CORRESPONDENCE
Evidence for Coupling in Chromatographic Columns SIR: In recent years much controversy has existed over the relative merits of the equations for the height equivalent t o a theoretical plate (HETP) proposed by van Deemter et al. (I) and by Giddings (2). Discussions have been presented on the application of these equations to columns packed with nonporous, inert particles (3-5). For this simplified case the equations may be written as shown below:
h = - +2Y2 2 X
(1)
V
[due to van Deemter et al. (I)]
27 h=-+v
1
-2x+ - wvl
(2)
l
[coupling equation due to Giddings (2)] where h = reduced HETP = H/d, H = height equivalent to a theoretical plate (HETP) dp = particle diameter v = reduced velocity = udp/D u = mean interstitial velocity
(1) J. J. van Deemter, F. J. Zuiderweg, and A. Klinkenberg, Chem. Eng. Sci., 5,271 (1956). (2) J. C. Giddings, J. Chromatog., 5,61 (1961). (3) A. Klinkenberg, ANAL.CHEM., 38, 489 (1966). (4) J. C. Giddings, ibid., p 490. (5) A. Klinkenberg, ibid., p 491.
diffusion coefficient proportionality factor in eddy diffusion term ( I ) y = tortuosity factor ( I ) w = factor derived by Giddings (6) D
X
In correspondence on Equations 1 and 2 (3-5) it is stated that evidence in favor of the “coupling equation” has been found by Knox (7) who studied liquid systems. However, there has been little conclusive evidence of coupling for nonsorbing, gaseous systems operated under near ambient conditions of temperature and pressure. A study under such conditions has recently been made by Edwards and Richardson (8). In this work, details of which are presented elsewhere (8), pulses of argon were injected into a stream of air flowing through a column packed with glass beads ; all experiments were conducted at room temperature and pressure. Measurements were taken which allowed the HETP to be calculated, and the results are presented in Figure 1 as a plot of reduced plate height h against reduced velocity v. These results have been confirmed by Pryce (9). Many studies of flow in nonsorbing packed columns for both gas and liquid systems are reported in chemical engineering literature; a recent review of this work has been made by Gunn (10). From work at low values of reduced velocity, (6) J. C. Giddings, ANAL.CHEM. 34,1186 (1962). (7) J. H. Knox, ibid., 38, 253 (1966). (8) M. F. Edwards and J. F. Richardson, Cliem. Eng. Sci., 23, 109 (1968). (9) C. Pryce, Ph.D. Thesis, University of Wales, 1967. (10) D. J. Gum, Trans. Inst. Chem. Eng., 46, CE 153 (1968).
Column aiorneter
A\
a, 10
-
40
-
= =
\,
Particle s i z e s
-
x
+ o
b
8 . 2 5 crn 0,607 0,607cm C.300cm
0 ;Z03Cm 0;Z03cm
‘0,073cm
0,OSBcrn
h
I
-
’
EquatLon(2) (W 0.43)
0.4I 0.04
1
0‘4
I I
I (0
400
v
Figure 1. Experimental results of reduced plate height us. reduced velocity VOL. 41,NO. 2, FEBRUARY 1969
383
where peak spreading is controlled by molecular diffusion, it is concluded that y = 0.7, while from work at high reduced velocity, where the convective process of eddy diffusion predominates, the value X = 0.5 is indicated (8, IO). These values of y and X can be substituted into Equation 1 and the resulting relationship is presented in Figure 1. It is clear that Equation 1 does not represent the data adequately; however, as pointed out by Klinkenberg (5), Equation 1 does predict the correct asymptotic behavior at high and low values of reduced velocity. Using the same values of y and X in Equation 2, a good fit is obtained with the experimental data (see Figure 1) using the value w = 0.10. However, Giddings (6) has proposed a value of w = 0.43 for nonporous, inert packing materials. The effect of adopting this value is seen in Figure 1. It would appear, therefore, that while the form of the coupling equation is accurate in describing the characteristics of the h-v data, the value of w predicted by Giddings (6) is subject t o some uncertainty.
