Using computer modeling to predict and optimize separations for comprehensive two-dimensional gas chromatography

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Journal of Chromatography A, 1186 (2008) 196–201

Using computer modeling to predict and optimize separations for comprehensive two-dimensional gas chromatography Frank L. Dorman a,b,∗ , Paul D. Schettler b , Leslie A. Vogt b , Jack W. Cochran a a

b

Restek Corporation, 110 Benner Circle, Bellefonte, PA 16823, USA Department of Chemistry, Juniata College, 1700 Moore Street, Huntingdon, PA 16652, USA Available online 23 December 2007

Abstract In order to fully realize the separation power of comprehensive two-dimensional gas chromatography (GC × GC), a means of predicting and optimizing separations based on operating variables was developed. This approach initially calculates the enthalpy (H) and entropy (S) for the target compounds from experimental input data, and then uses this information to simultaneously optimize all column and runtime variables, including stationary phase composition, by comparing the performance of large numbers of simulated separations. This use of computer simulation has been shown to be a useful aid in conventional separations. It becomes almost essential for GC × GC optimization because of the large number of variables involved and their very complex interaction. Agreement between experimental and predicted values of standard test samples (Grob mix) using GC × GC separation shows that this approach is accurate. We believe that this success can be extended to more challenging mixtures resulting in optimizations that are simpler and transferable between GC × GC instruments. © 2007 Elsevier B.V. All rights reserved. Keywords: GC × GC; Computer modeling; Retention indices; Comprehensive GC; 2D-GC

1. Introduction The power of comprehensive gas chromatography (GC) × GC, as developed by Phillips and Liu [1], lies in the peak capacity improvement over conventional GC. GC × GC associates retention times on two different columns with each component of a sample mixture. The flow sequence is injector, column one, modulator, column two, and detector. The output of the first column is “sliced” into many of these time increments each of which is refocused onto column two. The purpose of the second column is to achieve an orthogonal separation as compared to the first column, resulting in separation along two axes, each with unique selectivity. A plot 1tR (slice number) versus 2tR spreads the peaks onto a two-dimensional surface. Detector response can be plotted in the third dimension. Significant simplification and cost savings could be achieved if GC × GC could be used with inexpensive, universal detec-

∗ Corresponding author at: R&D, Restek Corporation, 110 Benner Circle, Bellefonte, PA 16823, USA. Tel.: +1 814 353 1300x2186; fax: +1 814 353 9278. E-mail address: [email protected] (F.L. Dorman).

0021-9673/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2007.12.039

tion methods, such as flame ionization detection (FID), at least for routine analyses. However, calibration of such an instrument for a complex mixture by the traditional means of injection of pure components in pure form becomes a larger problem, as this technique is often employed for the most complex separations. A possible solution may lie in characterization of a complex mixture using GC × GC–TOF-MS (time-of-flight mass spectrometry) instrumentation, then “downloading” the method to less expensive instrumentation using a less complex detector. This alternative presents two new challenges, however. First, the method must now be carefully optimized to insure separation because instrumentation such as GC × GC-FID has no capability to identify unresolved components. This leaves the possibility of method development on GC × GC–TOF-MS then transferring the method to less expensive instrumentation such as GC × GC-FID for routine use. Thus, a mathematical algorithm is required to translate the GC × GC–TOF-MS settings for use with other detectors that differ in operating parameters. Optimization and translation are more difficult for GC × GC than ordinary one-dimensional GC irrespective of the detector issue. The mathematical algorithms that describe GC are well known, and are also easy to apply in the one-dimensional case. Although the theory remains the same for GC × GC, application becomes more difficult. For example, one expects simple

