The significar e of Equation 10 is that the direct rnwurement of K allows a comparison of these several equilibrium constants in terms of a simple relationship. As mentioned above, K H and K o are obtained independently by a potentiometric technique, and the resulting value of K H / K o is 3.09. The value of fiobtained is 3.38. Further investigation of equilibrium and kinetic deuterium isotope effects using NMR should provide interesting information concerning the nature of these effects. The investigation of isotope effects on the acid-base chemistry of amino acids would be of particular interest in view of the physiological effects of the presence of large amounts of DzO in biological systems. Such a n investigation should also include research into the nature of the electrical
symmetry and extension of the method described in this paper to the analysis of other isotopic mixtures. LITERATURE CITED
(1) Ameil, S., Peisach, AT., ANAL. CHEM. 34, 1305 (1962). (2) Arnett, E. M., Dugglesby, P. McC., Ibid., 35, 1420 (1063). (3) Bergquist, hI. S., Erickson, L. E. G., Acta Chem. Scand. 16, 2308 (1962). (4) Davis, D. R., Roberts, J. D., J . Am. Chem. SOC. 84, 2252 (1962). ( 5 ) Goldblatt, AT., Jones, W. hl., ANAL. CHEM.36.431 i1964). ( 6 ) Goldmin, hl., Arch. Sei. (Geneva) 10, 247 (1957). ( 7 ) Grunwald, E., Loewenstein, A., Lleiboom, S.J., J . Phys. Chem 27, 630 (1957). (8) Kirshenbaum, I., “Physical Properties of Heavy Water,” NcGraw-Hill, New York, 1951. (9) Kresge, A. J., Allred, A. L., J . -4m. Chem. SOC.85, 1541 (1963).
(10) Loewenstein, A., Meiboom, S., J . Chem. Phys. 27,1067 (1957). (11) Mazurek, M, Perlin, A. S., Can. J . Chem. 42, 710 (1964). (12) Paulsen, P. J., Cooke, W. D., ANAL. CHEM.36.1713 (1964). (13) Pople,‘ J. A., Schneider, W. G.,
Bernstein, H. J., “High F l u t i o n Nuclear Magnetic Resonance, p. 214, hlcGraw-Hill, New York, 1959. (14) Salomaa, P. Schaleger, L. L., Long, F. A., J . Am. Chem. SOC.86, 1 (1964). (15) Trenner, N. R., Arison, B. B., Walker, R. W., ANAL. CHEM.28,.830 (1956). (16) Urey, H. C., J . Chem. SOC. 1947, p. 562. (17) T’arian Associates, Palo Alto, Calif., Tech. Information Bull. 3, 1 (1960).
RECEIVEDfor review May 11, 1965. Accepted June 7, 1965. Investigation supported by Public Health Service Research Grant RG-08349 from the National Institutes of Health. Division of Analytical Chemistry, 149th Meeting, ACS, Detroit, April 1965.
END OF SYMPOSIUM
Precision Activation Analysis with 14-Million Electron Volt Neutrons WILLIAM E. MOTT and JOHN M. ORANGE Gulf Research & Development Company, Pittsburgh, Pa.
As part of a program to develop, for routine industrial use, a series of analytical methods based on activation with 14-m.e.v. neutrons, an extensive study was made of the factors affecting precision. Both the comparator and the indirect flux monitoring methods of analysis were studied. In each case the precision was limited by conditions inside, rather than outside, the accelerator-viz,, by variations in deuteron flux over the beam area and by inhomogeneities in the density of tritium in the target. Before the work described in this paper was initiated, precision was generally limited to about a 1 to 2% standard deviation even when counting statistics predicted much lower values. At the present time observed fractional standard deviations (root-meansquare errors) consistently agree with the expected values (from counting statistics), which in some analyses are frequently as low as 0.3%.
