Isocratic and gradient elution chromatography: A comparison in terms of speed, retention reproducibility and quantitation

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1 Journal of Chromatography A, 1109 (2006) Isocratic and gradient elution chromatography: A comparison in terms of speed, retention reproducibility and quantitation Adam P. Schellinger, Peter W. Carr Department of Chemistry, Smith and Kolthoff Halls, University of Minnesota, 207 Pleasant St. S.E., Minneapolis, MN 55455, USA Received 22 August 2005; received in revised form 30 December 2005; accepted 11 January 2006 Available online 3 February 2006 Abstract Chromatographers are cautioned to avoid gradient elution when isocratic elution will do. In this work, we compared the analytical properties of gradient and isocratic separations of a sample which can be done quite readily under isocratic conditions. We found that gradient elution gave a shorter overall analysis with similar resolution of the critical pair compared to isocratic elution without sacrificing repeatability in retention time, peak area and peak height or linearity of the calibration curve. We also obtained acceptable repeatability in peak area/height and linearity of calibrations curves for a sample that required gradient elution using a practical baseline subtraction technique. Based on these results and related work which show that columns can be reequilibrated by flushing with less than two column volumes of the initial eluent, we conclude that many of the reasons given to avoid gradient elution deserve serious reconsideration, especially for those samples which are easily separated isocratically. However, we believe isocratic elution will remain preferable when: (1) the sample contains less than 10 weakly retained components (i.e. the last peak elutes with k < 5) or (2) the gradient baseline impedes trace analysis Elsevier B.V. All rights reserved. Keywords: Gradient elution; Isocratic elution; RPLC method development; Quantitation; Baseline subtraction 1. Introduction After choosing the appropriate column (i.e. stationary phase type and column dimensions) and eluent system (i.e. organic modifier(s) and buffer), the next important step in RPLC method development involves choosing the elution mode (i.e. isocratic elution or gradient elution) that provides an adequate separation within an acceptable analysis time. Dolan has suggested that a standard gradient elution scouting run be done to choose the best elution mode for a specific column, eluent system and sample [1]. He states that samples which occupy less than 20% of the separation space of this scouting run are better separated by isocratic elution; conversely, he advises that samples which occupy more than 40% of the separation space should be done by gradient elution. To a first approximation, these guidelines make sense as gradient elution is required to solve the general elution problem [2]. Corresponding author. Tel.: ; fax: address: carr@chem.umn.edu (P.W. Carr). When the sample occupies between 20 and 40% of the gradient scouting run, most chromatographers still prefer to use isocratic elution based on the criteria listed in Table 1. In terms of finding acceptable separation conditions, the optimization of gradient elution is more complex as more variables influence the selectivity (primarily gradient steepness and initial eluent strength and secondarily dwell volume) compared to isocratic elution [3 7]. Also, the transfer of a gradient elution method between columns, instruments and laboratories is notoriously more difficult than the transfer of an isocratic elution method [8 10]. In terms of separation speed, gradient elution is generally considered to be an inherently slower technique than isocratic elution since a widely accepted rule of thumb indicates that the column should be flushed (i.e. equilibrated) with at least 10 column volumes of initial eluent before reliable retention can be obtained in the next run [11]. Furthermore, many chromatographers have a phobia of ghost peaks [12 18], baseline noise [19 21] and other disturbances (e.g. eluent mixing) [22] associated with gradient elution that can lead to inaccurate values of peak area and peak height and impede quantitation. Also, gradient elution instrumentation is more complex and requires more regular maintenance compared to isocratic elution /$ see front matter 2006 Elsevier B.V. All rights reserved. doi: /j.chroma

2 254 A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) Table 1 Current comparison of gradient and isocratic elution performance a Metric Gradient elution Isocratic elution Small k range (1 < k < 15) ++ Large k range (k max 15) ++ Peak capacity (10 or more solutes) ++ Method transfer ++ Quantitation (baseline disturbance) ++ Reequilibration time ++ Method development + Instrumentation simplicity + a Performance is judged qualitatively as excellent (++), good (+), fair ( ) or poor ( ). instrumentation [23]. The main factors that drive chromatographers to use gradient elution are multi-component samples, e.g. more than 10 components, which span a wide range in retention (k max /k min 15). That is, they seek to use the inherent higher peak capacity of gradient elution [24] to handle more complicated samples or to overcome the general elution problem. In prior work aimed at speeding up gradient elution by reducing the reequilibration time, we developed strategies to achieve very good repeatability (i.e. standard deviation in retention time better than min) and/or full equilibration of the column such that the retention time for all peaks became independent of the reequilibration