Pressure Changes in Gas Chromatography P. C. HAARHOFF and H. J. VAN DER LlNDE Atomic Energy Board, Private Bag 256, Pretoria, South Africa
b Changes in the column pressure during the elution of solutes are theoretically predicted by considering viscosity and flow rate variations across solute bands. Experimental pressure variations, determined by means of a diaphragm-type pressure gauge, are then discussed. Once the initial surge due to sample introduction has died away, pressure changes are satisfactorily explained by the theory. Pressure pulses accompanying solute bands were not observed, and an alternative explanation is put forward for the results obtained by Scott.
C
the column pressure during the introduction and elution of solutes in gas chromatography and their influence on chromatographic data have been discussed by several authors (1,4, 10,12,14-16). Weinstein (15,16) has thoroughly investigated the pressure surges which are observed for a relatively short period after sample introduction. Pressure pulses observed by Scott (12) are more difficult to explain. According to this author, a pressure pulse accompanies each solute band during its passage through the column, and the additional pressure is equal to the partial pressure of the solute-Le., the partial pressure of the carrier a t a given point remains constant. Pressure pulses associated with solute bands have also been observed by Amy et al. (1) and Locke and Brandt ( I O ) , but these apparently resulted from the way in which the apparatus was constructed (1, 10). A third pressure effect (4, 14) arises from resistance to gas flow through the column, the pressure gradient along the column being affected by local changes in the viscosity (4, 14) and flow velocity (2-4, 8, 9, 11) of the gaseous mixture. The above pressure changes will clearly increase as the sample size is increased, and may have an effect on the widths and shapes of elution curves, as has been discussed by Scott (12) for pressure pulses accompanying solute bands. This had to be taken into account in an investigation of the d e pendence of elution curves on sample size (6). A purely theoretical treatment of the effect of pressure changes would, however, have been speculative, since Scott could only explain his results by introducing an assumption which is HANQES IN
1742
ANALYTICAL CHEMISTRY
controversial (12). The present study was therefore undertaken in an attempt to learn more about pressure variations in gas chromatography by obtaining additional experimental data and by comparing this with quantitative predictions from theory. THEORY
Pressure disturbances are propagated through columns in a complex manner, and it would therefore be very difficult to carry out an accurate treatment of the pressure surges which are initiated by sample introduction. The importance of the latter may, however, be decreased by employing solutes which are relatively strongly retarded. For this reason, the discussion below is simplified by considering only the time interval after the initial pressure surge has died away. The influence of viscosity (4, 14) and flow rate (2-4, 8, 9, 11) variations across solute bands on the pressure a t a given point in the column may be assessed as follows. For simplicity, consider the elution of a single solute, regard the carrier gas as incompressible, and neglect any nonlinearity of the isotherm or band spreading due to nonideality. The mass balance equations for the solute and the carrier are then respectively
bX a +k)= - - (VX) at ax
(1
at
b -[v(l-X)] bz
where X is the moIe fraction of the solute in the mobile phase, v is the radial average of the linear flow velocity in the mobile phase a t a distance x from the column inlet and a time t , and k is the mass distribution coefficient-Le., the ratio of the amount of solute in the stationary phase to the amount in the mobile phase, a t equilibrium. The solution of Equations 1 and 2 is
vx
+
v(1-X) l+k
=u
U=
lfk(1-X)
(4)
Similar results have been obtained by several authors (2, 4, 8, 11). Equation 4 shows that the flow velocity of the mobile phase is greater in a solute band than in the regions devoid of solute. The flow velocity at the column outlet is consequently increased while a peak emerges, as stated by van de Craats (14); the effect is, however, not confined to the column outlet, as assumed by van de Craats (14). The pressure gradient is given by
where q ( X ) is the viscosity of the gas mixture and P is a constant. If pressure a t a certain point in the gas flow circuit is kept constant a t P,, and the resistance to gas flow of the circuit between this point and the column inlet is equal to the resistance of a length hL of the column, it follows from Equations 4 and 5 that
P
=
P,
- PqcuAL -
(1)
and
b (1 - X) =
where u is a function of t but not of x, and is the flow velocity in the regions where the solute concentration is negligible. Hence, (l+k)u
(3)
where qe is the viscosity of the carrier. (Note that X is a function of z and t . ) According to Equation 6, the pressure decreases constantly as z increases, a t a given instant. The possibility that relatively large pressure pulses may accompany the solute bands is thus not taken into account by the equation. This is a consequence of the assumption that the carrier gas is incompressible. If resistance to flow from the column outlet to the atmosphere may be neglected, pu may be eliminated from Equation 6 by evaluating the pressure a t the column outlet, Po. The pressure a t a given point before sample introduction may then be found by setting q ( X ) = qc and X = 0. If this pressure is subtracted hom P to obtain the pressure increment A P , one finds
K
U
tFjL U
Figure 1 . paratus
Schematic diagram of ap-
A.
