Anal. Chem. 1982, 5 4 , 2447-2456
LITIEiRATURE CITED Golan-Goldhirsh, A.; tiogg, A. M.; Wolfe, F. W. J . Agrlc. Food Chem. 1982, 3 0 , 320-323. Tserng, Kou-Yi; Kalhnn, Satlsh C. Anal. Chem. 1982, 54, 489-491. Felice, Lawrence J. Anal. Chem. 1982, 54, 869-872. Mltchum, R. K.; Korfnnacher, W. A,; Moler, G. F.; Stalling, D. L. Anal. Chem. 1982, 54. 719-722. Knuutinen, J.; Tarhanein, J.; Lahtlpera, M. Chromatographla1982, 15, 9. Richardson, S. J.; Miller, D. E. Anal. Chem. 1982, 5 4 , 765-768. Comlsarow, M. B.; Marshall, A. G. J . Chem. Phys. 1975, 6 4 , 110-119. Marshall, A. G. Anal. Chem. 1979, 5 1 , 1710-1714. Comisarow, M. B. Int. J . Mass Soectrom. Ion Phys. 1981, 37, 251-257. McCrery, D. A.; Ledford, E. B., Jr.; Gross, M. L. Anal. Chem. 1982, 5 4 , 1435-1437. White, R. L.; Ledford, E. 8.. Jr.; Ghaderl, S.; Wllklns, C. L.; Gross, M. L. Anal. Chem. 1980, 52, 1525-1527. Ledford, E. B., Jr.; Gtiaderl, S.; Whlte, R. L.; Spencer, R. B.; Kulkarnl, P. S.; Wilkins, C. L.; Gross, M. L. Anal. Chem. 1980, 5 2 , 463-468.
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Ledford, E. B., Jr.; White, R. L.; Ghaderl, S.; Wllklns, C. L.; Gross, M. L. Anal. Chem. 1980, 5 2 , 2450-2451. (14) Ghaderl, S . ; Kulkarnl, P. S.; Ledford, E. B., Jr.; Wllklns, C. L.; Gross, M. L. Anal. Chem. 1981, 5 3 , 428-437. (15) Cody, R. B.; Furnler, R. C.; Frelser, B. S. Anal. Chem. 1982, 5 4 ,
-- .-.. PR-101
(16) Nguyen, M. T.; Wronka, J.; Starry, S.; Ridge, D. P. Int. J . Mass Spectrom. Ion Phys. 1981, 40, 195-210. (17) Wllklns, C. L.; Gross, M. L. Anal. Chem. 1981, 5 3 , 1661A-1676A. (18) Bartmess, J. E.; Caldwell, G. Int. J . Mass Spectrom. Ion Phys. 1981, 41. 125-134. (19) Wllklns, C. L.; Giss, G. N.; White, R. L.; Brissey, G. M.; Onylriuka, E. Anal. Chem. 1982, 5 4 , 2280-2264. I~
RECEIVED for review June 1, 1982. Accepted September 8, 1982. The support of the National Science Foundation under Grants CHE-77-03964 and CHE-80-18245 and the support of the Protection Agency under Grant R807251010 are gratefully acknowledged.
Improvement of Speed of Separation in Packed Column Gas Chromatography Robert J. Jonker' aind Hans Poppe* Laboratory for Analytical Chemistty, Universl@ of Amsterdam, Nieuwe Achtergracht 766, 10 18 WV Amsterdam, The Netherlands
J. F. K. Huber Institute of Analytical Chemistry, University of Vienna, Wahrlnger Strasse 38, Vienna, Austria
The general strategy for the Improvement of speed of separation In packed colurnn gas chromatography is addressed. Starting from optimization equations for the dlsperslon In the gase phase, we dlscuss the varlous other ilmltlng factors such as sample capaclty, mass transfer in the statlonary phase, detection, and Injectbn. The packed column Is found to be superior to the open tirbuiar column when a high separatlon speed is to be combiiied wlth a reasonable slgnai to noise ratio and dynamic range. The optlmlzatlon leads to a signlflcant mlnlaturizatlon of the chromatographic system. I n the experimental part, columns between 32 and 250 mm in length, slurry packed with 10 hm siliceous partlcies, are shown to produce h-v curves with a mlnimum h value of 2.5-3.5 and a permeabliity factor of about 1.2 X lo-'. The fastest chromatograms show peak standard deviations of 2 ms, and more than 14 000 theoretical piatesls. The increased speed facilitates signall enhancement methods like ensemble averaging which Is demonstrated In an example.
