Chromatography with Two Mobile Phases - Analytical Chemistry (ACS

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Anal. Chem. 2006, 78, 1242-1248

Chromatography with Two Mobile Phases M. Wang, S. Hou, and J. F. Parcher*

Chemistry Department, University of Mississippi, University, Mississippi 38677

Experimental results for the investigation of chromatographic columns containing two mobile phases are presented. The eluent was composed of mixtures of methanol and carbon dioxide. The column was an uncoated fusedsilica-lined stainless steel capillary column. At certain experimental conditions, the eluent divided into two phases, both of which moved through the column. The predominant component of the liquid phase was methanol whereas the gas phase was composed of at least 93 mol % CO2. The columns were studied over a range of feed compositions (45-95 mol % CO2), pressures (61-101 bar), and temperatures (30-100 °C). The compositions and densities of each phase were calculated from the Peng-Robinson equation of state. The residence times of the two mobile phases were determined by tracer pulse chromatography. The partition coefficients of a probe solute, benzene, were measured along with the retention times of neon and the total volume of the chromatographic column as a function of temperature, pressure, and stoichiometric feed composition. The calculated column volumes, that is the volume of the liquid and gas, were constant over the full range of feed composition. The partition coefficient of benzene was constant at fixed pressure and temperature, varied logarithmically with density at fixed temperature and feed composition, and displayed a maximum at intermediate temperatures at fixed pressure and feed composition. The measured retention times of neon were consistently equivalent to the calculated residence times of the gas phase, indicating that neon did not dissolve in the liquid phase and could thus serve as an accurate dead time marker. The implementation of chromatography with two mobile phases produces a chromatographic “window”. There is a lower limit for the retention volume of all solutes, viz., the residence time of the gas phase, exactly the same as normal chromatography. However, elimination of the stationary phase produces an upper limit to the retention volumes of solutes. This upper limit is the residence time of the liquid phase, so there is a retention window such that tG e ti e tL for all solutes. One of the major problems often encountered with modern chromatographic methods is the contamination, deterioration, or gradual destruction of the stationary phase. Chemically bonded phases for HPLC are often protected from contamination by so* To whom correspondence should be addressed. E-mail: olemiss.edu.

chjfp@

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called guard columns. However, they are still subject to destruction by aggressive solvents or extreme pH conditions. Capillary GC columns usually contain a polymeric stationary phase that is also susceptible to contamination from sample residues and decomposition of the polymer by repeated excursions to high temperatures. The stationary phases can seldom be restored, so poorly performing columns must be replaced in toto. Such replacement is time and labor intensive and often economically undesirable. Elimination of stationary phases would be advantageous; however, presently countercurrent chromatography1 is the only practical chromatographic method designed to eliminate the need for a stationary phase. Chromatographic methods usually involve the distribution of solutes between two phases, one of which must be fixed (stationary) within the column. While this is often a restriction in practice, it is not a theoretical requirement. Separation can be achieved for solutes that distribute between two immiscible phases moving in relation to each other. In other words, the two phases can both migrate through the column as long as their velocities differ. Perilloux and Deans2 and Lucy and Hausermann3 described separate, but similar, types of chromatography they called “bubble column chromatography” and “co-current chromatography”, respectively. These techniques both used two mobile phases, viz., a gas or liquid flow segmented with immiscible liquid fillets. The gas or liquid bubbles and the liquid fillets between the bubbles moved at the same velocity, but the liquid on the wall of the column moved at a very low velocity. Thus, the average velocities of the two mobile phases differed. The techniques were used to analyze extracts of natural products and to measure vapor-liquid equilibria data for systems involving volatile liquids. Similar ideas have been used to develop dual mobile-phase chromatographic systems involving a condensable fluid such as carbon dioxide as one component. Introduction of CO2 as an eluent component facilitates the use of pressure as an experimental control parameter. In such systems, temperature, pressure, and eluent composition all play a significant role in the chromatographic performance of the column. The earliest reported work4 involved the use of mixtures of helium and CO2 as the eluent. In this case, there was no fixed “stationary” phase within the column. These experiments were limited to temperatures below the critical point of CO2 where films of helium-saturated, liquid CO2 were formed in empty capillary columns under certain conditions. The other phase in the column was CO2-saturated helium gas. These (1) Foucault, A. P. Anal. Chem. 1991, 63, 569A-579A. (2) Perilloux, C. J.; Deans, H. A. Ind. Eng. Chem. Fundam. 1972, 11, 138144. (3) Lucy, C. A.; Hausermann, B. P. Anal. Chim. Acta 1995, 307, 173-183. (4) Wells, P. S.; Zhou, S.; Parcher, J. F. Anal. Chem. 2002, 74, 2103-2111. 10.1021/ac051637+ CCC: $33.50

