Comprehensive Three-Dimensional Gas Chromatography with

Sep 27, 2007 - ... Life Science, United States Military Academy, West Point, New York ... is sufficient chromatographic resolution in each of the thre...
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Anal. Chem. 2007, 79, 8270-8280

Comprehensive Three-Dimensional Gas Chromatography with Parallel Factor Analysis Nathanial E. Watson,†,‡ W. Christopher Siegler,† Jamin C. Hoggard,† and Robert E. Synovec*,†

Department of Chemistry, University of Washington, Box 351700, Seattle, Washington 98195, and Department of Chemistry and Life Science, United States Military Academy, West Point, New York 10996

Development of a comprehensive, three-dimensional gas chromatograph (GC3) instrument is described. The instrument utilizes two six-port diaphragm valves as the interfaces between three, in-series capillary columns housed in a standard Agilent 6890 gas chromatograph fitted with a high data acquisition rate flame ionization detector. The modulation periods for sampling column one by column two and column two by column three are set so that a minimum of three slices (more commonly four or five) are acquired by the subsequent dimension resulting in both comprehensive and quantitative data. A 26-component test mixture and quantitative standards are analyzed using the GC3 instrument. A useful methodology for three-dimensional (3D) data analysis is evaluated, based on the chemometric technique parallel factor analysis (PARAFAC). Since the GC3 instrument produces trilinear data, we are able to use this powerful chemometric technique, which is better known for the analysis of two-dimensional (2D) separations with multichannel detection (e.g., GC × GC-TOFMS) or multiple samples (or replicates) of 2D data. Using PARAFAC, we mathematically separate (deconvolute) the 3D data “volume” for overlapped analytes (i.e., ellipsoids), provided there is sufficient chromatographic resolution in each of the three separation dimensions. Additionally, PARAFAC is applied to quantify analyte standards. For the quantitative analysis, it is demonstrated that PARAFAC may provide a 10-fold improvement in the signal-to-noise ratio relative to a traditional integration method applied to the raw, baseline-corrected data. The GC3 instrument obtains a 3D peak capacity of 3500 at a chromatographic resolution of one in each separation dimension. Furthermore, PARAFAC deconvolution provides a considerable enhancement in the effective 3D peak capacity. Comprehensive two-dimensional (2D) chromatographic techniques are common in the modern analytical laboratory. Examples of such instruments include LC × LC,1-3 LC × CE,4,5 CE × CE,6,7 * Corresponding author. Tel.:+1-206-685-2328. fax: +1-206-685-8665. E-mail: [email protected]. † University of Washington. ‡ United States Military Academy. (1) Bushey, M. M.; Jorgenson, J. W. Anal. Chem. 1990, 62, 161-167. (2) Holland, L. A.; Jorgenson, J. W. Anal. Chem. 1995, 67, 3275-3283. (3) Stoll, D. R.; Carr, P. W. J. Am. Chem. Soc. 2005, 127, 5034-5035. (4) Bushey, M. M.; Jorgenson, J. W. Anal. Chem. 1990, 62, 978-984.

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LC × GC,8,9 and GC × GC.10-12 More recently, GC × GC with time-of-flight mass spectrometric detection (TOFMS)13-19 and LC × LC with diode array20 or mass spectrometric21 detection have evolved into powerful tools. These instruments generate threedimensional (3D) data arrays, e.g., termed third-order data, that are amenable to powerful chemometric analysis, particularly parallel factor analysis (PARAFAC).22,23 Comprehensive separation techniques with three temporal dimensions are not as common. There are some notable examples, namely, LC × LC × CE24 and LC × GC × GC,25 the former example being one of the first advents of a 3D separation in the literature. A variant on these designs is a flow switching device,26 allowing three gas chromatographic dimensions to be utilized (GC × 2GC), producing two GC × GC separations simultaneously. We endeavor to produce a complementary instrument, however, with three comprehensive, serial gas chromatographic dimensions (5) Zhang, J.; Hu, H.; Gao, M.; Yang, P.; Zhang, X. Electrophoresis 2004, 25, 2374-2383. (6) Michels, D. A.; Hu, S.; Dambrowitz, K. A.; Eggertson, M. J.; Lauterbach, K.; Dovichi, N. J. Electrophoresis 2004, 25, 3098-3105. (7) Liu, H.; Yang, C.; Yang, Q.; Zhang, W.; Zhang, Y. J. Chromatogr., B 2005, 817, 119-126. (8) Quigley, W. W. C.; Fraga, C. G.; Synovec, R. E. J. Microcolumn Sep. 2000, 12, 160-166. (9) deKoning, S.; Janssen, H.-G.; vanDeursen, M.; Th.Brinkman, U. A. J. Sep. Sci. 2004, 27, 397-409. (10) Gorecki, T.; Harynuk, J.; Panic, O. J. Sep. Sci. 2004, 27, 359-379. (11) Xie, L.; Marriott, P. J.; Adams, M. Anal. Chim. Acta 2003, 500, 211-222. (12) Liu, Z.; Phillips, J. B. J. Chromatogr. Sci. 1991, 29, 227-231. (13) Hoggard, J. C.; Synovec, R. E. Anal. Chem. 2007, 79, 1611-1619. (14) Pierce, K. M.; Hoggard, J. C.; Hope, J. L.; Rainey, P. M.; Hoofnagle, A. N.; Jack, R. M.; Wright, B. W.; Synovec, R. E. Anal. Chem. 2006, 78, 50685075. (15) Pierce, K. M.; Hope, J. L.; Hoggard, J. C.; Synovec, R. E. Talanta 2006, 70, 797-804. (16) Mohler, R. E.; Dombek, K. M.; Hoggard, J. C.; Young, E. T.; Synovec, R. E. Anal. Chem. 2006, 78, 2700-2709. (17) Song, S. M.; Marriot, P.; Kotsos, A.; Drummer, O. H.; Wynne, P. Forensic Sci. Int. 2004, 143, 87-101. (18) Lu, X.; Cai, J.; Kong, H.; Wu, M.; Hua, R.; Zhao, M.; Liu, J.; Xu, G. Anal. Chem. 2003, 75, 4441-4451. (19) Focant, J.-F.; Sjodin, A.; Turner, W. E.; Patterson, D. G. Anal. Chem. 2004, 76, 6313-6320. (20) Porter, S. E. G.; Stoll, D. R.; Rutan, S. C.; Carr, P. W.; Cohen, J. D. Anal. Chem. 2006, 78, 5559-5569. (21) Chen, X.; Kong, L.; Su, X.; Fu, H.; Ni, J.; Zhao, R.; Zou, H. J. Chromatogr., A 2004, 1040, 169-178. (22) Bro, R. Crit. Rev. Anal. Chem. 2006, 36, 279-293. (23) Andersson, C. A.; Bro, R. Chemom. Intell. Lab. Syst. 2000, 52, 1-4. (24) Moore, A. W.; Jorgenson, J. W. Anal. Chem. 1995, 67, 3456-3463. (25) Edam, R.; Blomberg, J.; Janssen, H.-G.; Schoenmakers, P. J. J. Chromatogr., A 2005, 1086, 12-20. (26) Bueno, P. A.; Seeley, J. V. J. Chromatogr., A 2004, 1027, 3-10. 10.1021/ac070829x CCC: $37.00

