Retention Temperature and Column Efficiency in Programmed Temperature Gas Chromatography H. W. HABGOOD and W. E. HARRIS Research Council o f Alberta and Deparfmenf o f Chemisfry, Universify of Alberfa, Edmonton, Alberfa
b A theoretical consideration of linear programmed temperature gas chromatography shows that with only minor approximations the retention of a solute may b e readily predicted from isothermal gas chromatographic data. This was confirmed experimentally, While the retention may b e expressed in the usual way as a retention volume, there are advantages in characterizing each peak by its retention temperature. For any given column this retention temperature depends on the ratio of heating rate to carrier gas flow rate rather than on either one alone. An equation for the calculation of column efficiencies in programmed temperature gas chromatography is also presented.
W
HILE it is conventional to operate gas chromatographic columns at constant temperature, in many instances raising the column temperature either stepwise or continuously during the course of a n analysis is beneficial. A greater range of components may be separated in less time and the chromatographic peaks are more uniform in shape and hence more amenable to quantitative interpretation. Dal Nogare (2, 3) and others (7, 10) have reviewed earlier work and focused attention on the special case of linear programmed temperature gas chromatography in which the temperature is raised a t a uniform rate during the analysis. Particularly in the case of continuously rising temperature the peaks show a remarkable symmetry and general uniformity of shape. On the other hand, in an isothermal chromatogram it is not unusual for the ratio of peak height to width for the more volatile components to be 50 or more and for the least volatile, 0.1 or less. In these extreme cases it is often difficult to obtain precise measurements of peak characteristics for quantitative calculations. To permit use of the large amount of isothermal data that have been reported, the relation between isothermal retention volumes and retention volumes under a linear temperature program is considered in this paper. Other aspects considered are the relative peak width and the method for calculating the
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ANALYTICAL CHEMISTRY
number of theoretical plates as a measure of column efficiency. THEORETICAL
Retention Temperature and Volume. At constant temperature t h e retention volume is the integrated total carrier gas flow from the time of injection of the sample until the emergence of t h e center of t h e solute peak. Thus,
Here F , the flow rate, and (V)Tithe retention volume at temperature T , must both be in the same volumetric units, which in this work will be the volume of carrier gas measured a t flowmeter temperature (25" C.) and corrected to a mean column pressure in the usual way (6). ( V ) Tis measured from the time of sample injection (t = 0 ) to the center of the peak (t = tR). This retention volume differs from the recommended (1) quantity in that it is corrected to a standard temperature rather than column temperature. Under a linear temperature program the temperature is uniform over the length of the column but rises a t a rate of r degrees per minute. Using the relation dT f = dt
Equation 1 may be written in the following form:
where To is the temperature of the column when the sample was injected and TE,which is defined as the retention temperature, is the temperature of the column when the peak emerges. Because of the pressure drop across the column the actual linear flow rate increases toward the outlet. To the extent that this change may be neglected and further if the ratio F / r is held constant, this ratio may be taken outside the integral to give
I n Equation 4 the solute-column interaction is described by the integral
on the left-hand side and the particular program is characterized by the ratio r / F on the right. For any particular solute and column the retention temperature, TR, from a given initial temperature, To,should depend only on the ratio r / F . The relationship may be determined directly using various r / F programs or from isothermal retention volumes according t o the integral on the left-hand side. Curves of r / F us. temperature for the various components are then generally useful in giving the expected retention temperatures for any programmed temperature analysis. To evaluate the integral in Equation 4 the temperature dependence of ( V ) , must be known. Usually, the retention volume corrected for the dead space, V d p i . e . , the retention volume measured from the air peak-may be expressed analytically as an exponential function of the reciprocal of the absolute temperature (9). However, because ( V ) , is required in Equation 4, the exponential relationship cannot be used directly. Thus a n analytic evaluation of the integral is difficult and a graphical method seems preferable. The