Peak Modeling Approach to Accurate Assignment of First-Dimension

Anal. Chem. 2009, 81, 6797–6804

Peak Modeling Approach to Accurate Assignment of First-Dimension Retention Times in Comprehensive Two-Dimensional Chromatography Jacqui L. Adcock,† Mike Adams,‡ Blagoj S. Mitrevski,† and Philip J. Marriott*,† Australian Centre for Research on Separation Science, School of Applied Sciences, and School of Applied Sciences, RMIT University, GPO Box 2476 V, Melbourne, Victoria 3001, Australia Modeling of first-dimension retention of peaks based on modulation phase and period allows reliable prediction of the modulated peak distributions generated in the comprehensive two-dimensional chromatography experiment. By application of the inverse process, it is also possible to use the profile of the modulated peaks (their heights or areas) to predict the shape and parameters of the original input chromatographic band (retention time, standard deviation, area) for the primary column dimension. This allows an accurate derivation of the firstdimension retention time (RSD 0.02%) which is equal to that for the non-modulated experiment, rather than relying upon the retention time of the major modulated peak generated by the modulation process (RSD 0.16%). The latter metric can produce a retention time that differs by at least the modulation period employed in the experiment, which displays a discontinuity in the retention time vs modulation phase plot at the point of the 180° out-ofphase modulation. In contrast, the new procedure proposed here gives a result that is essentially independent of modulation phase and period. This permits an accurate value to be assigned to the first-dimension retention. The proposed metric accounts for the time on the seconddimension, the phase of the distribution, and the holdup time that the sampled solute is retained in the modulating interface. The approach may also be based on the largest three modulated peaks, rather than all modulated peaks. This simplifies the task of assigning the retention time with little loss of precision in band standard deviation or retention time, provided that these peaks are not all overloaded in the first or second dimension. In its relatively short history, comprehensive two-dimensional chromatography (here abbreviated as C2DC; e.g. HPLC × HPLC and GC × GC) has seen many analytical applications developed for this new technology,1-6 exploiting the increased resolution

and often sensitivity improvement that these techniques can provide.5,7 However, the majority of these methods have focused on qualitative analysis, or quantitative analysis of only a few compounds in a complex sample. This is most probably due, at least in part, to the lack of user-friendly software developed specifically for comparative and quantitative analysis in C2DC. The C2DC technique employs two columns arranged in series, with the effluent from the first-dimension (1D) column sampled and introduced onto the second-dimension (2D) column by means of an interface which may comprise one or more sampling loops, a cryogenic modulator, or a sub-sampling diaphragm valve. A range of uncertainties arises in quantitative analysis specifically because of the type of data generated by this process; unlike uni-dimensional chromatographic techniques that generate a single chromatographic peak for each analyte, the comprehensive method generates (and so must also take into consideration) multiple sub-peaks for every analyte.8 This results in a number of concerns for data analysis, including how to assign a single first-dimension retention time (1tR) to a group of sub-peaks for a single analyte, and how to identify and then obtain quantitative information for an analyte from the resulting set of modulated peaks. One consequence of modulation in C2DC is the loss of some information on precise retention in the 1D, and therefore an idea of the resolution measure for neighboring peaks in this dimension. The primary peak is “quantized” according to its peak width and the modulation period parameters, to produce apparent primary dimension retention times that are the same for any peaks that exist at that given location (retention time). Hence for those peaks there is no differentiation in 1D times. This quantization could be considered to have the same effect as a loss of 1tR precision. For some methods, analyses and software packages, it is common for the retention time of the largest sub-peak to be used as the estimate of 1tR, but this seems to be neither the best nor the most rugged metric for this measure; under this approach,

* To whom correspondence should be addressed. E-mail: philip.marriott@ rmit.edu.au. Phone: + 61 3 9925 2632. Fax: + 61 3 9925 3747. † Australian Centre for Research on Separation Science, School of Applied Sciences. ‡ School of Applied Sciences. (1) Adahchour, M.; Beens, J.; Brinkman, U. A. Th. J. Chromatogr., A 2008, 1186, 67–108. (2) Adahchour, M.; Beens, J.; Vreuls, R. J. J.; Brinkman, U. A. Th. TrAC, Trends Anal. Chem. 2006, 25, 821–840.