© 2007 American Chemical Society Published on Web 09/27/2007

Figure 1. (A) Schematic of the major components of the GC3 instrument. (B) Raw data section viewed from the 1D aspect frame showing the total signal for the elution of toluene. The total signal represents the complete first-dimension peak, each of the four smaller signal clusters represents a second-dimension peak, and each individual signal is a third-dimension peak. (C) Closeup view of the second-dimension peak cluster at 21.2 min in (B).

(GC × GC × GC or GC3). The idea of GC3 has been reported,27 in the context of a thermally modulated GC3 instrument, lending some thought to instrument design, the potential benefits of increasing peak capacity, and the difficulties of analyzing thirdorder data. However, the experiments presented were preliminary. Additional insight into instrumentation design and data analysis and interpretation for practical application of GC3 is still warranted. Fortunately, techniques to probe the complexities of 3D data have become readily available, PARAFAC being one of the most prominent. Herein the development and evaluation of a comprehensive, three-dimensional gas chromatographic instrument (GC × GC × GC or GC3) coupled with flame ionization detection (FID) is reported. The instrument utilizes two six-port diaphragm valves, interfacing three, in-series capillary columns as illustrated in Figure 1A. This design is analogous to the 2D gas chromatograph designed by this laboratory some years ago,28 building upon the pioneering work of Jorgenson1 and Phillips.12 Modulation periods for sampling column one by column two, and column two by column three, are set so a minimum of three modulation periods (more commonly four or five) are acquired by the subsequent dimension resulting in comprehensive, quantitative data. The (27) Ledford, E. B.; Billesbach, C. A.; Zhu, Q. J. High Resolut. Chromatogr. 2000, 23, 205-207. (28) Bruckner, C. A.; Prazen, B. J.; Synovec, R. E. Anal. Chem. 1998, 70, 27962804.

complete analyte signal, as viewed in 3D space is nominally an ellipsoid and, as such, exhibits a trilinear data structure. Since the GC × GC × GC-FID instrument produces trilinear data, the third-order chemometric data analysis method PARAFAC is used. PARAFAC is ideally suited to analyze the entire 3D analyte signal since the algorithm naturally quantifies the entire signal, whether a given analyte is, or is not, overlapped with any interfering components. PARAFAC mathematically resolves analyte signals, even with severe overlap in all three separation dimensions, providing deconvoluted concentration profile (analyte peak) for each separation dimension. Noise that is not trilinear is effectively filtered out by PARAFAC.13 The ability to provide this mathematical resolution significantly increases the effective 3D peak capacity of the GC × GC × GC-FID instrument, where the 3D peak capacity is the product of the peak capacities for all three dimensions.29 Although statistical overlap theory states that in the 2D separation of a complex mixture much of the peak capacity will likely remain unused,30-33 there should be a benefit in the usefulness of the total peak capacity afforded by adding a complementary separation to GC × GC to yield the GC3 separa(29) Giddings, J. C. Unified Separation Science; John Wiley & Sons, Inc.: New York, 1991. (30) Davis, J. M.; Giddings, J. C. Anal. Chem. 1983, 55, 418-424. (31) Davis, J. M. Anal. Chem. 1991, 63, 2141-2152. (32) Davis, J. M. Anal. Chem. 1993, 65, 2014-2023. (33) Davis, J. M. J. Sep. Sci. 2005, 28, 347-359.

