Units of Measurement in Gas Chromatography W. 1. JONES and RICHARD KIESELBACH Engineering Research laboratory, Engineering Department, E. 1. du font de Nemours & Co., Inc., Wilmington, Del. ,New units of measurement are proposed for practical analytical applications of gas-liquid partition chromatography, simplifying the recording and interpretation of experimental data and quantitatively characterizing the degree of resolution obtained in practical analytical separations. The resolution of two partition-chromatographic peaks can b e defined quantitatively as the product of two dimensionless time ratios: the relative separation and the relative sharpness of the peaks. This expression, simply calculated from easily measured variables, takes into account the effects of both column “efficiency” (number of theoretical plates) and the difference between the partition coefficients of the sample components producing the peaks. The units involved require no correction for column pressure drop.
T
basic principles of gas-liquid partition chromatography have been presented by James and Martin (3’). Their classical theory of the process was based upon the assumptions of equilibrium conditions within the chromatographic column, a constant partition coefficient of the sample between liquid and vapor phases, and an absence of axial diffusion of the sample along the column length. They shoJTed the relationship between the retention volume (the volume of gas required t o elute a sample component from the column) and the velocity ratio R, (the linear velocity of the sample peak relative to that of the carrier gas). Earlier papers in the field of liquid chromatography by Martin and others (2, 6) showed the relationship of R f to the fundamental partition coefficient of the particular sample-partition liquid system. James and Martin also presented expressions for the fractionating “efficiency,” H.E.T.P. (height equivalent t o a theoretical plate), of a chromatographic column, derived from measurements of the shape of the effluent concentration peak produced by the colHE
umn. Theirs and numerous subsequent papers by other workers have separately discussed the effects of various parameters influencing H.E.T.P. and the attainment of practical analytical separations by gas chromatography. Recently an excellent comprehensive treatment of the subject has been published by Keulemans (4). The now generally accepted units of measurement used by James and Nartin are well adapted to the classical treatment. Ambrose, Keulemans, and Purne11 ( I ) have clearly presented the interrelationships and theoretical utility of these units. From the standpoint of the practical analyst, however, the accepted units suffer several disadvantages. Measured retention volumes are of quantitative significance only when corrected for column pressure drop or when compared with the retention volume of some arbitrary standard material run under identical conditions (7). Separations obtained with two different columns operated a t the same effluent volume flow rate cannot be directly compared, because of the influence of column temperature and pressure drop on gas velocity within the column, which, in turn, controls H.E.T.P. A knowledge of the corrected retention volumes of two sample components and of column H.E.T.P. still does not provide any convenient quantitative measure of the degree of practical resolution obtained betn-een the two chromatographic peaks. The effects of various equipment and operating parameters on the resolution of sample components by a chromatographic column-e.g., column length, concentration of liquid phase in the column packing, carrier-gas velocity and viscosity, temperature, and pressureare all related to time-based phenomena: linear velocities and diffusion rates. Furthermore, the quantities most readily measured in the course of a chromatographic analysis are also time-basede.g., flow rates and elution times. The data obtained from the detector a t the column output are ordinarily recorded
as concentration us. time. These considerations have led the authors to propose a revised set of units for use in the practical application of gas chromatography. These units, based on kinetic rather than equilibrium data, lead to more convenient recording and interpretation of experimental results, and perhaps more importantly, facilitate quantitative evaluation and control of the effects of the various physical operating parameters on the separation process. UNITS
OF
MEASUREMENT
Average Linear Carrier-Gas Velocity, u,. The linear velocity of the carrier gas is an important parameter, to which many secondary parameters can be directly related. I n a practical column offering resistance to f l o ~ this , velocity, of course, is not constant along the column length, and cannot readily be measured directly. However, several quantities of interest can equally well be related to the average linear gas velocity, a quantity easily determined. The average linear carriergas velocity is defined as the length of the column divided by the elution time of a sample-e.g., air, unabsorbed by the partition agent. (-4n accurate measurement of this quantity requires that the volumes between the point of sample introduction and the column input and betnTeen the column output and the detector be reduced to a minimum. It is not difficult to make these volumes negligible for most practical applications.) up = L/t,
where u g = average linear carrier-gas ve-
locity L = column length t , = elution time of air The quantity u, is substituted for the more commonly measured volumetric flow rate of the carrier gas, because of the simplicity of relationships based
I
This article is t h e contribution of individual authors rather than of any particular group. In contrast t o t h e two preceding ones, it is not an a t t e m p t at standardization of nomenclature b u t is proposing secondary terminology which t h e authors feel will be of practical value on a day-to-day working basis. T h e authors have indicated t h e y heartily endorse t h e recommendations of t h e Amsterdam committee as fundamental definitions, a n d revised some of t h e nomenclature used in their proposal in order to be in agreement. I
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ANALYTICAL CHEMISTRY
(1)
