Anal. Chem. 1996, 68, 4468-4473
Effects of Temperature Programming and Pressure on Separation Number and Height Equivalent to a Theoretical Plate in Optimization of a Serially Coupled, Open-Tubular Columns Gas Chromatographic System Evangelos B. Bakeas and Panayotis A. Siskos*
Analytical Chemistry Laboratory, Department of Chemistry, University of Athens, PanepistimiopolissKouponia, 15771 Athens, Greece
The separation number (TZ) and the height equivalent to a theoretical plate (HETP, h) are studied in a system of two columns (GLC-GSC) coupled in series under temperature-programmed and isobaric conditions using a mixture of the first six homologous n-alkanes. The effects of four selectivity parameters (initial temperature, hold time, program rate, and midpoint pressure) on them have shown that TZ is strongly dependent on the midpoint pressure and h on the temperature. TZ and h are related inversely with a relationhip that involves the overall column length (Lf + Lb) of the system. Examination of the basic relationship between separation number and the average carbon number showed that it is linear for this system only in the case which is linear for the back column, and this depends on the midpoint pressure. The ability of fused silica capillary gas chromatography columns, coated with liquid or solid stationary phases, to separate a wide range of complex mixtures under isothermal or temperature-programmed conditions has been described extensively in the literature. The separation ability of a column may be described by the resolution (Rs), the number of the theoretical plates (N), the separation factor (R), the separation number (TZ), and the height equivalent to a theoretical plate (HETP, h). The efficiency of a capillary column for isothermal operation is traditionally described in terms of the h:
h ) (L/5.54)(w0.5/tR)2
and tRb ”. The separation number value expresses the efficiency as a function of the difference in retention times (tRb - tRa) of two homologues differing by one methylene group and the sum of the corresponding peak widths at half-height (w0.5):
TZ ) [(tRb - tRa)/(w0.5a + w0.5b)] - 1
(2)
The most important advantage of the separation number is that its value can be used to describe column efficiency under temperature-programmed conditions, although its dependence on temperature should be taken under consideration. In some cases it has been described as a “rubber ruler”, which should be used carefully or avoided.2 The effects of the column temperature and the flow rate on TZ have been studied extensively in gas chromatographic systems.1,3,4 The TZ has been related with the other parameters describing the column efficiency, such as the resolution, Rb/a, of the two homologues a and b,5
TZ ) (Rb/a/1.177) - 1
(3)
the separation factor (R), and the effective plate number (Neff)6
TZ ) 0.425[(R - 1)/(R + 1)]Neff2 - 1
(4)
(1)
where L is the column length (mm), tR the retention time (s), and w0.5 the peak width at half-height (s). In temperature-programmed gas chromatography (TPGC), where four operational parameters can be optimized, including the column length, the coating thickness, the carrier gas flow rate, and the temperature program rate, two expressions have been used to describe this property, the first being the TZ, which was first proposed in 1959.1 The separation number value is considered to be “the number of peaks that could be placed between the peaks of two homologous compounds a and b separated by a 4.7σ (σ ) band variance) resolution with retention times of tRa (1) Jones, L. A.; Barton, C. D.; Dean, T. A.; Gerigand, T. M.; Cook, J. R. Anal. Chem. 1987, 59, 1179-1186.
4468 Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
It has been suggested that Neff is the safest measure of a column’s efficiency since, contrary to TZ, it would not be manipulated by different temperatures. The Grobs7 have defended the utility of TZ, claiming that it is more replicable than Neff and that it is compatible with TPGC. Recently,3 TZ and h have been evaluated in isothermal gas chromatographic operation, relating those two parameters with (2) Krupcik, I.; Gorag, J.; Cuiochon, G.; Schmitter, J. M. Chromatographia 1981, 14, 501-506. (3) Jones, L. A.; Glennon, J. J.; Reiss, W. H. J. Chromatogr. 1992, 595, 209219. (4) Jones, L. A.; Kirby, S. L.; Carcanta, C. L.; Gerig, T. M.; Mulik, J. D. Anal. Chem. 1983, 55, 1354-1360. (5) Ettre, L. S. Chromatographia 1975, 8, 291-298. (6) Rooney, S. A.; Hartigan, M. J. J. High Resolut. Chromatogr. 1980, 3, 416418. (7) Grob, K., Jr.; Grob, K. J. Chromatogr. 1981, 207, 291-297. S0003-2700(96)00572-0 CCC: $12.00
© 1996 American Chemical Society
column length, L, and the retention times of two consecutive homologous compounds, a and b, given by eq 5.
