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Anal. Chem. 1888, 60, 2135-2137
Overtake Phenomena in the Movement Process of Components under Temperature Programming Gas Chromatography Lin Bingcheng*J Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, People's Republic of China
Lin Bingchang* Anshan Institute of Iron and Steel Technology, Anshan, People's Republic of China
Bernhard Koppenhoefer Institute of Organic Chemistry, University of Tuebingen, 7400 Tuebingen, Federal Republic of Germany
The movement of a partlcular component along a chromatographic column Is studied on the basis of the equilibrium equation. Numerlcai shnulatlons of temperature programming gas chromatography are performed by means of a computer program. The thermodynamic parameters of each component are used to calculate step by step the location x as a fraction of the column length for a given t h e t . Dlagrams for x versus t and dxldt versus f display the movement process of the dlfferent components along the column. The validity of this approach Is exempitfled for some amino acM enantiomers and for a series of homologous alcohols. Under the condition of temperature programming, overtake phenomena are observed frequently. Thus, a component iagglng behind at low temperature may catch up with and eventually overtake the component running In front when the temperature is raised.
Gaschromatography was performed on a Perkin-Elmer Model Sigma 1 and a Carlo-Erba Model 2001 AC gas chromatograph. Samples of N-trifluoroacetyl amino acid isopropyl esters were eluted from a 26 m, 0.25 mm i.d., df = 0.3 wm, glass capillary column coated with L-Chirasil-Val(15,16). Samples of alcohols were eluted on a 33 m, 0.25 mm i.d., homemade glass capillary column coated with immobilized methylethenylpolysiloxane(17). Chemicals. Amino acids were purchased from different Chinese companies,and aliphatic alcohols were kindly provided by Dalian Factory of Oil and Fat (People's Republic of China). Procedures. In a 1-mL Reactivial, a sample of the amino acid (1mg) is dissolved in 0.5 mL of a solution of HC1 in 2-propanol (prepared by mixing acetyl chloride and 2-propanol, 1/10 (v/v), at 0 "C). The esterification reaction is carried out for 30 min at 110 "C. The solvent is removed completely in a stream of dry nitrogen. The residue is reacted with 200 pL of trifluoroacetyl anhydride for 15 min at room temperature. Then the reagent is stripped off in a gentle stream of dry nitrogen in order to remove the byproduct trifluoroacetic acid. The derivative is dissolved in dichloromethane for chromatography.
Many authors have dwelt on the simulation of the chromatographic process. Some of them are concerned with the separation efficiency (1-3) and others with temperature programming (4-7). Most of these authors pay attention to the prediction of the overall chromatographic behavior as measured a t the end of the column, such as retention time and peak width, and then use the results to optimize the operation conditions (7-9). However, despite these numerous attempts, there is still a lack of detailed description of the movement of a component along the chromatographic column. Such an investigation may be of considerable significance for the efficient use of multidimensional systems, especially in the temperature programming mode. Today, the basic concept of multidimensional gas chromatography (GC) can be tailored to a variety of applications (10-12), and this technology has been connected with mass spectrometry (MS) and pyrolysis (12-14). The purpose of the present investigation was to develop a computer program to simulate the traveling process along the chromatographic column, so as to elucidate the behavior of the components in the course of the chromatographic experiment.
RESULTS AND DISCUSSION As predicted by Giddings and others (18-22), the nearequilibrium assumption (I) is a sufficient approximation for the chromatographic process. In our previous papers (23-26), we have demonstrated, by a comparison of numerical and experimental data for several compounds, that the mass transfer coefficient and diffusion coefficient can be neglected, even under the condition of temperature programming dx = - U dt 1 k'
EXPERIMENTAL SECTION Apparatus. Calculations were run on an IBM PC and a Perkin-Elmer Model 3600 computer. Present address: Institute of Organic Chemistry,University of Tuebingen, 7400 Tuebingen, F.R.G. Present address: Department of Chemistry,University of Tennessee, Knoxville, T N 37996-1600.