© 2006 American Chemical Society Published on Web 12/15/2005

two phases differed in both compositions and densities, moved at different velocities, and produced chromatographic resolution of simple test mixtures. However, the chromatographic resolution of these systems was severely limited due to the chemical similarity of the two phases. More recently,5 binary mixtures of CO2 and methanol have been used to extend the polarity range of such two-phase chromatographic systems. In this case, the low-velocity phase was CO2-saturated, liquid methanol and the other phase was methanolsaturated, gaseous CO2. It was demonstrated that test mixtures of simple hydrocarbons could be resolved under conditions where two phases existed within the column and that such resolution was lost if the temperature, pressure, or feed composition was such that only a single phase existed within the column. In the previous studies, the experimental controls were inadequate to demonstrate any quantitative aspects of the chromatography. The objectives of the present investigation were to report improved experimental techniques for the study of twophase CO2-methanol systems over a range of temperature, pressure, and feed composition and to develop a theory for the residence (retention) times of solutes and eluent components in such systems. THEORY The concept of residence times of components in closed systems is fundamental in many engineering processes. The idea of residence times is also applicable to chromatographic systems; however, this approach has seldom been used in the development of chromatographic theories. Nevertheless, Buffham 6,7 has derived model-independent theories for the various types of chromatography based on residence time concepts. The primary theory describing the residence times of components in a closed system with fixed material content in equilibrium with its feed, i.e., the steady-state theory, postulates that, “The mean residence time of species i in the steady state is equal to the ratio of the holdup of i in the system to the transmission rate of i through the system”.7 Using this definition, the residence (retention) time, ti, of any component i, in a chromatographic column with a single mobile phase would be6

ti ) ni/QCM i

(1)

where ni represents the total number of moles of component i in the column, Q is the volumetric flow rate of the mobile phase, and CM i is the molar concentration of i in the mobile phase. In classical chromatography with a fixed stationary phase, S ni ) nM i + ni

(2)

S where nM i and ni represent the number of moles of component i in the mobile and stationary phases, respectively. Equation 1 can be recast in terms of the retention factor, ki′ ≡ nSi /nM i , for the distribution of component i between the two phases and the average velocity of component i, ui ) L/ti, to give

(5) Lou, Z.; Xiong, Y.; Parcher, J. F. Anal. Chem. 2003, 75, 3557-3562. (6) Buffham, B. A. Proc. R. Soc., London A 1978, 364, 443-455. (7) Buffham, B. A. Proc. R. Soc., London A 1973, 333, 89-98.

ui )

(

)

1 uM 1 + ki′

(3)

where uM represents the velocity of the mobile phase. This equation leads to the retention volume equation for the elution of a plug of component i

VRi ) VM + KiVS

(4)

where VRi ) Qti is the retention volume, VM and VS represent the volumes of the mobile and stationary phases, and Ki is the partition coefficient for the distribution of i between the stationary and mobile phases. If component i is continuously present in the feedstock, instead of injected as a plug, the residence time of component i in the column is given by

ti ) ni/FZi

(5)

where F is the molar flow rate of the feed and Zi is the stoichiometric mole fraction of component i in the feed. The steady-state theory does not place any restrictions on the components in the system or the number of phases in the feed or the column. Equation 5 can be used to determine the total amount of i in a column from the residence time of an isotopically labeled analogue of the eluent component regardless of the number of phases within the column. This is the basis for tracer pulse chromatography.8 Equation 5 has been derived in a variety of ways mostly involving material balance equations and the ergodic hypothesis that the time average of an observable is equivalent to the ensemble average. In a two-phase system, in which both phases have finite velocities, the overall material balance equation for a binary system in a column that is in equilibrium with its feed is

F ) FG + F L

(6)

where FG and FL represent the molar flow rates of the gas and liquid phases, respectively, within the equilibrated column. The equivalent equation for any component i is

FZi ) FGYi + FLXi

(7)

where Xi and Yi represent the mole fractions of component i in the liquid and gas phases, respectively. These two equations can be combined to determine the molar flow rate of either phase as a function of the inlet flow rate, the compositions of the two phases within the column, and the stoichiometric composition of the feedstock in equilibrium with the column. This is the so-called “lever rule”. For the gas phase, the relation is

FG ) F

{

Zi - Xi Yi - Xi

}

(8)

(8) Parcher, J. F. J. Chromatogr. 1982, 251, 281-288.

