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Anal. Chem. 1985, 57, 2779-2787
215 cm/s. The components, retention times, and elution bandwidths are listed in Table V. Note that the chromatogram is complete in just over 10 s and that the first five sample components are well-resolved in about 6 s. Also note that the full width a t half-height of the toluene band is only 170 ms, corresponding to a standard deviation of 72 ms. Since the coating efficiency of the column used here was only 4570, considerably higher resolution and increased zone capacity could be achieved with a higher quality column. While the results reported here are preliminary, they do suggest that the electrically heated cold trap can be very useful as an inlet system for high-speed gas chromatography using short lengths of WCOT columns. Since the system operates a t very modest inlet pressures and uses conventional microsyringe sample introduction, the system should be applicable to a wide range of analytical and control problems, and it should be possible to convert almost any commercial gas chromatograph into a high-speed unit simply by installing a cold trap inlet system and a high-speed electrometer. While a stainless steel trap was used for the prototype system described here, a less active material such as Pt/Ir will be used in future studies. The principal limitations of the system are possible retention time biasing if sample components do not vaporize during the same high-current half cycle and significantly broadened and distorted reinjection bands for compounds with boiling points greater than about 190 "C. A trap with higher resistance or lower heat capacity should reduce these limitations. Alternatively, a more robust transformer, which would
allow the trap to heat to full operating temperature in a single half cycle, or a capacitive discharge heating technique could greatly extend the range of compound boiling points for which the inlet system would be useful.
LITERATURE CITED (1) Desty, D. H.; Goldup, A,; Swanton, T. W. I n "Gas Chromatography"; Brenner, N., Caiien, J. E., Weiss, M. D., Eds.; Academic Press: New York, 1960. (2) Desty, D. H. I n "Advances In Chromatography"; Giddings, J. C., Kelier, R. A., Eds.; Marcel Dekker: New York, 1965; Voi. 1, p 199. (3) Myers, M. N.; Giddings, J. C. Anal. Chem. 1965, 37, 1453-1457. (4) Doue, F.; Guiochon, G. Sep. Sci. 1970, 5 , 197-218. (5) Schomburg, G.; Husmann, H.; Weeke, F. J . Chromatogr. 1975, 9 1 , 603. (6) Deans, D, R. Chromatographia 1968, 7 , 18. (7) Gasper, G.; Arpino, P.; Guiochon, G. J . Chromatogr. 1977, 15, 256-26 1. (8) Wade, R. L.; Cram, S. P. Anal. Chem. 1972, 4 4 , 131. (9) Annino, R.; Leone, J. J . Chromatogr. Sci. 1982, 2 0 , 19-25. (10) Hopkins, B. J.; Pretorius, V. J . Chromatogr. 1978, 158, 465-469. (11) Jacques, C. A.; Morgan, J. J . Chromatogr. Sci. 1980, 18, 679. (12) Anderson, E. L. Ph.D. Dlssertation, University of Alabama, 1978. (13) Ducass, A.; Gonnord, M. J.; Arpino, P.; Guiochon, G. J . Chromatogr. 1978, 148, 321. (14) Biass, W.; Riegner, K.; Hulpke, H. J . Chromatogr. 1979, 172, 67-75. (15) Tranchant, J. "Practical Manual of Chromatography"; Elsevier: New York, 1969. (16) Leathard, D. A.; Shurlock, B. C. "Identification Techniques in Gas Chromatography"; Why-Interscience: New York, 1970; Chapter 9. (17) Kirsten, W. J.; Mattson, P. E.; Alfons, H. Anal. Chem. 1975, 4 7 , 1974-1979. (18) Giddings, J. C. "Dynamics of Chromatography": Marcel Dekker: New York, 1965.
RECEIVED for review March 26,1985. Accepted July 25, 1985.
Multiplex Gas Chromatography by Thermal Modulation of a Fused Silica Capillary Column John B. Phillips,* Derhsing Luu, and Janusz B. Pawliszyn'
Department of Chemistry and Biochemistry, Southern Illinois University, Carbondale, Illinois 62901 Glenn C. Carle
Solar System Exploration Office, NASA-Ames Research Center, Moffett Field, California 94035
Modulating the temperature of the first few centimeters of a fused slllca capillary gas chromatography column effectively modulates the concentratlons of retained substances flowlng contlnuously through the column. As the stationary phase Is heated and cooled, It alternately releases and adsorbs substances to and from the flowing carrler gas. The resulting chemical concentratlon signals follow the applled electrical signal. The slgnal form resembles a derivative of a chromatographic injectlon and results In a derlvatlve form chromatogram. Modulation efflclency and band length are dlrectiy dependent upon the capacity factor of the modulated substance and are predlctable. Large volume, contlnuously flowing, or headspace samples can be accepted directly without preconcentration. The minlmum detectable sample lntroductlon rate using a 9-m SE-52 column, a flame lonlzation detector, and a 1-h modulatlon signal Is 7.0 X g/s of p-dllsopropylbenrene. The linear dynamic range Is 6 orders of magnitude. The relative standard devlatlon Is less than 3%. Present address: Department of Chemistry and Biochemistry, Utah State University, Logan, UT 84322.
