Introduction to Modern Liquid Chromatography, Third Edition part 49 ppsx

436 GRADIENT ELUTION Developing a Gradient (or Isocratic) Separation 1. Review sample composition (Section 6.4) 2. Define separation goals (Section 6.4) 3. Initial experiment (Section 9.3.1) 4. Optimize k* (Section 9.3.2) 7. Optimize N* (Section 9.3.6) 6. Adjust gradient range and shape (Sections 9.3.4, 9.3.5) 8. Determine column equilibration time (Section 9.3.7) Prep-LC (Chapter 15) Isocratic? (Chapters 6-8) Bio sample (Chapter 13) Enantiomers (Chapter 14) Gradient? 5. Optimize a* (Section 9.3.3) Figure 9.14 Plan for gradient method development. • carrying out method validation and developing a system suitability test at the end of method development (Chapter 12) • developing an orthogonal method to ensure that all peaks of interest have been included in the primary assay procedure (Section 6.3.6.2; [27]) The method-development requirements above are the same as discussed in Section 6.4 for isocratic separation, so we will not consider them further in this chapter. The main differences between gradient and isocratic method development are in 9.3 METHOD DEVELOPMENT 437 the experiments used to arrive at a final separation (steps 3–8 of Table 9.2 and Fig. 9.14). 9.3.1 Initial Gradient Separation (Step 3 of Table 9.2) Ideally a full-range gradient (0–100% B) is preferred for the initial experiment; if the sample contain acids or bases, the A-solvent should contain a buffer (Section 7.2). However, initiating the gradient at 0% B can create problems for some columns, due to nonwetting of the stationary phase by organic-free water (Section 5.3.2.3; see also [28, 29]). For this reason it is better to initiate the gradient at 5% B or higher, unless it is known that the column can tolerate a totally aqueous mobile phase (0% B), or column pressure can be continuously maintained after an initial wetting of the column with 100% B. Problems with stationary-phase wetting are more likely for heavily bonded C 18 columns (larger H; Section 5.4.1) than for columns that are lightly bonded, contain embedded polar groups, or are end-capped with polar groups (stationary-phase de-wetting can be avoided for most columns by following the protocol of Section 5.3.2.3). If buffer solubility is limited for 100% ACN (at the end of a 5–100% ACN gradient), the final-%B of the gradient may need to be lowered or the buffer concentration reduced. However, when the buffer is added only to the A-solvent (the usual case), buffer precipitation may not be a problem. See Section 7.2.1.2 for further details on buffer solubility. 9.3.1.1 Choosing between Isocratic and Gradient Elution The first gradient run is important as a means of (1) assessing the likely difficulty of method development and (2) planning further experiments. Table 9.3 recommends specific starting conditions: 5–100% ACN/buffer (or water) in 10 min, a 100 × 4.6-mm, 3-μmC 8 or C 18 column, 30 or 35 ◦ C, and 2.0 mL/min. These conditions should result in an average value of k ∗ ≈ 5 for the separation (Eq. 9.5) that is large enough to provide acceptable average resolution, while restricting the pressure drop to ≈ 2500 psi. Other column configurations and flow rates are also acceptable (e.g., 150 × 4.6-mm, 5-μm column, 1–2 mL/min), as long as acceptable values of k ∗ and pressure are maintained. Equation (2.13a) can be used to estimate the column pressure; in gradient elution, the maximum pressure during the run is determined by the maximum mobile-phase viscosity—see Table I.5 of Appendix I. The gradient time t G can be varied to maintain a value of k ∗ ≈ 5, t G = 1.15k ∗ V m ΔφS F (9.17) or for k ∗ = 5andS = 4, t G = 23V m Δφ F (9.17a) For example, a 100 × 4.6-mm, 3-μm column (V m ≈ 1.0 mL) with acetonitrile as the B-solvent, a temperature of 30 ◦ C, and a flow rate of 2.0 mL/min should have a pressure of ≈ 2500 psi; a value of k ∗ ≈ 5 would require a gradient time of (23 × 1.5 × 0.95/2), or 11 minutes. Smaller diameter columns with flow rates reduced in proportion to the square of column-diameter are another option. 