Ca hydrocarbon mixture (200 p.p.m. each), the peaks were unduly broad for sample volumcs of 0.28 ml. and larger. The chromatograms for the 0.72-ml. and 0.80-ml. volumes are included to show the effect of similar voliimes injected from sample tubes of widely different internal diameters. The tulle bores are 2.35 and 0.51 mm., respectively. The l a t h volume gave a slightly better separation, even though it is larger, hecause of less mixing of the carrier gas with the sample in the narrow-bore tube. Peak Area Precision. There are two factors which can affect the precision of the peak area measurements made with temperature programmed capillary columns: the relatively small area of the sharp peaks, and the baseline drift caused b y increased column liquid bleeding. J3ase-line drift becomes more pronounced at the high detector sensitivities required for analyzing dilute hydrocarbon gas mixtures. This is shown in Figure 8, for the separation of a mixture containing 10 olefins and n-hexane in 99.9% nitrogen. Altjhough the column was programmed from only 0" to 50" C., some base-line drift occurred, which the operator periodically corrected with the detector balance control. To compare the peak area precision obtained for different chromatographic conditions, the range of the peak area measurements for each of the 11 hydrocarbons mas calculated and is given in Table IIT. These data were obtained with capillary or packed columns that were temperature programmed or operatJed isothermally using nitrogen or hydrogen as the carrier gas. The range values vary to a similar extent, for the different conditions except for those of Figure 8. These values are lower, even
Table 111.
Peak Area Precision for a Dilute Hydrocarbon Mixture
Peak no.,
Fig.
Concn., p.p.m. An&
Range of peak areas ( % of average peak area) na El& Bc Cd
Hydrocarbon Etliylene 83 2.1 7.0 Propylene 100 1.0 5.0 1.3 1-Butene IO2 4 3-Methyl-I-butene 97 1.3 5.3 2.7 2.2 3.2 3.8 5 l-PentJene 98 6 2-Methyl-2-butene 93 1.9 3.5 6.4 3.5 9.G 7 Cyclopentene 75 2.9 8 +Hexane 115 4.2 6.5 2.3 9 1-Hexene 104 1.1 6.5 4.5 6.2 8.0 11.8 10 1-Heptene 51 6.9 2.7 11 2,4,PTrimethyl81 15.5 1-pentene Chromatogram for these conditions shown in Figure 8. Runs, 3; carrier gas, Nz; capillary col.; temp. prog. e Runs, 4; carrier gas, Hz; capillary col.; temp. prog. d Runs, 4; carrier gas, HP; capillary col . isothermal. 8 Runs, 4; carrier gas, Nz; packed col.; 'isothermal. f Runs, 3; carrier ga8, NP; packed col.; isothermal. Results of an independent lab. Runs, 3; carrier gas, Nf; packed col.; isothermal. 8 1 2 :3
3.5
12.4 11.3 15.4
8.1
6.7 7.3 5.7 2.1
F g 3
6.6 8.1 11.7
2.0 4.3 2.1
5.4
12.4
5.6
9.1
5.3
6.1 1.7 2.2
1.4
8.8 17.0 3.0
5
Q
though some of the peak areas had to be corrected for base-line drift. The results of an independent laboratory are included in Table I11 to make a further comparison between packed and capillary columns. On the basis of these values, it is concluded that similar quantitative results for dilute hydrocarbon gas mixtures are obtained with capillary or packed columns. ACKNOWLEDGMENT
The author gratefully acknowledges the nssistance of Thomas Prater, who performed much of the experimental work, and Fred Harder and Jay Haggman, who constructed many of the components that were used in modifying the chromatograph.
LITERATURE CITED
(1) Averill, W., Ettre, L. S., Nafurc 196,
1198 (1962). (2) Bauer, E. I,., "A Statistical Manual for ChemistsJJJp. 11, Academic Press, New Yorli, 1960. (3) Boys, F. L., Chicago Gas Chromatography Discussion Group and the Mid-America Spectroscopy Symposium, Chicago, Ill., May 3, 1962. (4) Gill, H. A., Averill, W., Conference on Analytical Chemistry and Applied Spectroscopy, Pittsburgh, Pa., March 5-9. 1962. (5) McEwen, D. J., J. Chromatog. 9, 266 ( I 982). (6) Teranishi, R., Kimmo, C. C., Corse, J., ANAL.CIiEM. 32, 1384 (1980).
