Table I. Response to Electron Capture Detection and Retention Times for Some Derivatives of Chlorthalidone
Derivative of chlorthalidone
Relative retention
Tetramethyl Tetraethyl Tetrapropyl
1.oo 1.46 2.31
Table II. Precision of t h e Method of Determination at Different Chlorthalidone Levels
Minimum detectable quantity, mole/sec
x
10-16
1.5 1.5 1.4
Their relative retentions and sensitivities in MDQ units (9) are given in Table I. The tetraethyl derivative was selected as internal standard and was dissolved in the hexane used for the final solution. Determinations in Plasma. A gas chromatogram from a plasma sample to which chlorthalidone had been added to a concentration of 11 ng/ml is given in Figure 4. For comparison a plasma sample with no chlorthalidone added was analyzed, Figure 5 . As can be seen from the figures, no disturbing peaks are present at the retention time of tetramethyl chlorthalidone. A standard curve was prepared by analyzing plasma samples to which chlorthalidone had been added in different amounts. The curve is linear up to at least 0.3 ng of chlorothalidone injected and passes through the origin. The relative standard deviations when the method of (9) T. Walle and H . Ehrsson. Acta Pharm. Suecica, 7, 389 (1970)
PI asma, concentration of chlorthalidone, ngIm1
Relative standard deviation,
5.5 55.0
5.6 2.5
Yo
determination is applied to plasma samples are demonstrated in Table I1 for two different concentration levels. The method offers possibilities of determining plasma levels down to 2 ng of chlorthalidone per ml sample with acceptable precision. The minimum detectable concentration (defined as 3 times the background noise level) is about 10 times lower. The method has been proved t o work perfectly on other biological fluids such as whole blood after hemolysis and urine.
ACKNOWLEDGMENT The authors are indebted to Arne Brandstrom for valuable suggestions on the extractive alkylation procedure. Received for review January 22, 1973. Accepted August 16, 1973. The authors gratefully acknowledge the financial support of the Swedish Board for Technical Development regarding our “Ion Pair Research Project.”
Thermal Conductivity Detection: Prediction of Response from Kinetic Theory Daniel W. McMorris TR W Systems Group, One Space Park, Redondo Beach, Calif.
Peak area data obtained with a thermal conductivity detector (TCD) for the solutes H2, NP, 02, CH4, Kr, CO2, C2H6 in a He carrier are given. The dependence of peak areas on gaseous thermal conductivity is discussed in terms of an absolute theory of the sensor, the thermistors of which are operated in a constant temperature mode. The dependence of thermal conductivity on solute concentration was calculated from simplified versions of the Chapman-Enskog theory: corrections for solute internal energy were made using an empirical expression. The results are not presented but are summarized briefly. More detailed and successful calculations based on the Lennard-Jones 6-1 2 model with a theoretical expression for internal energy correction are presented and compared with experiment; correlation is good but the absolute predictions of the theory are about 70% high. The error may be ascribed to the effect of unidentified stray heat losses of the thermistor.
The thermal conductivity detector (TCD) developed for the chromatograph in the gas exchange experiment ( I ) of the Viking Lander Biology Instrument (VLBI) employs a 42
self-heated 0.014-inch diameter thermistor bead suspended in a helium carrier flowing through a 60-111 cavity. The use of helium renders negligible the calculated heat loss through the supports, and tests show that free and forced convection cooling are also negligible. Therefore, gas conduction is the dominant heat loss mechanism. The accumulation of test data in the VLBI Test Standards program provided an occasion for comparison with theory. Changes in heat loss are monitored by the electronics as changes in thermistor voltage. Neglecting wall effects, the theoretical voltage is derived by equating the electrical power input to the power dissipation of the bead into an infinite gas medium:
V 2 / R= 6(TT - TO; Tr, T,. (1) where V is the voltage, R is the resistance, and 6 the dissipation constant of the bead, TTand TG are the thermistor and surrounding gas temperatures, and Tu, is the detector wall temperature. TT is a function of R, given by the resistance-temperature characteristic of the thermistor. For a number of reasons, it was decided in this design to hold R and TT constant by means of a feedback loop, ( 1 ) V. I . Oyarna, Icarus. 16. 167 (1972)
A N A L Y T I C A L CHEMISTRY, VOL. 46, NO. 1, J A N U A R Y 1974
making the squared voltage directly proportional to the instantaneous dissipation constant. For a spherical bead of diameter d in a medium of thermal conductivity X ( 2 ) :
d = 2aAd(cal
- "c-' - sec-')
(2)
By differentiation, one finds the approximation: (3) where c, is the molar concentration of the solute in the detector chamber, and f i is an assumed constant of proportionality which may be called the "thermal conductivity factor." The instantaneous value of c, is usually difficult to measure. One may obtain a more useful form from the chain rule:
where dq,/dt and dqc/dt are molar flow rates of solute and carrier, respectively. Substituting into the previous expression and integrating:
1 fist (5) 2 9' The experimental peak areas J AV, d t corresponding to known injections of the solutes q , can thus be used to find relative values of the factor f i . If qc is known, then absolute f,'s can be determined. Conversely, theoretical prediction of detector performance depends on the prediction off,.