It is common to think of the chromatogram as a signal and to use signal processing techniques in extracting information from it. But, the chemical processes occurring within a column are traditionally thought of primarily in terms of the physical transport of substances rather than in terms of the signals carried by these substances. A few exceptions appear in the literature. For example, Reilley et al. (1) demonstrated the response of a chromatographic column to a variety of imposed concentration signals. Considering a familiar subject from a different perspective often leads to new appreciation and understanding ( 2 ) . In this paper we consider gas chromatography from a signal processing point of view. The fundamental features remain unchanged, but different aspects are emphasized. Some new terminology is introduced to clarify which features of chromatography are fundamental and which are only conventional. Eliminating some common but unnecessary conventions leads to alternative techniques with significant advantages in some applications (3). Chromatographic Information and Signals. Information is carried by signals. A detector's output signal carries information which may be recorded and presented in the form of a chromatogram. The detector itself, however, is not the
0003-2700/85/0357-2779$01.50/00 1985 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 57, NO. 14, DECEMBER 1985 Sample Sample
It Modulation
tlodulator
.)
Chromatogram
Conventional Chromatography
Chromatogram
Multiplex Chromatography
Flgure 1. Multiplex and conventional chromatography compared. Conventional chromatography Is a special case in which sample inlet and modulation are combined in a single device and modulatlon is limited to a single pulse signal form.
information source. I t is merely a transducer changing the physical form of the signal. Since information is present before the detector, signals must also be present before the detector, that is, within the column. Moving chemical concentrations carry information and, therefore, are signals in the column. These chemical signals differ from others, such as electronic signals, only in their physical form. Fundamentally, they are just as truly signals as are the more familiar varieties and may be treated by the same information and communication theory mathematics and associated signal processing techniques. Information and signal processing approaches have been previously applied in analytical chemistry. Some of the more explicit examples are the work of Eckschlager and Stepanek (4) and in the Fourier transform spectroscopies ( 5 ) such as FT-IR, FT-NMR, and FT-MS. Multiplex Chromatography, An explict use of signal processing concepts is advantageous in discussing chemical signals within the column and their connection to signals outside the column. Figure 1 compares conventional and multiplex chromatography in signal processing terms. The fundamental characteristics of the two are identical. The multiplex technique is just a generalization of the conventional in which a greater variety of chemical signals may be imposed on the column. The detector is a chemical-to-electronic transducer whose output is, ideally, a linear combination of the entering chemical signals. Information is lost during conversion from the chemical to the electronic domain as the many chemically distinguishable signal carriers are replaced by one carrier, the output electrical current. This information, if it is to pass through the transducer, must be encoded in some other form prior to conversion. The column sorts chemical signals according to the interaction chemistry between the signal carriers and the column stationary phase. Information represented by the chemical identity of the various signal carriers is thus encoded in the phases of the signals. Chemical identity information is lost a t the detector, but the same information when encoded as a signal phase shift is preserved. The column is a signal processor which performs a function analogous to a mono-
chromator in spectrometry and can be thought of as a dispersion device for chemical signals just as the monochromator is a dispersion device for certain electromagnetic signals. The injection port of a conventional chromatograph performs two distinctly different functions. It introduces sample to the instrument and, in addition, it imposes a modulation signal on the sample. In the conventional case, the modulation signal is the direct result of sample introduction and has the form of an injection pulse. But, sample introduction and sample modulation are really two separate functions. Implementing them with two independent devices allows each to be optimized independently. The two devices, inlet and modulator, transmit two different signals to the column. The modulation signal is known in advance and, thus, carries no information. The chopper signal in a spectrometer is analogous. The desired informationcarrying signal, the analytical signal, is already present in the chemical identities and concentrations of the sample at the inlet. These two signals, modulation and analytical, are multiplied together by the modulator to give a composite chemical signal which contains the information of the analytical signal but has the form of the modulation signal. In conventional chromatography, demodulation is not explicity required. Restricting modulation to only the single sharp pulse makes demodulation a unit operation which may then be ignored. But, the use of more general modulation signals requires demodulation to reveal the information carried by the analytical signal. Demodulation is a signal detection problem. Since, in general, more than one chemical signal is traveling along the column, more than one copy of the modulation is in the detector output signal. Each of these copies has it own phase shift with respect to the modulation signal source and its own amplitude. The demodulation problem is to find each of these copies of the modulation signal in the detector output and measure its amplitude. Signal amplitude as a function of phase is the chromatogram. A number of computational techniques are applicable to this problem (3,6). The simplest of these, cross correlation, is used here (7). Modulation Signals. Modulation is a fundamental requirement of chromatography because it provides a reference against which the phases of the chemical signals at the detector are defined. Without it, chemical identity information cannot be encoded. The modulation signal’s function form, however, is not fundamental. Any