centered rotator and for a deuteron beam of uniform cross section (flux of deuterons constant a t all points) centered on a uniform target (tritium content constant a t all points), in which case the activities induced in the two samples would be identical, the factor should have a value of 1.842 for the delay and counting conditions given in Tables I1 and 111. The higher values obtained with the rotor stationary suggest that the deuteron beam was not exactly centered on the rotor axis or that the target was very nonuniform; the varying values suggest that the beam or the tritium concentration in the target was not stable with time. Note also that even with the rotator operating, sharply focused beams gave poorer precision than defocused beams. Data for a set of ten runs made under optimum conditions (defocused beam, 1/2-inch diameter aperture) with the dual-sample
rotator over a period of two days are given in Table IV. The observed and expected relative standard deviations are in excellent agreement even at the low level of only 0.3301,, and the “ x 2 test” gives a very reasonable value of 0.11 for the probability P. CONCLUSIONS
The results of this study on factors affecting precision in activation analyses with 14-m.e.v. neutrons indicate that beam and target effects can. be greatly reduced if not entirely eliminated for practical purposes by using a defocused deuteron beam, a beam aperture, and a n irradiation device for rotating an unknown sample with a comparator around an axis parallel to the beam axis. There is evidence that a single-sample system with a flux monitor such as a BF3 counter, which has a response proportional to neutron output, is
superior to a nonrotating dual-sample system. This is particularly apparent when there is neither a beam aperture nor a method of ensuring that a well defocused beam is striking the target. LITERATURE CITED
(1) Anders, 0 , U., Briden, D. W., ANAL. CH EM. 36, 287 (1964). (2) ciilmore, J. T., Hull, D. E., Ibid., 35, 16:?3 (1963). (3) Iddinas. F. A., Anal. Chim. Acta 31.
206 (1934). (4) Mott, W. E., Rhodes, D. F., 2,nd National Meeting, Society Applied Spectroscopy, San Diego, Calif., October 1963. (5) Stallwood, R. A,, Rlott, W. E., Fanale, D. T., ANAL. CHEM. 35, 6 (1963). RECEIVEDfor review June 3, 1965. Accepted July 27, 1965. Presented at 1965 International Conference on Modern Trends in Activation Analysis, Texas A & h l University, College Station, Texas, April 1965.
Effect of Column Repacking on Mass Transfer in Gas Liquid Chromatography R. H. PERRETT Department of Chemistry, College of Advanced Technology, Birmingham 4, England
b The packing of a gas chromatographic column has been removed and subsequently replaced so that the effect of this process on the height of the equivalent theoretical plate for the elution of paraffin hydrocarbon gases could b e studied. The results have been analyzed to yield the coefficients in the rate equation: The variations in the values of the individual coefficients, so determined, brought about by the repacking process have been considered. As might b e expected, only small changes were observed in the values of A and 6’. The fact that the changes observed in C,’ and CL were also small led to some clarification of the nature of the former.
T
existence of a contribution by mass transfer in the gas phase to the broadening of gas chromatographic peaks has been generally accepted (6-9, 14). The nature of this contribution is, however, not yet clear. It has been shown (12, 14) that the direct extension of the theory developed by HE
1342
ANALYTICAL CHEMISTRY
Golay (8) for capillary columns is not sufficient to explain the size of the effect in packed columns. Several attempts have been made to clarify the situation in terms of more or less complex theories (6, 7, 14), with varying degrees of success. I n earlier work (14) an attempt was made to investigate the effect of column loading by comparing the C,’ term obtained from two columns with differing proportions of stationary phase. However, while comparisons could be made between results obtained under differing operating conditions from a given column, correlation of data obtained from the two columns was not straightforward. This observation might be explained in terms of differences arising either from the coating of the support solid or from the actual packing of the solid after coating. Comparison of the permeability data for the two columns indicated that the packing process was probably not the source of the differences, but no direct evidence on this point was available. This study has been designed to provide such evidence in systems similar to those investigated earlier.
