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Anal. Chem. lg82, 5 4 , 736-740
tional to the pressure difference, @ / L , where hpr is the average pressure difference of compressible fluid across the distance L in the column (15). The calculated values of A P / L for various inlet pressures are included in Table IV. Plots of L/tRo against h p r / L become h e a r on passing through the origin for the respective columns, which confirms the interpretation of t R o . On the other hand, the volumetric flow rate was not proportional to P / L , as described elsewhere (15). Considering the interdiffusion among two gases, A and B, the diffusion coefficient for A into B and vice versa should be the same. Once micropores are introduced into the system, however, the situation is changed. Carrier gas molecules previously occupying the micropores as stagnant phase are displaced by solute. Consequently, the diffusibility of the carrier may affect the value of Dmo and hence solute retention. Comparing Dmo in Table IV between two carriers, those for hydrogen carrier are almost 10 times larger than those in nitrogen. The self-diffusion coefficient, DeK,of hydrogen is also larger than that of nitrogen (Table V). The ratio Dfio/D,,K reflects these differences. Furthermore, the ratio among carriers, [Dmo/DeK]Hz/[Dmo/Dself]Nz, is 0.9 f 0.1. It can therefore be said that the diffusibility of the carrier gas is also related to the sample retention in a porous column. The physical interpretation of the Dmo term at this time is not clear; however, one might suppose that a sample whose D m is equal to Dm0 may once have been trapped in a pore such that it could not readily pass back into the carrier flow.
ACKNOWLEDGMENT The author is grateful to Hiroyuki Hatano for his interest, encouragement, and advice, and to Itsur6 Yamakita for useful discussions and close cooperation. LITERATURE CITED (1) Ohenstein, D. M. J. Chromatogr. Sci. 1073, 11, 136. (2) Brunauer, S.; Emmett, P. H.; Teller, E. J. Am. Chem. SOC. 1938, 60, 309. (3) Nelsen, F. M.; Eggertsen, F. T. Anal. Chem. 1958, 30, 1378. (4) Yamakita, I.; Kalzuma, H.; Yamamoto, H.; Kusumi, Y. Abstracts of the 18th Annual Meetlng of Chemical Society of Japan, 1965, p 397. (5) h r e t t , R. H.; Purnell, J. H. J . Chromatogr. 1962, 7, 455. (6) Carman, P. C. "Flow of Gases through Porous Medla"; Academic Press: New York, 1956. (7) Kaizuma, H.; Yamakita, I. Abstracts of the 20th Annual Meeting of the Chemlcal Soclety of Japan, 1972, 2103. (8) Glddings, J. C. "Dynamics of Chromatography, Part I"; Marcel Dekker: New York, 1965; p 230. (9) Kaizuma, H.; Nakamura, J.; Sugano, T. J . Chem. SOC. Jpn. 1980, 1415. (IO) Kalzuma, H.; Myers, M. N.; Glddings, J. C. J. Chromatogr. Sci. 1970, 8, 630. (11) Reference 8, p 198. (12) Fuller, E. N.; Schettler, P. D.;Glddings, J. C. I n d . Eng. Chem. 1066, 58, 21. (13) Reference 8, p 29. (14) Knox, J. H.; Maclaren, L. Anal. Chem. 1064, 36, 1477. (15) Kaizuma, H.; Ogawa, K.; Yamaklta, I. J. Chem. SOC.Jpn. 1975, 935. Translated Into English and kept at Los Alamos Science Laboratories, University of California, Code: 51-7339-2.
RECEIVEDfor review February 3,1981. Resubmitted October 21, 1981. Accepted December 31, 1981.
Supercritical Fluid Chromatography with Small Particle Diameter Packed Columns Dennis R. Gere" Hewlett-Packard Company, Avondale, Pennsylvanla 193 I 1
Robert Board and Douglass McManlglll He wlett-Packard Company, Palo Alto, California 94304
Supercrltical fluid chromatography Is carrled out wlth 10, 5, and 3 bm partlcle diameter packed columns. Reduced plate heights between 2.0 and 3.0 are achleved in the reglon of the van Deemter mlnlmum. Uslng polycycllc aromatic hydrocarbons as probe molecules, the relatlonshlp of denslty of supercrltlcal carbon dloxlde to log capaclty factor was studied between 32 and 100 O C . It Is observed that the efflclency of the columns contlnually Improves as the partlcle dlameter becomes smaller. Wlth a UV detector, mlnlmum detectable quantltles are In the range of 1 ng mass injected. Resolutlon per unit tlme Is 5-10 tlmes better than HPLC wlth the same columns due to more favorable dlffuslvlty In supercrltlcal fluids. Usable reglons of temperature, pressure, density, and flow rate are deflned.