TZ ) (L/5.54)1/2[(tRb - tRa)/(tRbhb1/2 + tRaha1/2)] - 1 (5) Previous studies4 have shown that TZ can be related to the average carbon number of two consecutive homologues having z and z + 1 carbon atoms, CH ) (Cz+1 + Cz)/2, whose retention times are determined by TPGC, as in eq 6,
TZ ) R(CH) + b
(6)
where R and b are the slope and the intercept corresponding to the above linear equation, provided by linear regression analysis. Multidimensional gas chromatography (MDGC, also known as two-dimensional chromatography or coupled column chromatography) is increasingly used for the separation of very complex mixtures. Despite the numerous applications of multidimensional chromatography, little has been found in the elementary aspects such as optimization or predictive modeling.8 In serially coupled, open-tubular columns gas chromatographic systems (SCOTCH systems), it has been shown that the separation power of the system strongly depends on the pressure at the midpoint and the temperature (isothermal or programmed).9 Recently, the effects of four selectivity parameters, the initial temperature (To), the hold time (to), the temperature program rate (r), and the midpoint pressure (Pm), on the resolution power of such a system, in terms of Cp criterion and the total resolution of the system, ∑Rs,t, have been studied in our laboratory.10 It was proved, for the first time, that the resolution of the system is affected linearly by the midpoint pressure and the initial temperature. There are very few reports in the literature concerning only the theoretical prediction of h in SCOTCH systems,11 but there are no reports concerning TZ and h under TPGC conditions. This paper extends our previous studies on the basic aspects of resolution capabilities of those systems, expressed in terms of TZ and h under temperature-programmed and isobaric conditions. The examination of the effects that these four selectivity parameters might have on TZ and h helps to preselect the experimental conditions for the proper selectivity tuning of the system. It should be mentioned here that not only does this work examine the correlation between the selectivity parameters and TZ and h, but it also provides information on the applicability of basic relationships of one-column GC systems to SCOTCH. The studied relationships include the inverse relationship between TZ and h (ref 3) and the linear relationship between TZ and average carbon number (ref 4). Finally, the aim of the work presented herein is to better understand the analytical behavior of such systems as this one used, consisting of GLC-GSC capillary columns coupled (8) Elcemman, G. A.; Hill, H. H., Jr.; Davani, B. Anal. Chem. 1994, 66, 625R626R. (9) Purnell, J. H.; Jones, J. R.; Wattan, M. H. J. Chromatogr. 1987, 399, 99109. (10) Bakeas, E. B.; Siskos, P. A. J. High Resolut. Chromatogr. 1996, 19, 277283. (11) Guiochon, G.; Gutierrez, J. E. N. J. Chromatogr. 1987, 406, 3-10. (12) Hinshaw, J. V., Jr.; Ettre, L. S. Chromatographia 1986, 21 (10), 561-572. (13) Jennings, W.; Yabumoto, K. J. High Resolut. Chromatogr. 1980, 3, 177179. (14) Maurer, T.; Welsch, T.; Engwald, W. J. Chromatogr. 1989, 471, 245-249.