4 Figure 1 .
Relative peak
separation Hypothetical chromatograms, arbitrary units tz fl
SI? =
fl
L=I
S =0.5
4
S =0.5
(2.4 I
I
I
0
I
Figure 2.
I
Time
I-+
Relative peak sharpness
Hypothetical chromatograms, arbitrary units
Q = fz/w
I
0
2
4
3
5
(7)
6
Time
upon this variable and because of the attendant ease of interpretation of experimental data Elution Time, t,. The time interval between the introduction of a sample into the partition column and the occurrence of the peak sample concentration a t the column output is defined as the elution time, t,, of the sample. For a given column-packing material a t a given temperature, the elution time of a compound is, to a good approximation, directly proportional t o column length and inversely proportional t o the average linear carrier-gas velocity 15-ithin the column. Elution time is inversely proportional to the R/ value of the compound, by definition of R, (S). Therefore, t2 =
L/u,R,
(2)
where t,
L
= elution time of sample
column length average linear carrier-gas velocity R , = ratio of sample t o carrier-gas velocities
up
= =
Of considerable practical significance is the fact that column pressure drop does not enter into this relationship. Relative Peak Separation, SI*. The degree to which two chromatographic peaks are separated in time can be characterized as a function of the particular sample column-packing system, irrespective of other factors influencing over-all column efficiency, such as column length and gas velocity. Doubling the length of a column (while holding average carriergas velocity constant) will double the elution time of a compound. This
point is illustrated in Figure 1. While the over-all resolution of the peaks is improved kith the longer column, the ratio of their elution times is unchanged. Consequently, the relative peak separation obtained with a given sample-packing system, irrespective of column length, can be defined as the ratio of the difference in the two elution times t o the elution time of the first peak: 12
- __ t 2 - tl tl
(3)
Relative peak separation serves as a convenient unit to characterize not only the separation of two sample peaks but also the action of a particular column packing on a single sample compound. As pointed out by Ambrose, Keulemans, and Purnell ( I ) , relative separation values between two sample components are not always adequate. However, the relative separation-of a sample peak from that of air, measured a t any carriergas velocity with a column of any length, is a constant, directly related t o R,. (4)
The relative separation of a sample peak from an air peak is:
Having recorded the values of S,, for various compounds on various column packings, one can easily calculate the relative separations of any particular pair of compounds on a particular packing by the relation
Relative Peak Sharpness, Q. Relative peak separation in itself does not indicate the degree of resolution obtained between two adjacent peaks, as i t does not reflect over-all column fractionating “efficiency.” As shown by James and Martin (S), the latter quantity is reflected in the relative sharpness of the chromatographic peaks. Thus, as shown in Figure 1, an increase in column length, while not affecting relative peak separation, improves resolution by increasing relative peak sharpness. Relative peak sharpness, &, can conveniently be defined as the ratio of elution time to the time width of the peak:
where ZL’ equals width of peak as measured a t the base-line intercepts of the tangents to the peak. A somewhat similar definition based upon volumetric flow rate has been proposed by Wiebe ( 8 ) . Figure 2 shows the effect of a change in Q on the resolution of two peaks of constant relative separation. The definition of column “efficiency” as Q rather than the number of theoretical plates, n, has three practical advantages. First, the degree of resolution between two chromatographic peaks is linearly proportional t o Q, while proportional to the square root of n. Thus it is easier to apply and to create a clear mental picture of the quantitative significance of & than n. Second, the value of Q is more easily and directly measured than that of n. Third, the number of theoretical plates is a theoretical concept relating t o an idealized mode of column operation, while Q is a direct measure of the quantity of practical interest, irrespective of any theoretical mode of column operation. VOL. 30, NO. 10, OCTOBER 1958
1591
The number of theoretical plates in a column is related to Q by the following formula : r
= 16Q2
This definition is, of course, as useful as that of the authors. However, in order to express this quantity as a simple product of relative separation and relative peak sharpness, it becomes necessary to define these latter quantities as
(9)
Resolution, R. A quantitative evaluation of the degree of resolution obtained between two chromatographic peaks, as influenced by both the chemical properties of the system and efficiency of the column, can now easily be calculated from measured values of relative peak separation and relative peak sharpness. R
&Si2
and
&=-
(10)
Figure 3 illustrates the appearance of chromatograms of different degrees of resolution. Because a chromatographic peak approaches in shape a Gaussian distribution, a complete physical separation of sample components can never be attained ( 3 ) . Even where the detector output appears to return to zero between adjacent peaks, the component producing each peak nonetheless contributes to some small extent to the area of the other. The degree to which this effect is evident is determined by the ratios of the concentrations of the two components in the sample. If, for esample, 0.01% of component 5 is present in the peak produced by component y, the error is negligible or not, depending upon whether 2 and y are present in equal or 1000 to 1 ratios. Thus, it is not possible to assign a value of R adequate t o ensure good resolution in all cases. The necessary value of R will depend upon sample component concentration ratios and the required dpgree of analytical accuracy. For
tl
w1 I
0
3
2
t2
4
Time
Figure 3.