It is worthy of note that the data presented in Figure 1 indicate n o variation with particle size in the h-v relationship. This finding is confirmed in many of the studies reviewed by Gunn (IO), who concludes that the h-v relationship is independent of particle size provided that the ratio of column diameter t o particle diameter is greater than about 12. Finally, it is clear that much of the literature on flow in packed beds, which is reported in chemical engineering journals, is directly relevant t o work on chromatography, and vice versa. However, there has been very little attempt to bring together the results in these two fields of study. M. F. EDWARDS School of Engineering Science University of Warwick Coventry, England RECEIVED for review August 19, 1968. Accepted October 7, 1968.
AIDS FOR ANALYTICAL CHEMISTS r
E. A. Mershad, M. L. Curtis, J. Y. Jarvis, and W. R . Amos Mound Laboratory, Miamisburg, Ohio 45342
To
MEET Atomic Energy Commission nuclear material accountability requirements and to improve the efficiency of 238Pu recovery operations, a procedure was developed for determining the amount of 238Puin wastes removed from glove boxes. For recovery purposes, 2asPu contaminated waste consisting of ion exchange resin, paper, rags, polyethylene, glass, and metal is segregated into various categories, such as resin, combustibles, and noncombustibles, prior to removal from glove box lines. The material is packaged in 1/2-gallon cans, 13.81 cm in diameter and 14.92 cm high, removed from the glove boxes in polyethylene bags, and packaged in 1gallon cans, 15.72 cm in diameter and 22.23 cm high. The 1-gallon cans are sealed by a special canning apparatus and enclosed in a polyethylene bag as a final precaution against alpha contamination. Each can, labeled with the appropriate waste category, may contain 238Pu ranging from negligible quantities to 10.3 grams. The 100-keV photons from 238Pu (1) were counted by a gamma pulse height analysis procedure. The method is relatively rapid, applicable to many types and densities of waste material, and accurate in the 16-mg to 10.3-gram concentration range.
EXPERIMENTAL
Apparatus. A schematic of the physical arrangement of equipment is shown in Figure 1 . Although the dimensions
(1) E. K. Hyde, I. Perlrnan, and G . T . Seaborg, “The Nuclear Properties of the Heavy Elements,” Vol. 11, Prentice-Hall, New York, N. Y . , 1964, pp 811-12. 384
0
ANALYTICAL CHEMISTRY
are not critical, recalibration is required if the geometry is altered. A 1-gallon can of waste is placed o n a turntable which is rotated at approximately 10 rpm. To correct for gamma absorption due to the variation in density of the waste, four calorimetered samples, each containing 5 grams of z3*Pu(as the dioxide), are used as external standards. This material is contained in stainless steel capsules 1.91 cm in diameter and 5.08 cm high. These capsules are placed in secondary aluminum capsules 2.70 cm in diameter and 6.67 cm high. The standards are mounted 0.32 cm apart in an aluminum brick to minimize scattering effects, ensuring that only those photons passing through the waste material are detected by the crystal. The detector is a 5-inch diameter by 1-inch thick NaI(T1) crystal, (Harshaw Chemical Co., Type 20MB4/A-X) with a n RIDL Model 10-17 scintillation detector preamplifier. The front and sides of the crystal are covered with 0.5-mm cadmium sheet to reduce neutron interference. When waste containing less than 1 gram of 238Puis assayed, a 0.64-cm stainless steel plate is placed between the crystal and the waste. With waste containing more than 1 gram of isotope, the 0.64-cm plate is replaced by a 1.27-cm plate. Not shown in Figure 1 is the shielding to reduce background levels. The external standards, sample, and detector system are shielded on four sides and on the bottom with 25.4 cm of polypropylene sandwiched with 0.64 cm of lead sheet. The instrumentation for measuring the gamma radiation is a 400-channel analyzer (RIDL Model 34-12B). Data printout is attained with a Friden printer (Model 44-10). The system is calibrated to 5 keV per channel, and the integrated counts under the 100-keV peak (channels 18 through 22) are used in the determinations. Background is stored in the first quadrant of the analyzer memory and is automatically subtracted from the sample data which are stored in the second quadrant.
