ment on or close to a tabulated value of 12 is an easy alternative to interpolation. Use of the table of the cumulative binomial distribution involves taking the difference between two entries for each ordinate desired and thus is less convenient than use of a table of the individual terms for distributions in which only a single tube is loaded. Craig has stressed the desirability of multiple tube loading as a device for reducing concentration changes during distribution, thereby reducing the probability of nonlinear partition isothernis or, alternatively, of increasing the capacity of the machine for solute. For these reasons, loading of several tubes is common and may in fact become the most frequent situat’ion. Preparation of exact theoretical curves for uniform multiple tube loads involves summing as many binomial distributions as there were tubes loaded. It is here that the cumulative binomial table shows great advantage, as, regardless of the number of tubes loaded, only a single difference between two entries need be taken for each ordinate. Specifically for cases where p 0.5 can be obtained by the relation: E(n, T , p ) = 1 - E (12, n - T 1, 1 - p ) . Consequently, in plotting curves for cases where p exceeds 0.5, valuer for the individual ordinates for the rth tube can be obtained by enterin; the table a t 1 - p and subtracting the (n - T z)th term from the ( n -- r)th term or by entering the table 3 t 1 - p and proceeding as above for cases where p < 0.5-i.e., subtrzioting the (T 3. 1)th term from the (T 1 - z)th term and finally reversing ,he numbering of the tube train, kecping in mind that where more than one tube is loaded the number of tubw involved in the distribution exceeds the usual number by z - 1 tubes. In other words, where 12 is the numller of transfers, the reversal of tube nLinbering is started by labeling the (12 -- z - 1)th tube as No. 0. A simple check on the differencing operations is provided by the sum of the ordinates which should be numerically equal to z, the numbw of tubes loaded. The theoretical curve for uniform tube loading of z tuhes is the sum of z adjacent binomial distributions with the same n and p only if each of the loaded tubes has i ,:: complete upper and lower lsLyer befcie the distribution is started. If only lower layers are loaded, the theoretical curve is the
+
+
+
sun1 of adjacent binomials with variable n. With the tube numbering system above, the apparent value of p indicated by the position of the experimental curve in multiple loaded distributions mill be higher than tho real value of p actually operating in the system. An estimate of this displacement to the right in number of tubes is given by (z - 1)/2. In practice, a trial and error selection of p and final positioning of the theoretical curve is usually carried out. ACKNOWLEDGMENT
The author is indebted to J. C. Lewis for helpful discussion and for bringing the Harvard cumulative binomial table to his attention. LITERATURE CITED
(1) Craig, L. C., Craig, D., “Technique
of Organic Chemistry,” 2nd ed., 5‘01.111, Part I, Chap. 11, Interscience, Neiv York, 1956. (2) Harvard University Staff of the Computation Laboratory, “Tables of
the Cumulative Binomial Probability Distribution,” Harvard University Press, Cambridge, Mass., 1055. (3) Liebermann, 8. U., J . Bid. Chem. 173, G3 (1948). (4) National Bureau of Standards, Washington, D. C., “Tables of the Binomial
Probability Distribution,’ Applied Mathematics Series 6, 1950. (5) Way, E. L., Bennet, B. hl., J . B i d . Chem. 192, 335 (1951).
(6) Weisiger, J. R., “Organic Analysis,” Vol. 11, pp. 277-326, Interscience,
New York, 1954. (7) Williamson, B., Craig, L. C., J . Bioi. Chem. 168, 687 (1947).
Halocarbon Oil as a Mulling Medium for Infrared Igpectra D a v i d S. Crocket a n d Helmut M. H a e n d l e r , University of New Humpshire, Durham, N. H.
a study of the infrared spectra D of ammonium fluorometallate compounds [Haendler, H. M., Johnson, URING
F. A,, Crocket, D. S., J . Am. Chem. SOC. 80,2662 (1958)], it was not possible to use Nujol mulls, because of the interference of the Nujol bands with those anticipated for the compounds. Halocarbon oil, series 11-14 (Halocarbon Products Corp., Hackensack, N. J.), produced excellent mulls, and gave no interference in the region from 4000 to 1300 cm.-l If Halocarbon is used in conjunction with Kujol, the region from 4000 to 650 em.-’ can be studied without interference from the dispersing medium. This particular mulling medium has apparently never been reported. Figures 1 and 2 show the infrared spectrum for ammonium liexafluoro626
ANALYTICAL CHEMISTRY
ferrate(III), (NH&Ft,FE, using a Nujol mull, in comparison T -ith the same compound in a Halocarbin mull. Concentrations in the two mulls are not identical. It is difficult to determine the spectrum of ammonium hexafluoroferrate(II1) in Nujol alone, although
there is a distortion of the Nujol bands. Figure 3 shows the infrared spectrum for Halocarbon from 4000 to 1300 C I ~ I . - ~and Nujol from 1300 to 650 cm.-l indicating the freedom from interference which can be obtained.