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improvement in one-dimensional GC by increasing column length. In contrast, for GC × GC, the situation is much less clear. Increasing the length of the second column will decrease the flow rate in both columns, thus changing both t1 and t2 and separation quality. Likewise, switching column two output pressures from vacuum (GC × GC–TOF-MS) to 1 bar (FID) changes the modulator pressure and hence the flow rate and retention times for both columns one and two. Even minor retention time shifts have the potential to affect major changes to the two-dimensional chromatogram since each time slice may now collect different components from column one. Thus, a component may completely disappear from one time slice and reappear in another. Not only does this confound identification by t1 and t2 , but it also changes the separation task of column two. This behavior is not unique to column length or outlet pressure changes, but a possible consequence of several variable changes. Thus, as a general rule even minor parameter changes, such as changing from GC × GC–TOF-MS to FID, will have complicated effects on the chromatogram. Optimizing stationary phase variables in GC × GC presents special opportunities. With one-dimensional columns [2], stationary phase composition is optimized by adding and subtracting components (polymer functionalities). GC × GC optimization presents the same opportunity (or opportunity) but also allows choice of column (one or two) for the addition/subtraction. The significant difference in the two columns will ordinarily be temperature. Thus, from a theoretical point of view, an important advantage of GC × GC is the exploitation of this difference. Computer simulation permits optimization by simultaneously adjusting the temperature programs and phase compositions for the two columns, thus making maximum use of the additional variables associated with GC × GC. Modulation rate (or time) is an important additional variable, which is the period of time the output of column one is stored before releasing it onto column two. Standard practice is to choose a modulation period that is longer than the retention time of any component on column two. Column two dimensions are usually chosen so that component retention times are only a few seconds. Other approaches have been used, however. Truong et al. [3], for example, have shown that improvement of sensitivity by a factor of 80 is possible by choosing time slices to include entire peaks. From a simulation standpoint, it is easy to choose a variable modulation rate that optimizes the performance in each part of the chromatogram. This complexity has yet to be achieved in practice, however. In any event, modulation rate joins the more than 10 variables that must be optimized for a given GC × GC application. Other researchers have attempted to develop predictive modeling procedures to address this separation. Their approaches typically utilize empirical-fit procedures based on either Kovats indices [4,5] or by calculation retention indices based on GC × GC retention data [6]. Additional predictive modeling efforts based on calculations of flow rates given various GC × GC columns configurations and the impart on the resulting separations have also been presented [7,8]. The approach used for this work uses calculated thermodynamic retention indices (H and S), and has been termed

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computer-assisted stationary phase design, or CASPD, in a previous publication [2]. For extension into comprehensive GC × GC, CASPD2d simulates GC × GC separations as a function of the many variables involved. The result of each simulation is automatically compared with previous output so that the process can proceed toward an optimized set of variables as previously reported in the one-dimensional version, CASPD. The input data consists of the adjusted retention time of each component on each stationary phase under two different temperature programs. This small amount of required input data can come either from one-dimensional or GC × GC instrumentation. Sufficient input data could be achieved rapidly using GC × GC–TOF-MS instrumentation. CASPD2d can then optimize variables for both GC × GC–TOF-MS and GC × GC-FID instrumentation including peak identification for the latter. 2. Experimental All separations (conventional and GC × GC) were performed using an Agilent Technologies (Little Falls, DE, USA) 6890N gas chromatograph with a split/splitless injection port and a flame ionization detector. The GC system was fitted with a thermal modulator system from LECO (St. Joseph, MI, USA) which uses cryogenically cooled nitrogen and heated air jets to modulate the effluent of column one onto column two. Instrument control and data processing was via ChromaTOF-MS GC × GC (LECO) for the modulated separations and ChemStation (Agilent Technologies) for the conventional separations. All separations used helium as the carrier gas and purification of the carrier as well as the FID gasses was accomplished using a multiple-stage sorbent trap (Restek, Bellefonte, PA, USA). All injections were Grob mix (Restek, catalog no. 35000 and CS-5024) for all analyses with an injection volume of 1.0 ␮L, using a 7683 autosampler (Agilent Technologies), and a spilt ratio of 10:1. Constant pressure regulation was used for all analyses. In order to obtain the thermodynamic retention indices for each analyte on each stationary phase, a conventional separation of the Grob mix was performed at two different oven temperature programs (different elution temperatures). The column hold up time (dead time) was also determined for each column by injection of methane at 100 ◦ C. Dead times were verified after all analyses to ensure that no change in linear velocity had developed during the course of data collection. All columns were measured to determine the actual length. Internal diameters (i.d.) and stationary phase film thickness (df ) were as listed from the manufacturer (Restek). Initial experiments were run using the intended first dimension column, which was polydimethylsiloxane (Rtx-1). Column dimensions were 30 m (nominal) × 0.25 mm i.d., 0.25 ␮m df Retention times for the target analytes on this column were entered into the modeling program as described below, along with the experimental parameters (column dimensions, pressure, temperature program, dead time, etc.). The modeling program then calculated the indices (H, S) for each component. This procedure was then repeated using a 14% cyanopropylmethyl/14% phenylmethylpolydimethylsiloxane (Rtx-1701).