438 GRADIENT ELUTION Table 9.3 Preferred Conditions for the Initial Experiment in Gradient Method Development (Small-molecule sample, 100–1000 Da, Assumed) Column Type C 8 or C 18 (type-B) Dimensions 100 × 4.6-mm a Particle size 3 μm a Pore diameter 8–12 nm Mobile phase Sample contains no acids or bases Acetonitrile/water Sample contains acids and/or bases Acetonitrile/aqueous buffer (pH 2.5–3.0) b Flow rate 2.0 mL/min Temperature 30 or 35 ◦ C Gradient 5–100% B in 10 min Sample Volume ≤50 μL Weight ≤10 μg k ∗ ≈ 5 a Other column dimensions and particle sizes can be used, as discussed in Section 9.3.1. b 10–25 mM buffer in A-solvent only; see Section 7.2.1 for further details on buffer composition, including concentration. t R = (6.5 − 2.7) = 3.8 min (t R ) avg = (6.5 + 2.7)/2 = 4.6 0246810 Time (min) t 0 5-100% B in 10 min 1 9 10 11 8 100% B 80% 60% 40% 20% 0% t R = 0.01(100 − 5) = 0.95 Figure 9.15 Use of a standard gradient run to determine whether isocratic or gradient elu- tion is best for the sample. In this example the ‘‘irregular’’ sample of Figure 9.4 was sepa- rated with the recommended initial conditions of Table 9.3: 5–100% acetonitrile in 10 min, 100 × 4.6-mm (3-μm) C 18 column, 2.0 mL/min, 30 ◦ C. Gradient indicated by (- - -). A representative, initial gradient run is shown in Figure 9.15, based on the ‘‘irregular’’ sample of Figure 9.5 and the gradient conditions of Table 9.3. This first experiment can be used to answer two questions [2,30–33]: (1) will gradient elution be required for the sample, and (2) if isocratic separation is possible, what isocratic mobile phase should be tried first in order to achieve 1 ≤ k ≤ 10 for all peaks? Before 9.3 METHOD DEVELOPMENT 439 using this initial gradient run to draw any conclusions (as in following paragraphs), it is important to establish that the column has been adequately equilibrated—see the discussion of Section 9.3.8.1. In the initial separation of Figure 9.15, retention times for the first and last peaks (1 and 11) are equal to 2.7 and 6.5 minutes, respectively. The latter retention times determine whether isocratic separation is feasible. First, calculate the difference in retention times (Δt R ) for peaks 1 and 11 (6.5–2.7), or Δt R = 3.8 min. Also, calculate the average retention time for the first and last peaks, (t R ) avg = (6.5 + 2.7)/2 = 4.6 minutes. Samples that have small values of Δt R can be separated isocratically with 1 ≤ k ≤ 10, while samples with larger values of Δt R may require gradient elution. An approximate rule for deciding whether to use isocratic or gradient elution is as follows: if Δt R /t G ≤ 0.25, use isocratic elution; if Δt R /t G ≥ 0.40, use gradient elution. For intermediate values of Δt R /t G , either isocratic or gradient elution may prove best. For the example of Figure 9.15, Δt R /t G = 3.8/10 = 0.38, so isocratic elution is (barely) an option while gradient elution seems preferable. When isocratic separation is feasible, the recommended %B for the isocratic mobile phase can be estimated from the value of (t R ) avg [2]. For the conditions of Table 9.3 isocratic %B ≈ 9.5[(t R ) avg − t D ] − 2 (9.18) Here t D is the dwell-time of the gradient system, equal to V D /F.Asanexample of the application of Equation (9.18), consider the separation of Figure 9.15 with peaks 9 to 11 omitted (so as to make this a better candidate for isocratic separation). The dwell-volume V D and dwell-time t D for this separation are approximately zero, while values of t R for the first and last peaks are 2.7 and 4.7 min, respectively. Values of Δt R and (t R ) avg are then 2.0 and 3.7 