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For components that reside only in one phase, the residence time of these components, and hence the residence time of the phases, are given by the relations

tG )

tL )

nGi

(9)

FGYi nLi FLXi

(10)

Equation 7 can then be expressed as the residence time of component i as a function of the residence times of the two mobile phases

nGi + nLi nGi nLi ) G + L ti t t

(11)

The retention factor can be incorporated into eq 11

( ) ( )

ki′ 1 1 1 1 ) + ti 1 + ki′ tG 1 + ki′ tL

(12)

In terms of the more commonly used concept of velocities, the average velocity of component i within the column is

( ) ( )

ki′ 1 ui ) uG + uL 1 + ki′ 1 + ki′

solutes; however, it may be difficult to find solutes that reside only in one phase. An inert gas, such as neon, can theoretically be used to measure tG. Likewise, a nonvolatile solute could be used to measure tL. However, in the systems described herein, it is not certain that neon is insoluble in the liquid phase at high pressures, and a nonvolatile solute could not be used because of the detection system. Thus, experimental determination of the phase residence times was problematic. An alternative to the experimental measurement of residence times is the application of an equation-of-state (EOS) that is appropriate for systems involving CO2 at high pressure. Such EOSs can be used to calculate the vapor-liquid equilibrium for two-phase systems. The densities and compositions of both phases can be calculated by equating the fugacities of each component in the two phases. There are many computer programs available for such calculations. However, one of the fastest, most accurate, and convenient programs was developed by Brunner et al.9,10 The program, PE-2000, offers 40 different EOSs with 7 sets of mixing rules for the calculation of VLE data. The intensive composition information from the EOS along with extensive tracer pulse chromatographic data for the total number of moles of each component in a particular column allows the calculation of the number of moles of each component in each phase. The four equations required for a binary, two-phase system are

(13)

In reality, any component of the system must move at either velocity uG or uL within the column; however, the observed average velocity is determined by the time a component resides in each of the two moving phases. In the case where uL ) 0, eq 13 reduces to eq 3 for a single mobile-phase system. The retention factor for any component can be obtained from eq 12:

ki′ )

{ }

G tL ti - t tG tL - t i

(14)

This equation reduces to the common chromatographic equation for ki′ in the limit tL f ∞. Equation 14 was first derived by Perilloux and Deans2 on the basis of a probability argument as well as continuity equations. Equation 14 is general, applicable to injected solutes as well as eluent components, and requires few assumptions other than equilibrium between the feed and the column.7 The equilibrium partition coefficient, Ki, for the distribution of a component between the two mobile phases is

nG FL Ki ) ki′ L G n F

(15)

L G FZCO2tCO2* ) nCO + nCO 2 2

(16)

L G + nMeOH FZMeOHtMeOH* ) nMeOH

(17)

XCO2 )

YCO2 )

L nCO 2 L L nCO + nMeOH 2 G nCO 2 G G nCO + nMeOH 2

G nMeOH )

{

}

1 - YCO2

YCO2 - XCO2

[(1 - XCO2)nCO2 - XCO2nMeOH] (20)

L G nMeOH ) nMeOH - nMeOH G nCO ) 2

{

YCO2

}

1 - YCO2

G nMeOH

(21) (22) (23)

nL

where and represent the total moles of the gas and liquid phases in the column and FG and FL represent the molar densities. To use this theory in a predictive fashion, the residence times of the two phases must be determined. These residence times could be experimentally measured by using appropriate probe 1244

(19)

where asterisks are used to indicate the retention times of tagged analogues of the eluent components. The quantities on the LHS of eqs 16-19 can all be either calculated from an EOS or measured chromatographically. The unknowns are the four quantities of each component in each phase, so the system is well-posed. The analytical solutions are

G L nCO ) nCO2 - nCO 2 2

nG

(18)

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Knowledge of the number of moles in the gas and liquid phases (9) http://www.tu-harburg.de/vt2/pe2000. (10) Roth, M. J. Chromatogr., A 2004, 1037, 369-391.