(3) Adahchour, M.; Beens, J.; Vreuls, R. J. J.; Brinkman, U. A. Th. TrAC, Trends Anal. Chem. 2006, 25, 726–741. (4) Marriott, P.; Shellie, R. TrAC, Trends Anal. Chem. 2002, 21, 573–583. (5) Dugo, P.; Cacciola, F.; Kumm, T.; Dugo, G.; Mondello, L. J. Chromatogr., A 2008, 1184, 353–368. (6) Dixon, S. P.; Pitfield, I. D.; Perrett, D. Biomed. Chromatogr. 2006, 20, 508– 529. (7) Ong, R. C. Y.; Marriott, P. J. J. Chromatogr. Sci. 2002, 40, 276–291. (8) Harynuk, J. J.; Kwong, A. H.; Marriott, P. J. J. Chromatogr., A 2008, 1200, 17–27.

10.1021/ac900960n CCC: $40.75  2009 American Chemical Society Published on Web 07/23/2009

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if modulation phase changes a little, the apparent 1D retention time may vary by one full modulation period (PM), which may be unacceptable for the purpose of a validated reporting procedure. Also, many procedures for obtaining quantitative information in the form of total peak area still involve the tedious and time-consuming task of manually identifying, integrating, and summing all the sub-peaks belonging to a single analyte. This can potentially lead to problems regarding the number of peaks to sum for accurate results,8-11 and questions related to limitations of this process may restrict the uptake of C2DC for routine quantitative analysis. There has been some work undertaken to address these issues. Chemometric techniques have been described,12-14 employing the generalized rank annihilation method (GRAM) for peak resolution and quantification. These techniques often require highly reproducible data, and some C2DC data may not be suited to this analysis. Kong and co-workers described the use of the exponentially modified Gaussian model for the deconvolution of peaks in GC × GC,15 and Mondello et al. reported the development of LC × LC software for automated peak identification and quantitation.16 While these investigations have developed many useful methods for the analysis of the complex data generated in comprehensive chromatography experiments, none of these approaches have detailed a straightforward method for the presentation of first-dimension retention times. In this work, we describe a method to first demonstrate that the 2D peak distribution in a comprehensive two-dimensional chromatography experiment can be modeled from a 1D Gaussian peak and knowledge of PM. Following this, we then describe a means to extract the requisite 1tR data for the original 1D peak from the modulated chromatogram, using the Gaussian distribution as a model of chromatographic peak shape, significantly advancing our previous proof-of-concept work.12 We systematically investigate the effects of PM and modulation phase on the proposed method using both modeled and real data, and examine the reproducibility of the modeled peak parameters. In the current form, the method is limited to applications where at least three modulated peaks can be identified for a compound, and is not appropriate for the modeling of grossly undersampled peaks (fewer than 3 modulated peaks). The present work will specifically examine the process of cryogenic modulation in GC × GC as a model for the C2DC experiment, which causes each 1D peak to be sampled a number of times into the 2D column, resulting in a series of sub-peaks or “pulses” of the 1D peak.12,17 These pulses still obey the cumulative distribution expected of a Gaussian peak,7 and the (9) Khummueng, W.; Harynuk, J.; Marriott, P. J. Anal. Chem. 2006, 78, 4578– 4587. (10) Amador-Mun õz, O.; Marriott, P. J. J. Chromatogr., A 2008, 1184, 323– 340. (11) Amador-Mun õz, O.; Villalobos-Pietrini, R.; Aragoń-Pin ã, A.; Tran, T. C.; Morrison, P.; Marriott, P. J. J. Chromatogr., A 2008, 1201, 161–168. (12) Xie, L.; Marriott, P. J.; Adams, M. Anal. Chim. Acta 2003, 500, 211–222. (13) Fraga, C. G.; Corley, C. A. J. Chromatogr., A 2005, 1096, 40–49. (14) Fraga, C. G.; Prazen, B. J.; Synovec, R. E. Anal. Chem. 2001, 73, 5833– 5840. (15) Kong, H.; Ye, F.; Lu, X.; Guo, L.; Tian, J.; Xu, G. J. Chromatogr., A 2005, 1086, 160–164. (16) Mondello, L.; Herrero, M.; Kumm, T.; Dugo, P.; Cortes, H.; Dugo, G. Anal. Chem. 2008, 80, 5418–5424. (17) Marriott, P. J.; Kinghorn, R. M. Anal. Chem. 1997, 69, 2582–2588.