ioET:7 : fl= 2 0.2
5 04 Z
a6
08
1.0
I
4WO
Figure 1 . Figure 1 . mull
1
l
I I 1 20w 1800 I600 I400 1200 loo0 800 Infrared !spectrum o f ammonium FREOUENCY, hexafluoroferrate(ll1) CM:’ using a Nuiol Infrared !spectrum o f ammonium hexafluoroferrate(ll1) using a Nuiol
I ”
3530
Figure 2. Infrared spectrum of ammonium hexafluoroferrate(" using a Halocarbon mull
Halocarbon oil series 11-14 has a viscosity similar to that of Nujol, and is as easy to work with. It has been used successfully in this laboratory, not only for inorganic compounds, but for organic compounds as well (Salts] of l-1CIethylpiperidones, Lyle, R. E., Adel, R. E., Lyle, G. G., J . Org. Chem., submi ;ted for publication). The instrument uried for this work mas a Perkin-Elmer h4'odel 21 with sodium chloride optics. ACKNOWLEDGMENT
08 10
4000
BOOO
2CaO
le00
1400
iboo
FREQUENCY
, CM:'
I200
1000
800
Figure 3. Infrared spectra of Nujol and Halocarbon oil showing interferencefree regions
The authors are indebted to Charlotte Lutinski, Perkin-Elmer Corp., for a. literature search on the use of Halocarbon oil as a mulling agent. WORKsupported in part by the Atomic Energy Commission.
Improved Scanner for Radioactive Paper Strips Frank Eisenberg, Jr., and Irwin G. Leder, National Institute of Arthritis and Metabolic Diseases, National lnstituies of Health Public Health Service, United States Department of Health, Education, and Welfare, Bethesda, Md. HE use of gas flow counters [LorvenTstein, S. LI.,Cohen, P. P., Nucleonics 14, No. 5, 98 (1956)l in the scanning of radioactive paper strips has resulted in an improvement over the older, relatively insensitive G-AI scanners [Solomay, S., Rennie, E. J., Stetten, D., Jr., Ibid., 10, No. 4, 52 (1952)]. The structural simplicity and high sensitivity for weak p-emitters of the Forro (Volk Radiocheinical Co.. 5412 North Clark St., Chicago 40, Ill.) iiianual chromatogram scanner have suggested its application to automatic paper strip scanning. By combining the Forro tube with the rigid metal strip carrier and drive mechanism available from the Nuclear Instrument and Chemical Corp., a simple, easily constructed automatic paper strip scanner has been devised which exhibits a reproducible and strictly linear relationship between corresponding points on the chromatogram and the record.
Construction. A Nuclear paper strip G-ilI scanner, previously in use in this laboratory, has been modified by replacement of tlie Jfodel 3031B shield and G-RI tube by the Foryo scanner. The other components-the Xodel 1615B scaler, the Model C-100 strip feeder and metal carrier strip, and the Model AW 1.0-ma. EsterlineAngus recorder have all been retained and can be purchased separately. T o conserve space, the strip feeder is driven by the recorder through a short coupling instead of the long flexible cable originally supplied. I n combining the Forro scanner with
I I
Figure 1. Modified Forro scanner in cornbination with Nuclear strip feeder
,
/I
DRIVE R O L L E R S
the Wuclear drive apparatus certain modifications have been introduced into both components. The scanner, shaded in Figure 1, is inverted with respect to its position in manual scanning, so that the paper is drawn under the tube rather than over. The feature of attaching the paper to a metal carrier strip for scanning has been retained, but because the guides for the carrier strip are part of the discarded lead shield, a new guide system has been devised. Flexafranie posts, grooved inch deep), have been mounted on the strip feeder base plate, tlie grooves serving to keep the carrier strip level in its passage through the rollers. Both posts are threaded and screived into tapped holes in the base plate; the right-hand post is threaded up to the groove. The height of the grooves is adjustable by turning the posts in or out. Lock nuts a t the base hold each post a t the desired height. The right-hand post
also supports the scanner and is mounted so that the scanner is as close to the drive rollers as possible and with the center of the window (,entered on the rollerb. Sufficient clearaiice should be provided to enable the sc'anner t o be raised for cleaning or replacing the window. A hexagonal nut, held in place by :I sctscrew tapped ir t o one face, maintains the instrument a t its proper height. Both posts are located symmetrically about the centei- line of the base plate. To keep the carrier strip moving a t right angles to the scanner and in close approximation t o the window, a rabbct inch wide x 7/32 inch high) has been milled frori the scanner block. The paper strip is held snugly against the n indow by 1hree polished aluininuni pins (1,~'~-inch dirtmeter), mounted on tlic scailner block a 3 s1ion.11 in the diagram. Pins 1 and 2 (each 12 mni. from the center of the tube) maintain the curvature of the paper around the tube; the third pin (4 mm. behind and 7 mni. below the second pin) provides ad& VOL. 31, NO. 4, APRIL 1959
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