also necessitates a conservation of “mass” indicating, for a constant sample size, an isosbestic point in the data curves. 3. If the points lie in a straight line, one can determine a k reaction rate constant, k , for A = B from the spacing of the points. 4. If the points fall on a line through the origin, the proportion of A and B is constant and the sample size is changing. The distance from the origin along this line is proportional to the sample size. 5 . If one uses a constant sample size and runs an unknown mixture and successive dilutions of this mixture with one component, the composition of the unknown mixture can be determined from its distance from the boundaries along a line parallel to 9. Figure 10 is an example for a 50:50 “unknown” mixture of A and B. Three other
samples are prepared by sequential dilutions (1 :1) with B. If the sample size is not constant, the points will not be in a line, but the analysis can still be obtained by passing line 9 through each original sample point and measuring as above. ACKNOWLEDGMENT
The discussions with William Lawton and the help of Paul Taylor with some of the experimental work and with the final drawings are greatly appreciated. RECEIVED for review October 8, 1971. Accepted February 14, 1972. Supported in part by the U.S.Atomic Energy Commission under Contract AT(11-1)-1222 and in part by the National Science Foundation under Grant GP-20727.
Effect of Dead Volume on Efficiency of a Gas Chromatographic System Virgil Maynard and Eli Grushkal Department of Chemistry, State University of New York at Buffalo, Buffalo, N. Y. 14214 A systematic experimental study of the dead volume contribution of connecting tubes to the efficiency of a gas chromatographic system has been done. A GC system was built which had a minimum of dead volume. Various connecting tubes were installed at the injector and detector ends of 193.5 cm X 1/Jnmand I/&. 0.d. columns. The effects of diameter, total volume, and length of connecting tubes were determined for both columns. Our results, while in general agreement with the theoretical results of others, indicate that in gas chromatography, pre-column dead volume can be a much more important contribution to the HETP than post-column dead volume. Also, lightly retained solutes are more sensitive to dead volume present in the system than are heavily retained solutes. In addition, the effect of the connecting tubings depends on the plate number generated in them. A GREAT DEAL of discussion in the literature of the past decade concerns the effect of dead volume, or extra-column contribution as it is sometimes called, on a chromatographic system. By dead volume we mean the empty spaces in the injector and connecting tubing before the column and the connecting tubing and detector after the column. In these sections, band broadening occurs without realizing any separation of components. To date the majority of the work on this subject concentrated on the theoretical prediction of the effect of dead volume on the efficiency and the resolution of the chromatographic system. Relatively few papers can be found which deal experimentally with extra-column effects. This experimental work was by no means systematic and is comprised of investigations of G C systems under a narrow range of laboratory conditions. In general, the problem of extra-column contributions can be divided into two parts: pre-column effects and postcolumn effects. Overall discussions on the theoretical as-
pects of these effects have been given by Giddings ( I ) , Guiochon (2), and, more recently, by Sternberg (3). The last mentioned work is, to date, one of the most comprehensive treatments of extra-column effects. Some of the equations derived by these three authors, which will be used later in our discussion section, are in fact equivalent. Schmauch (4) and Johnson and Stross (5) considered the effect of the thermal conductivity detector volume on the efficiency and resolution of a gas chromatographic system. Kieselbach (6) described the effect of the detector-amplifier time constant on the efficiency of nonretained solutes. Vandenheuvel (7) discussed the effect as well as the possible correction of post-column volume effects in the case of ionization detectors. McWilliam and Bolton (8,9) analyzed in detail the effect of the detection and recording systems time constants on the resolution of chromatographic peaks. Cram and coworkers (IO)described the measurement of the detector and electrometer time constants. The problems associated with injections, connecting tubing, and mixing chambers have been discussed by several workers. Kieselbach (6) described a method of obtaining a residual mixing volume which was recently used by Cram (IO). Krejci et al. (11) dealt with the problem of anomalous sorption in the injection port, Guiochon (12) investigated the effect (1) J. C. Giddings, J . Gas Chromatogr., 1, 12 (1963). (2) G. Guiochon, ibid., 2, 139 (1965). (3) J. C. Sternberg, Aduan. Chromatogr., 2 , 205 (1966). (4) L. J. Schmauch, ANAL.CHEM.,31,225 (1959). (5) H. W. Johnson and F. H. Stross, ihid., p 357. (6) R. Kieselbach, ibid., 35, 1342 (1963). (7) F. H. Vandenheuvel, ibid.,p 1193. (8) I. G. McWilliam and H. C. Bolton, ibid., 41, 1755 (1969). (9j Zbid., p 1762. (10) T. H. Glenn and S. P. Cram, J. Chromatogr. Sci., 8,46 (1970). (111 M. Kreici. K. Hana. and M. Roudna, J Chromatogr., 41, 145 (1969): (12) G. Guiochon, ANAL.CHEM.,35, 399 (1963). ’
