Gas Density Balance Calibration Technique Application to Relative Response Factors for Thermal Conductivity Detectors Jean Vermont and C. L. Guillemin Societe Rhone-Progil, Centre de Recherches d'Aubervilliers, 93308, France
The technique of using gas density balance as a calibrating detector has already proved its usefulness for the determination of relative response factors. Coupled with a new procedure, called "Separate Injections," this technique gives increased accuracy and saves time over traditional calibration techniques. Thus, the average accuracy of relative response factors, up to the extreme case of a solid with respect to a gas, is in the region of 1 to 2%. Moreover these factors can be obtained in a few days instead of a few weeks. Because of these characteristics, this technique appears to be a new way to investigate chromatographic detectors and is used to study the influence of the internal geometry of thermal conductivity (TC) detectors on relative response factors. Results from a study of five different commercial TC detectors, using C1 and C2 chlorinated hydrocarbons, show that relative response factors can vary up to 18% from a flow-through to a semi-diffusion TC detector. From a practical point of view, it may be concluded that no universal relative response factors exist and those which are published, should be followed by more information on geometry of the cells and basic operating conditions.
The errors of classical calibration techniques may originate in any successive step of calibration: weighing, standard purity, sample preparation, sample injection, etc. (1). The technique of using gas density balance as a calibrating detector, reported in several publications (2-4), eliminates some of these intermediate steps and allows the determination of relative response factors for other types of detectors. But a new procedure leads to an improvement in accuracy and time-saving, a t the same time giving an additional approach to the knowledge of usual detectors, for which so many theoretical studies have already been made. Review of t h e Technique of Using the Gas Density Balance as a Calibrating Detector. First of all, to avoid any confusion between nomenclatures existing in international literature, it must be recalled that the fundamental equation of GC used in quantitative analysis is expressed, either by Qi
=
~IAI
(1)
or
QlSi in which
Q1
=
Ai
is the amount of substance 1 injected; AI, the
( 1 ) G . Guiochon. M . Goedert, and L. Jacob, "Gas Chromatagraphy1970," R. Stock, Ed., Elsevier, London, 1971. ( 2 ) C. L . Guillemin, Melle F. Auricourt, J , d u Crest, and J. Vermont, J . Chromatogr. Sci. 7 , 493 (1969). (3) C . L . Guillemin, Melle F. Auricourt, a n d J . Vermont, Chromatographta. 9-10, 357 (1958). ( 4 ) C. L. Guillemin, Melle F . Auricourt, and P. Blaise, Fresenius' 2. Ana/ Chem.. 2 2 7 , 260 (1967).
corresponding peak area 1; and SI is the absolute sensitivity factor of Dimbat, Porter, and Stross (5). In general, one is interested in relative response factors; in the following one will designate, for instance, f 3/2 or f 3/1 the relative response factor of component 3 with respect to component 2 or 1. Briefly, the technique consists of mounting the gas density balance, which has a predictible response, in parallel with the detector to be calibrated (Figure la). One injects in I, without any particular precaution, a mixture of known qualitative composition but of any quantitative composition whatever. This mixture may consist of gases, more or less volatile liquids, or even solids. The simultaneous recording of the response of both detectors allows the knowledge of the relative weight concentrations of the components to be obtained by using the gas density balance chromatogram, as well as the calculation of relative response factors by comparing both chromatograms and applying the following equation:
Cz, C 3 are the relative concentrations in weight of solutes 2 and 3 (given by the gas density balance); Mz, M3, mg, respectively, stand for molecular weight of solutes 2 and 3 and carrier gas 1; A2 ( E ) , A3 ( B ) ,A2 ( x ) , A3 ( x ) are the peak areas of solutes 2 and 3, respectively, given by the balance ( E ) and the detector to be calibrated ( x ) . The advantages of this technique are: Elimination of pure calibration standards. Elimination of the problem of sampling simultaneously gases, more or less volatile liquids, and solids. The technique only requires qualitative mixtures of two or more known components. This calibration technique permits one to obtain relative response factors for all components without any restriction: isomers, isotopes, toxic or corrosive components etc. The technique allows one to obtain relative response factors for all types of detectors and operating conditions. Relative response factors are independent of irreversible absorption phenomena in the chromatographic column. The accuracy of the correction factors depends only on the peak area measurements and operation within the linear range of the two detectors.