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Column dimensions were 20 m (nominal) × 0.18 mm i.d., 0.20 ␮m df For the two-dimensional analyses, the column ensemble that was chosen was 25 m × 0.25 mm i.d., 0.25 ␮m df Rtx-1, followed by 2 m × 0.18 mm i.d., 0.20 ␮m df Rtx-1701. Data are available for the following compounds, which represent a subset of the Grob mixture: 2,3-butanediol, 1-octanol, nonanal, 2,6-dimethylphenol (2,6-DMP), 2,6-dimethylaniline (2,6-DMA), C-10 fatty acid methyl ester (FAME), and C-11 FAME. The Grob mixture compounds represent a wide variety of the types of analytes separated by GC methods, so the accurate prediction of their retention behavior indicates that prediction for other compounds should also accurate. Once the indices were calculated, it was possible to both predict and optimize the GC × GC separations that may be performed using any combination of these stationary phase chemistries. In GC × GC separations there is one possible complication, however, the modulation cycle is releasing analyte out of what may be a selective layer. Unless modulation is performed on uncoated tubing, the stationary phase may release analyte in a time-dependent manner based on the selectivity of the stationary phase for the analyte. In order to determine the significance of this possibility, and also test the accuracy of the modeling procedures, GC × GC separations were obtained in three different orientations. First, the modulator region was placed at the end of the first column (Rtx-1). Second, the modulator region was placed at the beginning of the second column (Rtx-1701). Finally, the modulation was performed on a short section of deactivated fused silica tubing (Restek catalog no. 10102) with an i.d. of 0.18 mm. Comparison of the data from these three orientations should show the effect of a selective desorption, if any. Comparison of the retention times of these analyses to the calculated values will show the accuracy of the modeling approach. 3. Theoretical CASPD2d simulates the performance of each of the two columns as well as the modulator for a variety of input variables. Output is a best-simulated two-dimensional chromatogram that was obtained by ranking in a manner reminiscent of the onedimensional version, CASPD 3.0. CASPD2d is a VBA-Excel program that is linked to a FORTRAN Library that contains the fundamental algorithms for flow, retention, and band spreading. The pressure profile through either column is parabolic, p(x)2 = p2i − (p2i − p20 )x/L. For column one p0 is the modulator pressure pm , as is pi for column two. The equation used for determining pm is obtained by applying the standard equation for an ideal gas flowing through a tube to both columns one and two with the result:   2 2 a + p a p π 2 1 i col1 0 col2 p2m = , 16R a1 + a 2 a1 =

η1 T1 L1 η2 T2 L2 and a2 = 4 r1 r24

(1)

The time for component i to travel from point x from the column

entrance to point x + ␦x is given by δti =

32ηL2 (p(x)2 − p(x + δx)ˆ2) 3r 2 p40 (P 2 − 1)

2

(2)

For helium the viscosity η is obtained from η = c1 + c2 T/(1 + c3 T), a best equation as determined by Table Curve [9]. The values of c1 , c2 and c3 were determined by a least squares fit to the viscosity data as reviewed by Hinshaw and Ettre [10]. CASPD2d converts the ordinary hold-ramp temperature time format to a sequence of vertices connected by linear segments on a graph of temperature versus time. The retention ratio  is given by =

1+β

1 N

i=1 Xi Ki

(3)

