A new separation technique takes advantage of sub-2-µm porous particles.

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1 Downloaded via on August 14, 2018 at 16:39:06 (UTC). See for options on how to legitimately share published articles. A new separation technique takes advantage of sub-2-µm porous particles. Jeffrey R. Mazzeo Uwe D. Neue Marianna Kele Robert S. Plumb Waters Corp. the workhorse technique in liquidphase separations. The HPLCremains method has two fundamental roots. One is gel-permeation chromatography for the characterization of polymers (1); the other is GC. HPLC began to emerge when GC researchers turned their attention to liquid-phase separations (2, 3). The original LC columns were typically cm long, with a 1 2 mm i.d., and packed with µm-diam particles. Shorter diffusion distances were known to provide better performance. However, it was not possible to prepare high-performance columns with particles with diameters <30 µm by using the dry-packing techniques that had been applied successfully in GC. One improvement was the development of superficially porous particles that resulted in better column performance at low retention factors (4, 5). A breakthrough was achieved in the early 1970s, when slurry packing techniques were developed for fully porous particles <30 µm in diameter (6 8). Researchers rapidly learned to pack efficient columns with 10-, 5-, and 3-µm particles (9 11). The first commercial columns packed with 10-µm particles became available in 1973 (12). During these early investigations, it became clear that the pressures required to operate long, small-particle columns at suitable velocities (above the minimum of the plate-height velocity curve) heat up the mobile phase because of friction (13, 14). This heat would ultimately limit the benefits of using smaller particle sizes unless measures were taken to compensate for this effect. Today, two driving forces continue to test the limits of HPLC. One is the need for faster separations, such as analyses of either simple samples or a few constituents in a complex sample (15 17 ). The second is the desire to achieve greater separation power to quantify or identify all the constituents of a complex sample or to compare the contents of complex samples with each other (18 22). The same driving forces resulted in the overwhelming breakthrough in the past decade of LC/MS techniques, which continue to spawn new approaches for faster or more powerful separations (23, 24). Examples are the use of very high temperature HPLC (25, 26) or alternative HPLC column technologies, such as 460 A ANALYTICAL CHEMISTRY / DECEMBER 1, AMERICAN CHEMICAL SOCIETY

2 DECEMBER 1, 2005 / ANALYTICAL CHEMISTRY 461 A

3 Height (µm) Linear velocity (mm/s) FIGURE 1. Van Deemter curves for hexylbenzene on particles that are 1.7 µm (red diamonds), 3.5 µm (green squares), and 5.0 µm (blue triangles) in diameter. Column dimensions, mm; mobile phase, acetonitrile:water 7:3 (v/v); temperature, 25.0 C. monoliths (27, 28). In addition, improved mass transfer and efficiency in countercurrent chromatography have been reported at elevated flow rates (29). In the late 1990s, the need to separate highly complex mixtures of protein digests renewed interest in smaller particles. Jorgenson had developed CE, a technique in which the heat generated inside a capillary could be efficiently dissipated; this enabled the operation of capillaries at very high voltages >30 kv (30). The same principle could be applied to HPLC. Columns with a diameter narrower than the standard column diameter of HPLC could be operated at much higher pressures because the frictional heat could be dissipated (31 33). If instruments with extended pressure range were available and smaller particles could be used, then a higher separation performance or a faster analysis could be achieved, compared with classical HPLC. The term ultra-high-pressure LC was introduced to define the use of sub-2-µm particles packed into very long (>150-mm) capillary columns (<50-µm i.d.) that ran at pressures up to 700 MPa. In Jorgenson s original work, 1.5-µm nonporous particles were used. The particles had been commercially available for some time but suffered from limited capacity because of their small surface area. Subsequent work was done with porous 1.5- µm particles (34). Ultra-high-pressure LC has demonstrated significantly improved chromatographic performance for the separation of complex peptide digests with long run times (32). Giddings had previously suggested that the available pressure was directly related to separation