min, respectively. The resulting value of Δt R /t G = 2.0/10 = 0.20, so isocratic elution is preferred (as discussed above). For the preceding example with (t R ) avg = 3.7andt D ≈ 0, the best mobile phase for an isocratic separation of this sample is 33% B (Eq. 9.18). This separation is shown in Figure 9.16a (same column, temperature, and flow rate), where 0.6 ≤ k ≤ 7. The retention range of the latter separation is just outside the target range of 1 ≤ k ≤ 10 (Eq. 9.18 is only an estimate!), but retention can be improved by a small decrease in %B. Thus values of k for the separation of Figure 9.16a should be increased by a factor of about 1.5, in order to achieve k > 1 for the first peak. Section 2.4.1 suggests that a decrease of 10% B in the mobile phase will increase log k by 0.4-units (‘‘rule of 2.5’’), whereas we wish an increase in log k byafactorof log 1.5 = 0.18 units. This suggests a decrease in %B of (0.18/0.40) × 10% = 4.5% B, to a final value of 28.5% B. The latter separation is shown in Figure 9.16b,where 1 ≥ k ≥ 10 as desired. There are two overlapping peak-pairs (2 + 3and5+ 6), which likely can be separated by varying other conditions (see Section 7.3.2 for ways to improve isocratic selectivity for this ionic sample). The recommendations above assume that if a sample can be separated iso- cratically with 1 < k < 10, then isocratic elution is the preferred option. This assumption has been challenged [34], on the basis that gradient elution is usually faster and equally satisfactory in other respects, when optimized conditions are used for both isocratic and gradient runs, and when column equilibration between successive gradient runs has been reduced as much as possible (Section 9.3.7). On 440 GRADIENT ELUTION 024 Time (min) 33% B 0.6 ≤ k ≤ 7 1 2 3 + 4 5 + 6 7 8 (a) 0246 Time (min) 1 ≤ k ≤ 10 28.5% B 1 2 + 3 4 5 + 6 7 8 (b) Figure 9.16 Isocratic separation of the sample of Figure 9.15 (peaks 1–8 only). (a) Separation with 33% B as predicted from the initial gradient separation in Figure 9.15. Conditions as in Figure 9.15, except isocratic; (b) separation for 28.5% B, as described in the text. the basis of results for a single sample [34], gradient elution was recommended whenever Δt R /t G ≥ 0.10. At present, however, many laboratories have a strong preference for isocratic elution—regardless of somewhat longer run times—because gradient elution is still considered more susceptible to problems than isocratic elu- tion, and less easy to transfer between laboratories. In time this bias against gradient elution may diminish, and gradient equipment may be improved so as to make very short equilibration times convenient. The proposal of [34] to use gradient elution whenever Δt R /t G ≥ 0.10 may then prove more popular. 9.3.1.2 Possible Problems The initial gradient run may also be used to highlight some potential problems with the separation: • tailing peaks • early elution •lateelution • complex samples •artifactpeaks Tailing peaks (Section 2.4.2) may be encountered in the initial gradient separation. In such cases it is important to correct the problem before proceeding further (Section 17.4.5.3). If the correction of peak tailing (by a change of separation conditions) is delayed until a later time, the resulting changes in selectivity with possible loss in resolution may require additional method-development experiments that could otherwise have been avoided. Figure 9.17 illustrates three additional problems that may be apparent from an initial gradient run. Early elution of peaks in RPC, as in Figure 9.17a, is not 9.3 METHOD DEVELOPMENT 441 246810 Time (min) 100% B 80% 60% 40% 20% 0% (a) Early elution 100% B 80% 60% 40% 20% 0% 0 20406080 Time (min) (b) Late elution (c) Complex sample 100% B 80% 60% 40% 20% 0% 0246810 Figure 9.17 Potential problems in gradient elution. (a) Non-retentive