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Here, dx/dt is the rate of travel of the solute along the column, U is the linear flow rate of mobile phase, and k is the capacity factor. Due to the pressure gradient along the column, the flow rate U is a function of the location 2,especially in the temperature programming mode. Moreover, the inlet pressure varies due to the change in carrier gas viscosity with the temperature (27). The general expression for U = U(x)is
Here, L is the column length, to is the dead time, and p is the ratio of inlet to outlet pressure. As reported previously (27), this approach can be used for the optimization of the chromatographic conditions by calculating the peak width w and the retention time t, for a particular set of compounds. Both figures describe the behavior of the component a t the end of the column, i.e., at the locus x = 1, where x is a fraction of
0003-2700/88/0360-2135$01.50/00 1988 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 19, OCTOBER 1, 1988
Table I. Comparison of Predicted and Experimental Retention Times, t , (in minutes), of N-Trifluoroacetyl Amino Acid Methyl Esters on L-Chirasil-Val’
No.
amino acid
predicted
measured
1 2 3 4 5
D-Ala L-Ala D-Val L-Val D-Thr D-de D-Ih L-dle L-Ile D-Leu D-Ser D-Pro L-Pro L-Leu
5.05 5.72 6.93 7.33 7.75 8.16 8.49 8.70 8.89 9.14 9.42 9.60 9.70 9.79
5.05 5.75 6.87 7.31 7.75 8.13 8.42 8.61 8.83 9.10 9.40 9.51 9.58 9.78
6
7
Flgure 1. Diagram of x versus t for 14 amino acid enantiomers using a temperature program wlth pressure correction. 14 10
8 9 10 11 12 13 14
The chromatographic conditions are similar to those given in Figure 5.
I I
__ 0
8
1 0 MIN
Figure 2. Chromatogram corresponding to Figure 1 (Chirasil-Val capillary column: initial temperature, 100 O C ; heating rate, 12 ‘Clmin; H,, 0.4 kg/cm2;FID).
the column length. In the following, we deal with the behavior during the whole chromatographic process. The movement of the solute along the column is described by the function for the locus x = x ( t ) , where t is a given time period after injection of the compound onto the column. In a similar way, the function dx/dt = dx/dt(t) is used to describe the longitudinal velocity of a solute at a given time t. The chromatographic separation of stereoisomers (enantiomers and diastereomers) is of increasing interest in most branches of chemistry and life sciences. By gas chromatography on the chiral stationary phase Chirasil-Val(15,16),the stereoisomers of a mixture of 17 amino acids are completely separated within 30 min (15) after derivatization to the N pentafluoro amino acid isopropyl esters. However, for the clean separation of a mixture of the 20 natural amino acids, the polarity of the stationary phase must be carefully adjusted (28). In view of the increasing importance of this type of enantiomer analysis, we have checked briefly the possibilities for a reduction of the analysis time for other amino acid derivatives. Thus, up to 30 stereoisomersof N-trifluoroacetyl amino acid isopropyl esters could be separated on an arbitrary batch of L-Chirasil-Val within less than 20 min, by optimizing the temperature program (29). The movement of 14 amino acid derivatives is shown in Figure 1. Due to the large differences in volatility of the components, temperature programming is necessary. Each curve represents the traveling locus of one component of the mixture. As stated, the time corresponding to the upper end of each curve ( x = 1)is the retention time t, of this component. The chromatogram corresponding to Figure 1 is shown in Figure 2. The retention times obtained from both numerical computation and chromatographic experiment are compiled
-10_
t
*I”
Figure 3. Diagram for dxldt versus t corresponding to Figure 1.