Figure 1. Basic schematic diagram of the system of two columns coupled in series. column A, BP1 (50 m × 0.22 mm × 1 µm); column B, PLOT Al2O3/Na2SO4 (50 m × 0.32 mm × 1 µm); column C, empty and deactivated column (50 m × 0.32 mm), INJ, injector; T-P, T-piece; SU, split unit; FID, flame ionization detector.
in series without intermediate trapping, which could help the performance of difficult separations in complex mixtures. EXPERIMENTAL SECTION Apparatus. The apparatus used (Figure 1) has been described extensively elsewhere.10 Briefly, a Perkin Elmer Model Sigma 2000 gas chromatograph equipped with a dual-FID was used. Two columns with very different characteristics were coupled in series: the front column (liquid phase) was a BP1 poly(dimethylsiloxane) column (50 m × 0.22 mm × 1.0 µm), and the back one (solid phase) was a PLOT Al2O3/Na2SO4 (50 m × 0.32 mm × 1.0 µm). As is shown in Figure 1, the coupling of the columns was made with a low-volume T-piece purchaced from SGE (Sydney, Australia). Helium was used as carrier gas, and the inlet and outlet pressures were fixed using the PT-1200 selectivity tuning system (SGE), properly modified as mentioned above for this work. Chemicals. A gas mixture of six n-alkanes, methane, ethane, propane, butane, pentane, and hexane (each 100 ppm), was obtained from Scotty I Analysed Gases. The n-alkanes were chosen according to the separation capabilities of the two columns used in the GC system. Procedure. A detailed description of the optimization procedure can be found in ref 10. It should be mentioned here that, for the optimization procedure, the criterion used was the Cp criterion [Cp ) ∑ms + (tR,max - tR,n)/tR,max, where mi ) 0 or 1 if the resolution Rs for a pair of consecutive peaks is lower or higher than a preseted value, tR,max is the maximum acceptable analysis time, and tR,n is the retention time of the last-eluted compound]. The four selectivity parameters were the initial temperature (To), the hold time (to), the program rate (r), and the midpoint pressure (Pm). The range of the parameters inserted in the experimental procedure were To from 60 to 90 °C, to from 1 to 10 min, r from 1 to 5 °C/min, and Pm from 104 to 138 kPa. The selectivity parameters (To, to, r) were controlled and monitored via the keyboard of the gas chomatograph. The inlet (Pi) and midpoint pressures (Pm) were indicated on the PT-1200 selectivity tuning system. The system was optimized for the base-to-base resolution of a mixture of 30 volatile organic compounds, including aliphatic and aromatic compounds ranging from C1 to C10. From the raw experimental data received from both FIDs, the set of the Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
4469
Table 1. Precision of the Studied Parameters and the Response Factors (TZ and h) in a Control Experiment Corresponding to the First Experiment of Table 2 (n ) 4)a precision
Pinlet, kPa
Pm, kPa
T, °C
tR, min
w0.5, s
TZ
hhex, mm
jx ( s Sr
25.3 ( 2.3 0.90
13.5 ( 1.2 1.10
80 ( 0.6 0.80
27.92 ( 0.02 0.100
0.031 ( 0.001 1.00
25.2 ( 0.1 0.397
0.825 ( 0.01 1.212
a
Others conditions as in experiment 1 of Table 2.