time [25]. We have shown that excellent repeatability in retention time is possible for a sample of nonionizable solutes, after the column is flushed with only a single column volume of unbuffered initial eluent [25]. In contrast full equilibration with 1 2 column volumes of flushing was only possible when a small amount (1 3%, v/v) of an ancillary solvent (i.e. n-butanol) was added to the eluent [25]. The use of an ancillary solvent, specifically n-propanol, was first suggested by Dorsey [26,27]. Thus, when only 1 2 column volumes of initial eluent are required to reequilibrate the column, the time needed for reequilibration in gradient elution no longer has a big effect on analysis time (i.e. gradient time plus reequilibration time). Consequently, the speed of a well-designed gradient elution separation may become comparable to and could often be better than an isocratic separation. Although recently the speed, schemes for optimization and ease of inter-instrument transfer [28,29] of gradient elution separations have been significantly improved, two important questions remain: (1) do gradient elution methods have any advantages over isocratic elution for samples which are also easily separated isocratically? and (2) to what extent do the putative baseline complexities of gradient elution affect quantification compared to isocratic elution? Isocratic and gradient elution have been compared in terms of bandwidth [30], peak capacity [31] and method development strategies [32]. However, we believe this is the first work which critically compares the advantages and disadvantages of each elution mode for a sample deliberately designed to be easily separated isocratically. Many studies have been performed to address the issue of baseline noise/disturbances in gradient elution chromatography. Obviously, the use of high purity solvents and reagents are required to minimize baseline problems in gradient elution [19,33,34]. Zhu et al. [35] described a way to remove contaminants from water-rich eluents which are a common source of baseline noise [14]. Also, problems with the instrumentation (i.e. poor eluent mixing or leaky valves) or UV detection below or near the UV cut-off of the eluent also leads to baseline noise [20,22]. Further, Berry described the use of Universal Liquid Chromatography to detect many additional components using UV detection between 190 and 210 nm under gradient conditions while minimizing baseline noise and ghost peaks [14,36 40]. Also, Winkler advised using the isobestic phenomenon in acetonitrile water trifluoroacetic acid mixtures to minimize baseline noise and obtain acceptable S/N for proteins and peptides [41,42]. The use of perchloric acid to achieve low ph with a very nearly transparent UV eluent should be considered when mass spectroscopy is not to be done. It is clear that regular instrument maintenance, high quality eluents and the appropriate detection method all influence the magnitude of baseline noise/disturbances under gradient conditions. To further minimize the effect of the baseline on the quantification of analytes under gradient conditions, some investigators have used advanced baseline correction algorithms [21]. Although each of these algorithms has specific advantages and disadvantages (see Ref. [21]), we use a commercially available baseline subtraction method to simplify correction of the baseline. Based on the repeatability in peak area and height, and linearity of calibrations curves as criteria, we critically compare the affect of the baseline on the accuracy of quantification under gradient and isocratic conditions for a sample which is easily separated isocratically. These same criteria are used to determine the affect of the baseline and a practical baseline subtraction technique on the accuracy of quantification for a sample requiring gradient elution. Despite the plethora of ways to minimize baseline noise/disturbances under gradient conditions, the baseline might still be deleterious to trace analytical determinations. However, trace analysis methods often involve a step to enhance the signalto-noise ratio by (1) increasing the sample concentration, (2) derivatizing the solute(s) or (3) improving the sensitivity of the detection method to minimize the adverse affects of the isocratic or gradient baseline on quantitation. Unfortunately, in cases where the quantity of sample is limited, the solute cannot be labeled or the detection method is not adjustable, baseline noise/disturbance under gradient conditions can significantly impede quantitation. Although there are many factors which influence the decision as to whether isocratic or gradient elution will provide the best separation, the main goal of this work is to show that many of the reasons to avoid gradient elution for a sample easily separated isocratically are too conservative. 2. Experimental 2.1. Instrumentation All chromatographic experiments were conducted using an Agilent 1100 chromatograph controlled by version A Chemstation software (Agilent Technologies; Palo Alto, CA). This instrument was equipped with a vacuum degasser, low

