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Mar 14, 2016 - (e.g., LECO Pegasus GC × GC offers this option). If the tcyc is longer than the tsamp, it is not possible to sample contiguous H/. C t...
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Continuum in MDGC Technology: From Classical Multidimensional to Comprehensive Two-Dimensional Gas Chromatography Chadin Kulsing,† Yada Nolvachai,† Paul Rawson,‡ David J. Evans,‡ and Philip J. Marriott*,† †

Australian Centre for Research on Separation Science, School of Chemistry, Monash University, Wellington Road, Clayton, Victoria 3800, Australia ‡ Defence Science and Technology Group, 506 Lorimer Street, Fishermans Bend, Victoria 3207, Australia S Supporting Information *

ABSTRACT: Recent advances in multidimensional gas chromatography (MDGC) comprise methods such as multiple heart-cut (H/C) analysis and comprehensive two-dimensional gas chromatography (GC × GC); however, clear approaches to evaluate the MDGC results, choice of the most appropriate method, and optimized separation remain of concern. In order to track the capability of these analytical techniques and select an effective experimental approach, a fundamental approach was developed utilizing a time summation model incorporating temperature-dependent linear solvation energy relationship (LSER). The approach allows prediction of optimized analyte distribution in the 2D space for various MDGC approaches employing different experimental variables such as column lengths, temperature programs, and stationary phase combinations in order to evaluate separation performance (apparent 1D, 2D, total number of separated peaks, and orthogonality) for simulated MDGC results. The methodology applied LSER to generate results for nonpolar−polar and polar−nonpolar 2D column configurations for separation of 678 compounds in an oxidized kerosene-based jet fuel sample. Three-dimensional plots were generated in order to illustrate the dependency of separation performance on 2D column length and number of injections for different stationary phase combinations. With a given limit of analysis time, a MDGC approach to obtain an optimized total separated peak number for a particular column set was proposed depending on 1D and 2D analyte peak distribution. This study introduces fundamental concepts and establishes approaches to design effective GC × GC or multiple H/C systems for different column combinations, to provide the best overall separation outcomes with the highest separated peak number and/or orthogonality.

I

next H/C analysis. Although wraparound could be beneficial to use the complete separation plane in MDGC and reduce the modulation time, wraparound is not preferred in separation due to difficulty in data analysis and quantifying retention or correlation of compound identity or class when wraparound arises. The classical H/C experiment requires a device, for example, Deans switch (DS), to alter the 1D flow direction between a short deactivated fused silica capillary (directed to a monitor detector) and the 2D column, and permits 1D or 2D separations, respectively. Addition of a cryo-focusing device allows trapping of heart-cut zones, which reduces peak broadening during transfer of zones from 1D to 2D columns.5 A fast-operating cryotrap remobilization process maximizes the frequency at which 1D zones may be sampled. The trapping device also enables multiple injection analysis where target analytes can be injected, H/C and trapped several times prior to the 2D separation, improving the limit of detection.6 Although the methods achieve higher resolution, the analysis time required for these various approaches may significantly

dentification of analytes at low levels in complex matrices presents difficulties in petrochemical analysis, for example. Multidimensional gas chromatography (MDGC) is a powerful separation technique that provides high-resolution analysis of such complex samples ideally giving individual molecular-based information on volatile analytes.1,2 This technique conventionally employs two “orthogonal” columns (providing a degree of difference in selectivity toward sample components) connected sequentially, with a device located between these columns offering an effective heart-cut (H/C) or modulation process.3 Compared to one-dimensional (1D) GC, MDGC is superior in terms of separation and column peak capacity (nc) as well as affording an improved detection limit, for example, as a result of the cryogenic refocusing effect and reduced chemical background. Different MDGC options have been implemented from both classical single to multiple heart-cut analyses employing a long 2D column2,4 where the minimum separation time required to complete the 2D separation (which is the retention time of the last eluting analyte on the 2D column, 2 tR,max) is conventionally longer than the H/C window (sampling time, tsamp). For multiple H/C, the time between one sampling window and the next should be ≥ 2tR,max in order to avoid wraparound of peaks in one H/C coeluting during the © 2016 American Chemical Society

Received: October 12, 2015 Accepted: March 12, 2016 Published: March 14, 2016 3529