the gases. On the other hand, the rigid sphere approximation does give a reasonable value for G which makes f l z = 0 in the case where the solute is identical with the carrier. With other models, one does not always find closed-form expressions for G. If A and B are simple constants, G can be determined simply by forcing the thermal conductivity factor to zero for the case of solute = carrier: m, = mi; u,? = u , (9) In the more general case where A and B vary with the solute, this procedure would be inadequate. Chapman and Cowling resorted to fitting procedures in the justification of the original theory [ ( 4 ) ,sections 12.5 and 13.51. There is another difficulty: The Chapman-Enskog theory assumes monatomic molecules. Although Littlewood assumed the internal energy to have negligible effect, an empirical correction can be used (5, 6): f12
= 0;
from which one may derive:
SAV& --=--
V
THEORY Littlewood ( 3 ) proposed the use of the Chapman-Enskog theory in its first approximation, which can be written in the form:
X,IF,,
=
G(
2m2
m,
+ m2
)1'2(%!)2
u1
where P, Q, and R are obtained in terms of molecular masses ml,m2, and collision integrals A and B. A, B, geometrical factor G and collision diameters 6 1 2 depend on the model chosen ( 4 ) . In the rigid sphere approximation:
.4
= 0.4;
B
0.6; G = 514; a12/ul= ( u l
=
+ u,)/2u1
(7)
where g i ,m, are molecular diameters and masses. Littlewood found the limit of f l z for a solute of large mass: lim '7,
n,
- i
-(i>
f 12 - - Q X
R
Fl2
=
- %3(%) UI
(8)
He obtained good results for heavy organic vapors in helium and interpreted the expression in terms of the scattering of carrier molecules by the larger and relatively motionless vapor molecules. In this study, we were concerned with both light and heavy solutes which do not all behave like hard spheres. The wide range of masses led us to return to the general expression above; however, it was not obvious that the rigid sphere approximation would be adequate for all of ( 2 ) R. B. Bird, E. N . Lightfoot, and W. E. Stewart, "Transport Phenome-
na," Wiley, New York, N . Y . , 1960. ( 3 ) A . B. Littlewood, Nature, 184, 1631 (1959). ( 4 ) S. Chapman and T. G . Cowling, "The Mathematical Theory of NonUniform Gases." 2nd ed., Cambridge Univ. Press, London, 1960.
A theoretical expression due to Hirschfelder is summarized and correlated with experimental data in (7) and may be used to derive: (12)
where DlzlD1 is a ratio of diffusion constants which is on the order of unity for light sources. Since the Ei are related to the extra specific heat of a polyatomic gas, the second term on the right-hand side of these expressions will be referred to as the specific heat correction. The Ei correlate well with the following expression (8):
where cp and c, are the specific heats at constant pressure and volume. They are not strongly temperature dependent, and reasonable values can be obtained from tables (8, 9) or estimated from ideal-gas formulas (8).These procedures were followed in the present work, as an alternative to direct determination of the E, from thermal conductivity and other data.