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Figure 1. Model of a 1D peak, based on the Gaussian distribution, with a retention time of 30 s, a standard deviation of 2.5 s, and an area of 1000.

number, retention times, heights, and areas of these peaks are related directly to the parameters of the original 1D peak. On the basis of this, the 1D peak can be modeled, and from this the values of 1tR, 1σ, and total peak area (A) can be accurately calculated and applied to quantitative analysis. The approach presented here developed for GC × GC, should apply generally to all C2DC methods such as LC × LC and other related techniques. THEORETICAL BASIS An ideal one-dimensional gas chromatographic peak can be approximated by a normal or Gaussian distribution (eq 1), where S(t) is the detector response (signal) as a function of time (t), A is the area of the peak, 1tR is the retention time of the peak, and 1 σ is the standard deviation of the peak. S(t) )

A

√2π1σ2

(

e

-

(t - 1tR)2 21σ2

)

(1)

From this equation a typical 1D peak can be modeled, as shown in Figure 1, where A ) 1000, 1tR ) 30 s, and 1σ ) 2.5 s. As described previously,9 it is possible to simulate the modulation of this peak. To do this, a series of modulation release times (xn) were calculated, based on the modulation period (PM), where xn ) (nPM) + x0, and x0 was the initial modulation start time. The area of the sampled section of the original 1D peak released (after trapping) at each modulation event (Arn) was calculated from eq 2 (using the “NORMDIST” function in Microsoft Excel). Arn )

∫

xn+1

xn

S(t) dt

(2)

These areas were then used to calculate a series of Gaussian peaks with 2σ ) 0.1 s and a total retention time of xn+1 + 2tR. A 2 σ value of 0.1 s was chosen to simulate typical results in a GC × GC experiment employing cryogenic modulation, where cryofocusing combined with a rapid separation on a short, narrow column, results in increased peak heights and decreased peak widths on the second dimension. This series of peaks combines to form the modulated primary peak (Figure 2). A modulation period (PM) of 3 s was used, giving a modulation ratio9 (MR ) 4σ/PM) of 3.33 and the second dimension retention time was set at 1 s.

Figure 3. Influence of modulation phase on the retention time of the largest modulated peak.

Figure 2. Modeling of sub-peaks showing; (a) in-phase modulation and (b) out-of-phase modulation. Modulation phase was varied by altering modulation start time (x0). (1tR ) 30 s, 1σ ) 2.5 s, A ) 1000, and PM ) 3 s.)

As can be seen in Figure 2, the pattern of the sub-peaks can change, depending on the relative timing of the modulation events in relation to the chromatographic signal in the 1D column. This pattern is referred to as the phase of modulation and has been discussed previously;7,18,19 in-phase modulation (0°) gives a completely symmetrical pulse sequence with a single maximum peak (Figure 2a), while out-of-phase modulation (180°) is again completely symmetrical, but has two (equal) maxima (Figure 2b).7 Other modulation phases that describe “asymmetric sampling” fit in-between these two extremes. When 1tR is measured (incorrectly) as being the retention time of the largest modulated peak, the 1tR value can be highly sensitive to and influenced by the phase of modulation. Reproducibility of the modulation phase can be affected by two factors: (1) the reliability of the timing of modulation events; and (2) the reproducibility of the 1D retention time (which for GC may be affected by flow rate and oven temperature reproducibility, and for LC by eluant and/or gradient reproducibility and temperature fluctuations). Small changes in any of these values can shift the phase of modulation, which can in turn change the peak identified as the largest modulated peak. This therefore can cause measurement of 1tR to be shifted by at least one full modulation period. The retention time of the largest modulated peak will be 1tR + 2tR + z, where z accounts (18) Murphy, R. E.; Schure, M. R.; Foley, J. P. Anal. Chem. 1998, 70, 1585– 1594. (19) Schoenmakers, P.; Marriott, P.; Beens, J. LC-GC Eur. 2003, 16, 335–336, 338-339.

