AC Research
Anal. Chem. 1998, 70, 2773-2782
Articles
Pressure-Induced Retention Variations in Reversed-Phase Alternate-Pumping Recycle Chromatography Kevin Lan and James W. Jorgenson*
Department of Chemistry, University of North Carolina at Chapel Hill, Venable Hall, CB 3290, Chapel Hill, North Carolina 27599-3290
The progressions of peak width and peak separation in reversed-phase alternate-pumping (AP) recycle chromatography are found to be inconsistent with conventional chromatographic theory. These discrepancies are explained by subtle pressure-induced variations of solute retention that become amplified by AP recycling. The presence of these retention variations is demonstrated by multiply injecting a single solute into an AP system at offset times. As the serially injected peaks are recycled, the separation time between the peaks is shown to vary significantly, indicating that the retention of the solute is dependent upon the position of the peak. A new model of chromatographic retention that appropriately accounts for this variable retention is presented. When this retention model is applied to an AP system for the binary separation of phenylalanine and a pentadeuterated phenylalanine, the model accurately describes the experimentally observed progressions of peak width and peak separation. Furthermore, the retention model predicts that the improvement of resolution in AP recycling closely matches the expectations of conventional theory, so the effectiveness of AP recycling is not significantly compromised by the variations in retention. Extending the column length is among the simplest means of improving separation efficiency in liquid chromatography. This approach, however, is limited by the increased back pressure of the elongated column. When only a small range of solute capacity factors is of interest, this obstacle may be avoided by reintroducing column effluent back to the head of the column, thereby effectively extending the column length. The recycling of the column effluent may be performed repeatedly and is limited only by the broadening of the solute peaks; when the peaks spread wide S0003-2700(97)01226-2 CCC: $15.00 Published on Web 06/04/1998
© 1998 American Chemical Society
enough to occupy an entire column length, further recycling causes overlap of the leading and trailing edges or loss of solute at the ends of the column. Direct-Pumping Recycle Design. In direct-pumping (DP) recycle chromatography,1 the effluent from a column is fed back to the pump inlet (Figure 1). Although this arrangement is conceptually simple, it requires the sample to pass through the internal volume of the pump, which leads to pronounced peak broadening unless special low-void-volume pumps2,3 are employed. Alternate-Pumping Recycle Design. Alternate-pumping (AP) recycle chromatography4,5 uses a novel design that passes the sample alternately between two similar columns without requiring the sample to pass back through the pump. The basic strategy of AP recycling is illustrated in Figure 2. Two columns are connected in series, with a detector placed between them. After injection, the solutes are partially separated by column A and detected (a). After the solutes pass completely through the detector and enter column B, the positions of the two columns are exchanged (b). Now the solutes can be further separated and detected; the process is repeated. The exchange of column positions described above can be performed by the actuation of an eight-port switching valve in the design6 shown by Figure 3a, which is a simple variation of the six-port AP design that is frequently employed5,7,8 (Figure 3b). (1) Porath, J.; Bennich, H. Arch. Biochem. Biophys. Suppl. 1962, 1, 152. (2) Mina´rik, M.; Popl, M.; Mostecky´, J. J. Chromatogr. Sci. 1981, 19, 250252. (3) Hirose, A.; Ishii, D. J. Chromatogr. 1986, 363, 391-393. (4) Biesenberger, J. A.; Tan, M.; Duvdevani, I.; Maurer, T. Polym. Lett. 1971, 9, 353-357. (5) Duvdevani, I.; Biesenberger, J. A.; Tan, M. Polym. Lett. 1971, 9, 429-434. (6) Chizhkov, V. P.; Yushina, G. A.; Sinitzina, L. A.; Rudenko, B. A. J. Chromatogr. 1976, 120, 35-45. (7) Henry, R. A.; Byrne, S. H.; Hudson, D. R. J. Chromatogr. Sci. 1974, 12, 197-198.
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Figure 1. Direct-pumping (DP) recycle design.
Figure 2. Simplified view of AP recycle operation. See text for explanation (Alternate-Pumping Recycle Design section of the introduction).
Figure 3. Alternate-pumping (AP) recycle design. (a) Eight-port AP design. (b) Six-port AP design.