experiments concerning the n-alkanes (C1-C6) fraction was selected for this study. At the end of each experiment, taking the values of area (A) and height (h) of the peaks from the integrator (Perkin Elmer 3600 Data Station) and assuming that the peaks were Gaussian or moderately skewed Gaussian, the value of the peak width was calculated for each peak according to the equation w0.5 ) (A/h)[(2 ln 2)/π]1/2,15 using a home-made program written in BASIC. Using the retention time (tR) and the calculated value of the width (w0.5) of each compound, the values of TZ and h were estimated using eqs 1 and 2 for each column individually and for the whole system using basic eq 12 (below). The TZ and h values were calculated using programs written in BASIC. The simplex algorithm was written in C-language (in our department). Furthermore, multiple linear regression analysis was applied to the selected data in order to derive mathematical expressions describing the relation among TZ, h, and the four selectivity parameters. RESULTS AND DISCUSSION Presicion of the Measurement System. The system was tested first for the estimation of the reproducibility of the four selectivity parameters (To, Pm, r, to) inserted in the procedure, and of the related parameters used for the calculation of TZ and h, namely retention time (tR) and peak width (w0.5). The first experiment of the simplex procedure, used as the precision experiment, was carried out four times before starting the procedure and after the initialization from time to time. No significant change of the Sr from the initially estimated value was observed during the implementation of the whole set of experiments. The results of the replicate runs are shown in Table 1. Dependence of the Height Equivalent to a Theoretical Plate (h) on To, to, r, and Pm. The data used are shown in Table 2. The h values used for this study were for the peak of the pair (pentane-hexane) used for the calculation of the separation number having the higher capacity factor (hexane). Although in multifactor optimization procedures, as the simplex, the effects of each selectivity parameter on the response parameter are combined with the effects of the other selectivity parameters, some observations could be made. The variation of h during the optimization procedure, as can be seen in Table 2 and Figure 2, shows a different behavior from that described in the literature for a one-column gas chromatographic system. The h exhibited its maximum value in experiment 6 (To ) 88 °C, to ) 4.40 min, r ) 3.0 °C/min, Pm ) 111.8 kPa) and its lowest value in experiment 7 (To ) 73 °C, to ) 4.89 min, r ) 4.0 °C/min, Pm ) 113.2 kPa). As is expected from the previous studies in GC systems with one column, the minimum values of h should be observed at (15) Dose, E. V. Anal. Chem. 1987, 59, 2420-2423.
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Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
Table 2. Experimental Conditions and Results in the Course of the Simplex Sequential Optimizationa expt no. To, °C to, min r, °C/min Pm, kPa Tel, °C 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
80 70 60 90 82 88 73 66 79 82 79 77 76 75 69 74 84 81 78 70 78 78 79 79 79 79 79 79
5.00 4.00 3.00 5.00 2.62 4.40 4.89 5.43 4.66 4.62 4.43 4.34 4.29 4.26 3.78 4.01 4.94 4.59 4.30 4.65 4.51 4.30 4.57 4.70 4.43 4.45 4.54 4.55
3.0 4.0 3.0 5.0 2.9 3.0 4.0 4.6 3.4 4.2 3.8 3.6 3.4 3.4 3.2 3.4 3.6 3.6 3.5 3.5 3.4 3.6 3.4 3.4 3.5 3.5 3.4 3.4
103.5 117.3 123.5 116.6 118.7 111.8 113.2 113.2 109.7 115.9 115.2 115.2 114.5 114.5 118.0 118.7 109.7 114.5 116.6 111.8 112.5 118.0 111.8 109.7 115.2 114.5 112.5 113.2
115.13 105.96 73.53 110.13 114.67 93.14 101.68 110.64 110.81 110.66 110.37 109.92 86.54 106.81 110.57 110.70 110.41 115.11 110.27 110.54 113.34 113.61 110.47 112.18 113.20 114.46 113.35 112.26
TZb
h,c mm
25.2 89.2 70.4 63.0 94.3 86.4 117.9 67.7 92.5 62.2 89.9 71.9 98.9 94.9 10.7 93.6 119.9 94.2 103.6 14.9 108.5 91.3 101.6 85.7 101.8 115.5 79.6 97.8
0.825 0.050 0.061 0.052 0.061 1.361 0.030 0.144 0.052 0.180 0.047 0.153 0.055 0.053 1.295 0.061 0.032 0.050 0.045 0.576 0.035 0.051 0.050 0.053 0.040 0.118 0.125 0.526
a Selected raw data obtained from ref 10. b Separation number of the n-pentane-n-hexane pair calculated using eq 2. c Height equivalent to a theoretical plate for the hexane calculated using eq 1.