RECEIVED for review December 17, 1962 Accepted July 8, l9G3. Tenth Anachem Conference, Detroit, Michigan, October 22-24, 1962.
A Gas-Density Detector for Gas Chromatography A, G, NERHEIM Research and Development Department, American Oil Co
b To better understand how
a gasdensity detector senses minute changes in composition of the effluent gas, a theory based on the conservation of energy was developed. Equations were developed to show the interrelationship of change in density, flow, and electrical response. On the basis of these equations a simplified gas-density detector was developed. Analyses of complex mixtures-aromatics, saturates, chlorinated and oxygenated compounds-gave accurate results without calibration.
I
N A gas cliromatograpliic system, the detector must respond t80 minute changcs in t81ie composition of t h o gas
1640
ANALYTICAL CHEMISTRY
., Whiting,
Ind.
exiting from the column. Usually the relationship between composition and detector response is complicated and unpredictable and the detector must be calibrated for the individual components ( 2 ) . With a gas-density detector, calibration is eliminated because response depends on a predictable relationship, the difference in the molecular weights of component and carrier gas (11). Because only the carrier gas and not the sample component touches the sensing elements, problems caused by the corrosion of the elements are avoided. Kumerous different carrier gases may be used, but the less cxpensive nitrogcn is quite satisfactory for most dctcrminat8ions. A nmrkable
gas-density detector was first described by Martin (3, 4). However, these detectors have remained so complcx in design and construction, despite efforts to simplify them (7, a), that they have not come into wide use (10). A simpler gas-density detector has been needed. To explain the response of the detector to changes in density, a concept based on the conservation of energy in the gas was developed. To show this dynamic interrelationship quantitatively, simplified equatioiv mere derived. Validity of the equations was confirmed experimentally, and they furnished the basis in attaining an optimum design for a simple gasdensity detector ($.
THEOilY
5
The basic flow pattern in a gasdensity detector is diagrammed in Figure 1. With the conduit network mounted vertically, the reference gas stream enters at A and divides, part flowing up to B and part down to D. The other stream, the effluent from a chromatographic coliinm, enters a t C and also divides, part flowing up to B and part down to D. The divided effluent streams ccmbine with the divided reference streams a t B and D , flow through BE and DE, and exit together a t E . Conduit B D is always filled with effluent :as. When components heavier than the carrier gas are present, the density of the gas in conduit B D is greater an11 the pressure at D is increasecl. With a coniponent lighter than the carrier gas, the pressure a t D is decreased. The change in pressure can be measured in two ways. In one way, used for the Martin gas-density detector, a flowmeter ir a conduit parallel to E D senses chauge in flow caused by changes in pressure :It B and D . The other way is to measure all of the change in flow in the conduits A B and AD and thus eliminate the parallel conduit. The flow in conduit loop ABCDA is related to the pressure drop around this loop :
or
5’
A(AP) = A ~ ( X B - XD)-
~ F A B c D ( A U=) 0 ( 5 )
Figure 1.
AP =
Flow in gas-density detector
P(xB
[F(U)]AB
Equation 2 applies when a component is not present in the effluent gas; Equation 3 applies when a component is present in the effluent gas in conduit BD. The difference between these equations is Equation 4 and may bc. simplified to Equation 5 by assuming AU to be the same in all conduits. The first term in Equation 5 represents the tlevelopment of potential energy because of Ap in the gas in BD. ?‘he second term represents the dissipation of energy because of Ahu caused by A p , By assuming viscous flow, factors from Poiseuille’s equation may be substituted in the second term:
- XD) f
P(XD
- [P(-U)IBC
-
- SO) -
[P(u)lCD
(2)
[E’(-U)lDA
where p = density ( X B - X D ) = vertical height of the gas in conduit BD P = constant for friction, and U = flow rate in conduits A B , BC, CD, and DA.