3 A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) pressure mixing chamber, autosampler, variable wavelength UV detector and quaternary pump. The intrinsic dwell volume [29] of the instrument including all tubing required to connect the column was determined to be 0.90 ml using the technique found in chapter 8 of Ref. [43] Reagents The organic co-solvents in this study were used as obtained from the manufacturer; acetonitrile was obtained from Burdick and Jackson (Muskegon, MI) and n-butanol was from Fisher (FairLawn, NJ). Trifluoroacetic acid (TFA; 99% purity) was from Sigma-Aldrich (St. Louis, MO). HPLC grade water was obtained in-house from a Barnstead Nanopure Deionizing system (Dubuque, IA). This water was boiled to remove carbon dioxide and cooled to room temperature before use. All eluents were prepared gravimetrically (±0.01 g) based on the density (at 25 C) of acetonitrile, n-butanol, water and trifluoroacetic acid [44] where eluent composition is reported as the v/v ratio. The eluents were stirred magnetically until they reached room temperature. All eluents were passed through a 0.45 m nylon filtration apparatus (Lida Manufacturing Inc.; Kenosha, WI) immediately before use. Uracil, acetophenone, butyrophenone, valerophenone, hexanophenone, 1-(diphenylmethyl)-4-methylpiperazine, alprenolol, perphenazine, promethazine, amitriptyline, phenol, methylbenzoate, chlorpheniramine, meclizine, methapyrilene, nitroethane, pheniramine and thioridazine were of reagent grade or better and were used as obtained from Aldrich without further purification. These solutes were used to make two stock solutions in 100 ml volumetric flasks; all volumetric glassware used was class A. The first stock solution contained approximately 50 g/ml uracil, 150 g/ml acetophenone and 300 g/ml of 1-(diphenylmethyl)-4-methylpiperazine, alprenolol, perphenazine, promethazine, amitriptyline, phenol and methylbenzoate dissolved in a 1/20/78.9/0.1 (v/v/v/v) n-butanol, acetonitrile, water and trifluoroacetic acid (TFA) eluent. The second stock solution contained approximately 150 g/ml of acetophenone, butyrophenone, valerophenone and hexanophenone, 50 g/ml of uracil and 500 g/ml of alprenolol, amitriptyline, phenol, chlorpheniramine, meclizine, methapyrilene, nitroethane, pheniramine and thioridazine dissolved in a 1/10/78.9/0.1 (v/v/v/v) n-butanol, acetonitrile, water and TFA eluent. The mass of each solute was recorded to ± g Calibration curves To generate calibration curves of peak area and peak height versus the mass of solute injected, we diluted the stock solutions by adding 10 ml of a stock solution (using a 10 ml volumetric pipette) to 25, 50, 100, 200, 250 and 500 ml volumetric flasks. Data was collected by injecting 2 L of each solution in order from lowest to highest concentration. A blank run (i.e. the method was run without injecting a sample) was performed before the first injection. This set of injections was repeated three more times performing only one blank run between each set of injections. Thus, four injections of each solution were made using a specific mode of elution (isocratic or gradient elution) and wavelength of detection (214 or 254 nm). We also varied the injection volume (from 0.5, 1.0, 2.0, 3.0, 5.0, 7.5 and 10.0 L) of one solution (the ml dilution of stock solution) to generate calibration curves. Again, four replicates at each injection volume were obtained using a specific elution mode and detection wavelength Column A5cm 4.6 mm i.d. column with 5 m Zorbax SB-C 18 particles and pore size of 80 Å was used throughout this study. The particles were a gift from Agilent Technologies. The stainless steel column hardware was obtained from Isolation Technologies (Hopedale, MA). The SB-C 18 particles were slurried in 2-propanol and sonicated (model PC3, L&R Manufacturing, Kearny, NJ) for 20 min before packing. The column was packed using the downward slurry method technique at a packing pressure of 35 MPa using pure 2-propanol as the driving solvent and a Haskel high-pressure pump (Haskel International Inc.; Costa Mesa, CA) Data analysis Data analysis was performed as described in Ref. [25] Baseline subtraction For sample 2 peak area and height were obtained by subtracting baseline noise/disturbances contained in the blank runs from the experimental gradient elution chromatograms with Chemstation software. Peak area and peak height were obtained directly from the experimental chromatograms for sample Results/discussion 3.1. Gradient elution scouting runs For this study, we used standard gradient elution scouting runs and the current method development guidelines suggested by Dolan [1] to determine which elution mode was best suited for the samples. With a column volume of roughly 0.6 ml and a flow rate of 1 ml/min; Dolan recommends a routine linear gradient elution scouting run from nearly 100% water to nearly 100% acetonitrile in 18 min. After performing the scouting runs, we calculated the range in retention of the solutes divided by the gradient time to be 0.27 for sample 1 (see Fig. 1) and 0.60 for sample 2 (see Fig. 2). According to Dolan s guidelines, sample 1 falls in the grey area where either elution method can provide an acceptable separation. However, if one ignores the earliest solute, which is very well separated from other components in the mixture, this sample only occupies 20% of the separation space and isocratic elution is definitely the preferred mode by conventional wisdom. For sample 2, we are confident that gradient elution is required as this sample occupies 60% of the separation space in the gradient scouting run.