for hold-up time in the modulator, and can be determined by the modulation phase. The variation of z with modulation phase is shown in Figure 3. The apparent discontinuity observed when modulation is 180° out-of-phase occurs because there are two equal modulation peak maxima, spaced one modulation period apart (Figure 2b). At this point, even very slight variations in modulation phase can shift the largest pulsed peak by one full PM value according to whether the modulation event arises just before or just after the peak maximum. Figure 4 further illustrates this effect. As well as affecting the retention time, modulation phase also affects the relative allocation of peak area of each sub-peak to the total peak area measurement. More specifically, it affects the number of sub-peaks that need to be summed to account for a given percentage of primary peak area. Marriott and co-workers have previously examined this in detail, based on the modulation ratio concept,8-11 and it will not be discussed further here. It is proposed here that by extracting the original 1D peak from the modulated chromatogram using a Gaussian distribution as a model of peak shape, it will be possible to obtain a more accurate estimation of both 1D retention time and peak area. There are two approaches to this: (1) modeling the peak based on the retention times and heights of the sub-peaks; and (2) modeling the peak based on the retention times and areas of the sub-peaks. All of these data can be exported from any commercial 1D chromatography software package after integration of the modulated chromatogram. EXPERIMENTAL SECTION A standard solution of n-bornyl acetate (0.5 µL/mL; Australian Botanical Products Pty Ltd., Hallam, Australia) was prepared in hexane (pesticide grade, Unichrom, Ajax Finechem, Taren Point, Australia) for the generation of chromatographic data for modeling. An Agilent 6890 GC (Agilent Technologies, Burwood, Australia) was used for all separations. The inlet temperature was 250 °C, and an injection volume of 1 µL was used with a 100:1 split ratio. Hydrogen was used as the carrier gas (1.3 mL/min, constant flow) and the GC was operated under isothermal conditions at an oven temperature of 100 °C for 20 min. The column set comprised a BPX5 column (SGE International, Ringwood, Australia; 30 m × 0.25 mm × 0.25 µm) as the 1D column and a BP20 column (SGE International; 1.5 m × 0.1 mm × 0.1 µm) as the 2D column. For GC × GC analyses, the instrument had been fitted with a longitudinally modulated cryogenic Analytical Chemistry, Vol. 81, No. 16, August 15, 2009

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Figure 5. Fitting a Gaussian distribution to sub-peaks based on retention times and peak heights; (a) the modeled peak is fitted to the sub-peak maxima, and (b) a comparison of the actual (i) 1D peak and modeled (ii) peak.

Figure 4. Effect of slight changes in 1tR on phase of modulation and position of the largest modulated peak (asterisked); (a) 1tR ) 29.7 s, (b) 1tR ) 30.0 s, and (c) 1tR ) 30.3 s. (1σ ) 2.5 s, A ) 1000, and PM ) 3 s for all cases.)

system (LMCS II, Everest model unit, Chromatography Concepts, Sandringham, Australia), cooled by liquid carbon dioxide to a temperature of -20 °C. A modulation period (PM) of 3 or 4 s was used throughout. The GC was equipped with an FID detector, operated at 100 Hz. ChemStation software was used for data acquisition and integration, and Microsoft Excel was used for peak modeling. To demonstrate specific cases that range from linear to grossly overloaded peaks in the GC × GC system, two examples were studied. The first was a series of n-dodecane standards (SigmaAldrich, NSW, Australia) ranging from 0.05 to 10 µL/mL. The second was a series of n-bornyl acetate standards ranging from 0.1 to 50 µL/mL. Each set of standards was injected into the column set described above. 6800


RESULTS AND DISCUSSION Modeling a 1D Peak using Sub-Peak Heights and Retention Times. Because of the way the modulation process samples the original 1D band, the sub-peaks reflect a distribution related to the distribution of the original 1D peak. By taking the retention times and peak heights of each of the sub-peaks, a Gaussian curve fitted through these points will be directly related to the shape of the original 1D peak. A curve is fitted based on eq 1 by systematically changing the variables A, 1tR, and 1σ until the results best fit the experimental data based on the method of non-linear least-squares curve fitting. The leastsquares fit is achieved using the Solver feature in Microsoft Excel. Using sub-peak retention times and peak height data, the fit shown in Figure 5a was obtained for the theoretical peak shown in Figure 1. In this case, a 180° out-of-phase modulation process is illustrated; a symmetrical distribution comprising pairs of peaks of equal magnitude about the peak maximum is obtained, and the modulated peak maxima can be fitted to, and be adequately described by, a Gaussian curve. The temporal difference between peaks (i) and (ii) in Figure 5b is related to the retardation of the modeled peak arising from the in-built factor for the sampling time of the peak. Table 1 shows a comparison of A, 1tR, and 1σ values found using the modeling process for peaks at selected modulation phases compared to the actual values (other intermediate modulation phases were also tested and all calculated values fit within the trends observed in the table). It can be seen that regardless of modulation phase, the method modeled the same peak shape