isothermal retention volumes for the solutes of interest may be summarized as plots of log (V - V d a ) T against 1/T, which are similar to the plots of the usual retention volume against reciprocal temperature. From such a family of lines and from the values of Vda determined for the particular apparatus, plots of ( l / V ) T against temperature are constructed as in Figure 1. The required integrals are the areas under these curves from an arbitrary initial temperature to higher temperatures, as plotted in Figure 2 against the upper temperature limit. The necessary isothermal retention ~ o l u m e smay be obtained by direct measurement or from the literature. Published values are the volumes of carrier gas a t column temperature and mean pressure. They must therefore be corrected to the chosen standard temperature in the present treatment as the flow rate is constant only as expressed a t constant temperature. Neglect of the compressibility of the carrier gas with changing pressure along the column appears justified by the experimental results which are repre-
Figure 1. Reciprocal of corrected retention volume including column dead space as a function of column temperature
dependent of temperature, it then appears reasonable to use the observed peak width, AV, and in the numerator to use retention volume which v,-odd Lc found for isothermal elution a t the retention temperature. Designating this latter quantity as ( V ) T Rn e then have
sentative of the usual analytical conditions. A complete theoretical treatment of linear programmed temperature gas chromatography should take account of the gradients in pressure and velocity along the column and their changes as the temperature is increased. Qualitatively, the decrease in pressure even under isothermal conditions speeds the rnovement of the sample near the outlet. The velocity of a solute band relative to that of the carrier gas increases exponentially T\ ith temperature. Hence, in programmed temperature chromatography the rising temperature of the column increases the sample velocity so strongly toward the outlet that the pressure effect will be insignificant except for columns in which the ratio of inlet pressure to outlet pressure is very high. Plots of r / F us. temperature (Figure 2 ) , n-hile presented on the basis of a particular starting temperature, may also be used with any higher initial temperature. I n this case one adds to the ordinate corresponding to the initial starting temperature the r / F value of the progrnm to obtain the ordinate of the retention temperature. For several solutes in a single program these ordinates nil1 now, oi course, be different. This operation can also be applied to predict the iiicrease in retention temperature if a column is doubled in length. For example, in this work, if r / F is taken as 0.27, the retention temperature for n-hexane is 100" C. Doubling the length of the column is equivalent to adding a second identical column starting a t 100" C. The retention temperature will then be given a t 0.27 = 0.54, the r / F value of 0.27 and is 126" C. The information in Figure 2 may be presented in an alternative form involving the retention volume directly. The retention volume equals (2'- T o ) ( F / r )
+
or the abscissa divided by the ordinate. If this quantity is plotted against temperature a family of curves is obtained similar to those for isothermal retention volumes against temperature. On this plot a particular program is shown by a straight line through Toof slope F/r. This method for the presentation of data is not recommended because an additional step is involved in calculations based on isothermal values; it is more difficult to allow for small variations in F / r during the program, and it is more difficult to use a single plot for columns of different lengths. Number of Theoretical Plates. For isothermal chromatography the plate theory (4, 8 ) gives the well-known expression for the number of theoretical plates : n
=
16
(6);
(5)
&-here AV is the volume equivalent to the base line intercept of the peak. While this equation has been applied directly to temperature programmed chromatograms (5), unreasonable values for n are obtained particularly for the later peaks. Such a result is not surprising. Equation 5 is merely a special case of the more general relationship n = 16
(2)'
in which An is the number of plates corresponding to the base width of the peak as it leaves the column. For isothermal gas chromatography the ratio n/An is obviously V / A V , giving Equation 5. For programmed temperature chromatography care must be taken in choosing the volumes to express the ratio n/An. If one assumes that the number of plates in the column is in-
