An analysis of commercial cpesylic acid (Koppers) is illustrated in Table I1 and is based on the following assump tions. All phenolic components were
RESULTS AND DISCUSSION
Separation of Esters. A mixture of equal weights of the trifluoroacetates of the 10 lowest homologs of methylated pheno. (phenol, three cresols, and six xylenols) was completely resolved into its 10 components on a 2-meter GLC column at 7 5 O C. The substr,ite employed was a 3 to 1 mixture of :'lO-silicone oil and tri-o-phenylphenyl phosphate on 80 to 100-mesh firebrick. This separation is shown, with peak identities, in Figure 1A . The use of the same column, but at 108' C. permitted the' separation of nine of the remaining 10 polymethylated isomers as shown in Figure 1B. The retention times of the ester of 2,4,6-trimethylphenol and that of 3,4-xylenoI did not permit separation, thus there are only 19 peaks evident.
methylated homologs and their identities assignable by retention timea alone; all conversions to trifluoroacetate esters were achieved in equal yields; aad the quantities present were proportional to integrated areas. Several limitations to this method of analysis have been found. The esters are not atable in the presence of water; traces of free acid catalyze hydrolysis. Also, as mentioned above, sterically hindered phenols react slowly and incompletely, thus jeopardizing quantitative reliability in analysis. Nonetheless, the method has been shown to be useful in the resolution of polyalkylated phenols and naphthols.
~~
Table II.
Components of Cresylic Acid
(In order of emergence) Phenol 0.3% 0-Cresol 0.4% m-Cresol 2.9% pCreSol 1.7% None 2,6-Xyleno 1 2,5-Xylenol 4.2% 2,4Xylenol 22.6% 3,5-Xylenol 51.3% 2,3-Xylenol 5.7% 3,4Xylenol 6.6% Unknown 4.3%
(3) Caaruthers, W., Johnstone, R. A. W., Nature, 185, 762 (1960). (4) Fitegerald, J. S., Australian J . Appl. Sci., 10, 169 1959). (5) Langer, S. ., Pantsges, P., Wender, I., Chem. Ind. London, 1958, . 1664. (6) Weygand, F., Ropsch, A., R e m , Ber., 92,2095 11959).
fI
LRERATURE ClTED
(1) Bourne, E. J., Stacey, M., Tatlow, J. C., Worrall, R., J . Chem. Soc., 19M,
3268. (2) Brooke, V. T., Chem. I d . London, 1959, p. 1317.
ALEXANDER T. SHULQIN
The Dow Chemical Co. Walnut Creek, Calif.
RECEIVED for review December 20, 1963. Accepted January 13, 1964.
Effect of Pressure Gradient on Chromatographic Column Efficiency SIR: Effect of pressure gradient on gas-chromatographic column performance has been misunderstood and misinterpreted in the past; the current publication by Giddirigs (2) does much to clarify the true role of this factor. This communication attacks the problem from a somewhat different and more pictorial viewpoint, which i t is hoped will serve to amplify the treatment of Giddings. The familiar plot of plate height us. linear velocity, from the modified van Deemter equation, as rhown in Figure 1, has led to much, ccnfusion, because there has been a tendency to overlook
the fsct that it represents the effect of linear velocity on plate height a t a fixed value of the gttseous diffusion coefficient. It is applicable to a series of runs made a t successive values of, for exaniple, the outlet linear velocity. It is not, however, applicable to considerations of the effect of the linear velocity changes that are caused by decompression within the column in a particular run at a given outlet linear velocity, because under these conditions the diffusion coefficient is not constaut as the velocity changes. I n the equation for local plate height, H;,
where in a single run, ua and D,. are constant, and the plot of H; us. u; a t fixed u,, becomes a straight line, as shown in Figure 2. Thus, at the head of the column, where the local pressure, p i , is high and ui is low, the local plate height is somewhat lower than at the tail of the column where p; is lower and ui is higher. It is thus entirely incorrect to state that when the optimum linear gas velocity is used, the front of the column operates a t too low a velocity, increasing the HETP, while the tail of the column is operating a t too high
Velocity, u;, and diffusion coefficient, Do;,values are those which apply at the point (2) considered. However, U;P;
=
UaPa
* DwPa U Figure 1. Typical van Deernter plot of plate height vs. linear velocity for a series of runs at differtent linear velocities
where the subscript a denotes atmospheric pressure. The equation can then be written as
ut =
Po "0
PZ Figure 2. Local plate height vs. local linear velocity in a column during a single run VOL 36, NO. 4, APRIL 1964
e
921
a linear velocity, also increasing the HEPT. This is apparently a reasonable enough conclusion from the usual plot of the van Deemter equation as shown in Figure 1. Furthermore, when the decompression effect is taken into account (1, 3, 4), it is seen that a local plate height contribution made a t high pressure makes a greater _contribution to apparent plate height ( H ) than a similar local plate height contribution made at lower pressure, as shown by the equation
When the pressure gradient is small,
( ~ ; / p 3does ~ not differ significantly from unity anywhere in the column, but when the pressure gradient is large, ( ~ , / f i ) ~large i s a t the head of the column and small at the tail of the column. Thus, the head of the column makes a greater than normal contribution to apparent plate height, while the contribution of the tail of the column is reduced. The net effect of inlet-tooutlet pressure ratio on apparent plate height is, therefore, not significantly large, contrary to the earlier published views. What is significant, however, is the improvement of apparent plate height a t high average column pressure as compared with low average column pressure, although this gain is also nullified if speed of analysis is con-
sidered, since the number of plates obtainable per unit time under otherwise equal conditions varies inversely with pressure. LITERATURE CITED
( 1 ) Giddings, J. C., ANAL. CHEM.35, 353 (1963). (2) Ibjd., 36, 741 (1964). (3) Giddings, J. C., Seager, S. L., Stucki, L. R.. Stewart. G. H.. Zbid.. 32. 867 (1960j. (4) Sternberg, J. C., Poulson, R. E., Zbzd., 36, 58 (1964). I
.
