Anal. Chern. 1990, 62, 985-990
985
Threshold Criteria Used for the Optimization of Selectivity by Tuning Intermediate Pressure for Series-Coupled Columns in a Dual-Oven System Eva Benicki, JBn KrupEik,* Dugan Repka, and Peter Kuljovskjl Slovak Technical University, Faculty of Chemical Technology, Department of Analytical Chemistry, Radlinskdho 9, 812 37 Bratislava, Czechoslovakia Rudolf E. Kaiser Institute of Chromatography, P.O. Box 1141, 0-6702 Bad Duerkheim 1, Federal Republic of Germany
A computer-assisted procedure based on threshold criteria was employed for the optimization of selectivity by tuning the column coupling-point carrier gas pressure of two capillary columns of different polarities operated at different temperatures in a dual oven gas chromatograph using constant inlet and outlet carrier gas pressures. The optimization procedure was monitored by Optimization criterion (C,) calculated from the following equation: C, = Cl"m, ( f R , m a x - fR,n)/tR,max, where n is the number of solutes in a sample, m, = 1 if the resolution of peak pair is higher than a threshold, fR,max is the maximum acceptable analysis time, and tR,"is the last peak retention time. Three kinds of thresholds were compared in this paper: constant threshold; floating threshold predicted from the resolution factor; floating threshold predicted from the separation numbers. The use of a resolution factor caiculated for each peak pair gave the best result. A comparable result was obtained by using the floating threshold. However, the last procedure was less tedious than the procedure based on the resolution factor.
+
INTRODUCTION A combination of the necessary separation efficiency and the optimum selectivity of the separation system is the best approach to multicomponental capillary gas chromatographic analysis ( I ) . Tuning the selectivity of a separation system would be the method of choice for adjusting a GC instrument to a given sample composition to effect complete separation (2). The following means can be used for the change of the separation system: changing the stationary-phase nature; packing the column with the mixed phases of different polarity; coupling two or more columns with different polarity in series. If fixed-length columns of different polarities are coupled in series, the selectivity of the system can be tuned as required by adjusting the retention time of the sample components in individual columns by varying the carrier gas flow rate in both columns (3-6), the temperatures of both columns (2,4-8),or the carrier gas flow rates and temperatures of both columns simultaneously (2,4-6). The overall selectivity of two columns coupled in series can be adjusted somewhere between the selectivities of the individual columns coupled in series depending particularly on the carrier gas flow rates as well as temperatures in individual capillary columns. The number of parameters that influence the global optimum selectivity of two chosen capillary columns
* To whom the correspondence should be sent.
coupled in series is relatively high (e.g. two carrier gas flow rates and a number of parameters determining column temperatures at temperature programming runs). The procedure for searching for the global optimum selectivity requires many experiments when the optimization procedure is based predominantly on an experimental approach and a high degree of reproducibility and precision of retention data when the optimization procedure is based on mathematical or chromatographic models. Both these requirements are limiting factors in chromatographic laboratories. Therefore in most optimization procedures some working parameters are arbitrarily set up (from the chromatographer's knowledge), and the aim of such an optimization procedure is to find a local optimum within reduced parameters space. For separation of a multicomponent sample Hinshaw and Ettre proposed to optimize the overall selectivity of two columns coupled in series placed in one oven by tuning the carrier gas flow rates in the individual columns and/or oven isothermal temperature (6). They used an optimization procedure based both on a chromatographic model and on the window method according to Laub and Purnell (9). In our previous paper we described a computer-assisted procedure for the adjustment of an optimum selectivity by a simultaneous variation of isothermal temperatures of two columns coupled in series and placed in two independently heated ovens (10). The optimization procedure was relatively simple since the retention of all solutes, a t any combination of oven temperatures (TA,TB),had been predicted from the dependence of retention indices [I(TA,TB)]at both temperatures (TA and TB)by using a quadratic polynomial equation. The optimization criterion consisted of a number of separated peaks (the primary part) and the duration of analysis (the secondary part) assuming the fact that the resolution power of the column is constant. The aim of this paper is to introduce a computer-assisted procedure based on threshold criteria for optimization of selectivity by tuning the coupling point carrier gas pressure (p,) of two capillary columns of different polarities coupled in series and operated at different temperatures in a dual oven gas chromatograph. Three kinds of thresholds are compared: constant threshold; required resolution factor; floating threshold predicted from the separation number. The validity of the introduced computer-assisted optimization procedure is verified by the separation of a complex mixture of normal, cyclic, branched, and aromatic hydrocarbons.
