Abstract. The paper shows a computer-assisted procedure for the optimization of selectivity of two columns coupled in series by tuning the working temperature.
Mikrochim. Acta [Wien] 1990, III, 1-10
Mikrochimica Acta 9 by Springer-Verlag 1990
Computer-Assisted Optimization of Selectivity by Tuning Temperature and Carrier Gas Pressure Drop in Two GC Capillary Columns Coupled in Series* Eva Benickfi, Jfin Krup6ik**, Peter Kuljovsk), Dugan Repka, and J/m Garaj Department of Analytical Chemistry, Faculty of Chemical Technology, Slovak Technical University, Radlinsk6ho 9, CS-812 37 Bratislava, Czechoslovakia
Abstract. The paper shows a computer-assisted procedure for the optimization of selectivity of two columns coupled in series by tuning the working temperature (using the isothermal mode) and columns coupling-point pressure at constant inlet and outlet carrier gas pressures. The optimization procedure validation was tested by the separation of 32 hydrocarbons in a column series with the aim to resolve the maximum number of components in the shortest possible analysis time. Key words: gas chromatography, capillary columns, series coupling of capillaries, optimization of selectivity.
The separation ofmutticomponent samples by high resolution gas chromatography (HRGC) can be improved by optimization of basic working parameters (selectivity and separation efficiency)and by shortening the time of analysis [1]. The selectivity of HRGC can be inter alia changed by coupling two or more columns of different polarities in series. The overall column series selectivity depends on the individual column selectivities which are given by the following basic column characteristics [2-5]: (i) nature of stationary phase, (ii) column length, (iii) gas and liquid volumes ratio (phase ratio). If two columns coupled in series are placed in a thermostat, the overall column series selectivity can be adjusted between the selectivities of individual columns by tuning the column temperature and/or the carrier gas flow through the individual columns [2-5]. The column temperature can be changed stepwisely (isothermal * Dedicated to Professor J. F. K. Huber on the occasion of his 65th birthday ** To whom correspondence should be addressed
2
E. Benicka et al.
mode) or continuously (temperature programmed mode). The carrier gas flow rates through individual columns can be changed by the variation of the inlet, the columns coupling-point and the outlet carrier gas pressures [2-7]. The aim of this paper is to show a computer-assisted procedure for the optimization of selectivity of two columns coupled in series by tuning the working temperature (using the isothermal mode) and columns coupling-point pressure at constant inlet and outlet carrier gas pressures. The optimization procedure validation was tested by separation of 32 hydrocarbons with the aim to resolve the maximum number of components in the shortest possible analysis time. Theoretical
The selectivity of a stationary liquid in GLC can be monitored by the selectivity factor ~ [1], _
!
(1)
'
tR, i
where t~ is adjusted retention time of compounds j and i. In our last paper [8] we have shown that the stationary liquid selectivity can easily be monitored by the number of peaks (Nr) resolved on a chromatogram equally to or better than a required resolution, N =
m,,
(2)
1
where n is the number of peaks detected on a chromatogram and mi = 1 if experimental resolution factor (Rji, exp)is greater than the required one (Rj~,roq),else mi = 0 for all peak pairs. The use of Nr is superior to e if the selectivity of the chromatographic system is monitored for a multicomponent sample HRGC separation as in this case capillary columns system selectivity increases with the increase of the number of peaks separated. The maximum peak number that can be resolved between two n-alkanes (with z and z + 1 carbon atom number), with the resolution factor Rji = 1.18, is given by separation number (TZ), calculated according to Kaiser 1-9]from following formula, TZ -
1,
tR,z+l -- tg,z
(3)
Wz + Wz+l where w is peak half-height width of n-alkanes z and z + 1, respectively. The minimum required separation number (TZ~eq) for resolving two components with retention indices (I i and Ix), can be calculated from Eq. (4) [10], 100 T Z r e q - - Ij -- [i
1.
