and
where Dv =
counting rate for UX1 per ml of bed counting rate for UX1 per ml of solution
Taking logs and reananging, we get log Dv = log K'
4-2 log (UOz+'),
- 2 log U O Z , + ~
Since (UOz+Z)7is constant, the differential, d l o g Dt/dlog (UOz+') = -2 Hence, a log-log plot 0:'either D, us. UOz+2or D us. UOz+2 concentration should be a straight h e of slope -2. That this is really so, can be seen from Figure 1. In the above calculations, the activity coefficient term in the exchange reaction was ajsumed constant and the possibility of hydrolysis or nitrate coniplexing of U(V1) and Th (IV) was ignored. However, since Th(1V) is a minor component and is more strongly complexed by nitrate than UOz+z,the slope may be more negative than - - 2 at high UNH concentrations.
The data are in good agreement with those of Murase, Lind, and Nelson (5)) who used a 10-ml bed of Dowex 50-X8 to process 2 liters of 0.4M UNH. This corresponds to a feed of 200 bed volumes. Table I shows a D, of 280 at 0.4MUNH, so that the bed volume used was adequate to collect practically all of the UXI present in the feed. It follows from the data of D and D, in Table I that any concentration of UNH in 0.1N nitric acid could be processed to get a quantitative recovery of z34Th(UXI) tracer from natural uranium, provided a proper volume of the resin bed is chosen from these data, The method of employing cation exchange resin, developed by Murase, Lind, and Nelson (5) and Smit et al. (6)and systematically discussed here is rapid, since the ammonium carbonate is readily removed, to get the tracer in carrier-free form. ACKNOWLEDGMENT
The author is grateful to Frederick Nelson, Oak Ridge National Laboratory, for his suggestive comments on the discussion part of this paper. RECEIVED for review August 2, 1966. Accepted November 30, 1966.
Conditions for Optimum Sensitivity in Thermogravimetric Analysis at Atmospheric Pressure Lee Cahn and Norbert C. Peterson Cahn Instrument Company, Paramount, Calif. WEIGHTSENSITIVITY is it critical parameter in thermogravimetric analysis (TGA). Finer sensitivity permits improved precision and accuracy with a given sample size, or reduction of sample size for a given precision level. Smaller samples will give sharper resolu :ion and more accurate temperature values at a given scanning rate, or permit faster scanning for the same level of performance. Or, benefits may be taken in all of these parameters. The situation can be compared with that already shown for differential thermal analysis (DTA) (1). Balances are now available (2) with sensitivities of 0.1 pg in room air, and in vacuum at elevated programmed temperatures. Larger fluctuations in TGA in air at atmospheric pressure mu st then be explained by real physical phenomena associated with those being measured, such as aerodynamic forces on the sample, rather than as balance artifacts. Sensitivities finer than 1 pg can be attained under either of two conditions (3): in sample hangdown tubes of 9-mm inside diameter at atmospheric pressure, or in larger tubes at reduced pressures (41-mm i.d. at 150 torr). The 9-mm diameter tubes limit sample size to about 15-20 mg, and require some care in tube alinement. The reduced pressures require a vacuum pump and may be less convenient when flowing gas streams are used. There has thus been interest in operation with larger tubes at atmospheric pressure with and without flowing gas streams.
(1) C. Mazieres, ANAL.CHEM., 36,602 (1964). (2) L. Cahn and H. Schultz, "Vacuum Microbalance Techniques," VoI. 3, p. 29, Plenum Pres, New York, 1963. (3) L. Cahn and H. Schultz, ANAL.CHEM., 35, 1729 (1963).