THEORY Deans (3) has shown that the selectivity of two capillary columns coupled in series can be inter alia changed by varying the carrier gas flow rate through individual columns. Hinshaw
0003-2700/90/0362-0985$02.50/00 1990 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 10, MAY 15, 1990 injection
m d Ettre (5,6) have shown that the contribution of individual column selectivity to the overall selectivities of these columns coupled in series, by tuning the carrier gas flow rates through the individual columns, can be monitored by the so-called relative retentivity (@) @A
=
~M,A/~M,AB
(1)
and
w
where t M is the gas hold-up time, A and B are symbols for the first and the second column, respectively, and AB is the symbol for columns coupled in series. Kaiser et al. (4)have used Kovlts indices of sample components for monitoring the selectivity of capillary tandem columns, though the comparison of the different stationary phases selectivity based on Kovgts indices can be problematic (6). The carrier gas flow rates through individual columns coupled in series can be tuned by the change of inlet pressure (p,), columns coupling-point pressure (p,), outlet pressure (p,), and/or simultaneous changes of the above-mentioned two or three pressures. In commercial GC instruments it is, however, convenient to set up the inlet ( p , )and outlet (pol pressures and tune the gas flow rates through individual columns coupled in series by changing the column coupling-point pressure (pm). Kaiser et al. ( 4 ) have shown that the dependencies of Kovlts indices of all sample components [Z,(p,)] on column coupling-point pressure (p,) can be described by the polynomial equation libm)
=
+ a 1 P m + a29m2 + a39m3(3)
u 6
R,
1 A
(3)
where the coefficients a can be determined by multiple linear regression analysis (MLRA) of experimental data. With the coefficients of eq 3 known, Kovlts indices (0of all sample components can be calculated by computer at any pmvalue from an experimental range of intermediate pressures (pm).Subsequently, Kovdts index differences of all neighboring peaks ( AZJl = I, - I,) can be calculated at any pmvalue and compared with a threshold value (Uml,,). We have recently shown (10, 11) that for monitoring of multicomponent GC separation, the following criterion can be used:
Detail
01
T -pie(*
Figure 1. Scheme of GC instrument containing two capillary columns placed in two separately heated ovens: 1, sample introduction, 2, SP 1000 capillary column: 3, interface: 4, T-piece; 5, SE-30 capillary column; 6, FID; 7, pressure regulator; 8, Fractovap 2350 GC; 9, Fractovap 4180 GC.
the experimental data of n-alkanes; floating threshold [ AZ-,,(p,J,)] predicted from separation numbers [ TZi(p,,,J,)] obtained by analyzing the n-alkanes.
EXPERIMENTAL SECTION where n is the number of solutes in a sample, m, = 1 if IAZJ I for j = i f 1, elsewhere rn, = 0, and tRn is the last peak retention time. The value of maximum acceptable analysis time (tmax)is arbitrarily chosen so that a t any analysis t,,,
urn,,,
'The first term of the right-hand side of eq 4 gives the tR,n.