(4)
The minimum retention index difference (Almin) can, for the considered column with a given separation number, be calculated from modified Eq. (4), mlmin --
100 TZ + 1
(5)
Computer-Assisted Optimization of Selectivity
3
W e h a v e f o u n d [11] t h a t the s e p a r a t i o n n u m b e r is n o t a c o l u m n c o n s t a n t a n d increases even for i s o t h e r m a l o p e r a t i o n s with the increase of the r e t e n t i o n indices of c o n s i d e r e d n-alkanes. In the case of two p a r a m e t e r o p t i m i z a t i o n , the s e p a r a t i o n n u m b e r (TZ) is e x p e c t e d to d e p e n d o n b o t h these factors, too. W i t h respect to the definition of T Z [9] a n d r e s o l u t i o n factor of two consecutive n-alkanes (Rz, ~+1) [12] Eq. (5) can be expressed as follows,
Almin,i(T, Pro, Ii)
Rji'req 100 -- 1.18 T Z ( T , p,,, ~) + 1 '
(6)
where Rji,req is the r e q u i r e d r e s o l u t i o n factor and Almi,,i(T, p,,, ~) is a t h r e s h o l d (6) used in Eq. (2) for a decision w h e t h e r the peaks i and j are c o n s i d e r e d as s e p a r a t e d or not. As the aim is to resolve the m a x i m u m n u m b e r of peaks with a r e q u i r e d r e s o l u t i o n factor within the shortest analysis time, the o p t i m i z a t i o n criterion (Cp) consists of two terms,
Cp = N r + (tma x -- tR,n)/tmax,
(7)
where tR, . is the r e t e n t i o n time of the last peak, tmax is the m a x i m u m acceptable time of analysis a n d Nr is calculated f r o m Eq. (2) with r e g a r d to Eq. (6).
Experimental
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). Both columns coupled in series were obtained from Supelco (Supelco, Bellefonte, Pennsylvania, USA). The first column (A) was 60 m long fused silica capillary, 0.25 mm I.D. coated with 0.25-#m film of polar stationary phase (NUKOL). The second column (B) was a 60 m long fused silica capillary with 0.25 mm I.D. coated with 1.0-#m film of non-polar stationary liquid (SPB-1). Both columns were placed in Fractovap 4180 GC instrument. They were coupled by a T-piece connected to the Fractovap 4180 GC injection port allowing to tune the carrier gas pressure in the columns coupling point. An all-glass inlet stream splitter injector port of Fractovap 2350 was used as an inlet to the whole column series. The detector signal was recorded by a computing integrator Chromatopac CR-3A (Shimadzu, Kyoto, Japan). The scheme of used instrumentation is given in Fig. 1.
Experimental Conditions Constant inlet pressure of hydrogen p~ = 380 kPa (abs.), split ratio 1 : 100. The columns coupling-point pressure Pmwas tuned from 300 to 350 kPa (abs.) as the "normal" value at the coupling-point was 290 kPa approximately. Column temperature was tuned from 60~ to 100~ A sample of hydrocarbons (Table 1) was diluted with n-pentane to 0.03~o (V/V) content per compound. 1 #1 of this solution was injected with 10-#1 syringe. Curve fittings and optimization calculations were performed on an HP 85B microcomputer with enlarged facilities 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, California, USA).
4
E. Benick/t et al. injection
H2
H2
Fig. 1. Scheme of two columns coupled in series used in this study (for details see text); 1 injector, 2 interface, 3 column A, 4 T-piece, 5 column B, 6 FID, 7 pressure controller, 8 Fractovap 2350 GC, 9 Fractovap 4180 GC
Results and Discussion The optimization of selectivity by simultaneous tuning of column temperature (T) and columns coupling-point pressure (Pro) w a s verified by the separation of hydrocarbon sample in column series. Nine chromatograms were recorded at working conditions predicted according to three-level experimental design. Working parameters were changed in the following manner: (i) temperature from 60~ to 100~ with a step 20~ (ii) columns coupling-point pressure from 300 kPa to 350 kPa with a step 25 kPa. The reproducibility of measurements was evaluated from chromatograms recorded at T = 80~ and p,, -- 325 kPa repeatedly during the whole experiment. The retention ofalt individual hydrocarbons was monitored by retention indices, I = 100z + 100
log(t'R'i/t'g'~) log(tR,~+l/tR,z)
(8)
where t~ are adjusted retention times for which t~,z+ 1 > t~, i > t~,~, i denotes component of interest and z carbon atom number in n-alkane chain. We describe the dependence of retention indices [I(T, Pm)] on temperature (T) and C C P P (Pro) values of hydrocarbons separated by the following equation,
Ii(T, Pm) = Ao,i + AI,iT + A2,iPm + A3,i Ta + A4, iP2m+ As,iTpm,
(9)
Computer-Assisted Optimization of Selectivity
5
Table 1. List of compounds in hydrocarbon sample Peak no.