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tion. Finally, stationary-phase selection aimed toward optimization of the selectivity with three separation dimensions is considered. The design of a 3D separation system requires selection of three complementary separation modes, i.e., separations that provide suitable differences in chemical selectivity. This selection for LC × LC × CE is more straightforward when one considers size exclusion liquid chromatography coupled to reversed-phase liquid chromatography and capillary zone electrophoresis.24 The three separation modes are intrinsically different. However, with three GC columns, the selection is not so obvious. Methods have been developed to quantify the extent to which separation modes are complementary.34,35 In this report, commercially available stationary phases are chosen equivalent to the columns that, as reported in a previous three column gas chromatography experiment, provided complementary chemical selectivity.26 Using a test mixture of 26 compounds covering 9 chemical functionalities, retention time scatter plots were inspected, which displayed a high degree of scatter suggesting that the selected separation dimensions are sufficiently complementary. In order to visualize the 3D data produced by this instrument, we initially plotted the data as different colored semitransparent surfaces of equal intensity in a 3D Cartesian coordinate system, the analyte signals thus forming a 3D data “volume” for each analyte, i.e., an elliptical cloud as described by Moore and Jorgenson.24 However, such plots can be difficult to interpret when interactive plotting is not possible; so for publication, more traditional 2D contour plots were created by summing the data along one of the chromatographic dimensions. PARAFAC results are presented as one-dimensional (1D) intensity profiles (or chromatograms) for each of the three separation dimensions. Another important tool required for GC3 is a method to quantify the results. Two techniques are formulated and reported herein. One technique is a manual integration method akin to the method utilized for a 1D chromatogram (referred to as “traditional integration”), and the other technique is quantification via the PARAFAC algorithm. The traditional integration method and the PARAFAC method are compared with toluene calibration standards, and analysis of several other sets of calibration data is done with the traditional integration method. The GC3 instrument and data analysis tools are evaluated using quantitative calibration standards and a 26-component mixture of commercially available chemicals. When necessary, overlapped analyte ellipsoids are deconvoluted with PARAFAC. We speculate that the GC3 instrumental design reported herein or a variation thereof will open new doors toward greatly increasing the usefulness of 3D separation techniques. Ideally, the methods and instrumentation reported will allow these tools to become as accessible to the analytical laboratory as the predecessor 2D techniques with multichannel detection, i.e., GC × GC-TOFMS. EXPERIMENTAL SECTION An Agilent 6890 gas chromatograph (Agilent Technologies, Santa Clara, CA) was modified to produce a GC3 instrument as shown in Figure 1A. Two high-speed, six-port diaphragm valves (Valco Instruments Co. Inc., Houston, TX) fitted with 5-µL sample (34) Slonecker, P. J.; Li, X.; Ridgway, T. H.; Dorsey, J. G. Anal. Chem. 1996, 68, 682-689. (35) Abraham, M. H.; Ballantine, D. S.; Callihan, B. K. J. Chromatogr., A 2000, 878, 115-124.

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loops were face mounted as described by Sinha et al.36 This valve installation allows the instrument to operate over the entire column temperature range. The stock electrometer integrated with the Agilent FID was replaced with a high-speed electrometer built in-house. Data acquisition was accomplished using a National Instruments SCB-68 Data Acquisition Board coupled to LabVIEW 7 software (National Instruments, Austin, TX). Data were collected at 100 kHz and boxcar averaged to 500 points/s. Three columns with different stationary phases were installed in positions one, two, and three (Figure 1A) utilizing the installed valves as the modulation interfaces between columns one and two and columns two and three. A 25-m, 530-µm-inner diameter (i.d.), 5-µm film thickness (5% phenyl)-methyl polysiloxane stationaryphase column (DB-5; J&W Scientific/Agilent Technologies, Santa Clara, CA) was installed as column one. A 5-m, 250-µm-i.d., 1-µm film thickness trifluoropropyl-methyl polysiloxane stationary-phase column (Rtx-200; Restek, Bellefonte, PA) was installed as column two. In column three, a 100-µm-i.d., 0.1-µm film thickness poly(ethylene glycol) stationary-phase column (DB-Wax; J&W Scientific/ Agilent Technologies) was installed. Over the duration of this study, two different lengths of DB-Wax column were used for column three, either 55 or 100 cm. These two instrument configurations are summarized in Table 1. Two main studies were conducted utilizing the two GC3 configurations. The first study utilized a 26-component control mixture to evaluate the instrument design, column selection, peak capacity, and resolving power. The mixture was prepared as a stock solution of approximately equal quantities by volume of the following compounds: octane, nonane, decane, undecane, acetone, 1-heptyne, 2-pentanol, 1-bromoheptane, 1-pentanol, 1-heptene, 2-heptanone, toluene, 1-chlorohexane, ethylbenzene, 1-bromohexane, bromobenzene, 3-octanone, diethylmethyl phosphonate, 1-bromooctane (Sigma-Aldrich, Milwaukee, WI); pentane (JT Baker, Phillipsburg, NJ); heptane, benzene, 1-propanol (Fisher Scientific, Fair Lawn, NJ); ethanol (AAPER Chemical, Shelbyville, KY); hexane (Fluka, Buchs, Switzerland); and chlorobenzene (Alfa, Danvers, MA). A 4-µL neat injection of this stock solution was made with a HP 7673 autoinjector into a 225 °C split/splitless inlet running in splitless mode using hydrogen carrier gas. For the present study, this volume did not adversely broaden the column one peaks; however, in order to maintain column one separation efficiency, in future studies it may be prudent to use a smaller injection volume. Effluent from column one was injected onto column two with a six-port diaphragm valve set to actuate for 400 ms at a modulation period (Pm) of 5 s. Effluent from column two was injected onto column three via a second six-port valve set to actuate for 25 ms at a modulation period of 200 ms. The pulse widths on both valves readily cleared the sample loops. The inlet (column one) and auxiliary pressure controllers (columns two and three) were set to constant pressure mode at 4.3 (29.6 kPa), 7.0 (48.2 kPa), and 38 psi (261.9 kPa) for columns one, two, and three, respectively. Thus, columns two and three were operated near their optimum linear flow velocity, column two at 280 cm/s, and column three at 690 cm/s for configuration A and 630 cm/s for configuration B. Column one was operated at 24 cm/s, well below the estimated optimum of ∼120 cm/s in order (36) Sinha, A. E.; Johnson, K. J.; Prazen, B. J.; Lucas, S. V.; Fraga, C. G.; Synovec, R. E. J. Chromatogr., A 2003, 983, 195-204.

