Recorder-Integrator Errors in Gas Chromatography Area Measurements Charles H. Orr, Miami Valley Laboratories, The Procter and Gamble Co., Cincinnati 39, Ohio
of gas chromatography for Iestimate quantitative analysis it is essential to the error which is introduced by N THE USE
the method of integration of peak areas. When an integrating device is coupled to the recorder so that integration takes place as the curve is being traced, a significant error in the area occurs because of the nonlinearities of both the recorder and the integrator. A method which requires easily obtained data has been developed for evaluating this error.
curve, then the equation of the curve of the input signal from the detector is (6)
v = vma.e-k's2
where urnaxis the maximum input signal, k is a constant which is a function of the width at half-height of the peak, and x is the time as defined above. From Equations 1, 4, and 5
N =
and L
=
s s
cdx
(1)
vdx
The expression under the integral in Equation 7 can be written as Z
a,(
Z b,up),
= Z
d,vr
= Z
d,vmarre- ~.k'z' (8)
using the value of u from Equation 6 where d , is a new coefficient (see Equation 14 for more complete definition) and r is a new power index, which is equal t o pn. From Equations 2 and 6 the following is obtained
where A; =
c
=
L =
u = 5
=
tr = t
=
integrated area from recorderintegrator combination, in counts magnitude of integrator counting rate, counts per minute signal in terms of area introduced into recorder-integrator combination by detector, in millivoltrminutes magnitude of input signal at any instant, in millivolts t - t,, minutes retention time of peak maximum any time between start and finieh of a chromatogram
Thus
n-m
anhn
c=
(4)
n-1
and
(10)
(11) where I is the value of the integral and simplifying, we obtain
R
di
dz +4 5
V-
+ 4d33
--+mara
+ ... (12)
R is now in units of counts (output, N ) per millivolt-minute (input, L ) . If the recorder and the integrator set used in this particular case (see Experimental part) were completely linear we would have
(5)
1 millivolt-minute = 6000 counts (13)
If it is assumed that the chromatographic peaks being integrated are close approximations of the normal error
so that multiplying the denominator of R by 6000 converts the units of L to counts and since the units will then cancel, R becomes dimensionless.
b,vP P-1
158
ANALYTICAL CHEMISTRY
The data for evaluating the constants in Equations 4 and 5 were obtained by the following method. Using a Leeds I% Korthrup Type 8662 portable precision potentiometer the number of millivolts required to give 0, 5, 10, 15, 20. . . , 95, 100 divisions of deflection to the recorder (Wheelco Model 80004600-5266) was determined and recorded. Then the recorder pen was manually set a t 1, 2, 3 . ., 10, 15, 20, 30, . . ,, 100 scale divisions and the integrator (Perkin-Elmer Model 194 printing integrator) was permitted to count for 1 minute a t each position. Scale divisions were converted to heights, h, in inches and the constants in Equations 4 and 5 were evaluated using these data and the method of averages. This conversion is not essential to the method since scale divisions can be used equally well. It was performed in this case so that planimeter or manual areas in square inches could be compared directly.