A supercritical fluid is a substance which has been raised to a temperature, called the critical temperature, above which a low density fluid (gas) can be compressed to a high density fluid (liquidlike) without a discontinuity in density (Le., without a gas to liquid condensation), regardless of the external pressure applied to the system. The fluid has a viscosity 0003-2700/82/0354-0736$01.25/0
approximately that of a gas and 2 orders of magnitude less than that of a corresponding liquid. This relatively low viscosity coupled with a diffusivity midway between that of a gas and a liquid leads to very favorable column efficiencies between those achieved in capillary column gas chromatography (GC) and high-performance liquid chromatography (HPLC). The density of a supercritical fluid just at the critical temperature and critical pressure is typically one-third of the density of the corresponding liquid and much greater than that of the corresponding gas. Further, by increasing the pressure of the system, the density of the fluid can reach rather significant values exceeding that of some liquids used in HPLC. Solute solubility (including low volatility compounds) is appreciable in supercritical fluids and vastly greater than in gases a t similar temperatures, approaching the solubility in normal liquids. The combination of these parameters forms the basis of a powerful chromatographic technique that is complementary to both GC and HPLC. In addition to the separation and detection of volatile compounds, many relatively nonvolatile solutes encountered in HPLC can be separated and detected in at least 5-10 times shorter analysis times than in a corre0 1982 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 54, NO, 4, APRIL 1982 t
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pumping efficiency, Le., a relatively high volume flow rate and high pressure of the aupercritical fluid could be maintained continuously. The two liquid pumping heads are placed in close thermal contact with clamp-on heat exchangers, through which a water-methanol. mixture from an external recirculating chiller (Poly Science Corp.) is circulated. The pump then pressurizes the COzabove the critical pressure, while the temperature increases up to 40 "C as it passes through the combination pulse damperlpressure transducer/flow controller hardware. The fluid stream is then carefully equilibrated at the separating column temperature through a length of tubing in the column oven prior to entering the injector valve. Alternatively a precolumn can be used to precondition the mobile phase when necessary. The injector valve (Rheodyne Model 7125, 20-pL loop) is mounted in an insulated thermostated enclosure to ensure operation above the critical temperature of COz. After passing through the injector and analytical column, the supercriticalfluid, still maintained at or above supercritical conditions, is passed through a variable wavelength UV absorbance detector (Hewlett-Packard Model 79875.4). The existing HPLC cell of this detector is incapable of high-pressure operation; thus a thermostated, 10-mm path length 1mm i.d., 8-pL high-pressure cell was designed as a drop-in replacement, enabling operation to 425 bar, 100 O C .
Figure 1.
Slmplified flow diagram of apparatus.
sponding HPLC separation. Recent ireview articles by Schneider (1)and Klesper (2) and a report by Novotny, Lee et al. (3) summarize the current practice, limitations, and potential of this technique. In this paper we have evaluated small particle diameter packed HPLC columns for use in supercritical fluid chromatography (SFC) separations. Polycycllic aromatic lhydrocarbons (PAH) were used to probe column parameters, such as efficiency and capacity factors, on packed column SFC using commercially available HPLC equipment and 10,5,and 3 pm particle diameter (dp) stationary phase. The HPLC required some straightforward adaptations to allow it to use supercritical carbon dioxide as a mobile phase. EXPERIMENTAL SECTION Apparatus. Tlhe chromatograph used in these investigations was a Hewlett-Packard 1084B liquid chromatograph, which had been modified to permit operation with liquid carbon dioxide (at the pump stage) ixnd supercritical carbon dioxide as the chromatographic eluent (mobile phase). The diaphragm pumps facilitate the handlnng of carbon dioxide as its energy content is raised from a liquid (-10 "C to +5 "C) up to the supercritical fluid state. The mechanical modifications to the basic instrument were minimal and allow simple reconversion to the HPLC mode in the same instrument. Figure 1 is a simplified flow diagram of the apparatus. Reservoirs A and B are pressure vessels (usually standard COz gas bottles