Table 1. Parameters for the Two GC3 Configurations Studieda instrument configurations

column dimension stationary phase: modulations/peak injection dimensional run time dead time (methane) peak width (toluene) peak capacity (toluene)

column one: DB-5

column two: Rtx-200

column three: DB-Wax configuration A

column three: DB-Wax configuration B

25 m × 530 µm i.d. × 5 µm df (5% phenyl)methyl polysiloxane 4 modulations/ peak 4-µL autoinjector pulse

5 m × 250 µm i.d. × 1.0 µm df trifluoropropylmethyl polysiloxane 5 modulations/ peak Vinj ) 5 µL (∆Tinj ) 400 ms) Pm ) 5 s t0 ) 1.8 s Wb ) 1.0 s PC2 ) 5 at Rs ) 1 (with wraparound)

55 cm × 100 µm i.d. × 0.1 µm df poly(ethylene glycol) 500 Hz data collection rate Vinj ) 5 µL (∆Tinj ) 25 ms) Pm ) 200 ms t0 ) 80 ms Wb ) 48 ms PC3 ) 2.5 at Rs ) 1 (without wraparound)

100 cm × 100 µm i.d. × 0.1 µm df poly(ethylene glycol) 500 Hz data collection rate Vinj ) 5 µL (∆Tinj ) 25 ms) Pm ) 200 ms t0 ) 160 ms Wb ) 57 ms PC3 ) 4 at Rs ) 1 (with wraparound)

run time, 60 min t0 ) 105 s Wb ) 20 s PC1 ) 175 at Rs ) 1

a Instrument configurations A and B consisted of columns one, two, and either 3A or 3B, respectively. All peak capacities and peak widths are calculated using toluene as a typical analyte.

to ensure sufficient peak width for quantitative modulation onto column two. Column one and column two were operated slower than the optimum flow velocity in order to slightly widen the peaks in the first and second dimensions to ensure sufficient peak width and sampling rates for each subsequent separation dimension. Detection was accomplished with the modified FID described above. The FID was run at 275 °C with nitrogen makeup gas. The GC oven was operated with a temperature program starting at 35 °C and held at that temperature for 2 min. The oven was then ramped to 110 °C at a rate of 2.5 °C/min. After attaining 110 °C, a second ramp was performed at 7.5 °C/min to 240 °C, where the oven was held for 10.67 min. This oven program resulted in a total run time of 60 min. Although not implemented for the present report, separate temperature-controlled regions or ovens for each column would be useful in avoiding retention time correlation but are not necessary to achieve comprehensive separation as shown in the results reported herein. The 26component mixture was analyzed in triplicate with the length of column three equal to either 55 or 100 cm (configurations A and B in Table 1). The second study was a quantitative analysis of standards to determine the linearity of concentration versus signal of the new instrument design. Toluene standards were prepared in acetone and serially diluted. Toluene standard concentrations are given in the first column of Table 2. The toluene standards were analyzed by GC3 using the 55-cm-long third column (configuration A in Table 1). Another set of standards was created as a mixture of 1,4-thioxane, sec-butylbenzene, 1-octanol (Sigma-Aldrich), 1-bromohexane and 3-octanone. A stock solution of all five chemicals in acetone was prepared and serially diluted. The concentrations of the five standards are given in the first column of Table 3. These standards were analyzed using the same GC3 method as the toluene standards. All data were saved as tab delimited files using LabVIEW 7.0 and imported to MATLAB 7.1.0 (The Mathworks, Natick, MA) running on a desktop PC. Data analysis was performed both manually and by PARAFAC. The PARAFAC algorithm from the N-way toolbox for MATLAB version 2.1123 was used in the same manner as previously reported for GC × GC-TOFMS13 with one exception. In the cited study, the selected model was chosen

Table 2. Calibration Data for Toluene Calculated Using Two Different Quantification Methodsa concentration (×10-6 g/mL) 2920 730 183 46 11 3

mean integrated signal

RSD (%)

102.8 31.7 9.0 2.3 0.6

2.4 1.7 4.3 8.3 7.1

mean PARAFAC signal

RSD (%)