Table 1. Comparison of Parameters Found for Modeled Peaksa with the Actual Values for the Original 1D Peakb

1

tR (s) 1 σ(s) A tallest peak (s) a

actual

0°

90°

180°

30.0 2.50 1000 (30.0)

32.5 2.65 11975 32.5

32.5 2.65 11974 33.25

32.5 2.65 11972 31.0 & 34.0

Using sub-peak heights and retention times. b PM ) 3 s; 2tR ) 1 s.

and position; however, the calculated 1D retention time equaled 1 tR + 2tR + 1/2PM and the standard deviation of the peak was slightly larger. These variations are due to the time taken to pass through the 2D column and the delay caused by interface sampling. For LC × LC this delay could be the duration taken for filling of a loop then flushing it to the 2D column; for cryogenic trapping in GC × GC it will be the retardation of the band migration during modulator trapping then release to the 2 D column. The retention time on the 1D column can be easily corrected, as the period of modulation is a known experimental value, and the magnitude of 2tR can be found directly from the total modulated peak retention time, with the subtraction of the appropriate modulation event time (xn ) (nPM) + x0). It may be possible to correct the modeled standard deviation with further mathematical treatment of the data, but that is outside the scope of this paper. This method will not provide the peak area or height of the original peak, as neither the sub-peak area nor the width is taken into account, and the height of the sub-peaks alone cannot be directly related to the area or height of the original 1D peak. Figure 5b highlights the differences between the original 1D peak and the modeled peak. Modeling a 1D Peak using Sub-Peak Areas and Retention Times. Using the sub-peak areas and retention times to model the 1D peak is a similar process to that of using peak heights. Assuming that PM is a constant value, we can interpret the Gaussian distribution cumulative area for each of the modulation events. On use of the relationship shown in eq 2, where the area of each sub-peak originating from a single compound can be related to a specific portion of the original 1D peak, a Gaussian curve was fitted to the data. Here, the areas of each of the sub-peaks correspond to consecutive portions of the modeled peak, each with a width of one PM. As previously, the variables A, 1tR, and 1σ in eq 1 were varied systematically until the best fit was achieved based on the method of least-squares using the Solver feature in Microsoft Excel. When using sub-peak areas instead of peak heights to fit the data, much more accurate results were obtained, as can be seen in the comparison of actual and modeled variables in Table 2 (again, other intermediate modulation phases were tested and all calculated values fit within the trends observed in the table). The peak variables match perfectly and are clearly superior to the modeling based on peak heights; the modeled peak has the same width and area as the original peak, the only difference being a 1 s shift in 1tR. This shift is due to the 1 s retention of the compound on the 2D column chosen in the modeling. The value of 2tR can be found directly from the total modulated peak

Table 2. Comparison of Parameters Found for Modeled Peaksa with the Actual Values for the Original 1D Peakb

1

tR(s) 1 σ(s) A tallest peak (s) a

actual

0°

90°

180°

30.0 2.50 1000 (30.0)

31.0 2.50 1000 32.5

31.0 2.50 1000 33.25

31.0 2.50 1000 31.0 & 34.0

Using sub-peak areas and retention times. b PM ) 3 s; 2tR ) 1 s.