one of a great many different forms may be used, subject only to the restriction that the phase shifts of the chemical signals be unambiguously defined. The choice depends on the application for which it is to be used. Reilly et al. (I) demonstrated that the choice of signal form can affect the efficiency of a chromatographic determination. A conventional injection port modulates the sample in the functional form of a single sharp pulse whose amplitude is proportional to concentration. The single sharp pulse has two advantages as a modulation signal. First, because it is a single pulse, it provides a clearly unambiguous phase reference for which no demodulation is required. And second, because it is a sharp pulse, it provides power a t high frequencies. A high-frequency signal is more sensitive to phase shift than is a lower frequency signal and thus provides more precision in determination of phases. The maximum frequency which can be applied is ultimately limited by the column’s ability to transmit a chemical signal and the detector’s ability to transduce it to the electronic domain without distortion. Other signals, for example a random sequence of pulses, also provide unambiguous phase references and have power at high frequencies, These satisfy the fundamental requirements just as well as the single sharp pulse and for some applications may have significant advantages. Conventional
The restricted duration of the modulation signal in conventional chromatography is like the restricted slit width in conventional infrared spectrometry (5). It limits the quantity
4-l
:2 -I-'
c
k-
instrument output signal to avoid demodulation computations. Eliminating either restriction results in a throughput advantage which greatly improves instrument performance in certain
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ANALYTICAL CHEMISTRY, VOL. 57. NO. 14. DECEMBER 1985
Derivative Form Signals. Chemical concentrations cannot be negative. The negative part of the derivative signals in Figure 2d,e is negative only in reference to the average concentration passing through the modulator. The impossibility of negative concentration limits the amplitude of the negative part and may distort the derivative form if the modulator is driven too strongly. The amplitude of the positive part is limited by column capacity. Within these limits, a concentration pulse followed by a vacancy is a derivative or pseudo-derivative form chemical signal. Derivative and pseudo-derivative signal forms are similar but differ in the distance between the positive and negative parts. In the derivative form the two parts are in effective contact with each other. Sample material moves across the steep concentration gradient from the positive to the negative part by diffusion-like band broadening processes. As the two parts cancel each other out, the intrasignal length gradually increases and the signal amplitude decays. A derivative form signal with the same overall length and amplitude as a pulse form signal must have steeper concentration gradients because it contains two changes of gradient direction while the pulse contains only one. The steeper gradients of the derivative form result in more rapid amplitude attenuation due to hand broadening. 'More of the power of a derivative form is a t frequencies too high to he transmitted through the column. These rapidly decay leaving only the lower frequency components of the signal. In the pseudo-derivative signal form, however, the two parts are not in effective contact and the gradient between them is not so steep. Band broadening may bring substance from the tail of the positive part into the tail of the negative part maintaining the derivativelike appearance of the signal, hut the central portion of each part is essentially unaffected by the presence of the other and the amplitude of each decays with band broadening at the same rate as a Gaussian pulse. A signal may start out as a pseudo derivative at the modulator, hut after sufficient hand broadening, it will eventually acquire a derivative form. EXPERIMENTAL S E C T I O N Reagents. Decane, dodecane, and tridecane were obtained from Matheson Coleman and Bell (Norwood, OH) and p-diisopropylhenzene from Alltech Associates (Waukegan, IL). These were all reagent grade. Carrier gasses were prepurified grade nitrogen and hydrogen from Air Products (Allentown, PA), A sheet fabric softener, Bounce (trademark of Prodor and Gamble), was used to demonstrate analysis of a real sample, Equipment. The experiments were performed on a Varian (Walnut Creek, CA) Model 3700 gas chromatograph equipped with a flame ionization detector. SE-52 fused silica open tubular columns 18.0 cm, 9 m, and 12 m long from Alltech Associates (Waukegan, IL) were used. The column internal diameter was 0.244 mm, and the stationary p h e thickness was 0.2 Irm. A North Star (San Leandro, CA) Horizon computer with 48K bytes of memory and dual floppy disk drives was interfaced to the gas chromatograph. Computer peripherals included a Tecmar (Cleveland, OH) Model AID-212 analog-to-digital converter, a Houston instruments (Austin, TX) Complot plotter, a Hazeltine (Greenlawn, NY) 1420 display terminal, and a Semidisk (Beaverton, OR) Model 4931A-1 bulk memory. The electrometerto-computer interface included a law pass filter with 20 Hz cutoff and an amplifier with a gain of 200. The amplifier was required to reduce digitization noise in low-level signals (16). Modulator. Figure 3 illustrates modulator design and construction. A pair of 36-gauge wires were wrapped tightly around the column at each end of the modulator region. The modulator region and the lead wires were then painted with three coats of an electrically conductive paint which was allowed to cure for at least 24 h before use. The film was examined microscopically and determined to be 0.04 mm thick. This paint, which is intended for use in repairing electrical heating elements on glass windows, was obtained from a local automobile parts store. A typical modulator had a resistance of 0.5 n/m. The computer controlled
-SILICA
CAPILLARY
-MOBILE
PHASE
E
-STATIONARY
PHASE
-CONDUCTIVE
PAINT
Flgure 3. A modulator to generate derivative or pseudoderivative chemical concentration signals by thermal desorption in a fused silica column.
Flgure 4. Heated headspace sampler for multiplex gas chromatography: (a) aluminum block, (b) glass tubing, (c) temperature sensor, (d) heating element, (e) septum. (f) threaded brass fining, (g) carrier gas supply through fused silica tubing. (h) fused silica column.