Carrier gas cylinder Pressure reduction valve Reference fiaw rertrlctor Needle valve Differential flow controller One-way check valve Heated injection chamber H. Column 1. T-piece .I. Detector K. Bubble flow meter 1. Diaphragm-type pressure gauge M. I-liter buffer vessel N. Vent P. Pressure supply
6. C. D. E. F. G.
where P , is expressed in terms of the pressure a t the column inlet before sample introduction, Pi, the column length is L, and
If q ( X ) is greater than or equal to qC for all values of X , Equations 4 and 5 show that the pressure drop inside the solute band is greater than that outside the band. Before the band arrives a t a point 2, the pressure drop from 2 to the outlet is thus less than it was before the solute was injected. AP is thus negative. When the solute band has passed the point x, the pressure drop from the inlet to x is less than it was before injection, and AP is thus positive. The pressure a t a given point in the column should thus decrease after a solute is injected, then increase beyond the original value as the solute band passes the point, and finally decrease to the original value when the solute is eluted. It may easily be shown that the above behavior is in accord with Equations 7 and 8. When q ( X ) is less than qo for some or all values of X , AP might first increase and then decrease during elution, but opposing pressure effects result from the decrease in the viscosity and the increase in the flow velocity (Equation 5). Schematic diagrams depicting pressure changes due to viscosity effects have been given by van de Craats (14). Numerical evaluation of the above pressure variations is facilitated by approximating X by a probability function of x,via.
and considering only values of t for which the calculated maximum values of X are less than about 0.5. I n the above equation, which may readily be verified by integrating X over x, the compressibility of the mobile phase has been neglected. t is the elution time of the solute, M the number of moles of the solute, M , the number of moles of the carrier in the column when no solute is present, and N the number of theoretical plates. The above equations may be used as a basis for the discussion of experimental results, if it is kept in mind that they do not take the existence of pressure waves into account.
+5w 0
---2
0
100
200
EXPERIMENTAL
t (sec.)
Apparatus. Pressure variations during elution were observed with the aDparatus shown schematically in Figure 1. An Aerogravh Model A-90-P2 gas chromatogripli was employed, and ihe gas flow circuit of the instrument was used without any alteration. The differential flow controller was of the type described by Guild et al. (6),and thus did not have any effect on the flow when the needle valve was fully opened. Although the pressure gauge which was employed was less sophisticated than that used by Scott ( l a ) ,it yielded results of sufficient accuracy for the present purpose. It consisted of a circular, enclosed copper diaphragm, 10 cm. in diameter, to the reference side of which wire resistance strain gauges were affixed. Two gauges were used t o measure the radial strain and two to measure the circumferential strain. Movement of the diaphragm as a result of a pressure change altered the former strain component more than the latter, and pressure changes could therefore be observed by means of a Wheatstone bridge and a millivolt recorder. The dead volume of the connection between the columns was about 0.3 ml., and the total dead volume of the T-piece and the measuring side of the pressure gauge was about 5 ml. In typical experiments, about 40 ml. of mobile phase flowed through the connection between the columns while the solute concentration a t the point of pressure measurement was significant. It is, therefore, very unlikely that the dead volumes which were employed had an important effect on the results. It was found that, for optimum performance, the pressure on the reference side of the diaphragm should exceed that on the column side by about 5 cm. Hg, and this pressure difference was employed. The 1-liter vessel in Figure 1 minimized pressure surges when the reference pressure was changed, and ensured that movement of the diaphragm did not alter the reference pressure. A mercury manometer was connected to the measuring side of the pressure gauge for calibration of the latter. The response time of the gauge
Figure 2. Pressure variations at column midpoint during elution of ether samples Solid liner: Experimental Dashed liner: Theoretical Carrier gar: A. Hydrogen 6. Helium Conditions: See Table I
was very short and was not a limitation in the experimental work. Linearity of the response was furthermore sufficient for the present purpose. A sensitivity of 0.10 mv. per cm. Hg was obtained by using a 3-volt potential over the Wheatstone bridge. When the pressure was changed from PI to PZ and immediately changed back to PI, the correct pressure was registered. When the pressure was changed back to PI only after 5 minutes, however, the recorder overshot the PI mark by about 10% of the signal corresponding to (P1- P2),registering the correct pressure after about 1 minute. This did not have an important effect on the experimental results. RESULTS AND DISCUSSION