1
To whom all correspondence should be directed.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
1427
m
I 1 1/16"
1/4"
1/8"
Figure 1. Schematic of 1/4-in. 0.d. dead volume at either the injector end (carrier flowing from left to right) or detector end (carrier flowing from right to left) of '14 and l/&. columns of injection time on the efficiencyof the gas chromatographic system. All these investigations were done, as mentioned previously, under a narrow range of experimental conditions. No systematic approach to the effects of dead volume can be found. In recent years, pre-column reaction chambers (i.e. pyrolyzers) and post-column instrumentation (i.e. mass spectrometers) have gained in popularity. These ancillary instruments require connecting tubes either to or from the chromatographic column. It is thus of great practical importance to investigate in detail the effect of these connecting tubes on the efficiency of a chromatographic system. More specifically, one needs to know under what experimental conditions will the chromatographic efficiency be adversely disturbed by the connecting tubing. As we shall shortly demonstrate, a seemingly minor change in the connecting tubing can destroy an otherwise perfectly acceptable system. Although our work was done with a gas chromatographic system, we would like, later on, to compare some of our results with those obtained in liquid chromatographic systems. It is generally recognized that, because of slow mass transport, dead volume effects are more severe in liquid systems. Unlike in gas chromatography, these effects were investigated in much greater detail in liquid chromatography (13-20). EXPERIMENTAL
Apparatus. A home made gas chromatographic system was designed and built to have a minimum of dead volume. The associated electronic equipment was also selected so as to minimize instrumental contributions to band broadening. A Hotpack drying oven was converted for use as the GC oven. A fan and several baffles were installed to eliminate temperature gradients. The heating system consisted of two 750-watt electric heaters with simple on-off switches, one 750-watt heater under variac control, and one 750-watt heater under direct control of a Fisher Proportional Temperature Control. Temperatures at any point in the oven could be held to *0.02 degree. Temperature gradients were held (13) I. Halasz, A. Kroneisen, H. 0. Gerlach, and P. Walkling, 2.Anal. Chem., 234, 81 (1968). (14) I. Halasz, H. 0. Gerlach, A. Kroneisen, and P. Walkling, ibid., P 97. (15) R. J. E. Esser, ibid., 236, 59 (1968). (16) J. F. K. Huber, J. Chromatogr. Sci., 7, 172 (1969). (17) A. M. van Urk-Schoen and J. F. K. Huber, Anal. Chim.Acta., 52. 519 (1970). (18) G. Deininger and I. Halasz, J. Chromatogr. Sci., 9,83 (1971). (19) A. Ouano and J. A. Biesenberger, ibid., p 193. (20) R. P. W. Scott and P. Kucera, ibid., p 641. ~I
1428
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
to within = t O . l to 0.25 degree. Temperatures were measured at four different points in the oven close to:the column. Temperatures were measured with copper-constantan thermocouples in conjunction with a Leeds & Northrup Model 8686 Millivolt Potentiometer. In general, for oven temperatures under 100 "C, the only heater used was the one controlled by the Fisher Controller. The injection system consisted of a Seiscor Gas Sampling Valve Model VIII, which was actuated by a solenoid valve. Samples were injected by allowing the sample carrier gas (helium) to bubble through a liquid sample chamber, become saturated with the vapors of the liquid sample, and then pass through the sampling valve. The sample chamber and the valve were thermostated inside the oven to ensure repeatability of injection volume. The detector was a Beckman GC-4 FID. The potential across the plates was held at 300 volts by a battery. The signal from the detector was amplified by a Keithley Model 417 K chromatograph electrometer. The output from the electrometer was displayed on an Esterline-Angus Model S-6014 Speedservo 5-inch strip chart recorder. Reagents. Commercially available helium was used as sample carrier and as the carrier gas. The carrier gas flow was regulated with a Veriflow regulator. The sample carrier flow was regulated by a Nupro needle valve. The samples used in all the experiments were ultra-high purity methane purchased from Matheson Gas Products and spectranalyzed n-heptane from Fisher Scientific. Procedure. Our experimental setup is illustrated in Figure 1. The columns were packed with 10 Apiezon L on 80-100 mesh AW DMCS Chromosorb W. Two columns were used. One was 193.5 cm X 0.490-cm i.d. ( I / h . 