Behavior of inert Gas Packets in Chro matographic Columns STANLEY D. NOREM The Perkin-Nmer Corp., Norwalk, Conn.
b A careful study of the behavior of inert gas packets (“air peaks”) in open tubes and various packed chromatographic columns yields valuable insight into the nature of the departure of these columns from ideality, and indicates some of the benefits to be realized in the development of improved support materials. The experimental difficulties attendant to such measurements are described, including the rather stringent demands placed upon the ancillary equipment. The usefulness of such studies is shown by comparative experimental data for two columns, one packed with a typical diatomaceous earth support, the other with glass beads of approximately the same mesh size. gas chromatographic separations are performed in tubes several feet in length and a fraction of an inch in diameter, which have been packed with some form of diatomaceous earth. The outstanding property of diatomaceous supports is an enormous surface area, which permits disposition of the retentive oil as a thin film in intimate contact with the moving gas stream. Such physical factors as control of mesh size and uniformity of packing are important, and the quality of conventional columns has been improved considerably. In recent years, other forms of column such as the open tubular column of Golay and new types of packed columns-e.g., the glass microbead columns of Cooke and Frederick (@-have been employed. In assessing the relative merits of these various types of column, care must be taken to avoid the comparison of a column of one type which has been optimized for a specific analytical application with one of another type which has not. The aim of this study was the establishment of simple experimental procedures whereby the effects of column geometry and dimension could clearly be separated from the effects of capacity ratio, liquid film thickness, and unwanted chemical attractions. Once this separation is realized, the column engineer can proceed toward the development of superior materials and the more efficient utilization of existing supports. OST
40
ANALYTICAL CHEMISTRY
The mathematics of column theory permits the separation of the various causes of band spreading, and the height equivalent to a theoretical plate may be symbolically expressed in the expanded form of the van Deemter equation (6): HETP
=
A
+ 7B + C ~ +V C ~ V
(1)
The second term on the right is the spread due to static or lengthwise diffusion in the gas phase. The third and fourth terms are the spreads due to dynamic or mass transfer effects in the gas and liquid phases, respectively. The first term, A , which is independent of carrier gas velocity, v , is the controversial multipath term originally proposed by van Deemter, Zuiderweg, and Klinkenberg (9). Giddings (3) has offered a more elaborate treatment of multipath effects. In any event, there is growing evidence in this laboratory and elsewhere (8) that, over the usual range of operating conditions, this term may be made negligible by careful column construction, and its presence may usually be attributed to some instrumental artifact. It is, of course, entirely absent from Golay columns. The convenient form of the H E T P equation suggests a series of simple experiments which can lead to improved understanding of columns. In a study of the shape of inert gas packets or air peaks, the fourth term may be neglected entirely. These peaks can therefore be used to determine an upper limit of column performance. If the liquid phase mass-transfer term is eliminated, the problem of column evaluation may be stated simply. The minimum H E T P and optimum carrier gas velocity of a column are directly related to some characteristic physical dimension, such as tube radius in the Golay column or particle diameter in a packed column. The pneumatic resistance of a column is also related to dimensions, however, and it is these three quantitiesminimum HETP, optimum velocity, and pneumatic resistance-which determine the intrinsic “goodness” of a column type. Were this not the case, one could decrease the particle size indefinitely, thereby decreasing the H E T P and increasing the optimum
velocity ad insniturn. (There may, of course, be practical limits other than pressure drop for certain support materials such as a liquid phase distribution which does not scale because of a fixed pore size.) A striking example of the importance of this relae tion is the use of Golay columns in lengths of several hundred feet. Thpressure drop across such columns is comparable to that across a few feet of packed column of the same plate height. The conventional packed column exhibits a pneumatic resistance characteristic of one physical dimension and an H E T P which is characteristic of another, larger dimension. It was, in fact, the enormity of this difference which led Golay to the concept of the open tubular column. It is proposed, then, that the first step in the evaluation of a column type be the study of the passage of inert peaks. As an example of the utility of this procedure, data are presented below for two distinct types of packed column: one packed with irregular. porous granules, and the second with spherical, solid beads. It is instructive to consider first the open tube or Golay column, however. This type lends itself to simple experiment and has been the subject of exact mathematical treatment. The equation for the H E T P of an air peak in a Golay column is (6) : HETP
20
= v
1 +24 D r2t’
(2)
Here D is the diffusion coefficient of air in the carrier gas in square centimeters per seeond, T is the tube radius in centimeters, and v is the linear gas velocity a t the column outlet in centimeters per second. The equation may be rewritten H v = 2 0 4- K~ r2 o2
(3)
This permits the convenient graphical display of experimental data, in which a plot of HETP times velocity us. velocity squared yields a straight line, the intercept of which is 2 0 . Such a plot serves as a rapid and convenient device for measuring the diffusion coefficient of the sample in the carrier gas. -4similar procedure has recently