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occur.12 A MR setting of about 2−4 would be considered usual. To meet this criterion, a longer 2D column requires slower PM, which reduces MR and risks collection of a larger number of components at the modulator over a wider time range; this will reduce apparent resolution on the 1D column. These established approaches offer a “continuum” between GC × GC and multiple H/C analysis, involving interplay between sampling/cycle time and both 1D and 2D separation efficiencies. At the limit, one may consider all comprehensive 2D separation systems to be defined as multiple H/C with different tsamp, tcyc, and Ninj. GC × GC is conventionally defined when the applied tcyc is equal to the tsamp in the absence of wraparound, to enable the whole sample analysis to be completed within a single run. Conversely, comprehensive analysis with longer 2D columns may be obtained by increasing Ninj. Among these advanced technologies, effective evaluation and experimental design methods that can contrast the different approaches employing different column configurations have not been established. Generally, a specific approach will require consideration of goals of the analysis, the needs for separation of target components from matrix, and whether this requires a higher efficiency 1D or 2D column. Trial-and-error experiments may provide an optimization strategy for the best outcome, but there is no guarantee that the best configuration within the “continuum” of possibilities has been selected. Designing the best comprehensive MDGC system is thus critical and is experimentally costly, including cutting different varied lengths of the tested columns as needed. This study develops a fundamental approach for evaluation of comprehensive MDGC (either GC × GC or comprehensive multiple H/C continuum) results for 678 compounds in kerosene-based jet fuels, which have undergone thermal oxidization and includes a variety of alkanes, alkenes and aromatic hydrocarbons, oxidized species (aldehydes and ketones), and additives (e.g., antioxidants and alkyl ether amines). Simulation is based on integration of a time summation model and temperature (T)-dependent linear solvation energy relationship (LSER) data, previously applied for simulation of GC × GC results for a sample containing a large number of analytes including kerosene.13 Separation performance was evaluated according to apparent number of analytes to be resolved in 1D, 2D and overall 2D separation and orthogonality. The studied MDGC systems employed both nonpolar−polar and polar−nonpolar stationary phase combinations. Further study of sampling/cycle time optimization and effects of temperature programs and flow rate on separation performance are simulated and discussed.

increase, according to the implementation procedure. Thus, successful sample analysis is a balance between time and the degree of separation required. Alternatively, comprehensive two-dimensional gas chromatography (GC × GC) applies the 2D separation approach to the whole sample in a single analysis, in a manner that largely preserves the 1D separation, according to a modulation process between the columns7,8 operated at a period faster than the width of an analyte peak on the 1D column. This is quantified by the modulation ratio (MR, the ratio of the 1D peak width to modulation period, PM) value. This interrupts the passage of solute between the columns, repeatedly focusing the solute from the 1D column and then releasing it to the 2D column. In order to complete separation on 2D within the PM, the 2D column must deliver very fast elution, by using one or more of the following: short, narrow bore, thin film columns; higher temperature or flow velocity conditions; low retention factor phases. Strategies to improve 2D separation efficiency may require an increase in PM, (to allow use of a longer 2D column without wraparound); however, this reduces 1D separation, or capacity, by extended sampling of 1D effluent through collecting more analytes during the modulation step.9 Thus, 2 tR,max should be < PM. Fast elution conditions (e.g., < 3−5 s) invariably reduce total 2D separation efficiency (number of plates), so this constrains the difference in retention time (tR) of components that might be reliably resolved. Adjustment of PM and 2D column length (2L) to obtain the optimized overall GC × GC performance is thus a challenge. In all cases, it is useful to consider the following questions: (i) How many components do we expect to elute at any one time from a 1D GC separation? (ii) What is the expected maximum difference in retention factors between components (i.e., most strongly and least retained compounds) that need to be separated? (iii) What is the most difficult pair of compounds that must be separated (i.e., smallest separation factor, α) that will be compromised by the fast elution condition? With the aim of reducing analysis time in MDGC using multiple sampling, as well as maintaining high-resolution 1D and 2D separation, multiple H/C with short tsamp and rapid cycle time (tcyc) was performed by integrating Deans switch and modulator operation.10,11 This technique performs multiple H/ C processes contiguously arranged on the basis of repetitive tcyc, corresponding to the selected 2D separation time (e.g., every 1 min). In this case, tsamp is practically set to be less than (or equal to) and proportional to the tcyc, which is optimized to be 2tR,max; for example, we collect 1D eluate for 0.25, 0.5, or 1 min (tsamp), then allow 1 min (tcyc) to separate this eluate on the 2D column prior to the next collection. The focus here is on constant tcyc, although this parameter could be varied over time in GC × GC (e.g., LECO Pegasus GC × GC offers this option). If the tcyc is longer than the tsamp, it is not possible to sample contiguous H/ C throughout the single run. In this case, coverage of the whole sample requires additional injections. The number of injections required to perform comprehensive MDGC (Ninj) is then equal to the ratio of tcyc to tsamp. A larger Ninj corresponds to shorter tsamp, thus maintaining 1D resolution and fewer sampled components to be separated during 2D separation. At the limit, this therefore describes a classical GC × GC experiment. Thus, to a certain extent, 2L controls the rapidity with which 1 D sampling can be conducted and is partly encapsulated in the MR concept. The normal requirement in GC × GC is that 2 tR,max should not exceed PM, otherwise wraparound may

