binding power for that solvent. In an R P P C experiment patterned after the one by Hamlin et al. (2) on the separation of uranyl ion and a copper(I1) impurity using nitric acid as the mobile phase, we found that TBP imbibed on microporous polyethylene granules is a stable, effective stationary phase. Uranium as uranyl ion could also be extracted from aqueous solution on to a bed of a liquid ion exchanger immobilized on nicroporous granules. Using as stationary phase a n equimolecular mixture of mono-2-ethylhexyl phosphoric acid and di-2-ethylhexyl phosphoric acid, uranyl ion was extracted from an aqueous solution of uranyl nitrate. It could be eluted from the bed with concentrated hydrochloric acid.
DISCUSSION
LITERATURE CITED
( 1 ) Green, T., Howitt, F. O., Preston, K., Chem. Id.1955, 591. (2) Hamlin, A. G., Robert, B. J., Loughlin, W., Walker, S. G., ANAL. CHEW 33; 1547 (1961). (31 Pierce. T. B.. Peck. P. F.. Xatirre 194,84 (1962). ’
The relative ease with which one may immobilize a variety of organic solvents suggests that microporous polymeric granules should greatly extend R P P C techniques. Important classes of compounds such as steroids, soluble ribonucleic acids, pesticides, and low molecular weight proteins may be isolated and separated advantageously using the chemically inert polymeric granule carriers. Preliminary results suggest the granules may be useful stationary phase carriers in low temperature gas chromatography as well as in liquidliquid partition chromatography.
.
I
WALTERA. WINSTEN Department of Chemistry Hofstra College Hempstead, L. I., N. I’. RECEIVEDfor review May 28, 1962. Accepted July 16, 1962. The subject matter of this communication was presented at the Metropolitan Regional Meeting of the American Chemical Society in New I’ork City, January 22, 1962.
Third and Fourth Harmonic Alternating Current Polarography SIR: Theories of the faradaic hipedance which take account of its nonlinearity (3) lead to the expectation of components of current of all harmonics when a sinusoidal potential is superimposed on the d.c. potential applied under conventional polarographic conditions. Using apparatus described by Smith and Reinmuth ( 5 ) , and applied by these workers to study of second harmonics, we have obtained third and fourth harmonic polarograms. Typical examples are shown in Figures 1-3. Second, third, and fourth (and presumably higher) harmonics share the advantage over the fundamental that contributions from the nonfaradaic double layer charging current are significantly lower because of the better approximation to linearity of the double layer process. The amplitudes of the successively higher harmonics at small amplitudes decrease roughly with
the inverse power of the harmonic. This is reflected in the experimental polarograms shown; the amplitudes of the applied alternating potentials (-50 mv.) were of necessity much larger than those usually employed in fundamental measurements. In addition, the theoretical expressions describing the higher harmonic components become progressively more cumbersome in form. Thus, both experimental and theoretical considerations suggest the virtues of second as opposed to third and fourth harmonic measurements in analytical applications. First through fourth harmonic polarograms in simple systems show one through four peaks a seriatum. Theory indicates that for the simplest case, diffusion limited Nernstian (reversible) charge-transfer, the forms of suc-
cessively higher harmonic alternating current polarograms should be those of successively higher derivatives of the corresponding conventional d.c. polarogram. The curves shown have qualitatively this behavior, but with the modification that, because of rectification of the detector output before recording, the absolute values of the derivatives rather than the derivatives themselves are suggested. Presumably phase sensitive detection would show alternate positive and negative peaks with the most anodic peak being positive in each case. Positive and negative are used laxly here to denote relative phase angles. The relative peak heights of the third harmonic polarogram of a reversible process should be in the ratio 1 to 3 to 1. Ferric oxalate closely ap-
w
a a
3
0
-0.45
Figure 1. Third harmonic polarogram of 10-VA Fe+a in 0.3M K&OI, 0.1M H2C204, 0.05M KCI Applied: 50 mv. p.p. 50 c.p.r. M e o w e d : 150 c.p.r. component Peak hdght: 2 pa. p.p.
- 0.50
-0.55
- 0.60
-0.61
POTENTIAL (VOLTS) Figure 2. Third harmonic polarogram of 1 O - W Cd t2 in 1M KNOa Applied: 50 mv. p.p. 50 C.P.S. Measured: 150 c.p.r. component Peak height: 7.7 pa. p.p.
