Experimental Study of the Quantitative Precision for Valve-Based

Data acquisition was accomplished using a National Instruments SCB-68 data acquisition board coupled to LabVIEW 8.2 software (National Instruments, Au...
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Experimental Study of the Quantitative Precision for Valve-Based Comprehensive Two-Dimensional Gas Chromatography W. Christopher Siegler,# Brian D. Fitz, Jamin C. Hoggard, and Robert E. Synovec* Department of Chemistry, Box 351700, University of Washington, Seattle, Washington 98195-1700, United States ABSTRACT: For complex sample analysis, there is a need for multidimensional chromatographic instrumentation to be able to separate more compounds, often in shorter time frames. This has led to the development of comprehensive twodimensional chromatographic instrumentation, such as comprehensive twodimensional gas chromatography (GC  GC). Lately, much of the focus in this field has been on decreasing peak widths and, therefore, increasing peak capacity and peak capacity production. All of these advancements make it possible to analyze more compounds in a shorter amount of time, but the data still need to remain quantitative to address the needs of most applications. In this report, the relationship among the modulation ratio (MR), peak sampling phase (ϕ), retention time variation (ΔtR), and how these parameters relate to quantitative analysis precision via the relative standard deviation (RSD) was studied experimentally using a valve-based GC  GC instrument. A wide range of the number of modulations across the first dimension peak width, that is, a MR range from ∼1 to 10, was examined through maintaining an average first dimension peak width at the base, 1wb of ∼3 s and varying the second dimension separation run time from 300 to 2900 ms. An average RSD of 2.1% was experimentally observed at an average MR of 2, with a corresponding peak capacity production of ∼1200 peaks/ min possible. Below this MR the RSD quickly increased. In a long-term study of the quantitative precision at a MR of 2.5, using 126 replicate injections of a test mixture spanning ∼35 h, the RSD averaged 3.0%. The findings have significant implications for optimizing peak capacity production by allowing the use of the longest second dimension run time, while maintaining quantitative precision.

n ongoing thrust in the chromatography field is to be able to separate increasingly complex mixtures in shorter amounts of time. Peak capacities can be increased simply by going to longer separation times; however, this is not desirable if a short analysis time is needed. This requires instrumental methods to have higher peak capacities per unit time (i.e., higher peak capacity production). One way to achieve high peak capacity is to perform multidimensional separations, such as comprehensive two-dimensional (2D) gas chromatography (GC  GC),17 LC  LC,813 LC  GC,14,15 LC  CE,16,17 CE  CE,18,19 as well as, GC  GC  GC,20,21 LC  GC  GC,22 and LC  LC  CE.23 One of the requirements for a 2D separation to be comprehensive requires the peaks eluting from the first dimension to be representatively sampled by the modulator for the second dimension separation.24 In this regard, modulation sampling from one dimension to the next is often achieved through total transfer; that is, all of the effluent from the first dimension is subsequently transferred to the second dimension. For comprehensive instruments that do not utilize total transfer, the sampled portion and sampling frequency (i.e., second dimension separation run time, which is the modulation period)25,26 in the modulation transfer become even more critical for maintaining quantitative reproducibility while concurrently impacting peak capacity production. Although increasing the modulation period increases peak capacity production, which is beneficial, the first dimension peaks are concurrently sampled fewer times (keeping the first dimension peak width constant); hence, the extent to which the data are quantitative and the 2D separation remains comprehensive may be