D
in the literature indicate that the precision of analytical results obtained by the fast neutron activation method is usually limited by factors other than counting statistics. Despite this there have been ATA GIVEN
1338
ANALYTICAL CHEMISTRY
7 5230
few definitive studies of this rather fundamental and very important problem, probably the most thorough to date being by Xnders and Briden (1). They examined many of the gross factors affecting precision in oxygen analyses including the monitoring of the neutron flux in the sample being analyzed. Gilmore and Hull (2) and Iddings ( 3 ) also studied flux monitoring techniques and their role in limiting precision in oxygen analyses. About the same time, hIott and Rhodes (4) found that for expected relative standard deviations below 1%, differences between observed standard deviations (rootmean-square error) and those expected from counting statistics could usually be related to variations of the flux in the unknown sample not reflected in the count of the flux monitor, whether a BF3 counter, a proton recoil counter, an associated particle counter, or a simultaneously irradiated comparator. These flux variations were attributed to changes in deuteron flux over the beam area and by inhomogeneities in the density of tritium in the target. They concluded that whereas relative standard deviations of 1 to 2% should be relatively easy to achieve, any signifi-
cant advancement in precision would require improved sample irradiationflux monitoring systems in which simultaneous irradiation of unknown sample and standard would be a necessary, but not a sufficient, condition for success. When considering the precision problem, two facts become clear. First, improved precision is a necessity if fast neutron activation analysis is to compete favorably on a broad scale with other methods of elemental analysis. Second, poor precision is not inherent in the fast activation approach, only in some of the techniques employed. It becomes of interest, therefore, to study beam and target effects and ways to compensate for them. This paper reports on such a study and describes irradiation systems now in use at Gulf Research that with homogeneous samples give observed standard deviations down to 0.3y0 when the appropriate number of counts are collected from sample and monitor. FAST NEUTRON ACTIVATION FACILITY
Neutron Generator. A 130-kv. deuteron accelerator, which was designed and constructed a t t h e Gulf Research Center in 1957, is t h e core of the fast neutron activation facility,
Figure 1.
Drift tube section with dual-sample rotator
This machine uses a Texas Nuclear r-f ion source and is capable of delivering to target 2 ma. of deuterium ions. Xeutrons are produced by bombarding either a 13/,,inch diameter watercooled tritiated titanium target with a magnetically analyzed (45' deflection) beam of D,+ ions or a '/te-inch diameter target with a straightthrough beam of unanalyzed ions. The choice of target depends on the type of analysis being performed and the neutron flux required, the larger target always being used for high flus work. Although the main advantage of the magnet is that it greatly reduces the time lost in changing from one target assembly and irradiation system to another, an additional advantage is that through the use of the pure D1+ beam, target heating is reduced and target life extended. (The commonly quoted values for the yield of D,+ and D2+ ions from the r-f source, 90% D,+ and 10% D2+, are seldom realized with other than a freshly cleaned source bottle.) As in other generators of this type a n electron suppressor is located near the target to prevent electrons leaving the target during ion bombardment. Also near the target in the Gulf machine is a centered disk, which has a n aperture and four insulated quadrants. Each quadrant is connected through a meter to ground so that the disk can he used to define as well as to control the size of the beam spot striking the target. The end section of a drift tube assembly for the straightthrough heam, showing the location of the electron suppressor
(11
I I
and the heam aperture, is pictured in Figure 1. Sample Irradiation Systems. Two irradiation systems are in routine use at Gulf Research. T h e first employs a single pneumatic tube (6) for transferring samples between the irradiation and counting positions. It is equippel with timers and solenoid valves that automatically time and control the irradiation, transfer, and counting sequence. Samples are automatically cycled as many times as desired. They are transferred from the irradiation position to the counter in about 0.5 second by dry air at 30 p.s.i. A residual pressure is maintained in the tube during the irradiation and counting periods to assure reproducible positioning of sample containers. For a container positioned in front of the target, the distance from the front surface of the target to the center of the sample is 0.56 inch. When using this system, the neutron output of the accelerator is monitored with a BFa counter mounted in the shield wall. The three types of sample containers used in the pneumatic tube are depicted in Figure 2. Containers A and C are for solids, Container B for liquids and solids. Container B, a commercial l/rounce polyethylene bottle normally used for eye drops, is sealed very effectively when the driving cap is screwed down onto the dropper tip. I n the second irradiation system (see Figures 1 and 3), for routine analysis, a standard and a n unknown are irradiated simultaneously in a device