increased column temperatures. However, in this case of two coupled columns, the minimum values of h are observed at low column temperatures (experiments 7, 17, and 21) . The same behavior exists for the maximum values of h (experiments 1, 6, 15, and 20), which are found at high column temperatures. This is indicative of a strong dependence of h on the column temperature. Although in the first five experiments of the procedure it can be seen that, at increased values of the midpoint pressure, the values of h are decreasing, this cannot be concluded from the rest of the experiments. For example, the maximum values of h (experiments 6 and 15) are observed when the value of Pm is in the middle of the range used. The same observation can be made for the minimum values of h as well (experiments 7, 17, and 21), where Pm does not exhibit an increasing or decreasing trend. It seems as though Pm does not play an important role in determining the values of h. In order to evaluate the dependence of h on the selectivity parameters of the system (initial temperature To, hold time to, program rate r, and midpoint pressure Pm), multiple linear regression analysis was used, and eq 7 was derived, which
hs ) 0.1571to - 0.0327tor
(7)
Table 3. Statistics of Model Fitting Results (Coefficients, Standard Deviation, and Uncertainty of the Coefficients and Correlation Coefficient) for Eqs 7-14a eqb
variable
coefficient
Sr
t(Sr/n1/2)
R2
7
to tor a To r To2 r2 Tor a Pm Pm2 ToPm Pm ToPm ToPm TZb TZb2 TZf2 TZbTZf hb hfhb
0.1571 -0.0327 39.60 -2.0561 18.9171 0.0176 -1.1389 -0.1406 65.36 -1.1160 0.0048 0.0094 0.6490 -0.0050 0.0095 0.8943 -0.0039 0.0054 0.0122 0.5329 2.9667
0.0084 0.0002 1.41 0.0521 0.5753 0.0004 0.0672 0.0033 1.86 0.033 0.0001 0.0002 0.0139 0.0002 0.0005 0.0120 0.0001 0.0003 0.0005 0.0019 0.0064
0.0032 0.0001 0.54 0.0201 0.2221 0.0002 0.0259 0.0013 0.72 0.013 0.00004 0.00008 0.0054 0.00008 0.0002 0.0046 0.00004 0.0001 0.0002 0.0007 0.0025
0.8435
8
9 10 11 12 13
14
Figure 2. Dependence of the separation number (TZ) and height equivalent to a theoretical plate (h) on the temperature (T, °C) and the midpoint pressure (Pm, kPa) during the experimental procedure. b
is in agreement with the above observations: the h depends only on the initial hold time and the temperature program rate (see column temperature) and not on the midpoint pressure. The h on the front column exhibited the same behavior and gave eq 8 by multiple linear regression analysis, showing that the
hf ) 39.60 - 2.0561To + 18.9171r + 0.0176To2 - 1.1390r2 - 0.1406Tor (8)
h of this column depends on the temperature parameters To and r. On the other hand, the h of the back column depends only on the midpoint pressure:
hb ) 65.36 - 1.1160Pm + 0.0048Pm2
(9)
The statistics of eqs 7-9 extracted by multiple linear regression analysis are given in Table 3. Dependence of the Separation Number TZ on the To, to, r, and Pm. The seperation number values were determined for the pair of C5-C6 n-alkanes (Table 2). The TZ exhibited its maximum value in experiment 17 (To ) 84 °C, to ) 4.94 min, r ) 3.6 °C/min, Pm ) 109.7 kPa) and its lowest value in experiment 15 (To ) 69 °C, to ) 3.78 min, r ) 3.2 °C/min, Pm ) 118.0 kPa). If the elution temperatures of hexane are calculated for these two sets of experimental data (see Table 3), it can be seen that the maximum value of TZ has been observed at the lowest column temperature (86.6 °C), and the minimum value of TZ is observed at a higher column temperature (110.4 °C). This is in accordance with the conclusions of Jennings and Yabumoto,13 who showed that, on increasing the column temperature, the TZ decreases. This is consistent with the fact that increased temperatures result in decreased tR and w0.5 values, owing to an increase in the solute molecular coefficients in the mobile and stationary liquid phases, particularly for low-molecular weight solutes.16
0.8976
0.9317 0.9015 0.9559 0.9134 0.9920
0.9831
a The uncertainty is given for 95% confidence interval (n ) 28 runs). See text.