The efficiency of the packed column in gas chromatography has been the subject of little innovative effort during the last decade. This is quite understandable because of the tremendous efforts which were rightly spent on the development and analytical applicaition of high efficiency open tubular column chromatography. Also the incentive for speeding up an analytical method already capable of yielding a result every 10-30 min has not beem very strong, as is often argued that sampling, sample pretreatment, and interpretation of the results etc. require times of comparable magnitude. 'Present address: Hewlett-Packard strasse, 7517 Waldbronn 2, GFR.
GmbH, Hewlett-Packard-
0003-2700/82/0354-2447$01.25/0
The latter argument does not apply in automatic control applications. Also the introduction of microcomputers in laboratory gas chromatographs, resulting in automation in all steps of the analytical process, leads to the demand and possibility of higher analysis rates. These higher rates, when available, in turn can be used for speeding up selectivity optimization procedures and routine analysis, in which many more samples per unit time can be analyzed with one chromatographic system. Also, the higher analysis rate probably will enlarge the field of averaging methods like ensemble averaging or correlation chromatography (1) both for decreasing the detection limit and for increasing the precision of the analysis. All of this suggests that an increase in the speed of gas chromatography is a very interesting topic. From the kinematic point of view the open tubular column is vastly superior to the packed column alternative, mainly because of the much higher permeability factor obtained in this geometry (2). However, as soon as the quantitation aspect of chromatography is brought in, the drawbacks of the open tubular geometry, associated with the connected low sample capacity, become manifest. We shall discuss this aspect in the following. This paper is devoted to the increase of speed and efficiency in packed column gas chromatography, when a few hundred to a few thousand theoretical plates are required. This leads to separation times of 0.1 to several seconds, applicable, e.g., in process control and monitoring systems, with or without the combination with signal enhancing methods. This work corroborates and extends efforts in the same direction carried out in previous work (3-8).
THEORETICAL SECTION Column Dynamics. Mobile Phase Effects. Know and Saleem (9) derived equations for optimum speed and resolution in column elution chromatography. For gas chroma@ 1982 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 14, DECEMBER 1982
tography and inlet pressure limitation they derived the following expression for the minimum retention time under optimal conditions 27 *p(rp2+ 1)2(r,2-
~ R o
(hmi24-')(V)
16
NR2
Po (1)
where tROis the retention time of the unretarded component, taken here as a measure of the time lag and time demand of the separation, thus assuming that the time needed for reequilibration of the column to the starting conditions is negligible; hminis the minimum value of the reduced local theoretical plate height, H/d,, where H = du,2/dz + 2(dp/dz). (l/p)uZ2,with uz2 and p being the peak variance and the pressure at the position z (10); 4 = u(z)q/(dp/dz)d; = [ ( a L ~ / d , 2 ~ ~ ) ( 4 / 3 )-( 1)/(rp2 a , ~ ~ ~- 1)2)]= shape factor of permeability, where u is the average flow velocity, L is the column length, and d, is the particle diameter of the column packing; NR is the theoretical plate number required for a given resolution R ; 9 is the viscosity of the carrier gas; pois the inlet pressure; a, is the pressure ratio of inlet pressure, pot and outlet pressure, pL. This result is obtained provided the particle size, d,, and the column length, L, are chosen according to
and averaged pressure while increasing the inlet pressure. Making use of the additivity of the variances with eq 7 and 8 the maximum tolerable contribution of all other processes, Le., those not connected with diffusion in the gas phase of the column, can be formulated. In some cases the peak width in time units will be the critical factor (time constant of stationary phase, time constant of the detector, time constant of the data reduction, time constant of sample pretreatment, etc.). However, in other cases where processes are intrinsically volume dependent (injection volume, detector volume, volume of connecting tubes), the peak width in volume units is important. In this paper the optimization approach according to Know and Saleem is taken as the main directory; the other conditions are supposed to be adaptable to the requirements set by this approach. Other assumptions are also possible (11). With the aid of formulas 4 to 8 the column can be adapted to the limitation set by one of the subsystems (injectiod limited, data handling limited, stationary phase limited, etc.). These cases will not be dealt with in this paper, nor the case were the column is adapted in such a way that it operates at an average pressure determined by selectivity considerations (4, 5). Stationary Phase Effects. For a uniform layer of thickness, df, of the stationary liquid phase, s, the contribution to the theoretical plate height due to slow difusion (12,13) is given by the expression