0.d.) and the other was 193.5 cm X 0.177-cm i.d. (I/*-in. 0.d.) copper tubing. Short pieces of stainless steel connecting tubing of 0.0812-cm i.d. with a total volume of 30 p1 were used in all cases to connect the columns to the injector and detector. Dead volumes of 4.9, 9.9, and 19.8 cm X 0.490-cm i.d. and 10 cm and 76 cm x 0.177-cm i.d. connecting tubes were installed one at a time in both the injector and detector ends of the column. With some exceptions, to be detailed later, the effects of all these dead volumes were evaluated for both columns. The raw data were obtained as follows: The column and appropriate dead volume were installed in the oven and the 0.02 "C. The recorder temperature was adjusted to 50 chart speed was adjusted such that peak width at half-height was always greater than 1 cm but usually less than 2 cm. The pressure at the entrance to the injection valve was adjusted within a range of 6 to 100 psig and allowed to equilibrate. This resulted in a carrier gas velocity between 2 and 30 cmjsec. Five runs were made at each pressure setting. RESULTS AND DISCUSSION
Theoretical Background. As we have stated previously, there are several theoretical approaches to the dead volume problem. For example, Sternberg (3) has derived four equations which describe dead volume contributions to band broadening at a change in diameter. The first of these describes the contribution of connecting tubing by using the Golay equation and by utilizing the fact that the partition coefficient is zero : 2Dc
H,=-+Uc
rc2Uc 2406
(1)
where Do is the diffusion coefficient of the solute in the gas phase, Uc is the carrier gas velocity within the connecting tube, rc is the radius of the connecting tube, and H , is plate height in that tube, The variance in length units is: 6c2
LcHc
(2)
where L, is the length of the connecting tube. Sternberg’s second equation describes the time based variance of the dead volume acting as a mixing chamber. rm2
=
y;(
(3)
where Vc is the volume of the mixing chamber and F is the flow rate. His third equation describes events within a diffusion chamber where a solute diffuses into a stagnant pocket and then back into the flowing stream. Here the time based variance is given by :
where d is the depth of the pocket. Sternberg’s fourth equation describes a non-additive time based variance, which depends on the cross sectional areas of the two connecting tubes, and which he calls a “new” effect:
where A is the tubing cross sectional area. Giddings, in his discussion of dead volume effects (1) described several phenomena. His equation which takes into account the contribution of stagnant volumes is essentially the one given by Sternberg (3) for diffusion chambers (our Equation 4). Giddings’ (I) treatment for connecting tubing, however, is somewhat different than that of Sternberg (3). Giddings shows that the contributions to H d u e to the connecting tubing is :
H
t ml
1
U (cm/sec)
Figure 2. General diagram of a dead volume contribution to plate height Upper curve is with dead volume present. Lower curve is with no dead volume in system. H(ND V )is plate height with no dead volume present, H , is the dead volume contribution to plate height
I
I
I t u r b u l e n t f l o w region
laminar f l o w r e g i o n
H c = -L( - )V , Nc V L is the column length, N , is the number of plates generated in the connecting tubing, Vcis the volume of this tubing, and Vis the retention volume of the solute in the actual chromatographic column. Guiochon’s equation for a plug injector ( 2 ) can be reduced to Giddings’ connecting tube expression (our Equation 6). Equation 6 is attractive because it contains all the important variables, namely the volume of the dead volume, its efficiency, and the dependence of the dead volume effects on the partition coefficients of the solutes (via V ) . Consequently, our experimental results will be analyzed and explained according to Equation 6. In general, we shall compare the van Deemter plots of systems with and without connecting tubing. The difference in the HETP between these two systems, as shown in Figure 2 , is due to the dead volume. The magnitude of this difference will be compared with that predicted by Equation 6. In order to solve Equation 6, we must have a value for N , which may be calculated as shown below. Within the connecting tube, two separate regions of flow can be distinguished whenever there is a sharp diameter expansion, as occurs in the injection process. Immediately after such an expansion, the fluid flow which was laminar becomes extremely turbulent (21). This region of turbulent flow extends for approximately eight inside diameters along the larger tube. This turbulent region may be treated in the following way which is illustrated in Figure 3 . We assume that the connecting tube is an open-tubular column in which the flow eddies of the turbulent region act as a stationary (21) Walther Kaufman, “Fluid Mechanics,” McGraw-Hill Book Co., New York, N.Y., 1963, p 111.