number of peaks resolved on a chromatogram equal to or better than the required resolution (threshold) and it is a primary part of the criterion C., The second term of the right-hand side of eq 4 is the secondary part. Since C, criterion is hierarchical, the second term of the right-hand side of eq 4 is used for the judgment of such analyses where an equal number of peaks are resolved equally or better than a required resolution. From eq 4 it follows further that the decision, whether the peaks on a chromatogram (experimentally obtained or reconstructed by a computer) are considered as resolved or not, depends primarily on the value of the threshold. In this paper, three kinds of thresholds are exploited for the calculation of the C, values: constant threshold (AI,,,,,,) for all peak pairs at any pm;required resolution factor (Rj,,,es)compared with that predicted for any pm[R,,(p,)] from
Gas Chromatographic Instrumentation. The gas chromatographic system of two independently controlled ovens consisted of two Carlo Erba GC instruments (Fractovap 2350 and Fractovap 4180, Carlo Erba Strumentazione, Milan, Italy) interfaced with a separately heated stainless steel tube (150 mm, 1.5 mm i.d., 0.3 mm wall thickness) inserted into a glass tube (120 mm, 2.5 mm i.d., 1.0 mm wall thickness) as shown in figure 1. The column inlet of the first column (column A was fused silica capillary 40 m long, 0.2 mm i.d. coated with SP 1000 placed in the Fractovap 2350 GC) was coupled to an all-glass inlet stream splitter injection port. The outlet of column A was led through the interface to the Fractovap 4180 where it was coupled to the first inlet of the T-piece (see detail in Figure 1). The second inlet of the T-piece was coupled to the Fractovap 4180 GC injection port allowing for a change of carrier gas pressure in the T-piece. The outlet of the T-piece was coupled to the inlet of column B (glass capillary column 40 m long, 0.3 mm i.d. coated with SE-30). The outlet of column B was inserted into the jet of the Fractovap 4180 GC FID. The detector signal was led to an electrometer, Model EL 480 (Carlo Erba Strumentazione, Milan, Italy), and recorded by a computing integrator Chromatopac CR-3A (Shimadzu, Kyoto, Japan). Operating Conditions. Hydrogen was used as a carrier gas with a constant inlet pressure of 235 kPa (abs). The inlet stream splitter was operated with a split ratio 1:lOO. The outlet pressure
ANALYTICAL CHEMISTRY, VOL. 62, NO. 10, MAY 15, 1990 987 Table I. List of Hydrocarbons in Sample and Comparison of their experimentally found [I(e)] and Predicted [Z(c)] Kovtits Indices at p m = 150 kPa
peak no. 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 29 30 31 32 33
name n-octane 2,3,5-trimethylhexane 2,4-dimethylheptane 4,4-dimethylheptane
I(e)
I(c)
800.0
800.0 815.1 822.1 825.3 837.6 837.6 856.7 859.5 859.5 876.0 955.9 900.0 919.6 984.0 933.7 933.7 937.2 940.1 1004.9 1029.9 979.1 1061.5 1000.0 1018.3 1069.1 1075.4 1026.0 1076.3 1083.0 1102.7 1100.0
815.4 822.4 825.4 838.0 3,5-dimethylheptane-a,fl 839.0 3,3-dimethylheptane 856.9 2,3-dimethylheptane 859.8 3,4-dimethylheptane-n 859.8 3,4-dimethylheptane-P 876.1 3,3-diethylpentane 955.3 iso-propylbenzene n-nonane 900.0 919.6 4,4-dimethyloctane n-propylbenzene 983.6 933.7 2,6-dimethyloctane 933.7 3,3-dimethyloctane 937.2 3,4-diethylhexane 940.2 2-methyl-3-ethylhexane 1004.5 1,3,5-trimethylbenzene 1029.5 1,2,4-trimethylbenzene t ert-butylcyclohexane 979.1 1,2,3-trimethylbenzene 1061.0 n-decane 1000.0 sec-butylcyclohexane 1018.3 1,3-diethylbenzene 1069.0 n-butylbenzene 1074.8 n-butylcyclohexane 1025.9 1,4-diethylbenzene 1076.0 l,2-diethylbenzene 1082.7 1,3-dimethyl-4-ethylbenzene 1102.4 1100.0 n-undecane
of the carrier gas was atmospheric @, E 101 kPa). Columns were operated isothermally with arbitrarily chosen temperatures T A = 70 "C and TB = 50 "C. A sample of hydrocarbons (Table I) was diluted with n-pentane to 0.03% (v/v) content per compound. One microliter of this solution was injected with a 1 0 - ~ L Hamilton syringe. Eight chromatograms were recorded by separating a hydrocarbon sample in the tandem column, varying the coupling-point pressure (CCPP) of hydrogen used as a carrier gas from p m = 130 kPa to p m = 200 kPA in 10-kPa steps. Computation. Curve fittings and optimization calculations were performed on an H P 85B microcomputer. The facilities of the HP BASIC were enlarged by using Matrix ROM, Advanced Programming ROM, and Printer/Plotter ROM. For multiple linear regression analysis, programs from Statistical Analysis Multipac were used (all products were purchased from Hewlett-Packard, Palo Alto, CA).