in Table I. For most entries, t, could be predicted with high accuracy. Usually, we observe the chromatogram by means of a detector placed at the end of the column. In contrast to this, in Figure 1the entire movement of the components along the column has been visualized. The “race” observed for components 11,12, and 13 is particularly interesting. For the first 8 min, the most part of the retention time, the three components are well separated, 11 (D-Ser) lagging behind 12 (DPro) and 13 (L-Pro). However, when 11 approaches the middle of the column, it is remixed with 12 and 13, respectively. Eventually,at the end of the column, this component is eluted in front of the two competitors. In our experience, such “overtake phenomena” (coined in analogy to similar events in daily life) are encountered frequently in chromatographic columns. In order to get a more detailed picture of the process in the column, the speed dx Jdt of each component has been calculated as a function of time t and depicted in Figure 3. The behavior of 11, 12, and 13 deserves particular attention. In the initial isothermal mode, all components move with a constant velocity. 11 as a compound strongly interacting with the chiral solvent (the absolute values of free energy of phase transition being large, see Table 11) has a relatively low velocity. When the column is heated, all components are accelerated to a certain degree, but the acceleration of 11is larger than that of 12 and 13. Only shortly after heating (points a and b in Figure 3), the speed of 11exceeds that of 13 and 12. Though in Figure 2,14 is eluted after 12 and 13, we can predict from the cross section in velocities (points c and d in Figure 3) that under certain conditions 14 may overtake 12 and 13.
ANALYTICAL CHEMISTRY, VOL. 60, NO. 19, OCTOBER 1, 1988
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Table 11. Retention Time and Thermodynamic Data of Some Derivatives of Amino Acid Enantiomers retention time, min
AH,
AS,
AG,
comp
120 O C
130 "C
140 O C
kcal/mol
cal/(grad mol)
kcal/mol (298 K)
elution order 12 OC/min
D-Ser D-Leu
7.88 8.55 8.15 8.30 1.46
5.60 5.93 6.08 6.17 1.49
4.30 4.47 4.82 4.88 1.53
-13.94 -14.18 -11.84 -11.91
-21.87 -20.82 -16.53 -16.65
-20.46 -20.38 -16.76 -18.87
11 14 12 13
D-hO
L-Pro to(m.)
Table 111. Location of Some Homologues in the Column under Temperature Programming (2 OC/min)
a b
7
8
9
10
11
12
0.51 -
0.51 0.27
0.51 0.26
0.50 0.27
0.52 0.26
0.53 0.26
Relative location of ith compound when the (i - 1)th compound eluted. *Relative location of the ith compound when the (i - 2)th comDound eluted.
chromatography, after some parameters are modified and temperature programming is supplemented by solvent gradient elution.
ACKNOWLEDGMENT We are indebted to E. Bayer and G. J. Nicholson, Univenity of Tuebingen, and Lu Peichang, Dalian Institute of Chemical Physics, for helpful discussions. Registry No. 1, 338-69-2; 2, 56-41-7; 3, 640-68-6; 4, 72-18-4; 5, 632-20-2; 6, 327-56-0; 7, 319-78-8; 8, 327-57-1; 9, 73-32-5; 10, 328-38-1; 11, 312-84-5; 12, 344-25-2; 13, 147-85-3; 14, 61-90-5.
LITERATURE CITED
Figure 4. Diagram for x versus t for some homologues of alcohols. .a=
%ll"
I
12 L
5
fY6 /'
Figure 5. Diagram for d x l d t versus t corresponding to Figure 4.