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EXPERIMENTAL SECTION Graphical Illustration and Nomenclature. Conventional GC × GC analysis requires PM to be at least equal to the minimum time required to complete 2D separation without the presence of wraparound which is 2tR,max. In order to improve 2D resolution, increasing 2D column length (2L) can be employed, permitting longer PM. If PM exceeds peak width in 1D (e.g., 0.5 min), then this affects the apparent analyte 1D peak width, because peaks will now be recognized as having a width corresponding to, for example, 0.5 min. Repetitive modulation with peak width durations tsamp (with Ninj > 1) describe comprehensive multiple H/C. Step-by-step processes illustrating the benefit of increasing Ninj in multiple H/C to reduce coelutions in 2D of 10 hypothetical analytes are given in Figure 2. Processes 1−7 represent real-time modulation of analyte pulses moving from the 1D column (middle) to either the restrictor (short deactivated fused silica column; the upper channel in Figure 2) or the 2D column (the lower column); the directions are selected by using the Deans switch. In GC × GC (Ninj = 1), analytes always flow directly from 1D to 2D columns, as indicated by the single direction arrow for processes 1−7; no H/C is done. The modulation “event” occurs in panels 3 and 7. The other panels are “accumulation” stages. This results in 4 analytes focused into the same pulse prior to elution in the 2D column in process 7 (reducing 1D resolution, e.g. combining 4 resolved peaks on 1D column into a single peak). In multiple H/C with Ninj = 2 (two injections required to fulfill comprehensive analysis), the analyte flow direction changes in step 3 in H/C 1 altering the flow direction of two analytes (gray spheres) to the restrictor. The flow direction in H/C 2 was then set to be the complement of H/C 1 operation in order to fulfill comprehensive analysis (see the right column in Figure 2). The overall comprehensive H/C analysis results in a reduced number of focused analytes to be 2 in process 7 (2 orange analytes separated in H/C 1 and the other 2 gray analytes separated in H/C 2) which improved 1D resolution compared to the GC × GC analysis. An illustration for the

i

∫T i

T R ,j 0, j

1 i

t M(T )[1 + 10ei(T )Ej + si(T )Sj + ai(T )Aj + bi(T )Bj + li(T )LLSER, j + ci(T )]

dT

(2)

where c is an intercept constant. e, s, a, b, and l (stationary phase descriptors) represent stationary phase contributions to the interactions being dispersity, dipolarity, H-bond with acid functionalities, H-bond with basic functionalities and dispersion/cavity formation for gas to liquid phase, respectively. The corresponding analyte descriptors are E, S, A, B, and LLSER. The studied stationary phases are 5% (phenyl)methylpolysiloxane (5 ms), polyethylene glycol (WAX) and an ionic liquid phase (SLB-IL82). Their temperature-dependent LSER descriptors were obtained/extrapolated from literature.18−20 The studied sample contains 678 compounds in oxidized jet fuels, the descriptors of which were obtained from the LSER database with the possible compound types and carbon number obtained from previous literature.13,21,22 The list of analytes is provided in Supporting Information Table S1. On the basis of eq 2, a script for simulation of itR,j of analytes in temperature-programmed 2D separation was developed using Microsoft Visual Basic. In practice, instead of the proposed simulation approach, analyte retention time profiles for each experiment can be obtained by using fully automated peak picking software such as that available in GC Image.