performance, and this was subsequently investigated by several groups (35 40). The benefits of sub-2-µm particles can be harnessed at more moderate pressures by using microbore columns of up to 150 mm long to create the operating regime ultra-performance LC (UPLC; 41). This article will discuss the principles of and current developments in UPLC. Advantages of sub-2-µm particles The trend in LC has been the continued reduction in particle size. Harnessing the chromatographic potential of sub-2-µm particles leads to significant improvements in terms of resolution, analysis speed, and detection sensitivity. Knox recognized the potential benefits of these particle sizes >30 yr ago (42). The van Deemter plots in Figure 1 demonstrate the performance improvements that 1.7-µm particles offer over the currently used 5.0- and 3.5- µm sizes. The 1.7-µm particles give 2 3 lower plate-height values. The particles also achieve the lower plate height at higher linear velocities and over a wider range of linear velocities. The result is better resolution and sensitivity as well as reduced analysis time. In isocratic separations, the resolution is proportional to the square root of efficiency. Particle size and efficiency at the optimum linear velocity are inversely proportional. Therefore, resolution is inversely proportional to the square root of particle size. With this knowledge, we can calculate that 1.7-µm particles will offer 1.7 and 1.4 greater resolution than 5.0-µm and 3.5-µm particles, respectively, at equal column lengths. The optimum flow rate is also inversely proportional to particle size. Because analysis time in isocratic separations is inversely proportional to flow rate, 1.7-µm particles offer 1.7 higher resolution than 5.0-µm particles in a third of the time, or 5 higher productivity (resolution per unit time). The benefit of 1.7-µm particles over 3.5-µm ones is 1.4 higher resolution in half of the time, or 3 higher productivity. More efficient peaks translate to narrower and taller peaks. Peak width is inversely proportional to the square root of efficiency; the peak height is inversely proportional to peak width. Therefore, when smaller particles are used to make the peaks narrower, the peak height is also increased. If the detector is assumed to be concentration-sensitive (as is the case for UV detectors) and the detector noise remains constant, then sensitivity, as defined by S/N, will also increase. Specifically, in comparison with 5.0- µm particles, 1.7-µm particles offer 1.7 higher sensitivity. When compared with 3.5-µm particles, 1.7-µm particles provide 1.4 higher sensitivity for the same column length. It is well established that column efficiency at the optimum linear velocity is proportional to column length L divided by particle size d p. If the experimental goal is to maintain resolution but achieve it in a shorter analysis time, then smaller particles offer a significant benefit. For example, with 1.7-µm particles, column lengths that are 3 shorter than those used for 5.0-µm particles will give the same efficiency and resolution. Because the optimum flow rate is 3 higher, the result is that the same resolution obtained with 5.0-µm HPLC separations can be achieved 9 faster with 1.7-µm particles in UPLC. In comparison with 3.5-µm particles, the benefit with 1.7-µm particles is a 4 shorter run time. Under the condition of constant L/d p, the sensitivity gain is inversely proportional to the column length used to generate the 462 A ANALYTICAL CHEMISTRY / DECEMBER 1, 2005

4 constant efficiency. Thus, in addition to obtaining the same resolution 9 faster with 1.7-µm particles than with 5.0-µm particles in a HPLC separation, the sensitivity is improved by a factor of 3. In comparison with 3.5-µm particles, the sensitivity is improved by a factor of 2 for 1.7-µm particles. Note that the discussion was limited to isocratic separations; the benefits of UPLC apply equally to gradient separations. Achieving optimum efficiency Several practical issues must be addressed to achieve optimum performance. At constant L and optimum flow rate, back pressure is inversely proportional to the third power of d p (43). Therefore, the 3-fold reduction in d p in UPLC translates to back pressures that are 27 higher compared with HPLC separations when 5-µm particles are used. It follows that the instrumentation must be capable of operating at higher pressures. This includes fittings, pump seals, injector valves, and the chromatographic column. The first commercial instrument designed for UPLC operation is rated for use up to 