Influence of Injection Time on the Efficiency of Gas Chromatography Columns SIR: For some years much work has been devoted to the study of the efficiency of columns in gas chromatography and the numerous factors which may influence it. The influence of the injection time seems to have been completely neglected. I n fact this time is never zero and in some circumstances may play a major role in limiting the performance of the column. THEORETICAL
I n almost every case the injection is considered as a 6 function and the chromatographic process gives to the zone eluted from the column a standard deviation u,the H E TP being given by: HL (1) where L is the column length. u may be related to various phenomena (diffusion, mass transfer, etc.), each giving an additive contribution to H . To estimate the influence of inJection time on the HETP, we shall assume that the concentration of the solute in the carrier gas a t the entrance of the column is given by a Gaussian function. This is an approximation but it seems far better than a 6 function or even a square function (C = 0 when t < 0 or t > E ; C = Co when 0 < t < e). For an automatic injection, or in the hands of trained manipulators, the injection u2 =
-I€
time and thus the standard deviation of the assumed Gaussian function may be regarded as constant. The injection process is completely independent of the other spreading phenomena a t work in the column (1). Thus, this process adds a constant term to the zone variance insofar as the standard deviation in time 7 is considered. The use of the standard deviation in distance u is more conventional. u is the length along which the zone is swept in a time 7 . so: u =
T.RU
where R is the ratio of zone velocity to gas velocity u; R < 1. To obtain an expression for H we need only to add the term u2 to the conventional ones as in the van Deemter equation; this gives the standard deviation of the zone after the chromatographic process has occurred, when a zero time of injection is not assumed. u2 =
LHo
Table 1.
Example of Contribution of Injection Time to HETP
cm. per L, R second cm. 0.4 10 200 0.5 20 100 u,
7,
seconds 0.25 0.5
Table II.
2.5
Column Parameters
Column 1 Length (meters) Temp. ( " C.) Phase
Ht, mm. 0.05
Column 2
0.50
6
25
80
5% DC 703
silicone oil on firebrick Gz
Size (mesh) 30/60 Compounds Air & n-CTHie used R values Air: 1 n-CTHie: 0.09
Activated alumina 120/150
n-CsH12 & n-CsHtr n-CsHlz: 0.24
n-CsHia: 0.075
+ T'R~uZ
As it may be expected, the new term is negligibly small for strongly retained compounds. Table I gives an order of magnitude for two cases. This shows that, especially for fast analyses, great attention is necessary
to keep sufficiently small the contribution of injection time to zone spreading. It is difficult to find a good relationship between the standard deviation 7 and the injection time t as usually measured-Le., time between the instant when the plunger begins to be pushed down and the instant when its motion is finished. It seems reasonable to assume for t a value of between 4 7 and
s 7. 3
i /'+ 2
u = 2 0 c m./ sec.
1
10
20
30 t'( sect)
Figure 1 . Variation of H with square of injection time (column 1 , air)
500
0
Figure 2. air)
Variation
uL ( c r n ' . see.?)
1000
of H with square of flow rate (column 1, VOL. 35, NO. 3, M A R C H 1963
399
EXPERIMENTAL
Table 111.
The study was made with apparatus carefully designed for fast analyses. The catharometer is of a new design, having a dead volume of 40 pl. and a response time of less than 0.1 second, the recorder (Graphispot, S.E.F.R.A.M., Paris) has a time constant of 0.25 second. Experiments were made with two columns described in Table 11. Values of H were measured for different values of injection time using several flow rates; the beginning and the end of the injection were recorded on the chromatogram using a margin marker. Typical results for air peaks are shown Figures 1 and 2. From these results i t may be concluded that H is given by the expression: H = H oh + t2R2u2 7
Values of X
Solute
Column 1
Air n-C6 n-Ca
0.027
n-C,
0.07
Column 2
... ...
0: 005
0.030
...
H O being the conventional expression of H.E.T.P. as previously given and discussed ( 1 ) . Table I11 gives the values of h found in our experiments. Some discrepancies may be noted, especially for n-pentane on column 2, but the results do not shorn any trend. These values are consistent with a n injection time equal t o 6 T which gives a of 0.028. This value may of course depend on the manner in which the beginning and end of the injection are appreciated. These experiments are
not sufficient t o ascertain this last point but the dependence of H on the square of t, R, and u,and the inverse of L is supported by the experiments reported here. Two conclusions may be drarrn: careful attention must be paid t o the design of injection system when very fast analyses are sought; when a van Deemter curve is drawn for a column, a constant injection time is used. Thus, for a large flow rate the new term becomes very important and H increases with u2. LITERATURE CITED
(1) Giddings, J. C., "Chromatography," Erich Heftman, ed., pp. 20-31, Reinhold, S e w York, 1961. GEORGES GUIOCHON
Ecole Polytechniyue Paris, France for review October 22, l%2. RECEIVED Accepted Ileceniber 12, 1962.
Chronopotentiometry at Rotating Disk Electrodes SIR: Interest in rotating disk electrodes is steadily increasing among students of electrode processes ( 5 ) probably because the theoretical behavior for both reversible and irreversible processes is developed, use of the electrodes is convenient, and results are remarkably reproducible. Attention has been given to experimental studies using constant potential electrolyqis ; although rotating disks have been useful also for constant current processes. For instance, chronopotentiometry a t moving electrodes is possible, but does not appear to have been reported in the literature. At first glance, such an application may not seem feasible because convection limited processes are not so conveniently controlled a5 diffusion limited processes. Our preliminary data suggest that chronopotentiometry a t rotating disk electrodes is possible, but t h a t reproducibility of transition times is not so great as n a s originally hoped. It has been found, experimentally, that id 2 becomes nearly constant for a given rotation speed a t sufficiently large applied constant currents. The available range moveq t o of current for constant i+ higher values with increasing rotation speeds and the greater double layer charging current produces positive del iations in i+. A mathematical treatment of the transition time can be given and some important results are reported here. When i t is assumed that diffusion prevails n-ithin the boundary layer of thickness 6 (the Levich thickness)
400
ANALYTICAL CHEMISTRY
and convection determines the concentrations outside, the boundary conditions for the reaction 0 ne- + R are :
+
C o ( ~ , t )= Coo
z
b0
t = 0
(la)
It has been shown in slightly different form by Bowers, et al. ( 3 ) that: C,(O,t)
=
where the term on the right side of Equation 3, preceding the bracket, is the fundamental constant of a static chronopotentiometric experiment. This equation predicts that i r 1 I 2 and r increase ivith decreasing values of current for a given value of 6. I3y writing boundary conditions given in Equations ICand Id, we have approximated the actual condition of the boundary layer. Gregory and Riddiford (6) have shown that the boundary layer in fact extends over a distance of twice the Levich thickness from the disk, and that nithin this boundary layer. diffusion gradually predominates over convection such that, a t the surface of the diqk, transport is purely diffusive. It is poisible that a better approximation would be to operate in terms of the thicknes. of the fictitious Nermt layer (-0.8934 6). u
coo - 2 x x
(2b)
Both of these reduce to the semi-iiifinite case nhen 6 -+ m . At the traniition time, CO(O,r) = 0 and
II-ith decreasing current. i ~ ' / ? increases rapidly and becomes difficult to meabure n-hen the outer boundary of the depletion layer interzects the Levich thickness a t time T or befcre.