Note that the extracolumn volume is limited to the relatively small void volumes of the switching valve, the detector cell, and the tubing required to make the appropriate connections. The main advantage of the eight-port design over the six-port design is that only a single detector is needed to monitor the transfer of solutes from one column to the other. A slight drawback of eight-port design is that the direction of flow through the detector is reversed each time the valve is actuated. Nonetheless, most detection methods that are compatible with recycle chromatography are also relatively insensitive to the direction of flow. (8) Kucera, P.; Manius, G. J. Chromatogr. 1981, 219, 1-12.
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Comparison between DP and AP Designs. Recycling Limitations. To make a fair comparison between DP and AP designs, we must consider the case where each of the two AP columns is half the length of the DP column, i.e., where the two systems have equal back pressures for the same chromatographic conditions. As mentioned previously, the practical limit of recycling is determined by the extent of peak broadening. Since the DP column is twice as long as an AP column, the DP design can tolerate twice the level of peak broadening. Thus, in cases where the internal pump volume is very small compared to the peak volumes, the DP design offers a significant advantage over the AP design. Unfortunately, the theoretical benefit of the DP design is not realized when a typical HPLC pump is used with an analytical column. Chamber volumes for most HPLC reciprocating piston pumps are on the order of 100 µL. Such void volumes severely broaden analytical peaks,9 which have peak volumes on the order of hundreds of microliters or less. Furthermore, the reciprocating piston action produces a piecewise inversion of the inlet stream concentration profile, which alters the peak shape and further broadens the peak. These complications greatly reduce the efficiency and extent of DP recycling; hence, AP recycling is the superior option for most analytical purposes. Cost of Instrumentation. From Figures 1 and 3, it is clear that the AP design is more instrumentally demanding than the DP design. The major instrumental differences are the number of columns, the pressure limit of the detector cell, and the type of switching valve. Of these differences, only the first two deserve economic consideration since the type of switching valve has only a marginal effect on cost. An obvious difference between AP and DP designs is that the former requires an additional column, which can amount to a significant cost if expensive columns are used. Since recycle chromatography effectively extends column length, it may seem worthwhile to purchase shorter columns in an effort to reduce the cost. Unfortunately, shorter columns usually cost only slightly less than their longer counterparts, so little is gained with this strategy. Another difference between the two designs is that the AP design places a second column after the detector. Thus, the detector cell must be able to withstand the back pressure of one column, or half of the total back pressure. The standard cells on most UV absorption detectors are incompatible with these pressures, so high-pressure cells are needed. Although prices vary by detector model, high-pressure cells invariably cost more than standard cells. Control of Instrumentation. The principal difficulty in the operation of an AP instrument is the necessity to actuate the switching valve at regular intervals so that the solutes are recycled between columns. When the total analysis time is short, this procedure may be performed manually with little inconvenience. Longer analyses, however, are best controlled by computer or another form of automation. Ideally, a computer with an integrated data acquisition and valve control system would identify peak locations and adjust the timing of the valve actuations accordingly. Although such software is not commercially available (9) Martin, M.; Verillon, F.; Eon, C.; Guiochon, G. J. Chromatogr. 1976, 125, 17-41.