It can be seen from Table 3 that, although the lowest column temperature has been observed in experiment 3, the value of TZ is not the maximum. This discrepancy can be explained on the basis of the maximum value of Pm, which is higher than that in experiment 17. As known, upon increasing the pressure (flow rate) of the carrier gas in the column, the TZ decreases. Here, we have a combination of the effects of temperature and pressure on TZ. These observations lead to the conclusion that TZ depends strongly on the column temperature and the midpoint pressure of the system. In order to evaluate the dependence of TZ on the selectivity parameters of the system, multiple linear regression analysis was used, and eq 10 was derived.
TZs ) 0.0094ToPm
(10)
As can be seen from the equation, the separation number of the system depends only on two selectivity parameters: the initial temperature and the midpoint pressure. This is in accordance with the dependence of the total resolution of the system, which depends on the same parameters.10 The relationship between TZ and Rs is very well known (eq 3). As for the h, the effects of the four selectivity parameters on the TZ of each column were studied, and, by multiple linear regression analysis, eqs 11 and 12 were derived for the front and back columns respectively.
TZf ) 0.6490Pm - 0.0050ToPm
(11)
TZb ) 0.0095ToPm
(12)
As can be seen, a combined effect of the midpoint pressure and the initial temperature exists for both columns, but only for (16) Desty, D. H.; Goldup, A. In Gas Chromatography; Scott, R. P. W., Ed.; Butterworths: London, 1960; p 162.
Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
4471
Table 4. Values of TZ Derived Using Eqs 2 and 5 expt no.
TZa
TZb
expt no.
TZa
TZb
1 2 3 4 5 6 7 8 9 10 11 12 13 14
25.2 89.2 70.4 63.0 94.3 86.4 117.9 67.7 92.5 62.2 89.9 71.9 98.9 94.9
24.8 88.4 68.9 62.6 93.0 85.0 116.4 67.5 91.4 61.0 88.9 70.8 98.1 94.0
15 16 17 18 19 20 21 22 23 24 25 26 27 28
10.7 93.6 119.9 94.2 103.6 14.9 108.5 91.3 101.6 85.7 101.8 115.5 79.6 97.8
10.5 93.1 118.3 94.4 101.1 15.0 107.8 90.4 100.4 84.7 100.9 115.3 78.5 97.1
a Separation number calculated using eq 2. b Separation number calculated using eq 5.
the front column does the midpoint pressure affect the TZ of the column independently. The statistics for eqs 10-12 are given in Table 3. Relationship of Separation Number, Height Equivalent to a Theoretical Plate, and Column Lengths of the System of Two Columns Coupled in Series. As can be seen from Figure 2, during the experiments which gave the maximum h value of the system, at the same time the minimum value of the separation number was observed. This leads to the conclusion that a possible relationship between them exists. Recently,3 it was suggested that an inverse relationship between h and TZ exists in isothermal operation of a one-column system, according to eq 5. This equation relates, for first time, the TZ, the h, and the column length in a one-column GC system. The separation number for the C5-C6 pair was calculated for the system using eq 2. Using eq 5 for the calculation of TZ values it was proved that the values were the same with those calculated by eq 2 if L ) Lf + Lb, where L is the total column length, Lb is the column length of the back column, and Lf is the column length of the front column (Table 4). The values of TZ calculated from eqs 2 and 5 are not significantly different, with their percent differences ranging from 0.30 to 2.41%. This slight difference is caused by the use of h for the calculation of TZ by eq 5. This agreement of the values of TZ shows that the inverse relationship proposed by Jones et al. for one-column GC system holds also for a system with two columns coupled in series under temperature-programmed conditions. Contribution of the Nature of Individual Columns to the TZ and h of the System. As will be shown later and from the results of the previous work,10 each column contributes differently to the parameters of the system of the two columns coupled in series. In order to evaluate the effects of the separation numbers of the individual columns on the overall separation number of the dual-column system, multiple linear regression analysis was used, and eq 13 involving the separation numbers was extracted,
TZs ) 0.8943TZb - 0.0039TZb2 + 0.0054TZf2 + 0.0122TZbTZf (13)
showing that the major contribution to the system’s separation 4472
Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
number is from the back column. This is in accordance with the chemical characteristics of the back column. The solid stationary phase of it (Al2O3/Na2SO4) separates better the light hydrocarbons (C1-C6) than the stationary phase of the front column, which does not exhibit good separation characteristics for the light hydrocarbons, especially for the C1-C4 fraction. Multiple linear regression analysis has also showed that the h of the system depends strongly on the h of the back column according to eq 14. The statistics for eqs 13 and 14 are given in Table 3.
