Precision and Accuracy of the Analysis. In general, the precision and accuracy of the results are similar to those found in gas chromatography. Preferably, the instrument is calibrated for a particular analysis with known quantities of the sample components. Flow rate and column temperature should be kept constant. With the present system, the flow rate can be kept constant within 2% above 10 ml/hour and the temperature within 1 “C above 35 “C. Under these conditions, the precision of the retention time and peak areas per unit amount of solute was better than 3%. The sample introduction technique of the operator may improve or impair the accuracy of the results. The column life did not affect the precision within a six month period of continuous use at different temperatures.
In practical work, the sample preparation may also greatly influence quantitative results. The optimum sample preparation method should be worked out individually according to the sample origin and history. ACKNOWLEDGMENT
The technical assistance of Anthony R. DeNoto is gratefully acknowledged. RECEIVED for review February 24, 1969. Accepted May 21, 1969. This work was supported by grants from the National Institutes of Health (HE 03558) (FR 00356) and the National Aeronautics and Space Administration (SAR-NGR 07-004067) (SAR-NsG 192-61).
Precise Gas-Chromatographic Measurements J. E. Oberholtzerl and L. B. Rogers Department of Chemistry, Purdue Uniaersity, Lafayette, Ind. 47907 A gas-chromatographic system capable of determining retention times with a precision of better than 10.02% has been developed using digital control of sample injection and digital data acquisition with subsequent computer calculation. An air oven, controlled to 1 0 . 0 1 O C , provided temperature uniformity of better than 10.02 O C . A combination of sampling valves and of an exponential dilution flask is described which could prepare samples with a precision of 14.4% at the parts-per-billion level. The combination also permitted semi-automatic studies to be made as a function of sample concentration. The overall system provided automatic measurements of HETP, skew, and kurtosis with high precision. Heats of solution were measured with a precision of better than 1 1 0 cal/mole.
MOST RECENT DEVELOPMENTS in gas-chromatographic instrumentation and column technology have been in the direction of more sensitive detectors, faster separations, and more precise and accurate quantitative analysis of the separated mixtures. Considerably less attention has been given to the precise determination of retention behavior. Keulemans ( I ) for example, has noted that the only qualitative information available on a peak representing less than 0.1 pg of a compound must come from its retention behavior. He has suggested the refinement of instrumentation for gas chromatography so that the reliability of retention data and the factors that affect the reliability can be determined. Gas chromatography (GC) is becoming increasingly useful for making physicochemical measurements. A recent review by Young ( 2 ) treats in detail the application of gas-liquid chromatography (GLC) to the study of solution thermodynamics. Kiselev (3) has discussed the value of gas-solid chromatography (GSC) in the development of a generalized theory of interaction at the gas-solid interface. Other re1 Present address, Arthur D. Little, Inc., 15 Acorn Park, Cambridge, Mass. 02140
(1) A. I. M. Keulemans in “Gas Chromatography 1966,” A. B. Littlewood, Ed., Institute of Petroleum, London, 1967, p 211. (2) C . L. Young Chromatogr. Rec., 10, 129 (1968). (3) A. V. Kiselev, Zh. Fiz. Khim., 41, 2470 (1967). 1234
ANALYTICAL CHEMISTRY
views (4, 5 ) describe the broad spectrum of physicochemical measurements to which G L C and GSC have been applied. The success of GC measurements for physicochemical studies depends heavily on the precise determination of the retention time and second moment (variance) of the eluted peak (4, 6). The retention time along with experimental conditions-e.g., temperature and pressure-are the prime determinants of quantities such as activity coefficients and mixed virial coefficients. The second moment is a source of information on gaseous diffusion coefficients, adsorptiondesorption kinetics, and other mass-transport properties, Recent attempts to generalize chromatographic theory have invoked the third and higher central