good, and the discrepancies may be attributed to the inaccuracy of measurements. However the data presented here are too few to ascertain definitively that the programmed temperature retention index is equal to the isothermal index a t a temperature 20" C. below the elution temperature. The choice of 20" C. is somewhat arbitrary; since the temperature of the column during the time the peak travels through it is always below the elution temperature, the correction which must bc made to account for the variations of inllices with temperature is the easiest by computing the isothermal index a t some temperature below the elution tempersture. A temperature of 20" C. seems to give the best results, but the exact value may depend on the program rate. A more theoretically sound way of correcting for the variation of retention indices with temperakure would take advantage of the theoretical work of Giddings (1) which showed that a programmed temperature chromatographic separation is very alike to an isothermal one a t a temperature T' given by 0.92 TR to a good approximation. Table I1 gives the corresponding value T' = 0.92 TR and the isothermal retention indice a t this temperature (temperatures are given in " C., although the relation between 1" and TR holds in " K.). The data given in Table I11 compare the two methods of correction. The
last one appears to be slightly but definitely better, The correlation data were computed either with the whole data available or with only those for which all isothermal retention indices were available. The standard deviation obtained is about twice that which may be obtained by isothermal measurements. Better results would probably have been obtained if a lower starting temperature had been used, especially with methyl ethyl ketone. If this relationship is really true within less than 10 units, this result is important because it provides an easy and fast way to use isothermal retention data in the form of retention indices and increments of retention indices in programmed temperature gas chromatography. The lack of such a way to compute easily programmed temperature retention data from isothermal data was until now one of the most important drawbacks of this very useful technique. Since submission of this paper a work of Van den Do01 and Kratz (6) has appeared, describing substantially the same results, but with no correction for temperature dependence of retention indices. ACKNOWLEDGMENT
The authors are indebted to E. Kovats and C. Landault for fruitful discussions. We thank J. Bargain for
Table 111.
Correlation Data
Mean
Variance
of absolute
of absolute
f2.7 +0.78 -0.75
9.75 8.3 7.2
differences differences For the Whole Data
TR) l i ( T ~- 20) Ii(0.92 TR) Ii(
Excluding Methyl Ethyl Ketone and n-Hexyl Acetate Ii(TR)
$1.1 0 -0.5
li(TR - 20) l i ( 0 . 9 2 TR)
11 7.7 6.5
the loan of a Microtek 2500 R by SociBtB Techmation, Paris, France. LITERATURE CITED
(1) Giddings, J.
C., "Gas Chromatography," K. Brenner, J. E. Callen, M. D. Weiss, ed., p. 57. Academic Press, New York, 1962. (2) Giddings, J. C., J. Chromatog. 4, 11 I\----,. 1 RfiO\
(3) Habgood, H. W., Harris, W. E., ANAL. CHEM.32, 450 (1960). (4) Kovats, E., Helv. Chim. Acta 41, 1915 (1958). (5) Van den Dool, M., Kratz, P. D. C., J. Chromatog. 1 1 , 463 (1963). (6) Wehrli, A., Kovats, E., Helv. Chim. Acta 42, 2726 (1959).
GEORGE GUIOCHON Laboratoire du Professeur L. Jacque Ecole Polytechnique 17, Rue Descartes, Paris 5e, France RECEIVED for review September 16, 1963. Accepted December 2, 1963.