Figure 3. Idealized flow in dead volume after a sudden expansion. The diagram shows a region of turbulent flow 16 re (or 8 inside diameters) in length followed by a region of laminar flow
phase-i.e., the solute “partitions” between the fast flowing inner region and the relatively stationary outer region. The model is somewhat crude but the problem of mass transfer in turbulent flow is one which has vexed fluid mechanicians for many years (21-25). By using this assumption, the plate height may be calculated from the Golay equation. All of the terms in this equation may be easily evaluated except R, the relative velocity of the zone. R is difficult to evaluate, again because of the complexities of the mass transfer in the turbulent region. For this reason, we have arbitrarily assigned to R the reasonWhen this is done the Golay equation is able value of reduced to: (7) H C lis the plate height in the turbulent region. In reality, of course, the mass transfer in the turbulent region is faster than indicated by Equation 7 and DG should be replaced by a different dispersion coefficient. In this simplified model, (22) M. C . Chaturvedi and J. Hyd, Dic. Proc. A.S.C.E., 89, 3515 (1963). (23) T. Wood, Chem. Eng. Sci., 23,783 (1968). (24) F. W. Schmidt and K. Wimmer, AZChE J., 17, 1248 (1971). (25) S. E. Kaye and S. L. Rosen, ibid., p 1269. ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
1429
80
-
Table I. Methane: '14 in. Dead Volumes; Injector End 193.5 cm X 1/4-in.Column; U = 20 cm/sec
70
-
60
-
50
-
H (cm) Deadvolume Obad Calcd Ncl NCt H, None 0.0681 ... .. .. ... 5 cm 0.1349 0.1089 5 4 0.0408 10 cm 0.1329 0.1155 29 3 0.0474 20 cm 0.1434 0.1436 77 3 0.075: Values for U,used to calculate Ncl and Net: 5 cm-8.43 cm/sec; 10 cm-10.40 cm/sec; 20 cm-10.36 cmisec. DG (methane at 323 OK, 5.35 atm) = 0.146 cm2/sec.
Pressure (PSI GI 40
-
30 -
20
-
10-
I 10
01 0
I
I
20
30
I 40
,t
1 50
I
I
I
60
70
80
1
(sed
Figure 4. Plot of inlet pressure us. retention time for 193.5 cm x '/4-in. column Experimental points not shown. Curves represent, reading from left to right: no dead volume, 5 cm, 10 cm, and 20 cm x in. dead volumes at the injectorend of the column
-
05
I
I
I
1
I
I
f
%
1
IO
I
I
I
I I
I
15
I
I
I
20
I
8
1
(2 51
U (cm/sec)
Figure 5. Plot of HETP us. corrected carrier gas velocity for 193.5 cm X '/4-in. column
where t R ( D V ) is the retention time of the solute with the dead volume in the system and f R ( N D V )is the retention time of a solute with no dead volume in the system. This correction takes into account the difference in actual cross sections between the '14 in. 0.d. empty tubing and the in. packed column. It is interesting to note that at a given inlet pressure, doubling the dead volume roughly doubles the separation of the lines in Figure 4. This is most noticeable at high inlet pressures. The retention time of a solute within the column, at a given inlet pressure, should be independent of its retention within a connecting tube since the pressure drop across a connecting tube is negligible. Figure 4 allows us to correct the retention time of methane and to obtain a measure of the carrier gas velocity, U,, within the, connecting tube. In preparing the van Deemter plots, which will be introduced shortly, the velocities used were obtained from the actual residence time of the solute in the column only. Following the turbulent flow region is one of laminar flow. The Golay equation yields an expression for the plate height here which is identical to Equation 1. H,L will designate the plate height in the laminar flow region of the connecting tube. In reality the transition from the turbulent region to the laminar one is gradual-Le., the turbulent "stationary phase" thickness decreases continuously. However, for the sake of mathematical, as well as conceptual simplicity, we assume that the turbulent region ends abruptly. The number of plates produced in the connecting tube is then the sum of the plates produced in the two flow regions:
Solute: methane, with no dead volume in system (O), 5 cm X 1/4-in. dead volume (O), 10 cm X 1/4-in.dead volume (A), and 20 cm X I/&. dead volume (0)All . dead volumes are at injector end
however, DG may be calculated from tables compiled by Giddings and coworkers (26). r, and d, as shown in Figure 3, are the radius of the connecting tube and the thickness of the stationary turbulent phase, respectively. U,, the mobile phase velocity in the connecting tube, which could be calculated from the retention time in the column taking the compressibility factor into account, may be more easily calculated from a plot of pressure at the head of the column us. the retention time. Such a plot is shown in Figure 4 for the 5 , 10, and 20 cm X 1 / 4 in. 0.d. connecting tubes. In these cases for a given pressure, there are different values of the retention time. The retention time within the connecting tube, tR'(DV), is then: (26) E. N. Fuller, P. D. Schettler, and J. C . Giddings, Znd. Eng. Chem., 58 ( 5 ) , 19 (1966). 1430
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
(9)
Here L,, and L C 1are the lengths of the turbulent and laminar flow regions, respectively, The result of Equation 9 may then be substituted into Equation 6 and H , may be calculated. Plate heights were determined directly from the chromatograms by measuring the retention time, tR, and the width at one-half the peak height, W I / ~ Measurements . were made with a precision, engine divided, 30-cm rule. The plate number, N , was determined from the well-known equation : N = 5.54
(&)'
Plate height H or HETP was then determined from N : H = LjN
(11)
A Wang 720 programmable calculator was used to fit the van Deemter equation to the data by the method of least squares.