Xi is the volume fraction of each moiety in the stationary phase. N is the number of moieties in the stationary phase. The parameter β is the ratio of stationary to mobile phase, ≈4fd/d where d is the internal column diameter and fd is the film thickness. Finally Ki , the partition coefficient of component i between the stationary and mobile phases is determined by Ki = e−(Hi −T Si )/RT

(4)

In this equation Hi and Si are the thermodynamic indices that determine the partition coefficient, Ki . Eqs. (1) and (4) imply that Eq. (2) is limited to time intervals for which temperature is effectively constant. Our approach has been to choose each ␦t so that ␦T is less than some limiting value. The retention time of component i on one of the columns is then determined by summing all the ␦ti ’s as ␦x is stepped down the column length (Eq. (2)). The routine that does this insures that the increments are chosen small enough so that the end of the column is not overstepped, nor a vertex in the temperature program is overstepped, and that the temperature remains effectively constant (␦Tlimiting = 0.1 K ≥ ␦T) during transit of the component through each δx. We have experimented with a number of values of ␦Tlimiting ranging from 0.001 to 10 K and found that any value of ␦Tlimiting < 1 K gives the same retention time (but takes longer to calculate). We thus chose ␦Tlimiting = 0.1 K to provide a safe margin. These restrictions do not necessarily mean that ␦x is small. For an example, an isothermal run with x = 0, these conditions set ␦x = L and Eq. (3) reduces to that for isothermal retention times. Provision is made within CASPD2d for determining the values of the retention indices Hi and Si from experimental data. The sample mixture is separated under two different temperature programs. The program then iterates to find the values of the entropy and enthalpy that produce a match between simulated retention times and the experimental data entered. Two calibration runs (at different temperatures) of a five-component sample mixture onto a column with four stationary phase moieties will produce 40 data points and retention indices. Eq. (2) can then be used to calculate retention times for both column one and column two under any combinations of inlet or outlet pressure, temperature program, internal diameter, film thickness, and stationary phase composition. Once calibrated, the interface with

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Excel permits a large number of chromatograms to be calculated and evaluated, covering a variety of variable combinations of column and runtime variables including different temperature programs and stationary phase compositions. Each calculated column is evaluated on the basis of a critical peak resolution Rs crit . Rs is defined for peak i and peak j as [11]: Rs =

0.5|ti − tj | σi + σ j

(5)

CASPD2d evaluates Rs for each peak pair and compares it on a pass–fail basis with Rs crit (default is Rs crit = 1 but this is user adjustable). Column evaluation is the weighted sum of failures; high values correspond to poor values. Default weights are unity but this is adjustable from eluant pair to pair giving the user much flexibility in distinguishing between critical and noncritical separations by editing a weighting table. Peak widths for each peak are determined from the van Deemter plate height equation modified for ideal gas flow in capillaries:    H B σi = f1 + Cl v (6) ti , H = L vatm + Cg vatm The parameters B, Cg , Cl , and f1 are determined as follows [12]: B = 2Dg , Cl =

Cg =

2(1 − )fd2 , 3Dl

6(2 − 16 + 11)r 2 , 24Dg f1 =

9(P 4 − 1)(P 2 − 1) 8(P 3 − 1)

2

(7)

In order to limit entry of calibration data, Dg and Dl are currently set to constant values for all components. Two different kinds of modulator action are possible: constant and variable frequency. Constant frequency modulation divides column one output into time slices of constant duration. The end of one slice is the beginning of the second. To determine the composition of each time slice, CASPD2d first includes all those components that peak within the slice. Then it adds in any peak that is within 4σ of either edge of the slice. The retention times of the resulting mixture on column two are calculated. The weighted number of peak failures is calculated as before (but using Rs values calculated from column two only). The total number of peak failures is obtained by adding the failures for each time slice. The highest quality run (lowest number of peak failures) is kept along with parameters that produced it. Generally, the modulator will degrade the separation achieved by column one and optimizing the modulator period can improve this. Varying modulator operation accomplishes this by eliminating this degradation by adjusting modulation rate slice by slice so that components are not spread among more than one slice. In parts of the chromatogram that contain well-separated peaks each time slice is adjusted so as to contain just column bleed and (essentially) no peak, or (almost) all of one peak and (almost) no column bleed. Besides leaving column two with nothing to do, this result makes maximum use of refocusing for maximum peak sensitivity. When peaks get close enough together so that some overlap occurs, CASPD2d adjusts time slicing by placing a time slice edge so the distance between