2 -df2 Ki He = a3 De (1 ~
+
where D d is the diffusion coefficient in the mobile phase, m, at the outlet pressure, pL. With a given carrier gas and outlet pressure the value of the carrier gas dependent factors D,Q~ and q are fixed. The values of 4 and the minimum values of the h-v plot, hminand vmin, are dependent on the type of column used and can be considered as constant in the optimization (9). With the use of higher pressure ratios the fadors containing np are virtually constant ( 4 ) . Therefore the equations can be written as tRo
=
c3NR2/P0
i
)
~
(9)
where D, is the diffusion coefficient in the liquid, while the increment due to resistance in the gas-liquid interface, resulting in a low value in the desorption rate constant, kd, is given by (14) K:
where ii is the averaged migration velocity of the unretarded component and K is the capacity factor. If the column is optimally adapted to the inlet pressure it can be shown that
(4)
This shows that the speeding up of GC by means of higher pressures leads to a miniaturization of the column, which is accompanied by the necessity for the miniaturization of critical instrumental parts. The extent of this miniaturization is substantial; if the pressure is raised by a given factor, a miniaturization of the column of the same order w ill result. The main assumption in the Know and Saleem analysis is that no broadening process occurs other than those connected with the diffusion in the gas phase of the column. In the pressure limited case the standard deviation of the peak of a nonretarded component in time units is given by
which is constant for a certain column efficiency and independent of the inlet pressure. If the thickness of the liquid layer remains the same, the plate height contribution of the resistance to mass transfer in the stationary phase remains constant if the column is miniaturized. This results in a relative increase of the importance of this term for peak broadening. In case the optimal adapted parameters are used this gives the following expressions for h, and hA,the plate height expressions in reduced notation
(7) and in volume units it can be shown to be 2 NR ovo = - CZAt, 3 PL in which A is the area of the column cross section and t, is the fraction of the column occupied by the mobile phase. Notice that ob is inversely dependent on the inlet pressure, whereas bvois independent of the latter. This is the result of the cancellation of the changes in optimal column length
Accepting an arbitrary value of l / 3 as the allowable increment in reduced plate height, the following conditions for De, df, and kd can be derived:
ANALYTICAL CHEMISTRY, VOL. 54, NO. 14, DECEMBER 1982
Table I. Limiting Values of the Stationary Phase Mass Transfer Parameters' df2/
N
dd
DAmax), ddmax), kdmax), kdmin), Ils I.tm Ps m s-'
0.8 2.0 1.6 2.5 4.2 0.86 3.6 500 12.5 0.61 5.1 8.4 1000 25 42.0 0.27 125 11.3 5000 841.0 0.19 16.0 250 10000 a Assumed parameteris: h,h = 2.5; v m h = 1.5; C$= Pa s and helium as carrier gas (11 = 2 X 1.25 x = 4 m2 Pas-' ; p o =: 5 X l o 6 Pa andl D, = lo-'" m 2 D p 100
s
.
Table I illustrates the extreme demands on the speed of the mass transfer process in the stationary phase. In order to allow for a sufficient1,y fast mass transfer in a liquid layer, it has to have a thickness on the order of 1Mm, assuming a uniform thickness. In view of the anticipated difficulties in obtaining a liquid coverage with this specification (15),and because it was not expected that such a layer would have a significantly higher sample capacity than an adsorption system, it was decided to direct the research toward gas-solid chromatography. In a following publication we shall discuss the behavior of gas-liquid systems in very fast separations. Till now we did not find any evidence that the value of the desorption rate constant of the interface limits the speed of separation. System Design. Sampling. Different types of injection modes should be distinguished. First the injection of a compound, i, in the gas or vapor phase for which the partial pressure is lower than the vapor pressure of that compound at the injection temperature is considered. Assuming that the gas or vapor behaves as an ideal gas, the contribution to the peak width, of an injection of a volume of gas which is at the inlet pressure is given by (4)
with J/ being a constant depending on the flow regime in the injector, 12lI2 < $ < 1. Because of the higher compression at the top of the column, the peak variance due to injection is dependent on the premure ratio. This of course, has to be compared to the peak broadening due to the column (eq 8), leading to an expression for the maximum volume that can be introduced into the column accepting a 10% loss of resolution.