and the inlet flow rate allows the calculation of the molar flow rates of each phase from eqs 6 and 8. The residence time of the two mobile phases can be determined from eqs 9 and 10. The equilibrium constants for the distribution of chromatographic solutes between two phases both composed of CO2 and methanol can then be determined from eqs 14 and 15. The model of two mobile phases with different residence times leads to some interesting implications for this type of chromatography. In classical chromatography with a fixed stationary phase, there is a lower limit to the residence time of any solute. This is the residence time of the mobile phase that is usually measured from the retention time of a so-called dead time probe, i.e., a solute that does not dissolve in the stationary phase. However, there is no upper limit on the residence time of chromatographic solutes. This is the source of the so-called “general elution problem” because later eluting solutes are dispersed and diluted with time and the detection problems consequently increase with residence times of the solutes. On the other hand, in the case of chromatography with two mobile phases, no solutes could have residence times less than tG or greater than tL. That is, there is an upper limit to the residence times of chromatographic solutes, so that

tG e ti e tL

(24)

Obviously, this limit would apply only to solutes that dissolved in the liquid phase. Solutes that precipitate out to form a third phase would have an infinite residence time. The limits expressed in eq 24 define a chromatographic window for the residence times of solutes and restrict the peak capacity of such systems. This concept is similar to that observed experimentally in both sizeexclusion and miceller electrokinetic chromatography. The advantage of the chromatographic window is that the column will be renewed in the period tL and cross-contamination of sequentially injected samples can be avoided. EXPERIMENTAL SECTION The experimental apparatus was essentially an SFC instrument with a mass-specific detector.4 Several changes in the basic apparatus were required to overcome the difficulties commonly observed when pumping a compressible fluid such as CO2 at low flow rates. The pressure and composition of the binary feed were fixed at the pumps, and the volumetric flow rate was monitored. To accomplish this, the volumetric flow rate of the methanol pump was set proportional to the volume flow rate of the CO2 pump in order to maintain a constant feed composition. The CO2 pump was operated at a constant pressure to control the pressure in the column. The methanol pump was operated at a flow rate proportional to the measured flow rate of the CO2 pump. The feed composition was calculated from the following relation:

ZCO2 )

QCO2FCO2 QCO2FCO2 + QMeOHFMeOH

(25)

where F represents the molar density of the pure components at the pump conditions. The ratio of the volumetric flow rate of the methanol pump to the CO2 volumetric flow rate needed to achieve

a given feed composition was determined from the following relation:

( )(

)

FCO2 1 - ZCO2 QMeOH ) QCO2 FMeOH ZCO2

(26)

The ratio of volumetric flow rates was fixed even when the flow rate of the CO2 pump varied to maintain constant pressure. The SFC pumps were ISCO model 500D pumps. The CO2 pump was operated at a temperature of 15 °C. The pumps were controlled by a computer program written in Visual Basic 6.0 with thirdparty software11 to allow the basic program to access the COM ports of the computer. The average flow rate of each pump was accurately determined by integrating the measured flow rates over the time of the experiment. This approach allowed the accurate control of both the composition of the column feed and the pressure of the column. The combined pump flow rates were typically in the range 200-300 µL/min with oscillations ranging from 200% at low pressure to 10% at high pressure. Small amounts of the tracer probes, neon, and test solute (benzene) were injected from gas sampling valves located at both the inlet and outlet of the analytical column.12 This arrangement allowed for the accurate determination of the residence time of the solutes in the column without regard to the residence time in the extracolumn portions of the instrument. The flow rate of the eluent through the column was controlled by a frit restrictor located at the column outlet. The sampling valves and restrictor were maintained at 250 °C in a valve oven separate from the column oven. The column was a fused-silica-lined stainless steel tube (762 cm by 0.0508 cm i.d.) with a calculated geometric volume 1.54 mL. The methanol and CO2 streams were combined in a flow-through tee valve to eliminate dead volume in the lowflow, methanol stream. At least four sequential injections were performed for each experiment. The data reported in the tables represent the results from the later injections in the sequence. On average, the columns were allowed to reach equilibrium over a period of at least 60 min. RESULTS AND DISCUSSION Experiments were carried out in three modes. The three primary experimental variables were pressure, temperature, and feed composition. The experimental protocol involved the variation of one of these parameters while the other two were fixed. Constant Pressure and Temperature. A series of experiments were carried out at 61 bar and 60 °C with feed compositions in the range of 5-55 mol % methanol in CO2. The calculated phase diagram for the binary CO2-methanol system is shown in Figure 1 where the experimental feed compositions are marked with triangles. Under conditions of constant pressure and temperature, the compositions and densities of the two phases in the column were constant for any feed composition within the two-phase region, i.e., with ZCO2 such that XCO2 e ZCO2 e YCO2. The Peng-Robinson13 (11) http://www.jspayne.com. (12) Liu, Y.; Yun, K. S.; Parcher, J. F. J. Chromatogr., A 1994, 679, 392-396. (13) Peng, D.; Robinson, D. B. Ind. Eng. Chem., Fundam. 1976, 155, 59-64.