4 256 A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) Fig. 1. Gradient elution scouting run for sample 1. Conditions: 5 cm 4.6 mm column with 5 m SB-C 18 particles; 25 C; 1 ml/min; 254 nm detection; 1 L injection of the stock solution of sample 1; eluent A: 1/98.9/0.1 (v/v/v) n-butanol/water/trifluoroacetic acid; eluent B: 1/98.9/0.1 (v/v/v) n- butanol/acetonitrile/trifluoroacetic acid; 100/0 to 0/100 A/B to 100/0 in 18 and 0.01 min; hold at 100/0 A/B for 7 min Locating acceptable isocratic and gradient elution separation conditions for a sample easily separated with isocratic elution To simplify the method development process, we decided to use a fixed column format (i.e. the column dimensions and particle type were not varied), a fixed flow rate (2 ml/min) and a fixed eluent system (i.e. various amounts of acetonitrile/water containing a constant amount of n-butanol (1%, v/v) and trifluoroacetic acid (0.1%, v/v) for both the isocratic and gradient separations. We believe that holding the column, eluent system and flow rate constant allows for a fair comparison of the analytical aspects of isocratic and gradient elution. Also, we wanted to avoid an exhaustive search for the optimum stationary phase type and eluent system requiring a staggering number of training runs. Clearly, finding the true global optimum is a rarity in chromatography and the effort is not justified in most practical work. However, we grant that our conclusions might change if the flow rate, column dimensions and Fig. 2. Gradient elution scouting run for sample 2. The conditions are described in Fig. 1. Fig. 3. Isocratic retention data for components in sample 1 vs. the volume fraction of acetonitrile in the eluent. The acetonitrile water eluent also contained n-butanol and trifluoroacetic acid at constant volume percents of 1% and 0.1%, respectively. The ln k data shown was obtained at 15 C. The symbols and lines represent phenol ( ), alprenolol ( ), perphenazine ( ), methylbenzoate ( ), 1-(diphenylmethyl)-4-methylpiperazine ( ), acetophenone ( ), promethazine ( ) and amitriptyline ( ). particle size were to be optimized for each of the two elution modes. Overall, we performed nine isocratic experiments (i.e. training runs) using three different eluent compositions at three different temperatures to predict retention as a function of eluent strength and column temperature. In principle one needs only four runs to obtain the essential data to predict retention as a function of eluent and temperature. We did nine training runs to obtain some idea of the goodness of fit of the model to the data. We assumed that linear solvent strength theory (i.e. LSST, see Eq. (1)) is accurate where S is the slope of ln k (isocratic retention factor) versus ln k = ln k w Sφ (1) φ and ln k w is the solute s retention at φ = 0. Although there is some curvature in the LSST plots (see Fig. 3), we assumed a straight line and used first order least squares regressions to obtain S and ln k w for each solute. To predict retention as a function of column temperature, we generated plots of S and ln k w as a function of temperature (see Fig. 4). We then generated fits of the LSST parameters for each solute as a function of temperature using the Pade approximation (see Eq. (2)) where T is the LSST parameter = A + BT 1 + CT column temperature (in K) and A, B and C are dependent on the solute. Choosing the appropriate gradient elution training runs is more complicated as five parameters (initial and final eluent strength, temperature, dwell volume and gradient time) affect the selectivity. However, the gradient scouting run provides an estimate of acceptable initial and final eluent strengths. Also, (2)

5 A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) Fig. 4. Isocratic data for the dependence of ln k w and S values on column temperature. The symbols and lines represent the same solutes as described in Fig. 3. Fig. 5. Gradient data for the dependence of ln k w and S values on column temperature. The symbols and lines represent the same solutes as described in Fig. 3. the effect of dwell volume on the selectivity is easily modeled once we can predict gradient elution retention as a function of eluent strength and column temperature. Thus, we only need to extract the gradient LSST parameters as a function of column temperature to locate suitable gradient elution separation conditions. To obtain the gradient S and ln k w values at one temperature, we choose appropriate initial and final eluent strengths, held the dwell volume constant and performed separations at three different gradient times. We then used the Solver function in Excel to obtain the gradient LSST parameters by minimizing the sum of the squares of the residuals of t R, predicted against the experimental values (i.e. n i=1 (t R, predicted t R, experimental ) 2 i ). We fit the gradient S and ln k w values for each solute as a function of temperature (see Fig. 5) using the Pade approximation (see Eq. (2)). Thus, method development for the isocratic and gradient elution separations was done as similarly as possible. We first used Drylab 2000 Plus to locate reasonable values of eluent strength and column temperature in isocratic elution. Drylab creates a map of the critical pair resolution (i.e. resolution of the worst separated pair of peaks) versus the eluent strength and column temperature (see Fig. 6). From this plot, the best separation conditions appeared to be at the highest critical pair resolution (i.e. column temperature (T) of 30 C and eluent strength of 1/21/77.9/0.1 (v/v/v/v) n-butanol/acetonitrile/water/trifluoroacetic acid. However, this separation would take quite a long time and the last peak Fig. 6. Plot of the isocratic critical pair resolution of sample 1 as a function of the volume fraction of acetonitrile in the eluent and column temperature. The training runs used to generate Fig. 4 were input into Drylab 2000 Plus to obtain this plot. The numbers in the legend represent the critical pair resolution; thus, the colors black, blue, yellow and orange correspond to critical pair resolutions of 0, 1, 2, 3, and 4, respectively.