Retention Indices in Programmed Temperature Gas Chrolmatography SIR: As Guiochon (4) and van den Do01 and Kratz (6) have pointed out, retention indices sho d d be applicable in programmed temperature gas chromatography (PTGC) with the modification that log VR in the isothermal expression for retention index would be replaced by I&,where lTE is the net isothermal retention volume and TR is the retention temperature in PTGC. Thus, for esample, a compciund X eluted between n-octane (C,) and n-decane (Clo) would have retention indices for isothermal and programmed elution, respectively, given by the following expressions: I , ( X ) = 800
IdX)
+
= 800
+
Guiochon has also noted that the linearity with carbon number of TR is
less general and less complete than the linearity of log Vg but still sufficient that I,, should, in many cases, be identical with I,. While van den Do01 and Kratz have presented data to show that the increment in TR between successive homologs is "remarkably constant," examination of these data shows significant variations with both carbon number and program. Guiochon has also pointed out that if I , varies with temperature then agreement would be , I, for a temperature expected of I %with somewhat below the retention temperature. It is important to establish the relationship between I,, and IC if advantage is to be taken of the extensive available tribulations of I,. (It is somewhat unfortunate that the standard polar stationary phase recommended by Kovats, viz., Emulphor 0, a polyethylene glycol of molecular weight 500, has a relatively low upper temperature limit so that i t is not too satisfactory for PTGC.) We feel that the experi-
mental comparisons of I,, and Ii which have been presented (4, 6) might advantageously be supplemented by some calculritions of typical behavior. First of all it is worth distinguishing, as shown schematically in Figure 1, the two possible situations: an isothermal retention index invariant with temperature and one which changes with temperature. On the standard plot of log VR against reciprocal of the absolute temperature, the reference normal alkanes are shown as a family of straight lines. Compounds with temperature dependent and temperature independent indices are represented by the dashed lines A and B , respectively. Line B is uniformly one quarter of the distance between the lines for octane and decane so that it corresponds to a retention index of 850 while line A , over its length as drawn, corresponds to indices ranging from 870 to 980. Wehrli and Kovats (7) describe the temperature variation of Ii by a simple linear coefficient dIi/dT based on a 60" VOL. 36, NO. 3, MARCH 1964
663
1400
1200
x
ul
n
CI
z
In
9 I
1000
Z
>
Q
Y
d
3
.--
ANALYTICAL CHEMISTRY
C
1
I
I
100
200
3
TEMP.
Figure 1. Schematic representation of temperature dependent and temperature independent retention indices
664
- -----------c,
25
I/T
temperature interval. This is adequate for small temperature intervals but a linear variation in 1 / T , as shown in Figure 1, is a better representation for the wider temperature ranges involved in PTGC. Many compounds have retention indices which vary less than 0.1 unit per degree ( 7 ) and for such cases the assumption of a constant retention index, as in B, is reasonable. In such a case, the compound behaves like a member of the normal alkane series with an appropriate fractional carbon number. Under linear PTGC, retention temperature in an homologous series tends to increase fairly uniformly with carbon number except, in some cases, for compounds of low carbon number. For such compounds with a program of sufficiently low ratio of heating rate to flow rate and sufficiently high initial temperature, the retention temperatures may remain close to the initial temperature so that there is considerable initial curvature t o a retention temperaturecarbon number plot. In effect, this initial region may be thought of as intermediate between isothermal and programmed behavior; the solutes are not sufficiently immobilized near the column inlet at the injection temperature to obtain the full advantages of programmed temperature elution. However, to the extent that the retention temperature-carbon number plot is linear, I,, will be identical with I,. In the region of initial curvature the retention temperature will be closer than
-9
Figure 2. Comparison of isothermal and programmed temperature retention indices for cycloalkanes on a nonpolar column calculated from the data of Wehrli and Kovats (7) shown as solid points. I,, values are plotted against the cycloalkane retention temperature