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RESULTS AND DISCUSSION Effect of Sampling Time. The studied model takes into account the tsamp effect on 1tR in comprehensive 2DGC as well 3531

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Figure 2. Step-by-step processes (rows 1−7) illustrating a cycle containing 10 analytes in GC × GC (Ninj = 1, left column) and multiple H/C (Ninj = 2, right columns) analysis. Analytes represented by orange spheres and the gray spheres are the focused analytes affected by the two methods. The corresponding Deans switch flow in each case is indicated by the arrows. The depiction in this figure is performed with very low MR, where several analytes were focused into a single peak in one modulation event, in order to provide a clear and simple example of an extreme case of sampling. It is worth noting that such a low MR is not used in most instances of GC × GC although is not strictly forbidden.

as 2tR variation (due to elution temperature on the 2D column depending on 1tR) because the passage of analytes is interrupted during the sampling period. This results in rounding-up of 1tR values to be multiples of the value of the applied tsamp, which can be directly added into the simulation for correction of 1tR prior to calculation of 2tR. For example with tsamp = 10 s, with a repetitive sampling process starting at the beginning of the separation, 1tR of an analyte will be shifted from 11 to 20 s (Roundup [11/10] × tsamp = 20). The elution temperature of this analyte on the 2D column should then be the prevailing temperature at 20 s. Note that optimized tsamp (or PM in GC × GC) is the minimum value of tcyc, which here is equal to 2tR,max for all chromatographic simulations. The application of comprehensive multiple H/C with Ninj analysis replicates allows adjustment of tsamp to be proportionally shorter than the tcyc (here tsamp = tcyc/Ninj). The effect of peak splitting (where one analyte peak may be sampled into two neighboring events)

during the sampling/modulation period is not taken into account in this study. Ideally, addition of peak splitting into more than one sampling event should not affect the total number of peaks to be resolved. For quantification purposes, analysis of one or several slices of a component can be performed. Thus, it is reasonable to select a slice representing all the slices for each compound (here, the modulated slice being closest to the peak apex was selected). The other slices of a certain analyte (e.g., minor slices) can coelute with other modulated slices from other analytes. When the bin coverage counting is performed, a single occupied bin will be counted as one regardless of the coeluted slices occupying this bin. Thus, addition of modulated slices will insignificantly affect the calculation of bin coverage (number of peaks to be resolved). In addition, peak spitting can cause the situation that one analyte was counted >1 times in the bin coverage calculation due to the split peaks. This will result 3532

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Figure 3. Simulated grid-scale normalized chromatograms for the jet fuel sample containing peak positions occupying bins throughout the 2D space (1 dot = 1 occupied bin) on (A) 5% (phenyl)methylpolysiloxane (5 ms) × polyethylene glycol (WAX) and (B) SLB-IL82 × 5 ms column sets, with variation of 2D column length (2L) and number of injections to complete the comprehensive analysis (Ninj). The other conditions used for simulation of both (A) and (B) are the same; 1L = 30 m, 1D column flow rate (1F) = 2F = 1.5 mL/min and temperature program = 3 °C/min from 40 to 280 °C and held at 280 °C until the last analyte is eluted. Note that these figures are constructed assuming no wraparound.

of 10 °C/min. The 2wb was 0.3 s with 2L = 0.5 m and 2tR = 2 s, and 2wb was 3 s with 2L = 20 m and 2tR = 120 s, roughly approximated from experimental peak widths previously reported.10 By assuming that H (plate height) for all the investigated columns is the same, the 2wb values at different 2L were approximated according to the relationships in eqs 3 and 4.

in the bin coverage value being larger than that of the total number of analytes, which is not preferred in the conventional bin calculation process. Repetitive counting then needs to be removed, which will finally be the same as counting the number of peaks by ignoring the effect of peak splitting. Effect of Analyte Peak Width and Calculation of Apparent Number of Separated Peaks. Conventional peak capacity23 (nc) is calculated by filling in the whole available separation space between the first (e.g., the peak eluting at void time) and the last eluting analytes with an average peak width assigned. Selectivity has not been included in the nc calculation. Selectivity effects of peak capacity was included in this study via calculation of the apparent number of separated peaks distributed in the 2D separation space, defined as the apparent number of peaks that a system can separate (Papp,total). Comparison of this parameter across different separation systems is limited to measurements undertaken on the same sample. Otherwise, use of an extremely efficient system with very high overall peak capacity to separate a sample containing a few analytes would be considered to have a much lower Papp,total than use of a much less efficient system for separation of a complex sample containing several thousand analytes with only a few dozen components separated. Thus, the maximum Papp,total values do not exceed the total number of analytes in the samplehere a jet fuel comprising 678 compounds. After peak positions are identified in the 2D separation, Papp,total is the number of successfully separated peaks with acceptable separation time in the 2D space, defined here as the difference in retention times of any two adjacent peaks (ΔtR) which equals or is larger than the average peak width at baseline in each dimension (1wb and 2wb), the magnitude of which depends on column length and representative tR. For 1D separation, 1L is fixed to be 30 m in all cases in this study. The 1 wb is set to be 30 s for the separation with the flow and temperature ramping rate being 1.5 mL/min and 3 °C/min. The 1wb value is set to be 15 s at the temperature ramping rate