at present, a basic acquisition/control procedure is not difficult to program on a computer. Solvent Consumption. DP recycle chromatography continuously recycles the mobile phase within the system, so no new mobile phase is required during the recycling operation. Because of this feature, DP recycle chromatography is sometimes referred to as closed-loop recycle chromatography to distinguish it from AP recycle chromatography. However, this choice of nomenclature is ambiguous and inaccurate. An AP recycling instrument can be made to operate in a closed-loop fashion by using a fourport switching valve to redirect the “waste” outlet of the eightport switching valve back to the pump inlet. Alternatively, the outlet tubing from the eight-port switching valve may be placed directly in the mobile phase reservoir. In either case, the mobile phase is completely conserved within a loop. Thus, the distinguishing characteristic of DP recycling is that it is inherently closed-loop whereas AP recycling may be operated in either normal or closed-loop mode. Practical Applications of Analytical Recycle Chromatography. Reduced Turnaround Time. Recycle chromatography may be particularly helpful when results are needed quickly. Instead of optimizing the separation method on a conventional chromatographic system, time may be saved by developing a reasonably good separation method and then using recycle chromatography to achieve the desired results. Recycle chromatography is especially useful when a demanding separation needs to be performed only a few times or when the availability of the sample is so limited that it prohibits extensive methods development. Inherently Difficult Separations. Recycle chromatography provides a relatively simple and inexpensive means of attaining the separation power needed to resolve solutes of similar chemical and physical nature. AP recycle chromatography has already been applied to chiral,10 oligomeric,4,11 isomeric,7,12,13 and isotopic8,14,15 separations for this purpose. Faster Separations. Hala´sz et al.16 have shown that the maximum number of effective plates generated per unit time normally occurs near a capacity factor of 2. Despite this conclusion, conventional separations are rarely performed under timeoptimized conditions because solutes with such low capacity factors usually do not remain on the column long enough for adequate separation. Thus, most conventional separations are optimized on the basis of column length instead of analysis time, i.e., the analysis time is prolonged so that more separation is achieved on the given length of column. In recycle chromatography, the column length is effectively extended, so this constraint becomes much less restrictive. Recycle chromatography thus allows solutes under time-optimized conditions to migrate through a longer column length, leading to an overall improvement in analysis time. (10) Isaksson, R.; Roschester, J. J. Org. Chem. 1985, 50, 2519-2521. (11) Dawkins, J. V.; Forrest, M. J.; Shepherd, M. J. J. Chromatogr. 1991, 550, 539-547. (12) Pokorny´, S.; Luka´sˇ, R.; Jancˇa, J.; Kolı´nsky´, M. J. Chromatogr. 1978, 148, 183-187. (13) Dawkins, J. V.; Moody, C. J.; Price, D. Macromolecules 1995, 28, 29852987. (14) Tanaka, N.; Araki, M. J. Chromatogr. 1986, 352, 307-314. (15) Tanaka, N.; Hosoya, K.; Nomura, K.; Yoshimura, T.; Ohki, T.; Yamaoka, R.; Kimata, K.; Araki, M. Nature 1989, 341, 727-728. (16) Hala´sz, I.; Endele, R.; Asshauer, J. J. Chromatogr. 1975, 112, 37-60.
THEORY Several investigations have shown that solute retention may vary significantly as a function of pressure in liquid chromatography.17-21 This finding is a major concern in AP recycle chromatography because solutes are subjected to different average pressures on the basis of their relative retentions. The explanation for this unusual property is straightforward. Consider the binary separation depicted in Figure 2. The less retained solute (light band) is always closer to the outlet end of the column than the other solute, regardless of the switching valve position. Thus, the less retained solute is always at a lower pressure and experiences a lower average pressure than the other solute. If the retentions of the solutes vary significantly over these pressure differences, the rate of peak separation will be affected. Likewise, if a single peak becomes broad enough that the leading and trailing edges are subjected to substantially different pressures, the rate of band broadening will also be affected. Differential Retention Experiment. The differential retention experiment provides a novel method of probing retention variations in an AP system. In such an experiment, an initial injection of a solute is made in the usual fashion, but it is followed shortly afterward by a second injection of the same solute. These two peaks are then recycled through the AP system. If the retention of the solute is independent of space (and therefore pressure), the difference between the detection times of the two peaks remains constant. However, any variation in the solute’s retention causes a shift in peak separation due to the effects described previously. Retention Profile Model. The capacity factor k′ is related to the linear velocity v of the solute band by
k′ )
u -1 v
(1)
where u is the mobile phase linear velocity (Table 1). Rearrangement of this equation yields
1 1 + k′ ) v u
(2)
which shows that the reciprocal velocity of the solute is directly related to the capacity factor. Thus, reciprocal velocity may be interpreted as a measure of chromatographic retention. Let us denote the function of reciprocal velocity versus column position x as the retention profile. When the retention profile does not change over time, let us refer to the retention profile as temporally invariant. Conventional isocratic elution systems, for example, have temporally invariant retention profiles. The definite integral of a temporally invariant retention profile indicates the amount of time required for a peak to traverse the (17) Bidlingmeyer, B. A.; Rogers, L. B. Sep. Sci. 1972, 7, 131-158. (18) Prukop, G.; Rogers, L. B. Sep. Sci. Technol. 1978, 13, 59-78. (19) McGuffin, V. L.; Evans, C. E. J. Microcolumn Sep. 1991, 3, 513-520. (20) MacNair, J. E.; Lewis, K. C.; Jorgenson, J. W. Anal. Chem. 1997, 69, 983989. (21) Ringo, M. C.; Evans, C. E. J. Phys. Chem. B 1997, 101, 5525-5530.