the modulator current from a regulated 40-V-dc power supply using an Opt0 22 (Huntington Beach, CA) Model ODCSP electronic switch. A resistor was placed in series with the modulator to limit the current to about 2 A. Modulation Signal Generation and Data Acquisition. A modulation signal was generated by using a pseudo-random number algorithm (17). The probability of a pulse occurring during a data acquisition time interval varied between 3.125% and 25.00% except during a dead time interval following each pulse which varied between 0.200 and 1.00 s. Base line drift was removed from the detector output signal hy subtracting a moving average from each data point, a procedure which acts as a highpass digital filter, Sample Introduction. The injection port of the gas chromatograph was replaced with an aluminum block headspace sampler illustrated in Figure 4. The temperature of the block was regulated by the original injection port controller of the Varian 3700. A glass liner with an outside diameter of 0.5 in. (1.2 cm) and a length of 4.0 in. (10 cm) was installed within the block and held gas tight on either end by Alltech High Temperature Blue septa. The fused silica column was connected to the lower end of the sample holder by passing it through a needle hole in the septum. A carrier gas supply was similarly connected to the upper end of the sample holder through fused silica tubing. Liquid samples were placed in the bottom of capillary tubes which were then inserted into the sample holder. The sample evaporation rate was adjusted by varying the capillary diameter, length, or temperature and was determined hy using the method given by Savitzky and Siggia (18). A 0.5 X 5 cm piece of fabric softener was placed directly within the sample holder tube. R E S U L T S AND DISCUSSION Modulator. Figure 3 illustrates a thermal desorption modulator. Retained substances entering a length of fused silica open tubular column partition between mobile and stationary phases just as they do in any column. Under quiescent conditions, mobile and stationary phase concentrations are each constant and independent of position along the modulator. On command from a signal source, an electrical current passes through a thin film of electrically conductive paint on the column rapidly heating the paint, the
ANALYTICAL CHEMISTRY, VOL. 57, NO. 14, DECEMBER 1985
,
2783
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4.8
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10
15
20
25
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Figure 5. Multiplex chromatogram of decane, dodecane, and tridecane in nitrogen carrier gas on a 18.0-cm SE-52 fused silica column: modulator length, 1.0 cm; data acquisition rate, 5 Hz; modulator pulse duration, 0.100 s;modulation signal duration, 3584 data points (60 min); average time between pulses, 2.5 s (including a dead time of 0.4 s); carrier gas flow rate, 0.36 cm3/min; oven temperature, 80.0 OC. Sample rates were as follows: decane, 1.5 X lo-'' g/s; dodecane, 1.8 X lo-'' g/s; tridecane, 2.2 X lo-'' g/s.
column, and the stationary phase within the column. The sudden temperature pulse releases any substances held by the stationary phase, increasing their concentrations in the mobile phase. The mobile phase carries the concentration pulse out of the modulator and into the following column. After completion of the electric current pulse, the modulator cools to the oven temperature and retained substances again partition into its stationary phase. The depleted mobile phase carries a concentration vacancy into the following column. The success of this modulator depends on the fact that fused silica columns have very low thermal masses and can rapidly change temperature. Electrically conductive paint provides excellent thermal contact with the column while adding very little mass. A series of electrical pulses generates a long chemical signal following the timing of the applied pulses. This device is, thus, a transducer which converts signals from the electrical domain to the chemical domain and in the process takes a derivative of the applied electrical signal. It is a modulator because its output is the product of two signals, the entering chemical signal and the applied electrical signal. Multiplex Chromatograms. Figure 5 is a multiplex chromatogram. The analytical signal is a mixture of three hydrocarbons in a nitrogen carrier gas. The modulation signal is a long pseudo-random series of electrical pulses. Figure 6 is the numeric integral of the chromatogram in Figure 5. It contains three peaks corresponding to the three hydrocarbons in the mixture. The base line is approximately flat indicating that the two parts of the derivative signal are equal in area as expected. Relationships developed for conventional single pulse signals also apply to the derivative and pseudo-derivative forms. Some additional relationships are relevant to the more complex structures of the derivative forms. Table I presents some retention and modulator efficiency parameters calculated from the chromatograms in Figures 5 and 6. Modulator and Column Frequency Response. Electromagnetic signals are commonly characterized in terms of either temporal frequency or spatial wavelength. These two can be used almost interchangeably because there is only one signal carrier and its speed is constant. In a column, however, there are many signal carriers with many different migration speeds. Also, band broadening processes depend on concentration gradients along the column which are spatial, not temporal, quantities. Thus, length and spatial frequency
Figure 6. Numeric integral of the derivative chromatogram in Figure 5.
Table I. Retention a n d Modulator Efficiency Parameters Calculated from t h e Chromatogram i n Figures 5 a n d 6 parameter retention time (s) capacity factor, k expected (ideal) initial band length (cm) measured terminal band length (cm) measured intrasignal duration (s) measured intrasignal length (cm) expected length of 1 u (cm) expected band length, postive signal part (cm) column-limited band length at half-height, pseudo-derivative signals (cm) column-limited band length at half-height, derivative signals (cm) measured band duration at half-height, positive signal part
decane dodecane tridecane 4.4 2.1 1.32
10.0 5.9 1.14
17.6 11.2 1.08
11.5
8.4
5.4
0.82 3.4 0.69 0.32
1.42 2.6 0.87 0.14
2.1 2.1 0.93 0.082
1.6
2.0
2.2
1.1
1.4
1.5
0.41
0.83
1.32
1.7
1.5
1.4
1.0
1.0
1.0
1.13
1.35
1.98
4.6
2.4
2.0
3.1 2.7
6.9 1.7
12.2 1.4
(9)
measured band length at half-height, positive signal part (cm) expected band length, negative signal part (cm) measured band duration at half-height, negative signal part (9)
measured band length at half-height, negative signal part (cm) expected signal asymmetry ratio measured signal asvmmetrv ratio
rather than time and temporal frequency are the appropriate signal attributes. Detectors are both chemical and electronic devices and are usually limited by both temporal and spatial frequency response. For example, the response of the thermal conductivity detector is limited by both the rate at which its filaments change temperature and by the cell internal volume. Similarly, a thermal desorption modulator is both chemical and electrical and is limited by both the rate at which it can change temperature and by the length of the column affected by a temperature change. Any changes occurring in the applied modulation signal faster than the time required to change temperature or which result in a chemical signal shorter than a characteristic length related to the modulator length cannot be accurately transduced to the chemical domain.