100 MPa (41). This pressure limit allows for the use of columns up to 150-mm long for small-molecule separations. The gradient system uses a four-piston pump in which the first two pistons pre-pressurize the solvents to be delivered by the high-pressure pistons. Another area of concern is the heat generated at higher pressures. The radial thermal gradient in a chromatography column can be predicted on the basis of the heat balance equation (44, 45). The maximum radial thermal gradient that develops along the y axis is proportional to the superficial velocity of the mobile phase, the pressure drop per unit length, and the square of the column radius. It is inversely proportional to the average effective heat conductivity of the column in the radial direction. It follows that the maximum radial thermal gradient in two columns packed with the same particles, operated with the same mobile phase at the same pressure, is proportional to the square of the ratio of the column radii. If the pressure limit of a chromatography unit is extended 3-fold, a 3 higher radial temperature gradient is generated inside the column at the pressure limit of the instrument. A 1.7-fold reduction in the column radius is required to compensate for the higher temperature gradient caused by the higher pressure. For example, a 2.1-mm-i.d. column at 100 MPa generates the same radial thermal gradient as a 4.6-mm column at 33 MPa if the two columns are packed with the same particles. The relationship between the column radius r and the radial thermal gradient generated in a column is summarized in Table 1 (found in Supporting Information online). The radial thermal gradient generated in the same-diameter column packed with particles of different sizes is proportional to the fourth power of the d p ratio at the optimum flow rate under isothermal conditions. It would thus be necessary to reduce the column diameter significantly to compensate for the thermal effect in columns packed with small particles. Predicted radial thermal gradient ( C) For example, a 70-µm-i.d. capillary column packed with 1.7-µm particles would have the same radial thermal gradient as a 4.6- mm-i.d. column packed with 5-µm particles at optimum flow. If a small-particle-packed column and a traditional 5-µm column of the same diameter are operated at the same flow rate, then the radial thermal gradient should be proportional to the square of the d p ratio. If a 5-µm- and a 1.7-µm-particle packed column of the same diameter are operated at the same pressure (e.g., at the pressure limit of the instrument for fast separations), the radial thermal gradient on the small-particle packed column would be lower in proportion to the square of the d p ratio. Unfortunately, no satisfactory way exists to measure the local radial thermal gradient in packed columns. The outlet solvent temperature or the wall temperature gives only a first indication about the order of magnitude of heat generated inside the column. However, the efficiency and tailing obtained on the sub-2- µm-particle packed columns give a clear indication about the importance of the radial thermal gradient. In Figure 1, the measured height equivalent of a theoretical plate (HETP) values are plotted as a function of the linear velocity on columns of the same diameter and length packed with 1.7-, 3.5-, and 5.0-µm particles. In Figure 2, the predicted radial thermal gradient is shown as a function of linear velocity. In spite of the significantly higher thermal gradient predicted for the sub-2- µm-particle packed column, no excessive efficiency loss was observed. The result indicates that a thermal gradient of this order of magnitude is not a determining factor of efficiency. We have found that for d p of µm, as long as the column s i.d. is <2 mm, efficiency losses due to thermal gradients are minimal. Because peak volumes decrease with the smaller column diameters and smaller particles, a minimum extracolumn variance is critical for maintaining chromatographic efficiency. The UPLC Linear velocity (mm/s) FIGURE 2. Radial thermal gradient vs linear velocity for hexylbenzene on particles that are 1.7 µm (red diamonds), 3.5 µm (green squares), and 5.0 µm (blue triangles) in diameter. Column dimensions, mm; mobile phase, acetonitrile:water 7:3 (v/v); temperature, 25.0 C. DECEMBER 1, 2005 / ANALYTICAL CHEMISTRY 463 A