sample; (b) excessively retentive sample; (c) sample contains too many components. Gradient indicated by (- - -). uncommon for small, polar molecules, especially ionized acids or bases. Some improvement in separations such as that of Figure 9.17a can be obtained by a reduction in initial %B for the gradient (if feasible), or by the use of an initial isocratic hold as in Figure 9.9d. For other, more effective, means of dealing with early elution, see Section 6.6.1, or try normal-phase chromatography (Chapter 8)—especially HILIC (Section 8.6), which is especially well suited for use with gradient elution. Late elution as in Figure 9.17b (or an absence of peaks during the gradi- ent) suggests that the sample may be too nonpolar for separation with the usual RPC conditions. In such cases an acetonitrile/buffer gradient can be replaced by a gradient from acetonitrile to a less-polar solvent such as tetrahydrofuran or (better) methyl-t-butyl ether, either of which is a stronger RPC solvent than ace- tonitrile (buffer solubility should be checked for either of the latter two gradients, although a buffer is often not required for very nonpolar samples). Alternatively, a less hydrophobic column (lower value of H; Section 5.4.1) or normal-phase chromatography (Chapter 8) can be tried. 442 GRADIENT ELUTION Complex samples with > 15 components can result in crowded chromatograms, as in Figure 9.17c. For such samples it is unlikely that a single reversed-phase sep- aration will be able to separate all peaks to baseline. If every sample component is of interest, it may be necessary to develop a more powerful separation scheme. Two-dimensional (2D) chromatography (Sections 9.3.10, 13.4.5) is the most com- monly used option for dealing with complex samples; fractions from an initial run are further resolved in a second, ‘‘orthogonal’’ separation. If only a few sample components are of interest, however, a better choice is sample preparation (Chapter 16), followed by a conventional isocratic or gradient separation. Another problem that is sometimes encountered in gradient elution is the appearance of artifact peaks that do not correspond to sample components. Artifact peaks usually arise from impurities in either the A- or B-solvents used to form the gradient, but occasionally dissolved air in the sample can result in an ‘‘air peak.’’ This problem can be anticipated by carrying out a ‘‘blank’’ gradient (without injection of the sample) at the very beginning of each day. A blank gradient is also useful for recognizing (and correcting) baseline drift during the gradient (Section 17.4.5.1). See the related discussion of Section 7.4.3.1 for further details. 9.3.2 Optimize k ∗ (Step 4 of Table 9.2) Further improvements in separation can be guided by Equation (9.16), that is, the optimization of k ∗ , α ∗ ,andN ∗ . This approach for gradient elution is exactly analogous to the similar use of Equation (2.24) for isocratic method development, as described here and in following Sections 9.3.3 to 9.3.6. The initial gradient conditions recommended in Table 9.3 will result in an average value of k ∗ ≈ 5 for most small-molecule samples, those with molecular weights <1000 Da (for higher-molecular-weight samples, see Chapter 13). Thus, unlike isocratic method development, the first gradient-elution experiment can be carried out in a way that guarantees 1 ≤ k ∗ ≤ 10. The initial separation of the irregular sample of Figure 9.5 with these conditions is shown in Figure 9.15 and repeated in Figure 9.18a. The latter separation is reasonably promising, with only one overlapping peak-pair (5–6, indicated by the arrow). The next step is to vary separation conditions so as to improve peak spacing (selectivity) and resolution. 