97.3 31.5 8.8 2.2 0.6 0.1

1.9 1.5 4.6 6.7 3.2 1.3

a Method one is the baseline-corrected sum of the total 1D signal for toluene (integration), however, not summing over baseline noise sections. Method two is the total ellipsoid sum (3D data volume) obtained from a PARAFAC deconvolution of the toluene 3D signal. The mean signal data reported are the mean of three replicate injections. The relative standard deviation (RSD) for each concentration, and each integration technique are included. The calibration lines presented in a logarithmic format are included in Figure 4.

because it had one fewer factors than the model where splitting occurred in the analyte of interest, as verified by comparison of mass spectral match values. Obviously, mass spectral match values cannot be used for model selection with the GC3 FID data, and thus, splitting in all of the dimensions was verified by visual inspection of the model produced by the algorithm. PARAFAC was utilized during the analysis of the 26-component mixture chromatograms to deconvolute 1-heptene, heptane, and 2-pentanol, which were severely overlapped in at least two of the three dimensions. Analysis of the 26-component mixture data was performed manually in all other cases. The toluene quantitative data were analyzed by both PARAFAC and traditional integration. The other five standards were only analyzed by traditional integration for brevity. Traditional integration was performed by baseline correction and summation of the total area of all the peaks induced by the autoinjector injection and modulation of valves one and two, in a 1D sense, for each individual analyte. Baseline correction was done by repetitively subtracting the mean of a number of slices taken from the beginning and end of the chromatogram from the entire chromatogram. The baseline regions of the 1D chromatogram in between the peaks arising from the same compound are not included in the integration. This integration method requires chromatographic resolution in all Analytical Chemistry, Vol. 79, No. 21, November 1, 2007

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Table 3. Calibration Data for Five Compounds Other Than Toluene Calculated Using the Baseline-Corrected Sum of the Total 1D Signal Method (Integration)a concentration (×10-6 g/mL)

mean integrated signal

RSD (%)

1,4-thioxane R2 ) 0.999

3630 1820 908 454 227 113

63.9 33.3 16.1 7.1 4.8 2.6

2.0 0.6 2.2 5.7 5.7 3.7

1-bromohexane R2 ) 0.999

3320 1660 830 415 208 104

58.0 30.1 14.5 6.6 4.1 2.1

2.3 1.8 2.1 4.0 2.2 3.8

3-octanone R2 ) 0.999

1450 725 363 181 91 45

43.7 21.8 10.1 4.3 2.9 1.5

3.6 2.3 2.2 7.1 3.6 6.4

sec-butylbenzene R2 ) 0.999

3380 1690 845 423 211 106

114 55.2 26.4 13.3 8.3 4.1

2.9 0.6 2.1 2.2 6.4 8.8

1-octanol R2 ) 0.996

1950 975 488 244 122 61

48.5 23.2 8.7 3.6 2.2 1.0

4.0 5.4 4.2 7.1 6.3 7.4

analyte

a The mean signal data reported are the mean of three replicate injections. The relative standard deviation (RSD) for each concentration is also reported. The average percent standard deviation for all of the concentrations is 4.1%. The squared Pearson product moment correlation coefficient (R2) is listed under the name of each analyte.

dimensions and is thus only applicable in an academic context for the purposes of this report. Practical quantitative analysis utilizing GC3 requires a technique such as PARAFAC for automatic summation of the 3D data volume (ellipsoid), which will be demonstrated to also improve the signal-to-noise (S/N) ratio relative to integration of the raw, baseline-corrected data. RESULTS AND DISCUSSION Parts B and C in Figure 1 display an example of raw, GC3 data in 1D form as it appears following detection, prior to data processing that utilizes knowledge of the modulation periods to obtain a 3D data cube. The data are for toluene, with the chromatogram collected using configuration A described in Table 1. In Figure 1B, the complete signal is visible. The first-dimension peak is composed of each of the smaller second-dimension signals separated by the modulation period between column one and column two (5 s). In Figure 1C, the second-dimension signal induced by the modulation from column one to column two at a first column retention time of ∼21.2 min is displayed. In this closeup figure, the fine detail is clearly visible. The seconddimension signal is composed of each of the third-dimension peaks 8274 Analytical Chemistry, Vol. 79, No. 21, November 1, 2007