t
IO 0
Figure 6. Plot of HETP us. carrier gas velocity for 193.5 cm X 1/4-in. column Solute: methane, with no dead volume in system (0),5 cm X 1/4-in dead volume (O), and 10 cm = li4-in. dead volume (A). All dead volumes are at detector end Experimental Results. The first case we studied was with in. 0.d.) dead volumes the 4.9,9.9, and 19.8 cm X 0.490 cm in. column with at the injector end of the 193.5 cm X methane as solute. In this case the dead volume and the column are equal in diameter, although the void cross sectional area of the column is smaller due to the packing. The results are plotted in Figure 5. Qualitatively, there are several important points to observe about this graph. First, there is no apparent dead volume effect at low velocities while there is a large contribution at high velocities. Second, the minima are shifted to lower velocities and higher values of the H E T P when a dead volume is in the system. Finally, the curves are all least square fitted to the data. The best fit is obtained only when there is no dead volume present. To check our mathematical model, we have computed the contribution of these three connecting tubings to H , using Equations 1 and 6-9. Arbitrarily we took the case when the carrier velocity in the column was 20 cm/sec and the corresponding least squared plate height values. At this column gas velocity, we have computed the actual carrier velocity in the connecting tubings. These are shown in Table I. The table also shows the contribution of the two regions (turbulent and laminar) in the empty tubing, as well as the experimental and calculated H values. The agreement between theory and experiment, although not perfect, is rather good, considering the approximations involved in estimating N,. It is interesting to note the closeness of the H values for the cases of 5-cm and IO-cm dead volumes. In fact, the two values are within our experimental error. As the length of the dead volume increases, the laminar contribution of N , dominates. In the case of the 5-cm connecting tubing N C L= Nee. In fact if we assume only laminar flow, the total N , is about 10, which is roughly equal to N,z Nee. Consequently, we most likely overestimate Nee, When the same dead volumes are placed at the detector end of the same column, there is no observable dead volume effect as shown in Figure 6. There are several reasons for this. Qualitatively, it can be explained since there is no diameter expansion at the detector end of the column as both the column and the connecting tubing have the same diameter. In fact, at the detector entrance, there is a diameter contraction (from '/4in. 0.d. to in. 0.d.). In this case stagnant pockets may exist. It can be shown, however, that the
+
I
I
I
'
l
5
'
'
'
,
I
t
I
'
l
l
IO 15 U (cm/sec)
,
'
I
20
I
(
'
L
Figure 7. Plot of HETP us. carrier gas velocity for 193.5 cm X 1/4-in.column Solute: heptane, with no dead volume in system (O), 5 cm X 1/&. dead volume (E), and 10 cm X 1/4-in.dead volume (A). All dead volumes are at injector end
.25 -
20-
H . (crn).