moments of the peak profile (7,8). Because of the sensitivity of higher moments to experimental error, verification of such theories puts even greater demands on chromatographic apparatus to produce very precise and accurate records of the entire elution profiles. As pointed out in a very recent paper (9), the primary factors that have appeared to need better control and measurement were column temperature, pressure, and carrier-gas flow rate. In addition, sample introduction ought to be more reproducible in terms of size, shape, and timing of the injected sample than the conventional manual techniques. Finally, to take full advantage of those improvements, the detector read-out system would have to be precisely synchronized with the injector and be capable of recording the peak profile with high fidelity. Previous applications of digital systems to gas chromatography (4, 8, 10) have been aimed mainly toward faster and (4) J. C. Giddings and K. L. Mallik, Ind. Eng. Chem., 59 (4), 18 (1967). ( 5 ) R. Kobayashi, P. S. Chappelear, and H. A. Deans, ibid., 59 (IO), 63 (1967). (6) J. C. Giddings. “Dynamics of Chromatography, Part I , Principles and Theory,” Dekker, New York, N. Y. 1965. (7) K . de Clerk, T. W. Smuts, and V. Pretorius, Sep. Sci., 1, 443 (1966). (8) 0. Grubner in “Advances in Chromatography,’’ Vol. 6, J. C. Giddings and R. A. Keller, Eds., Dekker, New York, N. Y., 1968, pp 173-209. (9) M. Goedert and G. Guiochon in “Gas Chromatography, 1969,” A. Zlatkis, Ed., Preston, Evanston, Ill., 1969, p 68. (IO) J. T. Walsh, R. E. Kramer, and C. Merritt, Jr., ibid., p. 256.
41r
I
)--L*
DIGITIZER PUNCH JIUPPLYl SAMPLE
DILUTION 6
4dBByB-
INJECTION
VALVE
-i
I50 p s i
DIGITAL
H ~ R O L
CONTROLLER
Figure 1. Block diagram of high-precision gas chromatograph
+ Vent
easier data collection and manipulation. However, the present paper describes a gas chromatographic system capable of producing retention data with at least an order of magnitude better precision than conventional systems. The use of digital control of sample introduction and digital data acquisition played key roles in increasing the system and in permitting semi-automatic operation. All but one of the components of our chromatographic system were commercially available. However, several had to be modified, as described later, in order to achieve optimum performance. The performance was examined both in terms of characteristics of individual components and in terms of overall performance. The latter included isothermal tests of run-to-run reproducibilities of peak parameters and of sample sizes from the dilution flask. The most severe test involved measurements of heats of solution for a series of normal alkanes in SE-30. Not only the precision reported for a given alkane but also the differences between the heats of solution for adjacent homologs were very revealing. SYSTEM DESIGN
The major components of the chromatograph are shown in Figure 1. The design and operation of the digital controller which synchronized sample introduction with data acquisition has been described previously (11). Characteristics and performance of the other major components will be discussed in succeeding sections. Sample Dilution and Introduction. Throughout this work, three pneumatically-operated gas sampling valves were used somewhat interchangeably: A Carle Model 2014 with Model 2050 Pneumatic Actuator (Carle Instruments, Inc., Anaheim, Calif.), a Seiscor Model VI11 (Seismograph Service Corp., Tulsa, Okla.), and a custom-machined valve (valve K ) identical to the one described by Kieselbach (12). Figure 2 shows the flow control, sample dilution, and sample introduction system. The solid line traces the path of the helium carrier gas from its storage cylinder to the chromatographic column. The 150-psig gas supplied from the tank regulator was reduced to 60-psig by Rzand was purified as it passed through T2 which was immersed in liquid nitrogen (LN2). Final flow control was effected by the flow controller, F . The sampling valve, GSV2 introduced the sample into the carrier stream. Column inlet pressure was measured by G, while the outlet pressure, which was assumed to be atmospheric, was measured by a laboratory mercury barometer. The pressures were recorded to the nearest 0.01 psi and 0.1 mm Hg, respectively. ( 1 1) J. E. Oberholtzer, ANAL.CHEM., 39, 959 (1967). (12) R . Kieselbach, ibid., 35, 1342 (1963).