Nplate =

Nplate

L H

(3)

⎛ tR ⎞2 = 5.545⎜ ⎟ ⎝ wh ⎠

(4)

By solving eqs 3 and 4 wh =

5.545

H(t R )2 L

or 2

wb =

H (t R ) 2 2 wh = 5.545 1.18 1.18 L

(5)

where wh is the representative peak width at half height. According to the experimental data above, H was approximated from the inverse of the slope of Nplate vs L (eq 3) to be 0.0008 m and used for all simulations in this study. By using eq 5, 2wb at any 2L and tR can be approximated. Papp,total is estimated from the total number of peaks having baseline separation in a 2D chromatogram, where tR of two adjacent peaks in each separation dimension has a ΔtR ≥ wb. In order to calculate Papp,total, mathematical bin grids were drawn in a normalized chromatogram which can be generated by normalizing each analyte tR according to t R,normalized = 3533

t R − t R,min t R,max − t R,min

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Figure 4. Three-dimensional plots of apparent number of separated peaks (Papp,total) as a function of 2D column length (2L) and number of injections (Ninj) to complete the comprehensive analysis for simulated jet fuel sample separation results on (A) 5 ms × WAX and (B) SLB-IL82 × 5 ms column sets, with simulated grid-scale normalized chromatograms employing optimized 2L at different Ninj for each column set indicated by the black dotted arrows. C,D,E show corresponding profile lines along the 3D surface. The other conditions used in A−E are the same as those in Figure 3. Effects of 2F rate and temperature ramping rate are shown in F: 3 mL/min and 3 °C/min in (b) and 1.5 mL/min and 10 °C/min in (c), compared to the conditions used in A−E as plotted in (a).

where tR,min and tR,max are retention times of the least and most retained analytes. Plots between 1tR,normalized and 2tR,normalized were then constructed. The total number of available bins (binstotal) is equal to the conventional peak capacity in 2DGC, nc = 1nc × 2nc ∼ Roundup[(Δ1tR/1wb) × (Δ2tR/2wb)] where ΔitR = itR,max − itR,min. Since we assume all bins have the same dimensions, each bin grid in the normalized chromatogram has 1 D and 2D lengths being 1/(Δ1tR/1wb) and 1/(Δ2tR/2wb), respectively. Consequently, the position of each grid at different location from the coordinate (0,0) in the normalized chromatogram can be described by the values 1m × (1wb/ Δ1tR) and 2m × (2wb/Δ2tR), where im is a whole number representing the number of separation dimensions being 1, 2, 3, .... Each analyte coordinate in the normalized 2D plot can then be transformed from (1tR,normalized,2tR,normalized) to be (1m × (1wb/ Δ1tR),2m × (2wb/Δ2tR)) providing that the conditions (1m − 1) × (1wb/Δ1tR) ≤ 1tR,normalized < 1m × (1wb/Δ1tR) and (2m − 1) × (2wb/Δ2tR) ≤ 2tR,normalized < 2m × (2wb/Δ2tR) are true. By using Microsoft Excel formulae with IF, AND, TRUE, and SUM functions, a “grid-scale normalized plot” can be generated by transforming all analyte positions in the normalized 2D plot into the scales of grids (see Supporting Information Figure S3). Papp,total can then be calculated by counting the total number of bin grids containing analytes. Since a bin grid is counted as one when there are ≥1 analyte inside the grid regardless of the number of analytes, the total number of bins containing analytes (Papp,total) can be counted by removing the duplicated

coordinates of any analytes in the grid-scale normalized plot. This counting is performed by using “Remove Duplicates” command in Microsoft Excel. Effect of Stationary Phases and the Impact of Increasing Number of Injections (Ninj) on Separation Performance. In order to understand the dependency of the optimized separation condition on stationary phase combination and the advantage of increasing N inj, results in comprehensive 2DGC with Ninj = 1 (GC × GC) and Ninj > 1 (multiple H/C) for two column sets including nonpolar− polar (5 ms × WAX) and polar-nonpolar (SLB-IL82 × 5 ms) phase combinations were simulated. The capability to resolve analytes in the jet fuel in 1DGC (1Papp) was simulated for 5 ms, WAX and SLB-IL82 being 113, 100, and 96, respectively. Gridscale normalized comprehensive 2DGC results simulated with different 2D column lengths (2L) and injection number (Ninj) are shown in Figure 3. General trends can be clearly observed without requiring calculation of Papp values. The use of a short polar column (WAX) as the 2D column resulted in insufficient 2Papp where analyte peaks are clearly located in a narrow row range of the bins. Thus, most analytes are horizontally (rather than randomly) aligned in the grid-scale normalized chromatograms (e.g., see Figure 3A for 2L = 0.5 m). Increasing 2L improved analyte peak capacity and distributed analyte peaks better in the 2 D dimension and improves 2Papp (see Figure 3A) for 2L = 0.5, 1, and 5 m at Ninj = 1. Increasing Ninj did not provide significant improvement in both 1D and 2D separation. Compared with 3534