retention time as described above, and so, 2tR can be subtracted from the value to calculate 1tR accurately. This method is also suitable for the modeling of 1D peaks when the sub-peaks are overloaded on the second-dimension. While the retention times and heights of the overloaded subpeaks may be distorted, column overloading does not result in a change in peak area, and so modeling based on peak area will still be accurate. Providing there is at least one sub-peak that is not overloaded, which can be used to determine the correct retention times of all the modulated peaks (each should be spaced PM apart), the method will be able to model the original 1D chromatographic band. To demonstrate two cases that are expected to represent tendency to overload the first column, then the second column, n-bornyl acetate and n-dodecane of increasing concentration were introduced to the GC × GC system. Figures 6 and 7 describe these results. In the n-dodecane case (Figure 6), the 1D stationary phase exhibits good linear chromatography over the 0.05 to 10 µg/ mL concentration range used (0.1-5.0 µg/mL data shown). This can be appreciated by the two sub-peaks at the extremities of the modulated peak distribution (∼10.61 and ∼10.86 min) exhibiting similar relative responses. While the sub-peaks at ∼10.69 and ∼10.77 min for chromatograms (a) 0.1 and (a) 1.0 have similar relative heights, for (a) 5.0 the sub-peak at ∼10.69 min is not much taller than that at ∼10.77 min. This is partly associated with the added overloading of the tallest (a) 5.0 peak causing its height to be somewhat less than expected. Figure 6b shows that even at a concentration of 0.25 µg/mL the tallest peak starts to exhibit some overloading. By 1.0 µg/mL 2D overloading is clearly evident. Since even at the higher concentrations the first sub-peak is not overloaded, it can be expected that the model of 1D retention time should still be accurate. By contrast, Figure 7 shows that n-bornyl acetate is strongly overloaded on the 1D column, and this was evident at the 5.0 µg/mL and more so for the 10 µg/mL solution (Figure 7 (a)10 concentration level; data for 5.0 µg/mL not shown). The 5.0 µg/mL n-dodecane was still controlled by a linear isotherm (i.e., is symmetrical). The sub-peaks for 5.0-50 µg/mL exhibited overloading on the second column (Figure 7(b)) although the peak commencement point is consistent with the increasing concentrations of all solutions 0.1-50 mg/mL. In this case, the peak model cannot be applied to the overall distribution on the 1 D column because peak overloading cannot be modeled by a Gaussian curve. Modeling Based on Three Sub-Peaks. In an attempt to simplify the method further, the modeling of the 1D peak was repeated, but now using only the data from the three largest sub-peaks (retention times and peak areas). Three was chosen Analytical Chemistry, Vol. 81, No. 16, August 15, 2009

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Figure 6. Injection of varying concentrations of n-dodecane using a low-polarity—polar column set. (a) Modulated sub-peaks for sample concentrations shown (0.1 to 5.0 µg/mL). (b) Expanded sub-peaks located at about 10.69 min for sample concentrations shown (0.05 to 5.0 µg/mL).

Figure 7. Injection of varying concentrations of n-bornyl acetate using a low-polarity—polar column set. (a) Modulated sub-peaks for sample concentrations shown (0.1 to 50 µg/mL). (b) Expanded sub-peaks located at about 18.13 min for sample concentrations shown (0.1 to 50 µg/mL).

as there are three unknown variables in the Gaussian equation to solve for (1tR, 1σ, A), and interestingly is consistent with prior studies which evaluated quantitative data in GC × GC limited to the three largest sub-peaks.8-11 Using this limited data set, the exact same peak parameters were obtained in this model. Using either of these methods, height or area, a model of the 1 D peak can be obtained, which is not affected by modulation phase. However, it is much more accurate to model the peak using the sub-peak areas rather than the peak heights. It is possible to adequately model the 1D peak using only the data from three sub-peaks, which further simplifies this method. This is useful because it is easier to identify only the three largest sub-peaks corresponding to any given compound. This provides a more accurate and precise way to report 1tR which is not influenced by changes in the modulation phase. It is also 6802


possible to accurately calculate the primary peak area using only the peak area and retention time data from three subpeaks, instead of summing all of the sub-peaks, for the Gaussian peak model. Application to Real Data. Using the retention time and peak area approach, the method was applied to real data in a GC × GC experiment. n-Bornyl acetate was selected as a symmetrical peak with appropriate dimensions (peak width and retention) for this study. Five replicate injections of n-bornyl acetate without modulation yielded the data shown in Table 3, with a total retention RSD of 0.03% and area reproducibility of RSD 3.8%. n-Bornyl acetate was reinjected 8 times under modulation conditions, with PM ) 4 s. The results in Table 3 show the characteristics of the modeled peaks, using either all sub-peaks for the modeling process or only the three largest sub-peaks; the

Table 3. Retention Time (1tR), Standard Deviation (1σ), and Peak Area (A) Data for Non-Modulated and Modeled Modulated n-Bornyl Acetate Peaks

tR(s)a

1

retention time of the largest modulated peak (s) 1σ(s)

A

peak area (%)b

Non-Modulated Peakc replicate 1 replicate 2 replicate 3 replicate 4 replicate 5 mean RSD (%)