hs ) 0.5239hb + 2.9667hbhf
(14)
Examination of the Relationship between Separation Number and Average Carbon Number of Two Homologous Compounds. The basic linear relationship TZ ) R(CH) + b, which holds for gas chromatographic systems with one capillary column, was examined for the present system with the two coupled columns under isobaric conditions (constant head pressure). In order to illustrate the phenomenon of linearity or nonlinearity of this relationship in such a system, two columns coupled with very different characteristics have to be applied.14 This means that the choice of two capillary columns coated with stationary phases of very different polarities is not illustrative, but the combination of the two columns used in this system (GLCGSC) is. The behaviors of the n-alkanes in these two columns are very different, as can be seen from the very different slopes of the equations. For this purpose, the C3-C6 n-alkanes fraction of raw data was chosen.10 The data for methane and ethane were excluded for this work in order to avoid the nonlinear effects which are observed from these compounds as the first members of this series of compounds. The estimated values of the slopes, the intercepts, and the correlation coefficients for the individual columns and for the two columns treated as a system are given in Table 5. From the data in Table 5, it is obvious that the above-mentioned relationship is linear only for the front column, F (Rf ) 0.99345 0.98834) and the two columns coupled in series, S (Rf ) 0.998810.83619, except for experiment 10, where Rf ) 0.77415), but not for the back column, B (Figure 3). In experiment 15, the slope of the system took a negative value as the slope of the back column. Taking into account that TZ depends strongly on the midpoint pressure of the system (see above), and examining the experiments where the linearity of the system is quite good, it can be seen that, when the midpoint pressure increases, the relationship between separation number and average carbon number tends to be nonlinear. On the other hand, at low values of Pm, the linearity is satisfactorily good. It must be mentioned here that the only case in which the back column exhibited good linearity is in experiment 1, where the midpoint pressure has its minimum value. This constitutes proof that the linearity of this relationship in a system of two capillary columns coupled in series is dependent on the midpoint pressure. It is also observed that the linearity for the whole system depends on the behavior of the back column. This is illustrated in experiment 15, where the system's slope is negative and, at the same time, the slope of the back column becomes negative.
Table 5. Slope, Intercept, and R2 of the Equation TZ ) r(CH) + b, Derived by Linear Regression of the Data for the Front Column, the Back, Column, and the Two Columns Coupled in Series front column
back column
two columns coupled in series
expt no.