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Table 1. Glossary of Mathematical Symbols name
symbol
mobile phase linear velocity solute linear velocity capacity factor pressure sensitivity pressure gradient temporal peak width, temporal separation
u v k′ mP ∇P σt
spatial peak width, spatial separation
σx or σ
normalized retention gradient HETP retention gradient HETP base HETP separation distance base separation rate resolution efficiency column length cycle number
M H Hk H0 s w0 Rs N L n
definition dxmp/dt, where xmp is the position of a mobile phase plug dxp/dt, where xp is the position of the solute peak u/v - 1 (note that this formula is not the official definition) ∂k′/∂P dP/dx temporal standard deviation of a peak, time between the two peaks of a differential retention experiment spatial standard deviation of a peak, distance between the two peaks of a differential retention experiment (-dk′/dx)/(1 + k′) dσ2/dx HETP contribution attributed to the retention gradient 2 H0 ≡ lim σ2f0(dσ /dx) (the sum of all conventional HETP contributions) distance between the peaks of two different solutes w0 ≡ lim sf0(ds/dx) s/4σ, where σ is the average standard deviation of the two peaks x2/σ2, where x is the position of the solute peak length of one column number of column lengths traveled by a peak at the time of detection
bounds of integration. For example, a peak at position a requires time t to reach position b:
1 dt dx ) t dx ) ∫ ∫ v(x) dx b
a
b
a
(3)
When the bounds of integration are the positions of the two peaks in a differential retention experiment, this definite integral represents the temporal separation between the peaks (Figure 4a). Note that the temporal separation is distinctly different from the spatial separation of the peaks, which is the physical distance between the two peaks at a given time, i.e., the value of b minus a in the example above. When two peaks of a differential retention experiment traverse a region that has a temporally invariant retention profile, the temporal separation between the peaks remains constant. For example, if two peaks are introduced 100 s apart onto a conventional isocratic chromatographic system, the peaks would be detected 100 s apart, regardless of the retention profile and regardless of where along the column the detection takes place. Therefore, the definite integral between the two peak positions must remain constant when the retention profile is temporally invariant (Figure 4b). Unlike temporal separation, the spatial separation varies depending on the retention profile. Suppose, for example, that a temporally invariant retention profile is monotonically decreasing. Under these conditions, the leading peak of a differential retention experiment is always at a lower retention (and a higher velocity) than the other peak. This difference in retention causes a monotonic increase in their spatial separation. Nonetheless, the temporal separation still remains constant. This apparent paradox can be resolved by noting that the increasing spatial separation is balanced by the increasing velocities of the peaks. Although AP recycle chromatography is performed isocratically, the retention profile of the system is not always temporally invariant. The retention profile changes only when the six- or eight-port valve is actuated so that the column positions are exchanged. Consider the effects of a valve actuation on a 2776 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
differential retention experiment. When column positions are switched, the recycled peaks are suddenly subjected to higher pressures (Figure 4c). During this relatively instantaneous process, the spatial separation stays the same, but there is an abrupt shift in the retention profile due to the pressure change. Consequently, the temporal separation, which represents the definite integral of the retention profile, also changes at this instant. The new temporal separation can then be measured as the difference between the detection times of the two peaks. Effect of Pressure in RPLC. The relationship between pressure and retention in a reversed-phase system has been explored by McGuffin and Evans for a homologous series of derivatized fatty acids19 and by MacNair et al. for various small organic electroactive compounds.20 The results from these studies suggest that the relationship between capacity factor k′ and pressure P may be approximated as a line over a large range of pressures. Let us assume that this relationship holds over the range of column pressures and denote the slope of this line as pressure sensitivity, mP:
mP ≡ ∂k′/∂P
(4)
Pressure sensitivity affects the retention profile of a system because the absolute pressure within a column declines along the direction of the flow. When mobile phase is pumped through a uniformly packed column at ordinary chromatographic pressures, the pressure gradient ∇P is virtually constant in space x:
∇P ≡ dP/dx
(5)
which is necessarily negative in value based on the convention that flow occurs in the positive x direction. When pressure is the only variable influence on the capacity factor, eqs 4 and 5 indicate that the capacity factor gradient is constant:
dk′/dx ) mP∇P
(6)
Note that the capacity factor gradient and the pressure sensitivity are opposite in sign.