5 (a) (b) (c) (d) FIGURE vs 4.8-µm particles. Separation on 50-mm columns packed with (a) 1.7-µm and (b) 4.8-µm particles; (c) 30-mm column packed with 1.7-µm particles; (d) 100-mm column packed with 4.8-µm particles. All columns are C 18 -bonded bridged-ethyl hybrid particles with 2.1-mm i.d. Pressures across columns are (a) 53, (b) 2.4, (c) 32, and (d) 4.8 MPa. instrument has an extracolumn peak variance of 1 6 µl 2, with 2 5-µL injection loops. The variance of a standard HPLC instrument is ~ µl 2, so the reduction in extracolumn bandspreading is substantial. In addition, for gradient separations, a lower delay volume is required to minimize the impact on gradient delay times. The UPLC instrument delay volume is 109 µl when the standard mixer is used, compared with µl for a modern HPLC instrument. As part of the reduction in extracolumn bandspreading, a UV flow cell was designed that has a volume of 500 nl, with a path length of 10 mm. This large path length and minimal volume are achieved when light-guided flow cells are used that rely on total internal reflectance of the light. A typical HPLC flow cell has a path length of 10 mm and a volume of 8 15 µl. In some of the very fast UPLC separations of <1 min, peak widths are <1 s. At least 20 points across a peak must be obtained to maintain good quantitation performance. Therefore, the data acquisition rate for the UV detector must be >20 points/s. The tunable UV detector in the first commercial UPLC instrument is capable of an acquisition rate of 40 points/s. To test the theoretical improvements at constant L, experiments were conducted on a UPLC instrument to compare the performance of 1.7- and 4.8-µm particles made with the same base particle and bonded with the same chemistry (Figures 3a and 3b). Columns of mm dimension were used to separate a mixture of caffeine and its metabolites. The optimum flow rate for the 4.8-µm-particle column was determined to be 0.2 ml/min, or 1.6 mm/s under the test conditions. The 1.7-µm-particle column was run at 0.6 ml/min. The separation time is 2.5 faster with the 1.7-µm-particle column, compared with a theoretical value of 3. Critical pair (peaks 2 and 3) resolution is 1.5 higher with the 1.7-µm-particle column, compared with a theoretical value of 1.7. The peak height of peak 4 is 1.4 higher with the 1.7- µm-particle column; the theoretical value is 1.7. As demonstrated in Figures 3a and 3b, the actual benefits that were measured in terms of resolution, speed, and sensitivity agree very well with the theoretical predictions. To test the theoretical improvements under constant L/d p conditions, we used the UPLC instrument to compare columns of dimensions mm (4.8-µm particles) and mm (1.7-µm particles) with the same surface chemistry. The same mixture of caffeine and its metabolites and the identical flow rates used in Figures 3a and 3b were applied to each column (Figures 3c and 3d). The separation time is 8 faster with the 1.7-µm-particle column, compared with a theoretical value of 9. The critical pair (peaks 2 and 3) resolution is the same on the 1.7-µm-particle column, in agreement with theory. The peak height of peak 4 is 2.5 higher with the 1.7-µm-particle column, compared with a theoretical value of 3. As demonstrated in Figures 3c and 3d, the actual benefits that were measured in terms of speed and sensitivity once again agree very well with theory, and equivalent resolution was obtained. Packing materials The key to UPLC is the sub-2-µm porous particles packed inside the columns. Because these particles operate at a higher pressure 464 A ANALYTICAL CHEMISTRY / DECEMBER 1, 2005

6 than conventional HPLC, certain challenges associated with the particles must be addressed in particle design. In the pioneering ultra-high-pressure LC studies, monodisperse, nonporous particles were used (46 48). Failed packing attempts (3 lower efficiency) were also reported with porous particles of a wider d p distribution (49). Scanning electron micrographs of packed capillary columns demonstrated a very tight and ordered bed structure with the uniformly sized nonporous particles. However, columns with porous packing material with a wide size distribution showed extensive nonuniformity (48). Reduced HETP values close to 2 were reported on small, µm-i.d., sub-2-µm-nonporous-particle packed fused silica capillaries under ultra-high-pressure LC conditions with on-column detection (46 49). On the basis of these studies, it was generally assumed that only monodisperse, nonporous particles with d p distributions <5% RSD are suitable to obtain high efficiency under ultrahigh-pressure conditions. These particles not only form a tightly packed bed but also are the strongest among silicabased packing materials. However, they suffer from the major drawbacks of very low