EXPERIMENTAL Figure 1 shows response data for the six VLBI Gas Exchange gases, plus some extra data on ethane, all taken during the VLBI Test Standards program. Peak areas obtained with the Varian digital integrator checked within 370 with independent area values from computer analysis of the detector output. Table I summarizes the experimental thermal conductivity factors derived from Figure l. The injections were made on a 22-ft long, h j - i n . 0.d. column filled with Porapak Q, from a precision gas mixture made up by Matheson Gas Products and quoted accurate to within 1%of the individual fractional concentrations. The reproducibility of the gas sampling valve was nominally 1%.
( 5 ) J. 0. Hirschfelder, C. F . Curtiss, and R . 6.Bird, "Molecular Theory
of Gases and Liquids," Wiley, New York, N . Y . , 1954. (6) R . S. Hansen, R . R. Frost, and J. A . M u r p h y , J. Phys. Chem.. 68, 2028 (1964). ( 7 ) B. N . Srivastava and A. K . Barua, J . Chem. Phys., 32, 427 (1960). (8) E. H. Kennard, "Kinetic Theory of Gases." McGraw-Hill, New York. N . Y . , 1938.
( 9 ) "International Critical Tabies." Vol. 5, E . W . Washburn, Ed., National Research Council, 1929.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 1, J A N U A R Y 1974
43
1o4
103
/ 102
10
1.0
I
0.1
50
I
I
I 1
I
I
I
5x102
1 5 x103
5x104
5x10’
PEAK AREA Figure 1. Relation between injected gas quantity q L and peak area and peak area is in microvoltseconds.
44
.f AV dt for the
A N A L Y T I C A L C H E M I S T R Y , VOL. 46, N O . 1, J A N U A R Y 1 9 7 4
V L B l gases. Injected gas quantity is in nanomoles,
Table I. Experimental Response Factorsa Area response (volt-sec-mole- ’)
Gas
Nz
0.084 X 1O5 3.31
0 2
3.15
CH4
2.83 4.30 3.75 4.30
H2
Kr
co2 C2H6
fe x
0.037 1.47 1.40 1.26 1.91 1.67 1.91
Conditions: Detector temperature, 32 “C; thermistor temperature, 96 “C; thermistor voltage, 5.025 V . flow rate, 15.0 cm3-min-’; pressure, 1 atm
approximation overestimates the specific heat correction for heavy solutes. Calculations for heavy organics using Equation 11 gave very poor results when compared with experimental values of Rosie and Grob ( 3 ) . Accordingly, the final calculations given in Table I1 were done using the specific heat correction given by Equation 12. (Details given in the Appendix.) In this approximation, ethane lies on a line with its neighbors, and it is also found that reasonable results are obtained for solutes heavier than ethane. An attempt was made to compare the monatomic predictions of Equation 6 with literature data on mixtures of noble gases (10-12). Due to variations between different experimenters and a generally insufficient number of ex-
Table I I. Chapman-Enskog Theory in Lennard-Jones 6-1 2 Approximation Input data ( A = 0.443=, B = 0.654a,
c/kC
10.22 38.0 79.8 88.0 144 190 21 3 230
LTC
2.576 2.915 3.749 3.541 3.796 3.610 3.897 4.418
rn
Output data
r = 336
4.00 2.02 28.0 32.0 16.0 82.9 44.0 30.0
(G =
OK*)
1.12ge, U I ( V I = 2.128,
-Ui(di
= 2.009)
CPd
Yd
U121vif
Ui2(dif
fthimon)‘
fth‘
20.9 28.6 29.0 29.2 35.5 20.8 36.6 48.5
1.66 1.41 1.40 1.40 1.31 1.68 1.30 1.22
2.40 2.84 2.75 2.92 2.87 3.02 3.27
2.27 2.69 2.61 2.78 2.73 2.87 3.11
-0.337 -2.59 -2.47 -2.42 -3.06 -3.21 -3.64
-0.089 -2.47 -2.35 -2.22 -3.06 -3.02 -3.35
/
ft h rex
2.40 1.68 1.68 1.76 1.60 1.81 1.75
*
n Reference ( 5 ) , Equations 8.5-15, 16, 17, Table I-N. Average temperature of TT and Tw in Equation 1. Reference (5),Table I-A. Reference (9). e From Equation 9. f Reference (5),pp 552 et seq. Columns one and four of Reference (6),Table I-M were fitted by analytic substitution (see Appendix). g f t h l m i , , , is , the monatomic thermal conductivity factor from Equation 6; f t h includes the specific heat correction from Equation 12.