1150
I
' IP,/
1100
1050
1000
20 19 i
8oorEE3 750 130
From eight chromatograms recorded by separating the sample of hydrocarbons (Table I), coefficients a in eq 3 were determined by MLRA of experimental values of Kovdts indices [Zt(pm)]of all sample constituents a t different pm values. It follows from Figure 2 that, for the chosen columns coupled in series, the polarity of the column tandem increases with an increasing of the value of pmand retention indices of aromatic hydrocarbons can be varied dramatically with the tuning of the pmvalues. With the coefficients of eq 3 known, Kovgts indices of all compounds given in Table I were calculated on a computer for all CCPP values from 130 to 200 kPa in 2.5-kPa steps. This step was chosen because the used pressure regulator built in the Fractovap 4180 GC allowed the setting up of pressure in minimal 5-kPa steps. Subsequently, Koviits index differences of all neighboring peaks [AZ,L(pm)= Z,(pm)- Z,(p,)] were calculated and compared with a threshold value [AZm,,(pm)]. T h e dependence of the last peak retention time (tRJ on
190
170
P,
[kpol
Figure 2. Dependence of Kovsts indices [I@,)] of hydrocarbons listed Table I on the CCPP values @), (for details see text).
in
h
2930
170
150
190
pm[k Pa
1
Figure 3. Dependence of the last peak retention time [t,,,@,)] on the CCPP values @ ), drawn from the data of eq 5: (0)corresponds to n -undecane; (m) corresponds to 1,3-dimethyl-4-ethylbenzene.
the pmvalue, needed in eq 4 for prediction of C, at any pm value, was approximated by the following cubic equation:
(5) = b@mZ + b#m3 where b are coefficients found by MLRA of experimental data. Figure 3 shows the dependence of the last peak retention time (tR,J on the CCPP value (pm). Since the identity of the tR,n(Pm)
RESULTS AND DISCUSSION
150
= bo
+ b$m
last peak was changed with the change of pmvlues, the dependence shown in Figure 3 is not consistent. A considerable drop of tR,, with pmis shown in Figure 3 for pmranging from pm= 130 kPa to pm= 145 kPa, as under these conditions nundecane (peak no. 33) was the last peak. T h e dependence of tR,, does not change dramatically for pm> 145 kPa, as at these pressures 1,3-dimethyl-4-ethylbenzene(peak no. 32) is the last peak. Even in this part of the t R n on p m , dependence is, however, not regular. In the interval pm= 145 kPa to pm = 170 kPa it decreases and for pm> 170 kPa slightly increases since the last peak retention time [ t ~ , ~ ( p , ,depends ,)] on both capacity factors [h,(p,)] and the gas hold-up time [ t ~ ( p ~ ) ] as follows from the equation tR,n(Pm) = t M ( P m ) [ 1
+ kn(pm)l
(6) From the above written text it can be concluded that the main role of the computer-assisted selectivity optimization proce-
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 10, MAY 15, 1990
1 4 0
!50
170
-
:90
pmCkPJ
Figure 4. Computer-reconstructed dependence of the optimization criterion (C,) on the CCPP values @), where constant threshold (AIan = 4.0 i.u.) was used.
5
IC
on the CCPP
values (p,).