transfer in the liquid layer is instantaneous, the HETP equation for a tubular column is (6): HETP
HELIUM
Figure 1 . valve
Diagram of gas-sampling
been suggested as a general method by Giddings and Seager (4). EXPERIMENTAL
For convenience, a plastic tube having an inside diameter of 6.6 mm. and a length of 12 feet was used as a Golay column. The packed columns studied, however, were of the dimensions commonly encountered in analytical gas chromatography, as dictated by the available packing materials and pressure drops. The two packed columns used were 7-fOOt lengths of standard quarter-inch 0.d. tubing, one packed with 30/60-mesh Johns-Manville Chromosorb, the other with 40/60-mesh Potters Brothers glass microbeads. The columns mere v, ithout liquid phase. The study of air peaks in packed columns places rather serious demands upon the experimenter. For purposes of rough estimation, a packed column may be idealized and regarded as a somewhat tortuous bundle of open tubes of radius equal to the average particle diameter. Equation 2 may then be applied. Assuming the approximate values D = 0.6 sq. em. per second (air in helium) and T = 0.038 em. (average diameter, 40/60 mesh), the optimum outlet velocity is seen to be of the order of 100 cm. per second. For a reasonably efficient column, in which the H E T P is a small multiple of the particle diameter, this indicates that time half-band widths of the order of second and less must be measured if data a t the optimum and beyond are to be obtained. (In the case of the glass bead column, the actual halfband widths measured ranged from second to 7 3 milliseconds.) This places demands upon the sample size and method of introduction and upon the detector volume and response which are not met by the usual laboratory chromatograph. I n defense of the average commercially available instrument, horvever, it is instructive to calculate the effect of a relatively small degree of retention upon the time-half width of a peak a t the end of the column. I n the ideal case, in which it is assumed that mass
=
- + 1 +24(6k1 ++k)lI l k * $
ZD
(43).
A modified four-way valve was used, as shown in Figure 1. The volume of the upper passage, about 10 pl., was purged with air, a rubber cone inserted to seal the upper port, and the valve rotated 180". The momentary disturbance of the carrier flow was assumed to be insignificant. DETECTORS
Used with the 6.6-mm. diameter Golay column described above, a smallvolume thermistor detector has a
OPEN TUBE 6.6MM DIA.
a io
'
20
I
(4)
where the capacity ratio, k = capacity of the stationary phase caDacitv of the mobile phase A' s a i p l e with a capacity ratio of 3 will have an optimum carrier gas velocity which is 0.37 times that for an air peak ( k = 0). The actual peak velocitywillbe one fourth of this The minimum H E T P will be 2.8 times the air peak minimum. Combining these factors, it may be seen that the time half-band width a t optimum conditions ill be 18 times that of the air peak a t its optimum. An additional increase will be provided in most cases by a reduction in the value of D for retained components. Thus a system which may be more than adequate for analytical purposes may be completely unsuitable for the study of inert peaks, particularly when gases of high diffusivity are used. It was felt that sample injection could best be effected by abrupt series insertion of a small volume of air, of "pulse width" small compared with the final half-band width. The attendant calculations are straightforward and are not given here.
30 v (CWSEC)
Figure 3. van Deemter plot for air peak in helium carrier Showing flt of experimental points to calculated solid curve
/
ARGON
M
400 y2
[CmfISECfl
Figure 2. Experimental plot of Hv vs. for air peaks in two carrier gases, in 6.6-mm. diameter open tube
v2
response sufficiently rapid (about '/3 second) to avoid serious instrumental limitations. I t was, however, obviously inadequate for the packed column studies. The detector used for the packed column measurements was a specially constructed, hot wire cell with straight filaments. The volume of the cell was about 15 p1. The thermal response time of such a detector is of the order of a fevi milliseconds. The column effluent m-as split to avoid excessive flow sensitivity, with about one fifteenth of the total flow passing through the detector. Under these conditions, the pneumatic time constant of the detector was never greater than one half the total half-band n-idth, and no skewing of the peaks was observed. Great care was taken to eliminate any dead volumes from the system, since a t the higher velocities the slightest instrumental band spread becomes a significant part of the total. Peaks were recorded on a Sanborn 151 recorder, a galvanometric type with a frequency response which is essentially flat to 50 cycles per second (down 3 db. a t 100 cycles per second). RESULTS A N D DISCUSSION
Golay Column. Hv us. u2 plots for air peaks in two carrier gases, argon and helium, are shown in Figure 2. Values of D xere calculated from the H u intercept and from the slope. Results are shown in Table I. The slope and intercept values for argon are in good agreement, while those for helium are only fair. Departure of the experimental points from a calculated van Deemter curve based upon the intercept value of D is shown in Figure 3, for helium carrier. The increasing deviation with velocity can probably be traced to the detector time constant. At 30 em. per second, the 10% departure corresponds to a 5% error in half-band width measurement, or about 40 milliseconds. Packed Columns. Figure 4 is a van Deemter plot of air peaks in VOL. 34, NO. 1, JANUARY 1962
41
CHROMOSORB 30/60 MESH
0 1 IO
Ib
2'0
$3
50
"
4b
v ICM/SEC.l
Figure 4. Experimental van Deemter plot for air peak in Chromosorb column
7'0
5'C
9'0
IL.