The first term, involving density and height, represents potential energy. The remaining terms represent the dissipation of energy. Because the terms for the development and dissipation of energy balance out, pressure drop around loop ABCDA is zero. Changes in hp around loop ABCDA are related to changes in p and U . AP
A P = 0 = ( P A-
Ps) $. ( P a - PC) f (PC - P D ) f (PD - P A ) (1)
P(XB
[E’(U)]AB
-
q
=
[F(-U)]DA
- X D )+ P ( x D
-
= gravitational constant D = diameter of conduit
Q
In the loop ABCDA the presence of a component changes the viscosity only in BD. To simplify the experimental evaluation of the terms in Equation 7, the effect of any change in viscosity is considered negligible.
0 (2)
X B )
-
[F(U-k A u l I . 4 ~ - { F [ - ( U - A U ) l } o c [F(U f A U ) ] C D [F(-u - A U ) ] D A = 0 ( 3 )
= pressure (at A , R, C, and D ) . A simple form of Bernoulli’s theorem can be derived by assunling that pressure drop develops as po1,ential energy and dissipates as friction, and by neglecting other forms of energy:
EXPERIMENTAL VERIFICATION
- XO)- [ F ( A u ) ] A B -
A(Ap) = A P ( ~ B
[ ~ ( A ~ ) ]B c[F(AU)lco
= viscosity
L = length of conduit U = flow rnto
- XD) $- P ( X D - X B ) [F(--)li?C - [F(U)lCD -
AP‘ = ~ ’ ( X B
where
where
OF
THEORY
To evaluate each terrn in Equation 7 , an apparatus with gas flow as shown in
-
Figure 1 was constructed. Filament
[ F ( A U ) I D A 0 (4) 10
8 6 Lo
0
4
K
m.
5 i Ea
2
o 2
4
6 8
2
A .10
I 15
20.
I 25
.
I.
I
30
35
128qLAU
40
GM. t -
grrD4 (X,-X,)
FLOW IN CONDUIT, ML. PER MINUTE Figure 2. Effect of change in flow on response
6
4
Figure 3.
IO
8
io5
CM3
Agreement of experiment and theory VOL. 35, NO. 1 1 , OCTOBER 1963
6
1641
flowmeters located in conduits BB’ and DD’ were connected via an electrical bridge to a recording potentiometer. To establish the relationship between AU and electrical response, the conduits BCDE were removed, and rotameters with needle valves were connected t o the flowmeter conduits. With nitrogen flow to A maintained constant a t 50 ml. per minute, flow was diverted from AD to A B and vice versa by adjusting the needle valves. For each conduit, response varied linearly with flow. Therefore, the linear relationship between AU and response was established as shown in Figure 2. The linearity, unlike the nonlinear relationship of conventional flowmeters, may be explained as a direct response to AU as this increment of flow is diverted from one flowmeter to the other. With the diversion of flow shown by the sign, the established nonlinear relationship between flow and response is shown by each flowmeter:
Ei
=
K( U
+ AV)’
and
E? = K(U - AU)’ Because the electrical bridge responds to the difference, El - Ez, which equals 4KUALU, response is linear for this apparatus. To determine AU produced by Ap, conduits BCDE were attached, and with reference and ! ffluent streams flowing a t 50 ml. per minute, known volumes of methane, propane, and butane were injected a t C. The response to the introduction of “sample” was a Gaussian neak. The height of the seak resrekented AU. By assuming that the gases behaved ideally, Ap was calculated from the peak by width at half peak height - the following equation:
-
L
where p n = density of nitrogen, grams/cm.* M , = molecular weight of component
M n = molecular weight of nitrogen V = volume of component charged, cm. B = band width at half peak height, cm. C = l/chart speed, minute/crn. R = flow rate of carrier gm, cm.3/ minute. Of the remaining terms in Equation 7 , tlie viscosity was assumed t o be that of nitrogen; the diameter and length of each conduit were measured directly; and various values of effective height, X B - X D , were obtained by tilting BD from its usual vertical position to angles of 60, 45, 30, and 0 with the horizontal. In Figure 3, Ap for methane, propane, and butane is plotted against 128qLAUl rgD4 (X,- X D ) . Data for components heavier than nitrogen fit the theoretical curve with a positive slope. 1642
ANALYTICAL CHEMISTRY
REFERENCE
@ M M ID d
MM
ID
I O MM
Figure 4.