IMPROVEMENT OF THE TECHNIQUE Apparatus. Figure l b . The special apparatus is built by Carlo Erba (Milano). Basically the system remains the same except that it includes two ovens with an injection port and a column in each of them. The gas density balance, the detector to be calibrated, and the flow divider are placed in the second oven. To make the different flow systems independent of each other, the flows are controlled with pressure regulators. In the case of a T C detector (Figure l b ) , three gas lines are to be provided for feeding the reference TC cell, feeding the column (5) M. Dimbat, P. E. Porter, and F . M . Stross, Anal. Chern.. 28, 290 (1956).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 4, APRIL 1973 e 775
Table I. Linearity of Flow-Divider Split ratios of t h e flow-divider FID/B
113
7(FID)
Average of 10 runs 0.998
I
I
1.022
0.998
1.077
1.027
I I
,
1
AIR I
I
CGAS
t CARRIER GAS
I
I
!
I
0.2%
1.029
1.027
I
CGAS
0.1%
0.5%
0.1% 0.999
0.4% 1.081
out with an EA1 PACE system.
When calibrating different detectors, a parallel flow system is preferable to a series system to avoid any influence of the detectors on each other ( e g., FID detectors). Such a “flow divider” is not comparable to a classical “splitter” used for capillary colilmns; the former divides a homogeneous binary mixture of solute diluted in carrier gas downstream the column with a split ratio of 1 to 1 or 1 to 30; the latter splits a heterogeneous mixture in front of the column with a split ratio a t least of I to 1,ooO. Since this calibration technique does not need information on the absolute values of concentration in the mixture, the absolute value of the split ratio of the flow divider does not need to be known either. However, the split ratio has to be constant during an entire run. The constancy of the flow divider has been tested by successive injections of different quantities of the same compound (either propane or benzene), and the ratio of the peak areas recorded by one detector (FID) has been compared with the corrcjponding ratio given by the second detector ( R ) ,since no response factor is to be used in such a procedure. If the split ratio does not vary during a run, the two ratios of peak areas should be the same, as has been found effective (see Table I). New Procedure. The new procedure eliminates quantitative blending of samples in favor of separate injection of components. In the following, this procedure will be called “separate injections.” In the weighing method, Q z and Q3 being the weight of components 2 and 3, the weight percentage of component 2 is given by the elementary Expression 4
c2
C1 I
I
A%a
1.007
1.009
U
-
0.999
of 10 runs
1.000
A% stands for relative deviation between the ratio of the peak areas recorded by FID and B detectors. Peak area measurements were carried
I
Average J%a
1.001
0.2%
I
Average of 10 runs
1/30
1.006
(FID)
(B)
A%a
b.3%
0.8%
(0)
1/15
0.998
/
r
Average of 10 runs
A%a
Propane
Benzene
1/10
,
‘4) which may be written in chromatography
Figure 1. G a s density balance calibration flow system ( a i Previous flow system: i b J New flow system for TC cells; i c i N e w flow system for FID