Fig. 1. Comparison between the three configurations of column ensemble and modulation point. Configuration A places the modulator at the end of column one, configuration B places the modulator at the beginning of column two, and configuration C places the modulator on a short section of deactivated tubing which connects the two columns together.

the two peaks is bisected. Finally, when peaks are essentially co eluting the time slice widens again so as to include both peaks in their entirety. Both latter adjustments depend on column two to provide complete separation. Of course, optimized modulator operation would not work at the beginning of the development phase when one does not yet know the retention times, but optimized modulator operation might be a useful part of some application development programs. 4. Results and discussion When choosing a modulation point, it is important to decide if sample refocusing will be performed on a section of coated column, or on deactivated tubing. If modulation is performed on a section of column that has stationary phase, desorption will be a function of both analyte re-volatilization, and analyte/stationary phase selectivity. In other words, if the analyte is strongly retained by the stationary phase, either due to the stationary phase type, or amount (thickness), the complete desorption will be slower than what would be suggested by volatilization mechanisms alone. In order to test the importance of this, modulation was performed on three different column ensembles: (A) at the end of the first column (Rtx-1), (B) at the start of the second column (Rtx-1701), and (C) on a section of 0.18 mm i.d. phenyl/methyl-deactivated fused silica transfer column placed between the two columns. Fig. 1 is the comparison between the three configurations of column ensemble and modulation point. As observed in this figure, location of the modulation point does effect the observed retention times of the analyte. Retention of most analytes is longer when modulation is performed at the end of the first column (A). Since this point is the furthest from the end of the column ensemble for the three configurations, this is at first not surprising. The difference in column distance to the end of the ensemble in not significantly different, however, so most of this added retention is

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Fig. 2. Predicted retention time minus the adjusted experimental retention time for the components in the Grob mixture at the end of column one (modulation point).

due either to a greater distribution coefficient of the analyte in the stationary phase of column one, or due to the larger stationary phase film thickness of column one versus column two. Since all compounds seem to have a similar effect, it is assumed that this phenomenon is due to the greater stationary phase film thickness. The effect of stationary phase selectivity does appear to have an impact, however, as observed in the relative shifts in retention of the individual results from each other. Additional experimentation may need to be done to definitively answer the effect of modulation point, and if it is experimentally significant for certain methods. As a result of the differences observed in this experiment, all following data were obtained using configuration C (modulation on the transfer line between the columns) in order to compare modeling data without the possible influence of stationary phase chemistry at the modulation point. Data from the individual analyses on the Rtx-1 and the Rtx1701 were input into the CASPD2d program, and the H and S were calculated as described in previous publication [8]. Agreement between predicted retention times and actual were very good. Fig. 2 is the graph of predicted retention time minus the adjusted experimental retention time for the components in the Grob mixture at the end of column one. The adjusted experimental retention time is the actual retention time of each compound minus 0.05 min (3 s), which corrects the actual retention time for components that elute during the second modulation cycle after elution from the first column. Since all of the components that were used in this specific analysis eluted during this second modulation cycle, the 0.05-min correction was applied to all compounds. As observed in the figure, the agreement between predicted retention time and actual is very good. Variance of less than 1% was observed for all compounds. This implies that it is possible to accurately calculate at what time each component reaches the modulation point. At this point the CASPD2d program has demonstrated the ability to accurately predict when analyte are arriving at the modulation point. The analyte are now modulated, or “reinjected”, onto the second column. In most cases, the actual