A

r 2011 American Chemical Society

compromised if the modulation period is increased beyond an acceptable level. Optimizing the peak capacity production should be accomplished concurrent with maintaining a high level of quantitative precision. This inter-relationship has been theoretically studied for total transfer, valve-based LC  LC27 and experimentally for total transfer, thermally modulated GC  GC.26 In pioneering reports by Seeley,28,29 the quantitative dependence for nontotal transfer modulation GC  GC designs, with regard to the number of modulations across a peak and the peak sampling phase on the observed peak area, was studied theoretically and, to some extent, experimentally. If the duty cycle of the modulation and the phasing of the modulations across the peak are known, the expectation value for the peak area can be calculated.28 By spanning across the full range of 100% in-phase to 100% out-of-phase modulation, one can obtain the minimum number of modulation periods across a peak necessary to remain below a certain error in quantitative precision. Theoretically, a quantitative precision (relative standard deviation (RSD)) of 0.1% or less can be obtained with at least three modulations across the width of the base of a peak.28 In the more recent report,29 an initial study was presented that indicated experimentally that the RSD was ∼1% for a modulation ratio (MR)26 greater than ∼2.5, and below this MR, the RSDs rapidly increased. Received: February 3, 2011 Accepted: May 31, 2011 Published: May 31, 2011 5190

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In this report, we seek to build upon these reports,28,29 by providing an in-depth experimental investigation, to put into context the relationship between the MR and the peak sampling phase (ϕ), which could result from run-to-run retention time variation (ΔtR), and how these relate to the RSD. Additionally, we seek to provide insight into what extent MR is related to peak broadening for a nontotal transfer, valve-based GC  GC instrument and, hence, the impact on the experimentally achievable comprehensive 2D peak capacity nc,2D via the first dimension broadening factor, β.25 The inter-relationships among the MR, β, ϕ, ΔtR, and RSD will be extensively studied experimentally. A test mixture was separated on a valve-based GC  GC instrument20,21,3033 such that all of the analytes have a four standard deviation width at their base, 1wb of ∼3 s on the first dimension. The test mixture was initially analyzed with eight replicate injections while varying the second dimension run time (i.e., the modulation period PM) from 300 to 2900 ms so as to span the MR range of ∼1 to 10. The peak areas (summed signal) for each analyte replicate as well as the quantitative precision for each set of modulation replicates were calculated in order to determine at which MR the precision becomes problematic. While eight replicate injections were likely to provide a good indication of how the instrument performs over a small time period (in this study, it was only over a time span of approximately two hours), an in-depth study into the long-term precision of the instrument was also conducted by performing 126 replicate injections spanning approximately 35 h at a PM of 1180 ms which corresponded to an average MR of 2.5. The results reported herein may have broad implications for all comprehensive 2D separations in which not all of the analyte is transferred from the first column separation to the second column separation.

’ THEORY For a comprehensive 2D separation, the theoretical peak capacity with a chromatographic resolution criterion of Rs = 1 is given by the following equation: nc, 2D ¼

1

t 2t 1w 2w b b

ð1Þ

where 1t is the first dimension separation time and 2t is the second dimension separation time, which is equal to the modulation period, PM. The 2D peak capacity production34 is obtained by dividing both sides of eq 1 by 1t, and substituting the MR for 1wb / PM to yield the following: nc, 2D 1 1 ¼ 1t MR 2 w b

ð2Þ

If fewer modulations per first dimension peak can be tolerated, at the constant 1wb (and still achieve a satisfactory RSD), the 2D peak capacity production can be increased (to the extent that the second dimension peak widths do not overly increase as PM is increased). We also seek to investigate what extent undersampling via β25 (going to a lower MR) has on 2D peak capacity and peak capacity production with the nontotal transfer GC  GC design. If an undersampling correction is required, the 2D peak capacity is given by the following: 

nc, 2D ¼

nc, 2D β

ð3Þ

where β is the undersampled first dimension peak width, 1w*, b divided by the true (fully sampled) first dimension peak width, 1 wb, from eqs 1 and 2, given by the following: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1  w ð4Þ β ¼ 1 b ¼ 1 þ 3:4ð1=MR Þ2 wb An expression similar to eq 3 for peak capacity production is not shown for brevity. To better view and critically evaluate multiple analytes on the same plot, the relative signal area (RSA) for each analyte at each MR will be used, which removes changes in detected sensitivity from one analyte to the next. The RSA was calculated by dividing the peak area at each MR by the average peak area for the most highly modulated first dimension peak width, that is, the 2D separations that were collected with a PM of 300 ms for 1wb of ∼3 s, resulting in a MR of ∼10. Because the phase condition for each analyte is not readily known with experimental data (in contrast to theoretical studies), we elected to plot the RSA results as a function MR, and not as a function of ϕ.