6 258 A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) would have k 15. We are interested in a locating separation conditions providing reasonably robust resolution (i.e. R s, critical pair 2) in a short analysis time. Thus, a more efficient way to choose adequate separation conditions is to plot R s, critical pair divided by the time between two successive injections as a function of the eluent strength or column temperature. To make plots of the ratio of R s, critical pair /analysis time versus eluent strength or column temperature under isocratic conditions, we used an Excel-based Monte Carlo search procedure that simultaneously varied the eluent strength (from 1/10/88.9/0.1 to 1/35/63.9/0.1 (v/v/v/v) n- butanol/acetonitrile/water/trifluoroacetic acid) and the column temperature (between 15 and 45 C) to randomly generate 15,000 separation conditions. This is clearly vast overkill but certainly insures that we find the optimum conditions. We then deleted those conditions that did not give reasonable resolution of the critical pair (i.e. R s, critical pair < 1.5); all situations provided tolerable back pressures (i.e. P < 38 MPa). We caution that acceptable situations under conditions outside the training data range may be erroneous due to extrapolation errors. Next, we made plots of R s, critical pair /analysis time as a function of eluent strength and column temperature (see Fig. 7). The regions of space in Fig. 7 (and Fig. 8, see below) which appear to be missing data correspond to conditions which do not satisfy the separation goals. After careful examination of Figs. 6 and 7, it is evident that the best isocratic elution separation is possible at a temperature of 25 C and eluent strength of 1/31/67.9/0.1 (v/v/v/v) n- butanol/acetonitrile/water/trifluoroacetic acid. Although Fig. 7 shows that a higher ratio of R s, critical pair /analysis time is possible at lower temperatures, we choose 25 C as this temperature appeared to provide a more robust separation (i.e. many acceptable situations were generated around this as compared to lower temperatures). Furthermore, the R s, critical pair at 25 C is acceptable (i.e. >2) and it gives a faster analysis time compared to separations at lower temperatures. To find acceptable gradient separation conditions for the same sample we used our Monte Carlo search program to simultaneously vary gradient time (between 0.1 and 60 min), column temperature (between 15 and 35 C), the initial and final eluent strength (from 1/0/98.9/0.1 to 1/35/63.9/0.1 (v/v/v/v) and 1/20/78.9/0.1 to 1/60/38.9/0.1 (v/v/v/v) n- butanol/acetonitrile/water/trifluoroacetic acid, respectively) and the effective dwell volume [29] (between 0 and 5 ml) to generate 15,000 conditions. After removing those that did not meet our separation goals (i.e. R s, critical pair > 1.5 and P < 380 bar), we generated plots of R s, critical pair /analysis time as a function of the initial eluent strength and column temperature (see Fig. 8). Again, we caution that acceptable separations predicted by extrapolation outside the gradient training runs should not be trusted. Examining Fig. 8, the best separation conditions appear to be at a column temperature of 25 C and initial eluent strength of 1/31/64.9/0.1 (v/v/v/v) n-butanol/acetonitrile/water/trifluoroacetic acid. Examination of the acceptable gradient elution situations showed an effective dwell volume of 0.90 ml [29], final eluent strength of 1/42/56.9/0.1 (v/v/v/v) n- butanol/acetonitrile/water/trifluoroacetic acid and a gradient time of 2 min give a very similar R s, critical pair and shorter analysis time compared to the best isocratic elution separation. Given the narrow optimum range in the initial eluent composition and other variables (see Fig. 8) we could have gone on to a second round of searching over a narrower set of conditions. For example we could have searched over the range: gradient time (1 10 min), column temperature (17 37 C), the initial and final eluent strength (1/25/73.9/0.1 to 1/35/63.9/0.1 and 1/30/68.9/0.1 to 1/50/48.9/0.1 (v/v/v/v) n- butanol/acetonitrile/water/trifluoroacetic acid, respectively) and the effective dwell volume ( ml). Assuming that a resolution of 1 min, 2 C, 0.02, and 0.5 ml in gradient time, temperature, eluent strengths and effective dwell volume, respectively, is required to perform a reasonable grid search, one would have to generate 21,780 conditions. Although the number of conditions needed for a systematic grid search is similar to that used in our random search (i.e. 15,000), we found that as few as 500 randomly generated conditions over the full multidimensional Fig. 7. Ratio of critical pair resolution divided by the analysis time versus the volume fraction of acetonitrile in the eluent and column temperature for the isocratic separation of sample 1. The Monte Carlo search program described in the text was used to generate the data for these plots.

7 A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) Fig. 8. Ratio of critical pair resolution divided by the analysis time vs. the volume fraction of acetonitrile in the initial eluent and column temperature for the gradient separation of sample 1. Other details are described in Fig. 7. space repeatedly found conditions which gave results within 5% of the optimum resolution per unit time revealed by either full search. Clearly, it is improbable that the resolution of a systematic search limited to only 500 possible sets of conditions would find such a narrowly defined optimum in this five-dimensional space. Thus, the Monte Carlo method provides a simple but effective way to locate reasonable gradient conditions. Future work will more thoroughly investigate the use of Monte Carlo search schemes in chromatographic optimization Comparison of the isocratic and gradient elution separations for a sample easily separated by isocratic elution We performed the separations outlined above and obtained the isocratic and gradient chromatograms shown in Fig. 9. The isocratic separation is acceptable as phenol (i.e. the first peak after the dead time) is well retained (k 2), the last peak has reasonable retention (k 14), and the critical pair resolution is However, the gradient separation requires less time while giving virtually the same critical pair resolution (1.90) within experimental error. The gradient elution analysis time was only 3.4 min (2.4 min run time and 1 min instrument cycle time (i.e. data analysis and injection time) whereas the isocratic elution analysis time required 5 min at the same flow rate. The experimental values of R s, critical pair /analysis time in each elution mode are higher than predicted for both elution modes (0.42 and 0.56 for isocratic and gradient elution, respectively) due to a conservative estimate of the plate count. Theoretically, increasing the gradient time from 2.0 min to 2.2 min would improve the gradient critical pair resolution to the value obtained in isocratic elution. Thus, gradient elution clearly provides a faster separation and similar critical pair resolution compared to isocratic elution for a sample that is easily separated isocratically. Another advantage of separating sample 1 by gradient elution is that the peak widths of the later eluting peaks are significantly narrower compared to isocratic elution (see Figs. 9 and 10). Specifically, the peak width of amitriptyline is almost three times less in gradient elution. Also, the peak width in gradient elution Fig. 9. Optimized isocratic (A) and gradient (B) elution separations for sample 1. Conditions: Eluent A: 1/31/67.9/0.1 (v/v/v/v) n-butanol/acetonitrile/ water/trifluoroacetic acid; Eluent B: 1/60/38.9/0.1 (v/v/v/v) n-butanol/ acetonitrile/water/trifluoroacetic acid; detection at 254 nm; 2 ml/min flow rate; 2 L injection of stock solution diluted ml; 25 C. (A) 100/0 A/B and run ended at 4.0 min; critical pair: 3, 4. (B) 100/0 to 60/40 to 100/0 A/B in 2 and 0.01 min and the run was ended at 2.4 min; critical pair: 8, 9. Solutes: uracil (1), phenol (2), 1-(diphenylmethyl)-4-methylpiperazine (3), alprenolol (4), perphenazine (5), acetophenone (6), promethazine (7), methylbenzoate (8) and amitriptyline (9).