R
b
R2
R
b
R2
R
b
R2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
9.505 13.313 9.505 11.020 6.527 10.186 14.673 16.266 11.575 10.840 11.082 12.401 11.949 12.313 15.433 12.027 12.464 11.073 12.410 14.960 11.804 11.681 10.991 12.985 12.395 11.453 15.287 11.401
29.273 -8.191 29.273 -30.376 -19.102 -30.225 -43.124 -35.678 -34.307 -31.684 -32.982 -36.749 -34.797 -36.312 -45.005 -35.507 -36.026 -32.527 -37.193 -43.218 -35.475 -34.648 -32.575 -38.859 -36.838 -34.103 -40.498 -30.749
0.9894 0.9962 0.9894 0.9953 0.9837 0.9886 0.9914 0.9925 0.9990 0.9893 0.9883 0.9938 0.9909 0.9892 0.9908 0.9918 0.9935 0.9875 0.9911 0.9895 0.9892 0.9869 0.9924 0.9891 0.9875 0.9933 0.9900 0.9938
8.693 20.438 38.048 12.821 26.000 25.848 16.055 12.456 30.104 7.361 16.208 8.394 19.721 21.976 -29.794 21.261 21.294 25.363 31.348 6.516 17.108 22.882 15.613 25.722 14.028 13.803 11.893 20.385
-2.750 -7.954 94.394 2.075 -66.258 -28.592 52.786 -23.678 -65.451 38.563 10.980 -23.452 3.183 -16.699 201.43 -6.449 22.275 -35.982 -57.415 -22.744 4.005 -15.383 5.634 -19.826 56.412 17.869 -6.451 -8.7855
0.9997 0.9138 0.6802 0.714 0.9914 0.6155 0.3697 0.6784 0.9155 0.2450 0.6725 0.7783 0.6647 0.8063 -0.4550 0.5888 0.5329 0.8435 0.8458 0.9005 0.8227 0.8291 0.8416 0.5995 0.4091 0.4899 0.5432 0.9039
7.729 26.518 35.909 18.357 22.272 35.476 36.635 32.457 32.831 16.119 29.322 36.453 31.093 28.857 -17.660 31.176 42.028 32.038 36.512 6.276 29.433 32.273 25.515 34.337 37.846 21.954 32.783 29.612
-7.501 53.187 -106.00 -24.800 -58.886 -99.482 -78.498 57.872 -85.516 -18.813 -68.901 -35.672 -67.334 -59.109 128.57 -73.766 -108.59 -79.525 -93.819 -21.529 -67.914 -72.469 -50.397 -81.695 -88.16 -32.828 -24.563 -61.024
0.9982 0.9756 0.9949 0.8792 0.9987 0.9977 0.9711 0.9834 0.9909 0.7742 0.9829 0.9901 0.9657 0.9618 -0.3799 0.9755 0.9937 0.9910 0.9871 0.9099 0.9876 0.9831 0.9614 0.9656 0.9796 0.8362 0.9971 0.9727
Figure 3. Graph of the relationship TZ ) R(CH) + b for the front column (F), the back column (B), and two columns coupled in series (S).
The same observation was made above, where the contribution of the back column to the system characteristics was shown. CONCLUSIONS For a system of two capillary columns coupled in series, the separation number (TZ) and the height equivalent to a theoretical plate (h) were studied, for the first time, during an optimization of the programmed temperature and the pressure, and the following conclusions were drawn: The separation number, TZ, of the system depends strongly on the midpoint pressure and the initial temperature. On the other hand, the h of the system depends on the initial time and the temperature program rate. The behavior of h differs from that for a one-column GC system, where h is decreasing with decreasing temperature.
An inverse relationship between TZ and h was observed. It was proved that eq 5,3 which relates these parameters with column length, is also applicable to the system of two coupled columns if L ) Lf + Lb, where Lf and Lb are the lengths of the columns. The basic linear relationship TZ ) R(CH) + b holds for the system with two columns coupled in series, and it is linear only in the cases when linearity of this relationship was observed for the back column, and this depends on the midpoint pressure of the system. In conclusion, the present paper examines the applicability of some fundamental relationships, concerning the separation abilities of a system (TZ and h), which hold in one-column gas chromatography, to SCOTCH systems without intermediate trapping in order to further extend this technique in resolving complex mixtures of compounds. ACKNOWLEDGMENT The authors express their thanks to Agricultural Bank of Greece for providing the basic GC instrumentation and Dr. D. P. Nikolelis for proofreading. E.B. is grateful to the State Scholarships Foundation for awarding him a scholarship for Ph.D. studies.
Received for review June 11, 1996. Accepted September 16, 1996.X AC960572V X
Abstract published in Advance ACS Abstracts, October 15, 1996.
Analytical Chemistry, Vol. 68, No. 24, December 15, 1996
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