followed by the flow divider, and feeding the reference of the balance. The flow divider with a split ratio of 1 to 1 in this previous case, is a T union (Carlo Erba, 2-mm i.d. or a Swagelok fitting union tee 0.d. 1/16), equipped with two capillary tubes of 30-cm length and 0.25-mm i.d. Needle valves are inadequate in this part of the flow system (2). Thus, pressure drop in front of the flow divider is in the order of l/z bar with a flow rate of about 6 l./hr He. In the case of the flame ionization detector (Figure IC), several lines are to be provided for hydrogen, air, and additional carrier gas flow to maintain constant the flow ratios between carrier gas/ hydrogen and airlhydrogen. The split ratio of the flow divider is 1 part to the FID and 30 parts to the balance. Capillary tube lengths, respectively, are FID, 300 cm, 0.25 m m ; balance, 10 cm, 0.25 mm. 776
0
ANALYTICAL CHEMISTRY, VOL. 45, NO. 4, APRIL 1973
where f z , f 3 , A B , and A S , respectively, are the absolute factors and peak areas of components 2 and 3 . In the case of the gas density balance (6). the absolute factor is known and given by the following expression:
Thus, with the balance Calibration technique, it is easy to obtain a virtual relative standard mixture from any absolute and separate injections of, for instance, components 2 and 3. However, the separate injections must be made in such a manner that peaks do not overlap. The rest of the method remains the same as previously described: the simultaneous recording of the response of the two detectors allows the calculation of relative response factor according to Equation 3 . Advantages of t h e New Procedure. The new procedure has few limitations: it is simple, more accurate, considerably more (6) A . G . Nerheim, Anal Chem , 35, 1640 (1963)
Table II. Relative Response Factors in Weight of CI Chlorinated Hydrocarbons Usable in the Linearity of TC Detectors, Types A, B, C, D, E and in the Conditions Given in the Text. Ethylene = 1 B
A
Compounds Ethylene Methyl chloride Methylene chloride Chloroform Carbon tetrachloride
Molecular weight
28. 50.49 84.93 119.38 153.82
i
(atx 1oo)ji
1. 1.45 2.15 2.74 3.44
f2% fi.ayo f1.4% fl%
7
C
(atx
1. 1.51 2.15 2.77 3.17
'
1oo)p
f1.2% fi.3% f2.2% f1.2%
D
i ( a t x 1oo)p 1. 1.45 *o.a% 2.17 13.6% 2.64 fl.6% 3.22 11.2%
E
.i ( a t x ioo):'1 i 1. 1. 1.415 f o . 8 ~ ~1.45 1.965 f1.6% 1.90 2.47 f3.2% 2.95 f2%
(atx
roo)/?
f2y0 f1.6%
~
~
Table I l l . Relative Response Factors in Weight of Cp Saturated Chlorinated Hydrocarbons Usable in the Linearity of TC Detectors, Types A, B, C, D, E and in the Conditions Given in the Text. Ethylene = 1 B
A
Compounds Ethylene Ethyl chloride 1,l -Dichlorethane 1,2-DichIorethane 1 , I ,1-Trichlorethane 1,1,2-Trichlorethane 1,1,1,2-Tetrachlorethane 1,1,2,2-TetrachIorethane
Pentachlorethane Hexachlorethane
Molecular weight
28. 64.52 98.96 98.96 133.41 133.41 167.85 167.85 202.30 236.74
f
(at
1. 1.61 2.44 2.49 3.10 3.08 3.57 3.56 4.15 4.82
x 100)D
f2.4% f1.6% f 1.2% f1.2% f1.2% f2% f1.6% 421%
fO.8%
f
1. 1.805 2.38 2.31 2.725 2.79 3.45 3.40 3.88 4.315
C
x l00)P
(at
r
1. f2.2% 1.66 f2.6% 2.42 f0.8% 2.31 f1.4% 3.05 *3.a% 2.94 f2.4% 3.37 3~1.4% 3.41 f1.2% 3.80 f3.a% 4.65
(at
x loo)/
-
D
E
(at x 1 O O ) j
f
10.4% f1.4% f0.8% f 1% f 1%
f0.6% f1.2% f1.6% f1.4%
r
(at x 1 O O ) l f
1.
1.