expected to the next lower reference hydrocarbon and I,, will tend to be low. However, apart from this initial region, the nonlinearity between successive even numbered alkanes is likely to be small and, when I, is independent of temperature, good agreement is expected between I,, and Zi. If, as in case A of Figure 1, the retention index varies with temperature, one would expect the programmed value to represent some sort of average of the isothermal values over the range of the program, the averaging process being similar to that which has been discussed by Giddings (3) and weighted toward values near the retention temperature. A simple example has been worked out to illustrate the variations in retention index that might be encountered in practice. The cycloparaffins on a nonpolar column were chosen from the data of Wehrli and Kovats (7) as a series representative of a fairly large temperature coefficient in retention index. These authors give the retention indices for the cycloparaffins from cyclopentane to cyclododecane on an Apiezon L column a t temperatures of 70°, 130°, and 190' C. Since the absolute retention volumes of a suitable range of normal paraffins on Apiezon L a t various temperatures were not conveniently available, use was made of the retentions reported by Baumann,
Klaver, and Johnson (1) for the normal paraffins on SE 96(50) silicone fluid. While the assumption that the cycloparaffins and n-paraffins would show the same relative retentions on SE 96(50) as on Apiezon L is probably unjustified in practical work, it does not affect the principle of the example to be described here. The calculation procedure was as follows: S e t retention volumes for the n-alkanes per gram of stationary phase were derived from the data of Baumann, Klaver, and Johnson and plotted as log V E us. 1/T in the same manner as in Figure 1. From these values and the retention indices given by Wehrli and Kovats the log V Eus. I/Tstraight lines for the cycloalkanes were calculated. Using these two sets of isothermal retention volumes and assuming a dead space volume of 5 ml. per gram of stationary liquid and an initial temperature of 25' C., the retention temperatures of the n- and cycloalkanes were calculated by numerical integration as functions of the ratio of heating rate to flow rate according to a previously developed equation (6). From these retention temperatures it was possible to determine for any program the retention indices as in Equation 2. Isothermal retention indices were calculated from the isothermal data as in Equation 1. The results are shown in
Figure 2 as plots OS retention index against temperature for isothermal and programmed tempersture operation; in the latter case the abscissa value is the retention temperature of the cycloalkane. The isothermal values given by Wehrli and Kovats are shown as solid points on the ieothermal lines. As might be expected, the I,, values, being averages over the temperature range of the program, show a smaller variation with temperature than do the Ti values and in a rough way the programmed value equals the isothermal value for a temperature 30” to 50” C. below the retention temperature. This is consistent with Giddings’ “significant temperature” concept (8) as were also similar effects observcd in calculations of intrinsic resolution in PTGC (2). Close to the initial temperature, particularly for the lower homologs, the programmed values are unexpectedly low. This is believed to be due to the previously mentioned .r.ery strong curvature often found a t the lower end of the retention temperature-carbon number plot. Even apart from these low values for the lower temperatures, the lines in
Figure 2 do not form a perfectly regular series but this is believed to be due to irregularities in the experimental data. In any case the general pattern is clear. The example here presents the case of a relatively large temperature coefficient of retention index and most substances will be less extreme in their behavior. However, it is apparent that direct comparison of a PTGC retention index with standard isothermal values is inadequate for a refined identification, although i t may still be very useful for a preliminary decision among fairly widely divergent alternatives. Some knowledge of the temperature coefficients of isothermal retention indices will permit more precise differentiation through calculations of the sort presented here. I n principle, the variability of retention index with temperature is an additional characteristic parameter which should be of positive value in identification. ACKNOWLEDGMENT
We are grateful for t,he opportunity to see Dr. Guiochon’s manuscript prior to publication.
LITERATURE CITED
(1) Baumann, F. Klaver, R. F., Johnson, J. F., ’“Gas Chromatography 1962,” M. van Swaay, ed., p. 152, Butterworth’s, London, 1962. (2) Fryer, J. F., Habgood, H. W., Harris, W. E., ANAL.CHEM.33, 1515 (1961). (3) Gidding?? J. C., “Gas Chromatography, S . Brenner, J. E. Callen, M. D. Weiss, eds., p. 57, academic Press, New York, 1962. (4) Guiochon, G., ANAL. CHEY.36, 661 (1964). (5) Habgood, H. W., Harris, W. E., ASAL. CHEY.32, 450 (1960). ( 6 ) van den Dool, H., Kratz, P. D., J. Chromatog. 11, 463 (1963). ( 7 ) Wehrli, A., Kovats, E., Helv. Chim. Acta 42, 2709 (1959). H. W. HABGOOD Research Council of Blberta Edmonton, Alta., Canada W. E. HARRIS Department of Chemistry University of Alberta Edmonton, Alta., Canada RECEIVED for review October 7 , 1963. Accepted December 2, 1963. Division of Analytical Chemistry, 145th Meeting, ACS, New York, S . Y., September 1963. Contribution S o . 231, Research Council of Alberta.