Pressure variations during the elution of solutes were observed by placing a &foot column on either side of the pressure gauge, thus effectively observing the pressure at the midpoint of a 10foot column. Pressure difference curves obtained during the elution of 10-pl. samples of ether with hydrogen and helium a t room temperature are shown in Figure 2. Details of the columns and of the variables required below are given in Table I. The needle valve was fully opened during the experiments, so that the differential flow controller did not affect the flow. It is evident from Figure 2 that pressure pulses similar to those described by Scott ( l a ) were not observed during the above runs. A small pre-peak was found when helium was used as carrier, but its height was less than 1% of the maximum partial pressure of the solute at the column midpoint. [The latter pressure was of the order of magnitude VOL. 37,
NO. 13, DECEMBER 1965
1743
~
Table 1. Experimental Conditions for Figure 2 and Parameters Required in Calculations Column: copper tubing, L = 304 cm., x = 152 cm., 1.d. = 4.7 mm.; stationary phase: 207, w./w. cyanosilicone oil (XF 1150) on Chromosorb P Regular 45-60 mesh; sample: ethyl ether; temperature: 28" C. k = 4.80 M = 0.963 X IO-' mole Po = 65.4 cm. Hg Vether = 75.3 micropoise ( 7 )
Carrier gas Hydrogen Helium 174 seconds 138 seconds
i N
Flow rate
Pi
(outlet)
M*
VC
628 134 nil./min.
847 130 ml./min.
105.4 cm. Hg 137.8 cm. Hg 1 . 8 4 x 10-3 2 . 2 7 x 10-3
mole
89.2 micropoise ( 7 )
mole
197 micropoise ( 7 )
of 15 cm. Hg for the two runs depicted in Figure 2, and pressure peaks of this height should thus have been observed if Scott's postulate (12) held for mole fractions as large as those employed above.] I n view of the absence of pressure pulses, experimental pressure changes were compared with those predicted by Equations 7-9 (dashed lines in Figure 2). Numerical integration was used to determine AP, a t various instants and at the column center, from Equations 7-9, using the data in Table I. Approximate values for the viscosities of solute-carrier mixtures were found from Wilke's equation (17'). The resistance to flow of the circuit between the pressure reduction valve and the column inlet was determined and was found to be small in comparison with that of the column when the needle valve was fully opened. AL was accordingly set equal to zero in Equation 7-Le., the pressure a t the column inlet was taken as constant and equal to that after the reduction valve. The agreement between the experimental and theoretical results in Figure 2 is good, considering the approximations that have been introduced in the above treatment, which include the assumptions that the carrier is incompressible and the elution curves are probability functions, and the determination of the viscosities of solutecarrier mixtures by means of Wilke's equation ( 1 7 ) . (As a result of the term (-1) in Equation 8, calculated values of AP are sensitively dependent on calculated viscosities.) The pressure changes which have been observed may therefore be ascribed t o viscosity and flow velocity changes across solute bands. The viscosities of hydrogenether mixtures do not differ much from that of hydrogen, but rn a result of local flow velocity increases, the local pressure gradient becomes larger as the 1744
ANALYTICAL CHEMISTRY
ether concentration increases. The discussion following Equation 8 shows that AI' should thus first be negative and then positive, in agreement with Figure 2. Since the viscosity of helium is much greater than that of ether, AP first increases and then decreases when helium is used as carrier. Figure 2 also shows that the instant a t which the band center passes through the column midpoint is not accurately predicted by Equations 7-9. This is due to the fact that the compressibility of the mobile phase, and the resulting variation in the flow velocity of the carrier along the column length, is not taken into account by these equations. In an attempt to observe regions of high pressure in solute bands ( l a ) , further experiments were carried out, in which some of the variables given in Table I were changed, others being kept constant. Sample sizes ranging from 1 11. to 20 pl. of ether were first employed, with outlet flow rates from 50 to 140 ml. per minute. I n each case the pressure us. time curve was similar to the relevant curve in Figure 2, the magnitude of the pressure change being roughly proportional to (Pi - Po) and the sample size. For the 1-11. samples, the pressure change was hardly noticeable, even though the maximum partial pressure of the solute a t the column midpoint was more than 1 cm. Hg. Pressure pulses accompanying sample bands also could not be observed when 1 ml. samples of air were injected. By adjusting the needle valve, the parameter AL in Equation 7 was made equal to about 2L. The