-
*
IC
I S MM
‘‘\-30
M M ID
Gas-density detector
Data for the component lighter than nitrogen fit the theoretical curve with a negative slope. The positive slope shows that increased density diverts flow through AB, while negative slope shows that decreased density diverts flow through A D . Although ( X B XD),and hence the potential energy, varied by a factor of 10, no significant deviations from experimental error were observed. Despite the scatter of the data, the correlations provide fundamental evidence that Equation 7 describes the operation of the detector and justifies the simplifying assumptions. THE APPLICATION OF THEORY IN DEVELOPING A DETECTOR
The practical problems involved in designing and operating a detector can be assessed quite satisfactorily from Equation 7. The flow rates of reference and effluent gas must be high enough t o maintain AU and thus dissipate the energy developed by Ap. Increasing the
J
flow rates of reference and effluent gases increases the linear dynamic range; increasing the flow rate of effluent gas decreases response time because the volume of conduit BD is filled and emptied more quickly. Linear dynamic range and response time-two important performance characteristics-may be enhanced by increasing flow rate. On the other hand, both may also be enhanced by decreasing detector dimensions, but a t the expense of sensitivity. Enhancement of one characteristic a t the expense of another necessitates compromise in design. To minimize the compromise in design, the basic conduit flowmeter system was modified as shown in Figure 4. Restricting the diameter around the flowmeters to increase flow velocity increases both sensitivity and dynamic range. Restricting the diameter and length of the effluent gas conduit BD
while increasing the diameter of reference gas conduits A B and AD can reduce response time without loss of sensitivity. With these modifications, the flow developed by the potential energy may be used more effectively. To utilize each kind of flowmeter most effectively, two different electrical bridges, shown in Figure 5, were used. -4 parallel bridge mas used with thermistors and a series bridge was used with filaments. In the parallel bridge, the current through the element with the lower resistance increases and that through the element with higher resistance decreases. Because of the negative temperature coefficient of the thermistors, the change in current in the parallel bridge enhances the decrease of resistance in the heated element and the increase of resistance in the coolcd element. h cumulative effect-increasing current coupled with decreaqing resistance in one element paralleling a simultaneous decreasing current coupled with increasing resistance in the otherresults in a larger net change in resistance than that obtainable using a series bridge. In a series bridge, the same amount of current goes through each of the sensing elements. Because of the positive temperature coefficient of the filaments, a net change in resistance is larger than that obtainable with a parallel bridge. Xo cumulative resistance change occurs aith filaments in either bridge.
1
I RECORDER
I PARALLEL BRIDGE, FOR THERMISTORS
SERIES BRIDGE, FOR FILAMENTS
Figure 5. meters
Electrical bridges for flow-
35
7I I
30r
I
I
I
Table I. Comparison of Detector Performance with Filament and Thermistor Flowmeter Elements
i'
SensiOpti- tivFlowmum ity, meter cur- mv. elerent, ml./ Noise, ment ma. mg. mv. Filament 110 250 0.006 Thermistor 5 3200 0.013
25
ln
Detection limit, mg./ml.
~~
Z
0
Eco
20
w'
rc
Figure 6. Effect of flow rate on respon:e time
W
co Z
15
2co W E
IO
50
25
0
75
100
125
Ap =
7
0.623
Vd F
--
n.herr time, seconds volume of B D 4.9 ml. flow rate, ml./second
T
= response
Vd F
= =
Response time decreases with flow for both detectors as shown in Figure 6 and approaches the theoretical limit. Because the gas-density detector is a flow-through rather than a diffusion device, only peak shape but not peak area is affected by the response time (12).