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Figure 1. Calculated phase diagram of CO2 and methanol at 60 °C. The Peng-Robinson interaction parameter k12 ) 0.072.

EOS with quadratic mixing rules was used to calculate the compositions of the liquid (XCO2 ) 0.26) and gas phases (YCO2 ) 0.97). The calculated densities of the two phases were FG ) 3.01 M and FL ) 20.85 M. The densities of pure CO2 (15 °C) and methanol (25 °C), viz., 19.10 and 25.00 M, respectively, were obtained from the NIST tables.14 The experimental results at 60 °C and 61 bar are summarized in Table S1 (Supporting Information). Experiments at fixed pressure and temperature should yield constant calculated total column volumes and partition coefficients for the probe solute, benzene. Likewise, if neon was not retained in the liquid phase, the measured retention times for neon and the calculated residence times of the gas phase should be equal. To test these predictions, the total column volume was calculated from the number of moles in and the density of each phase for each experiment. As the concentration of methanol in the system increased, the volume of liquid in the column increased; however, the calculated average column volume for this data set was constant at 1.9 ((0.1) mL over the full range of feed compositions. This value was higher than the calculated geometric volume of the column (1.54 mL) due to the volume of the tubing connecting the column to the injection valves. The calculated value for the partition coefficient of benzene between the two phases was 37 ((3). The value could not be validated by comparison with literature data; however, the constancy of the value over a range of feed compositions indicates that the model is at least qualitatively correct. The relation between the retention times of neon and the residence times of the gas phase is shown in Figure 2 for all the data reported herein. The residence times varied with the feed compositions because the molar flow rate of the gas phase decreases with ZCO2 as shown by eq 8. The density of the gas phase was constant, so the volume flow rate of the gas phase diminished with ZCO2 and both the residence times of the gas phase and the retention times of neon increased. However, the close correlation between these two parameters indicates that neon was not retained in the liquid phase to any measurable extent. The concept of a chromatographic window is illustrated in Figure 3, which is a plot of the calculated residence times of the (14) http://webbook.nist.gov/chemistry/fluid.

1246 Analytical Chemistry, Vol. 78, No. 4, February 15, 2006

Figure 2. Calculated residence time of gas and measured retention time of neon.

Figure 3. Calculated residence time of gas, liquid, and benzene at different feed compositions.

gas and liquid phases and the observed retention times of benzene as a function of the feed composition. The residence times all converge at high methanol concentrations and any chromatographic resolution would be minimal. However, at higher CO2 concentrations, the window opens because of the decrease in the velocity of the liquid phase. The relative velocities of the two phases are directly proportional to the number of moles in each phase. The residence time of the low-density gas phase was relatively constant; however, the velocity of the condensed liquid phase decreased significantly as the amount of liquid in the column diminished. Based on this observation alone, the chromatographic resolution would increase with decreased methanol concentrations. Constant Temperature and Feed Composition. Experiments were carried out at 60 °C at a feed composition of ZCO2 ) 0.90 over a range of pressure from 61 to 101 bar. Below ∼56 bar, the CO2 in the pump would be gaseous even at 15 °C, and above 101 bar, the CO2-methanol eluent would form a single, liquid phase and all the solutes would elute at tL. The results for this series of experiments are reported in Table S-2 (Supporting Information). Again, the calculated column volumes over the full pressure range were constant at 1.97 ((0.05). The results for the residence times of the gas phase and the retention times of neon are shown in Figure 2.

Figure 4. Partition coefficient of benzene versus the density of the gas phase.