VOL 34, NO. 10, SEPTEMBER 1962
1335
Figure 3. Fourth harmonic polarogram of 1 O-3M Cd +2 in 1M KNOI Applied: 60 mv. p.p. 37.5 c.p.r. Measured: 150 C.P.S. component Peak height: 3.3 w . p.p.
The spread of thr po1rrogr:im along the potential axis should be related reciprocally to the number of electrons involved in charge-transfer. For example, the separation of the two satellite peaks in the third harmonic polarogram for a reversiblc reaction should be 120;n mv. (at 30" C.). Again ferric oxalate shows expected behavior (-130 mv.) while cadmium nitrate does not (-90 mv.). LITERATURE CITED
( 1 ) Bauer, H. H., Elving, P. J., J. Am. Chem. SOC.82, 2091 (1960).
(2) Bauer, H. H., Smith, D. L., Elving, P. J., Ibid., 2094. (3) Matsuda, H., 2. Elektrochem. 61, 489 (1957). (4) Paynter, J., Reinmuth, W. H., Ab-
proximates this behavior (Figure l ) , while cadmium nitrate does not. The cadmium polarograms show distinct deviations from ideality in both third and fourth harmonic polarograms, Figures 2 and 3 (also in second har-
rnonic and intermodulation (4) polarograms). Anomalies have also been noted in the fundamental (I, 2) a1though generally a t much higher frequencies. This case will be discussed further in later work.
stracts, Analytical Division, 140th Meeting, ACS, Chicago, September 1961. ( 5 ) Smith, D. E., Reinmuth, W. H., ANAL.CHEM.33,482 (1961). JOHXPAYNTER W. H. REINMUTH De artment of Chemistry CoErnbia University New York 27, N. Y.
Evaluation of Liquid Mass Transfer Coefficients in Gas Chromatography SIR: Several variants of an extended rate equation for chromatography have recently been proposed (1-4, 6-8). One form (1, 2) which has been shown to be satisfactory for R number of gas chromatographic s y s t e m is: H =A
+ B0/uo + Coouo + Cruoj
wherein the zeros symbolize column outlet conditions and f is the JamesXlartin compressibility correction factor. The other quantities have their usual significance and their evaluation from H / u data is normally a lengthy process. A rapid method of evaluation of C I is based on the following argument. The constants Bo and C," are directly and inversely proportional, respectively, to the gas phase interdiffusion coefficient a t the column outlet pressure, D,". Thus, if measurements of H for a given column and solute are made over a range of velocities, with different carrier gases, or with the same carrier a t different column outlet pressures, we have HI = A
1336
+
Blo/(uo)l
+ (CsOu~h+ Cizil
ANALYTICAL CHEMISTRY
and HZ= A
+ B Z ~ / ( U+Q )( ZC o o u +~ ) Ciaz ~
where, for convenience, zi replaces Qf. Hence, if values of H , and H z are chosen such that (UO)~/(UO)~ = (D:)I/(D,O)athen, terms in A , BO, and C,O should be equal and, on subtraction, A H = Ci (zii
- az) =
CtAG
From this equation, numerous values of Ci can be rapidly deduced from any appropriate pair of H / u curves. The test of the equation lies in its ability to
0.14
1
15 30 uo (CM. SEC. -1)
45
Figure 1. Plot of H vs. outlet carrier gas velocity, uo, (75 measurements) for elution of n-butane at 40.7' C. Upper curve, hydrogen
give consistent values of C I over a wide range of velocities, in particular a t low velocities where CIZ?contributes little to H . Figure 1 shows Hluo data for the elution by hydrogen and by nitrogen of n-butane a t 40.7' C. The column used was 150 x 0.4 cm. and contained 20% by weight octadecane/hexsmethyldisilazane treated 100- to 120-ASTM mesh Sil-0-Cel. For elution of almost any solute by Hz and N2 a t the same rolumn outlet pressure the ratio ( U O ) ~ % / ( % ) N ~= 3.8 represents a reasonable general choice. Values of uo, in this ratio, used for calculation to test the above argument are shown in the figure by tie lines; the relevant values of AH and Ati, and the derived values of C Iare listed in Table I. The consistency of the data, which relate to a velocity range as broad as 2 to 60 cm. per sec., is convincing evidence of the practicability of this method of obtaining reliable values of Cl. In the simplest experiments, two elutions only would be needed. The method depends on the assumed dependence of C,O and BO on :)I and the