EXPERIMENTAL
The apparatus was similar in design t o t h a t described earlier (16, 14). The air thermostat maintained the temperature of the column constant to 10.03O C. The sampling technique for gases was similar t o that described by Pratt and Purnell (15) and katharometer detection was used. The columns were packed in stainless steel U-tubes with internal diameter of 0.40 cm. Chemicals. The stationary phase used throughout was n-octadecane (m.p. 31’ C.). T h e paraffin gases used were olefin-free gases of 99.9% purity. As in previous work, a mixture of gases-ethane, propane, isobutane, and n-butane-at atmospheric pressure was made u p and stored in a large bulb. The same mixture was used throughout the experiments described. T h e solvent was supported on Sil-0-Cel C22 sieved to give a mesh range of 100 to 120 B.S.S. Procedure. Column 1A was packed in the U-tube and consolidated by tapping t h e tube walls. When further reduction in the volume of packing was judged t o result only from slight abrasion of the particles, the column packing was taken to be complete. T h e volume and weight of the packing Apparatus.
were determined and the tube ends were filled with glass wool. T h e column was then connected into the gas flox system and allowed to equilibrate a t the experiinental temperature, 40" C. The gas flow rate was measured by means of a soap bubble flowmeter therniostated a t 25' C. b y circulating water. At least three samples of the gas mixture were then eluted before the piocess was repeated at a different flow rate. From the resultant chromatograms the values of the H E T P for the eluates were calculated using the expression:
H
=
L ~
Solute
A, cm.
Propane Isobutane n-Butane
0.02 0.015 0.015
Propane Isobutane n-Butane
0.01 0.014 0.01
1.01 0.88 0.90
2.0 3.6 3.7
Propane Isobutane %-Butane
0.02 0.012 0.015
1.00 0.88 0.85
3.4
COLUhlN
(y)'
X
Table 1. Rate Equation Coefficients Nitrogen elution Hydrogen elution B', B', A, sq.cm. C,' X CL X sq. cm. C,' X CL X cm. sec.-l lo4, sec. lo4,sec. set.-' lo4, sec. lo4, see. COLUMN 1A 0.015 0.23 5.5 16 0.95 2.0 13 0.015 0.19 10.7 15 0.82 2.0 16 0.015 0.18 11.8 12 0.81 3.1 11
5.55 The volume flow rate was corrected to atmospheric pressure and column temperature, making allowance for the
1B
16 14 11
COLUMN 1C 15 3.7 16 3.9 11
0.015 0.010 0.010
0.25 0.22 0.24
5.5 13.5 13.9
16 15.5
0.015 0.015 0.015
0.27 0.22 0.22
8.5 12.5 14.0
13 16 12
11
Sil-0-Cel is much less fragile, so the deterioration of the latter solid should be less rapid. Thus after only two repackings the physical change in the solid would be slight and would lead to little or no change in the properties of the column.
0.15
H ( c d
RESULTS
The coefficients in the rate equation were determined as in other work (11-14). Table I shows the values of A , B', Cg', and CL for columns IA, lB, and 1C for the two carriers hydrogen and nitrogen. Figures 1 and 2 illustrate the degree of fit of the experimental points to the theoretical curves. I n addition to the HETP data the experiments yielded permeability data for the columns (Table 11). The
0.IC
I 5
0.0s
I 10
1
I
IS
ao
kR/WC.>
Figure 1.
Elution of propane from column 1 C b y nitrogen
saturation of the carrier by water vapor ( I , 12). The linear gas velocity was calculated from this value using the value 0.7 gram (em.) - 3 for the bulk density of Sil-0-CeI (12). Thus the variation of H E T P with linear gas velocity was determined with both nitrogen and hydrogen as carriers. T h e filament current in the katharometer ( 2 ) and the sample size (3) were fixed well nithin the limits found in preliminary studies to avoid the possibility of spurious values for the H E T P arising from these sources. The column was then unpacked and the packing inspected visually before being repacked in the tube, using the method described above. A very small amount of coated ,solid (always less than 0.01 gram) was added to make good the slight wastage. The new column (113) was then replaced in the thermostat and investigated in the same may as column 1A. This process -3s repeated to give similar results for column 1C. The disintegration of Celite 545 has been shown to be significant onlv after three repacking p k e s s e s (14 and
0.20
-
H [em.)
0.15-
0.10-
20
30
B Icm.lrrc.)
Figure 2.
40
Elution of n-butane from column 1 B b y hydrogen VOL. 37,
NO.
1 1 , OCTOBER 1965
1343
specific permeability, Bo’, was calculated using the relationship
from the lines obtained by plotting the pressure drop against the mean volume flow rate. The values of the viscosities of the gases at 40’ C. were calculated from the experimental values a t 0’ C. by means of a Sutherland equation (10) and were taken as 226 X 10-6 poise for nitrogen and 116 x 10- poise for hydrogen. I n Table I11 are shown k values for the elution of the solute gases from the columns as measured on the chromatograms. DISCUSSION
The value of the eddy diffusion term,
A , is reasonably constant for all the columns with both carrier gases. The
Table II. Permeability Data Column Carrier m Bo’ X lo’ 9.35 2.03 1A Hz 9.31 2.04 1B H2 8.75 2.17 1C Hz 18.83 1.97 1A Nz 19.15 1.94 1B N2 17.5 2.12 IC Nz
Table 111.
