and water. Figure 8 is a chromatogram of a 0.1-ml. sample of the combustion condensate. The compounds shown in Figure 2 were eluted in 12 minutes. The three zones which appeared after methanol remain unidentified. Their infrared spectra did not indicate the presence of alcohols, but rather of unidentified compounds. The fourth zone again showed itself to be crotonaldehyde, and the last was identified as water. The third column was used for the determination of water from the combustion. Figure 9 is a chromatogram of a prepared sample of methanol and water, along with the chromatogram of a gas sample taken from the combustion mixture. This column was found very suitable for the analysis of water produced in the combustion of pure hydrocarbons or gasolines. The last column was specifically developed for the determination of formaldehyde produced in the cool-flame combustion of hydrocarbons. CI and Ca hydrocarbons, if present in high concentrations, will interfere. This analysis for formaldehyde has not been tested quantitatively. Figure 10 is a chromatogram of a prepared mixture of formaldehyde and acetaldehyde, along
with a chromatogram of a 20-ml. gas sample from the cool-flame combustion of n-hexane. The conditions for efficient operation of this column are critical; however, adherence to those deacribed above gives reproducible results. DISCUSSION AND CONCLUSIONS
The method described was specifically designed for the analysis of cool-flame combustion products of hydrocarbons. Within its limitations, it is dependable and gives reproducible results. Because of the numerous compounds produced in the combustion of hydrocarbons, columns were designed to eliminate classes of compounds by increasing or decreasing their retention times, instead of trying t o separate all types on a single column. This method simplifies analysis, in that unknown chromatographic zones are classified according to their common functional groupings, and secondary analysis is thereby limited to investigation of a limited number of possible compounds. ACKNOWLEDGMENT
The writers express their appreciation to the Firestone Tire and Rubber Co. for the research fellowship granted
to one of them (HRLI), and to the Air Research and Development Command for support under contract number A F 18(600)-787. Appreciation is also extended to Vincent G. Wiley and Orion E. Schupp 111, for their cooperation in the analysis and infrared interpretations, respectively. Pure compounds were obtained from t h e American Petroleum Institute Research Project 45, Ohio State University. LITERATURE CITED (1) Barusch, h i . R., Pame, J. Q,,Znd. Eng. Cheni. 43, 2329 (1951). (2) James, A. T., Martin, A. J. P.,
Biochena. J. (London)50, 679-90 (1952). (3) Kyryacos, G., Boord, C. E., ANAL. CHEX 29, 787 (1957). (4) Kyryacos, G. Boord, C. E., “Gas
Absorption Cdromatoyraphy in the Bnalysis of Cool-Flame Combustion Products,” Division of Analytical Chemistry, 131st Meeting, ACS, Miami, Fla., April 1957. (5) Oberdorfer, P. E., Ph.D. dissertation, Ohio State University, 1954. (6) Oberdorfer, P. E., Boord, C. E., Division of Petroleum Chemistry, 128th Meeting, ACS, Minneapolis, Minn., September 1955.
RECEIVED for reviex December 12, 1957. Bccepted August 26, 1958. Division of Analytical Chemistry, 132nd Meeting, ACS, Yew York, N.Y., September 1957.
Response Time and Flow Sensitivity of Detectors for Gas Chromatography L. J. SCHMAUCH Research Department, Standard
Oil Co.(Indiana), Whiting, Ind.
,The response time of a gas chromatography detector must b e short for adequate representation of column resolution in a chromatogram. long response time always causes band broadening and sometimes asymmetry; either may result in overlap of bands that were separated in the column. Mathematical and experimental approaches show a quantitative relationship between band shape and the ratio of response time to band width. Flow sensitivity is low enough if base line and peak height are not significantly affected b y fluctuations in flow rate. Techniques for measuring response time and flow sensitivity provide a means for judging the adequacy of a detector.