Figure 2. Flow control, sample dilution, and sample introduction system
R1,R2-precision pressure regulator, N and Z Model R/182NC (Negretti and Zambra, Ltd., Stockdale, Aylesbury, Bucks., U.K.) Tl,T*-gas-purification trap, cylindrical stainless steel, 4 cm X 25 cm long, filled with Linde Molecular Sieve 5A F-flow controller, Brooks Model 8743 ELF (Brooks Inst. Div., Emerson Electric Co., Haffield, Pa.) G-precision pressure gauge, 75 psig full-scale capacity (Heise Bourdon Tube Co., Newton, Conn.) M-soap-bubble flowmeter, 50-ml capacity D-exponential dilution flask, 200 ml (Varian-Aerograph, Walnut Creek, Calif.) GSVl, GSVz-automatic gas sampling valves (see text) Vl, V3-needle valve V2,V,, Vs--on-off toggle valve
The chromatographic column was connected to the injector and detector using 0.051-cm i.d. capillary tubing. Measured retention volumes were corrected for the 0.096-ml extracolumn dead volume in the connecting tube. Because the system used a flame ionization detector, measurement of carrier flow rate at the column exit was almost impossible. For that reason, the following less-than-ideal procedure was employed for flow measurements. By closing VJ and opening V , the carrier flow was diverted from the column to the flow meter, M . Needle valve V , was adjusted so that the flow measurement was made with the flow controller working into an impedance equal to that of the chromatographic column. The sample dilution line, indicated by the dashed line in Figure 2, utilized an exponential dilution flask, D, for the preparation of samples of successively lower concentration (13). Flow rate in the dilution line was controlled by VI, Valve Vz, which was normally closed, could be opened to flush rapidly from the dilution flask any remaining sample prior to introduction of a new sample. Gaseous samples could be injected into the dilution flask using GSVI. In addition, the flask was fitted with a septum to permit syringe injection of liquids directly into the flask. The dilution flask and the line of GSV2 were wrapped with electrical heating tape to permit operation with relatively nonvolatile liquids. All of the components in Figure 2, with the exception of the traps, were contained in a box thermostatted at 35 "C. A circulating fan and a 300-W heater, controlled by a mercurycontact thermoregulator, held the temperature constant to 10.05 "C.
(13) C. H. Hartmann and K. P. Dimick, J . Gas Chromatogr., 4, 163 ( 1966). VOL. 41, NO. 10,AUGUST 1969
1235
Temperature Control and Measurement. In applications requiring precise temperature control, liquid baths have often been employed because of their high thermal mass. In our work, an air oven was chosen for its convenience of operation and ease of going to higher temperatures. The column oven was a Becker Model 1452 SH (Becker Delft N. V., Delft, Holland). The column compartment of the oven was a n upright cylinder approximately 18 cm in diameter and 26 cm deep. A larger concentric cylinder around the column compartment contained the heating elements. A large centrifugal blower at the bottom of the oven forced air up and over the heating elements into the top of the column compartment and then pulled the heated air down past the column at high velocity. The oven came equipped with a mercury-contact thermoregulator which was found to maintain the mean temperature to within +0.02 "C; however, the dead band of the thermoregulator caused short term variations of 1 0 . 1 "C with a period of 60 seconds. T o improve short term stability, the contact thermoregulator was replaced by a Melabs proportional temperature controller, Model CTC-1A equipped with a Model 1102 low-mass platinum sensor (Melabs, Inc., Palo Alto, Calif.). Temperature measurements were made using a platinum resistance thermometer, Model 104T transfer standard (Rosemount Engineering Co., Minneapolis, Minn.) in conjunction with a Model E-1002 Mueller Bridge (Gray Instrument Co., Phila., Pa.). A sensitive light-beam galvanometer permitted the temperature to be read within 0.001 "C. Temperature stability was monitored continuously with a resolution of 1 "C fullscale on a strip chart recorder connected to a thermistor in a simple Wheatstone Bridge. Placement of the temperature sensor was an important factor in the attainment of temperature stability. Maximum stability was obtained by mounting the sensor near the center of the oven lid so that it was in contact with the heated air just as it entered the column compartment. The readout sensors were also mounted through the oven lid, but were farther down (about 15 cm from thelid) near the column. The temperature stability of the oven at 80 "C as monitored by the thermistor was found to be 10.013 "C for a short term ( 5 min) while long term stability of the mean temperature was somewhat better. The response speed of the resistance thermometer, which had a stainless-steel sheath surrounding the sensing element, was considerably less than that of the glass covered thermistor. Short term fluctuations indicated by the resistance thermometer were within 1 0 . 