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Figure 5. (A) Diagram illustrating the improved orthogonality calculation (upper plot) compared to the conventional calculation approach (lower plot), with calculated O values based on the developed approach here as functions of 2L for different number of injections to complete the comprehensive analysis (Ninj = 1, 2, 4, 8, 20, 40, 100 represented by •, Δ, × , + , □, * and ⧫, respectively) for simulated jet fuel sample separation results on (B) 5 ms × WAX, and (C) SLB-IL82 × 5 ms column sets.

the same 2L column, 2Papp can be improved by using the nonpolar 5 ms (with higher 1D capacity) as the 2D column (e.g., compare Figure 3A and 3B for 2L = 0.5 m). However, further improvement in 2Papp by increasing 2L resulted in greater 2tR,max. tcyc should thus be increased in order to avoid wraparound. This leads to reducing 1Papp where analyte peaks are forced to locate in a limited number of columns of the bins. This resulted in most analytes being vertically aligned in the 2D grid-scale normalized chromatograms (e.g., see Figure 3B for 2L = 5 m at Ninj = 1). This is the situation when increasing Ninj provided significant improvement in the peak distribution in 1D direction (see Figure 3B for 2L = 5 m at Ninj = 4). The benefit of increasing Ninj on improved separation is more pronounced at greater 2tR,max observed at longer 2L (see Figure 3B for the comparison of increasing Ninj values for 2L = 0.5 and 30 m). A diagram illustrating improved Papp,total by increasing Ninj and 2L is provided in Supporting Information Figure S4. It should be noted that the actual time or peak position will not clearly illustrate how many peaks are resolved in the absence of peak width data. For example, almost the same pattern was observed in the simulated 1tR vs 2tR plots for 1 D 5 ms (30m) and 2D WAX (0.5m) with n = 1 and 1D 5 ms (30m) and 2D WAX (30m) with n = 12 (Supporting Information Figure S5A,C); the use of grid-scale normalized

chromatograms clearly differentiate these two results (Supporting Information Figure S5B,D). The grid-scale plots illustrate the number of resolved peaks, and at the same time, the actual time and peak width are already captured inside the grid sizes in the grid-scale plots. Also note that the grid-scale normalized chromatograms will be more significantly different from the corresponding 1tR vs 2tR plots especially when small 2tR values were simulated (e.g., with a short 0.5 m 2D WAX phase as shown in Supporting Information Figure S5A,B) because the 2tR difference between any two adjacent peaks becomes relatively less than the analyte peak width, resulting in incompletely resolved peaks, and will be counted as only one grid occupying these peaks. Thus, each bin grid-scale might represent multiple peaks, but these will be unresolved due to the scale of the bin dimensions. These peaks will then be counted simply as a single peak centered in the bins. On the other hand, the grid-scale chromatograms showed similar results to that of conventional 2D results in the 1D direction (e.g., with a long 30 m 2D 5 ms phase as shown in Supporting Information Figure S6A,B) because the influence of the modulation process with extended sampling time already dominates the separation pattern. Further understanding can be obtained when calculating Papp,total values. Three-dimensional plots for Papp,total for each column set were plotted against 2L and Ninj, shown in Figure 4A,B, with corresponding 2D plots shown in Supporting 3535

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Analytical Chemistry

a suitable approach for O calculation should clearly differentiate these two 2DGC results where (a) is expected to result in greater number of separated peaks and occupied bins (and thus better O), rather than (b) where no peaks can be separated in the 2D column. Two conventional approaches for O calculation, both of which are based on the use of normalized chromatograms, are considered in this study. The first approach involves O based on AO scale, which is calculated according to the peak distribution in the normalized chromatogram relative to four main asterisked axes in the 2D space by ignoring the bin coverage (Σbins, the number of bins containing peaks).24 Although the AO scale is effectively applied for a wide range of applications,13,24 this approach, including several other methods applying conventional normalization process such as geometric and factor analysis approaches,25,26 unavoidably results in the same O for both (a) and (b) in Figure 5A, which may not be suitable for the calculation of O in this study. However, it should be noted that these previously established approaches are applicable to evaluate the MDGC results as presented in this study as long as suitable normalization methods are adopted. Alternatively, Σbins can be taken into account according to the previously established approach.27 Briefly after normalization, correlation of distribution pattern of 2D peaks (Cpeak) can be calculated from R2 of the correlation of 1tR,normalized and 2 tR,normalized as