G
has become important for separating and analyzing volatile compounds, and for determining such physical constants as AS CHROMATOGRAPHY
partition coefficients and heats of solution. The method requires detection of changes in the composition of a flowing gas; accuracy, therefore, is markedly affected by the characteristics of the detector. Two of these characteristics are response time and flow sensitivity. Response time determines how rapidly the detector responds to a change in gas composition. If this time is long, composition is not adequately measured as the gas passes through the detector. I n such a case, the output of the detector may not correctly represent the shape and resolution of chromatographic bands emerging from the column. If the detector is flow-sensitive, changes in gas flow rate are reflected in the output. If the shifts are large, the shape of the chromatographic band is again altered. Both response time and flow sensitivity have been recognized as detector parameters (2, 4). One procedure for
measuring response time has recently been reported (6), but no procedure for flow sensitivity has yet been published. Both parameters are measured by new procedures devised in these laboratories. Response time is determined from the response of the detector to an instantaneous change in gas composition; flow sensitivity is measured by observing the detector output as a function of gas flow rate. The effect of response time on peak height, band width, retention time, band separation, and calculated theoretical plates has been estimated mathematically. Experiments showed the effect of response time on separation of adjacent bands, as well as how both parameters change with operating conditions. The results of the study supply criteria for rating the adequacy of a detector. RESPONSE TIME
The response time of a detector is a combination of the time needed to inVOL. 31, NO. 2, FEBRUARY 1959
* 225
100
b
I
Figure 2. Equipment for measuring response time rn z
GAS
2 BO ?! -
0
I4
L
60
z
VI
0
z
c V
s
W L-1 L
l0-
u)
40
w
z
U W
a U 0
w
z VI 0
W 0
%
K
20
5 -
K
I
eo
0
I
I
40
60
I
0 ’
50
0
T I M E , SECONDS
Figure 1 .
Measurement of response time
troduce the gas into the measuring region and the time needed by the measuring transducer to reach a new equilibrium. The transducer usually responds in a fraction of a second. The introduction time for the gas, however, can be much longer; it depends on the mode of introduction, the extremes of which are diffusion and direct flow. If diffusion is used, the component concentration, C,, within the measuring region has been derived (1) as:
Figure 3.
responding to Co is the value approached by the curve when t is much greater than T - that is, when the curve has leveled off. T is the time when the output curve reaches 63.2% of the output corresponding to Co; in the example T is 11 seconds. The output curve does not truly represent the applied concentration change because of the finite value of T . A perfect match would be obtained only when T equals 0 - that is, with an infiniteIy fast detector. If direct flow is used to introduce the gas and there is no mixing,
c, where Co is the concentration a t the opening of the diffusion channel, t is the time between introduction and measurement, and 7 is the response time of the detector. I n this case, 7 depends on the volume of the measuring region, diameter and length of the diffusion channels, and the diffusion constant of the gas pair; it is sometimes referred to in the literature as “time constant.” To determine T , an instantaneous change in the concentration of a component is applied to the detector and output vs. time is recorded. When such a change is applied, C,
=
Co(l
- e-tlr)
(2)
from which 7 equals t when C, equals 0.632 CO.T may be calculated from the output curve, which represents C,. Such a curve is shown in Figure 1;the ordinate is graduated in recorder-chart divisions instead of concentration units because only the relative values of Cm and Co need be known. The output cor226 *
ANALYTICAL CHEMISTRY
100
150
200
FLOW R A T E , M L . P E R M I N U T E
=
F co-Vd t
(3)
where F is the flow rate and V d is the detector volume. I n this expression, t ranges only from 0 to V d / F ; thereafter, the volume is filled and C, equals CO. To permit comparison with diffusion detectors, a T value can be measured a t the same 0.632 CO. Thus, (4)
Here, the output curve, Equation 3, would match the applied concentration change only if V d ,and hence 7,equals 0. From either type of detector, output curves do not exactly follow Equations 2 or 3 because of contributions from the pen speed of the recorder, speed of amplifier (if one is used), and delays in the transducer. Although the mathematics is therefore not exact, the resulting evaluation of detectors is valid. Measurement. Response times were determined with the equipment shown schematically in Figure 2.