with eductor tubes) which supply liquid COzat ambient vapor pressure of 57 bar through 2 pm particle filters to the two high-pressure diaphragm pumps, Reservoir B was a standard shipping cylinder of carbon dioxide (Union Carbide, Liquid Carbonic anaerobic grade or Scott specialty gases bone-dry grade) holding approximately 30 kg of liquified COP This quantity is sufficient €or upward of 200 h of operation. Reservoir A is alternately a smaller, 1000 cms pressure vessel (Whitey Co.) which is confiied to allow separate f i g and weighing. It is sometimes used as a high-pressure weighing bottle and permits the introduction of known quantities of various modifiers into the COz stream. The pumps, designed to pump normal liquids at near ambient conditions,required some modification to allow efficient pumping of liquid COz, which is normally not a liquid at ambient temperature and pressure. With an eductor (siphon) tube, it is possible to draw liquid COPfrom the bottom of a supply tank into and through the HPLC pimp. Cooling the otherwise unmodified high-pressure pump heads to 0 "Cor below greatly enhances the
A thermostated restriction downstream of the UV cell was used to control and maintain the pressure of the system. Two different types of restrictors were used, each having differing effects on chromatographic operation. Initial experiments were done by using a homemade fixed orifice, adjusted to give a desired outlet pressure and column pressure drop (fiied in relation to each other) at a given volume flow rate. Use of this fixed orifice, in combination with flow programming produced (density) pressure-flow gradients which were found to be chromatographically useful. For experiments requiring independent control of pressure and flow, a manually adjustable back-pressure regulator (TESCOM Corp. Model 26-1721-24-043) was installed as the restrictor, allowing the column to operate iiaobaricallyat pressures up to 425 bar, while independently varying the linear velocity (volume flow rate). For calibration purposes, and to determine rigorously the volume-pressure-density relationships of the various physical states of C02involved, a thermal mass flow meter (Matheson FM 4550) was inserted into the ambient-pressure flow path downstream of the restrictor. Alternately a simple soap bubble flow meter was used for calibration and check of the flow conditions. Reconversion t,o a standard liquid chromatograph consists of warming the pump heads, reconnecting the liquid solvent reservoir tubing to the pumps, and removing the effluent restrictor. Operation as a supercritical fluid chromatograph is little different in practice than HPLC operation; the operating controls of the HP 1084B systlem remain as they were. The modifications to the equipment have not created unusual maintenance problems; two instruments have been in operation for more than a year with no major problems with the pumping system. Chromatographic Column. The chromatographic columns were 4.6 mm internal diameter and varied in length from 10 to 25 cm. The columns were either the Excalibar-ODS variety (Applied Science Corp.) or packed at Hewlett-Packard with Li chrosorb RP-8 (Merclr) or ODS Hypersil (Shandon). The column efficiency and retention experimental data pretientad in this paper were all obtained by using Excalibar columns packed with Spherisorb. Spherisorb ODS is a spherical packing with a bonded ODs (octadecylsilane) phase intended for reversed-phase chromatography. Precise measurements were made of the following fundamental parameters: column inlet pressure, the column outlet pressure, the column temperature, the mass flow rate and the volume flow rate of the effluent C02 gas. These measurements allow calculation and monitoring of the density of the supercritical fluid mobile phase, the linear velocity of the mobile phase in the separating column, arid the average column pressure.
RESULTS AND DISCUSSION Operating Region. Figure 2 is a graphical representation of the reduced pressure vs. the reduced density with various
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 4, APRIL 1982
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Flgun 2. R e d d bothenmlplots of hreduced variables. presswe and densny. for carbon dioxW. Area A k part of the onephase CO* supercritical fluM experlmemal region of this study. Area 13is a onephase CO, Uquid region. Area C is a iwo-phase region of CO, gas and liqukl. P , is reduced pressure, d R is reduced density. T , Is reduced
.
4
8
(2
IS
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RETENTION TIME I6econdsl
-re 3. RapM elution of naphblene via SFC Hldp = 2.7: 33 OC: average column pressure, 322 bar; column pressure drop, 184 bar.