Thus the admissible injection volume decreases inversely proportional to the inleit pressure. The discussion of the sampling of liquids is more complicated. At the higher pressures needed for high speed gas chromatography the flash evaporation, normally encountered in low-pressure GC, will often not occur, since usually the vapor pressure of the solvent will be lower than the inlet pressure. The undiluted vaporized sample is not the equilibrium state at the inlet temperature. This results in a one-step distillation process, which may have a positive effect on the separation. Detection. The specifications on the detection device are set by the relations for the peak width in time and volume units (eq 7 and 8). It is foAunate that the standard deviation in volume units for optiirnized columns appears to be independent of the inlet presiwure. Therefore many geometrical and mechanical detector designs as used in normal GC can
2449
be used if the principle of measurement allows for fast response and when amplifiers are adapted to the new time scale, which is roughly a factor of po faster than the unusal one. The importance of the latter point may be inferred from eq 7, which, for helium as a carrier gas at 5 MPa and a theoretical plate number of 3000, yields for utoa value of 6 ms. Some detection systems, e.g., the coulometric detection, thermistor thermal conductivity detection, slow scanning FTIR or mass spectrometry, may present a problem in the interfacing to ultrahigh speed GC, because of the intrinsic slowness of the detection process or the data management limitations. Most gas chromatographic detectors can handle only a limited range of volumetric flow rate, F. Starting from the optimized parameters it can be shown that the flow rate at the column outlet, F L , is given by
In packed column gas chromatography the area of the column cross section can be chosen at will and can be adapted to the special demands set by the detector, for example, the maximum pump capacity of the mass spectrometer (7). This is of importance not only from an economical point of view but also in cases of trace analysis with a mass flow sensitive detector. Quantitative Analysis. The main reason for using packed columns rather than open tubular columns is the much higher sample capacity obtained with the former type. This, however, has to be reexamined as a function of the inlet pressure, because the miniaturization might lead to the loss of this advantage. The relation between peak broadening and sample load in dependency of the plate number has been studied previously (16). For the present discussion we use the following rule, which is a result of these studies and which can also be derived from the work of others (17). It applies to a shape of the distribution isotherm which is described by a quadratic expression in the mobile phase concentration, the most relevant approach in analytical chromatography. The rule stated that the acceptable mass of sample, mi("), is proportional to the amount of stationary phase contained in one theoretical plate, irrespective of the number of plates. where p is the constant determined by the nature of the solute and the stationary phase, Ni is the theoretical plate number of the column for component i, and V, is the volume of the stationary phase in one plate. This, of course, is derived under the assumption that a constant loss of resolution due to overload is accepted. A comparison of different geometries with respect to loadability is then equivalent to a comparison of the values of V,/Ni, which can be expressed as follows
V,/Ni = A(av)LdfNR-l
(20)
where A is the cross sectional area of the column (m'), (av) is the specific area per unit column volume (m2/m3),and df is the layer thickness of the stationary phase (m). We will now discuss the effect of increasing po, and the concurrent miniaturization of the column, on the maximum load and on the detectability for mass flow and concentration sensitive detectors. If the column is optimally adapted to the inlet pressure and the capacity factor is taken as constant, the volume of the stationary phase and therefore the loadability will decrease in proportion to The maximum response of a concentration sensitive detector
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 14, DECEMBER 1982
that is possible without loss of resolution under optimally adapted conditions will be proportional to
whereas the limit of detection remains much the same (eq 8). For a mass flow sensitive detector the derivation yields OLD
for the maximumresponse. The limit of detection is decreased proportional to the increase of the inlet pressure (eq 7). The important difference between packed and open tubular columns is that in the case of packed columns A and av can be chosen freely without affecting the efficiency, whereas in the case of open tubulars A and av will change in proportion to the degree of miniaturization. For open tubular columns the following relations for A and av are valid under optimally adapted conditions:
and
where dc is the column diameter. Inserting eq 24 and 25 in eq 22 and 23 for the detector response shows that the maximum response of a concentration sensitive detector coupled with an open tubular column will be proportional to
For mass flow sensitive detectors it follows likewise
The standard deviations of the peaks in volume units for open tubulars decrease in proportion to the square of the inlet pressure. In order to maintain resolution, make-up gas has to be used. Thus the potential gain in absolute detectability in the case of a concentration sensitive detector coupled with an open tubular column cannot be realized. In the case of mass flow sensitive detection, the dynamic range (i.e., the ratio of the amount of major and minor components that in one run can be analyzed by the system) of packed columns is increased by the miniaturization. The dynamic range of the open tubular configuration, however, which at normal dimensions is already limited, reduces during miniaturization more than proportional and becomes so limited that only major components can be distinguished from the noise (18). The above stated must be interpreted in view of the high analysis rates which are already possible at low pressure drops with open tubular columns, as a result of the favorable permeability factor. Only in special cases are higher analysis rates needed. The resulting miniaturization of the column will limit the dynamic range.
EXPERIMENTAL SECTION Equipment. The high-pressure GC as described before (4) was used with the following modifications: The electrometer amplifier of the FID (type 12016, Tracor, Austin, TX) was a modified version of the tube type (type DC 60 CH, Atlas Messand Analyse Technik GmbH, Bremen, GFR). The output signal was fed into a VF converter (Analog Devices Inc, type 460 J, Norwood, MA).The signal from the thermal conductivity detector (MK.158, Servomex, Crowborough, England) was amplified by a low noise preamplifier (113, PAR, Princeton, NJ) before VF conversion. The output frequency was presented to a 800 channel
Flgure 1. Scheme of the feedback of the preampllfler: R , : R , = lO:l, R3:R4 = 9:1, R4