.I 5-
m
.IO 0
~ " " " 5" " " " " I" O ' " "
u (crn/sec)
15
20
2
Figure 8. Same as Figure 7 except all dead volumes are at detector end
contribution of these "diffusion chambers" to H is minimal. More importantly, since velocities are much faster at the detector end, the sample spends far less time in the connecting tube than at the injector end. Giddings (27) has already solved the problem more quantitatively. The local plate height is given as: H, = L ( ; ) '
(12)
where 7 2 is the time variance of the peak over the time interval t , and 7 is small whenever tis small which is true at the column exit. Since the retention time in the connecting tube at the exit is small, there is no need to correct the velocity here. Using the same column and dead volumes as before, we then repeated our work using heptane, a strongly retained solute. The results are shown in Figures 7 (dead volume at injector end) and 8 (dead volume at detector end). Here we see no, or very small, dead volume effects. In fact, there appears to be slightly lower values of HETP with a dead (27) J. C . Giddings, ANAL.CHEM., 35, 353 (1963). ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
1431
Table 11. Methane: l/S-in. Dead Volume; Injector End 193.5 cm X 1/4-in.Column; U = 20 cm/sec H (cm) Deadvolume Obsd Calcd Ncl Ncl HC None 0.0681 ... .. .. ... 10 cm 0.0613 0.0686 47 1 0.0005 Value for U,used to calculate Ncr and N e t is 80.06 cm/sec. Table 111. Methane: Equal Volume Dead Volumes at Injector End of 193.5 cm X l/4-in. Column. U = 20 cm/sec
U (cm/Sec)
Figure 9. Plot of HETP us. carrier gas velocity for 193.5 cm X l/4-in. column Solute: methane, with no dead volume in system (01, 10 cm X '/&. dead volume at injector end (O), and at detector end (A)
i I\
t 20
1
I\
.IO
.o50
U (crn/sec)
Figure 10. Plot of HETP us. carrier gas velocity for 193.5 cm x 1/4-in.column
Solute: methane, with no dead volume in system (0),10 cm X l/An. dead volume (O),and 76 cm X '/& dead volume (A). All dead volumes are at the injectorend
volume present, but this is within our experimental error. The reason we see no decrease in column efficiency is that V, the retention volume for heptane, is approximately 13 times greater than for methane under our experimental conditions, with the result that in Equation 6, V >> V, and Hc- 0. Stated differently, we can say that when u 2 generated in the column is large as compared with U S generated in the connecting tubings, the effect of the latter is small. The next case we treated occurs whenever a connecting tube is of a smaller diameter tubing than the column itself. We used a 10 cm X 0.177-cm i.d. (l/s-in. 0.d.) connecting tube and we obtained the van Deemter plots shown in Figure 9. Here again we see only a small dead volume effect, even though there is an expansion at the injector end. This may be explained because the volume of the connecting tube is quite small compared to the retention volume of the methane. The calculations are shown in Table 11. As with heptane, experimentally, H seems to be slightly lower in value with the dead volume in the system. When the 10 cm X l/s-in. dead 1432
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
H (cm) Deadvolume Obsd Calcd N,I NCt HC None 0.0681 ... .. .. ... 10cm X 1/4-in. 0.1329 0.1154 29 3 0.0474 76cm X lis-in. 0.0562 0.0718 410 1 0.0037 Values for U,used to calculate N,I and Net: 10 cm x 1/4-in.10.40 cm/sec; 76 cm X l/&.-80.06 cmjsec. Table IV. Methane: Equal Length Dead Injector End, 193.5 cm X li8-in. Column. H Icm) Deadvolume Obsd Calcd N,i None 0.0440 ... ... 10cm X 1/4-in. 0.7506 2.538 26 10cm X '/s-in. 0.0488 0.0527 168 Values for U,used to calculate N,r and N,t: 1.48 cm/sec; 10 cm X 1/s-in.-11.44 cmisec. 323 OK and 5.03 atm) = 0.155 cm2/sec.
Volumes at the U = 20 cm/sec N,t ..
HC .
.
I
10 2.494 9 0.0087 10 cm X '/hD G (methane at
volume is at the column end, no noticeable effects can be found (Figure 9). Next we wanted to find out if the dead volume effects are due to the volume of the connecting tube or to its geometry. Here, we used 76 cm X 0.177-cm i.d. (l/g-in. 0.d.) and a 10 cm X 0.490-cm i.d. (1/4-in. 0.d.) connecting tubes, both of which have equal volumes of 1.87 cma. The results for methane as solute are shown in Figure 10. It is obvious that the 10 cm x 0.490 cm dead volume has a much larger effect on the column efficiency, In fact, the 76 cm X 0.177 cm dead volume appears to slightly decrease the plate height below that of the no dead volume standard. The reason for the greater dead volume contribution by the li4-in. tubing is apparent from the calculated values of N,L shown in Table 111. Here, although ( V c / V ) zis the same for both dead volumes, the 76-cm connecting tube produces many more plates than the 10-cm connecting tube. We also studied the effect of having a connecting tube of a larger inside diameter than the column itself. Here we used a 193.5 cm X 1/8-in.column and lis-in. and I/&. dead volume. Figure 11 shows the results of this study with methane as solute and a 10 cm x 0.177 cm (l/&n. 0.d.) connecting tube and a 10 cm X 0.490 cm (1/4-in. 0.d.) connecting tube at the injector end. Here we see a tremendous dead volume contribution due to the li4-in. dead volume but no measurable effect for the 1/8-in. dead volume. The calculated results are shown in Table IV. With the 1/4-in. dead volume, our calculated value for H is 3 times larger than the experimental value, perhaps due to the approximation made in calculating N,. The stagnant pocket at the connecting tube-column junction can be shown to have almost no effect on the plate height. It is interesting to compare the effect of the 10 cm X '/s-in. connecting tube in front of the l/s-in. column with the effect
I.