Cl and Cz are 300-ml. containers filled with 1/4-inch pieces of expanded ver-
Response time of five detectors
miculite; that in Cz was wet with the component, the Concentration of which is to be changed. S1 and Szare a/,-inch solenoid valves that are opened alternately to introduce eluting gas or combined eluting gas and component vapors into the detector. VI, Tiz, and J’a are 1/8-inch needle valves; Va was provided to adjust flow rates. Adjustments of VI and Vz gave side streams of sufficient velocity through the 2-mm. tee ahead of the detector to prevent back-mixing and a diffuse concentration change. The recorder had a 10mv. range and a 1-second pen speed; the chart traveled a t 2.5 inches per minute. The procedure for measuring response time was as follows: With S1 opened and 8 2 , VI, and Vz closed, V3 was adjusted to give the desired flow rate. Khen the recorder indicated stable operation, the electrical zero of the detector was adjusted. V Z was then regulated to give a recorder deflection of about 10% of full scale. S O was opened, $1 was closed, and the detector gain was regulated for full-scale deflection. Vl was then adjusted to give a recorder deflection of about 90% of full scale. S1 was opened, S2 was closed, and the chart drive was started. When equilibrium was reached, the test was begun by simultaneously closing 81 and opening S2. The test was concluded after the detector output had leveled off. The output curve of Figure 1 was so obtained with a thermal conductivity cell; the changing component was cyclohexane and the eluting gas was nitrogen a t a flow rate of 56 ml. per minute. The detector must be so operated that output is reasonably linear with concentration. For example, bridge currents or wire temperatures of a thermal conductivity cell should not be so high that peak inversions (6) result. Such peak inversions would distort the re-
t -1, U
t -tr 5
Figure 5. Effect of T / C T in a direct-flow detector on chromatographic band
Figure 4. Effect of T / C T in a diffusion-type detector on chromatographic band
lationship betn cen rcsponse and time and n ould complicate the calculation Of T .
Response times of five detectors a t 25' C. w r e measured a t various flow rates. Figure 3 shoirs the results of tests on four thermal conductivity cells, labeled A to I), and a gas-density balance (6) labeled E . Cell A uses the diffusion principle for exposing the detecting elements to the gas stream. Cell B uses semidiffusion. Cells C and D have elements close to but not directly in the floviing gas stream; they have chamber volumes of 2.7 and 0.6 ml., respectively. At any given flow rate, the diffusion-type cell has the longest response time. The direct-flow cells have response times directly related to their volumes. The gasdensity balance has a measuring volume similar to that of cell C, and about the same response time, hkasurements of ccll D !$ere discontinued nhen the r d u e s approached the pen speed of the recorder. The response times decrease mith increasing flow rates because chamber volumes are filled faster in direct-flow detectors and diffusion channels are partially entered by the flowing gas in diffusion types. The faster responses a t high flow rates give less distortion of chromatographic bands; as a result, in regions nhere columns show little change in efficiency with flow rate ( 7 ) , efficiency may seem t o increase n ith flow rate, Significance. T h e effect of response time on representation of chromn-
tographic bands vias examined mathematically as well as experimentally. I n t h e mathematical treatment, t h e effect of t h e response time of a diffusion-type detector and that of a direct-flow detector nere considered separately, The measuring transducer i t as assumed t o respond rapidly and linearly n i t h concentration, and the chromatographic band n as taken as the normal curve of error given by the equation: zp
nherez =
- t, , t , is the retention time, t
and u is the standard deviation-lialf the band nidth a t 6O.i% of the maximum. In the diffusion-type detector, the response is governed by Equation 1; Rhen Co from Equation 5 is substituted therein and the expression is rearranged, the concentration within the measuring volume brcomes
(6)
where the integral limits indicate the area under the band betn-een the front edge and t . For small values of z the integral was evaluated with tabulated areas for the normal curve of crror (9). For large values, when T is much smaller than u, the expression was rearranged to the asymptotic series:
5,
22
(1
1
- fT;1+
3 15 105 r4 - 5p + 11'8 - . ) (7 - -
,
4.