Name
1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
2,3,4-Trimethylpentane 2,2,5-Trimethylhexane n-Octane 2,3,5-Trimethylhexane 2,4-Dimethylheptane 4,4-Dimethylheptane 3,5-Dimethylheptane (c~,/~) 3,3-Dimethylheptane 2,3-Dimethylheptane 3,4-Dimethylheptane (e,/~) 3,3-Diethylpentane Isopropylbenzene n-Nonane 4,4-Dimethyloctane n-Propylbenzene 2,6-Dimethyloctane 3,3-Dimethyloctane 3,4-Diethylhexane 2-Methyl-3-ethylheptane 1,3,5-Trimethylbenzene 1,2,4-Trimethylbenzene tert-Butylcyclohexane
1,2,3-Trimethylbenzene n-Decane sec- Butylcyclohexane
1,3-Diethylbenzene n-Butylbenzene n-Butylcyclohexane 1,4-Diethylbenzene 1,2-Diethylbenzene 1,3-Dimethyl-4-ethylbenzene n-Undecane
where A are the coefficients determined, similarly as the coefficients of all other polynomials in this paper, by multiple linear regression analysis of experimental data. Using Eq. (9), the retention indices of all compounds given in Table 1 were calculated for all combinations of temperatures (from 60~ to 100~ with a step I~ and C C P P values (from 300 to 350 kPa with a step 5 kPa). Those steps were chosen because the instrument used (Fractovap 4180 GC) allowed to set-up the parameters precisely in such increments. As the success of optimization procedure depends inter alia on the reproducibility of resetting the oven temperature and the C C P P value, we have studied the reproducibility of analyses repeated at 80~ and 325 kPa by measuring the retention
6
E. B e n i c k a et al.
indices of all sample hydrocarbons. We have found that the standard deviation of retention indices (~x) depended on the nature of solutes and increased from o-I = 0.02 I.u. for branched alkanes up to o-~ = 0.69 I.u. for alkylaromatics. The value of o-I is related to the width of interval in which the retention indices of solute can be tuned by the variation of working parameters. The ratio of standard deviation of indices to the width of this interval is, however, constant for all compounds [-(o-,,i/(Im,x,i - Imin, i))" 100~o ~--- 0.7%]. Subsequently, retention index differences of all neighboring peaks [Alji ] were calculated and compared with a threshold [Almia(T, p,,, ~)] determined by using Eq. (6). The values of separation number [TZi(T, Pm, ~)] were found for corresponding T, p,, and I values from the following polynomial, TZi(T, Pro, Ii) = Bo + B 1 T + B2P m + B3~ + B 4 T 2 + Bsp 2 + B6//z + Bv TPm + B8 T~ + B9Pm~,
(10)
where B are the coefficients determined by regression analysis of experimental data for n-alkanes C8-C12 where I i = 100(2z + 1)/2 and z is carbon atom number in n-alkane chain. The standard deviation of TZ measurements (O'TZ= 0.65) was estimated from six repeated measurements of n-alkanes. The maximum difference of predicted and experimentally found TZ values was within ATZ = + 1.6. It follows from Eq. (7) that the duration of analysis at all combinations of parameters T and Pm must be known for the optimization criteria calculation. The dependence of the last peak retention time on the temperature and the C C P P value was complicated because the nature of the last peak was changed with the variation of parameters T and Pro. The use of second order polynomial for its description was erroneous (predicted and experimental values difference exceeded 4.5 min which was over 5~o). Better prediction of the last peak retention time (error lower than 1.5~) was obtained from the capacity factors [k,(T, p,,)] and gas hold-up time [tM(T, p,,)] from the equation
tR,n(T, Pro) =
tM( T, Pro) + k,(T, pm)'tM(T, Pro)"
(11)
The dependence of capacity factor on T and p,, was approximated by using the following equation, ln[k,,(T, p,,)] = C o + C1/T(abs ) + C2p,~ + C3p~,
(12)
where T(abs) is absolute temperature and C are coefficients. The dependence of gas hold-up time on T and p,, was approximated by the second-order polynomial tM(T, Pro) = Do + D1 T + D2P m + D 3 T 2 q- D4p 2 + D 5 Tpm ,
(13)
where D are coefficients. The standard deviation of tM measurements was a,u = 0.054 min and maximum difference of predicted and experimentally found t M values was within _+0.035 min. The standard deviation of capacity factor of the last peak (k,) was ak, = 0.05, that is 0.57~/o rel. Maximum acceptable analysis time [tmax] was chosen 250 rain, since the column series was relatively long and the secondary part of optimization criterion in Eq. (7) should not exceed 1 unit.