If the number of theoretical plates varies with temperature, the total number of plates through which the solute passes in the program will be some average value of n. In order that Equation 7 should yield this value it would be necessary to multiply ( V ) T R by the ratio nav/nTRJahere nTEis the number of plates for isothermal elution a t the retention temperature. Use of the equation as it stands will tend to give an n close to that obtained a t TR. This should be a useful quantity even though n varies somewhat with teniperature. A further factor which has been neglected is the temperature rise during the emergence of the peak from the column. The general effect will be to make the trailing edge somewhat sharper than the leading edge. Because isothermal peaks frequently tend to be the reverse of this, programming often produces a marked increase in the symmetry. No attempt has been made t o consider this effect in a quantitative way. EXPERIMENTAL
Apparatus. Apparatus for linear programmed temperature gas chromatography should maintain a constant carrier gas flow as the temperature is raised and should permit the temperature t o be raised a t a uniform rate. T h e relatively simple equipment shown in Figure 3 meets these requirements fairly well. A very nearly constant gas flow rate was obtained by having t h e main pressure drop in the system occur in a length of thermometer capillary tubing ( B in Figure 3) ahead of the column. With appropriate selection of the capillary, the cylinder regulator could be set a t a pressure about 10 times greater than the maximum pressure drop across the column, and then the variations in this latter with temperature would change the flow rate less than 2%. Depending upon flow rate, the pressure drop across the column varied from 3 cm. a t 30' C. to 6 cm. a t 200' C. for a regulator setting of 15 p.s.i.g. (flow 14 ml. per minute), and correspondingly from 21 to 44 cm. a t 60 p.s.i.g. (flow 120 ml. per minute). The column was a 2-meter length of '/4-inch copper tubing coiled t o VOL. 32,
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2 inches in diameter. It n a s fittcd inside a Dewar flask 23/4 inches in diameter, filled with mineral oil, and provided with a stirrer and knife heater. Rates of heating up to 20" per minute could be selected by a variable transformer. While v i t h a fixed setting on the transformer the rate fell off somewhat at higher temperatures, it was easy to raise the voltage slightly during a run to compensate for this. To maintain a constant temperature an appropriate low voltage was applied. A small cooling coil was inserted to lower the temperature betyeen runs. A Gow-Mac thermal conductivity cell rrith TE I geometry and coiled filaments n a s used as detector nith a 1t o 20-mv. variable range recorder. The conductivity cell n as thermostated a t about 110" C. in an aluminum block, and the line to it from the outlet of the column was separatcly heated to prevent condensation of solutes. The column n as packed n it11 Apiezon L grease on firebrick (Burrell S o . 341-117). Samples were injected by a 50-pl. syringe which reached directly into the gas stream. The usual sample size was about 1 p l . of liquid.
"30
50
100
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TEMPE RATURE,"C. RESULTS
Isothermal and programmed temperature chromatograms Tyere run for a mixture of the normal hyclrocarbons from C I to Cs, toluene. nz-fluoro-, mchloro-, and m-bromotoluene. The reciprocal isothermal retention \-olumes us. temperature curves for these substances are shorn-n in Figure 1. These curves were obtained most convenientlj from the nearly linear curves 11-hich resulted from plotting the measured values of log ( V - V , , ) T against 1/T. The solid lines shonn in Figure 2 nere obtained from the data of Figure 1 in the nianner described ab0T-e. The plots of Figure 2 perniit the prediction of the retention temperatures of all linear programmed chromatogranis of the substances shon-n n hich start a t or above 30" C. Each chromatogram is characterized by its r / F d u e which, as ordinate. determines the abscissa temperatures of peak emergence. Eyperimentally observed retention temperatures for the programmed temperature chromatograms all starting a t 30" C. are also shown in Figure 2 as the individual points a t the appropriate r,/F values. Both r and F \\ere varied orer more than a tenfold range and the agreement n ith the calculated curves is excellent. -4typical chromatogram with a linear temperature program is shonn in Figure 4; the temperature n-as raised a t a rate of 4.8" per minute and the gas flow n-as 44 ml. per minute. Even though the various compounds in this mixture range in boiling point from -42" to 184" C.. all of the peaks are ne11 spaced and well shaped. I n effect, each peak is eluted a t its on n favorable tem452
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ANALYTICAL CHEMISTRY
Figure 2.
Plot of integral and experimental test of Equation 4
S d i d lines. Integral areas under curves of Figure 1 from 3 0 ° t o T o C. Points. Observed retention temperatures for various programs whose r and F are given a t righl
Figure 3. Apparatus for programmed temperature gas chromatography A. B.