-~
DISCUSSION The Chapman-Enskog expression was programmed with different molecular models and specific heat corrections. The first calculations were done for rigid spheres with the specific heat correction of Equation 11. The correlation with experiment was fair, but the calculated values averaged high. More realistic numbers were obtained by substituting Lennard-Jones 6-12 values of collision integrals A and B. Fortuitously, these integrals were nearly constant for all of the solutes (cf. ( 5 ) , p 528 and Table I-N); therefore, G was determined uza Equation 9. It was found, and is easily verified, that the Lennard-Jones collision integrals lead directly to smaller answers from the Chapman-Enskog expression, and also indirectly via Equation 9 (they yield a lower value of G). Complete calculations were then carried through using the Lennard-Jones 6- 12 approximation for the collision diameters as well as the collision integrals, and using Equation 11 for the specific heat correction. Due to the way in which force constants are averaged, u12/u1 was found to be lower than in the rigid sphere approximation, which aided in bringing the calculations closer to experiment. The calculated values were still high, but all gases except ethane lay close to a straight-line fit. The problem with ethane was found to be fundamental. The specific heat correction of Equation 12, which has the most secure foundation (7), involves a ratio D12/01 which is very similar to the ratio F12/X occuring in Equation 6. It is proportional to a ratio (r1/u12)* which is less than unity for heavy solutes. (The U ’ S here are “diffusion diameters,’’ different but closely related to the “viscosity diameters” of Equation 6.) If Equation 11 is considered to be an approximation to Equation 12, then it is clear that this
perimental points, such data were not found to be more reliable than &20% for the determination of thermal conductivity factors. Within that accuracy, the ChapmanEnskog expression was found valid as implemented in this paper, and no systematic bias was found. Data for diatomic gases N2 and 0 2 in helium (13) gave some indication that Equation 12 undercorrects for these light solutes. However, the greater part of the residual systematic error evident in the far right column of Table I1 may be ascribed to error in the assumptions that were made regarding stray heat loss of the thermistor. The effect of such stray losses is to reduce the detector response by a factor which, for the present, must be determined empirically.
CONCLUSIONS The absolute response obtained from Littlewood’s rigid sphere approximation is, in the more exact Lennard-Jones approximation, lower due to the combined effects of the collision integrals and the collision diameter. In addition, the response is subject to a specific heat correction in the case of a polyatomic solute. The approach illustrated by the present work is accurate enough to be useful for predictions of TCD response to fixed gases and light organics for which Littlewood’s approximation and its variations (14) are not valid. Further, the equations given here may be compared directly wit,h such approximations in the interest of elucidating their physical basis. W. Van Dael and H. Cauwenbergh, Physica, 40, 165-181 (1968). E. Thornton, Proc. Phys. SOC. (London). 76, 104 (1970). S. C. Saxena. lnd. J. Phys., 31. 597 (1957). M . P. Saksena and M. L. Sharma. J. Phys. 2 , Ser. 2, 2, 898 (1969). (14) E. F. Barry, R . S. Fischer, and D . M . Rosie, Anal. Chern., 44, 1559 (1972). (10) (1 1) (12) (13)
A N A L Y T I C A L C H E M I S T R Y , VOL. 46, NO. 1, J A N U A R Y 1974
45
The practical difficulties in estimating valid molecular parameters and correcting for polar gases are similar to those encountered in implementing Littlewood’s approximation, and are discussed elsewhere ( 1 5 ) .
APPENDIX The collision diameter u12(”) in the present work was calculated from data in the first two columns of Table I1 as follows: 0 1 2 ( U ) = u 1 2 J Q 1 2 ‘ 2 9 2 ’ * (TlZ*)
where
~ 1 = 2
(u1
+ ~ 2 ) / 2 T; ~ z=* k
T / G
(15) E. F. Barryand D M . Rosie,J. Chrornatogr.,59, 269 (1971).
where I = ln(T12*), IO = ln(20), YO = 0.7432, YI = -0.1112, Y2 = 0.005706, Y4 = 0.005018. The above expansion gave an adequate fit of the fourth column of Table I-M of ( 5 ) for T ~ z * between 2.5 and 20, and obviated the need for supplying these tabular data as part of the program. U 1 2 ( d ) was similarly computed from Q12(1J)* using: Yo = 0.6640, Y1 = -0.1064, Yz = 0.007620, and Y4 = 0.004356, which fits the first column of the table over the same range. Received for review March 21, 1973. Accepted July 13, 1973.
