive two-dimensional gas chromatograph using a nonpolar stationary phase in the primary column and a moderately polar stationary phase such as DB225 in the secondary column distributes substances in the first dimension according to the strength of their dispersive interactions with the nonpolar stationary phase and in the second dimension according to the strength of their specific nondispersive interactions with the polar stationary phase, independent of any dispersive interactions the two stationary phases may have in common. Because any interactions in common with the two stationary phases cannot influence second dimension retention, the two axes correspond to two independent chemical properties, which are conveniently labeled as volatility and polarity. The two axes are independent, and the method is orthogonal. The chromatogram in Figure 8 is nearly orthogonal because the method and the sample are both orthogonal or nearly orthogonal with respect to the same two chemical properties. CONCLUSION There are two approaches to obtaining orthogonality in hyphenated or multidimensional methods. The first is to find orthogonality by combining techniques based on chemistries which are assumed to be independent because they are different. Hyphenated chromatographic-spectroscopic methods in general are examples of this approach. As demonstrated in the introduction, this approach may fail because strong correlations often exist across even seemingly unrelated techniques. The second approach is to create orthogonality by varying the operating conditions of the second dimension of separation as a function of the progress of the first dimension. This approach requires that operating conditions be readily tunable, which is often true in chromatography but is not true in most spectroscopies. Thus, because retention in gas chromatography is easily tunable through temperature, comprehensive two-dimensional gas chromatography (GC/GC) can be orthogonal, as demonstrated here. ACKNOWLEDGMENT This material is based upon work supported by the National Science Foundation under Grant No. CHE-9024923. We thank Alltech and J&W Scientific for supplying the chromatographic columns. Received for review October 19, 1995. Accepted February 16, 1996.X AC951048B X

Abstract published in Advance ACS Abstracts, March 15, 1996.