I
I
2 51
I
2.0-
15-
H. (cm).
1.0-
A
I
Figure 11. Plot of HETP us. carrier gas velocity for 193.5 cm X I/&. column
Figure 12. Plot of HETP us. carrier gas velocity for 193.5 cm X l/a-in. column
Solute: methane, with no dead volume in system (O), 10 cm X l/&. dead volume (O), and 10 cm X l/&. dead volume (A). All dead volumes are at the injector end
Solute: methane, with no dead volume in system x 1i4-in. dead volume at injector end (a), and at the detector end (A) (O), 10 cm
Table V. Heptane: 10 cm X 1/4-in.Dead Volume at Both Ends of the 193.5 cm X Column. U = 15 cm/sec H (cm) Dead volume Obsd Calcd NEz N,, HC None 0.1646 .. .. ... At injector 0.1790 0.'1744 39 9 0.0098 At detector 0.1799 0.1752 34 10 0.0106 Values for U,used to calculate Ncl and Net: for dead volume at injector-1.11 cm/sec; for dead volume at detector431 cmjsec. D G(Heptane at 323 O K , 5.03 atm) = 0.0590 cm2/sec,DG (1 atm) = 0.296 crnzisec.
of the 10 cm X 1/4-in,tubing in front of the 1/4-in.column. Because of the smaller diameter of the '/a-in. empty tubing, the plate number generated in it is much larger (Table IV) than in the 1/4-in.empty tubing (Table I). This results in a much smaller contribution from the '/*-in. connecting tube. When the connecting tube diameter is larger than the column diameter, we can see dead volume effects even when the dead volume is at the detector end as shown in Figure 12. Here the dead volume effects are more noticeable at the lower velocities. This can be explained by the fact that diameter expansions at the column exit destroy the efficiency. Also it is only at higher velocities that t , and hence 7,becomes small (cf. Equation 12). In any event, the effect of the connecting tubes is much more severe at the column inlet. When we use a retained solute, the HETP values are shifted to higher values when the dead volume diameter is larger than the column diameter at both the detector and the injector end. The effect though, both experimental (Figure 13) and calculated (Table V), is smaller due to the low value of V,/V. It is of interest to compare our results with similar work in liquid chromatography. Ouano and Biesenberger (19) investigated the effect of connecting tubes in gel permeation.
IO ~ 0
"
5
'
~
IO
~
~
15 U (cdsec)
~
~ 20
~
Figure 13. Same as Figure 12 except the solute is heptane
They found that the extra-column effects are much more severe when the connecting tubes are before the column. This is in agreement with our results. Unlike us, however, they did not investigate the effect of the dead volume on retained solutes. Instead they demonstrated that as the molecular weight of the unretained solute increases, the dispersion due to the connecting tube is greater. This effect can be attributed to viscous flow effects in the liquid system, and it is not expected to be found in gas chromatography. Recently Scott and Kucera (20) also investigated the problem of connecting tubes in liquid chromatography. Their work centered on post-column connecting tubes only, and of such dimensions that they increase the column variance by no more then 5x. Some of their conclusions concur with ours-Le., the importance of column void volume as compared with the volume of the connecting tubing. In fact some of their equations can be reduced to those derived ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
1433
~
~
by Giddings ( I ) . In gas chromatography, however, we see no additional peak dispersion when the post-column connecting tubing is equal to or less than the diameter of the column. In addition, as was pointed out by Deininger and Halasz ( I @ , the extra column effect diminished as the retention volume (or the partition coefficient) increased, This is expected to hold true both in liquid and gas chromatographic systems. CONCLUSIONS
Systematic study of connecting tubes in gas chromatography indicates some important practical conclusions. The effect of the connecting tubes seems, in general, to be worse when in front of the column. However, as the diameter of the connecting tube decreases, or as the solute becomes more retained (higher partition coefficient), the contribution of the dead volume diminishes. When the diameter of the dead volume is larger than the column, the efficiency of the system will be adversely affected whether the connecting tubes are in the front or the back end of the column. In this connection our results with connecting tubings having equal volume but different diameter should be noted. It is important to realize the effect of the number of plates generated in the connecting tubes. The velocity dependence of the dead volume effects should also be noted. The practical implications of this study are important. When attaching the chromatographic system to post-column instrumentation, the requirements on the connecting tubes