Under conditions of constant feed composition and temperature, pressure influences the composition and densities of both phases. Thus, the partition coefficient of benzene will change with pressure. However, it has been often reported in the SFC literature that the density of the fluid (mobile) phase is the determinant factor for the retention of chromatographic solutes. In particular, the solute partition coefficients should vary logarithmically with density.10,15-17 Figure 4 illustrates that this model is valid for the benzene retention data reported in Table S-2 (Supporting Information). Constant Pressure and Feed Composition. The results for a series of experiments at temperatures from 31 to 90 °C at a column pressure of 61 bar with a feed composition of ZCO2 ) 0.90 are reported in Table S-3 (Supporting Information). The calculated column volume was 2.00 ((0.05) mL, and the residence time data for the gas phase are shown in Figure 2. Under these experimental conditions, the compositions, densities, velocities, and volumes of both phases changed with temperature. It is commonly observed that if the gas-phase density is low, the partition coefficients of chromatographic solutes vary logarithmically with 1/T and the slope of the plot is a measure of the enthalpy of the distribution process for a given solute. However, in cases where the gas-phase density was high or varied significantly, it has been observed that such plots at constant pressure display a maximum at some temperature and at low temperatures (high gas-phase density) the retention of solutes decreased as the temperature decreased.18-20 Figure 5 shows the relationship between the partition coefficient of benzene and 1/T at fixed pressure and feed composition. In this case, the maximum partition coefficient is observed at a temperature of 40 °C. At higher temperatures, the partition coefficient of benzene diminished due to the decreased solubility of benzene in the liquid. At lower temperatures, the partition coefficient also diminished but now due to the increased density (solvent strength) of the gas phases. (15) Martire, D. E.; Boehm, R. E. J. Phys. Chem. 1987, 91, 2433-2446. (16) Roth, M. J. Phys. Chem. 1990, 94, 4309-4314. (17) Chester, T. L.; Innis, D. P. J. Microcolumn Sep. 1993, 5, 127-133. (18) Shen, Y.; Hung, H.; Zhou, L. J. High Resolut. Chromatogr. 1996, 19, 169175. (19) Wu, Y. J. Liq. Chromatogr. 2004, 27, 1203-1236. (20) Leyendecker, D.; Leyendecker, D.; Schmitz, P.; Klesper, E. Chromatographia 1987, 392, 101-122.

Figure 5. Partition coefficient of benzene versus reciprocal temperature.

Figure 6. Calculated residence time of gas, liquid, and benzene at different temperatures.

In this series of experiments, it was observed that the chromatographic “window” varied with temperature and the potential resolution increased as the temperature increased. This phenomenon is illustrated in Figure 6. These results are similar to those observed in Figure 3, viz., the window was widest at conditions where the amount and hence the velocity of the liquid phase was minimal. CONCLUSIONS Careful control of the experimental conditions and instrument configuration allowed the accurate determination of the flow rate of compressible, binary fluids even at low flow rates of the order of 200 µL/min. Operation of the SFC pumps at constant pressure and constant proportional flow rates provided a constant-composition feed solution to a chromatographic column while maintaining constant pressure. Integration of the variable total flow rate provided an accurate measure of the average flow rate. The instrumentation was used to investigate the potential chromatographic application of columns with two mobile phases. Unlike liquids, mixtures of CO2 and liquids form two phases over a wide range of temperature, pressure, and stoichiometric composition. If the experimental conditions within a column are such that two phases are formed, these two phases will both migrate through the column. If the velocities of the two phases differ sufficiently, distribution of solutes between the phases can result in separation. In this study, quantitative measurements of Analytical Chemistry, Vol. 78, No. 4, February 15, 2006

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phase compositions and velocities were carried out for the methanol-CO2 system. It was demonstrated that a chromatographic “window” exists for such systems and that an upper limit exists for the retention time of any solute. This upper limit is the residence time of the slower moving liquid phase. This means that all of the injected solutes would be eluted from the column in a finite time period. In each experiment, the volume of both the liquid and gas phases were calculated. The sum of these two volumes represented the total volume of the column. The average value for the 25 reported experiments was 2.0 ((0.1) mL. A mass spectrometric detector was used for the experiments reported herein in order to obtain tracer pulse data to measure amount of eluent in each phase. Practical application of this type of chromatography could, however, be achieved with any appropriate SFC detector. The reported results indicate that it may be possible to perform certain chromatographic separations in columns without any

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stationary phase. Thus, the common problems of stationary-phase deterioration, decomposition, and contamination could possibly be eliminated in some cases. ACKNOWLEDGMENT This work was supported by a grant from the National Science Foundation. The GC/MS instrumentation was a gift from HewlettPackard. SUPPORTING INFORMATION AVAILABLE Tables S-1-S-3 provide detailed experimental data. This material is available free of charge via the Internet at http:// pubs.acs.org.

Received for review September 13, 2005. Accepted November 18, 2005. AC051637+