’ EXPERIMENTAL SECTION An Agilent 6890 gas chromatograph instrument (Agilent Technologies, Santa Clara, CA, U.S.A.) was modified to produce a valve-based GC  GC instrument. A high-speed, six-port diaphragm valve VICI model DV-12-1116 (Valco Instruments Company Inc., Houston, TX, U.S.A.) fitted with a 5 μL sample loop was face mounted to the GC instrument.30 Installation of a face mounted valve enables the instrument to operate over the entire column temperature range. The stock electrometer for our Agilent flame ionization detector (FID) had been replaced with a high-speed electrometer built in-house, although, in principle, the stock Agilent FID at 500 Hz would be sufficient for this experiment. Data acquisition was accomplished using a National Instruments SCB-68 data acquisition board coupled to LabVIEW 8.2 software (National Instruments, Austin, TX, U.S.A.). Data were collected at 100 kHz and boxcar averaged to 500 Hz. The GC  GC instrument was configured as described below. A 30 m, 250 μm inner diameter (i.d.), 0.5 μm film thickness (5% phenyl)-methyl polysiloxane stationary phase column (DB-5; J&W Scientific/Agilent Technologies, Santa Clara, CA, U.S.A.) was installed as the primary column (column 1), while a 1 m, 180 μm inner diameter (i.d.), 0.2 μm film thickness trifluoropropyl-methyl polysiloxane stationary phase column (Rtx-200; Restek, Bellefonte, PA, U.S.A.) was installed as the secondary column (column 2). A seven-component test mixture was used to experimentally study the relationship among the MR, ϕ, and ΔtR, and how these relate to RSD of the quantitative analysis. The test mixture was prepared by combining equal masses of the following compounds: ethyl acetate, heptane, toluene, 1-chlorohexane, cyclooctane, decane, and octanol and diluting the resulting mixture 1:10 by volume in acetone. A 1 μL neat injection of this solution was made onto the GC  GC instrument with a HP 7673 autoinjector into a 250 °C split/splitless inlet with a 250:1 split using hydrogen as the carrier gas. The effluent from column 1 was injected onto column 2 with a six-port diaphragm valve set to actuate for 20 ms at the following modulation periods (PM), for the first study—300, 500, 700, 900, 1100, 1300, 1500, 1700, 1900, 2100, 2300, 2500, 2700, and 2900 ms—and at a PM of 1180 ms for the second study. The pulse width on the valve was sufficient to 5191

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Table 1. Peak Metrics from a Gaussian Best Fit Function of the First Dimension Raw Data for all Analytes with the Corresponding MR for a PM of 300 ms analyte

1

tR (min)

1

wb (s)

MR

2

wb (ms)

(1) ethyl acetate

3.7

2.6

8.8

(2) heptane

4.9

3.0

9.9

12

(3) toluene

6.1

3.1

10.0

24

(4) 1-chlorohexane

7.5

2.9

9.7

18

(5) cyclooctane (6) decane

8.5 9.5

3.2 2.9

11.0 9.8

17 14

10.5

2.9

9.8

78

(7) octanol

23

of ∼2.5. The method of peak quantification was to sum the baseline corrected signal for a given analyte peak across all second dimension modulations. Additionally, a Gaussian best fit function was applied to obtain 1wb values for each analyte at the different MR values.

