aromatic compounds (not shown in the figure) have very high molar response. Thiophene, for example, gives a relative molar response of 475; pyridine, a response of 560; and benzene, a response of 290. It would appear that interesting conclusions concerning the decomposition of organic matter in flames might be gained by further studies of this nature. No corrosion or plugging of the burner tip occurred after a year of use and several hundred injections of corrosive metal compounds. The development of this versatile, trouble-free detector has overcome a difficult experimental problem in the determination of metal halides by gas chromatography. I t provides conclusive evidence of metal elution for those compounds, such as certain thermally unstable metal chelates, which tend to decnmpose upon injection and elution.
ACKNOWLEDGMENT
The authors thank R. L. Fisher for assistance in running the metal fluoride samples. LITERATURE CITED
(1) . . Albert, D. K.. ANAL.CHEM.36. 2034 (1964). ’ (2) Berg, E. W., Truemper, J. T., J . Phys. Chem. 64,487 (1960). (3) Brody, S. S., Chaney, J. E., J . Gas Chromatog. 4, 42 (1966). (4) Dal Nogare, S., Juvet, R. S., “GasLiquid Chromatography,” p. 183, Interscience, New York, 1962. ( 5 ) D’Silva, A. P., Kniseley, R. N., Fassel, V. A., ANAL. CHEM.36, 1287 (1964).
(8) Grant, D. W., Vaughan, G. A., “Vapour Phase Chromatography,” D. H. Desty, ed., p. 413, Butterworths, Washington, D. C., 1957. (9) Juvet, R. S., Durbin, R. P., ANAL. CHEM.38, 565 (1966). (10) Juvet, R. S., Durbin, R. P., J . Gas Chromatog. 1 [12], 14 (1963). (11) Juvet, R. S.. Fisher, R. L.. ANAL. CHEM.37, 1752’(1965).’ (12) McCormack, A., Tong, S. S. C., Cooke, W. D., Ibid., p. 1470. (13) Malmstadt, H. V., Barnes, R. M., Rodriguez, P. A., J . Chem. E d u c . 4 1 , 263 (1964). (14) Monkman, J. ,4., Dubois, L., “Gas Chromatography, H. J. Xoebels, R. F. Wall, and N. Brenner, eds., p. 333, Academic Press. New York. 1961. (15) Watanabe, H., Kendallj K.K.,Jr., A p p l . Spectry. 9, 132 (1955).
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(6) Gilbert, P. T,.!Jr., “Flame Spectra of the Elements, Bulletin 753-A, 2nd ed., Beckman Instruments Co., Fullerton, Calif., 1961. (7) Grant, D. W., “Gas Chromatography, 1958,” D. H. Desty, ed., p. 153, Butterworths, Washington, D. C., 1958.
RECEIVED for review November 26, 1965. Accepted January 24, 1966. Work supported by the National Science Foundation under grant NSF-GP-2616 and the International Atomic Energy Agency, Vienna.
Concentration Dependence of Elution Curves in Non-Ideal Gas Chromatography P. C. HAARHOFF and H. J. VAN DER LINDE Atomic Energy Board, Private Bag 256, Pretoria, South Africa
b An expression for gas chromatographic elution curves, which takes nonideality, nonlinearity and sorption effects into account and applies when single solutes are eluted, is derived. The conditions under which the expression is valid are established. These conditions are encountered in the majority of gas chromatographic experiments. The theory is experimentally verified, and it is shown that both sorption effects and nonlinearity must be taken into account to explain asymmetry of chromatographic peaks. A number of important applications of the theory are discussed.
T
HE migration of solute bands of negligible concentration through chromatographic columns has been intensively investigated (3, 20, 26). When the solute concentration is increased, the processes in the column become more complex, and a t least two additional effects must be taken into account. These are nonlinearity of solute! distribution between the phases (9, 16) and flow velocity increases in solute bands due to sorption effects ( 1 , 16, 18, 20, 21, 27’). X simple theory of the latter phenomenon is presented elsewhere (15) and an experimental illustration thereof is provided by the flow velocity increases
observed when peaks emerge from a column (16, 29). As a result of the increase in the flow velocity with increasing solute concentration, regions of high concentration tend to move more rapidly through the column than do regions of low concentration. Tailing peaks are consequently obtained when nonlinearity is not of importance. Although concentration phenomena have been dealt with in a considerable number of treatments of frontal analysis (16, 18, 27), relatively few attempts have been made to incorporate either sorption (1, 11, 22) or nonlinear (7, 8, 16) effects in theories of nonideal elution development, probably as a result of mathematical difficulties. Houghton (16) recently made a very important advance by obtaining a closed expression for the elution curve of a single solute which takes nonlinearity as well as nonideality into account. As far as is known, a closed expression which embraces sorption effects has, however, not yet been obtained. The gas chromatographic elution of a single solute band of finite volume and concentration a t the column inlet is considered below. An expression for the elution curve, which takes nonideality, nonlinearity, and sorption effects into account, is derived. The treatment is made possible by the mathematical expressions obtained by Houghton (16)
and the introduction of reasonable, simplifying assumptions. The conditions under which the latter is valid are discussed, and the theory is verified by experiment. The results which are obtained should facilitate the investigation of a considerable number of important problems in chromatography, These include the design and operation of preparative chromatographic columns, the reduction of peak asymmetry, the determination of retention volumes a t infinite dilution, and the determination of the curvature of isotherms. -Asymmetry of chromatographic peaks can only be adequately accounted for by taking both sorption effects and nonlinearity into account, as is done in this work. THEORY
The movement of a solute band through a column may be described by setting up a number of differential equations. To obtain a reasonably simple solution of these, approximations usually have to be introduced. When band broadening occurs only as a result of nonideality, and inlet volume effects are negligible, theoretical investigations may be greatly simplified by assuming that the number of theoretical plates is large (or by employing equivalent assumptions) (10, 30). Gaussian elution curves then result. This implies that, if sufficiently small VOL. 38, NO. 4, APRIL 1966
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samples could be injected into successively longer but otherwise identical columns, operated under identical conditions, the elution curve shape would tend to a Gaussian distribution. When the above-mentioned theories are extended to take inlet volume effects into account ( I S , SO), the limiting shape of an elution curve is determined by the ratio of the inlet volume to the peak width (in volume units) for infinitesimal samples. This limiting shape could again, in principle, be determined by using successively longer columns. However, since the peak width increases as the square root of the column length ( L ) , the inlet volume would have to be increased in proportion to fiduring the experiments. I t is shown below that when concentration effects are considered, and the column length is increased while the sample inlet volume and concentration are respectively varied in proportion to 1/z and l/