that rotates the sample containers around a n axis parallel to the deuteron heam axis. The rotator is cable driven at 300 r.p.m. and is attached by four supporters directly to the target hackplate. Holders on the rotor are spring loaded to accept '/*inch diameter x lS/~&ch long sample containers. The complete assembly was precision machined, balanced, and aligned in order to minimize ordinary sample positioning errors. A locking device, attached to the bearing housing and rotor, allows stationary irradiations in positions that can he precisely reproduced. The distance from the center of the active surface of the target to the center of a sample mounted on the rotator is 0.50 inch. An irradiation system soon to be employed for routine oxygen and fluorine analyses is shown in Figure 4. This system has two pneumatic tubes, one for transferring a comparator between the irradiation position and counter, the other for transferring the unknown sample. Again, the comparator and unknown are rotated around an axis parallel to the beam axis while being irradiated. The speed of rotation is 300 r.p.m. Within a second after the end of an irradiation, the rotating sample holder is automatically stopped by the magnetic brake and locked into the sample ejection position by the solenoid, and the samples are ejected from the holder and transferred to their respective counters. Gamma Ray Counting System. Gamma-ray counting is performed with a 5-inch diameter X 5-inch thick NaI(T1) scintillation crystal having a 1-inch diameter X 31/rinch long well. The counter assembly (6) is housed in a 12-inch thick steel shield lined with '/?inch of bora1 and '/= inch of cadmium. The output of the counter is fed through a n amplifier to either a discriminator-scaler or a multichannel analyzer, the latter being needed only to determine the optimum discriminator setting for a given matrix material. When the dual irradiation and transfer system is in use, the unknown will he counted with the well crystal, the standard with a solid 3-inch diameter X 3-inch thick NaI(TI) crystal and discriminator-scaler setup. I n contrast t o Anders and Briden (f),we have not found that the use of a well crystal
-
IC1
Figure 2. Sample containers far irradiation with pneumatic transfer tube
Lor..
Figure 3. Rotating dual-sample irradiation system VOL 37. NO. 11 OCTOBER 1965
1339
7
100
1
SAMPLE
t
CONTAINER
DIAYCTER*
I
i" IRRADIATIOW
IRRADIATION
'"TN 40
L
1
LLOCKIWSOLENOID
\ I TbkOET
I
\
LROTOR
20
FRONT V I E W
SIDE VIEW
Figure 4. Dual-sample rotator with pneumatic tubes 0.34
unduly complicates sample handling with a pneumatic tube. I n fact, the advantages of the well counter seem to far outweigh the disadvantages. FACTORS AFFECTING PRECISION
The major factors affecting precision in fast neutron activation analysis with the small neutron generators available commercially today are, as a rule, external to the generators. These causes of poor precision must be understood and either eliminated or counterbalanced before a study of the more subtle generator-centered causes can make much headway. Of particular importance are two causes that, either alone or in combination, can produce data from identical samples with observed relative standard deviations of 2 to 6% and higher. They are unreliable positioning and orientation of samples during activation and counting, and unstable sample counting and flux monitoring systems. Unreliable Sample Positioning and Orientation. If the positioning of a sample for irradiation varies from run-to-run, there will be fluctuations in the induced activity because of the nonuniform nature of the fast neutron flux; if the positioning for counting, varies, there will be fluctuations in t h e number of counts collected, all other conditions being equal, because of the action of the inverse square law. The effect of the sharp gradient in neutron flux with distance from the target on the activity of a sample is shown in Figure 5. We see that in terms of precision, a positioning error of about =t0.01 inch standard deviation with a 1/2-inch diameter sample and a target to center-of-sample distance of 0.50 inch would result in a n observed relative standard deviation on the induced activity of about 3%. .4t 0.75 inch the same positioning error would lead to an observed standard deviation of about 1%. Also, because of the sharp flux gradient and the solid angle effect, runto-run differences in sample orientation during counting can be important. T h a t is, the side of a sample facing the 1340
0
ANALYTICAL CHEMISTRY
0.42
0.50 0.50 0.66 0.74 0.02 0.90. DISTbNCE FROM TARQET TO CENTER OF SAMPLE 1111.1
0.94