here Tt' = t Results of evaluatillg several T / U ratios are plotted in Figure 4. Band shape and position depend upon the relative magnitudes of T and U. The original band is obtained \Then T = 0 and r / u = 0; as T / U beconies larger, band n idths and retention times observed on the chromatogram are larger than the true values. Asymmetry and pronounced trailing also occur as peak heights diminish. I n the direct flow dctector, the portion of the chroinatographic band held 11 ithin the measuring volume produces an average or integrated xalue. Thus, for the band given by Equation 5 , the average concentration, C, becomrs: 17
where Az is At/u and represents that yolume of the band within the detector. If At is the time to fill the detector volume, V d ,a t from- rate F , (9)
Because, from Equation 4, V d equals ~ F / 0 . 6 3 ,2 32 =
VOL. 31,
-L-u 0.632
NO. 2, FEBRUARY 1959
227
IO0
1I
tL
s
I
I
95
-I
a
5 0
90
K 0 LL
I
85
/
0
$ 80 0.8
I
I
I
__----DIRECT-FLOW-
0
02
0.8
06
04
c
I .o
T/U
Figure 7, Effect of response time on apparent resolution
13-
12
-
1.1
-
B A N D WIDTH
blb
0
02
04
06
08
10
T/U
Figure 6. Effect of response time on band shape and position
The average concentration then becomes :
This expression n a s evaluated u i t h tabulated areas for the normal curve of error and plotted in Figure 5 for qeveral r / u ratios. The band shape and position again depend upon the relative magnitudes of T and u , The original band is obtained nhen r,’u is 0; as r / u becomes larger, band widths and retention times after detection increase. Symmetry is preserved, but peak heights decrease. For both diffusion and direct-flo\v detectors, the effects of changes in r / u on peak height, retention time, and band nidth are shon n in Figure 6 Peak heights diminish faster for diffusion types as r / u is increased. The displacement of retention time, Az7, equals A t r / u and is similar for both types; if retention times are calculated as the difference betneen that of the component and of a permanent gas, band displacements tend to cancel. Diffusion causes more band broadening, represented as relative band n idth, u ’ / u , where U ’ is the half-band nidth after detection; the difference in U ’ / U for the front and rear of the band indicates asymmetry and trailing. If the T / U ratio is 0.2 or less for both types of 228
ANALYTICAL CHEMISTRY
detectors, distortion is small and reasonably good band representation can be expected. Band broadening and trailing result in increase of valley height betneen adjacent bands. The increase in valley height decreases the apparellt resolution of t n o adjacent bands Such increases can be estimated by adding the tail of one band to the front of the succeeding band. Figure 7 shons the effect of increasing the r / u ratio on change in valley height, expressed as per cent of the original peak height, for ta o bands 7 u’s apart. At the r / u ratio of 0.2 needed to minimize distortion, loss in resolution is slight. An experimental demonstration of the effect of response time on apparent resolution of bands mas made by splitting the gas effluent from a chromatographic column to providc equal flows through tmo detectors. This technique enables direct comparison of chromatograms without close control of such factors as sample size, uhicli could change column resolution. Figure 8 conipares chromatograms obtained in this manner n i t h thermal conductivity cells A and C a t 25’ C. A mixture of Cb and Co paraffins and olefins n as separated in a dinonyl phthalate column a t 80’ C. and a total flow rate of 60 ml. of nitrogen per minute. Cell currents were adjusted to give nearly the same peak heights for the major chromato-
graphic band. The higher the peahto-valley ratios and the less the trailing (most evident for the last component), the better the resolution. Cell C gavc better resolution because, a t 30 ml per minute, the T / U ratio is about 4.6 5.5 for the major band while that of cell A is about 13.5/5.5. The slower cell nould require longer columns and more tinic for analysis to attain the sanic apparent degree of band separation. Band distortion due to long response time can also lead to errors in the ea!culated number of theoretical plates. r, of a column. The recommended equation for this calculation is: T
= 16
(i)’
nhere y is the length of the base line intercepted by tangents drawn a t the points of inflection of the band, and x is the length-including dead volumefrom the start of the run to the middle of y (3). I n terms of t, and u, the expression for a direct-flow detector becomes : (13)
If r is the number of plates for the band emerging from the column and r’ is the number calculated from the band after detection, the ratio of observed to true plates is given by:
(14
This expression FTas evaluated by taking values of AtJu and U ’ / U from Figure 6. How the ratio changes as T / U increases is shown in Figure 9. The error in calculated theoretical plates is large at high T / U ratios but reasonably small a t the suggested ratio of 0.2 or less. FLOW SENSITIVITY
Flow sensitivity of a detector is the variation in output with flow rate of the
1 1
w
>
v)
r 0 J
2 J
'1
iL Y vi
05
m
-
0
+ 0
I
3 w
09/i
0
0
I
081
02
0
04
08
06
I O
T / U
2
I
0
3
4
T!ME.MINUTES
Figure 8. Chromatograms from cells of different response times
eluting gas. Flow scnsitivitj- affects a chromatographic band hy changing the amplitude of the band when the flow rate changes and by adding flow noise when the flow rate fluctuates. The magnitude of this parameter varies n ith the principle and design of the detector. The gas-density balance is so designed that it is not flon-sensitive. The output of thermal conductivity cells can vary n ith the heat capacity in addition to the thprnial conductivity of the flowirig gas. Output due to heat capacity varier n-ith flow rate, whereas that due to thermal conductivity does not. Thrrefore. the more flow-sensitive the cell, the larger the contribution of heat capacity. Measurements were made of flow sensitivities of three thermal conductivity cells a t 25" C. by observing the electrical output as a function of nitro-
Figure 9. Effect of r / u on calculated theoretical plates for direct-flow detectors
gen floiv rate through the measuring chamber. The results are sliown in Figure 10, together with the initial temperatures of the measuring elements calculated from the observed electrical resistances. Because of forced cooling of the hot elements, the sensitivities of cells B, C, and D increase with a n increase of Aom rate; cell A had too long a response time to warrant further study. K h e n the temperature of the measuring c.lcmciit 1s raised to increase the detc,c.tor output for a chromatographic Ijand, flon. vnsitivity increases as shonn 115. r d l D. K h e n the cells are ronipared a t nearly the same outputs for a l ~ a n d .cells C a t 100" C. and D a t 200" C. are less flon-sensitive than cell B a t 100' C. A t a nitrogen flow rate of 50 ml. per minute or less, the unbalance caused by flow sensitivitv of cell C or D is n o t more than 1% df
full-scale deflection on a 1-mv, recorder; therefore, upsets are slight ivhen flom s are interrupted, as during sample introduction kq-some techniques. Flow noise results from fluctuation in flow rate. T o show lion such changes in flow rate affect detector output, the slopes of the curves in Figure 10 are shon-n in Figure 11 as microvolts chaiigr in output for 1% change in flovi ratr. For a given cell, the higher the flow rate or the temperature of the measuring element, the greater the flow noise. Flow sensitivity data plotted in thi, manner can he used to specify acceptable limits of operation. For example. with a I-mv. recorder, a fluctuation of 1 p v . ivould not produce flow noise if flow rate is controlled to lyG,Thus, el'eii cell l3 mould be acceptable for flow noise a t rates below 50 ml. of nitrogen per minute.
I O (.o
0
?
0 8
4
5
5
06
L
0 3
t
0 4
0 2
0
0
50
IO0
I50
FLOW R A T E , M L
Figure 10. tivity cells
N p PER
200
250
300
MINUTE
0
50
IC0
150
zoo
250
300
F L O W R A T E , ML. N 2 P E R M I N U T E
Flow sensitivity of thermal conducFigure 1 1 .
Flow noise from thermal conductivity cells VOL. 31, NO. 2, FEBRUARY 1959
229
CONCLUSION
judging the adrquacy of gas chromatography detectors, both flow time should be sellEitivity and under the operating conditions to be used, ~l~~~ sensitivity is acceptable if output is not significantly h some ~ affected by flow ratc, ~ detectors are not sensitive to flow rate, other they may be sensitive to operating variables as pressure. The pressure sensitivity of such detectors may be analyzed like flow sensitivity. The response time of any detector influences peak height, which is especially important in trace analysis; it affects band broadening and symmetry. *and asymmetry is not always caused by column factors; diffusion-type detectors can produce
some effects. Adequate representation of band shape is obtained where the 7 / 0 ratio is 0.2 O r less. The fastest response is needed for the sharp bands appearing early in a chromatogram. If the u of such bands is 5 seconds, then the response time be about second. ~ ~ A recorder h pen speed of 1 second limits over-all speed of detection even with a very fast detector. Faster response n-ill not improve detection Significantly unless the speed of the associated equipment is also improved. LITERATURE CITED
(1) Daynes, H. A , , “Gas Analysis by Measurement of ThPrmal Conductivity,” p. 93, Camhridge Press, London,
1033.