Column 1A
Carrier Hz X2
Hz Nz Hz
1B 1C
N2
Table IV.
Capacity Ratios k
IsonPropane butane Butane 3.38 5.08 1.55 3.32 5.01 1.50 3.34 5.04 1.51 3.29 4.97 1.49 3.31 5.00 1.50 3.23 4.83 1.46
Labyrinth Constants Y
Column IA
Carrier H2
0.88 0.85 _ 0.93 N2 0.92 0.92 Hz N, 0.99
IC
Car-
rier Hz
Nz Hz Nz Hz No
1B
1C
1344
pane
N2 H, - ~
1R --
Column 1A
Pro-
0
nbutane Butane 0.90 0.87 0.80 0.84 0.96 0.98 0.97 1.06 0.96 0.93 0.97 0.97 Iso-
average value is 0.015 cm. This compares with a mean nominal particle size of 0.014 cm. and is in agreement with earlier work (1.2,14). In view of the low value of A leading to a value of unity for 2 i , it is not unexpected that the value of y obtained from the B’ results is also near unity. Table I V shows the values for y obtained using calculated diffusion coefficients; the mean value is 0.92. It is noteworthy that the values of y obtained for the original column (1A) are consistently rather lower than those obtained for the repacked columns (1B and IC), but between the latter there is a much greater consistency. This evidence and that of the permeability data (Table 11) indicate that, at least, the coefficients obtained for the two repacked columns (1B and 1C) may be fruitfully compared, even if comparison between them and the original column (1A) is a little more speculative. The initially calculated values of C L obtained in this study required very little change during the refining process. The refined values of C L are shown in Table V together with the values of dr2/Dr, calculated on the assumption that the retention volume dependence of C L is that obtained by van Deemter for uniform film distribution (4).
It is immediately apparent that the values of C L are in good agreement for all three columns and on this evidence the columns do not appear to have been affected by the repacking process. Moreover, there is no evidence for any redistribution of the solvent on the solid as a result of the repacking process. The function of k calculated for a uniform film distribution appears to be the appropriate one, but since there are no independent data for diffusion coefficients of the gases in the solvent used, only qualitative conclusions can be drawn about this point. The values of df2/DL for n-butane and isobutane are much closer together than the values for propane are to either. The values obtained for the ratios of the diffusion coefficients evaluated from the mean values of d f 2 / D Lare shown in Table VI.
Table V. Liquid Phase Mass Transfer Data C L X lo4, sec. df2/DL X lo3 Ca iC, nC4 CS iC1 nC4 13 1 16 f. 1 11 zk 1 8.1 zk 1 13.5 zk 1 11.8 1
16 16 16 15 13
15 14
15.5 16 16
ANALYTICAL CHEMISTRY
12
11 11 11
12
10.0 10.0 10.0 9.4
8.1
12.6
11.8
13.0 13.4 13.4
12.9
11.8
11.8 11.8 12.9
Table VI.
Propane
Interdiffusion Coefficients in n-Octadecane
9.3\
Isobutane
13.0/
n-Butane
12.2
\ / 1‘3>
1.4
0.94
These values for the ratios of the diffusion coefficients are not unreasonable. I n Table I11 the values of k indicate little or no loss of solvent during the series of experiments, though in this comparison too, if an odd column were to be chosen, it would be column 1A. Thus on this evidence it might be expected that comparison between column 1A and the subsequent ones would present the most difficulty. The values of C,’ are extracted from Table I and shown in Table VII. The values obtained for C,’ in columns 1B and 1C for the elution of the butanes are in excellent agreement, and these two columns are the most likely to be comparable on the evidence of the other terms. However, the best agreement between the C,’ terms obtained for the elution of propane is that between columns 1.4 and 1B. This may be, a t least to some extent, fortuitous, since the scatter in the experimental values of the H E T P is highest for propane elution, as may be seen in Figures 1 and 2. The magnitude of the C,’ terms found in this work is such that the values of x calculated from the extended Golay expression for C,’
are all near 2. This is in accord with previous findings that x ranges from 1.5 to 7 (12, 14)-that is, 50 to 100 times bigger than the most generous calculation would predict. Thus, this study confirms the conclusion drawn in the earlier work, that the extended Golay expression accounts for only a very small part of the observed C,’ term. Hence an alternative mechanism must be sought. The mechanism proposed earlier (1.2, 14) to account for the term required the existence of systematic irregularities in the paths across the width of the column and the magnitude of the coefficient was calculated by Golay (9) to give the forms
or for the more 1ikel.y radial difference 0
ID 1E
0.15-
The systematic differences across the column ( p , p ’ ) could arise either from different path lengths or from different exposure to stationary phase. I n the previous attempt to compare the C,’ terms of two columns with different solvent-support ratios, the differences observed were very much greater than could be interpreted in terms of the change in capacity ratio of the columns. Moreover, the effects of changing the capacity ratio by change of temperature were not the same as those resulting from change of column. If the C,’ term arises from differences of path length, the large differences noted in the earlier work could be the result of a failure to reproduce these differences in the packing process, However, since the C,‘ term is not markedly altered in the repacking process, there is no reason why the path difference should not have been reproduced in the earlier work. The results shown in Figure 3 indicate that separate columns made up from two portions of coated solid prepared in one batch yield the same HETP curve. Thus the large difference previously noted must have arisen from the coating stage and not from the packing process, and the systematic irregularities must be differences in the exposure of solute to solvent. The results of Hildebrand and Reilley (5) obtained with mixed beds indicate that Carbowax 400 when used as a stationary phase tends to be redistributed during the passage of carrier gas. There is, however, no evidence from the C L terms obtained in this study that significant redistribution of solvent has taken place, and only a very slight maldistribution of solvent is required
Table VII.