Figure 1. (A) Raw data at MR ∼ 10 shown for all analytes separated by GC  GC. The first peak (not numbered) is the acetone solvent peak. Analytes are numbered as listed in Table 1. (B) Zoomed-in view of the data for ethyl acetate (MR ∼ 9). (C) A section of the 2D contour plot for the heptane and toluene signals, with a 1wb ∼ 3.0 s and a 2wb ∼ 25 ms; nc,2D ∼ 240 peaks/min is achieved (per eq 2). (D) Relative peak width as a function of MR for ethyl acetate for MR greater than or equal to 2. Experimental relative peak width, with black symbols and error bars (eight replicates), is 1wb (at the MR indicated) normalized to 1wb at MR ∼ 9. Fractions, f, injected by the modulator valve are indicated for MR ∼2 and 9. The β function is also indicated (eq 4).

readily clear the sample loop volume. The flow rate at the end of column 1 (following the valve modulator) was held at 1.2 mL/min for the entire GC  GC separation (requiring a column 1 head pressure of 17 psig), while the auxiliary pressure controller for column 2 was set to maintain a constant pressure of 20 psig. The column 2 head pressure is independent of that of column 1 via the valve modulator interface, and the column 1 combination with the valve sees atmospheric pressure at the valve vent. The 5 μL sample loop fill time was 250 ms, which is sufficient time to fill the sample loop for all of the PM conditions, so a constant amount of analyte was injected per each modulation (simply the number of modulations across the peak changed with MR). Hence, at a PM of 300 ms (MR ∼ 9), the fraction, f, of column 1 effluent injected onto column 2 was f ∼ 83%, while at a PM of 1500 ms (MR ∼ 2) the f ∼ 17%. Detection was accomplished with the modified FID described above. The FID was operated at 275 °C with nitrogen as the makeup gas. The GC oven was operated with a temperature program starting at 35 °C, where it was held for 2 min, and then increased at a program rate of 15 °C/min to 150 °C, where it was held for 1.5 min. This oven program resulted in a total separation run time of 11.5 min. To rigorously study the impact on RSD over a sufficiently wide range of MR values, the instrumental parameters were selected to maintain a first dimension peak width at the base, 1wb, of ∼3 s throughout the entire separation for each of the seven test analytes. This enabled an in-depth study of modulation ratios, spanning the range ∼110. For the first study, eight replicate separations of the test mixture were performed; for the second study, 126 replicate separations were performed at an average MR

’ RESULTS AND DISCUSSION The raw data of the GC  GC chromatogram of the test mixture is shown in Figure 1A, and this is referred to as the most “highly modulated” condition corresponding to a second dimension separation run time, that is, a modulation period (PM) of 300 ms. The raw data in Figure 1A is shown prior to separating the data at PM intervals and stacking to form a 2D image. The elution order of the test mixture is as follows: acetone (the diluent), ethyl acetate, heptane, toluene, 1-chlorohexane, cyclooctane, decane, and octanol. A zoomed-in view of the ethyl acetate data (indicated with an asterisk in Figure 1A) is shown in Figure 1B. Even though 12 modulated peaks can be counted, there are approximately nine modulated peaks at the width at the base (four standard deviations in time), 1wb, using the 300 ms modulation period for the ethyl acetate peak, which is more than sufficient for comprehensive sampling. Indeed, this is a sufficiently sampled condition (MR ∼ 10) to obtain the true peak first dimension peak width per eq 4, and it serves as a benchmark for the lower MR conditions. Figure 1C shows a section of the GC  GC separation in a 2D contour plot format (with heptane and toluene). For the test mixture, the first dimension retention time, 1tR, the average first dimension and second dimension peak widths at the base, 1wb and 2wb, respectively, and the average MR for a PM of 300 ms of the replicates for each analyte are reported in Table 1. To ensure good accuracy in peak width determinations, the four standard deviation peak widths at the base in the first dimension were calculated by fitting a Gaussian through each of the second dimension peak maxima. From Table 1, it can be seen that an average 1wb of 2.9 s and an average MR of 9.9 were obtained for the lowest PM, 300 ms, across all of the replicates of each analyte. Thus, the average 1wb ∼ 3 s experimentally achieved resulted in the desired MR range ∼110. Also, the average 1wb and 2wb peak widths for the two analytes in Figure 1C are 3.0 s and 25 ms, respectively, corresponding to a peak capacity production nc,2D of 240 peaks/min. In Figure 1D, we inquire to what extent undersampling, as defined in eq 4,25 applies to the valve-based GC  GC design in this study. As explained in more detail in the Experimental Section , a constant amount of analyte was injected per each modulation, and only the number of modulations across the peak 5192