1100.05 1099.83 1099.48 1099.98 1099.34 1099.74 0.03

49.46 48.99 48.92 51.12 53.41 50.38 3.80

replicate 1 replicate 2 replicate 3 replicate 4 replicate 5 replicate 6d replicate 7e replicate 8f mean RSD (%)

Modeled Modulated Peak, PM ) 4 s (All Peaks) 1084.10 1087.69 3.17 1083.85 1087.71 3.18 1084.02 1087.67 3.17 1083.85 1087.69 3.15 1083.80 1083.71 3.14 1084.42 1084.31 3.16 1084.01 1084.89 3.14 1084.14 1085.47 3.12 1084.02 1086.14 3.15 0.02 0.16 0.63

49.80 48.64 47.85 50.06 49.46 49.04 46.12 48.73 48.71 2.59

98.99 98.66 98.68 98.58 98.81 98.61 98.07 98.01 98.55 0.35

replicate 1 replicate 2 replicate 3 replicate 4 replicate 5 replicate 6d replicate 7e replicate 8f mean RSD (%)

Modeled Modulated Peak, PM ) 4 s (3 Peaks) 1084.02 1087.69 3.29 1083.75 1087.71 3.36 1083.93 1087.67 3.31 1083.76 1087.69 3.29 1083.69 1083.71 3.33 1084.30 1084.31 3.36 1083.96 1084.89 3.04 1084.11 1085.47 3.06 1083.94 1086.14 3.26 0.02 0.16 3.98

50.91 50.20 49.07 51.37 51.22 50.88 45.34 48.24 49.65 4.15

101.21 101.81 101.18 101.14 102.32 102.31 96.40 97.01 100.42 2.34

replicate 1 replicate 2 replicate 3 replicate 4 replicate 5 mean RSD (%)

Modeled Modulated Peak, PM ) 3 s (All Peaks) 1082.95 1083.69 3.15 1083.50 1083.69 3.14 1083.14 1083.71 3.14 1083.22 1083.67 3.10 1083.63 1083.64 3.15 1083.29 1083.68 3.14 0.03 0.00 0.66

44.86 45.00 47.09 47.82 47.34 46.42 2.99

98.20 98.37 98.54 98.21 98.66 98.40 0.21

a2 tR has not been subtracted from the modeled 1tR values. b Compared to the sum of the areas of the sub-peaks. c Data from integrator report. d Modulation start time offset: +0.01 min. e Modulation start time offset: +0.02 min. f Modulation start time offset: +0.03 min.

reproducibility data for these values was calculated. As can be seen, there is no significant difference between the two sets of modeling results when either all sub-peaks or the largest 3 subpeaks are chosen (RSD 0.2%). Furthermore, replicates 6, 7, and 8 had the phase of modulation deliberately changed, by altering the modulation start time. This was done by instructing the modulator to commence its operation slightly earlier or later (e.g., by + 0.01 to 0.03 min) and is intended to simulate a situation of modulation timing uncertainty. The method still reliably modeled the peak to generate the same 1tR and 1σ values, as required and expected, despite changes in modulation phase. This is an important observation because the phase of modulation varies over all peaks in a C2DC result because the 1D peaks enter the interface at random times (their phase is not a controllable parameter in normal analysis). The method should give accurate 1tR prediction irrespective of phase. By contrast, the retention time

Figure 8. Comparison of a modulated n-bornyl acetate peak (PM ) 4 s; graphed against the right-axis) and the corresponding modeled 1 D peak (graphed against the left-axis).