Computer-Assisted Optimization of Selectivity
7
Table 2. The dependence of optimum working parameters (T, p,., tg..) and optimization criterion (Cp) on the required resolution factor Rji, req ~ T [~ Pm [kPa] tg,, [min] @....
Rji, req ~
1.0
67 310 113.50 32.54
1.5
91 350 70.25 28.72
R=I 35{
................
000--
- 00@00@@00--00--
- 0000000000000000000@@0
0
000000@@
@@@@@000000
0000
@@@@g@@@@@ r~1
00@000
12-
@@@@00
E
00@@@00
0
@00000@@00
O0
ooo
@ooeeeeoo
Pm,op~ - --
30f.
@@@ 0000000@@0000000
@@00000 i@@ 9 n @OOOO@O@@O0000
.............
O0
e @ e @ @ e @ e @ o o o o o o o o ....... :
I
i i
oo
0
oo . . . . . . . . o . . . . . . . . . . . . . . . . . .
t Topt
60
T
[~
100
Fig. 2. Schematic dependence of the number of peaks separated on a chromatogram with the resolution factor Rji > 1.0 on the oven temperature (T) and columns coupling-point pressure (p,,); o 28, 9 30, 9 32 number of peaks resolved
17 18 b! 12
i/
j~O
28 30 27 .r ~3; 33,
22
,
0
20
40
32
i
i
i
i
60
80
100
120 T i m e [m~n]
Fig. 3. Computer reconstructed separation of the hydrocarbon sample kPa. For identification of peaks see Table 1
a t Top ' =
67~ and p,, = 310
8
E. Benick/t et al. R =1.5 350
~
. . . . . . . . . . . . .
@ooo-
-ooooo@@@@@@@@@@@o
Pm, opt
............
00000000 @@@@@
@@
000
@0
@@@@@@@@@ rl
@0 tl
000
E O0
000
O0
60
o00
0
000
0
0
oooeoooooo
o
oo
300 . . . . . . . . . . . . . . . 6 o . . . . . . . o o o o o o e o e e o o o o o o . . o o
........
..............
i t
Topt
I
so
i 100
T [oc~
Fig. 4. Schematic dependence of the number of peaks separated on a chromatogram with the resolu-
tion factor Rji > 1.5 on the oven temperature (T) and CCPP value (Pro); o 26, 9 27, 9 28 peaks resolved
number of
1718 15 910 8 7 ii1
20 25 23
29 2~ 33
21 !
;36 i
0
,
10
20
J t 30
3031
i
J
i
40
50
60
32
r
70 80 Time [mini
Fig. 5. Computer reconstructed separation of the hydrocarbon sample at Topt = 91~
a n d p,, = 350
kPa. For identification of peaks see Table 1
The parameter space was searched for the maximum value of optimization criterion, which represented the optimum combination of parameters T and p,,. Since the threshold value [Almin,i(T, Pr,, Ii)] depends, according to Eq. (6), on the required resolution, different optima can be found in the cases with different values Rji,req, as it is shown in Table 2. A schematic dependence of the number of peak separated on a chromatogram for Rji,req > 1.0 on the temperature (T) and columns coupling-point pressure (p,,) is shown in Fig. 2. Fig. 3 shows a computer reconstructed chromatogram at optimum conditions (T = 67~ Pm = 310 kPa) corresponding to the resolution factor Rji, req ~ 1.0. In these conditions 32 peaks from the sample were separated in 113.5 min.
Computer-Assisted Optimization of Selectivity
9
Table 3. Retention indices [I(T, Pro)] of all sample constituents and the values of the floating threshold [Almin,i] as they were found at both above-mentioned optima Rji, req = 1.0
R j i , req =
1.5
Peak no.