loading capacity and high sensitivity to extracolumn contributions because of the low total surface area of the packing material in the column. We designed porous particles with suitable mechanical strength and d p distribution for high-pressure UPLC applications. It is known that the higher the particle density, the greater the mechanical strength of the particles (50). The particle density (often termed apparent density) app is defined as the particle mass over the particle envelope volume by m app = sk = V part 1 TPV in which m sk is the mass of the particle, V part is the envelope volume of the particle, TPV is the total pore volume per unit mass (also called specific pore volume), and sk is the skeleton density of the particle. A skeleton density of 2.20 g/cm 3 for silica and 2.02 g/cm 3 for bridged-ethyl hybrid particles can be used in the calculations (51). The specific pore volume of packing materials with similar skeleton density defines their mechanical strength. Packings with a lower pore volume than that of standard HPLC materials (TPV ~1 cm 3 /g) are preferred for very high pressure applications. The packing material used in UPLC has a TPV = 0.68 cm 3 /g and app = 0.85 g/cm 3. Packed-bed stability is influenced by the mechanical strength of particles. But it also depends on the success of bed consolidation during column packing, which is affected by the d p distribution of the packing material. Material strength and packedbed stability studies similar to those reported in References 41 and 42 were performed. The pressure flow-rate dependence was measured by increasing the pressure and measuring the solvent flow rate through the packed bed (52). After consolidation, the packed-bed stability was established by determining the change in permeability. The permeability of the packed bed is plotted as a function of pressure in Figure 4. The specific permeability K 0 was calculated by using K 0 = F L/r 2 P, in which F is the flow rate (m 3 /s), is the solvent 1 + sk Permeability ( m 2 ) FIGURE 4. Permeability vs pressure. Permeability calculated without any corrections for temperature and pressure effects on viscosity (open squares). Permeability calculated with the effects of average temperature of the column on viscosity taken into account (closed triangles). Permeability calculated with both temperature and pressure effects on the viscosity taken into account (closed diamonds). (a) (b) ,000 15,000 20,000 25,000 30, % % Pressure (psi) FIGURE 5. Alprazolam and d5-alprazolam in rat plasma. (a) UPLC/MS/MS on a 50-mm column packed with 1.7-µm particles. (b) HPLC/MS/MS on a 50-mm column packed with 3.5-µm particles. viscosity (cp), and P is the pressure drop (N/m 2 ) (11). From this graph, we obtain an understanding of the stability of the particles. We can also get information about the influence of pressure and frictional heating on the viscosity of the solvent. We observe that the permeability remains constant (closed diamonds), DECEMBER 1, 2005 / ANALYTICAL CHEMISTRY 465 A

7 100 % an indication that the packing material and the packed bed were stable under the forces applied. The solvent viscosity was used to calculate the permeability, and it was taken into account that solvent viscosity decreases with increasing temperature and increases with increasing pressure. The average temperature of the column at different applied pressures was estimated from the measured outlet solvent temperature, whereas the inlet solvent was at ambient temperature. Because the frictional heat generated in the column is a function of pressure and flow rate, the outlet solvent temperature increases with increasing pressure (the columns were not thermostatted). The average pressure in the column was used to estimate the pressure effect on the solvent viscosity. The viscosity was obtained at the average temperature and pressure of a packed column. The value for viscosity was based on measured and calculated viscosity data published by Kubota et al. and Guiochon et al. (53, 54). Under our experimental conditions, the average solvent viscosity was essentially constant (closed diamonds); thus, pressure and temperature effects cancelled each other out. To illustrate the effect of corrections, we calculated the permeability without any corrections (open squares) and taking into account only the temperature effects on the viscosity (closed triangles); these values are also plotted in Figure 4. Although the overall viscosity does not vary with pressure, this does not imply that the local viscosity of the solvent is constant. Under high-pressure