+ + w2
Resolution
Hypotheticai chromatograms, arbitrary units R = QS
the ordinary case, where neither peak exceeds the deflection span of the recorder, a n R value of about 2.5 represents complete resolution within the precision of the usual recording instrument. A simple formula correcting for the effect of concentration ratio is under development and will be published in the future. Having recorded the values d S,,for various compounds on various column packings, one now can calculate their relative separations and the value of Q necessary to attain a required degree of resolution with any of the packings tested, by application of the relationships presented above.
These expressions, while usable, are unnecessarily cumbersome, because their added complexity contributes nothing to their value. The authors therefore prefer their simpler expression for resolution. LITERATURE CITED
(1) Ambrose, D., Keulemans, A. I. M., Purnell, J. H., AKAL.CHEM.30, 1582 (1958).
( 2 ) Consden, R., Gordon, A. H., Martin, A. J. P., Biochem. J . 38,224 (1944). (3) James, A. T., Martin, A. J. P., Ibid., 50, 679 (1952). (4) Keulemans, A. I. M., “Gas Chromatography,” Reinhold, New York, 1957. (5) Martin, A. J. P., Synge, R. L. M., Biochem. J . 35, 1358 (1941). (6) Phillips, C. S. G., Second Symposium
DEFINITION OF RESOLUTION
on Gas Chromatography, Amsterdam, May 22, 1958. (7) Sullivan, L. J., Lotz, J. R., Rillingham, c. B., ANAL.CHEM. 28,495 (1956). (8) Wiebe, A. K., Delaware Section, .4CS, February 18, 1956.
Phillips (6) has proposed a definition of resolution
RECEIVED for review February 13, 1957. ilccepted April 16, 1958.
Identification of Low-Boiling Sulfur Compounds in Agha Jari Crude Oil by Gas-Liquid Chromatography H. J. COLEMAN, C. J. THOMPSON, C. C. WARD, and H. T. RALL Petroleum Experimenf Station, Bureau o f Mines, U. S. Department of the Interior, Bartlesville, Okla. Gas-liquid chromatography and supplemental mass spectrometry analyses were used to identify eleven sulfur compounds in Agha Jari, Iran, crude oil. This investigation produced new analytical data concerning the low-boiling sulfur compounds in Agha Jari crude oil, information which is of direct interest to the refiner. A comparison with similar data from other crude oils may shed some light on the origin of petroleum and of the sulfur compounds found in it.
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ANALYTICAL CHEMISTRY
E
publications ( 2 , 8,9) from this laboratory have reported the separation and identification of sulfur compounds in Wasson, Tes., and W l mington, Calif., crude oils using such techniques as isothermal distillation, adsorption, fractionation, and infrared and mass spectrometry. Although these procedures are reliable, many of the steps are time-consuming, and relatirely large quantities of crude oil must be processed to produce enough final sulfur compound concentrate for fractionation ARLIER
and subsequent identification of the components by mass or infrared spectrometry. The use of gas-liquid chromatography now makes it possible to circumvent some of the more objectionable steps in the separation and identification procedures employed previously. Literature references concerning the application of gas-liquid chromatography to mixtures of sulfur compounds are limited. Sunner, Karrman, and Sunden ( 7 ) report the quantitative separation of a number of aliphatic