the stationary phase. After an AP valve actuation, the sudden change of local column pressures causes mobile phase constituents to be preferentially extracted into or released from the stationary phase.23-25 This relatively instantaneous process introduces an eigenzone, a region of altered mobile phase composition, along the entire column. Fresh mobile phase then pushes the eigenzone through the system as a plug. Since a more retained solute is closer to the head of the column than a less retained solute, the fresh mobile phase must first pass the more retained solute before it encounters the less retained solute. Thus, a less retained solute remains within the eigenzone for a longer time than a more retained solute. Because spatial temperature variations and eigenzones dynamically affect the retention profile, we know that eq 6, which purports that the capacity factor gradient is constant, is not completely accurate for most AP systems. Nonetheless, we assume that the capacity factor gradient can be effectively modeled as being constant with respect to space and time. This assumption greatly simplifies many of the derivations that follow. Band Broadening. Recall that the spatial retention gradient across a peak affects the rate of band broadening in AP recycle chromatography. This contribution toward band broadening can be modeled by viewing the two peaks of a differential retention experiment as markers for the leading and trailing edges of a much broader peak. The rate of separation between these markers can then be used to predict the rate of band broadening attributable to the retention gradient. Let us assume that any variation in the retention profile is relatively small. (Suppose, for example, that the retention profile does not change by more than 10%.) Under this condition, the temporal separation σt and spatial separation σx are approximately related by Figure 4. Retention profile model of a differential retention experiment on an AP system. (a) The shaded area under the curve represents the temporal separation between two bands of the same solute. (b) The spatial separation increases as the bands travel through the system, but the temporal separation remains the same. (c) Exchanging the column positions results in a sudden increase in the temporal separation.
Effects of Other Variables in RPLC. The retention model that we have established has addressed only the effects of the pressure gradient. There are, however, other influences on retention that are much more difficult to model because the magnitudes of their gradients vary in space and time. Two marked examples are the spatial temperature gradient and eigenzones. Spatial Temperature Gradient. A spatial temperature gradient arises from the frictional heating of the mobile phase as it is forced through a column. This gradient varies continuously in space under nonadiabatic conditions.22 In AP systems, the temperature gradient also varies in time due to the regular exchange of column positions. Despite the complicated behavior of the temperature gradient, it is similar to the pressure gradient with respect to its effect on the separation environment; a less retained solute experiences a higher average temperature than a more retained solute. Eigenzones. Another complicated gradient arises from the pressure-dependent partitioning of mobile phase constituents into (22) Martin, M.; Eon, C.; Guiochon, G. J. Chromatogr. 1975, 110, 213-232.
1 σt ) σx v
(7)
which can be derived from (3). An important implication of this approximation is that the changes in the spatial separation are proportionally reflected in the temporal separation immediately following a valve actuation. Thus, spatial separation can be monitored by measurements of temporal separation. Rearrangement of (7) and substitution of (2) yields
σx )
1 uσ 1 + k′ t
(8)
Because the temporal separation and the mobile phase linear velocity are both constant under temporally invariant conditions, we have the following expression for the derivative of the spatial separation with respect to space:
dσx -dk′/dx ) uσt dx (1 + k′)2
(9)
(23) Berek, D.; Macko, T. Pure Appl. Chem. 1989, 61, 2041-2046. (24) Berek. D.; Chala´nyova´, M.; Macko, T. J. Chromatogr. 1984 286, 185-192. (25) Chala´nyova´, M.; Macko, T.; Kandra´cˇ, J.; Berek, D. Chromatographia 1984, 18, 668-672.