1.60 2.25 2.24 2.78 2.70 3.24 3.30 3.87 4.63
f1.8% f3.6% 2.01 f3.6% f 2 . a ~ ~2.37 fl% 2.14 f 1.8% f1.2% f 2% f0.8%
f1.4% f3.4~~ f2.8%
Table I V . Relative Response Factors in Weight of C2 Unsaturated Chlorinated Hydrocarbons Usable in the Linearity of TC Detectors, Types A , B, C, D, E and in the Conditions Given in the Text. Ethylene = 1
Compounds Ethylene Vinyl chloride Vinylidene chloride 1,2-cIs-Dichlorethylene 1,2-trans-DichIorethylene
Trichlorethylene Perchlorethylene
28. 62.50 96.95 96.95 96.95 131.39 165.83
C
B
A
Molecular weight
~
t
1. 1.57 2.44 2.32 2.32 3.02 3.59
7 (at x loo)/? 1. f3.8% 1.765 f1.2% f 3 . 2 ~ ~2.34 f2.6% 4~0.8% 2.33 f2.6% f2.6% 2.32 fl.2% 2.84 f2% f2.6% f2.2% 3.30 f1.2%
(at
x ioo)ii
timesaving and cost-reducing. Pure standards are not required; any impure compound or mixture can be used provided that the columns (Figures l b and IC) separate the different components. But the very important point is the possibility of getting any relative response factor with equal accuracy with respect to any reference compound; for instance, in an extreme case of a solid with respect to a gas, by carrying out separate injections. For example, with the previous procedure. in the case of a chemical family presenting a wide range of physical characteristics. like the nineteen C1 and C2 chlorinated hydrocarbons, obtaining the relative response factor of hexachlorethane (solid) with respect to ethylene (gas) became tedious and more or less inaccurate because of the error propagation due to the great number of intermediate standard mixtures needed. Figure 2 shows schematically the errors on both sides of the linear relationship between relative response factors of chlorinated hydrocarbons and their molecular weight. It is obvious t h a t error is individually restricted for each factor with the new procedure, whereas with the previous one an error propagates itself through the entire series (see Tables 11, 111, and IV). Next we consider the accuracy of peak area measurement. The procedure of separate injections with the first flow system (Figure la), using one column a t isothermal temperature, would give too narrow peaks for light components, making an accurate triangulation or integration difficult. With the new flow system (Figures 1 b and IC) which include two columns operating a t two different
t 1. 1.58 2.39 2.49 2.285 2.97 3.34
.(at x 100) 7
D
t
1. f0.4% 1.58 13.4% 2.14 3~1.6% 2.30 fl.2% 2.08 3~1.4% 2.53 i1.2% 3.
(at
E
x
100)/i
t
1. 1.57 2.05
fl%
fi.a%
(at
x ioo),'t
f3.60/6 *2%
f1.8% f2.8% f1.6% f2%
M Figure 2. S c h e m e showing errors on both sides of t h e linear relationship between relative response factors of chlorinated hy-
drocarbons and their molecular weight 1 , Previous procedure (error propagation); 2, N e w procedure (constant error)
isothermal temperatures, gases or light components are injected in the first injection port, whereas the second one is used for liquids or even solids. Thus error on peak area measurement will be of the same order of magnitude for peaks of nearly identical shape. ANALYTICAL CHEMISTRY, VOL. 45. NO. 4. APRIL 1973
0
777
4 Figure 3.
Internal geometry of some commercial TC detectors. (by courtesy of Carlo Erba and Gow-Mac, Bendix-Greenbrier). c. Semi-diffusion type, cells in series; D ,Flow-througll type, cells in parallel, E, Flow-through type.
A . Semi-diffusion type, cells in parallel: 8 and in series
APPLICATIONS This technique not only allows rapid, accurate, and reliable determination of any response factor needed for routine control in laboratory or in process GC (7), but also appears to be a new way to investigate the classical detectors such as TC and FID. As mentioned by Kaiser (8) and also by Deans (9), the relative response factors found in literature show large deviations from one author to another, making their use difficult as far as reliability. Among the papers devoted to theoretical or experimental approaches to the calibration problem (10-15), no one deals with the influence of TC cell inner geometry on relative response factors. Influence of Internal Geometry of TC Cells. Five commerical TC detectors A, B, C, D, and E have been studied whose schemes are given in Figure 3. The A detector is a semi-diffusion type with two measuring cells mounted in parallel. The B and C detectors are still of semi-diffusion type but with two measuring cells mounted in series. The D detector is a flow-through type with the (7) C. L. Guillemin, J. Vermont, P. Juston, P. Ferradini, A. Arthur, and A. Peyron, J. Chrornatogr S c i , 9 , 155 (1971). (8) R. Kaiser, "Gas Phase Chromatography." Butterworths. London, 1963, p 9 1 . (9) D. R . Deans, J. Chromatogr. Sci.. 9, 729 (1971). (10) D.M.Rosie and R . L. Grob, Ana/. Chern.. 29, 1263 (1957). (11) A. E. Messmer, D. M. Rosie. and P. A. Argabright, Ana/. Chem.. 31, 230 (1959). (12) W. A. Dietz. J. Gas Chromatogr.. 5, 68 (1967). (13)E. F. Barry and D . M . Rosie. J , Chromatogr. 63, 203 (1971). (14) D. M. Rosie and R. S. Fischer, 150th National Meeting, ACS, Atlantic City. N.J., 1965. (15) A. 6 . Littlewood, "Gas Chromatography,'' 2nd ed., Academic Press, New York. N . Y . . 1970.