Fig. 3. Surface plot of Grob test mixture plotted as apparent retention time on the second dimension, vs. retention time in the first dimension, with intensity on the z-axis. Operating conditions: oven program −40 ◦ C initial, hold for 0.2 min, ramp at 17 ◦ C/min to 200 ◦ C, final hold 1 min. Modulator offset = 30 ◦ C. Modulation time = 3 s; second dimension oven 10 ◦ C offset to primary oven. Inlet—10:1 split at 250 ◦ C with constant pressure of 20 psi. Detector temperature = 250 ◦ C.

eluting band at the end of column one is modulated in several (ca. 3) slices, so the program tracks multiple modulation cycles per compound based on the modulation period. As these peak slices are eluted at the end of the column ensemble, the ChromaTOF-MS software recombines the slices that correspond to the same components so that a three-dimensional image is created as shown in Fig. 3. In this figure, Grob test mixture data are plotted as apparent retention time on the second dimension, versus retention time in the first dimension, with intensity on the z-axis. For comparison of theoretical versus actual retention time, x–y plots of apparent second dimension retention time versus first dimension retention time for both CASPD2d-calculated and experimental data are easier to interpret. Fig. 4 is the comparison of CASPD2d-predicted values and adjusted experimental values for the separation of the components of the Grob mixture. As observed in Fig. 4, the calculated retention times agree quite well with the experimental retention times. In the first

Fig. 4. Comparison of CASPD2d-predicted values and adjusted experimental values for the separation of the components of the Grob mixture. GC conditions are the same as in Fig. 3.

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dimension, the predicted values agree completely with the experimental values. Most of the compounds agree well in the second dimension as well, except for 2,6-DMP. This compound is within 1.5 s of agreement in the second dimension, but additional investigation is necessary to determine where this error is coming from. One possibility is that this compound eluted in the first modulation cycle, but this would be unusual. It is also possible that the H and S for 2,6DMP on the Rtx-1701 column are in error. In any event, the value is within the correct order of magnitude so the conclusion is that the modeling algorithms are accurate. In order to be able to accurately optimize 2D separations, however, this source of error will need to be determined through additional experimentation. 5. Conclusion Using the approach of calculation of thermodynamic indices for the set of target analytes, modeling of a comprehensive two-dimensional GC separation was successful. Agreement for all compounds was accurate in the first dimension and the second dimension, with one exception that requires additional investigation. The ability to successfully model and optimize these separations will be very beneficial for determining analysis conditions for comprehensive two-dimensional separations.

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Acknowledgements The authors wish to thank Agilent Technologies for loan of the GC system and autosampler, LECO Corporation for the thermal modulator system and GC × GC software, and Restek Corporation for consumables and financial support. The authors would also like to thank Juniata College Chemistry Department for facilities and financial support. References [1] J.B. Phillips, Z. Liu, Chromatographic technique and apparatus, US Patent 5,135,549 (1992). [2] F.L. Dorman, P.D. Schettler, C.M. English, D.V. Patwardhan, Anal. Chem. 74 (2002) 2133. [3] T.T. Truong, P.J. Marriott, N.A. Porter, J. AOAC Int. 84 (2001) 323. [4] J. Beens, R. Tijssen, J. Blomberg, J. Chromatogr. A 822 (1998) 233. [5] C. Vendeuvre, F. Bertoncini, D. Thiebaut, M. Martin, M.C. Hennion, J. Sep. Sci. 28 (2005) 1129. [6] S. Bieri, P.J. Marriott, Anal. Chem. 78 (2006) 8089. [7] J. Beens, H.G. Janssen, M. Adahchour, U. Brinkman, J. Chromatogr. A 1086 (2005) 141. [8] J. Harynuk, T. Gorecki, J. Chromatogr. A 1086 (2005) 135. [9] TableCurve 2D, Jandel Scientific, Corte Madera, CA, 1994. [10] J. Hinshaw, L. Ettre, J. High Resolut. Chromatogr. 20 (1997) 471. [11] R.L. Grob, Modern Practice of Gas Chromatography, 3rd ed., Wiley, New York, 1995, p. 37. [12] J.C. Giddings, Unified Separation Science, Wiley, New York, 1991, p. 272.