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Substitution of (8) into (9) yields
It follows from (13), (15), and (16) that
dσx -dk′/dx ) σ dx 1 + k′ x
(10)
Since the capacity factor gradient is effectively constant and the retention profile varies relatively little in space (e.g., 99%, Sigma Chemical Co., St. Louis, MO) and L-phenylalanine-ring-d5 (D5Phe, 98%, Cambridge Isotope Laboratories, Woburn, MA) were used as test compounds for the chromatographic system. (D5Phe is the deuterated form of phenylalanine where each of the aromatic hydrogens is substituted with a deuterium.) Potassium nitrate (Fisher Scientific, Fair Lawn, NJ) was used as a dead-time indicator. All samples were dissolved in mobile phase and filtered through 0.2-µm membranes (Gelman Sciences Acrodiscs, Ann Arbor, MI). 2780 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
Figure 5. Differential retention experiment: sample, 1.0 mM Phe; mobile phase, 10:90 ACN/water, 25 mM Na2SO4, 0.1% TFA; flow rate, 1 mL/min. The two injections were separated by approximately 0.20 of the time between valve actuations (83 s for this case). Peaktracking software attempts to keep the first peak centered at a relative detection time of 0.40 between valve actuations.
The mobile phase is a 10:90 mixture of acetonitrile (Optima grade, Fisher Scientific)/purified water (Barnstead Nanopure System, Dubuque, IA) containing 0.1% trifluoroacetic acid (Sigma Chemical Co.) and 25 mM sodium sulfate (Mallinckrodt Specialty Chemicals Co., Paris, KY). The mobile phase was filtered through a 0.2-µm nylon membrane (Alltech, Deerfield, IL), degassed under vacuum, and allowed to reach room temperature prior to use. There was continuous helium sparging of the mobile phase during the experiments. Data Analysis. Resolved peaks were fit to exponentially modified Gaussian (EMG) functions using in-house software written in LabVIEW 4.1 (National Instruments). Unresolved peaks were fit to sums of EMG functions using the same software. This software employs the Levenberg-Marquardt method26 for finding the least-squares regression solution. Peak variance was determined by finding the second normalized central statistical moment of the EMG.27 The separation between two peaks was determined by the difference between the times of the EMG maxima. RESULTS AND DISCUSSION Differential Retention Experiment. Figure 5 shows the results of a differential retention experiment on Phe. The peak separation steadily increases with every cycle, indicating the presence of a retention gradient. A plot of the natural logarithm of peak separation versus cycle number (Figure 6) yields a straight line, as predicted by (33). The slope of this line is the product of the normalized retention gradient and the length of one column (25 cm), so the measured normalized retention gradient is 6.60 × 10-4 cm-1. The data point from the first cycle was not included in the least squares regression for reasons given in the Theory section on Measurement of the Normalized Retention Gradient. The slightly staggered progression of the data points in the plot is caused by small differences between the retention profiles of each column. (26) Sen, A.; Srivastava, M. Regression Analysis: Theory, Methods, and Applications; Springer-Verlag: New York, 1990. (27) Grushka, E. Anal. Chem. 1972, 44, 1733-1738.
Figure 6. Natural logarithm of peak separation versus cycle number for the differential retention experiment in Figure 5. The solid line represents the least-squares regression line. The data point from the first cycle, shown by the solid circle, was excluded from the regression for reasons given in the text (Theory section, Measurement of the Normalized Retention Gradient).
Figure 7. Binary separation: sample, 0.5 mM Phe and 0.5 mM D5Phe; mobile phase, 10:90 ACN/water, 25 mM Na2SO4, 0.1% TFA; flow rate, 1 mL/min. Phe was kept at a relative position of 0.55 between valve actuations.