0 0 5 "C while, over an eight-hour period, the temperature remained constant to within 1 0 . 0 1 "C. Because there was undoubtedly some damping of short term temperature fluctuations by the chromatographic column tubing, the data from the resistance thermometer were probably more representative of the actual temperature of the column packing. Vertically, the temperature was homogeneous to within h0.02 "C from the top of the oven to the bottom. However, serious horizontal gradients of the order of 0.2 "C were found to exist. To promote mixing of the air as it entered the column compartment from the heating zone, a stationary impeller, similar t o a centrifugal blower, was mounted at the top of the column compartment. With that device in place, the entire region occupied by the chromatographic column was homogeneous to within 1 0 . 0 2 "C. Sample Detection and Data Readout. The detector system consisted of a HY-FY I11 flame ionization detector (FID) (Varian Aerograph, Walnut Creek, Calif.) connected to a Keithley Model 417 High-speed Picoammeter (Keithley
1236
ANALYTICAL CHEMISTRY
Instruments, Cleveland, Ohio). A Keithley Model 240A Power Supply provided detector polarization voltage. A 2.5-V (5.0 A) filament transformer could be switched into the polarization line to power the flame ignitor. The 417 picoammeter had a small, removable head, which contained all the high-impedance circuitry and could be mounted away from the main chassis of the instrument. The head and the F I D were mounted in a pedestal close to, but not touching, the oven so that they were isolated from oven vibrations. They were connected with only 7.5 cm of RG-58/U coaxial cable in order to minimize input capacitance, which degrades electrometer frequency response, and to reduce mechanical and thermal disturbances, which result in an increased noise level. The detector was supplied with electrolytic hydrogen and USP compressed air. Both were passed through 5A Linde Molecular Sieve traps at room temperature prior t o reaching the detector. The traps were regenerated biweekly at 300 "C. With a chromatographic column in place and carrier gas flowing, the noise level was about 2 x 10-14 A, a level that is normally considered to be flame noise. The analog output from the picoammeter was fed to a Model CRS-30D digitizer (Infotronics Corp., Houston, Tex.) and also to a strip chart recorder with a full-scale pen response time of 0.2 sec. The digitizer produced a punched paper-tape record of the digital value of the chromatogram ordinate at precise time intervals which could be varied from 0.05 t o 12.8 seconds per data point. The data rate was chosen so that 20-30 data points were obtained across a chromatographic peak. The readout provided a maximum resolution of one part in 105, somewhat greater than 16 binary bits. The system accepted signal levels of 1, 10, 100, and 500 mV full scale. At the faster data rates, the digitizer had a noise level in the digital output of about 0.1 of full scale even with the amplifier inputs shorted together. However, when the digitizer amplifier was disconnected from its voltage-to-frequency converter (V-F), the digital output was constant to 1 unit at any data rate. The noise problem was attributed t o insufficient isolation of the power supply for the amplifier from the one which powered the solenoids in the tape punch. Because the picoammeter had a high level output (3 V), the problem was circumvented quite successfully by driving the V-F directly by the picoammeter. Prior t o each experimental run, a six decimal-digit identification was set on rotary thumbswitches and entered manually onto the paper tape. The first digit indicated which of the eight data rates had been selected, and the remaining digits represented the serial number of the run. The digitizer was then slaved t o the controller which initiated readout in synchronization with the sample injection. The digitizer was stopped manually after the desired data for the run had been recorded. COMPUTATIONAL PROCEDURES Data Handling. The punched paper-tape output from the digitizer was read directly into core memory of a CDC 6500 computer by a n on-line high-speed photoreader a t the Purdue University Computer Science Center. All experimental parameters, with the exception of the data rate, were entered on the punched cards. The data rate was required on the paper tape so that the tape translation program could adjust for the change in tape format with the digitizing rate. Calculations. The beginning and end of the chromatographic peak were determined from, the first derivative of the digital data. Completely resolved peaks were involved in