OPTIMIZATION PROCEDURE BASED ON A PREDICTED RESOLUTION FACTOR
18 17
0
Figure 6. Dependence of the gas hold-up time [fU@,)]
15
20
25
30
35
40
T i m e lminl
As already mentioned, the maximum value of the optimization criterion (C,,,= = 18.38) found in the previous paragraph by using the constant threshold (AZ- = 4.0 i.u.) is lower than a real value, since the resolution of later eluted peaks can be interpreted erroneously. It is obvious that the decision, whether the peaks in a peak pair are resolved or not, is correct only in those cases where the experimental value of the resolution factor of each peak pair is compared with a required value of the resolution factor. In general, a resolution factor (Fiji) can be calculated from the following equation:
Figure 5. Computer-reconstructed separation of the hydrocarbon sample (Table I) obtained at p m = 160 kPa.
dure is to look for a line perpendicular on the pmaxis (Figure 2 ) a t which the maximum value of C, is obtained.
OPTIMIZATION PROCEDURE BASED ON A CONSTANT AIMINVALUE The resolution power of the separation system is usually not considered when a window diagram or capacity factors dependence on the relative retentivity @B are used for the optimization of tandem column selectivity by tuning the pm value (6). In our previous papers (IO,11) we have shown that the constant threshold value is acceptable for the decision as to whether a peak pair is considered to be separated or not if capacity factors of compounds of interest are higher than 1.5. In this part of our work we shall show the results obtained for the optimization of tandem column selectivity by tuning the CCPP values (p,) with a constant threshold value AImin. As the resolution power of the capillary column increases with the increasing value of capacity ratio, the constant threshold value had to be determined from the data of compounds eluted with small capacity ratios despite the fact that the later eluted compounds already resolved on the chromatogram, were, on the basis of this threshold, considered as not resolved. The constant threshold (Urnin = 4.0 index units (i.u.)) was found from the data of 2,4-dimethylhexane and 4,4-dimethylhexane analyzed in the tandem column at pm= 150 kPa. Hence, a computer-reconstructed dependence of the optimization criterion (C,) on the pmwas obtained (Figure 4) from eqs 3-5 and the constant threshold (Almin= 4.0 i.u.). It follows from Figure 4 that an equal number of peaks if resolved within the range of pm= 152.5 kPa to p m = 160 kPa. The highest CCPP = 160 kPa), as at this value is, however, the optimum (pm,opt CCPP value optimization criterion reached maximum (CP,,= = 18.38 where 18 peaks were resolved within 37.16 min). Figure 5 shows the separation of the hydrocarbon sample (Table I) in columns A,B coupled in series (see Experimental Section) at pm,opt = 160 kPa.
1 . 1 8 ( t ~-j tR,i)
Rj,, =
wj
+ wi
(7)
where tR is retention time and w is peak half height width of adjacent peaks i and j . A modification of eq I , with respect to the pmchanges, leads to the equation
R.. 11 =
1 * 1 8 t ~ b m ) [ k j ( P m )- ki(Pm)l wj(Pm,kj)
+ wibmtki)
(8)
where tM is a gas hold-up time and k is the capacity ratio found for adjacent peaks i and j at corresponding pmvalues. It was statistically approved that the dependence of t M ( P m ) on pm can be approximated by the following quadratic equation:
where c values are the coefficients. Figure 6 shows the computer-reconstructed dependence of the gas hold-up time [tM(Pm)]on the CCPP values 0,). Capacity ratios ki(p,) of all peaks, at corresponding pm values, were calculated from the KovPts index formula; corresponding pm values were found from the following equation:
where d are coefficients. Figure 7 shows the dependence of capacity ratios [k,@,)] on the CCPP values (p,) found for n-octane (C&, n-nonane (C9),n-decane (Clo), and n-undecane (CIJ. The half height peak width [wi(p,,ki)] depends on both capacity factor ki(p,) and pmvalues. This dependence is, however, complex and can be described by the following equation:
ANALYTICAL CHEMISTRY, VOL. 62, NO. 10, MAY 15, 1990
d
989
50
30
I/
20
170
153
190
Flgure 7. Dependence of capaclty ratios of n-alkanes [k,@,)] on the CCPP values @),.