Column 1A 1B IC
Cawier 1-11
n Icm.)
0.10-
v -
Figure 3.
I
I
I
20
40
60
Elution of acetone from columns 1 D and 1 E by hydrogen
to give C,‘ terms of the magnitude noted. If the solvent maldistribution can persist, the heavier, more thickly coated solvents might be expected to distribute themselves in a radially uniform manner in the column and lead to a C,’ term of the form suggested.
D L
d
= = =
= = p , 1‘ = x =
r
labyrinth constant liquid film thickness interdiffusion coefficient liquid phase column diameter column radius path differences constant
in
NOMENCLATURE
LITERATURE CITED
height of equivalent theoretical plate A = eddy diffusion constant B’ = longitudinal diffusion coefficient aT 1 atm. C,‘ = gas phase mass transfer coefficient a t 1 atm. CL = liquid phase mass transfer coefficient u’ = linear gas velocity a t 1 atm. = mean linear gas velocity .ii L = packed length of column w = peak width at half height 2 = distance on chromatogram from injection to peak maximum Bo’ = specific permeability m = experimental slope 9 = gas viscosity V = tube volume k = capacity ratio h = eddy diffusion coefficient
(1) Adlard, E. R., Khan, h l . A,, Whitham, B. J., “Gas Chromatography,” R. P. W.
H
=
Gas Phase Mass Transfer Terms C,‘ X lo4, sec.
Propane 2 . 0 i 0.5 2.0 3.4
y
d,
Isobutane 2 . 0 i 0.5 3.6 3.7 10.7 13.5 12.5
%-Butane 3.1 =k 0.5
3.7 3.9 11.8 13.9 14.0
Scott, ed., p. 251, Butterworths. London 1960.’ ( 2 ) Bohemen, J., Purnell, J. H., Chem. Ind. 1957. 815. (3) BohemLn, J., Purnell, J. H., J . Chem. Soc. 1961, 2630. (4) Deemter, van, J. J., Zuiderweg, F. J., Klinkenberg, A,, Chem. En$. Sci. 5 , 271 (1956). (5) Hildebrand, G. P., Reilley, C. N., ANAL.CHEST. 36, 47 (1964). (6) Giddings, J. C., Schettler, P. D., Ibid., 36, 1483 (1964). ( 7 ) Giddings, J. C., Seager, S. L., Stucki, L. R., Stewart, A. H., Ibzd., 32, 867 (1960). (8) Golay, M.,“Gas Chromatography,” D. H. Desty, ed., p. 35, Butterworths, London, 1958. (9) Golay, AI., 2nd International Symposium, I.S.A., Michigan, 1959. (10) lloelwyn Hughes, E. A,, “Phy4cal Chemistry,” p. 597, Pergamon, New York, 1957. (11) Perrett, R. H., ANAL. CHEM. 37, 1346 (1965). (12),Perrett, R. H., Ph.D. thesis, Cambridge, 1962. (13) Perrett, R. H., Purnell, J. H., AN.IL. CHEN..34. 1336 (1962). (14)Ibid., 35, 430 ii963j. (15) Pratt, G. L., Purnell, J. H., Ibid., 32, 1213 (1960). ’
RECEIVEDfor review April 9, 1965. Accepted J d y 9, 1965.
VOL. 37, NO. 1 1 , OCTOBER 1965
1345