778
ANALYTICAL CHEMISTRY, VOL. 45, NO. 4, APRIL 1973
cells
two measuring cells in parallel. The E detector is a flowthrough type with the two measuring cells in series. All these detectors have been investigated with the new procedure and the following conditions: Gow-Mac filaments WX, bridge current 250 mA, carrier gas hydrogen with a flow rate of 3 !./hr in the outlet of the detector, temperature of the detector block 100 and 150 "C. Conditions for the gas density balance: Gow-Mac Model 373, carrier gas hydrogen, reference flow rate 44 l./hr, measuring flow rate 3 l./hr, bridge current 300 mA. For more information about the gas density balance, see (16). Tables 11, 111, and IV give the relative response factors of C1 chlorinated hydrocarbons. Each factor represents an average of 16 runs given a t the 95%level of confidence.
t stands for the Student function. These factors are valuable within the linear range of each detector, previously checked either in the case of gases with accurately calibrated valves [see the acidimetric technique ( 8 ) ] or in the case of liquids with syringes. Peak area measurements have been carried out either by triangulation [Condal-Bosch method f17)] for B and E detectors, or with an EA1 computer system (PACE) for A, C, and D detectors. The accuracy of each relative response factor is of the same order of magnitude (It1 to 2%). The regression curves (Figures 4, 5, and 6) show the relationship between (16) C. L. Guillemin and F. Auricourt. J . Gas Chromatogr.. 4, 338 (1966), (17) L. Condal-Bosch, J. Chem. Educ.. 41, A235 (1964).
F
F
3
4
2
3
1
2
50
100
150
200
-1
' '
I
1
I
Figure 4. Relationship between relative response factors of CI chlorinated hydrocarbons with respect to ethylene, and their
Figure 5. Relationship between relative response factors of C2 saturated chlorinated hydrocarbons with respect to ethylene,
molecular weights, for different types of TC detectors
and their molecular weights, for different types of TC detectors
relative response factors and molecular weight of C1 and Cz chlorinated hydrocarbons, for each of the five TC detectors. The slope of the curve of semi-diffusion T C detectors is higher than that of flow-through types. But among the semi-diffusion types, the A detector with a very complex inner geometry (semi-diffusion, cells in parallel) has the highest values of relative response factors. B and C detectors being of the same type, although small differences exist in tube-diameters, give practically the same slope of curves with a deviation of 1.5% between the two. The same conclusion can be drawn from Figures 4 and 6 for D and E flow-through detectors. However, the difference between the slopes of a flow-through detector, cells in series, and a semi-diffusion detector, cells in parallel, can reach up to 18%. Such deviations in the past were too often attributed to the operator, while they were in reality a physical phenomenon linked to the internal geometry of the T C detectors. If one refers to the equation of the absolute sensitivity of a TC detector, given by Littlewood (15)
where K' is a composite constant, M z is the molecular weight of vapor 2, u1.2 is ( u ~ u2)/2. u1 and 02, respectively, are molecular diameters of carrier gas 1 and vapor 2. (12R)lJis total heat flux, R and I are the resistance of and the current in, the hot element. J is Joule's constant. A is thermal conductivity of carrier gas 1. G is ( 2 L)/ln(r1/r2) ~ function of the dimensions of the TC cell, where L is length, rz radius of the filament wire, r l is the radius of the cell. a is the temperature coefficient resistance, E is emf across the bridge, and R1 and Rz are resistances of the filaments. Thus, the absolute sensitivity of a TC detector is due to both electrical parameters and physical parameters of solute and carrier gas. Both theory and practice are in good agreement in the case of the influence of molecular weights on absolute sensitivity a. The greater the molecular weights, the smaller the absolute sensitivity (Equation 8) and the greater the relative response factors are (Equation 9 and Figures 4 , 5 , and 6). From Equations 2 and 8, the relative response factor f 3/2 becomes equal to:
+
where C2,
C3,
A z , A S , M2,
M3,
respectively, are concen-
ANALYTICAL CHEMISTRY, VOL. 45, NO. 4, APRIL 1973
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779
Table V. Commercial Chromatograph Equipped with A Type TC Detector Experimental, average of 2 runs
Standard mixture in
f
Components
1,2-Dichlorethane Perchloroethylene
weight
Oh
53.12
53.49 46.51
46.88
Deviation, %
-0.7% +O.8%
4 Table VI. Commercial Chromatograph Equipped with D Type Detector
mixture in weight %
Experimental, average of 2 runs
Oxygene (+Argon)
24.27
24.24
-0.1%
Nitrogen
75.73
75.76
+0.05%
Standard U
,j==-=
3
Air
&
(
Components
Deviation, %
Table V I I . Commercial Chromatograph Equipped with D Type Detector Experi-
2
components
1,2-DichIorethane Carbon tetrachloride 1,1.2-TrichIorethane Perchlorethylene 1,1,2,2-Tetrachlorethane
20 0 Figure 6. Relationship between relative response factors of C? olefinic chlorinated hydrocarbons with respect to ethylene, and their molecular weights, for different types of TC detectors
trations, peak areas, and molecular weights of compounds 2 and 3. T is a proportionality factor. However, Equation 8 does not predict the effect of type of TC detectors (semi-diffusion or diffusion types) on relative response factors. The geometrical constant G = 2a L/(ln r 1 / r 2 ) is related only to the TC cell itself and the filament, and does not take into account the position of the cell with respect to the main flux of vapor diluted in carrier gas in the case of a diffusion or semi-diffusion detector. The absolute sensitivity of such a TC detector should also depend on the instantaneous flux of the solute in the binary mixture: solute-carrier gas (18).
N?
=
D2.1 x P dp - RTxp,'S
Where N2 stands for the instantaneous flux in g.moles/ (sec) (cmz) of component 2 in carrier gas 1. P is total pressure, pl, p2 are partial pressures of carrier gas 1 and component 2, R is constant of gases, T is absolute temperature, Z is distance in direction of diffusion. D2,1 is the coefficient of diffusion or diffusivity of component 2 in mixture 2 , l . (18) R. C. Reid and T. K . Sherwood, "The Properties of Gases and Liqu i d s , ' ' Chemical Engineering Series, McGraw-Hill, New Y o r k , N.Y.. 1958.
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ANALYTICAL CHEMISTRY, VOL. 45, NO. 4, A P R I L 1973
Standard mixture in weight %
mental. average of 2 runs
Deviation. %
24.93 6.26 21.63 25.77 21.38
25.36 6.20 21.30 25.67 20.75
+1.7% - 1% - 1 .SO% -0.4% - 3%
The instantaneous flux toward the filament will be smaller in detectors of type A, B, and C compared with the flow-through detectors D and E, as is obvious from Figure 3. Figures 4, 5, and 6 confirm indeed that the sensitivity of the diffusion dependent detectors A, B, and C, is lower than for detectors D and E. The relative response factors are therefore smaller for the latter detectors. If, as Rosie showed (14), the other TC cell parameters (filament and block temperature, carrier gas flow rate, etc.) have little or no influence on relative response factors, one can assume that internal geometry of TC detectors is the most important parameter which limits the existence of any universal relative response factors. In the future, these relative response factors should be determined for any type of detector in well defined operating conditions. In the case of publication, details must be stated: type of detector as previously mentioned, nature of filaments. current, temperature of the detector block, nature and flow rate of carrier gas. Validity of Relative Response Factors in Quantitative Analysis. Average precision of relative response factors determined by this technique being of the order of 1 to 2% and error of peak area measurements by means of a computer being less than 0.5% for signals in the order of 100 mV, the probable error due to error propagation (1, 19) will be the following: gc
=
vg2f
+
2 2% as
a maximum
(11)
Tables V, VI, and VI1 show deviation between standard m