8 260 A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) Fig. 10. Comparison of the peak width obtained in isocratic and gradient elution versus retention time. The minimum value of the peak width at half height obtained in isocratic ( ) and gradient ( ) elution from all runs performed at 214 and 254 nm was used to generate this plot. remains almost constant for all solutes eluting after 1 min as these analytes have a similar effective retention factor (k * ) [45]. Thus, gradient elution helps provide narrower peak widths which do not increase as a function of retention time as observed in isocratic elution. At a flow rate of 2 ml/min, the instrument requires approximately 1.2 min to flush 99% of the final eluent from the pumping system [25]. Thus, the column inlet was flushed with less than a column volume of initial eluent before the next gradient analysis was begun. Although this condition does not give full equilibration as defined in our earlier work [25], in practice one only needs to achieve acceptable repeatability in retention time [25]. Therefore, we compared the repeatability of retention time in isocratic and gradient elution (see Fig. 11). Even with minimal reequilibration of the column, gradient elution and isocratic elution provide similar and acceptable repeatability (see Fig. 11) and % RSD (data not shown) in retention time. It is important to realize that the addition of n-butanol to the eluent is not required to obtain acceptable repeatability in gradient elution [25]. Also, the addition of a fixed amount of n-butanol to the initial and final eluents does change the selectivity and increases the eluent Fig. 11. Repeatability of retention time in isocratic and gradient elution. The median value of the repeatability (n = 4) obtained in isocratic ( ) and gradient ( ) elution for all runs performed at 214 and 254 nm was used to generate this plot. The solutes are defined in Fig. 9. Fig. 12. Overlay of four blanks runs at 254 nm and 214 nm using the conditions described in Fig. 9B. strength. The increased strength of the initial eluent decreases the gradient range (i.e. an initial eluent strength of pure water is no longer possible). Therefore, we urge that when an ancillary solvent such as n-butanol is needed that it be used from the outset. It is really only needed when fast, full equilibration of the column is desired [25]. We then compared the accuracy and precision of quantitation in each elution mode. To investigate the degree of baseline noise and disturbances in gradient elution, we overlaid repeated baselines from the blank runs (i.e. no sample was injected) performed at 214 and 254 nm (see Fig. 12). Obviously, the baseline change with time is smaller in magnitude and more repeatable at 254 nm than at 214 nm. Also, the only region where baseline reproducibility is poor in gradient elution is between injection and elution of uracil; this is where there is no separation possible and thus no useful information can be collected. For practical purposes, we believe that the gradient baselines are highly repeatable under the conditions used for sample 1. Furthermore, the results in Fig. 12 suggest that one can minimize baseline disturbances due to the eluent components by collecting data at 254 nm or another wavelength where an acceptable signal-tonoise ratio is obtained. To further investigate the accuracy of quantitation, we compared the repeatability in peak area and peak height. All peak areas and peak heights were obtained directly from the experimental chromatograms (i.e. no baseline subtraction was performed). To account for run-to-run variations in the volume of sample injected, we divided the peak area (or height) of each solute by that of amitriptyline. Fig. 13 (note both axes

9 A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) Fig. 13. Peak area and height repeatability as a function of the amount of sample 1 injected. The repeatability is the % RSD (n = 4) in the peak area or peak height ratio (i.e. peak area or height of the solute divided by the peak area or peak height of amitriptyline, respectively). The median repeatability of all solutes except amitriptyline was used to generate these plots. When varying the amount of sample injected, we either made 2 L injections of various dilutions of the stock solution or varied the injection volume of one solution (the ml dilution of the stock solution). The symbols and lines represent isocratic elution at 214 nm ( ), gradient elution at 214 nm ( ), isocratic elution at 254 nm ( ) and gradient elution at 254 nm ( ). Other conditions are described in Fig. 9. are logarithmic) compares the repeatability for both calibration methods used (see Section 2.3). In every case, the repeatabilities in both area and height ratios in gradient elution are similar to those observed in isocratic elution. Furthermore, Fig. 13 indicates that the best way to improve the repeatability in peak area and peak height is to inject more of the sample (i.e. mass or volume). Unfortunately, column overload (i.e. peak tailing) will increase the peak width to a similar extent in each elution mode as more mass is injected [43]. The linearity of plots of area versus the amount of solute injected was compared via the correlation coefficient (see Table 2) and the precision in the slope (see Table 3). Table 2 shows that isocratic and gradient elution provide similar and acceptable correlation in calibration curves of peak area versus solute mass for all peaks in sample 1. Table 3 shows similar precision in the slope of the peak area calibration curves for isocratic and gradient elution. Also, comparable trends in the correlation coefficient and precision of the calibration curve slope are obtained for calibration curves generated using the peak height (data not shown). Overall, the accuracy of quantitation in gradient elution does not appear to be any worse than isocratic elution for sample Revised RPLC method development guidelines Considering that sample 1 is somewhat better and more quickly separated using the gradient elution method whereas the current guidelines clearly indicate that it should be done by isocratic elution suggest that the current RPLC guidelines should be revised [1]. We advise that isocratic elution is the best choice for samples less than only 10%, not 20%, of the separation space of the gradient scouting run and for samples containing solutes that span a very narrow range in retention (i.e. k max < 5). However, samples occupying more than 10% but less than 20% of the separation space are equally well and probably better separated with gradient elution. The final choice depends not only on the sample and chromatographic conditions, but also on the goals of the chromatographer and available resources (i.e. instrumentation and optimization/computer simulation programs). However, we have shown here that many of the reasons why gradient elution is avoided, most especially the presumed longer analysis time (i.e. slower sample through-put) and retention reproducibility, should be seriously reconsidered.