pressure curves which were obtained were similar to those in Figure 2, and although the maximum and minimum pressures changed when AL was increased a t a given P,, the changes were in agreement with qualitative predictions based on Equation 7. Pressure pulses accompanying solute bands could furthermore not be observed, with helium as carrier, when the second &foot column was replaced with a 1-foot column or empty tube, or the first &foot column with a 1-foot column. (Pressure changes were somewhat obscured by the initial surge effect in the latter case.) Finally, the pressure gauge was replaced by an ordinary mercuryin-glass manometer, with total dead volume between the mercury and the ends of the two &foot columns less than 1 ml. The manometer was slightly heated to avoid condensation of the ether. With helium as carrier, pressure variations (observed visually) were similar to those registered by the pressure gauge, although the pre-peak was about twice as large as before. After completion of the above work, an explanation for the pressure effects observed by Scott (12) suggested itself. It appears thct Scott's pressure gauge was situated a few inches from the col-
umn outlet (IS). AP curves such as those in Figure 2 may be calculated from Equation 7 for increasing values of 5 , the distance of the pressure measurement point from the column inlet. Let API and AP2, respectively, denote the greatest pressure change observed before and after the sample passes the pressure gauge. For pressure measurement a t the column midpoint, the calculated values of AP1 and AP2 are of opposite sign but similar magnitude. (See Figure 2.) When 2 is increased, it is found that the magnitudes of API and AP2, respectively, decrease and increase, and for measurements a t a distance of a few band widths from the column outlet, peak-shaped (positive or negative) pressure variations are obtained. When 5 is increased further, the height of the calculated pressure peak diminishes, and AP = 0 a t the column outlet. The above predictions have been experimentally verified, using an apparatus described by Scott (IS). At the column midpoint, pressure curves were similar to those in Figure 2. Peakshaped pressure variations, small in comparison with the solute partial pressure, were obtained a t a distance of a few band widths from the column outlet. Their magnitude decreased when the distance to the column outlet was decreased further, and no pressure changes were observed a t the column outlet. CONCLUSION
Although the pressure drops and sample sizes employed in the experiments described above were varied over a wide range, significant pressure pulses accompanying solute bands were not observed. Peak-shaped pressure variations occurred near the column outlet, but their variation with the position of pressure measurements indicated that they were not due to high pressure regions in the solute bands. It is, therefore, concluded that pressure pulses do not accompany solute bands during elution, and that the pressure variations observed by Scott (12) have the same origin as those shown in Figure 2. The theoretical approach which has been adopted provides a satisfactory explanation of the observed pressure fluctuations, in terms of local viscosity and flow rate changes, once the initial surge has died away. Pressure variations may, therefore, be taken into account by means of this approach when the effect of sample size on elution curves and the accuracy of analyses is for example investigated. ACKNOWLEDGMENT
We thank the Reactor Engineering Division for providing the pressure gauge.
LITERATURE CITED
(1) Amy, J. W., Brand, L., Baitinger, W.,
“Progress in Industrial Gas Chromatography,” Vol. 1, H. A. Szymanski, ed., p. 147, Plenum Press, New York, 1961. (2) Bosanquet, C. H., “Gas Chromatography 1958,” D. H. Desty, ed., p. 107, Butterworths, London, 1958. (3?(Bosanquet, C. H., Morgan, G,., O., Vapour Phase Chromatography, D. H. Desty, ed., p. 35, Butterworths, London, 1957. (4) Golay, M. J. E., Nature 202, 489
(1964). (51, Guild L. V., Bingham, S., Aul, F., Gas dhrornatography 1958,” D. H. Desty, ed., p. 226, Butterworths, London, 1958.
( 6 ) Haarhoff, P. C., van der Linde, H. J., ANAL.CHEM.,in press. ( 7 ) Hodgman, C. D., “Hmdbook of Chemistry and Physics, 44th ed.,
Chemical Rubber Publishing Co., Cleveland, Ohio, 1962. (8) Krige, G. J., D.Sc. thesis, University of Pretoria, Pretoria, South Africa, 1965. (9) LittlyTood, A., “Gas Chromatography, p. 40, Academic Press, New York, 1962. (10) Locke, D. C., Brandt, W. W., “Gas Chromatography, L. Fowler, ed., p. 55, Academic Press, New York, 1963. (11) Schay, G., “Theoretische Grundlagen
der Gaschromatographie,” Cha IV, VEB Verlag der Wissenschaften, gerlin, 1961.
(12) Scott, R. P. W., ANAL. CHEM.36, 1455 (1964). (13) Scott, R. P. W., ANAL. CHEM.37, 1764 (1965). (14) van de Craats, F., “Gas Chromatography 1958,” D. H. Desty, ed., p. 248, Butterworths, London, 1958. (15) Weinstein, A., ANAL. CHEM. 32, 288 (1960). (16) Ibid., 33, 18 (1961). (17) Wilke, C. R., J. Chem. Phys. 18, 517 (1950).