Information Figure S5. Papp,total obtained for all simulated separations with the 5 ms × WAX set are mainly governed by the 1D separation (1Papp ≫ 2Papp, Supporting Information Figure S5A) while Papp,total values of most of the separations employing SLB-IL82 × 5 ms are more strongly affected by the 2 D separation especially at Ninj < 3 or 2L > 10 m, see Supporting Information Figure S5B. At Ninj = 1 (GC × GC analysis), increasing 2L initially resulted in improved Papp,total on the 5 ms × WAX column set. The Papp,total values on this column set at 2L > 10, as well as Papp,total on the SLB-IL82 × 5 ms set, decreased with increasing 2 L due to the significant increase in 2tR,max (and thus tcyc) resulting in reduced 1D resolution. Increasing Ninj in multiple H/C analysis resulted in progressive improvement in Papp,total at longer 2L. By increasing Ninj from 1 to 2, the optimized 2L (resulting in optimized Papp,total) on the SLB-IL82 × 5 ms set changed from 0.5 to 30 m, respectively, compared to the corresponding change from 10 to 20 m on the 5 ms × WAX setrefer to the corresponding grid-scale normalized chromatograms employing optimized 2L at different Ninj indicated by the black dotted arrows in Figure 4. This indicates the greater benefit of increasing Ninj on the polar−nonpolar column set. Increasing Ninj even leads to better performance of SLB-IL82 × 5 ms (see column set B in Figure 4C), although the performance of 5 ms × WAX is better in GC × GC analysis (Figure 4E). The effect of increasing Ninj on the optimized column sets is clearly shown by the switching trend from better performance on 5 ms × WAX to the SLB-IL82 × 5 ms set at 2L = 15 m simulated in Figure 4D. In addition, temperature program and flow rate (F) also affects dependency of Papp,total on 2L. The trend is mainly governed by the change in overall analyte selectivity and efficiency as represented by wb. For example, if the effect of narrower wb is dominant while overall selectivity remains similar (e.g., by appropriately increasing 2F), the magnitude of Papp,total increases especially at longer 2L (see (b) compared (a) in Figure 4F). On the other hand, if the effect of decreasing overall selectivity is dominant with wb being insignificantly narrower (e.g., by increasing temperature ramping rate from 3 to 10 °C/min), the magnitude of Papp,total decreases (see (c) compared with (a) in Figure 4F). Apparent Number of Separated Peaks (Papp,total) for Improved Orthogonality Calculation. The concept of Papp,total is also incorporated into the orthogonality (O) calculation in order to take into account L and wb effects because conventional O and bin coverage calculations are not significantly sensitive to such effects. An extreme ideal case is given in Figure 5A where two 2DGC results for 678 compounds separated with the same column set but with different 2D column lengths result in exactly the same 1tR and 1 wb; however, 2tR and 2wb values of the same analytes in one separation are always 10 times and 2 times higher, respectively, than those in the other separation (see corresponding 1tR versus 2 tR plots (a) and (b), respectively, in Figure 5A). Note that with a longer 2D column in GC × GC one would need to use a longer modulation period, which would consequently lead to apparently wider peaks in the 1D separation (peaks cannot be narrower than the bin width). Thus, this example should only apply to MDGC with multiple injections. In this case, both (a) and (b) will be normalized to generate the same chromatogram (see the middle 2D plot in Figure 5A). Since this study investigated column length effects,

Cpeak = 1 − R2

(7)

Total number of bin grids (binstotal) and Σbins were counted. The bin coverage ratio (Cpert) was calculated as eqs 8 and 9. Cpert =

∑ bins 0.63 × binstotal

O = Cpert × Cpeak

(8) (9)

However, the conventional bin coverage based approach requires binstotal to be the same as total number of separated analytes (analytestotal). This unavoidably results in the same O value for both (a) and (b) being 0.38 (see the lower plot pathway in Figure 5A). In order to include the dependency of wb, tR, and L, the calculation of Cpert was therefore modified. Because the parameter Papp,total defined above already takes into account such dependency, Cpert can be calculated as Cpert =

Papp,total analytestotal

(10)