I50
4. &
100
50 0 1
0 ID
-
MM
Figure 1. Noise, pg peak-to-peak us. inside diameter of sample tube, in air at atmospheric pressure
A systematic investigation was undertaken to determine the effect on sensitivity of tube diameter at atmospheric pressure, the limiting pressure for 1 pg noise as a function of tube diameter, and the effect of flowing gas streams. EXPERIMENTAL
All measurements were made using a Cahn model R G Electrobalance in a glass vacuum bottle (2-4) with chromelalumel thermocouple. A Marshall No. 1804 furnace, rated to 980" C, was programmed manually with a variable autotransformer at about 10" C/min. All runs were made from ambient to 950-80" C. Sample tubes were quartz or Vycor, of the various diameters reported. For the flowing gas runs, tubes of the Cahn Flothru ( 4 ) type were used, about 780 mm (4) Bulletin 119, Cahn Instrument Co., Paramount, Calif. VOL. 39, NO. 3, MARCH 1967
4
403
1
g+2, 3 lt
87
7
0 -2 I
1
Figure 2. Portion of blank thermogram between 850900" C in still air at atmospheric pressure, 16-mm i. d. tube
long, with standard taper inner joints attached at the top and bottom of the sample tube for inlet and outlet, respectively. Tubes for static atmosphere were about 550 mm long. Gas flow was regulated with an inexpensive pressure regulator and orifice, so that flow into the tube was independent of the flow resistance beyond the orifice. The regulator was a Bastian-Blessing No. 2403 Rego low pressure regulator (5-10 inches of Hg) with a T10 setting. A National Welding Co. needle valve was used as the orifice, and a Fischer and Porter No. 08F-1/16-08-4/36 0 Flowrator flowmeter was used to measure the air flow rate. All runs were made with a Pt sample pan, and nichrome or Pt stirrup. Total load on the sample suspension was 114 mg, of which about 50 mg was Pt for blank. RESULTS AND DISCUSSION
Static Atmosphere. EFFECTOF TUBEDIAMETER. Figure 1 shows noise as a function of tube diameter in still air at atmospheric pressure. At the larger diameters substantial noise is observed, while at 19 mm there are only 3 pg peak-topeak, readily readable to below 1 pg. At 16 mm the noise is only about 0.5 pg peak-to-peak, readable to about 0.1 pg. Figure 2 shows the portion of a blank thermogram between 850-900" C for a 16-mmi.d. tube. PRESSURE.Figure 3 shows the pressure for 1 pg peak-topeak noise as a function of tube diameter. It may be of value for those who must use larger tubes and wish to use as high a pressure as possible consistent with maximum sensitivity. It crosses the 760-torr level at about 17 rnm, again indicating that tubes smaller than this will have negligible noise. Figures 1 and 3 agree with the previous work (3)where overlap occurs, providing additional confirmation of the measurements. TEMPERATURE. In the course of runs with the larger diameter tubes, where significant noise was observed, maximum noise usually occurred between 150" and 650 C. The region from 650" to 950-80" C was usually more quiet than the lower region, Thus it may be possible to extrapolate these results to even higher temperatures. BAFFLES.Baffles were tried and found to be of little value. With the 19-mm tube, baffles did reduce the noise to below 1 pg peak-to-peak, They were not sufficient at 22 mm and not necessary at 16. It seemed worth the difference of 3 m in diameter to dispense with them.
404
'"-4 - \
I
ANALYTICAL CHEMISTRY
a a
W
a cn cn W a
n
I
0
I
IO
20 ID
I
-
30 MM
1
1
40
Figure 3. Pressure, torr, for 1 pg peak to peak noise us. tube diameter, m m
i+7izEzz3
Z
l
E" - 2
Figure 4. Portion of blank thermogram, 850-900" C, in air flowing at 40 cm/min at atmospheric pressure, in 16-mmi. d. tube
Flowing Gas. TUBEDIAMETER. Noise as a function of tube diameter seems to be the same with flowing gases as with static ones. With a 16-mm diameter tube, noise was less than 1 pg, while with a 19-mm tube pressure had to be reduced to about 500 torr to reach this level. With these initial data, no further work was done with other diameter tubes. NOISE us. GAS VELOCITY.Noise appears nearly independent of gas velocity, from 5 cm/min. t o at least 500 cm/ min., which was the highest velocity studied. At 5 cm/min the noise is less than 1pg, while at 500 it is about 2 pg. The 16-mm tube thus seems ideal for both static and dynamic gas applications. It also seems a good selection for vacuum operation, except where exceptionally large samples must be accommodated. It can conveniently take a sample pan up to 10-12 nun, which can be used for conventional samples up to 150-200 mg if they are required. If we assume that the mean of a noisy trace can be read to of the peak-to-peak variation, the sensitivity limit would be only 0.1 pg for still air, 0.2 pg for 10 cm/min, and 0.4 pg for 500 cm/min.
RECEIVED for review August 22, 1966. Accepted December 21,1966.