Some special features are displayed in the movement of homologues, as shown in Figure 4. There is no crossing, and the curves are rather uniformly shaped. It is demonstrated in Table I11 that whenever an ith component is eluting, the (i 1)th component is about at the same location in the column (indicated by the triangles in Figure 4). As expected, the corresponding x values are around 0.5, as an approximation for sufficiently large k'values. The diagram for dx/dt versus t of homologues is shown in Figure 5. For linear temperature programming, all components will be eluted from the end of the column with about the same speed, again as an approximation for sufficiently large k' values. In principle, the movement of the components,as expressed by the x-t diagram, can be predicted for any kind of chromatographic condition. Since the course of the chromatographic process is followed numerically step by step, even rather sophisticated modes of temperature programming can be treated. This concept may be also useful for high-performance liquid chromatography and preparative liquid
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(1) Seferovic, W.; Hlnshaw, J. V., Jr.; Ettre, L. S. J. Chromatogr. Sci. 1988, 24, 374-382. (2) Laub. R. J. Anal. Chem. 1984, 5 6 , 2115-2119. (3) Leciercq, P. A.; Cramers, C. A. HRC C C , J. High Resolut. Chromatogr. Chromatogr. Commun. 1985, 8 , 764-771. (4) Bartu, Vladimir; Wicar, S.; Scherpenzeei, G. J.; Leciercq, P. A. J. ChrOmatogr. 1986. 370(2). 219-234. (5) Bartu, Viadlmir; Wicar, S.;Scherpenzeei, G. J.; Leclercq, P. A. J. Chromatogr. 1988, 370(2), 235-244. (6) Dose, Eric V. Anal. Chem. 1987. 5 9 , 2414-2419. (7) Dose, Eric V. Anal. Chem. 1987. 5 9 , 2420-2423. (8) Sibiey, E. M.; Eon, Claude; Karger, Bany L. J. Chromatogr. Sci. 1973, 1 1 , 309-319. (9) Bartu, Viadimir; Wicar, S.Anal. Chim. Acta 1983, 150, 245. (10) Zhang, Jlnging; Lin, Bingcheng; Lu, Peichang Chromatograph& 1987, 7, 487-491. (11) Ye, Fen; tin, Bingcheng; Lu, Peichang Chromatograph& 1987, 7 , 492-498. (12) Elder, James F.. Jr.; Gordon, Bert M.; Uhrlg, Mary S. J. Chromatogr. SCi. 1988, 24, 26-33. (13) Colling, Edwin L.; Burda, Barbara H.; Kelley, Peter A. J. Chromatogr. SCl. 1988, 24, 7-12. (14) Ligon, Woodfin V., Jr.; May, Ralph J. J. Chromatogr. Scl. 1988, 24, 2-11. (15) Frank, Hartmut; Nicholson, Graeme J.; Bayer, Ernst J. Chromatogr. Scl. 1977, 15, 174-176. (16) Koppenhoefer, Bernhard; Allmendlnger, Hans; Nicholson, Graeme J. Angew. Chem. 1985, 97, 46-48. Angew Chem., Int. Ed. Engl. 1985, 24, 48-49. (17) Xiu, Zhengjia, Li. Haochun; Lu, Peichang Chlnese J. Chromtogr. 1988, 3, 121-124. (18) Giddings, J. Calvin DyI"Ilcs of Chromatcgraphy; Marcel Dekker: New York, 1965; p 174. (19) Giddings, J. Calvin; Robison, Richard A. Anal. Chem. 1982, 3 4 , 885-890. (20) Gddlngs, J. Calvin; Robison, Richard A. Anal. Chem. 1982, 3 4 , 885-890. (21) Guiochon, Oeorges A. Abstracts of the 15th International Symposium on Chrometography. Nurenberg, FRO, 1984. (22) Ting, Chinchun; Chu, Paolin Scl. Sin. (Engl. Ed.) 1982, 6 , 1269. (23) Lin, Bingchang; Wang, Jida; Lin, Bingcheng J. Chem. Bull. University (Chinese) 1987, 4. (24) Lin, Bingchang; Lln. Bingcheng; Lu, Peichang J . Chromatogr. (Chinese) 1985, 3 , 239-244. (25) Lin. Bingchang; Wang, Jida; Lin, Bingcheng Abstracts of the 16th International Symposium on Chromatography, Paris, France, 1986. (26) Un, Bingchang, Wang, Jida; Lin, Bingcheng J. Anal. Chem. (Chlnese), 1987, 6, 334. (27) Lu, Peichang; Lln, Bingcheng; Chu, Xinhua; Luo, Chunrong; La, Guangda; Lai, Hauchun HRC CC, J. High Resolut. Chromatogr. Chromatogr. Commun . 1988. 9 , 702. (28) Nicholson. Graeme J.; Frank, Hartmut; Bayer, Ernst HRC CC, J. High Resolut. C h m t o g r . Chromatogr. Commun. 1979, 2 , 411. (29) Lin, Bingcheng; Chu, Xinhua; Luo, Chunrong; LI, Haochun; Lu, Peichang Abstracts of First Beijing Conference and Exhibition on Instrumental Analysis, Beijing, China, 1985.
RECEIVED for review February 2, 1988. Accepted June 10, 1988. Lin Bingcheng is grateful to the Alexander von Humboldt-Stiftungand to the Krupp-Stiftungfor financial support.