RECEIVED for review March 19, 1965. Accepted June 14, 1965. The Director General of the Atomic Energy Board is thanked for permission to publish this paper.
Gas Chromatographic Determination of 2,3-Diketones at Nanogram Concentrations Using Electron Affinity Detect0 r B. J. GUDZINOWICZ1 and
K. A. JOHNSON
Research Department, Jarrell-Ash Co., WaHham, Mass.
b By proper selection of operating parameters, aryl and alkyl 2,3-diketones can be quantitatively determined by gas chromatography using the electron affinity detector at concentrations ranging from 0.10 to 1.2 nanograms. Calibration data are presented for acetylpropionyl, acetylbutyryl, and acetylvaleryl, in addition to benzil, furil, and p-diacetylbenzene. Although p-diacetylbenzene does not possess vicinal ketone groups, it is a good electron acceptor because of its conjugated structure. This is in contrast to 2,4-pentanedione (acetylacetone) which exhibits no tendency to capture electrons. By injecting a constant volume of a known three-component diketone mixture into the chromatograph at various potentials applied to the detector, the resulting chromatographic data clearly show the effect of applied potential on both peak resolution and distortion, and give the well established applied potential/response relationship.
I
N CONTRAST to
the numerous methods available for the determination of carbonyl compounds based on either volumetric (5, 11, 18, Z2), gravimetric (8, I S ) , spectrophotometric (9, 14), or descending and centrifugal thin layer ( I @ , paper (Z), and liquid-liquid (3, 17) chromatographic techniques, few procedures have been reported in the literature specifically for the analysis of aryl and/or alkyl 2,3-diketones a t low concentrations.
I n all diketone methods reported 4, 6, 12, 20, 22), these were either qualitative, concentration-limited, or time-consuming and incapable of identifying individual species in multicomponent mixtures without prior separation. To circumvent some of the disadvantages previously encountered for carbonyl analysis, gas chromatography has been successfully applied for the separation of multicomponent samples. Recently, Soukup, Scarpellino, and Danielczik (19) described a direct method for the analysis of carbonyls as their 2,4dinitrophenylhydrazone derivatives in contrast to those using an exchange procedure with alpha-keto acids (15,II). With the flame ionization detector, Soukup et al. (19) reported that the detectability of these hydrazones was between and 10-5 mg. On the other hand, with the electron affinity detector, Gudzinowicz ( 7 ) showed that 2,4-dinitrophenylhydrazones can be quantitatively determined a t I- to 8nanogram concentration levels, the hydrazone’s favorable electron-capturing ability resulting primarily from its 2,4-dinitrophenyl radical. Although no quantitative data have appeared in the literature relative to the gas chromatographic analysis of 2,3diketones, Lovelock (10) reported that the -CO-COelectrophoric group in diacetyl showed a high affinity for electrons relative to that of chlorobenzene which was taken to be unity. Based on this observation, the present work was undertaken. The purpose of (1,
this paper is to show that both aryl and alkyl 2,3-diketones can be determined without difficulty a t 0.1- to 1.0-nanogram concentration levels. EXPERIMENTAL
The Jarrell-Ash Model 28-710 chromatograph equipped with flame ionization and electron affinity detectors and a Bristol Dynamaster hlodel lP12H560, 1-mv., 11-inch strip-chart recorder was used for these 2,3-diketone studies. The chromatographic column was made of borosilicate glass (6 feet by 3/ls-ineh i.d.) packed with 5y0 by weight of General Electric’s SE-30 methyl silicone gum rubber on 80- to 90-mesh Anakrom AS (Analabs, Inc., Hamden, Conn.). Prior to use, the packed column was conditioned a t 250” C. for 72 hours. To determine the chromatographic behavior and elution characteristics of the alkyl 2,3-diketones, the flame ionization detector (FID) was initially employed with argon as the carrier gas. For this preliminary investigation, the other F I D gas chromatographic operating parameters used were column temperature, 27” and 50” C.; injector temperature, 120” C.; detector temperature, 140” C.; air flow rate, 1.00 cu. feet/hour; hydrogen gas pressure, 5.0 p s i ; argon carrier gas flow rate, 58.2 cc./minute; sensitivity setting, 1 x 10-9 and 1 x 10+ ampere; and recorder chart speed, 2.0 minutes/inch. With the electron affinity detector (EAD), the chromatograph was maintained as noted below: column tem1
Present address, American Cyanamid
Co., Stamford, Conn.
VOL. 37, NO, 13, DECEMBER 1965
1745