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Figure 2. Reconstructed first dimension peaks using a best-fit Gaussian function for two replicate injections of ethyl acetate, providing 1wb values for comparison. (A) MR ∼ 9 (PM = 300 ms) with different retention times, producing relative signal areas (RSAs) of 0.989 (blue) and 1.028 (red). At this MR, an average RSA equal to 1.000 is defined, that is, for all analytes at the maximum MR ∼10. (B) MR ∼ 2.0 (PM = 1300 ms) with about the same retention time shift as in part A, producing RSAs of 0.255 (blue) and 0.275 (red).

decreased as the MR was decreased (hence, the total fraction, f, that was transferred decreased as the MR is decreased). Thus, as Figure 1D indicates, the peaks eluting from the first dimension were not broadened for this valve-based design (i.e., the experimental first dimension peak width ratio did not follow the β function), whereas the peaks would be broadened as the MR is decreased if the fraction that was transferred is 100% as a result of an “averaging” effect. Therefore, as is seen in Figure 1D, the peak capacity, nc,2D, is not impacted by what may appear to be undersampling as the MR is decreased. However, with the valve-based design, there is a trade-off between detection sensitivity (as quantified by the RSA) and maximizing peak capacity. To begin to examine the issue of quantitative reproducibility, an overlay of two replicate injections (out of eight replicates) for the ethyl acetate is shown in Figure 2A at MR ∼ 9, and in Figure 2B at MR ∼ 2, with about the same amount of first dimension retention time variation, ΔtR. The retention time variation exhibited in Figure 2 was the most severe that was observed in the entire data set. Overlays of Gaussian peaks fitted to the first dimension peaks are also shown. The Gaussian best fit functions provide 1wb values for comparison at different MR's as in Figure 1D. Peak areas for all of the analytes at the 300 ms PM (which provided the maximum MR) were calculated by summing the baseline corrected signal data across all of the second dimension modulated peaks and used to normalize the peak areas at smaller MR's, producing the RSAs. Hence, the RSAs

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Figure 3. (A) Plot of theoretical RSAs as a function of the MR for three special cases of phasing: ϕ = 0 with a red line (modulations in-phase across the peak), ϕ = 0.5 with a green line (modulations out-of-phase across the peak), and ϕ = 0.25 with a black line (halfway between inphase and out-of-phase). (B) To better view the RSA variation due to changes in phasing at a lower MR, the ϕ = 0.25 line in part A is subtracted from each theoretical line in part A, expressed as a percentage relative to the ϕ = 0.25 line, and plotted as a function of the MR (log scale).

ranged from 1.00 (on average) at the maximum MR to a smaller RSA at a lower MR. The peak data shown in red in Figure 2A yielded a RSA of 1.028, while the peak data shown in blue yielded a RSA of 0.989, hence, a difference of ∼4%. In Figure 2B, the peak data collected at a PM of 1300 ms corresponding to MR ∼ 2 produced lower RSAs than data collected at MR ∼ 9, at 0.255 (blue) and 0.275 (red), with a corresponding higher difference of ∼8%. Hence, as the MR is decreased, at a constant ΔtR, the quantitative variation increases, consistent with prior reports.28,29 This variation in RSA from one injection to the next could be attributed to various instrumental error contributions. For instance, run-to-run variation in the time of injection between each separation may cause a modulation phase shift. The retention time variation, ΔtR, due to flow and temperature effects can also be manifested as a change in modulation phase, Δϕ, which would result in differences in the RSAs. It is critical to understand the level of retention time precision that can be experimentally achieved and to find the minimum tolerable MR in order to maximize PM, which in turn will allow the maximization of the 2D peak capacity. For quantitative analysis, a key issue is how reproducible the peak areas are from one replicate injection to the next, which can be readily controlled by sufficiently reproducing the separation conditions. Referring to Figure 2 from Seeley’s report,28 if the modulation occurs in-phase with the peak (i.e., the first dimension peak maximum is captured within a modulation (ϕ = 0)), the sum of all the modulated signals is at a maximum, while the minimum peak area sum would be captured if the modulations across the 5193