= 622.6h
+ 4.832h2 - 0.3710h3
(16)
and
+ 0 . 2 4 1 3 ~ ~(17)
Performing the indicated integrations, using the fact that
a-m
h =
S o w if P. is the per cent error in the integrated area then, P, := ( X 100) = 100 (15)
c
(3)
h'ow c can be expressed as a power series in h and h as a power series in c' (where h is the recorder deflection in inches, u is as previously defined, a, and 6, are appropriate coefficients in the power series, and n and p are the power indices) so that
++ anb12 and 2a2blb2 + a3bI3
The two equations obtained were
then the ratio R is
E = -'IL
dl = albl, d2 = albp d3 = alba
EXPERIMENTAL
DERIVATION
To determine the error in the integrated areas of the chromatographic peaks, the ratio of the area taken out of the recorder-integrator combination to that put in is calculated. If we let
Evaluating the coefficients d, in Equation 8,
h = 9.810 - 0.601~2
Evaluating Equation 12 from these two equations and performing the operations whose results were presented in Equations 13and 14 we obtain R = 1.0180 0.0107~,~, - 0.0428~,,*
+
(18) -
Table I. Error in Area Integrals Due to Nonlinearity of Recorder-Integrator Combination Peak Height Error in aa % of Full Scale Area, Pa %
10
20 30 $0 50
60
70 80
90 100
1.86 1.85 1.74 1.56 1.28 0.92 0.47
-0.06 -0.68
-1.37
As part of the data collection there will be a set of values of vmsx as a function of h and the u ~ in Equation ~ ~ , 18 ~can be evaluated from these data. Csing Equations 15 and 18 the table of error values was constructed (Table I.) The following equation may be used with either Equation 15 or a table such as Table I to correct integrated areas: True area =
~
+ P,observed area
loo
100
(19) As an example, suppose a peak is 60% of full scale and has an integrated area of 347 counts. Then
True area = =
=
100
+ 0.92 347 counts
loo
(20)
0.990 X 347counte 343 counts CONCLUSION
Although this method was developed to determine the error in areas on gas chromatograms using a specific recorder-integrator combination, the derivation is general and can be applied to the automatic integration of any area, the boundaries of which are the normal error curve and a horizontal base line if the integrator is coupled to the recorder. If, however, the chromatographic peak is not the shape of the
normal error curve because of overloading, adsorption, or some other cause, the exact form of the functions used to represent c and u in Equations 1 and 2 would be different from the ones chosen here. However, in principle the method for obtaining the ratio R should be the same and should yield equally good results. Whether or not such a derivation should be carried through would depend on the frequency with which such curves appeared in the course of the normal work of any laboratory. ACKNOWLEDGMENT
Many thanks are due to TV. 1,. Courchene and T. J. Flautt for the discussions which led to the final form of this work.
Scavenging System for the Sample Cell of an infrared Gas Analyzer J. F. Kemp, National Mechanical Engineering Research Institute, South African Council for Scientific and Industrial Research, Pretoria, South Africa OR THE accurate analysis of a gas Fmixture by an infrared analyzer, it is necessary to limit the amount of contamination that takes place when a sample is expelled and a fresh one is introduced into the sample cell. If the infrared transmitting windoas of the cell are sufficiently sturdy, the cell can be scavenged by a vacuum pump. Alternatively, if sufficient quantities of the sample are available, the previous sample can be expelled by thoroughly ventilating the cell with the fresh sample. Sometimes the situation arises, however, where the cell windows are frail and the quantities of sample gas are limited. Under such circumstances, the method described here for scavenging the cell can be applied.
DESCRIPTION
piston, B, which is fitted with infrared transmitting windows W sand W!. The sample cell and piston are machined to obtain a small radial clearance between these two components. During an analysis the piston rests on the lower cell window, Wz. The sample is introduced into the cell as follows: The four-way tap, E , is first set to the position where the balloon is connected to nipple Gzand where nipple GI is connected to atmosphere via tube H. When tap J is opened the pressure in the balloon will slowly raise the piston, B, whose progress as it sweeps the sample cell can be followed by putting one’s ear to the open end of tube H, which serves as “stethoscope.” As soon as the piston is heard to make contact with the upper cell window, the four-
way tap is switched over to the setting where nipples GI and Gzare connected to balloon D and tube H, respectively. The piston n-ill then sweep the cell a second time to come to rest in its normal position on the lower cell window. While the piston is being raised, fresh sample gas escapes upward through the annular space between the piston and sample cell. thus providing a good scavenging action. A small amount of contamination does occur, however, because of the transmission of some of the previous sample from the space above the piston to the space below via the annulus boundary layer on the wall of the sample cell. The second scavenging stroke of the piston reduces the amount of contamination to npgligible proportions.
OF SCAVENGING SYSTEM
The system is presented schematically in Figure 1. A denotes the sample cell of the infrared gas analyzer with infrared transmitting windows W1 and W z , and nipples GI and Gz. The nipples are connected by thin plastic tubes to a four-way tap, E, whose other two arms are respectively connected to a length of plastic tube, H, and to a toy rubber balloon, D,which contains the sample gas. Balloon D is suspended from a rubber stopper in the neck of a glass bowl, C, which is provided with a nipple, F , and a length of suction tube, L. The sample is collected in balloon D by applying suction to the open end of tube L. Three-way t a p K permits scavenging of tube M through which the sample is transmitted to the balloon. The essential component for scavenging the sample cell is the light metal
Figure 1.
Scavenging system for sample cell VOL. 33, NO. 1, JANUARY 1961
159