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The velocity, u , a t which a given signal moves along the column is u = u / ( k 1) (1) where u is the mobile phase velocity and k is the capacity factor. The duration of a signal is just the distance over which i t is generated divided by the velocity with which it moves through that distance. When the modulator is hot, h = 0 and a signal propagates at the mobile phase velocity, u. When the modulator is a t the oven temperature, k > 0 and a signal propagates at the slower sample migration velocity, IJ. Thus, generation of the positive part of the signal requires time
+
t+ = b,/u
(2)
and generation of the negative part requires time t- = ( k l ) b m / u
+
(3)
where b, is the modulator length. For maximum modulation, the modulator should be hot for at least time t+and then held at the oven temperature for at least time t-. Since t+is less than t-, the positive part of the signal is sharper than the negative part. This sharpening effect, which can be seen in Figure 5 , is related to Grob’s (19) retention gap peak sharpening effect. The hot modulator is a temporary retention gap at the head of the column. Saxton (20) defined the terminal band length as the length of a band along the column as it emerges from the column. Since substances with a wide range of retention have the same terminal band lengths on a given column, this length can be taken as a measure of column efficiency. Similarly, the band length at the modulator is a measure of modulator efficiency. Assuming that temperature changes are rapid and that the minimum times (eq 2 and 3) are used to generate the signals, the initial band lengths, b+ and b-, of the two parts of the signal are b, = t+u = b m / ( k 1) (4)
+
b- = t-u = b,
(5)
Modulation limited only by the modulator length should give a total initial band length of b+ + b-. These ideal initial band lengths are given in Table I. The terminal band lengths determined from Figure 6 are significantly greater than these calculated ideal lengths. From the manufacturer’s test chromatogram, this column was determined to have an efficiency of approximately 1750 theoretical plates/m. The theoretical plate measure of column performance may be related to the band length measure through the definition of the effective number of theoretical plates, Ne, = [ ( t-~t m ) / ~ t I ’ (6) where ot is the time standard deviation of the peak. Substituting the appropriate lengths divided by velocities for the times in eq 6 and using eq 1to relate migration velocity to carrier gas velocity give ob =
[L/(Neff)1’2][h/(k + 111
(7)
where ob is the band length of one standard deviation. These band lengths, which are given in Table I for each of the sample substances, are measures of the spatial response limit of the column. Modulator Signal Amplitude. Under quiescent conditions the number of molecules within the modulator mobile phase is a constant independent of the stationary phase (21). The number of molecules retained within the stationary phase of the modulator is then also constant and is related to the number of molecules in the mobile phase by the capacity factor, k = n,/n,. The amplitude of the chemical signal generated by the modulator is proportional to the number of
molecules in the modulator stationary phase which is related to the amplitude of the entering chemical signal and the capacity factor. The amplitude of a derivative form signal is best defined as the absolute value of the difference between the maximum of the positive part and the minimum of the negative part. When heated, the modulator stationary phase releases all n, of the sample molecules contained within it allowing them to join the n, molecules already present in the modulator mobile phase to give a total of n, + n, molecules. After a t+ time delay for the positive part to move out of the modulator and on into the following column, the hot modulator contains n, molecules in the mobile phase and none in the stationary phase. As the temperature falls through the substance’s release themperature, the stationary phase retains a portion of these n, molecules leaving the rest in the mobile phase. The nJ,and fraction remaining in the mobile phase is n,/(n, the total number of molecules in the mobile phase is n, times this fraction. If the modulator’s mobile phase volume is V, then the quiescent mobile phase concentration is C = n,/ V and the concentrations of the positive and negative parts are
+
c+ = (n, + n,)/V = C(k + 1)
(8)
where the definition of the capacity factor has been used to substitute for numbers of molecules. Taking the difference of the two amplitudes gives
A = C+ - C- = C(h + 1) - C / ( h
+ 1)
(10)
where A is the amplitude of the modulation signal. Strongly retained substances are modulated more effectively than weakly retained substances. Unretained substances ( k = 0) are, of course, not modulated at all. Equations 8-10 do not apply to very strongly retained substances whose release temperature may be beyond the temperature limit of the stationary phase. The positive and negative parts are generated by different mechanisms and so differ in their amplitudes and band lengths. A convenient measure of this difference, or signal asymmetery, is the ratio of the sizes of the two parts from eq 8 and 9,
(C,
-
C)/(C - c-) = k
+1
Expected and measured asymmetry ratios are given in Table I. Equations 8-11 predict large positive part signal amplitudes and very asymmetrical signal forms for strongly retained substances. This effect is not observed because the modulator, column, and detector are unable to operate fast enough. Modulator Performance. An observed signal form may be limited by any one of the following: the response of the column, the response of the detector, the theoretical capabilities of the modulator, or the operational limits of the modulator. A short column (18.0 cm) minimizes the influence of chromatographic band broadening on signal forms. All test substances used here have significant retention in the column to slow their rates of elution and minimize the influence of the detector time constant. If the signals in Figure 5 are true derivatives, then the intrasignal lengths, the distances between the maximum of the positive and minimum of the negative parts, should be limited by the column at l o . Since the actual intrasignal lengths obtained are significantly longer than l a , these signals are still pseudo derivatives. The peaks in Figure 6 a t first glance appear to be Gaussian, but on closer inspection can be seen to have flattened tops. The measured intrasignal length for decane is about a factor of 5 (3.4 cm vs. 0.69 cm) greater than the 1 - u column limit. The dodecane and tride-
ANALYTICAL CHEMISTRY, VOL. 57, NO. 14, DECEMBER 1985
cane intrasignal lengths also exceed the column-imposed limit but by smaller amounts. There is no way to determine in an individual signd what part of this degredation in performance is due to the modulator temporal frequency limit and what part is due to the spatial frequency limit. Since decane is the fastest signal, however, it should be affected to the greatest degree by temporal response limits. The modulator, at worst, requires 0.82 s between release of sample during the heating phase and sorption of sample during the cooling phase. All substances see the same modulator timing cycle and so should have approximately the same signal durations, if time is the limiting factor. Since signal durations are observed to be strongly dependent upon retention, spatial effects must also be important. Tridecane is the slowest signal and should, therefore, be least affected by modulator temporal effects. Its measured intrasignal band length is due mostly to the modulator’s spatial response limits. The modulator, at worst, is generating a 2.1-cm gap between the positive and negative parts. Assuming that the signal generation mechanism is the same for both decane and tridecane, we can simultaneously calculate the temporal and spatial response limits for the modulator by using