of the largest modulated peak varies considerably (RSD 0.16%) indicative of the problem with choice of a single (largest) peak to give a “hypothetical” measure of 1tR. The experiment was repeated with PM ) 3 s, with modeling based on all sub-peaks; results are also shown in Table 3. The modeled 1tR values found were very similar to those found with PM ) 4 s, indicating the method is not affected by changes in modulation period. Furthermore, the relative standard deviations of the retention times of the modeled peaks (0.02%, 0.02%, and 0.03%) and the non-modulated peaks (0.03%) are very similar, suggesting that the variation shown in the 1tR values found for the modeled peaks is within normal variability expected from a GC experiment. However, the relative standard deviations of the retention times of the largest modulated peaks (0.16%, 0.16%, and 0.00%) are not within the range expected based on the 1D GC result. These values are the retention times that would be assigned to the compound under the practice of using the retention time of the tallest modulated peak. Clearly an RSD of 0.00% is unrealistic since chromatographic retention will have an associated uncertainty, as reported for the other data in Table 3. The 0.00% value for total 1tR is an artifact of the very short retention time of the solute on the 2D column, coupled with the precise timing of the modulator. The lack of variation observed for PM ) 3 s arose because, in the absence of phase shifts, the only variation seen is the 2tR variability, which is very small because the second-dimension retention is negligible. The wide variation in values observed for PM ) 4 s was caused by the change of modulation phase and is explained by the discontinuity shown in Figure 3. Interestingly, when PM ) 4 and 3 s are compared, the modeled 1tR value differs by 0.73 s (0.07%), but when using the largest peak, the 1tR values differ by 2.46 s (0.23%) where this apparently is due to phase effects for the different distributions. Overall, the proposed method provides 1tR data that are reproducible, are not affected by the modulation period or the phase of modulation, and the discontinuity seen in Figure 3 does not arise. Figure 8 shows an overlay of a modulated peak profile (a) and the corresponding modeled peak (b) for the bornyl acetate sample peak. It illustrates the difference in retention times caused by retention on the 2D column and the delay caused by interface sampling. The two profiles are plotted on different y-axes because of the zone compression and therefore signal ampliAnalytical Chemistry, Vol. 81, No. 16, August 15, 2009

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fication observed in GC × GC, which results in the modulated peaks being many times taller than the original peak. It can be seen in Table 3 that the tR of the experimental nonmodulated peak does not match the 1tR value found using the modeling approach. This is an artifact of the modulation method, and does not indicate a flaw in the modeling process. When the modulator is operating, cryo-trap coolant (liquid carbon dioxide) is released into the chromatographic oven. The GC temperature control slightly increases oven heating to compensate for the apparent oven cooling caused by the carbon dioxide. This results in slightly increased oven temperatures, and therefore slightly shorter elution times when the modulator is operating compared to when CO2 is not supplied. The proposed method calculates the 1tR time when the compound is predicted to elute from the first column with the modulator in operation, but in Table 3, it is compared to the non-modulated value as an indicator of the expected peak area (this will remain the same) and the normal variation in retention time and peak area for the GC. Notwithstanding this effect, the reproducibility of the modulation process and the retention times are excellent for all GC × GC analyses, as shown in Table 3. This implies that correlation of standards and sample peak positions are exceptionally well reproduced, over an extended period of time (e.g., for a full day of operation), when the cryo-fluid is applied to the modulator. Note that there is no independent way to calculate the exact 1tR values in any C2DC experiment, other than the method proposed here and so precise actual 1tR measurement and confirmation is lacking. CONCLUSIONS In conclusion, the method described provides a robust and reliable approach to reporting 1D retention times in comprehensive 2D chromatography. While the method should be common

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to all C2DC methods, here it has been described for a GC × GC experiment. Simply using the retention time of the largest modulated peak provides neither an accurate nor a reproducible 1 tR value, as small changes in the phase of modulation may vary the apparent 1D retention time by at least one full modulation period. Furthermore, this method provides a new way to measure peak area, which avoids manual summing of sub-peaks by the user, making C2DC more attractive for quantitative analysis. The method can also be used as a means to further investigate fundamental aspects of the modulation process, leading to a greater understanding of the role of the sampling interface in LC × LC and GC × GC. The improved precision of 1tR values should assist identification of components when compared with standards, or from sample-to-sample. It may also aid in the calculation of precise retention indices. A precise estimate of 1tR also removes the “quantized” nature of reported 1tR data as produced by some data systems. Whether this will aid chemometric data interpretation by removing uncertainties in data alignment by basing results on chromatographic reports rather than raw data remains to be evaluated. This work should improve the practice of reporting qualitative and quantitative data in C2DC by providing a validated measure for correctly reporting 1tR and 2tR, and in some instances also peak area values. Although the focus of this work has been GC, the results are equally applicable to other C2DC techniques. Future investigations will focus on the application of this approach to overlapping peaks, and the development of a method for modeling tailing peaks, and for automated calculation of 1tR data for multiple components in a sample. Received for review May 4, 2009. Accepted July 10, 2009. AC900960N

Peak Modeling Approach to Accurate Assignment of First-Dimension

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