Sensitivity was calculated from a peak area produced by 0.24 mg. of butane. The limit of detection was defined as twice the noise level divided by sensitivity (16). Limit of detection varied with current; therefore, an optimum current was determined for each type of flowmeter as shown in Table I. To determine current giving lowest limit of detection, the values were determined for a range of currents, Because the limit of detection is six times better for the thermistor detector, it is preferred to the filament detector a t room tem-
8X
perature. The greater sensitivity of thermistors probably results from the advantages of a higher temperature coefficient and resistance outweighing the disadvantages of small current and element area when used in the parallel bridge. Response in the form of chromatographic peaks produced by 5 rl. of two known blends was used to obtain precision and accuracy data shown in Table 11. To convert the peak area to quantity of component, a factor was derived from Equation 8:
FLOW RATE, ML. PER MINUTE
The bridges n ere ( onnected directly to a recording potentiometer. Because rcsponse nas adequat 3, the preamplifier rcquired nith some detectors was not necded. In special c:tses only, such as operation a t high temperature, a preainplifier may be helpful. Testing Detector Performance. h s e d on these refinements in conduit-flowmeter design, two glass detector-. nere mad( ( 9 ) . One contained li inatched pair of 1% filaments, the other a matched pair of 8K thermidors. Each pair T,as provided nith appropriate electrical bridges. Data for response t.me were obtained from the response of :he detector to an instantaneous change in gas density (9). -111 other determinations were made using conventional gat; chromatographic procedures. A reference and a chromatographic column \?ere attached to the detector in an insulated case at room temperature. Xtrogen was used in both column5 at the same flon rate of BO ml. per minute. Samples \\ere injccted to the inlet of th: chromatographic column n ith a 1iypode.mic syringe. I)Lcly)on.;etime is directly proportional t ? the time of filling or emptying conduit 13D. but cannot be lrss than the theoretical limit defined by ( I ) :
48 X 10-6
P,YM,
+ P,'II,
-
- pJfn
YP,M"
Mn (10)
diere Y
=
mole fraction.
APM, = Y p n ( M u
- M,)
(11)
By multiplying through Equation 12 with the molecular weight of the component, mole fraction (Y) was converted to a measure of the weight of the component ( YM,).
The appropriate factor, M , / ( M , - U,,), was used to convert peak area to a measure of the weight of component. Errors ranged from 1 to 3y0 in both blends. Although one blend contained only hydrocarbons and the other contained hydrocarbons and non-
Table 11.
Typical Precision and Accuracy Obtained with the Gas-Density Detectors Thermistor flowmeter ~_ Filament flowmeter Component Wt. yo Mean error Wt. yo Error
Blend I n-Pentane 2,2-Dimethylbutane 2-Methylpentane n-Hexane Blend I1 Ether 2-Methylpentane Chloroform Benzene
11.6 i: 0 . 3 18.9 f 0 . 3 3 1 . 2 f 0.4 38.3 f 0 . 4
-0.2 +0.1 0.0 +o. 1
11.6 f 0 . 3 18.9 f 0 . 3 31.1 f 0 . 4 38.4 i: 0.5
14.2 =k 0 . 3 13.2 & 0 . 3 29.7 f 0.4 42.9 i: 0.4
+0.2 +0.3 -0.3 -0.1
... ...
-0.2 $0.1 -0.1 $0.2
...
...
VOL. 35, NO. 1 1 , OCTOBER 1963
0
1643
hydrocarbons, accurate results within the confidence interval were obtained without calibrating. These results substantiate the assumption that effects other than change in density are not significant under these conditions. hrthermore, the validity of eliminating calibration by using the gas-density detector was independently substantiated by the analysis of the synthetic blends (6). DISCUSSION
Modifications of the approach are required for two components, hydrogen and ethane. Hydrogen causes a large Ap and AU (about 20 times larger than that of other components for a given weight). Flow rates must be increased not only to dissipate the energy developed by a large Ap, but to prevent highly diffusive hydrogen from reaching the sensing elements. Even with these precautions, results, although linear, are 5y0 low. Apparently other effects, such as viscosity effects, become significant with the 20-fold increase in flow rates. Ethane causes an extremely small Ap and AU because its molecular weight is nearly that of nitrogen. The
response is low enough to cause poor precision. The obvious solution is to use a carrier gas of a different molecular weight. For over five years, gas-density detectors have been used to analyze many digerent samples including olefins in naphtha, products of paraffin isomerization and light naphthas in crude (6, 6, 14). Calibrations of thermalconductivity cells would have been difficult and time consuming because of the large number of components, the presence of both liquids and gases in the samples, and the extreme nonlinear thermal-conductivity behavior of hydrogen in helium (13). With the gasdensity detector, no calibration was needed other than the 5% correction for hydrogen. Commercial models of the gas-density detector have been developed by the Gow-Mac Instrument Co. These more sophisticated detectors are made of metal, have interchangeable flowmeters, and may be operated a t 300” C.