separated by the modulation period between column two and column three (200 ms). The data in Table 1 also allow for calculation of peak capacities for the individual columns and for the total GC3 instrument. The estimated base width (extrapolated from the measured widths at half the maximum peak intensity) of the toluene peaks displayed in Figure 1B and C are reported in Table 1. By dividing the total run time of each dimension by the base width of the toluene peak, the peak capacities listed in Table 1 are obtained. Since multidimensional peak capacities are multiplicative, the total peak capacity for instrument configuration A is 2200 and for configuration B is 3500 (Table 1). All of the listed peak capacities assume a chromatographic resolution of one, using toluene as a typical analyte. Note the peak capacity listed for column three in instrument configuration A is slightly less than the dimensional run time divided by the average peak base width. This is because the front portion of the peak capacity is unused due to the dead time (the time it takes an unretained compound to pass through the column). A solution to the issue of having lower total peak capacity for configuration A is to allow “wraparound” (compounds eluting with retention times greater than the modulation period), instead of avoiding it, in particular on column three. Thus, wraparound is utilized more fully in instrument configuration B (Table 1). The raw data from the instrument are a 1D row-vector of FID signal. An example of a raw, 1D row vector was depicted in Figure 1B and C. However, in order to fully utilize the 3D capabilities of the instrument, it is convenient to rearrange the data to a 3D data array. Each 1D vector was separated at every column one to column two modulation time point and appended as a second row in a data matrix. The same was done at each column two to column three modulation time point, and these data were appended to a third matrix dimension. Thus, a 3D data cube was created where each cell location in the array contained the chromatographic retention information (the 3D array index) and the FID signal strength (the value at the index). Table 4 displays the average retention time data for the 26component mixture separated by GC.3 We compared the selected stationary phases in Figure 2 using the retention time values listed in Table 4. The first three subfigures (Figure 2A-C) compare columns one and two, columns one and three, and columns two and three, respectively. The stationary-phase compositions are listed in Table 1. For a suitably diverse sample mixture, two columns with sufficiently different retention selectivity will create points scattered across the plot as displayed in Figure 2A-C (albeit without the dead time region being utilized for column three). Thus, Figure 2A-C indicates the three columns are highly complementary for the analyzed mixture. Although the scatter plots in Figure 2A-C support the choice of stationary phases for the three separation dimensions, by not allowing wraparound on column three, there are no points in the chromatographic space where the apparent retention time is less than the dead time. If wraparound on column three were allowed, a larger portion of the separation space could be utilized. This is the reason the instrument configuration was modified from configuration A (in Table 1) to configuration B (replacing the 55-cm DB-Wax column with a 100-cm length). GC3 separation of the same 26component mixture with the longer third column produced the

Table 4. Retention Time Data for a Standard 26-Component Mixture Run Using Both of the Instrument Configurations Listed in Table 1a configuration A analyte

tr,1 (min)

(1) ethanol (2) acetone (3) pentane (4) 1-propanol (5) hexane (6) benzene (7) 1-heptene (8) heptane (9) 2-pentanol (10) 1-heptyne (11) toluene (12) 1-pentanol (13) octane (14) chlorobenzene (15) 1-chlorohexane (16) ethylbenzene (17) 2-heptanone (18) nonane (19) bromobenzene (20) 1-bromohexane (21) 3-octanone (22) decane (23) diethylmethyl phosphonate (24) 1-bromoheptane (25) undecane (26) 1-bromooctane average uncertainties (SD)

4.1 5.1 5.2 7.8 9.3 13.3 15.1 15.8 15.9 17.3 21.1 21.2 23.3 27.5 28.1 28.8 30.8 31.4 34.3 34.4 36.8 37.4 37.9

4.8 2.3 3.6 2.4 5.0 4.3 1.9 1.5 1.3 3.2 1.2 2.1 2.7 3.4 2.6 1.7 2.2 3.4 1.5 0.5 2.7 1.6 3.9

39.3 41.2 42.8 (0.1

3.4 1.4 3.1 (0.1

tr,2 (s)

configuration B tr,3 (ms)

tr,1 (min)

tr,2 (s)

145 102 80 180 84 113 89 86 164 104 121 197 90 142 106 121 126 93 139 107 108 94 156

4.2 5.2 5.2 7.7 9.5 13.3 15.1 15.8 15.8 17.3 21.1 21.0 23.3 27.5 28.0 28.8 30.7 31.3 34.3 34.3 36.7 37.3 37.8

0.2 2.8 3.8 3.2 0.4 0.1 2.6 2.3 2.3 4.1 2.3 3.5 3.4 4.4 3.8 2.8 3.9 4.3 2.7 1.8 4.2 2.5 1.1

104 96 104 (0.5

39.2 41.1 42.7 (0.1

4.7 2.4 4.4 (0.3

tr,3 (ms) 156 23 166 59 173 57 186 183 183 22 67 99 189 136 28 68 84 195 123 29 37 198 151 23 2 24 (1.2

a Retention times listed are the average of three replicate injections with the average uncertainties (SD) included at the bottom of the table. The numbers listed to the left of each analyte name are used to label ellipsoids (or peaks thereof) in all of the figures published with this study.

retention data listed in the right half of Table 4 and the retention time scatter plots displayed as Figure 2D-F. Lengthening column three increased the retention of all the analytes on column three, thus providing some wraparound and filling the previously unused portion of the separation space. This use of the total separation space allows the available peak capacity to be maximized. Slight shifting between column two retention data in configuration A and configuration B was also observed. Retention time shifting is a well-known occurrence in chromatography and algorithms have been developed for retention time alignment.37-39 As we arbitrarily chose run conditions that would induce wraparound in the second separation dimension, the shifting caused no significant issues in the analysis of the 3D data reported herein (as might be the case if attempting to identify signals of unknown origin when those signals have wrapped around multiple times) but implies the need for the development of a 3D retention time alignment algorithm. Figure 3A depicts the separation of the 26-component mixture described in Table 4 for configuration B. Since there is no convenient method to plot three separation dimensions on a 2D sheet of paper that is easily legible as the number of components (37) Pierce, K. M.; Hope, J. L.; Johnson, K. J.; Wright, B. W.; Synovec, R. E. J. Chromatogr., A 2005, 1096, 101-110. (38) Pierce, K. M.; Wood, L. F.; Wright, B. W.; Synovec, R. E. Anal. Chem. 2005, 77, 7735-7743. (39) Tomasi, G.; vandenBerg, F.; Andersson, C. J. Chemom. 2004, 18, 231241.