15E
li2
!BE
,u-
@
+@
\y 1
200
DP.1 -
'
Pm
Figure 10. Three-dimensional dependence of the separation number [TZ,@,,I,)] on the CCPP values @), and Kovlts indices [I,@,)] reconstructed by a computer from the data of eq 17. 1
p90 00
144
00
!58 00
172 00
186 00
200 00
Figure 8. Dependence of half height peak width [ w,@,,k,)] on the CCPP values (p,) and the capacity ratios [k,@,)] reconstructed by
a computer for n-alkanes from the data of eq 11.
P.
bP*I
Figure 11. Three-dimensional dependence of floating threshold [ A I d J p m , I , ) ] on the CCPP values 0,) and Kovhts indices [I,@,)].
in a relatively wide interval of pmvalues, 20 peaks are resolved equally or better than the required resolution. The largest pmvalue @, = 162.5 kPa) is, however, the optimum, as at this pressure the analysis time is shortest.
OPTIMIZATION PROCEDURE BASED ON A FLOATING THRESHOLD
Flgure 9. Computer-reconstructed dependence of the optimization criterion (C,) on the CCPP values @), where predicted resolution factors (R,,,) were used.
where the coefficients e were obtained from experimental data for n-alkanes C8-Cl1. Figure 8 shows a three-dimensional plot of half height peak width [wi(p,,ki)] on the CCPP values (p,) and the capacity ratios [ k i ( p , ) ] as found from the data of n-alkanes. With the coefficients in eq 3 and 9-12 known, resolution factors were calculated, at corresponding pmvalues, for all peak pairs, and compared with R,,i,re, = 1.18. The optimization criterion (C,) was calculated from eq 4, where m = 1 if Rj,i L Rj,i,req,elsewhere m = 0. Figure 9 shows the computer-reconstructed dependence of the C, on the pmfor the procedure based on a predicted resolution factor. In this case, the optimization criterion reached a maximum value (Cp,mu = 20.40) at an optimum CCPP value (pm,opt = 162.5 kPa) where 20 peaks were resolved with a resolution factor higher than 1.18 within 36.24 min. Figure 9 clearly demonstrates that
Comparison of the results shown in both previous paragraphs indicated that the optimization procedure based on the predicted resolution factor is superior to the method with a constant threshold but the former is more laborious. In this paragraph we shall show the optimization procedure based on a floating threshold which gives more realistic results than the method discussed in part 1and is thereby less complicated than the one discussed in part 2. This method is based on the concept arising from a separation number. Kaiser (12) has shown that the separation number (TZ) is a useful criterion to judge the column separation efficiency, which can be calculated from a chromatogram by using the equation
TZ =
tR,z+l
wz
- tR,z
+ wz+1
-1
where tR is retention time, w is half height peak width, and z is carbon atom number in a carbon chain of the test compounds. Grob and Grob (13)have shown that TZ values characterize the column separation efficiency both at isothermal and temperature programmed GC analyses. If normal alkanes represent the testing compounds, the minimum required separation number (TZ,,,) for resolving two compounds with
990
ANALYTICAL CHEMISTRY, VOL. 62, NO. 10, MAY 15, 1990
-
a floating threshold [AZmin(pm,li)] found from a modified eq 15 for each ith compound
I 25
Y
20
(16) TZi(p,,li) values were calculated, for a compound with Kovits index Zi(p,) from the following equation:
15
TZi(pmJi) = fo
10
I 1
;io
1'C