Figure 5. Variation of sample activity with distance from target target will be activated more than the side opposite so that the count in any given run will depend on how the sample is oriented in front of the counter. Difficulty here can be avoided either by spinning the samples in the irradiation and counting positions (1) or by using a well crystal. (If the samples are very inhomogeneous, they should be spun in the irradiation position even with a well crystal.) Unstable Sample Counting a n d Flux Monitoring Systems. Unstable counting equipment is often responsible for poor reproducibility. Although easily remedied when detected, instrumental troubles can never be eliminated once and for all. They are always potentially present, and without constant vigilance a drifting amplifier or a faulty timer can unexpectedly become responsible for some very unreliable results. Generator Centered Causes. There are essentially only two generator-centered causes of poor precision associated with the bulk of the small accelerator neutron facilities in operation today-via., t h e deuteron beam which fluctuates in diameter and uniformity, and t h e target which loses tritium nonuniformly across its surface. Variations in beam spot diameter and in the deuteron flux over the beam area can usually be related to instabilities in the focus and extraction power supplies and to changes in ion source characteristics. The effective beam spot diameter can also vary with the pressure in the vacuum system, a deteriorating vacuum, for example, will give rise to a continuous loss of definition in the beam spot. As a tritiated titanium target is bombarded with deuterons, tritium is continuously lost from the layer of titanium but not necessarily in a uniform manner, T h a t is, depending on the size and shape of the deuteron beam, a target can be. depleted of tritium at a faster rate a t one point than a t another, A target, therefore,
-
0
0.5
1.0
Figure 6. Local tritium content across surface of tritiated titanium target Measured with counter having 1 -mm. aperture
not only may initially be characterized by certain point-to-point differences in tritium content (see Figure 6) but with use it may quickly acquire a completely altered tritium distribution. I n machines that use magnetic deflection, an unstable accelerating voltage or an unstable deflecting magnetic field can also affect precision. Both tend to make the deuteron beam wander over the target. They produce the same effect as the two agents just discussed. T h a t is, they bring about changes in the neutron flux through a sample t h a t may not be properly recorded by the flux monitor. FLUX MONITORING
At the beginning of our study on the dependence of precision on beam and target factors the reproducibility of our data as measured with identical samples was limited to a relative standard deviation of 1 to 2% even though counting statistics predicted much lower values. As a first step toward understanding the problem, the beam defining disk described earlier was installed so that the size and shape of the
beam could be observed. The varying nature of the beam immediately became apparent. Further experimentation proved that when the main beam spot was centered in and made to fill the aperture (by adjusting the focus control), the magnitude of the variations at the target was reduced with a definite improvement in reproducibility. The effect of aperture diameter on precision is illustrated in Table I where the expected coefficient of variation, or relative standard deviation, is the value calculated from counting statistics-Le., the theoretical value-the observed relative standard deviation, the value calculated from the variance (see Table IV). The focused beam condition is arbitrarily defined as one in which the insulated quadrants of the aperture disk stop 10% or less (depending on aperture diameter) of the total beam, the defocused condkion as one in which the quadrants stop 25y0 or more of the beam. I n all cases the single transfer tube was used and flux monitoring was with a BF3counter in the shield wall. The next step was the simultaneous irradiation of an unknown and a comparator standard or flux monitor, t h e two samples being mounted in a fixed position in front of the target. As expected, the result:; showed that the neutron flux in the unknown was not the same as in the flux monitor. They also showed that with changes in beam conditions the fluxes in the unknown and monitor did not change in exact proportion. I n fact, in such a system, where the two samples are stationary and mounted close to the target, a beam change can cause the flux in one sample to decrease, t h a t in the other to increase. Our solution to this problem was to rotate unknown and comparator in t h e manner pictured in Figure 3 (ordinary spinning of samples about their own axes will not eliminate completely beam and target effects). Of the several devices tried for rotating samples we found this design to be the easiest to construct for high precision work and the most reliable to operate. Observed and expected relative standard deviations, VoBs = 1 o i 0 c O B s / x , VEX, = 1 0 0 ~ ~ ~ are ~ / compared X, in Tables I1 and I11 for focused and defocused beams. Data were obtained with the dual-sample rotator in both the stationary and rotating modes and with different beam apertures. The decay and geometry factors listed in Tables 11and I11 are the ratios of the number of counts collected from each sample when identical samples are irradiated with the rotator. A value, therefore, depends on the beam-targetsample geometry of each sample in its irradiation position and on the delay and counting times used for each sample. Thus, for a perfwtly aligned and
Table 1.