10 262 A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) Table 2 Linearity a of the peak area calibration curves for sample 1 b Solute 214 nm 254 nm Injector Solution Injector Solution Gradient Isocratic Gradient Isocratic Gradient Isocratic Gradient Isocratic 1-(Diphenylmethyl)-4-methylpiperazine Acetophenone Alprenolol Amitriptyline Methylbenzoate Perphenazine Phenol Promethazine Average Median a Linearity is reported as (1 R 2 ) 1000 where R 2 is the correlation coefficient. b Calibration curves generated by varying the injection volume used n = 26 data points; calibration curves generated by varying the solution concentration used n = 30 data points (see Section 2.3). Table 3 Precision a in the peak area calibration curve slope for sample 1 b Solute 214 nm 254 nm Injector Solution Injector Solution Gradient Isocratic Gradient Isocratic Gradient Isocratic Gradient Isocratic 1-(Diphenylmethyl)-4-methylpiperazine Acetophenone Alprenolol Amitriptyline Methylbenzoate Perphenazine Phenol Promethazine Average Median a The precision was calculated by multiplying the standard error in the slope by 100% and then dividing by the slope. b Calibration curves were generated as described in Table 2. Table 4 Linearity of the peak area and peak height calibration curves for sample 2 a Solute Peak area Peak height 214 nm 254 nm 214 nm 254 nm Injector Solution Injector Solution Injector Solution Injector Solution Phenol Pheniramine Methapyrilene Chlorpheniramine Nitroethane Alprenolol Acetophenone Amitriptyline Thioridazine Butryophenone Meclizine Valerophenone Hexanophenone Average Median a The definition of linearity and method for generating the calibration curves are described in Table 2.

11 Table 5 Precision a in the peak area and peak height calibration curve slope for sample 2 b A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) Solute Peak area Peak height 214 nm 254 nm 214 nm 254 nm Injector Solution Injector Solution Injector Solution Injector Solution Phenol Pheniramine Methapyrilene Chlorpheniramine Nitroethane Alprenolol Acetophenone Amitriptyline Thioridazine Butryophenone Meclizine Valerophenone Hexanophenone Average Median a The precision was calculated as described in Table 3. b Calibration curves were generated as described in Table Robustness of a gradient elution separation for a sample requiring gradient elution Gradient elution clearly gave a better separation than isocratic elution for sample 1. However, in this case the gradient required only a relatively small range in eluent strength which helped minimize baseline disturbances. When a sample contains solutes that span a wider retention range, such as sample 2, a larger range in eluent strength is required to provide an acceptable gradient separation. In this case, we expect that the repeatability in peak height or peak area along with the linearity of the calibration curves will worsen, mainly due to increased baseline disturbances. Thus, we investigated the accuracy of quantification for the gradient separation of sample 2. Fig. 14 shows the gradient elution separation of this sample. We used a conventional baseline subtraction technique to correct the baseline of the experimental chromatograms. Although the blank and experimental runs were performed as much as 80 min apart, Fig. 14 shows that baseline subtraction provides a chromatogram with only minor baseline disturbances. This baseline-corrected chromatogram allowed us to obtain peak area/height values automatically without manual integration or a tedious search for appropriate integration parameters. The repeatabilities in area and height after baseline subtraction are given in Fig. 15. Clearly they are both worse than those obtained in the isocratic and gradient elution separations of sample 1 (see Fig. 13). We attribute most of the decrease in precision to the increased baseline disturbances resulting from the larger range in eluent strength (see Fig. 16); the reproducibility of the baseline is acceptable but slight changes in the baseline from run-to-run do affect the accuracy of the baseline subtraction technique. Overall, the repeatabilities in area and height were no worse than 2% RSD when reasonable amounts of sample 2 were injected; in most cases, the precision in the area and height was better than 1% RSD. We calculated the correlation coefficient (see Table 4) and precision of the slope (see Table 5) for the area and height calibration curves. Again, we believe that baseline disturbances (see Fig. 16) contribute to the lower correlation coefficients and Fig. 14. Gradient elution separation of sample 2 before (A) and after (B) subtracting the baseline from the experimental chromatogram (i.e. A). Conditions: Eluent A: 1/10/88.9/0.1 (v/v/v/v) n-butanol/acetonitrile/water/trifluoroacetic acid; Eluent B: 1/90/8.9/0.1 (v/v/v/v) n-butanol/acetonitrile/water/ trifluoroacetic acid; 100/0 to 0/100 to 100/0 A/B in 5 min and 0.01 min; run ended at 8 min; detection at 254 nm; 2 ml/min flow rate; 2 L injection of stock solution diluted ml; 25 C.