temperatwe (isotherms). reduced temperature isotherms drawn in. The reduced pressure is
PR= P/Pc where PRis the reduced p m u r e , P the experimental pressure, and Pc the critical pressure. Similarly, dR = d / d . and TR= T/T,, where dR and TRare the reduced density and reduced temperature, d and T a r e the experimental density and temperature, d, and T. are the critical density and critical temperature. Figure 2 can be used to illustrate our experimental region. All of the experimental data described herein were obtained above both the critical temperature and the critical pressure from the injector, through the column and beyond the detector. This area is denoted A in Figure 2. Area A is a part of the one-phase region where only supercritical carbon dioxide exists. Area B is a region of a one-phase system where liquid carbon dioxide exists. Area C is a region of a twophase system where both carbon dioxide gas and liquid coexist. Previous workers have dieagreed (4-6) concerning the feasibility of working with small particle diameter packed columns where it is possible to create relatively large column pressure drops such that there is a significant difference hetween the inlet column pressure and the outlet column pressure. We find, within the constraints of our experimental region, that there is not a problem with the column pressure drop. This seems to not be a problem if the column pressure drop does not occur in a region where there is a significant density differentialfrom the column inlet to the column outlet. The greatest density differential we experienced was about 25%, which did not cause unusual peak broadening or distortion This could passihly explain anomalies seen in previous work. To put the experimental SFC parameters into perspective, note that the following conditions give the reduced parameters: 414 bar equals a reduced pressure 5.6,31.3 "C equal. a reduced temperature 1.00, and the experimental density of the supercritical carbon dioxide is 0.97 g/cm3. Further, a common mixture used in HPLC, W 5 0 water/acetonitrile has a liquid density at 25 OC on the order of 0.90 g/cm3. Chromatographic Parameters. Figure 3 demonstrates the rapid elution and detection of naphthalene from a 3 pm
a0
1.0
2.0
3.0
4.0
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RETENTION TIME lminute~l
Flgun 4. Saparaiion of nine PAHs: column pressure drop, 157 bar; Inlet pressure, 400 bar; outlet pressure. 243 bar; 33 OC.
particle diameter (dp) column (4.6 mm X 15 cm) a t a linear veloeity of 1.25 cm/s. The HETP value was 0.008 nun; thus, the column prcduced 18750 theoretical plates or 1100 plates/% With a k'= 0.41.this is eauivalent to 106 effective plates/s (to equals 12 8 ) . T h e sienal-bnoise ratio for 75 ne of naohthalene inieded was approximately 200:1, which projects to a minimum detectable quantity a t a signal-to-noise ratio of 2 1 of 0.75 ng. Figure 4 illustrates the separation of a nine-component mixture of PAHs under approximately the same conditions (33 OC, P = 321 bar, Li = 1.07 cm/s). The solutes are indicated hy name on the chromatugram and range from toluene at 0.27 min to 1,2,3,4-dihenzanthranceneeluting a t 4.22 min. The first two peaks, toluene and naphthalene, had a difference in retention time of 4.8 8 with a resolution factor of 1.2. The last two peaks, perylene and 1,2,3,4-dihenzanthracene,had a difference in retention time of 24.6 s with the last peak eluting a t 4.22 min ( R = 1.6). The wavelength of detection was 245 nm which was convenient for displaying all of the peaks at one attenuation. It is possible to optimize the overall sensitivity hy programming the wavelength for each peak or for groups of peaks, but this is not relevant to the current discussion. I
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 4, APRIL 1982
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2.50
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Flgure 5. HETP vs. linear velocity: curve A, data from SFC on 10 pm packing; curve 8, SFC on 5 pm; curve C, SFC on 3 pm; curve 11, HPLC on 10 pm; curve E, HPLC an 3 pm.
y t . +
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Naphthalene
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200
300
400
500
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PRESSURE I bar1
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Logarithm of the capacity factor vs. average colurrin pressure for naphthalene, anthracene, perylene, and coronene at various temperatures: (A)35 OC; (0)55 OC; (0)100 OC. Flgure 7.
0.020
.-
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Flgure 6. HETP vs. linear velocity with supercritical carbon dioxide on 3 pm packing: curve A, naphthalene; curve B, biphenyl; curve C,
anthracene.
