Table Ill.
Taken 16 33 33 16 33 33
Ca (rg.1 Found
6 3 3 6 3 3
Sa
16.3 32.9 33.1 16.7 33.3 33.0
0.14 0.28 0.17 0.30 0.29 0.21
, . .
, . .
, . .
... ...
0 11.8 0.13 0.13 16.9 6 0.14 3 32.8 0.24 11.8 0 0.10 16.8 6 16.2 0.23 6 0.22 32 9 3 0.29 9 50.3 The standard deviation,
12 16 33 12 16 16 33 49 5
-
Results on Ca, Mg, and Sr Mixtures
Taken ... ...
h k (fig.) Found
Taken
Found
...
43.8 43.8 87.6
43,l 43.4 86.9
... ...
...
12.2 12.2 24.3 12.2 24.3 36.5 7.3 12.2 24.3 7.3 12.2 24.3 7.3 12.2
Sr ( r g . ) Sa
7 0.18 ... 0.14 8 ... 2 ... ... 0.20 3 0.24 43.8 43.2 0 0.22 87.6 86.9 0.31 87.6 87.5 7 25.3 24.9 0.14 6 4 43.2 0.13 43.8 7 0.08 87.6 86.8 0.19 131.0 1 130 131 . O 3 132 0.10 0 0.22 87.6 87.2 44.0 0.29 43.8 8 44.2 0.28 43.8 6 s, was calculated for four separate analyses for each
the titration cell; therefore, this was assigned as a lower limit for this procedure. The use of smaller operating currents would probably decrease this limitation. The upper limit of the technique was set by the characteristics of the HDPlZ-coated filter paper. When more than a total of five microequivalents of mixed alkaline earths
11 11 24 12 24 36 7 12 24 7 12 24 6 12
~
Sa
0.24 0.20 0.20 ...
...
...
0.20 0.24 0.19 0.14 0.19 0.18 2.20 1.40 0.29 0.24 0.35
mixture.
were spotted on the paper, the separations became indistinct. The zones lost much of their concentric character and projections of one zone into another became quite pronounced. .ilso the zones were only slightly separated, making quantitative separation of the individual zones very difficult. The use of a higher concentration of H D P M on
the paper, larger filter papers, slower development, or any combination of these would probably extend this limit somewhat. ACKNOWLEDGMENT
The authors thank J. J. Richard for synthesizing the HDPM used in this work. LITERATURE CITED
( 1 ) Campbell, D. N., Kenner, C. T. ANAL.C K E M26.560 . ,~ (1954). (2) Ferguson, J. W., Richard, J. J., 0 Laughlin, J. W., Banks, C. V., Ibid., 36. --, 786 .I- 11964) \ - _ - _
(3) Fritz, J. S.,”U’aki, H., Ibid., 35, 1079 (1963). (4) Monk, R. G., Steed, K. C., Anal. Chim. i l c t a 26.308 11962). ( 5 ) Nelson, F., ‘Holldway, J. H., Kraus, K. A., J . Chromatog. 1 1 , 288 (1963). (6) Xemodruk, A. A , , Novikov, Yu. P., Lukin, A. AI., Kalinin a, 1. D..‘ Zh. Analit. Khim 16, 180 (1961). (7) O’Laughlin, J. W., Banks. C. V.. A N A L . CHEM. 36. 1222 (1964). (8) Reilley, C. N’., Porterfield, 1%‘. W., Ibzd., 28, 443 (1956). Ibid., (9) Richard, J. J., Burke, K. E., O’Laughlin, J. W., Banks, C. V., J . Am. Chem. Soc. 83, 1722 (1961).
RECEIVEDfor review May 18, 1964. Accepted July 23, 1964.
I
*
Minimizing Time for Gas Chromatographic Analysis of Complex Mixtures T. B. ROONEY and WILLIAM AZNAVOURIAN The Foxboro Company, Foxboro, Mass.
b Several authors have presented methods for minimizing the time required for the chromatographic separation of two components. In applying these methods to more complex mixtures, it has been assumed that the resolution of a particular pair of components will determine the length of column regardless of analysis conditions. In the situation where the pair of components that is most difficult to resolve depends on analysis conditions, these methods may b e impossible to apply. The use of a digital computer search technique overcomes this basic problem. At the same time, it makes feasible the use of more complex refinements of chromatographic theory, This paper presents the theory behind the digital search method, along with an example of the application of this method to the analysis of complex mixtures.
E
workers ( I , 9) have treated the problem of minimizing the time required for the chromatographic separation of two components. These ARLIER
21 12
ANALYTICAL CHEMISTRY
studies, however, have not adequately discussed the effect of component concentration on resolution. Further, the methods proposed for determining the optimum analysis conditions are not completely general when applied to complex mixtures. I n the situation where the pair of components that is most difficult to resolve depends on analysis conditions, these methods may be impossible to apply. The present study considers the effects of concentration on separation and discusses a general method for determining optimum analysis conditions using a digital computer search technique. The application of this method requires the experimental determination of several column parameters. To economize on experimentation, certain relationships between these parameters and the analysis conditions are assumed. Some of the relationships used in this presentation are empirical and very approximate. The method, however, is general and as chromatographic theory develops further, refinements may be easily incorporated.
The present study will consider the minimization of analysis time with respect to liquid loading arid exit velocity only. The other independent variables are treated as parameters which can be varied and thus studied indirectly. C O M P U T I N G THE TIME OF ANALYSIS
Ayers, Loyd, and DeFord (1) have shown that the time ( t i ) for the elution of the i t h component is given by
4
=
2/d1
+ IC