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Figure 4. (A) Experimental RSAs for all eight replicates of ethyl acetate as a function of the MR. The variation in the RSA at each MR is the experimental error of concern which correlates to the RSD. (B) Experimental RSAs for all eight replicates of heptane as a function of the MR. The offset in the x-direction of the heptane RSAs versus the MR trend from that of ethyl acetate is due to the two analytes having different 1 wb values, which correspond to slightly different MR values.

peak were out-of-phase, that is, the peak maximum fell at PM/2 (ϕ = 0.5), with other results falling somewhere in between these extremes. A third special case, when ϕ = 0.25, occurs when the modulations are halfway between in-phase and out-of-phase, and the sum of all modulated signals linearly decreases as a function of the MR. To put our studies in the context of this prior report,28 for the three ϕ conditions of 0, 0.25, and 0.5, we theoretically derived the RSAs for a peak with a 1wb of 3.0 s and a 2wb of 25 ms by normalizing the expected signal area at each MR to the average expected signal area at a PM of 300 ms, corresponding to MR ∼ 10. The resulting theoretical plots of the expected RSA for MR values ranging from 1 to 10 for the three phase conditions are shown in Figure 3A. To better view the most interesting portions of Figure 3A, that is, at a small MR and small RSAs, the line corresponding to the ϕ = 0.25 was subtracted from the in-phase and out-of-phase values, and these differences further normalized, at each MR, to the RSAs at ϕ = 0.25, resulting in Figure 3B. Through the evolution from part A to part B of Figure 3, we learn that when the ϕ = 0.25 line is not known, as would be the case for our later experimental study, it can be obtained with reasonable confidence by fitting a line through two points: the most highly modulated data, that for a MR of ∼10, and the origin of the plot for each analyte. Because GC  GC experiments (or applications) are generally performed at a constant MR, the deviations of the in-phase (ϕ = 0) and out-of-phase (ϕ = 0.5) relative to each other and to ϕ = 0.25 shown in Figure 3B provide quantitative insight into the range of experimental error that an analyst would anticipate as a

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Figure 5. For both plots, the analytes represented by red and green dots are ethyl acetate and heptane, respectively, while the other analytes are indicated with black dots. (A) Plot of the ϕ = 0.25 corrected RSA percentage (as in Figure 3B) as a function of MR for all analytes in Table 1. Indicated on the plot for ethyl acetate at MR ∼ 9 is the RSD at 1.3%, and at MR ∼ 1, a RSD of 8.8%. Also noted is the region corresponding to an average MR ∼ 2 with an average RSD of 2.1% for all analytes. (B) Plot of the RSD of eight replicates per analyte as a function of MR. Indicated are the RSD and MR data points for ethyl acetate at the highest and lowest MR values as well as the region at an average MR ∼ 2 (the same as depicted in part A).

result of run-to-run variations in the synchronization of the modulation process with the first dimension elution time of a given analyte. From Figure 3B, the run-to-run variation in peak area, under controlled conditions, does not appear to be theoretically troublesome until MR ∼ 2 or less is applied, which is consistent with prior reports,28,29 at which point the in-phase to out-of-phase quantitative results begin to vary significantly and, hence, variations in such things as run-to-run retention time on the first separation dimension become significant. Experimental evaluation of the theoretical findings provided by Figure 3B will now be described. The summed RSAs for ethyl acetate and heptane at each MR are shown in Figure 4, parts A and B, respectively. These two plots are prepared in the same format as Figure 3A and are representative of all of the analytes in the test mixture. Indeed, the results for these analytes follow the anticipated trends of the theoretical plot (Figure 3A). It is interesting to note, though not unexpected, that as the MR decreases, the modulation phasing across a given analyte peak changed, leading to different patterns in the RSA as the MR is decreased. The different patterns are due to the inter-relationship between the modulation phase with respect to each analyte peak profile in concert with run-to-run retention time variation on the first separation dimension. For example, with ethyl acetate, the RSAs varied between the RSAs theoretically expected if ϕ ranged from 0 to 0.25, whereas, for heptane the RSAs varied between the 5194