Ii
Almln,i
Ii
A/rain,i
1 2 3 4 5 6 7 8 9 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
754.1 783.2 800.0 816.7 823.0 827.1 837.6 839.8 857.7 861.0 880.7 965.8 900.0 921.2 994.9 934.3 936.1 940.7 942.1 1016.9 1044.2 986.8 1079.0 1000.0 1025.5 1081.8 1088.2 1031.8 1089.5 1097.9 1118.3 1100.0
1.7 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.4 1.3 1.4 1.4 1.3 1.4 t.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3
759.5 779.5 800.0 817.1 821.3 829.1 838.2 842.2 859.5 864.1 893.7 1027.0 900.0 922.3 1058.0 933.1 938.1 945.7 944.2 1083.8 1115.1 1008.5 1156.6 1000.0 1047.i 1141.8 1149.6 1049.7 1151.0 1163.4 1185.8 1100.0
5.1 4.6 4.2 4.0 3.9 3.8 3.7 3.6 3.5 3.4 3.2 2.5 3.1 3.0 2.5 2.9 2.9 2.8 2.9 2.4 2.4 2.6 2.3 2.6 2.5 2.3 2.3 2.5 2.3 2.3 2.3 2.4
Fig. 4 shows a s c h e m a t i c d e p e n d e n c e of the n u m b e r of p e a k s s e p a r a t e d with Rji,roq > 1.5 o n T a n d P m values, a n d in Fig. 5 there is a c o m p u t e r r e c o n s t r u c t e d c h r o m a t o g r a m of the sample at o p t i m u m c o n d i t i o n s ( T = 91~ P m = 350 kPa), c o r r e s p o n d i n g to the a b o v e - m e n t i o n e d r e s o l u t i o n factor. In these c o n d i t i o n s 28 peaks from the sample were s e p a r a t e d within 70.25 min. It is o b v i o u s t h a t in the c h o s e n p a r a m e t e r space it was n o t possible to find a n y c o m b i n a t i o n of p a r a m e t e r s , where m o r e peaks c o u l d be s e p a r a t e d with such a high r e s o l u t i o n factor.
10
Computer-Assisted Optimization of Selectivity
There are retention indices of all sample constituents and corresponding values of the floating threshold listed in Table 3, as they were found at both abovementioned optima. The change of working conditions causes a dramatic change of the threshold value. It is necessary to stress that the described optimization procedure leads to such optima that are on the borderline between two parts in the parameter space where the criterion differs at least by 1 unit. It is due to the monotonously decreasing dependence of the analysis time. This fact must be considered in the cases when the reproducibility of resetting the parameters is not very good. The values of optima parameters must then be shifted in spite of prolonging the analysis time.
Acknowledgement. The authors wish to acknowledge Dr. W. R. Supina for kindly supplying us with fused silica capillary columns.
References [-1] [-2] [-3] [4] [-5] [6] [7] [-8]
[-9] [10] [11] [12]
P. J. Schoenmakers, Optimization of Chromatographic Selectivity, Elsevier, Amsterdam, 1986. R. E. Kaiser, R. L. Rieder, L. Leming, L. Blomberg, P. Kusz, HRC & CC 1985, 8, 92. P. Sandra, F. David, M. Proot, G. Dirricks, M. Verstape, M. Verzele, HRC & CC 1985, 8, 782. J. V. Hinshaw, L. S. Ettre, Chromatographia 1986, 21,561. J. V. Hinshaw, L. S. Ettre, Chromatographia 1986, 21,669. D. R. Deans, I. Scott, Anal. Chem. 1973, 45, 1137. E. Benickfi, J. Krup6ik, D. Repka, P. Kuljovsk~, R. E. Kaiser (in preparation). D. Repka, J. Krup6ik, E. Benick~t, J. Garaj, T. Maurer, W. Engewald, in: Tenth lnternat. Symposium on Capillary Chromatography, Vol. I (P. Sandra, G. Redant, eds.), Huethig, Heidelberg, 1989, p. 682. R. E. Kaiser, Fresenius' Z. Anal. Chem. 1962, 189, 1. W. G. Jennings, Gas Chromatography with Glass Capillary Columns, Academic Press, New York, 1978, p. 70. N. Johansen, Chromat. Newsl. 1979, 7, 18. L. S. Ettre, Chromatographia 1975, 8, 291.
Received July 18, 1989. Revision November 20, 1989.