150
130
Pm CkP.1
Figure 12. Computer-reconstructeddependence of the optimization criterion (C,)on the CCPP values @), where floating threshold [AIrnIn,/@rnvIJl was used. 18 17
11
+ flip, + f 2 s m 2 + f J i ( P m ) + f4ili2(Pm)
(17) where f are the coefficients determined from the experimental data obtained for n-alkanes, where l i ( p , ) = lOO(22 + 1)/2. Figure 10 shows the dependence of TZi@,,Zi) on the p m values and Kovits indices [Zi(pm)]. For illustration, a dependence of floating threshold AImin(p,,ZJ on the CCPP values (p,) and Kovlts indices of compounds is shown in a three-dimensional plot on Figure 11. In Figure 12 a computer-reconstructed dependence of C, on p m values is shown, where a floating threshold was used for the calculation of optimization criterion (C,). The maximum value (C, = 20.34) corresponds to an optimum CCPP value ( p , = 150 kPa), where 20 peaks were resolved on a chromatogram within 39.66 min. Figure 13 shows a computer-reconstructed separation of the hydrocarbon sample at = 150 kPa). an optimum CCPP value (pm,opt
LITERATURE CITED c
5
ic
le
25
20
3c
35
4c
45
Time hi11
Figure 13. Computer-reconstructed separation of the hydrocarbon sample (Table I) obtained at p m = 150 kPa. Kovlts indices
(Zjand
Zi) can be calculated from the formula
(14)
100
TZ,,, = -Ij - I ; The minimum Kovits index difference AImincan be, for the column with a given separation number, calculated from the following equation:
u .=mln
100
TZ
+1
As it follows from the definitions of TZ (12) and the resolution factor of two consecutive n-alkanes (14), the value of Urnin corresponds to the resolution factor R,,; = 1.18. Kovlts indices of all peaks were, at corresponding CCPP values (p,), calculated from eq 3. Subsequently, the Koviits index difference of each peak pair (Uj,J was compared with
(1) Kaiser, R. E.; Rieder, R. I. HRC CC, J . High Resolut. Chromafogr. Chromatogr. Commun. 1979, 3 , 416. (2) Sandra, P.; David, F.; Proot, M.; Dirricks, G.; Verstape, M.; Verzeie, M. HRC CC, J . H@h Resoluf. Chromatogr. Chromatogr. Commun. 1985, 8, 782. (3) Deans, D. R.; Scott, I. Anal. Chem. 1973, 45, 1137. (4) Kaiser, R. E.; Rieder, R. 1.; Lin Leming; Blomberg, L.; Kusz, P. HRC CC. J. High Resoluf. Chromatogr. Chromafogr. Commun. 1985, 8. 92. (5) Hinshaw, J. V.; Ettre, L. S. Chromatographh 1986, 21, 581. (6) Hinshaw, J. V.; Ettre, L. S. Chromafographia 1986, 27, 669. (7) Toth, T.; van Cruchten, H.; Rijks, J. A. In Proceedings of the Sixth Int. Symposium on Capi/laiy Chromafography; Sandra, P., Ed.; Huethig: Heidelberg, 1985; p 769. (8) Tbth, T.; Garay, F. I n Proceedings of the Eight International Symposium on Capillary Chromatography; Sandra, P., Ed.; Huethig: Heidelberg, 1987; p 585. (9) Laub, R. J.; Purnell, J. H. J. Chromafogr. 1975, 772,71. (10) Repka, D.; KrupEik, J.; Benicki, E.; Leclercq, P. A,; RiJks, J. A. J . Chromatogr. 1989, 463, 243. (11) Repka, D.; KrupEik, J.; Benick& E.; Garaj, J.; Maurer, T.; EngewaM, W. I n Proceedings of the Tenth International Symposium on Capillary Chromatography; Sandra, P., Redant, G., Eds.; Huethig: Heidelberg, 1989; p 682. (12) Kaiser, R . E. Z . Anal. Chem. 1962, 789, 1. (13) Grob, K.; Grob, K. J. Chromatogr. 1981, 207, 291. (14) Jennings. W. G. Gas Chromatography with Glass Capillary Columns; Academic Press: New York; 1978, p 70.
RECEIVEDfor review August 11,1989. Accepted Januray 24, 1990.