ICKJSECI
Figure 5. Experimental van Deemter plot for air peak in glass bead column 53,
helium carrier on the Chromosorb column. I n this and all subsequent figures, the term "velocity" is simply the column length in centimeters divided by the passage time of the air peak in seconds. This does not necessarily represent the true average velocity of the carrier gas, since, as pointed out by Bohemen and Purnell ( I ) , a n inert peak is, in effect, retained in the intraparticle dead space of a porous granule. While curves based upon inert component velocity may be somewhat misleading in theoretical studies, their use can be defended in practical studies aimed at evaluating support materials, since the analysis time factor inherent in such a presentation is of real importance. The spread due to static diffusion, as indicated by the low-velocity part of the curve, is actually less than that predicted by the open tube equation. This result is in agreement with a recent publication by Kieselbach (7), who gives a value of about 1.2Dlv for the static diffusion term in a typical packed column. This is in contrast with the Golay column value of 2D/v. The minimum HETP is approximately 0.05 cm. and the optimum velocity is about 27 em. per second. Figure 5 is the corresponding glass
Table I.
Diffusion Coefficients of Air in Helium and Argon carrier D, Sq. Cm./Second Gas Intercept Slope
Helium Argon
0.67 0.18
0.57 0.19
Table II. van Deemter Constants Based upon Average Velocity of Inert Peak
B, sq.
Column Cm./Sec. Chromosorb 0.7 Glass bead 1.28 42
C, Sec. 9.25 x lo-'
4.85 X
ANALYTICAL CHEMISTRY
lo-'
bead plot. Here the static diffusion is roughly the same as that for the open tube. This is consistent with calculations of the average path length in a bed of close-packed spheres, which is only about 1.15 times the straightpath length. While the minimum HETP is about the same as that of the Chromosorb column, it occurs a t a velocity of about 49 cm. per second, almost a factor of 2 higher. This indicates that the dynamic term is substantially lower in the glass bead column. The practical effect of holdup inside the porous granules of the Chromosorb column is an apparent reduction of the static diffusion term and a corresponding increase in the dynamic or mass transfer term. This is roughly equivalent to the effect of using a carrier gas of lower diffusivity in a glass bead column. Comparative van Deemter constants are given in Table 11. A further advantage of the glass bead packing is s h o m in Figure 6, a plot of pressure drop us. average air peak velocity in the two packed columns. Although the two columns were packed with particles of roughly the same size, the pressure drop for a given passage time with the solid spherical packing is appreciably lower than with the porous granules. The true pneumatic resistances, based upon volume flows, are about equal. This is in agreement n-ith the experiments of Bohemen and Purnell ( I ) , which demonstrate that resistance to gas flow is due to the external surface of the particles only. These experiments confirm the theory that the performance of Chromosorb columns is limited by slowness of mass transfer in the gas phase. In contrast, the superiority of the glass beads for air peaks indicates that this type of support, like the Golay column, will be limited by effects in the liquid layer. The development of improved support materials should be aimed at
-*
i:- 33=.
a
55
l9G v
155
ChwSE.
Figure 6. Plot of pressure drop average velocity in two packed columns v5.
combining the merits of high surface area supports now commonly used with the solid center and regular geometry of the bead type. It is suggested that the first step in the evaluation of any new support material be a study of the behavior of the air peak. Once this information is in hacd, a meaningful interpretation of the behavior of retained peaks can much more readily be made. LITERATURE CITED
( I ) Bohemen, J., Purnell, J. H., J . Chem. SOC.1961, 360-7. (2) Cooke, W. D., Frederick, D. H.,
Eastern Analytical Symposium, ACS, New York, N. Y., Nov. 3, 1960. (3) Giddings, J. C., J . Chromatog. 5 , 61 (1961). (4)Giddings, J. C., Seager, S. L., J . Chem. Phys. 33, 1579 (1960). (5) Glueckauf, E., Golay, M. J. E., Purnell, J. H., Ann. N . Y . Acad. Sci. 72, 612 (1959).
(6) Golay, M. J;, E., "Gas Chromatography-1958, D. H. Desty, ed., p. 36, Butterworths, London, 1958. (7) Kieselbach, R., ANAL. CHEM.33, 23 (1961).
(sj-iiii.,p. 806.
(9) van Deemter, J. J., Zuiderweg, F. J., Klinkenberg, A., Chem. Eng. Sei. 5 , 271 (1956). RECEIVEDfor review May 2, 1961. Accepted October 23, 1961. Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, March 1, 1961, Pittsburgh, Pa.