are not too stringent. As long as that tube diameter is at most equal to the chromatographic column’s, the efficiency of the system will be maintained. This supports the contention of many workers who maintain that their system showed no loss of efficiency when connected to, say, a mass spectrometer. On the other hand, the connection between pre-column reaction chamber and the column can present a much greater hazard. This is especially true when the connecting tubes are of the same diameter as the column and when the net retention time of the solutes is small, as often occurs with pyrolyzers. Similarly, large volume injection valves can be detrimental to the efficiency. Much more careful attention must be given to pre-column contribution to the plate height. In general, it can be said that the connecting tubes on the front end of the column should be as small as possible (while keeping the pressure drop in mind) if the researcher is to obtain an efficient gas chromatographic system. ACKNOWLEDGMENT
We would like to thank Stanley Bruckenstein for the use of his Wang 720 calculator which was purchased with an AFOSR grant. We would also like to thank Jane Maynard who did many of the tedious manual measurements of chromatograms. RECEIVED for review January 17, 1972. Accepted March 13, 1972. The support of the Research Foundation of the State University of New York is also gratefully acknowledged.
Quantitative Determination of 5-Hydroxyindole-%AceticAcid in Cerebrospinal Fluid by Gas Chromatography-MassSpectrometry Leif Bertilsson, Arthur J . Atkinson, Jr., James R. Althaus, Ase Harfast, Jan-Erik Lindgren, and Bo Holmstedt Department of Toxicology, Swedish Medical Research Council, and Department of Pharmacology, Dioision of Clinical Pharmacology, Karolinska Institutet, S-104 01 Stockholm 60, Sweden
A highly sensitive and specific method for the quantitative determination of 5-hydroxyindole-3-acetic acid (5-HIAA) in human cerebrospinal fluid (CSF) has been developed. The 5-HIAA diheptafluorobutyryl methyl ester derivative has been analyzed by the combination of gas chromatography and mass spectrometry. By the technique called mass fragmentography, the two major ions (m/e 538 and 597) of the mass spectrum of the 5-HIAA derivative were recorded after elution from the chromatographic column. Dideuterium-labelled 5-HIAA has been synthesized and used as an excellent internal standard for the quantitation of 5-HIAA in CSF. The mass fragmentographic analysis takes less than 2 minutes and allows an accurate determination of 5HlAA in the range of 2-50 ng/ml of CSF, when 2 ml of CSF is used for the analysis. The standard deviation of the method is less than 7% in the 8-20 ng/ml range and 1-276 at higher concentrations of 5-HIAA. THESTRIKING ABILITY of certain chemical compounds to alter mood has provoked interest in the biochemistry of mental disease. A derangement of tryptophan metabolism in affective disorders was first suggested by the discovery that reserpine, a drug that causes profound depression in some patients, markedly lowers the concentration of 5-hydroxytryptamine in 1434
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
the brain (I). Because 5-hydroxytryptamine is converted by monoamine oxidase in brain tissue to 5-hydroxyindole-3acetic acid (5-HIAA), a number of clinical studies have been conducted in order to determine whether the concentration of this acid in cerebrospinal fluid (CSF) is lower in depressed patients than in patients not suffering from an affective disorder. In some investigations, significantly less 5-HIAA was found in the CSF of depressed patients (2-4) but in others the results were equivocal (5-7). In each of these studies, fluorometric (1) A. Pletscher, P. A. Shore, and B. B. Brodie, J . Pharmacol. Exp. Ther., 116, 84 (1956). (2) G. W. Ashcroft and D. F. Sharman, Nature, 186, 1050 (1960). (3) S. J. Dencker, U. Malm, B-E. Roos, and B. Werdinius, J. Neurochem., 13, 1545 (1966). (4) H. M. van Praag and J. Korf, Psychopharmacologia, 19, 148
(1971).
(5) K.Fotherby, G. W. Ashcroft, J. W. Affleck,and A. D. Forrest, J . Neurol. Neurosurg. Psychiat., 26,71 (1963). (6) M. B. Bowers, Jr., G. R. Heninger, and F. Gerbode, Int. J. Neuropharmacol., 8, 255 (1969). (7) B-E. Roos and R. Sjostrom, Pharmacol. Clitz., 1, 153 (1969).