conditions, a more significant axial viscosity gradient is present in columns, compared with HPLC conditions. At the top of the column, the solvent viscosity increases because of the high pressure, whereas a viscosity decrease due to frictional heating occurs at the outlet side. Frictional heat, specifically the radial heterogeneity of frictional heat, influences FIGURE 6. Separation of midazolam metabolites in rat bile HPLC 30-min gradient UPLC 30-min gradient UPLC 6-min gradient (top) HPLC on a 100-mm column packed with 3.5-µm particles with a 30-min gradient. UPLC on a 100-mm column packed with 1.7-µm particles with (middle) a 30-min gradient and (bottom) a 6-min gradient. column efficiency and tailing and ultimately defines the column design. Applications To illustrate the advantages of UPLC, we have applied it to metabolite identification and quantitative bioanalysis. In bioanalysis, the challenges are throughput (hundreds of samples need to be analyzed per week) and sensitivity (the required detection limits are in the picograms-per-milliliter range). For metabolite identification, throughput is less of an issue, but sensitivity and analyte resolution are important in facilitating the detection and characterization of drug metabolites. LC coupled to atmospheric-pressure ionization MS is the method of choice for quantitative bioanalysis. Figures 5a and 5b illustrate that UPLC/MS/MS affords a significant increase in both analysis speed and sensitivity compared with HPLC/MS/MS. The improved sensitivity can be attributed to the increased efficiency of the 1.7- µm particles, which results in significantly narrower peaks, better resolution from endogenous components in the matrix, and less ion suppression. The assay response was linear over the concentration range ng/ml. We performed 1000 injections to determine the robustness of the 1.7-µm particles toward precipitated plasma samples. Peak shape, retention time, and peak area were not significantly changed from the 7th (the first sample after the calibration line) to the 983rd injection. The overall RSD of the alprazolam peak area was 4.4% over the 1000 injections. The accurate detection and characterization of drug metabolites are essential to the pharmaceutical discovery and development process. As with bioanalysis, HPLC coupled to atmosphericpressure ionization MS has become the method of choice for metabolite identification (55). The complex nature of biological matrices such as urine, plasma, and particularly bile makes the resolution and detection of drug metabolites especially difficult because the compounds are extensively metabolized. The data in Figure 6 show the LC/MS analysis of the metabolites of midazolam in rat bile. More and narrower peaks occur in the 30-min UPLC chromatogram than in the 30-min HPLC chromatogram. This is highlighted by the width of the bile acid peaks eluting at 7.62, 12.97, 15.73, 18.54, and min in the HPLC chromatogram; they are wide and dominate the pattern, swamping many of the other peaks. In the UPLC chromatogram, these peaks are much narrower (retention times 7.0, 10.0, 11.5, and 13.0 min), with many other peaks clearly visible. The 6-min UPLC gradient also provides better separation performance than the 30-min HPLC gradient in one-fifth the time. 466 A ANALYTICAL CHEMISTRY / DECEMBER 1, 2005

8 Safety and reliability The higher pressure used with the UPLC system warrants a few comments about the safety and reliability of the instrument. Because this instrument is a commercial product, extensive reliability testing has been performed on all its parts, including the pump seals, the injector, and the fittings. The liquid flow path must comply with the safety standard EN to ensure that it will not break if used above the recommended pressure. This affects specifically the high-pressure side of the pump, the injector, and the fluid connections up to the column inlet, the volume of which is <100 µl. The pressure directive in EN is based on the maximum attainable pressure multiplied by the maximum system volume. The liquid volume, including the entire volume of the largest column, is <0.33 ml, and the maximum use pressure is 100 MPa. Therefore, the system is always below the critical threshold of 200 KPa L specified in the standard (by at least a factor of 6). We recommend following standard laboratory safety practices and wearing safety glasses. Conclusions UPLC is an exciting new area of LC. A natural extension of HPLC, this technique is easy to take full advantage of and requires minimal training. Although we have demonstrated