JAMES C. STERNBERQ Beckman Instruments, Inc. Fullerton, Calif. RECEIVED for review December 31, 1963. Accepted February 3, 1964.
Time Dependence of A.C. Polarographic Currents SIR: Considerable interest has attended the study of time dependence of d.c. polarographic currents. Examination of the variation of d.c. currents with mercury column height (varying drop-life) or the more sensitive studies of instantaneous currents over a single drop-life are of considerable use in d.c. polarographic studies of kinetics and mechanisms of electrode processes. Charge transfer, homogeneous chemical reactions, adsorption, depletion, and stirring effects all show characteristic influence on such investigations under suitable conditions (6, 7 , 12). Similar studies of ax. polarographic currents have not been reported. Most likely responsible for this is the fact that, until recently, a x . polarographic and faradaic impedance theory suggested no useful application of such measurements. Early theoretical work on the reversible and quasi-reversible (2) a.c. polarographic impedance indicated no time-dependent terms except for very short-lived transients (1) and the electrode area when the dropping mercury electrode is employed. If such is the case, then the faradaic alternating current amplitude observed at a dropping mercury electrode will be independent of mercury column height and will vary with t213 (t = time) over the life of a single drop. Phase angles between faradaic alternating current and applied alternating potential were predicted to be timeindependent, even with the dropping mercury electrode-i.e. , phase angles are independent of electrode area. These conclusions alone would suggest that little is to be gained from investigations of a.c. polarographic current dependence on mercury column height or a.c. polarographic current-time curves. However, the recent, more rigorous theoretical work of Matsuda 922
e
ANALYTICAL CHEMISTRY
(8) on the a s . polarographic wave with electrode processes controlled by diffusion and charge transfer kinetics (the quasi-reversible case) indicates that the simple behavior predicted by earlier theory is not always t o be expected. Influenced by Matsuda's work, we have undertaken a theoretical and experimental investigation of the time dependence of a x . polarographic currents. This communication deals with some preliminary conclusions. A more detailed account will be given a t a later date. THEORY
Matsuda's equation for the a.c. polarographic wave with a quasireversible electrode process and an applied alternating potential given by
E(t) =
Ed.c.
- AE sin ut
(1)
may be written (for small values of A E and reduced form of redox couple initially absent from solution) (8)
I ( d ) = I(rev.)F(W2) X
sin [ut
+ cot-'
(1
+
e)] (2)
@ = l - a
D = Do@DRa
f
(1.61
+
(1.13 -I-Ati/z)z
(3)
(4)
(7) (8)
and Z(rev.) is the amplitude term for the reversible a.c. polarographic wave given by n2F2ACo*( ~ D o ) ~ / ~ A E I (rev.) = (9) j 4RT cosh2 2 Notation used in this communication is identical to that used in a previous publication (13). These equations predict a time dependence, incorporated in the F(W2) term, not predicted by earlier theory. Matsuda's equations apply to the expanding plane electrode (8),a simplified model for the dropping mercury electrode. However, one should not conclude that the additional time dependence is introduced by drop growth, a factor also not considered by earlier theory. One can show easily, using Matsuda's approach, that for diffusion to a stationary plane electrode the a x . wave equation is identical t o Equation 2 except for the definition of F(XtlI2). For diffusion to-a stationary plane electrode, F(Xt1'2) is given by (16) F(XtlI2) = I (ae-'
+
where
= f08fRQ
(6)
- fl)ehZterfc(Xtllz) (IO)
Thus, time dependence also may occur with a stationary electrode. Drop growth influences the magnitude of the time dependence, but is not its source. The F(W2) term indicates that, with the dropping mercury electrode, a departure from the independence of the alternating current amplitude on mer-