b = t,(L/tR) + b,
(12)
where b is the measured intrasignal length, t, is the modulator response time, b, is the modulator response length, L is the column length, and tR is the retention time. Applying eq 12 to the Table I data for decane and tridecape gives a modulator response time of 0.4 s and a response length of 1.7 cm. In frequency terms these are 2.5 Hz and 0.6 cm-l as the temporal and spatial response limits, respectively. Given the modulator dimensions and operating parameters, these numbers are reasonable. Both temporal and spatial response limits are important. For substances with k > 3 spatial frequency response is the major contribution to band length, but for substances with k < 2 temporal frequency response is more important. The modulator works best for substances with capacity factors between 2 and 3 where the two frequency limits have about equal influence. The above assumption that the mechanism of modulation is independent of capacity factor cannot be strictly true. All substances in a sample mixture see the same heating and cooling rates, but their responses to temperature changes vary with retention. A weakly retained substance is released at a lower temperature and migrates along the column faster than a more strongly retained one. The positive part of the signal begins to move along the column as soon as the modulator becomes hot enough and continues to move at its migration velocity, u (eq l),during the rest of the heating and cooling cycle. The following negative part is not generated until the modulator temperature has fallen sufficiently after the eledric current pulse for the stationary phase to again retain the sample substance. This effect will tend to exaggerate the relative importance of time for weakly retained substances. The individual durations and lengths of the positive and negative signal parts are best measured at signal half-height because it is difficult to determine precisely where a peak reaches base line and because the two parts interact with and distort each other at the base line. Band durations and lengths measured at half-height are given in Table I. A Gaussian peak has a length of 2 . 3 5 ~a t half-height. No pulse form signal can pass through the column with a halfheight length less than this. A derivative of a Gaussian peak has a length of 1 . 6 0 ~at half-height. No derivative form signal can pass through with a half-height length of either part less than this. A column-limited pseudo-derivative signal has a
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length at half-height somewhere between these two cases depending on how strongly the parts interact. Table I contains estimates, calculated by using eq 7, of the column-limited band lengths at half-height for both the pulse form and derivative form signals. The positive part band length of tridecane is limited by the column. The positive part signal of decane is probably not limited by the column since its length significantly exceeds that expected. The dodecane signal is an intermediate case and may or may not be column-limited. The duration of the decane positive part signal is about the same as the temporal intrasignal response limit estimated above. These two durations should not necessarily be equal since they refer to two different features of the signal and are generated by different mechanisms. But, they are both ultimately dependent on the same rate of temperature change and so should be similar in magnitude. The asymmetry ratio for decane is about what is theoretically expected for a substance with its capacity factor. The modulator is apparently operating as predicted in generating the amplitudes of the decane signal parts. The decane band lengths, however, are all about a factor of 5 too large. Obtaining the expected asymmetry ratio while broadening all signal parts equally is unlikely unless modulator speed is the limiting factor and all signal parts are generated with about the same time constant. None of the negative part band lengths is limited by the column. The shortest one, tridecane at 2.0 cm, is still significantly greater than the corresponding positive part. If limited by the column, it would have about the same length as the positive part. Equation 5 predicts that the negative part will have a minimum length equal to the modulator length. The minimum may be further broadened by the time required for the modulator to cool through the sample substance’s release temperature. This time can be substantial, especially for weakly retained substances, as the modulator temperature asymptotically approaches the oven temperature. Applying eq 12 to the negative part data in Table I gives a modulator response time of 0.8 s and a response length of 1.2 cm. The response length corresponds quite closely to the modulator length and, as expected, the response time is greater than the times required to generate the positive parts and the intrasignal lengths. Overall, this modulator, and not the 18.0-cm column, is the limiting factor in signal band length and chromatographic resolution. The band lengths generated would not limit resolution an more typical length columns, however, and the present modulator design is acceptable for use with such columns. The band lengths are in the same 10-cm range as the initial band lengths obtained from the best on-column injection (22) or cryogenic trap (23) techniques. For use with longer columns, the modulator should be increased in length and operated a t lower frequencies, With a very short modulator such as this, the generated chemical signals will broaden into the true derivative form well before the end of the column is reached and then decay in amplitude more rapidly than necessary. Generating a signal sharper than that which can be transmitted through the column does not help resolution and, in the case of derivative form signals, may hurt sensitivity. A second pulse applied to the modulator before it has returned to its quiescent state will not generate the expected chemical signal form because the stationary phase has not yet been fully replenished. Such interaction between pulses violates the assumption of direct signal transduction from electrical to chemical domain. The mismatch between the assumed and actual modulation signals applied at the head
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ANALYTICAL CHEMISTRY, VOL. 57, NO. 14, DECEMBER 1985
Table 11. Calibration Data for p-Diisopropylbenzene in Nitrogen Carrier Gas on a 12-m SE-52Fused Silica ColumnQ sample rate, g f s 2.6 X 1.3 x 5.1 x 7.8 x 2.1 x 1.2 x 3.9 x 1.3 x 1.9 x 3.3 x 4.0 x 4.5 x 5.2 x
10-13 10-13 10-13 10-12 10-10 10-10 10-9 10-96
10-96 10-96
10-9b
10-9*
signal, Alpulse 8.1 x 4.1 x 1.6 x 2.4 X 6.5 x 3.8 x 1.2 x 3.9 x 6.1 x 8.1 x 8.5 x 8.4 x 8.2 X