C. D. E.
F. G. H. 1. K.
Pressure g a g e on eluent gas cylinder Short range thermometer capillary tubing Manometer Thermal conductivity cell in thermosfated aluminum block 23/4-inch Dewar flask of 1 -liter capacity Silicone rubber puncture seal, sample injection paint on column Thermometer Stirrer 5 0 0 - w a t t knife heater Soap bubble flowmeter
perature. Some of the hydrocarbons used were not highly pure samples and isomers were present. Calculated and observed retention temperatures were compared for these also and showed
similar agreement to that indicated for the other compounds in Figure 2. The number of theoretical plates for programmed temperature chromatography was examined and some typical
results are shown in Table I. The conventional practice 1%as adopted and column efficiencies were expressed as height of equivalent theoretical plate (HETP), which is the length of the column divided by n. The isothermal HETP values in Table I were interpolated from measurements taken under isothermal conditions over a wide range of temperatures and flow rates. For the programmed chromatograms HETP was calculated using Equation 7 as explained above. This is likely to give a value of H E T P closer to that pertaining to the retention temperature of the conipound rather than an average value for its passage through the column. As shown in Table J the results for normal hexane agree fairly well with the isothermal values. It would appear, therefore, as one niight expect, that a column used for programmed temperature chromatography has essentially the same number of plates as it does in i5othermal chromatogra ph y . CONCLUSION
I n view of the theory and results presented in this paper, it is recommended that results reported from programmed temperature gas chromatography include both the r / F value as n-ell as the retention temperatures of the peaks. The retention temperature is more significant than the conventionally reported retention volume. This work has shown that it is readily possible to predict from isothermal chromatographic measurements the relationship between r / F and retention temperature and retention volume, if desired. This relationship may also be determined directly from a number of runs with different linear temperature programs and as such will be equally useful in correlating retention temperatures. Likewise. column efficiency may be assessed either from isothernial or programmed temperature chromatograms. I n a practical analwis it is desirable to operate n column for high efficiency, mininiuni time of analysis, maximum sensitivity. aiid peak shapes most amenable to quantitative interpretation. I n choosing r and F some compromise is necessary and the hest values for one solute may not be best for others. I n general the higher r is, the sooner peaks emerge, but bemuse they emerge at higher temperatures the column efficiency is decreased. The emergence
?J
LJ z
W W z
3
3
C
I i
--
---
_ a
‘EV”EFATJ?E
Figure 4. mixture
Programmed temperature
’c
chromatogram
of
wide-boiling-range
Predicted retention temperatures ore shown as vertical lines
Table I.
Comparison of HETP Values for Hexane from Programmed Temperature Chromatograms with Those for Isothermal Chromatography
r/F, Degrees/ bI1. 0.0133 0.031 0.096 0.080 0.097 0.217 0.38 0.79 1.18
F MI./&Tin. 125 118 44 45 17 17 24 17 17
HETP, Cm. Isothermal* Programn 0.45 0.49 0.48 0.40 0.27 0.19 0.21 0.21 0.22 0.27 0.22 0.28 0.26 0.27 0.56 0.47 0.42 0.51
TR, O
c.
40
49 52
66 71 92 111
158 166
temperature may be decreased by increasing F , but this will eventually also lead to a decrease in efficiency and, with most detectors, a decrease in sensitivity. It is likely that most satisfactory operation will be achieved nith a flow rate somewhat higher than that giving minimum isothermal HETP Values and some intermediate heating rate. I n the work described here a flow of about 40 to 50 mi. per minute and a heating rate of 4O to 5 O per minute are indicated. LITERATURE CITED
(1) hmbrose, Douglas, Keulemans, A. I. hl., Purnell, J. H., ANAL. CHEM.30, 1582 (1958). (2) Dal Nogare, Stephen, Bennett, C. E., Ibzd., 30, 1157 (1958). (3) Dal Nogare, Stephen, Harden, J. D., Ibid., 31, 1829 (1959). (4) Deemter, J. J. Van, Zuiderweg, F. J., Klinkenberg, A., Chem. Eng. Sci. 5 , 271 (1956).
(5) Harrison, G. F., Kni ht, P., Kelly, R . P., Heath, hl. T., ‘ d a s Chromatography,” D. H. Desty, ed., p. 222, rlcademic Press, New York, 1958. (6) James, A. T., Martin, A. J. P., Biochm. . .. .J. .. 50. .., 679 - - (1952). ’adden, w.H., ASAL. CHEnf. 30, 1958). tin, A. J. P., Svnge, R. L. hl., \ - - -
>
,
I
141). C. H., Stross, F. H., J . Am.‘ Chew;. SOC. 78, 2999 i\ -18.56l. - - - I -
(10) Ryce, S. -4.,Bryce, IT. A , , ANAL.
CHEM.29,925 (1957).
RECEIVED for review August 17, 1959. Accepted January 4, 1960. Joint contribution from the Department of Chemistry, University of Alberta, and To. 106 from the Research Council of Alberta, Edmonton, Alberta. A preliminary ac-
count was given a t the Second Alberta Gas Chromatography Discussion in Edmonton, February 13, 1959, and part of this work was briefly described in an informal discussion session of the Second International Gas Chromatography Symposium, East Lansing, hiich., June 9, 1959.
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