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Table 2. Modulation Ratio (MR) and RSD Data without and with Using 1-Chlorohexane as the Internal Standard for 126 Replicate Injections at a PM of 1180 ms for Each Analyte RSD without

RSD with

MR

internal standard

internal standard

ethyl acetate

2.2

8.0%

3.2%

heptane

2.5

5.3%

6.9%

toluene

2.6

8.9%

1.7%

1-chlorohexane cyclooctane

2.5 2.7

10.3% 8.9%

1.9%

decane

2.5

10.4%

1.2%

octanol

2.5

11.4%

2.9%

average

2.5

9.0%

3.0%

analyte

a

Figure 6. (A) Peak areas (uncorrected) for selected analytes—ethyl acetate, 1-chlorohexane, decane, and toluene—calculated for each of 21 replicate injections from each of 6 vials, for a total of 126 replicates, with a PM of 1180 ms and an average MR ∼ 2.5. (B) Plot of the internal standard corrected peak areas (ratios) for all 126 replicates for the data in part A. 1-Chlorohexane was used as the internal standard, so the corrected signal is constant at 1.00. The RSDs for the other three analytes are all much lower and are similar to the RSDs found for the eight replicates in the first study (Figure 5 B). A full summary is provided in Table 2.

RSAs theoretically expected if ϕ ranged from 0.5 to 0.25. Additionally, because experimentally we did not exactly achieve a 1wb of 3.0 s for each test analyte, these two analytes, along with the other analytes, each had a slightly different maximum MR. Additionally, although retention time alignment could be applied to the data in principle, it is not likely that the observed variation in the RSAs could be corrected by alignment. The most relevant variation in Figure 4 to consider, that in the y-axis, is caused by the variation from replicate-to-replicate and is the experimental (quantitative) error of concern. In order to better visualize the data corresponding to the lower MR region and to correct for different slopes of the line for each analyte, caused by setting RSAs at slightly different maximum MR values for each analyte, the data were normalized relative to the ϕ = 0.25 line, as discussed earlier for Figure 3B, to produce Figure 5A for the experimental data. For these experimental results, the ϕ = 0.25 phase line was calculated by fitting a line through the origin and the RSA for the most highly modulated analyte (maximum MR for each analyte). The resulting line was then subtracted from the data set for each analyte, and the resulting values are then expressed as a percentage relative to the ϕ = 0.25 line. After the ϕ = 0.25 phase normalization process described above was performed on the experimental data, the quantitative precision (RSD) for the data for each test analyte, at a given MR, were calculated and are presented in Figure 5B. For each cluster of replicates for a given analyte in Figure 5A, a single RSD data

a

1-Chlorohexane was used as the internal standard.