raphy,” p. 31, Reinhold, New York, 1957. (3) Martin, A. J. P., U. S. Patent 2,728,219 (Dec. 27, 1955). (4) Martin, A. J. P., James, A. T., Biochem. J . 63, 138 (1956). (5) Martin, R. L., ANAL. CHEW 32, 336 (1960). (6) Martin, R. L., Winters, J. C., Ibid., 31,1954 (1959). (7) Munday, C. W., Primavesi, G. R., ‘‘Vapour Phase Chromatography,” D. H. Desty, ed., p. 146, Academic Press, New York, 1957. (8) Murray, K. E., AuslTakzn J . A p p l . Sci. 10, 156 (1959). (9) Nerheim, A. G. (to Standard Oil Company of Indiana), U. S. Patents 3,090,112 (May 28, 1963), and 3,082,618 (March 26, 1963); and Rushton, J. H., U. S. Patent 3,082,619 (hfaroh 26, 1963); and Tucker, E. B., U. S. Patent 3,050,984 (August 28, 1962). (10) Pecsok, R. L., “Principles a n i Practice of Gas Chromatography, p. 119, Wiley, New York, 1959. (11) Phillips, C. S. G., Timms, P. I,., J . C h T m t o g . 5,131 (1961). (12) Schmauch, L. J., ANAL. CHEM.31, 225 11959). ch, L. J., Dinerstein, R. A., 43 (1960). , J. C., Jones, F. S., Martin,
LITERATURE CITED
(15) Young; J. G., Second Symposium on Gas Chromatography, East Lansing, Mich., June 11, 1959. RECEIVEDfor review May 3, 1963. Accepted July 18, 1963.
(1) Desty, D. H., “Gas Chromatography,” D. H. Desty, ed., p. 200, Academic
Press, New York, 1957.
(2) Keulemans, A. I. M., “Gas Chromag-
Preparation of Methyl Esters for Gas Liquid Chromatography of Acids by Pyrolysis of Tetra methylammonium Sa Its ERNEST W. ROBB and JOHN
J. WESTBROOK 111
Philip Morris Research Center, Richmond, Vu.
b The tetramethylammonium salts of carboxylic acids are converted to the corresponding methyl esters in high yield when they are injected into a commercial gas chromatographic unit at a vaporizer temperature of 330” to 365” C. The tetramethylammonium salts are prepared either by titrating the acids with tetramethylammonium hydroxide or by ion exchange on an anion exchange resin. This reaction has several advantages compared with existing methylation procedures in the gas chromatographic analysis of acids. However, the yield of methyl ester is lower if the sample size is less than 50 pg.; and oxalic, malonic, malic, and citric acids do not yield any methyl ester by this procedure.
T
chromatography of carboxylic acids is difficult because their polarity and tendency to dimerize cause trailing, poorly shaped peaks, and HE GAS LIQUID
1644
ANALYTICAL
CHEMISTRY
nonreproducible retention times unless recourse is had to chromatographic phases especially designed for acids. In addition, their polarity results in excessively long retention times for the higher molecular weight acids. For these reasons mixtures of acids are commonly converted to their methyl esters before they are chromatographed, and a considerable number of papers have dealt with methods for methylating acids. Vorbeck et al. (9), and Kirkland (6) have discussed the relative merits of commonly used methylation procedures. Recently two techniques have been described in which acids are converted to esters by a pyrolysis reaction, the esters formed being swept directly onto a chromatographic column. In one procedure a mixture of the dry potassium salts of the acids and ethyl potassium sulfate is heated in a pyrolysis device (6, 8). In the other, the acids, mixed with boron trifluoride etherate
and alcohol, are injcctcd into :t hcatctl chamber ( 2 ) . In an attempt to dcvise a procedure in which the methyl esters would be formed during the chromatographic step, but which would not require any special apparatus, the authors considered the pyrolysis of tetramethylammonium salts of acids. This reaction was reported by Prelog and Picentanida (7), who found that when the tetramethylammonium salts of acids were heated, trimethylamine was driven off and a residue of nearly pure methyl ester remained. The reaction was later applied to the methylation of some sterically hindered benzoic acids by Fuson, Corse, and Homing (3). They reported that pyrolysis a t 200” to 250’ C. gave 60 to 90% yields of methj.1 esters. We have found that this reaction proceeds rapidly a t the temperatures obtainable in the injection ports of commercial gas chromatography units, so that when solutions of tetramethyl-