Simultaneous Determination of Sulfur and Phosphorus in Water by Neutron Activation Analysis SIR: Previous atteripts to determine sulfur by neutron activation analysis or by liquid scintillation methods have been described (1-6) The present paper provides data on determination of both sulfur and phosphorus in solution b l measurement of the total beta activity in terms of P32 by neutron activation analysis. The significant reactions to consider in this determination are : P31(n,r)P32 S32(n,p)P32 c13yn,41~32
(1)
(2) (3)
Because the P3I (n,y)Paz reaction results essentially from ZL thermal neutron flux, the amount of P32 formed via Equation 1 can be significantly reduced by cadmium shielding, in comparison to P32formed from Equations 2 and 3. Thus, sulfur and phosphorus may be determined in water by irradiation of two samples contaiuing these constituents, one sample being shielded with cadmium foil and the other unshielded. Equatiois of the form alxl
+ blyl = lil (cadmiim wrapped) uzzz+ bzyl k~ (unwrapped) =
(4)
(5)
HF. The solution was then diluted to 20 ml. with distilled, deionized water, acidified with HS03 before adding 5 ml. of an ammonium molybdate reagent [200 grams of (SH4)6?”107024’ 4H20, 800 ml. of distilled water, and 160 ml. a = counts per minute (c.p.m.) per of S H 4 0 H ] . The solution was stirred microgram (pg.) with the addition of 1 to 2 drops of 1% z = pg. of sulfur aerosol, and heated on a water bath for b = c.p.m. per pg. of phosphorus about 10 minutes with the formation y = pg. of phosphorus of a yellow precipitate (ammonium k = total P32 c.p.m. in sample phosphomolybdate). The mixture was then centrifuged, decanted, and the yellow precipitate washed in 10 ml. EXPERIMENTAL of distilled water, followed by another centrifugation and decantation. The Solutions were prepared by adding yellow precipitate was then dissolved sulfur either as S ~ C ~ Z H ~ S C S(soH ~ S Oin~ 1 ml. of T\”aOH to which 2 ml. of dium dodecyl benzene sulfonate, 99% citric acid solution (0.5 gram per ml.) pure),-Le., ABS, or as Na2S04(sodium was added. Then 10 ml. of a magnesia sulfate, reagent grade) with or without preparation (100 grams of hlgC12. iYa3P04.12H20 (sodium orthophos6H20, 10 drops of HC1, and 100 ml. phate) to distilled, deionized water. of distilled water) Rere added t o the Sulfur and phosphorus were determined solution while stirring. Dropwise adas P32by irradiation of 5-ml. aliquots dition of NH40H formed a white prein triplicate for 500 kw. hours a t a cipitate. ;Ifter the precipitate began thermal-neutron flux of 1.0 X 1013 to form, it was allowed t o stand for neutrons cm.+ second-’ in a Triga about 3 minutes, with the subsequent (General Atomic) Mark I reactor. addition of 4 ml. of XH40H. The After irradiation, phosphorus carrier mixture was then allowed to stand for [(KH4)2HP04],HS03, and Zr(N03)4 20 to 30 minutes before centrifuging were added to the 5-ml. irradiated samand final decantation. The white precipitate was then filtered through a ples to form a white precipitate [Zr8(PO4)4]. After centrifugation and depreviously tared TVhatman S o . 42 cantation, the white precipitate was filter paper disk and subsequently dissolved in 1 to 2 drops of concentrated washed by 1:10 NHIOH, 50% ethanol can be amount solution chloride
employed to calculate the of sulfur and phosphorus in after correcting the IC’s for the content of each sample where
’
VOL. 36, NO. 3, MARCH 1964
665