in the sample becomes relatively large, we made a 2D contour plot analogous to a GC × GC chromatogram as described in the introduction. Figure 3A was created by summing the third matrix dimension and plotting the resulting 2D data array. In order to depict the third chromatographic dimension graphically, portions of either the first or second dimension were summed, creating contour plots similar to Figure 3A. Parts B-D in Figure 3 were produced by summing along column one from 18 to 24, 24 to 30, and 30 to 36 min, respectively. These figures exemplify the benefit of a third separation dimension. In all three of the column three versus column two contour plots, the chromatographic resolution required to separate all the components was present in columns one and two. However, had there been lack of resolution in the first two dimensions, the addition of the third dimension provides additional resolution and also allows for utilization of PARAFAC to mathematically resolve the individual components. This will be demonstrated shortly. To begin to address the possibilities presented by the application of a chemometric tool like PARAFAC, discussion of quantitative analysis by GC3 is warranted. Figure 4 and Table 2 detail quantitative information obtained from toluene calibration standards analyzed by GC3 in both graphical and tabular forms. Two different methods were used to quantify the 3D ellipsoid signals in order to prove that the new 3D chromatograph produces reliable, linear, and quantitative data: traditional integration and PARAFAC. The expectation is to demonstrate that PARAFAC Analytical Chemistry, Vol. 79, No. 21, November 1, 2007

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Figure 2. Retention time plots of the data given in Table 4. The plotted points are the peak maximums of the 2D peak in units of time while the dashed lines represent the dead time for each column determined experimentally with methane. (A-C) Plots of the retention times of column two versus column one, column three versus column one, and column three versus column two for instrument configuration A (Table 1), respectively. In (B) and (C), it is important to note the blank space representing column three’s dead time without allowing wraparound. (D-F) Plots of the retention times of column two versus column one, column three versus column one, and column three versus column two for instrument configuration B (Table 1), respectively. Now that column three has been allowed to wrap around, the peak capacity of the third dimension is more fully realized.

produces results similar to traditional integration, with PARAFAC providing added benefits for dealing with overlapped ellipsoids and improving S/N. The results of both methods correlate well. Both methods produced linear calibrations with slopes on a logarithmic versus logarithmic scale of 0.92 and 0.96 for the 8276

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traditional and PARAFAC methods, respectively. A slope of one represents a perfectly linear relationship between the measured instrumental signal and sample concentration. Calibration lines for traditional integration were produced for five other chemicals with excellent linear correlation coefficients, presented in Table

Figure 3. (A) Complete 2D separation of the 26-component standard mixture listed in Table 4 created by summing the third-dimension signal. Also depicted are individual column three versus column two chromatograms created by summing portions of the first column separation signal. (B) Column one summed from 18 to 24 min. (C) Column one summed from 24 to 30 min. (D) Column one summed from 30 to 36 min.

3. PARAFAC analysis of the analytes other than toluene is not included herein for brevity. Further details of the quantitative benefits of PARAFAC deconvolution are shown in Figure 5. In Figure 5A, the raw signal of the complete 1.1 × 10-5 g/mL toluene 1D signal is displayed. Please note that this figure shows only three samplings of the first dimension peak compared to the peak in Figure 1B, which shows four samplings. The incongruity is due to a slight shift in the phase of the sampling. In Figure 1B, the effluent was sampled “in-phase” with the peak resulting in two larger slices and two smaller slices. In Figure 5A, the sampling was “out-of-phase”, resulting in one large slice and two smaller slices. The total firstdimension peak is sufficiently sampled in both cases for quantitative analysis. Parts B-D in Figure 5 show the results of the PARAFAC deconvolution for columns one, two, and three, respectively. Analogous to data reported previously for GC × GCTOFMS,13 the signal intensity data are only retained in one dimension and the other two are normalized. In the GC3 case, the relative signal intensity information is preserved in the first dimension. Due to the folded structure of the data, most of the noise not modeled by PARAFAC is retained in the third dimension as shown in Figure 5D. Figure 5D also shows one of the major benefits of PARAFAC deconvolution, which is an ∼10-fold increase

Figure 4. Logarithmic calibration lines for toluene utilizing the calibration data presented in Table 2. A linear regression was performed on both data sets with a slope of 0.92 for the baselinecorrected 1D signal sum and 0.96 for the PARAFAC ellipsoid sum. (9, traditional integrated sum of baseline corrected 1D signal; ×, PARAFAC ellipsoid sum).

in signal-to-noise ratio from the raw data to the deconvoluted data. This occurs because aside from filtering out noise that is not Analytical Chemistry, Vol. 79, No. 21, November 1, 2007

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Figure 5. (A) Baseline-corrected total signal for toluene at a concentration of 11 ppm (1.1 × 10-5 g/mL). The S/N is low even after the baseline correction. (B-D) PARAFAC peak profiles of columns one, two, and three for each of three replicates run at 11 ppm. Good reproducibility is achieved, and the S/N increase is a factor of ∼10.