10-15 10-13 10-l2 10-l2 10-9 10-9 10-9 10-9 10-9 10-9
lo4
sensitivity, C/g 3.12 3.15 3.14 3.08 3.10 3.17 3.08 3.00 3.21 2.45 2.13 1.87 1.58
'Experimental conditions are the same as in Figure 7. The correlation coefficient is 0.99996. bThese data are not included in the calculation of the linear correlation coefficient because the column is overloaded at these concentrations. of the column generates noise during demodulation. A chromatogram was obtained of the same sample under the same conditions as in Figure 5 except that the average time between pulses was 1.0 s rather than 2.5 s. Since the t- time (eq 3) for tridecane, the most strongly retained substance in this mixture, is 1.0 s, the modulator usually did not return to its quiescent state before the next pulse. As expected, the signal-to-noise ratio was poorer. Another chromatogram was obtained of the same sample under the same conditions as in Figure 5 except that the average time between pulses was 7.4 s rather than 2.5 s. If the modulation signal used for Figure 5 already has adequate time between pulses to assure a return to quiescent conditions after each pulse, then this decrease in modulation signal frequency should reduce the signal-to-noise ratio. In fact, the signal-to-noise ratio was again Foorer. A lower power modulation is less effective and results in less signal. The sample throughput was identical in these three chromatograms, but the modulation signal frequency varied. Too much modulation drives the physical device beyond its capabilities and gives poor results. Too little modulation allows more sample through unmodulated and also gives poor results. There is an optimum modulation signal frequency which depends on the capacity factor of the modulated substance. A compromise is required for mixtures containing substances with widely varying retentions. Calibration, Precision, and Detection Limits. Table I1 is a set of calibration data for p-diisopropylbenzene in nitrogen carrier gas. Calibration is linear over 6 orders of magnitude with a correlation coefficient of 0.99996. Over this range, modulator, column, and detector responses are all linear. The linear range will not necessarily be this wide for all sample substances, however. Above 1.9 x lo+ g/s, the calibration curve bends over and retention time gradually increases. This change in retention indicates that sample molecules are beginning to interact significantly with each other and the column is overloaded. Conder and Young (24) show that concentration overloading of the column can be expected when the mole fraction of solute g/s a t 3.0 exceeds 0.01. Our overload limit of 1.9 X cm3/min is a t a concentration of 3.8 X g/cm3 in the gas phase. From the capacity factor of the solute and the relative volumes of the mobile and stationary phases in the column, the partition coefficient is approximately 3000. The concentration of the solute in the stationary phase is thus 1.1 X g/cm3 which is a mole fraction of approximately 0.01. The flame ionization detector has a linear range of 7 orders of magnitude from its minimum detectibility to the limit of
its linear response. The upper part of its range, however, is not usable with capillary columns because the column response is nonlinear at those concentrations. Detector response remains linear below the minimum detectability, but signals are then lost in the noise. Multiplex chromatography extends the linear range downward below the detector's minimum detectability partially compensating for the loss of the upper part of the range. The relative standard deviation of a set of six replicate determinations of p-diisopropylbenzene was less than 3%. This precision is comparable to many other gas chromatographic techniques. A multiplex chromatogram was obtained by using hydrogen gas carrying p-diisopropylbenzene at 7.6 X g/s through a 20-cm modulator followed by a 9-m SE-52 column. At 3.0 cm3/min the sample concentration was 1.5 X g/cm3. The modulation signal duration was 3840 s with an average time A/pulse in between pulses of 8 s. The signal at 1.6 x the computed multiplex chromatogram was slightly above the detection limit. This is about 2 orders of magnitude below the concentration detection limit for a conventional single injection determination using the same column and detector. This large improvement is a direct result of the long modulation sigdal. The total quantity of sample introduced during g which is comparable to the conventhis time is 2.9 X tional determination detection limit. The modulator and column lengths used here were chosen to correspond to those which would be used in a typical determination of a real sample. A substantially lower detection limit is possible by using a very short column such as that in Figure 5. With less band broadening, the signal amplitude is attenuated less and lower concentrations can be detected. Contaminants in the carrier gas have substantially higher concentrations than the sample itself and produce larger signals a t short retention times in detection limit chromatograms. The noise in the vicinity of the p-diisopropylbenzene signal is partly residual correlation noise associated with these contaminants and partly detector noise caused by the continuous bleeding of unretained and slightly retained contaminants through the detector. This spreading of noise from larger signals to obscure smaller signals throughout the chromatogram is an example of a multiplex disadvantage. It is the limiting factor in the detection of low concentration samples. The contaminant source is presently unknown, but likely possibilities include bleeding from the septa in the headspace sample holder, memory effects from previous samples, and the presence of a few parts per million of light hydrocarbons in the carrier gas. Potential Applications. Figure 7 is the chromatogram of a scented fabric softener. The scent and softener substances are supported on a foamed polymer sheet and are intended to be released under moderate heating such as that encountered in a clothes drying machine. The sample was swept with a hydrogen gas stream to carry any released substances directly to the modulator and column. The largest signal is probably due to the fabric softener substance and the others due to the scent. The unscented version of this same commercial product has only the one large signal. Headspace sampling for multiplex gas chromatography is very simple and easy to apply to samples of this type. Such samples normally require some kind of preconcentration trapping before conventional single injection gas chromatography because the concentrations are very low. Freeing sample introduction from the time and volume constraints of the single pulse injection has important implications for sample acquisition and preparation. Some samples, trace pollutants in ambient air for example, are available in large volumes with very low concentrations. Such
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Flgure 7. Multiplex chromatogram obtained from headspace of a scented fabric softener at 100.0 O C in hydrogen carrier gas on a 9-m SE-52 fused silica column: modulator length, 20 cm; data acquisition rate, 1 Hz; modulator pulse duration, 0.200 s; modulation signal duration, 3840 data points (64 min); average time between pulses, 20 s (including a dead time of 10 s); carrier gas flow rate, 3.0 cm3/min; oven temperature, 140.0
OC.