Binary Separation. The separation of Phe and D5Phe is shown by Figure 7. The experimental progressions of peak variance (for Phe), peak separation, and the square of resolution agree with the theoretical curves predicted by (20), (24), and (27) (Figure 8). Note that the solid lines in Figure 8 do not represent best-fit curves; they represent theoretically predicted progressions based on measurements of base HETP, base separation rate, and normalized retention gradients. The base HETP and base separation rate were estimated by the peak variance and peak separation, respectively, of the second cycle (n ) 2): 2 H0 ≈ σn)2 /2L
(35)
w0 ≈ sn)2/2L
(36)
The normalized retention gradient of D5Phe (6.52 × 10-4 cm-1) was measured by a differential retention experiment under the same conditions as described for Phe (caption of Figure 5). The average of Phe and D5Phe normalized retention gradients was used for the theoretical progressions of the peak separation and the square of resolution. The experimental progression of the square of resolution shows a slight negative deviation from the theoretical line after
Figure 8. Theoretical predictions and experimental results of the binary separation in Figure 7. (a) Peak variance for Phe. The dashed line represents what is predicted by conventional isocratic theory, and the solid line represents eq 20. (b) Peak separation. The dashed line represents conventional isocratic theory, and the solid line represents eq 24. (c) Square of resolution. Conventional isocratic theory and eq 27 predict virtually the same progression for the square of resolution, which is shown by a single solid line.
the tenth cycle (Figure 8c). One possible explanation for this discrepancy is that it is caused by impurities in the D5Phe, which is only about 98% pure. The major impurities are less deuterated forms of phenylalanine, which have slightly higher retentions than D5Phe. As these impurities slowly separate from the major peak, they produce low shoulders that may cause the D5Phe peak to appear more tailed. Consequently, the EMG fit of the D5Phe peak may give a peak variance that is artificially high and a resolution from Phe that is artificially low. A more likely explanation for the accelerated broadening of the D5Phe peak is that it is caused by the temperature gradient. Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
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As D5Phe separates from Phe, the D5Phe peak spends a greater fraction of its time near the head of the two-column system. It is this region of the system that has the steepest temperature gradient,21 so the corresponding retention gradient further accelerates the rate of band broadening. SUMMARY Practical Feasibility of Recycle Chromatography. The AP design establishes the practical feasibility of recycle chromatography for analytical purposes. The only additional requirements of an AP system over a conventional system are the switching valve, the second column, and the high-pressure detector cell. By employing the eight-port AP design, only a single detector is required to monitor solutes during every cycle. The automation of the valve actuations in AP recycling is easily accomplished by computers, which are already used as data-recording devices in most modern systems. All of the materials needed to assemble an AP system are commercially available, and the instrumentation of an AP system generally costs only slightly more than that of a conventional system. Furthermore, the operational costs of an AP system can be reduced by using the system in a closed-loop mode. Application of AP Recycle Chromatography. The binary separation depicted in Figure 7 demonstrates the advantages of rapid separation and reduced turnaround time for recycle chromatography. In this separation, D5Phe and Phe have an average capacity factor of 1.43 and a selectivity R of 1.03. Despite the low selectivity between these solutes, a resolution of 1.06 was attained within 30 min (four cycles). Moreover, no methods development or optimization was involved with this separation. Differential Retention Experiment. The differential retention experiment demonstrates the presence of retention variations
2782 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
in an AP system and provides a novel means of measuring the effective spatial retention gradient. If capillary columns were used with a pure solvent as the mobile phase, it is likely that the differential retention experiment would allow the measurement of pressure sensitivity, dk′/dP, with minimal interference from thermal and eigenzone effects. Chromatographic Theory. A simplified view of AP recycle operation was presented (Figure 2) to help visualize the basic strategy and implications of AP operation. Using this model, the effects of the pressure gradient, spatial temperature gradient, and eigenzones are more easily understood. The retention profile model was developed as a more accurate representation of chromatographic retention. By conceptually applying the differential retention experiment, this model accurately describes the anomalous progressions of peak width and peak separation in a reversed-phase AP system. Furthermore, the model predicts that the square of resolution increases linearly over a relatively large number of cycles. This finding indicates that AP recycle chromatography can be used effectively as a means to improve separations despite the retention variations in the system. ACKNOWLEDGMENT This research was supported by the National Institutes of Health under Grant GM 39515. We thank Glaxo-Wellcome for their donation of the pump and columns, and Hewlett-Packard for their donation of the detector.
Received for review November 7, 1997. Accepted April 22, 1998. AC971226W