Figure 5 illustrates the plot of height equivalent to a theoretical plate (H:ETP) w. the linear velocity of the mobile phase supercritilcal fluid in curves A, E, and C. Curve A represents data from a 10 pm dp column and curve (2 from a 3 pm column. First of all, these van Deemter plots follow the normal pattern of GC and HPLC in .that the HETP becomes significantly smaller (more favorable) with smaller particle diameter. Further, the right-hand ascending branch of the hyperbola has a decreasing slope as we go from 10 pm to 3 pm dp. The 3 pm plot appears to be so flat as to Eiuggest that perhaps the minimum value could be reached at or even beyond a linear velocity of 1.25 cm/s. As expected, there appears to be a shift in the minimum in the curve to higher linear velocity in the progression 10 pm to 5 hm to 3 pm. For comparison, curve D depicts a van Deemter plot obtained from HPLC experiments with a 10 pm dp column and curve E depicts similar results from a 3 pm dp column (special experimental HPLC apparatus had to be used to minimize the extra column band broadening with the 3 pm column). Comparison of the HPLC data with the SFC data reveals that the minimum HETP value is approximately the same for the same dp, hut the linear velocity a t which the minimum is reached is substantially higher in both SFC!cases. This follows directly from consideration of the interdiffusion coefficients in liquids compared with their more favorable values in a supercritical fluid. Figure 6 illustrates the similar SFC van Deemter curves for three solutes, using the 3 Fm dp column. Curve A is the same data shown as curve C in Figure 5 for the c3olute naphthalene. Curve B represents data for biphenyl and curve C in :Figure 6 represents the data for anthracene. Once agdn it is seen that the van Deemter plots have very flat regions from a linear velocity of 0.40 cm/s up to perhaps 1.35 cm/s. Although there is some experimental scatter of
the data points, it was observed that the HETP, in a mixture of the three components injected together, was always smaller in the order naphthalene > biphenyl > anthracene. Schneider and Swaid (7) have determined binary interdiffusion coefficients in supercritical COz for benzene and some alkyl benzenes under a variety of analogous temperatures and pressures. The observed binary diffusion coefficients are of cm2/s. More recently, Schneider and the order of 2 X Feist ( 8 , 9 ) have determined the binary diffusion coefficient of naphthalene (and other compounds) in supercritical COz between 35 OC and 60 OC and over the pressure range 80 bar to 160 bar. Their data indicate that naphthalene under the conditions in Figures 5 and 6 would be of the order 1.5 X cm2/s. On the basis of where the respective van Deemter curves lie, it is suggestive that the experimental binary interdiffusion coefficient of biphenyl and anthracene will be even more favorable (larger in numberical value) than that of naphthalene under analogous conditions. Thus, we see from the data presented in Figures 5 and 6 that there is a smallor value of HETP for a given solute as the column particle diameter decreases and at a dp of 3 pm, very flat curves exist. Furthermore, the phenomenon is the same for a variety of PAH solutes. The flat van Deemter curve gives SFC a degree of freedom in choosing a working linear velocity that has previously not been available in either packed GC or packed HPLC separation columns. Figure 7 depicts the retention data for the solutes naphthalene, anthracene, perylene, and coronene, over the temperature range of 33 O C to 100 "C. The log k'vs. average column pressure curves have an interesting general shape observed by others in previous experiments (1,2,5,6,10). At relatively low pressures the log k' has a large value which decreases nonlinearly with increasing pressure. As the column temperature increases, the nonlinear curves cross over such that at high pressures, the retention is least at the highest temperatures, while at the low pressures, the retention is greatest at the highesit temperatures. For any given column temperature a group of solutes will have curves whose general position moves upward and outward (away from the origin) as the solute molecule becomes larger in size or molecular weight. Schneider and van Wasen (11)further found much simpler curves when log k'was plotted vs. the density of the supercritical C02 mobile phase. Figure 8 shows the data which we
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 4, APRIL 1982
u" Anthracene
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RETENTION TIME iminutesi
Figure 9. SFC chromatogram of PAH's with relatively large column O.OO,
i
-0.50
-1.00~ 0
pressure drop: column pressure drop, 123 bar; column inlet pressure, bar; column outlet pressure, 139 bar; average column pressure, bar; inlet density, 0.82 g/cm3;outlet density, 0.60 g/cm3;column temperature, 55 O C . 261 200
0.2
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0.8
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I
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DENSITY I g/cm31
Figure 8. Logarithm of the capacity factor vs. density of supercritical
carbon dioxide mobile phase for naphthalene, anthracene, perylene, and coronene at various temperatures: (A)35 OC; (0)55 O C ; (0) 100 OC.