12 264 A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) Fig. 15. Peak area and height repeatability as a function of the amount of sample 2 injected. The repeatability in the peak height and peak area ratios was calculated as described in Fig. 13. The symbols and lines represent detection wavelengths of 214 nm ( ) or 254 nm ( ); other conditions are described in Fig. 14. poorer precision, especially at 214 nm, compared to the values obtained for sample 1. However, the correlation coefficients for many of the solutes are still acceptable. Furthermore, the solutes that have relatively low correlation coefficients (R 2 < 0.999) or relatively poor precision in the calibration curve slope (% RSD slope > 0.30) are located in sections of the chromatogram where baseline disturbances are large or the repeatability of the baseline (see Fig. 16) is poor. Although baseline subtraction offers a reasonable way to account for baseline disturbances for the majority of the solutes in sample 2, this technique is not practical for all methods as additional analysis time is required and sample carry-over might be problematic. One way to avoid baseline subtraction and reduce the effect of baseline disturbances is to use a wavelength or detection method which is insensitive to components of the eluent but provides an acceptable signal-tonoise ratio for the analytes. For example, working at 254 nm compared to 214 nm significantly reduces the magnitude of the baseline disturbances while simultaneously improving the repeatability of the baseline (see Fig. 16). We also strongly advise the use of dilute perchloric acid (10 mm) instead of 0.1% TFA when mass spectrometry is not to be done and a low detection wavelength is required. Perchlorate is virtually transparent even at 210 nm. It is a stronger ion pairing agent than TFA [46 50] thus requiring a bit higher initial eluent strength. Fig. 16. Overlay of eight blanks runs (i.e. no injection made) at 254 and 214 nm using the conditions described in Fig. 14.

13 A.P. Schellinger, P.W. Carr / J. Chromatogr. A 1109 (2006) Conclusions Many of the reasons for avoiding gradient elution listed in Table 1 have been addressed for a sample which contains solutes that are easily separated isocratically. For this sample, gradient elution provides an overall faster analysis, narrower peaks and similar resolution of the critical pair compared to isocratic elution without loss in repeatability of retention time, peak area, peak height, or linearity of the calibration curve. While the results were obtained with only a single sample we believe that most of the findings especially those concerning peak width and detection are general and will hold up for many samples. It is our belief that the fact that because gradient elution inherently involves more parameters that impact selectivity (gradient steepness > initial solvent composition > dwell volume) as compared to isocratic composition (eluent strength) that gradient elution will generally be able to provide better selectivity. In combination with the inherently narrower peak width for later eluting species we infer that resolution in gradient elution will rather generally, certainly not invariably, exceed that of isocratic elution. Furthermore, when gradient reequilibration time is short, say 1 2 column volumes, the overall time from injection to injection will probably be less than that for isocratic elution because we can trade higher resolution for shorter analysis time. Also, we found that a simple random search algorithm is a very efficient way to locate acceptable gradient conditions when a large multidimensional space is searched. Thus, many of the previous reasons for avoiding gradient elution (i.e. long reequilibration times, poor precision and difficult optimization) appear much too pessimistic. We are currently studying additional samples. For sample 2, which required a wide range gradient, we have shown that simple baseline subtraction is a convenient way to obtain acceptable quantitative precision (i.e. linearity of a calibration curve and repeatability of peak area and peak height). However, more advanced detection methods or baseline subtraction algorithms [21] may be needed to improve precision to better than 1% RSD and eliminate the need for numerous blank runs. Based on these findings, we have moderately relaxed the RPLC method development guidelines suggested by Dolan [1]. For example, isocratic elution appears more preferable when the sample occupies less than 10%, not the previously recommended 20%, of the separation space of the standard gradient scouting run. Alternatively, isocratic elution is preferred for simple samples (i.e. less than 10 components) where the last peak elutes at k less than 5. Samples occupying more than 40% of the separation space certainly require gradient elution. However, for samples occupying between 10 and 40% of the separation space, either elution technique could be used but the only pragmatic reasons to avoid gradient elution is that gradient elution instrumentation is not available or the gradient baseline limits trace analysis. Acknowledgements The authors acknowledge financial support from the National Institutes of Health (grant # 5R01GM ). We also wish to recognize the impact of two very perceptive reviewers whose comments greatly benefited the final manuscript. References [1] J.W. Dolan, LC GC 13 (2000) 388. [2] L.R. Snyder, Gas chromatography, in: Proceedings of the International Symposium on Gas Chromatography (Europe), vol. 8, 1971, p. 81. [3] M.A. Stadalius, M.A. Quarry, L.R. Snyder, J. 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