this work; therefore, no procedures for resolution of fused peaks were necessary. An eleven-point, quadratic, first derivative convolute utilizing the method and coefficients of Savitzky (14) was chosen t o determine the point-by-point derivative. No data smoothing other than that inherent in the derivative convolute itself has been employed to date. After the beginning and end of the peak had been determined, the data points on either side of the peak were examined for noise or the onset of another peak as indicated by the absolute value of a first derivative that rose above a threshold of 1.0. I n the absence of noise, the base line was extended on either side by a distance of one half of the base width of the peak. The two base line segments were used to determine the equation of a linear base line by least squares. I n turn, the baseline equation was used to correct the peak for base line offset. Peak area was computed from the relation
I n Equation 6, T and Tu are the column and ambient temperatures (OK), respectively, while pzais the vapor pressure of water at ambient temperature and p a is the atmospheric pressure. The formula used to correct for gas compressibility was
(7) where p i is the column inlet pressure and po is the outlet pressure (assumed to be equal topu). The partition ratio, k, was obtained from V o R ,and the corrected retention volume of a “non-retained” sample, V,,, as follows: k
= (Van -
v.w)/V.w
(8)
+C
(9)
From the relation Ink
1=p1
where A is the peak area, y i is the value of the i-th ordinate corrected for base line, and p1 and p 2 are the data points corresponding t o the beginning and end of the peak, respectively. Because the individual y, values are actually integrals over the region i-1 t o i, Equation 1 holds rigorously within the limitations of digitizer dead time (0.06% maximum). The mean, pi’,of the elution curve, which was chosen to represent the retention time of a peak, was defined as z =pz
pi‘
~i
(ti
- 0.56)/A
(2)
1 = PI
where tt is the elapsed time, with reference to the start of data taking, corresponding to the output of y t . Equation 2 is not rigorous, for y . was ~ accumulated over a time interval, 6, from tl-,, to t l . This problem is the inverse of attempting t o obtain the integral of an area bounded by disconnected points. The first order solution to the problem (linear interpolation) assumes that the curve between tr-, is linear. Within the limits of that assumption, one may assign to y i a time midand t,; thus, the subtraction of 612 from t l . way between The second through fourth central moments of the peak distribution were calculated from 1=v2
(3) using values of K = 2,3,4. The central moments p 3 and p4 were transformed into pure numbers by dividing them by ( ~ 2 ) ~and ’ ~ respectively (8). The second central moment, pzris the peak variance, while the third and fourth are measures of skewness and flattening (excess o r kurtosis), respectively (8). The number of theoretical plates was calculated by the relation
N = (p~‘)~/gz
(4)
The corrected retention volume, VRo,was calculated from (5) where tn is the retention time of the peak mean, Fc is the flow rate corrected to column temperature and outlet pressure, j is the correction for carrier-gas compressibility, and V, is the extra-column dead volume. The corrected flow rate, F,, was obtained from the measured flow rate F, through the equation (14) A. Savitzky and M. J. E. Golay, AKAL.CHEM., 36,1627 (1964).
=
AHs RT
the heat of solution, AHs, was obtained by linear least squares analysis of a plot of In k cs. 1jT. I n Equation 9, R is the gas constant and C i s a constant of integration. Because the FID does not respond t o air and other permanent gases, methane is commonly used t o determine VM. Alternate methods have been proposed by Gold (15) as well as by Peterson and Hirsch (16). Both utilized the wellknown, empirical, linear relation between In k and carbon number for a homologous series of compounds (17). After substituting from Equation 8, the linearity could be expressed by the relation ln[(VoR - V.w)/V.wI = an
+b
(10)
where n is the number of carbon atoms in the molecule, and a and b are arbitrary constants. By supplying values of VoR for three numbers of a homologous series, it was possible to solve the three simultaneous equations for V,. I n this work, V.+,was determined from methane as well as from measurements on a homologous series of n-paraffins. However, the latter method has been generalized t o yield a more accurate value for V,was well as to reveal any deviation of the experimental data from Equation 10. Four or more values of V o R for members of a homologous series were utilized so that the three unknowns were over determined. The value of V , was systematically increased from zero, and, for each value of YAM, the V o Rdata were fitted to Equation 10 by least squares. The process was repeated until the best on the basis of the Gauss criterion (18), was revalue of V.%