obtained for naphthalene, anthracene, perylene, and coronene vs. density over the temperature range 33-100 "C. Only a limited number of temperature data are shown in Figure 8 to avoid further crowding of the graphs. As Schneider found, we observe that (over our experimental range) the curves are nearly linear and provide easy interpolation and extrapolation for developing an analytical separation. It is interesting to observe that for a given solute, over three different temperatures, neither the slopes of the curves nor the intercepts of the curves coincide. The same observation for the four solutes, a t the same temperature, results in different intercepts and slopes. From a theoretical standpoint, this suggests further studies; however, from a practical separation development, it suggests a very useful degree of freedom. From a graph such as Figure 8, one can select a density of mobile phase which will yield an optimum k'range of values for a given experimental setup. The next parameter selected then would be the operating column temperature. This then fixes the operating average column pressure. The linear velocity would next be selected after consideration of the column pressure drop-linear velocity relationship. It is valuable to note that the column pressure drop is linearly related to the average linear velocity of the mobile phase, irrespective of the inner diameter of the column. Thus, the inner diameter of the column to be used can be chosen by other factors such as the volume flow rate limitations of the pumping system and the analysis time constraints. From Figures 5 and 6, we saw that there was quite a bit of latitude available in linear velocity without a compromise of peak width. Therefore, with the data available from Figures 5 through 8, a fairly rigorous development of a practical separation can be carried out without consideration of other parameters. The data in Figure 8 also imply that the retention on this bonded octadecyl silane column is a result of a combination of the solubility of the solute in the mobile phase, as well as a finite and significant interaction with the stationary phase. There is only a very limited amount of solubility data available for solutes dissolved in supercritical carbon dioxide (12-16)Paulaitis (12,13) has measured the solubility of naphthalene, phenol, p-chlorophenol, and 2,4-dichorophenol as a function of pressure and temperature. As this type of data becomes more readily available, it will be possible to separate the variable of the competitive interaction between the mobile
phase and the stationary phase for a variety of solutes. Figure 9 is a chromatogram showing the separation of anthracene (k' = 3.3), perylene (k' = 21.0), and coronene (k' = 94.1). This chromatogram is of some interest because of the conditions of separation. The column inlet pressure was 261 bar (55 "C), the column outlet pressure was 139 bar, the average column pressure was 200 bar and the column pressure drop was 123 bar. The column was a 3 pm dp, 15 cm X 4.6 mm. The peaks are symmetrical and there appears to be no significant difference in the reduced plate heights across a very large range of k'values (H/dp = 12.5, 9.8, 8.2 for anthracene, perylene, and coronene, respectively). There has been some concern in the past (3) about a fundamental compromise between column efficiency and column pressure drop. Up to the rather extreme experimental values seen here, we have not observed such a compromise. ACKNOWLEDGMENT The authors wish to extend their appreciation for helpful technical discussions to Gerhard Schneider, Ernst Klesper, C. Wayne Moss, Michael Paulaitis, Harry Weaver, Paul Bente, Lenore Randall Frank, and Paul Larson and many others who have contributed to our knowledge and understanding of the techniques and experiments. We also acknowledge Richard Henry for supplying some of the Excalibar columns, as well as Gerard Rozing for the supply of columns and the HPLC van Deemter measurements of the 3 pm column. LITERATURE CITED (1) Schneider, G. M.; van Wasen, U.; Swaid, I. Angew Chem., Int. Ed. Engl. 1980, 19, 575-587. (2) Klesper, E. Angew. Chem., Int. Ed. Engl. 1978, 17,738-746. (3) Novotny, M.; Springston, S. R.; Peaden, P. A,; Fjeldstad, J. C.; Lee, M. L. Anal. Chem. 1981, 53 407 A-414 A. (4) Novotny, M.; Bertsch, W.; Zlatkis, A. J . Chromatogr. 1971, 61, 17-26. (5) Sie, S. T.; Rijnders, G. W. A. Anal. Chlm. Acta 1967, 38, 31-44. (6) Giddings, J. C.; Myers, M. N. Sep. Sci. 1988, 1 , 761-776. (7) Schneider, G. M.; Swaid, I. Ber. Bunsenges. Phys. Chem. 1979, 8 3 , 969-974. (6) Schneider, G. M.; Feist, R. S e p . Sci., in press. (9) Schneider, G. M.; Feist, R. Lehrstuhl I1 fur Phys. Chemie, RuhrUnlversitat Bochum, D-4630 Bochum, Deutschland, private communication. (10) Jentoft, R.; Gouw, T. H. J . Chromatogr. 1972, 67,303-323. (11) Schneider, G. M.; van Wasen, U. Chromatographia 1975, 8 , 274-276. (12) Paulaitls, M. E.; Mackay, M. E. Ind. Eng. Chem. Fundam. 1979, 18, 149-1 53. (13) Paulaitls, M. E.; Van Leer, R. A. J . Chem. Eng. Data 1980, 25, 257-229. (14) Bowman, L. M. Ph.D. Thesis, University of Utah, Salt Lake City, Utah, 1976. (15) Stahl, E.; Schllz, W. Chem-1ng.-Tech. 1978, 50, 535-537. (16) Stahl, E.; Schilz, W. Talanta 1979, 26, 676-679.
RECEIVED for review October 14, 1981. Accepted December 21, 1981.