trilinear, the PARAFAC algorithm removes a large portion of the noise as a factor separate from the analyte signal factor. This signal-to-noise benefit is why the calibration line for the PARAFAC deconvoluted signal displays standard concentration nearly 1 order of magnitude lower than the traditionally integrated signal calibration shown in Figure 4 and Table 2. The other major benefit of PARAFAC, and the most renowned, is that PARAFAC has the ability to mathematically resolve chromatographic components that are not sufficiently separated by the instrument alone. This benefit is readily provided by an instrument that produces 3D information (i.e., third-order data). Figure 6A displays the column two versus column three plot created by summing along the first column dimension from 12 to 18 min. Three of the components (1-heptene, heptane, 2-pentanol) in Figure 6A are not resolved in the second and third chromatographic dimensions. In Figure 3A, one can see that 1-heptene was resolved in the first chromatographic dimension, but heptane and 2-pentanol were convoluted in all three dimensions. This level of overlap will serve as a valuable test for PARAFAC deconvolution of the data produced by the GC.3 Prior to PARAFAC analysis, the data must be reregistered to account for the wraparound in the third column dimension in order to preserve the trilinearity of the data. The section of the data cube representing the three 8278 Analytical Chemistry, Vol. 79, No. 21, November 1, 2007

overlapped ellipsoids is extracted, and the points wrapped around in column three are moved to the end of each of the previous column three rows, thus preserving the structure of the data. The results of this operation are shown in Figure 6B. In Figure 6CE, the results of PARAFAC on the reregistered portion of the chromatogram (Figure 6B) are displayed (similar results from replicates are omitted for brevity). The three-factor deconvolution model completely resolved all the overlapped ellipsoids, including the heptane and 2-pentanol ellipsoids that had no apparent chromatographic resolution in any of the separation dimensions (i.e., only one ellipsoid could be observed on visual inspection). Also of interest is the fact that Figure 6C shows a fronting peak shape for the 2-pentanol first-dimension peak, possibly due to the alcohol interacting with the nonpolar (5% phenyl)methyl polysiloxane stationary phase.40 The 2-pentanol likely has stronger interactions with itself in the carrier gas than with the stationary phase for which it has minimal affinity. The fact that PARAFAC is able to overcome nonideal peak shape and extract this level of chromatographic information from nearly completely overlapped data makes it a powerful tool when applied with GC3, the only requirement being that the data are trilinear. Indeed, it is likely (40) Robards, K.; Haddad, P. R.; Jackson, P. E. Principles and Practice of Modern Chromatographic Methods; Elsevier Academic Press: Amsterdam, 2004.

Figure 6. (A) Column three versus column two contour plot for column one summed from 12 to 18 min. Note the overlap of 1-heptene, heptane, and 2-pentanol (labeled 7, 8, and 9 per Table 4). Heptane and 2-pentanol are completely overlapped in all three dimensions, and 1-heptene is resolved in only the first dimension. (B) Reregistration of 1-heptene, heptane, and 2-pentanol data to account for wraparound in the third dimension. This correction is required to execute a PARAFAC deconvolution of the 3D data. (C-E) PARAFAC peak profiles of columns one, two, and three demonstrating the complete resolution (combined chromatographic and mathematical) of all three compounds.

the difference in the peak shape and width for heptane and 2-pentanol that engendered their mathematical resolution. Furthermore, the addition of PARAFAC also allows for a dramatic increase in the effective peak capacity of the instrument, since analytes at much lower chromatographic resolution can be

mathematically separated. Utilizing the three column dimensions and assuming that a chromatographic resolution of one is required to identify an analyte, a total peak capacity of 3500 was obtained (per Table 1 for configuration B) based upon the stated number of modulations per peak. Indeed, all analytes studied with this Analytical Chemistry, Vol. 79, No. 21, November 1, 2007

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valve-based instrument had three (or generally more) modulated samplings (i.e., periods) in each dimension. Thus, the GC3 instrument reported herein is comprehensive in accordance with the recently published criteria.41 Periods of 6.67 s and 333 ms for modulation onto columns two and three, respectively, would provide the minimum number of modulations (three) for comprehensive separations, resulting in an equivalent peak capacity of ∼7000. This peak capacity is very respectable and is comparable to that from a GC × GC instrument with the same (60 min) run time. However, the GC3 separation should have, in principle, more selectivity due to the added separation dimension. CONCLUSIONS GC3 with PARAFAC deconvolution has been presented, and it holds promise as a powerful tool for chemical analysis. The instrument is simple and requires only minor modifications to a conventional 1D gas chromatograph. Instruments of this kind are useful to increase the chemical information content of an analysis (41) Khummueng, W.; Harynuk, J.; Marriott, P. J. Anal. Chem. 2006, 78, 45784587.

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per unit time.42 Future studies combining GC3 with TOFMS detection may also be of interest. It may also be useful to formulate an algorithm for 3D retention time alignment analogous to work already completed for 1D and 2D gas chromatography.37-39 It is noted that the valve and column configuration utilized in this report had a relatively low percent sample mass transfer from the autoinjector to the detector. The injected sample transfer rate was sufficient for this proof-of-principle demonstration, but needs to be improved for practical use, for example, environmental, metabolomic, fuel-related, and other complex samples. The data presented were quantifiable to reasonably low concentration levels, but improvements to the modulation interfaces are warranted to improve the limit of detection. Received for review April 24, 2007. Accepted August 3, 2007. AC070829X (42) Watson, N. E.; VanWingerden, M. M.; Pierce, K. M.; Wright, B. W.; Synovec, R. E. J. Chromatogr., A 2006, 1129, 111-118.