(2) Desty, D. H., .Tatwe 180, 22 (1957).
(3) Deety, D. H., “Vapour Phase Chrorna~ ~ @ $ ‘ & ~‘ji,, p Academic . Press, Sew (4) Dimbat, M,, Porter, p. E., Stress, F, H., ANAL.CHEW 28,290 (1956). (5) Johnson, H- W., Jr., Str08S, F. H.. Pittsburgh Conference
On
Analytiral
Chemistry and Applied Spectroscopy, March 1958. (6) Kepp!er, J. G., Dijkstra, G., Scholj, J. -4.7 In T a p o u r Phase Chromatograph~,’’ D. H. DestyJ ed.2 p. 22’s Academic Press, Yew York, 1957. (7) Keulemans, -4.I. M.,Kwantes, A , ,
Ibid., p: 15. (8) Martin, A. J, P., James, A. T., Biochem. J. 63, 138 (1956). (9) National Bureau of Standards (Supt. Documents, Washington 25, D. C J , Tables of Normal Probability Functions, Applied Mathematics Series 23 (1953). R~~~~~~~ for M~~ 5, 1g58, Accepted October 6, 1958. Division of Petroleum Chemistry, 134th hfeeting, ACS, Chicago, Ill., September 1958.
Correlation of Thermal Conductivity Cell Response with Molecular Weight and Structure Quantitative Gas Chroma tog ra phic Ana lysis A. E. MESSNER,
D. M. ROSIE,‘
and P. A. ARGABRIGHT
Esso Research und Fngineering Co., linden, N. J.
bA
correlation exists between the relative thermal detector response and molecular weight within a structurally similar homologous series. This enables one to predict response values for given compounds where related information is available. The relative response of a thermal detector is independent of temperature, concentration, and carrier gas flow rate over the range investigated. Because it is also independent of the thermal detector used, data here are applicable to all gas chromatographs using thermal detection and helium as a carrier gas.
R
Rosie and Grob (1) have shown that the molar response of a thermal detector to hydrocarbon vapors is unique for each compound To obtain more acceptable quantitative analytical results, it is necessary to correct observed areas rather than assume that the area is directly pioportional to the weight per cent. Results obtained with multicomponent blends showed that the avECENTLY
1 Present address Department of Chemistry, University o! Rhode Island, Kings-
ton, R. I.
230
ANALYTICAL CHEMISTRY
erage error may be reduced by more than 50% by applying relative response values. A careful examination of the data previously reported has shovn that a h e a r correlation exists between thermal detector response and molecular weight within a structurally similar homologous series. As an extension of this work, relative response data for a number of compounds differing in type as well as structure have been determined (Table I). The average relative response values of all compounds investigated are reported in Table I. The average coefficient of variation for these compounds was 2.8. Differences among observed responses less than this amount were assumed to be due to normally encountered experimental errors. I n the course of this investigation i t was deemed necessary to determine the dependence of relative response on concentration, individual sensing unit, and carrier gas flow rate. APPARATUS A N D MATERIALS
The instruments used were for the most part Perkin-Elmer 154 Fractometers, equipped with thermistor-type detectors. I n one instance, however,
experiments were performed on a Wilkens Aerograph which employs a hot wire thermal detector. I n all cases, the carrier gas a a s helium. Liquid samples of high purity were obtained from the National Bureau of Standards, Washington, D. C., or from the American Petroleum Institute, Carnegie Institute of Technology, Pittsburgh, Pa. When not available in high purity from either of the above sources, the compounds were rectified by distillation. Gas samples of research grade were obtained from the Phillips Petroleum Co., Bartlesville, Okla., or the Matheson Co., East Rutherford,
N. J.
EXPERIMENTAL PROCEDURE
Benzene was chosen as the internal standard and arbitrarily assigned a signal response of “100.0” units per mole. Each compound to be ‘investigated was mixed with a known amount of benzene and the resulting blends were run from two to five times, A minimum of two blends was prepared for each compound. The areas were determined by cutting out the peaks and weighing them on a n analytical balance. Reproducible analyses required that the operating conditions remain constant for the duration of the individual run (5 to 30 minutes).