Characterization of Wood-Preserving Coal-Tar Creosote Gas-Liquid Chromatography F. H. Max Nestler Forest Products Laboratory, Forest Service, U.S. Department of Agriculture, P. 0. Box 5130, Madison, Wis. 53705
Six whole coal-tar creosotes, two of which represent contemporary commercial production, were analyzed by GLC on an SE-30 packing. Retention data for 14 standard compounds were determined for the four liquid phases: SE-30, ApL, OV-17, DEGS. The linear relationship observed between log relative retention in SE-30 and atmospheric boiling point permitted the quantitative interpretation of isothermal chromatograms in terms of a simulated distillation analysis. The latter results agreed very well with precision fractional distillation data, but much less so with the American Wood-Preservers’ Association Standard Method. The boiling ranges selected for comparison of the three sets of data were those established for the AWPA Standard Method.
21 most probable components could be assembled. Of those listed therein, 15 were characterized as major components inasmuch as they were consistently identified by more than one investigator, and were present at more than 1%. Furthermore, quantitative data were interpreted to indicate that the 15 components could comprise almost 61% of whole creosote. Objectives of the present study were (a) to validate and extend the data and conclusions reported in the review and (b) to determine to what extent GC data could be correlated with the generalizations provided by the older methods of analysis. Objective (b) is particularly relevant to numerous long-term, in-service studies which are part of this Laboratory’s wood preservation research program.
In a review of the literature (I), the author has shown that the chemical composition of wood-preserving coal-tar creosote is poorly defined in its commercial application. A proposed federal specification (Z),for example, requires only that applicable material meet certain physical requirements. The methods of both general and specification ( 3 ) analysis in use during past decades, and still used, are archaic; at best they have provided broad, though valid, generalizations between gross chemical composition and the toxicity-preservative function. There is need for more detailed knowledge of chemical composition in order better to understand and document this toxic and preservative action of creosote in wood. From correlation of the data cited in the review, it was learned that the chemical compositon of whole, unfractionated creosote was known well enough that a table of
Gas Chromatography. The apparatus was described previously (4);experimental procedures were similar for this work. Column temperatures were 200, 225, and 250 “C; the injection vaporizer temperature was 300 “C for the majority of the data reported.
EXPERIMENTAL
(1) F. H . Max Nestler, U.S. Forest Sew. Res. Paper FPL 195, Forest
Products Laboratory, Madison, Wis., in press.
( 2 ) U S . Federal Supply Service, Creosote, coal tar, technical, Federal Specification TT-C-645b, Nov. 14, 1967. (3) American Wood-Preservers’Association, “The AWPA Book of Standards,“ 1971 ed.
46
Thermal conductivity detector response factors (discussed later) were measured a t a detector temperature of 250 “C after preliminary investigation of the effect of vaporizer and detector temperature changes upon this variable. Carrier gas flow rate (nominal) was varied over the range 25 to 150 ml/min, commensurate with solute retention times and peak shape (area). Four liquid phases were tested, each supported by AnakromABS-70/80 mesh, a t the loading shown in parentheses. These were, in order of increasing selectivity: GE SE-30, GC grade (15%), methyl silicone, nonpolar; ApL (lO.l”/o), Apiezon-L, hydrocarbon grease, nonpolar; OV-17 (9.1%), 50% phenyl silicone, medium polar; DEGS “stabilized” (15%), diethylene glycol succinate, very polar. A second, normal DEGS packing gave equal results. All packing components were commercially available products, with preference for those specifically designed or prepared for GC usage. Reagents. Reference solutes were purchased from the commercial sources noted in the last column of Table I. Where there was a choice, those having a stated purity better than 99% were selected. Far any showing the presence of impurity peaks, as deter(4) F. H Max Nestler and D F Zinkel, Anal. Chem., 39, 1118 (1967)
ANALYTICAL CHEMISTRY, VOL. 46, NO. 1, JANUARY 1974