the use of UPLC for reversed-phase separations, we expect that it will also be beneficial in the areas of normal-phase, hydrophilic interaction and ion-exchange chromatographies as well as chiral separation modes. We would like to acknowledge the following individuals from Waters Corp. for their contributions to this article: Eric Grumbach, Kate Yu, Jose Castro- Perez, Jennifer Granger, Susan Serpa, Stephen Shiner, and Yuehong Xu. Jeffrey R. Mazzeo is the director of applied technology, Uwe D. Neue is the director of external research, Marianna Kele is a senior scientist, and Robert S. Plumb is a senior pharmaceutical applications manager at Waters Corp. Mazzeo s research interests include smallparticle chromatography, LC/MS, and their applications. Neue s research focuses on the fundamentals of LC performance, designing stationary phases, and LC applications. Kele s research concentrates on LC fundamentals, UPLC, characterizing and evaluating packing materials, and sub-2-µm packing materials. Plumb s research focuses on small-particle chromatography, metabonomics, and LC/MS. Address correspondence about this article to Mazzeo at jeff_mazzeo@ waters.com. References (1) Moore, J. C. J. Polym. Sci. 1964, A2, (2) Giddings, J. C. Anal. Chem. 1963, 35, (3) Horváth, Cs.; Lipsky, S. R. Nature (London) 1966, 211, (4) Horváth, Cs.; Preiss, B. A.; Lipsky, S. R. Anal. Chem. 1967, 39, (5) Kirkland, J. J. Anal. Chem. 1969, 41, (6) Kirkland, J. J. J. Chromatogr. Sci. 1971, 9, (7) Kirkland, J. J. J. Chromatogr. Sci. 1972, 10, (8) Majors, R. E. Anal. Chem. 1972, 44, (9) Asshauer, J.; Halász, I. J. Chromatogr. Sci. 1974, 12, (10) Endele, R. Ph.D. dissertation, Universität des Saarlandes, Saarbrücken, Germany, (11) Endele, R.; Halász, I.; Unger, K. J. Chromatogr. 1974, 99, (12) Vivilecchia, R. V.; et al. J. Chromatogr. 1974, 99, (13) Halász, I.; Endele, R.; Asshauer, J. J. Chromatogr. 1975, 112, (14) Martin, M.; Eon, C.; Guiochon, G. J. Chromatogr. 1975, 110, (15) Aboul-Enein, H. Y.; et al. J. Liq. Chromatogr. Relat. Technol. 2003, 26 (17), (16) Jemal, M.; et al. Rapid Commun. Mass Spectrom. 2002, 16, (17) Romanyshyn, L.; et al. Rapid Commun. Mass Spectrom. 2001, 15, (18) Opitek, G. J.; Jorgenson, J. W. Anal. Chem. 1997, 69, (19) Murphy, R. E.; Schure, M. R.; Foley, J. P. Anal. Chem. 1998, 70, (20) van der Horst, A.; Schoenmakers, P. J. J. Chromatogr., A 2003, 1000, (21) Liu, H.; et al. J. Chromatogr., B 2002, 782, (22) Plumb, R. S.; et al. Rapid Commun. Mass Spectrom. 2003, 17, (23) Niessen, W. M. A. J. Chromatogr. 2003, 1000, (24) Tiller, P. R.; Romanyshyn, L. A.; Neue, U. D. Anal. Bioanal. Chem. 2003, 377, (25) Thompson, J. D.; Carr, P. W. Anal. Chem. 2002, 74, (26) Thompson, J. D.; Carr, P. W. Anal. Chem. 2002, 74, (27) Kanamori, K.; et al. J. Sep. Sci. 2004, 27, (28) Cabrera, K. J. Sep. Sci. 2004, 27, (29) Armstrong, D. W.; Bertrand, G. L.; Berthod, A. Anal. Chem. 1988, 60, (30) Jorgenson, J. W.; Lukacs, K. D. Anal. Chem. 1981, 53, (31) MacNair, J. E.; Lewis, K. C.; Jorgenson, J. W. Anal. Chem. 1997, 69, (32) MacNair, J. E.; Kamlesh, D. P.; Jorgenson, J. W. Anal. Chem. 1999, 71, (33) Tolley, L.; Jorgenson, J. W.; Moseley, M. A. Anal. Chem. 2001, 73, (34) Mellors, J. S.; Jorgenson, J. W. Anal. Chem. 2004, 76, (35) Giddings, J. C. Anal. Chem. 1964, 36, (36) Giddings, J. C. Anal. Chem. 1965, 37, (37) Giddings, J. C. Sep. Sci. 1966, 1, (38) Bidlingmeyer, B. A.; et al. Sep. Sci. 1969, 4, (39) Bidlingmeyer, B. A.; Rogers, L. B. Sep. Sci. 1972, 7, (40) Prukop, G.; Rogers, L. B. Sep. Sci. Technol. 1978, 13, (41) Swartz, M. LabPlus Int. 2004, 18 (3), 6 9. (42) Knox, J. H.; Saleem, M. J. Chromatogr. Sci. 1969, 7, (43) Martin, M.; Eon, C.; Guiochon, G. J. Chromatogr. 1974, 99, (44) Poppe, H.; Kraak, J. C. J. Chromatogr. 1983, 282, (45) Poppe, H.; et al. Chromatographia 1981, 14, (46) Lippert, J. A.; et al. J. Microcolumn Sep. 1999, 11, (47) Cintron, J. M.; Colon, L. A. Analyst, 2002, 127, (48) Wu, N.; Lippert, J. A.; Lee, M. L. J. Chromatogr., A 2001, 911, (49) Mellors, J. S.; Jorgenson, J. W. Anal. Chem. 2004, 76, (50) Neue, U. D. HPLC Columns: Theory, Technology, and Practice; Wiley-VCH: New York, (51) Wyndham, K. D.; et al. Anal. Chem. 2003, 75, (52) Carman, P. C. Trans. Inst. Chem. Eng. 1937, 15, (53) Kubota, H.; et al. Rev. Phys. Chem. Jpn. 1979, 49, (54) Guiochon, G.; Shirazi, S. G.; Katti, A. M. Fundamentals of Preparative and Nonlinear Chromatography ; Academic Press: Boston, (55) Lee, M. S.; Kerns, E. H. Mass Spectrom. Rev. 1999, 18, DECEMBER 1, 2005 / ANALYTICAL CHEMISTRY 467 A

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