Σbins in eq 8 is equivalent to Papp,total in eq 10, and binstotal is equal to the conventional peak capacity (nc) instead of analytestotal. Note that by assuming both (a) and (b) resulted in the same 1wb, being 30 s with different 2wb being 2.1 for (a) and 1.1 s for (b), the binstotal value can now be as much as 1436 and 274 bins for (a) and (b), respectively. Due to the fact that all analytes can be resolved without fully occupying the total 2D space, binstotal (or nc) can be much more than analytestotal, and the statistical number “0.63” was removed. The Papp,total values for (a) and (b) are different, being 304 and 129, respectively. Thus, by using eqs 7, 9, and 10, their O could now be differentiated. As expected above, the O value for (a) is higher than for (b), as shown in Figure 5A (upper plot). The O value for (a) (0.36) is also similar to the conventional O calculation (0.38). This approach was then applied for O calculation for the 3536

DOI: 10.1021/acs.analchem.5b03839 Anal. Chem. 2016, 88, 3529−3538

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Analytical Chemistry simulated 2DGC results in this study. O values as functions of 2 L at different Ninj are shown in Figure 5B,C. However, it should be noted that O calculation approach in this study is only applicable whenever the total number of analytes to be separated is known or at least can be approximated (e.g., by using high-resolution MS with automated peak-picking software).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

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Notes

CONCLUSIONS Fundamental approaches based on the combination of the time summation model and temperature-dependent LSER concepts for simulation and evaluation of comprehensive 2DGC configurations were established. Here we simulate a large set of results employing two different column combinations being nonpolar−polar and highly polar−nonpolar as clear examples for better understanding of the comprehensive 2DGC continuum via the two main parameters, being 2D column length (2L) and number of injections (Ninj) included in the experiment. The best 2D separation conditions and techniques were defined by column combinations. Among the tested columns, the 1D peak capacity toward jet fuel sample components (mostly nonpolar analytes) of the nonpolar column (5 ms) was the highest. In a single injection analysis with Ninj = 1 (GC × GC), separation is mainly governed by the 1 D column performance. Nonpolar−polar performance is thus simulated to result in better performance (better apparent number of separated peaks, Papp,total), where a certain 2L value is required to obtain optimized Papp,total in the separation. On the other hand, an increase in Ninj by performing multiple H/C allows longer 2D columns to be employed without wraparound (simulated here with longer 2L, resulting in improved Papp,total with increasing Ninj). Such capability ultimately leads to Papp,total governed by the 2D column peak capacity. To this end, although a highly polar−nonpolar combination resulted in less Papp,total in GC × GC compared to that of the nonpolar−polar set, Papp,total of the former set can be significantly improved with increasing Ninj in multiple H/C analysis, even resulting in larger Papp,total, but this outcome is obtained at the expense of time. A compromise between time and separation performance should thus be made. Furthermore, although a conventional O calculation cannot be effectively applied for the evaluation of 2DGC systems with variation of 2L and Ninj in this study, the new approach for O calculation provided clear evaluation, being in agreement with the system evaluation based on Papp,total analysis. The simulation confirmed that the higher peak capacity column should be used as the 1D column in GC × GC and provided priority toward time saving; the higher peak capacity column is better applied as 2D in comprehensive multiple H/C with large Ninj. It should also be emphasized that the 2L and Ninj should be specifically optimized for each column set. This study establishes relevant theoretical concepts and approaches to better understand optimization processes in comprehensive 2DGC. The application of these approaches is not limited to only jet fuel separation but also applicable to experimental design and column selection for separation of any sample.

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Additional details, figures, list of analytes, and the corresponding LSER descriptors (PDF)

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Y.N. acknowledges the Monash Institute of Graduate Research, School of Chemistry and Faculty of Science for scholarship support. We acknowledge funding from the ARC Discovery and Linkage program grants DP130100217 and LP130100048. P.M. acknowledges ARC funding for a Discovery Outstanding Researcher Award.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.5b03839. 3537

DOI: 10.1021/acs.analchem.5b03839 Anal. Chem. 2016, 88, 3529−3538

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Analytical Chemistry (26) Cordero, C.; Rubiolo, P.; Sgorbini, B.; Galli, M.; Bicchi, C. J. Chromatogr. A 2006, 1132, 268−279. (27) Zeng, Z. D.; Hugel, H. M.; Marriott, P. J. Anal. Chem. 2013, 85, 6356−6363.

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DOI: 10.1021/acs.analchem.5b03839 Anal. Chem. 2016, 88, 3529−3538