samples usually require preconcentration before conventional analysis. If the major components of a large volume sample form an acceptable carrier, then the sample can be simply pumped through the modulator and column eliminating the volume reduction step. We have determined methane in air using this technique (13). Headspace samples may be conveniently separated from nonvolatile matrices by evaporation into a carrier gas stream. The resulting dilution is unimportant because of the higher throughput volume.
LITERATURE CITED (1) Reilley, Charles N.; Hiidebrand, Gary P.; Ashley, J. W., Jr. Anal. Chem. 1982, 3 4 , 1198-1213.
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(2) Phillips, John B. Anal. Chem. 1981, 5 3 , 1463A-1470A. (3) Phillips, John B. Anal. Chem. 1980, 5 2 , 468A-478A. (4) Eckschlager, Karel; Stepanek, Vladimir Anal. Chem. 1982, 5 4 , 1 1 15A- 1 127A. (5) de Haseth, James A. I n "Fourier, Hadamard, and Hilbert Transforms in Chemlstry"; Marshall, Alan G., Ed.; Plenum: New York, 1982; pp 406, 407. (6) Chen, C. H., Ed. "Digital Waveform Processing and Recognition"; CRC: Boca Raton, FL, 1962. (7) Smit, H. C. Chromatographia 1970, 3 , 515-520. (6) Lovelock, J. E. J. Chromatogr. 1975, 112, 29-36. (9) Wells, Gregory J. Chromatogr. 1985, 319, 263-272. (IO) Laster, W. G.; Pawliszyn J. B.; Phlllips, J. B. J. Chromafogr. Scl. 1982, 2 0 , 278-262. (11) Valentin, J. R.; Carle, G. C.; Phillips, J. B. HRC CC, J. High Resolut. Chromafogr. Chromatogr. Commun. 1982, 5 , 269-271. (12) Valentin, J. R.; Carle, G. C.; Phillips, J. B. HRC CC, J . High Resolut. Chromatogr. Chromatogr. Commun. 1983, 6 , 621-622. (13) Valentln, Jose R.; Carle, Glenn C.; Philllps, John B. Anal. Chem. 1985, 57, 1035-1039. (14) Carney, Daniel P.; Phlllips, J. B. HRC CC, J . High Resolut. Chromatogf. Chromatogr. Commun. 1981, 4 , 413-414. (15) Carney, Daniel P. Ph. D. Dissertation, Southern Illinois University, Carbondale, IL, 1984. (16) Koel, M.; Kallurand, M.; Kulllk, E. I n "Advances in Chromatography"; Zlatkls A., Ed.; 1982; pp 433-441. (17) Lewls, T. G.; Payne, W. H. J. Assoc. Comput. Mach. 1973, 2 0 , 456-468. (18) Savitsky, A. C.; Siggla, S. Anal. Chem. 1972, 4 4 , 1712-1715. (19) Grob,.K., Jr. J. Chromafogr. 1982. 237, 15-23. (20) Saxton, Wilber L. HRC CC, J. High Resolut. Chromafogr. Chromatogr. Commun. 1984, 7 , 118-122. (21) Nichol, L. W.; Ogston, A. G.; Winzor, D. J. J. f h y s . Chem. 1987, 71, 726-730. (22) Knauss, K.; Fullemann, J.; Turner, M. P. HRC CC, J. High Resolut. Chromatogr. Chromatogr. Commun. 1981, 4 , 641-643. (23) Buser, H. U.; Soder, R.; Widmer, H. M. HRC CC, J . High Resolut. Chromatogr. Chromatogr. Commun. 1982, 4, 156-157. (24) Conder, J. R.; Young, C. L. "Physicochemical Measurements by Gas Chromatography"; Wiley: New York, 1979; p 43.
RECEIVED for review April 1, 1985. Accepted July 16, 1985. This work was partially supported by Research Corporation Grant 9166. Funds for the support of this study have been allocated by the NASA-Ames Research Center, Moffett Field, CA, under interchange No. NCA2-OR735-201. This work was presented in part at The 1984 International Chemical Congress of Pacific Basin Societies, Honolulu, HI, Dec 18, 1984.