Effect of Beam Defining Disk on Precision as Function of Aperture Diameter"
Aperture diameter, inch
Focused beam
Defocused beam
VEXP
VOBS
VEXP
VOSS
0.50 0.54 0.43 0.37
1.22 1.46 0.98 0.86
0.50 0.38 0.41 0.37
1.17 0.53 0.43 0.49
V
For a single pneumatic transfer tube and a BFI counter as flux monitor. lOOa standard deviation = - per cent. a
=
Relative
R
Table 11.
Relative Standard Deviations for Dual-Sample Rotator with Focused Beam
Aperture diameter, inch
VEXP
Samples stationary Decay and geometry VOSS factor'
5/s
'/z
VEXP
2.357 2.505 2.490
4.07 1.47 1.06
0.42 0.47 0.47
"/a
Samples rotating Decay and geometry VOSS factora 1.55 1.39 0.79
0.43 0.49 0.52
1.869 1,864 1.854
For activity produced (2.27-min A128) and for delay and counting conditions (one sample counted for 1 minute after a %minute delay, the other 1 minute after a 4-minute delay) this factor should be 1.842 for a homogeneous beam centered on a uniform target. 0
Table 111.
Relative Standard Deviations for Dual-Sample Rotator with Defocused Beam
Aperture diameter, inch
VEXP
Samples stationary Decay and geometry VOBS factor"
6/8
'/z 3/S 5/1~
VEXP
2.303 2.319 2.308 2.502 2,496
2.95 1.66 0.52 0.59 0.41
0.52 0.53 0.52 0.42 0.40
8/4
Samples rotating Decay and geometry VOBS factor5
0.52 0.52 0.40 0.42 0.40
0.60 0.52 0.41 0.51 0.40
1.846 1.842 1.840 1.842 1.841
a For activity produced (2.27-min Al*s) and for delay and counting conditions (one sample counted for 1 minute after a 2-minute delay, the other 1 minute after a 4-minute delay) this factor should be 1.842 for a homogeneous beam centered on a uniform target.
Table IV.
Reproducibility Data for Dual-Sample Rotator
Unknown sample counts"
Comparator counts"
143,405 140,308 140,803 140.971 151 ;634 163,730 150,127 153,126 153 ;406 143 673
222,361 219,116 218 ,848 218.773 236; 597 254,317 234,409 237,293 237,424 223,802
I
Total
3
= 148,118;
x2
= 2 2 13
UOBS
= (2'13
9"
Normalized samde EOUitSb (XI 148,524 147,469 148,171 148,399 147.598
;
1,481 182 'O')"'
= 487;
(X
-m
-I-406 - 649 53 +281 - 520 148 -623 +495 4-685 - 274 +2
+
+
(X
- B)Z
0 . 1 6 X 106 0.42 0.00 0.08 0.27 0.02 0.39 0.25 0.46 0.08 2 . 1 3 X 106 ~~
VOBS= 0.33%; VEXP= 0.33%
'06 = 14.3; F = 9; P = 0.11
1.48 x 105
a Normalized to an average sample weight (3.722 grams). Data collected over a period of two days. b Normalized to average comparator count (230,300).
VOL. 37, NO. 1 1 , OCTOBER 1965
1341
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.). The 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. The 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. The volume and weight of the packing Apparatus.