point is produced for Figure 5B. The two analytes, ethyl acetate and heptane, emphasized in parts A and B of Figure 4, are still represented in red and green while the other analytes are in black for clarity. The x-axis is plotted on a log base ten scale in order to expand the region at a low MR. As before, the change in phasing from one analyte to another for a given MR, represented by the sets of analyte replicates scattered around the ϕ = 0.25 phase line, is not the error of concern. The main quantitative variation of concern is the spread in the RSAs (y-axis values), producing the RSD results in Figure 5B, for each set of analyte replicates at a given MR. Although it might not be the case for each individual analyte, the general trend is that the RSD increases as the number of modulations across the first dimension peak is decreased. For example, ethyl acetate produced a 1.3% RSD at MR ∼ 9 and an 8.8% RSD at MR ∼ 1. Indeed, in a majority of cases, at a higher MR, the analyte replicate RSD is relatively constant, while, at a lower MR, the RSDs significantly increase and become less constant, with a significant jump below MR ∼ 2, which is consistent with the theoretical plot of Figure 3B. Because the RSD values that were calculated to produce each point in Figure 5B are only from eight replicates per each analyte and because the turning point toward higher RSD appears to occur at MR ∼ 2, a more encompassing study was conducted. For this study, 126 replicates were run, from 6 sample vials with 21 injections from each vial, at a PM of 1180, which for a 1wb ∼ 3.0 s peak width corresponds to a MR of 2.5. This study was conducted over a time period of 1.5 days. For clarity, the raw summed peak area for each replicate of only four of the analytes, along with the RSD for each analyte for all 126 replicates, is shown in Figure 6A. The MR and RSD of each analyte for all 126 replicates can be found in Table 2. Initially, the RSDs for all 126 replicates for each analyte are all much larger than the approximately 2.53.0% found with eight replicates, shown in Figure 5B. Although performing only 21 injections per each of the six vials should have succeeded in minimizing the risk of concentration changes happening from performing all 126 injections from one vial, small dilution differences occurring during the preparation of the different vials greatly increased the RSDs of all the replicates. As is readily noticeable, the trend in the raw peak areas trends with vial groups (21 replicates each); therefore, the use of one of the analytes as an internal standard was applied to improve the RSDs of all 126 replicates. Using 1-chlorohexane as the internal standard, the peak area sums for each replicate for the same four analytes, along with the RSD for each analyte for the 126 replicates, are presented in Figure 6B. The 1-chlorohexane 5195

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Analytical Chemistry internal standard corrected RSDs for each analyte can be found in Table 2 with an average RSD of 3.0% across all analytes and all 126 replicates. As expected, the use of an internal standard has brought the RSD of each analyte at an MR of ∼2.5 to essentially that observed in Figure 5B, where an internal standard was not required because only eight replicates were analyzed.

’ CONCLUSIONS One goal of this study was to assess at what MR the typical valve-based GC  GC experimental ΔtR, which translates into a Δϕ, starts to significantly have an adverse impact on the RSD. Consistent with prior reports,28,29 we found that staying at MR ∼ 2 or greater maintains a generally acceptable (relatively low) RSD across replicate injections. Additionally, the study provides insight into the trade-off between MR and 2D peak capacity, nc,2D. With 10 modulations across the first dimension peak (a MR ∼ 10), an average RSD of 1.3% for the seven analytes and eight replicates (Figure 6B) was obtained, corresponding to a peak capacity production of 240 peaks/min, whereas, at a MR of ∼2, an average RSD of 2.1% and 1200 peaks/min can possibly be obtained. Albeit, both of these peak capacity production rates assume that the peak width in the second dimension can remain at 25 ms throughout the entire second dimension separation run time, which is more easily achieved at the shorter modulation period lengths necessary for a MR of ∼10 than at the longer periods for a MR of ∼2, although, even for a MR of ∼2, the advent of constant flow rate controllers capable of achieving higher pressures and faster temperature program and cool down rates for the second column would be required to experimentally achieve the theoretical peak capacity productions. The nontotal transfer design also produced 2D separations that are apparently not dependent on the undersampling broadening effect via β, because the effluent transferred in each modulation was held constant as the MR was decreased. It is worth noting that the present study was conducted with analytes at relatively high concentration, and if they were at lower concentration, the impact on RSD would be more pronounced. In the end, the analyst must decide what RSD is required by the application because this, in turn, regulates what MR and, therefore, what chromatographic and instrument parameters are necessary. ’ AUTHOR INFORMATION Corresponding Author

*Phone: þ1-206-685-2328. Fax: þ1-206-685-8665. E-mail: [email protected]. Present Addresses #

ARTICLE

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dx.doi.org/10.1021/ac200302b |Anal. Chem. 2011, 83, 5190–5196