9.3.3 Optimize Gradient Selectivity α ∗ (Step 5 of Table 9.2) Changes in values of α ∗ can be achieved by varying any of the first seven isocratic conditions of Table 2.2: solvent strength (a change in t G is equivalent to a change in %B in isocratic elution), B-solvent (e.g., methanol replaces acetonitrile), temperature, column type, mobile-phase pH, buffer concentration, or ion-pair-reagent concen- tration. Each of these seven variables has a comparable effect on relative retention and selectivity for both gradient and isocratic elution. A growing body of evidence [35–42] suggests that gradient time and temperature should be changed first, as a preferred means for adjusting values of α* during initial method-development exper- iments (while maintaining 0.5 ≤ k ∗ ≤ 20). Therefore we recommend an increase in gradient time by a factor of 2 to 3 for the second method-development experiment. Starting with the separation of Figure 9.18a, gradient time was increased from 10 to 30 minutes, other conditions held constant; the resulting separation is shown in Figure 9.18b,withk ∗ ≈ 15. While there are significant changes in relative retention, 9.3 METHOD DEVELOPMENT 443 5-100% B in 10 min 50 o C; k* ≈ 5 R s = 1.1 (c) 02 4 Time (min) 9 1 2 4 5−7 8 10 11 3 5-100% B in 30 min 50 o C; k* ≈ 15, R s = 1.9 (d ) 024681012 Time (min) 1 2 3 4 8 9 10 11 5 − 7 0246 Time (min) 5-100% B in 10 min 30 o C; k* ≈ 5, R s = 0.1 (a) 1 3 4 5 + 6 7 8 10 11 9 2 02468101214 Time (min) 5-100% B in 30 min 30 o C; k* ≈ 15, R s = 0.1 (b) 11 1 3 2 4 5 + 6 7 8 9 10 024681012 Time (min) 1 2 4 5 7 6 3 8 9 10 11 100% B 80% 60% 40% 20% 0% (e) t 0 Figure 9.18 Gradient separations of the ‘‘irregular’’ sample of Figure 9.15 as a function of gradient time and temperature (a − d). Conditions: 100 × 4.6-mm (3-μm) C 18 column, 5–100% acetonitrile–pH-2.6 phosphate buffer; 2.0 mL/min; gradient times and temperatures indicated in figure; (e) shows gradient details for (d). 444 GRADIENT ELUTION there is no change in the separation of critical peak-pair 5–6. If a 3-fold change in gradient time does not significantly change the resolution of an overlapping peak pair, further changes in gradient time are unlikely to provide much additional benefit—as long as other conditions are held constant. The next step is a change in temperature. The third and fourth method-development runs are illustrated in Figure 9.18c,d, where the runs of Figures 9.18a and b are each repeated with a change in temperature from 30 ◦ to 50 ◦ C. Because peak-pair 5–6 was unresolved in the first two runs, the primary question is whether peaks 5 and 6 can be separated at the higher temperature. A large increase in resolution for peaks 5 and 6 is seen in Figure 9.18c (R s = 2.1), but peaks 6 and 7 are now critical (R s = 1.1). An increase in gradient time (Fig. 9.18d) results in better resolution of peaks 6 and 7 (R s = 1.9)—and of the entire sample. These results suggest that a further increase in gradient time might provide better overall resolution, but no significant increase in resolution resulted when t G was increased for this sample—due to the increasing overlap of peaks 2 and 3. The resolution of Figure 9.18d might be improved by a true optimization of gradient time and temperature (Section 10.2.2), but the conditions of Figure 9.18d will be regarded as adequate for the moment. 9.3.4 Optimizing Gradient Range (Step 6 of Table 9.2) The next step in gradient method development is to consider (1) whether the gradient range Δφ can be shortened (with a decrease in run time), and (2) whether the use of a segmented gradient (Section 9.3.5) might lead to either a faster separation or better resolution. The approximately optimized separation of Figure 9.18d is repeated in Figure 9.18e, overlaid by the gradient as it leaves the column (delayed by a time t 0 ). The first peak (1) leaves the column at 3.2 min, at which time its accompanying mobile phase is 14% B. Similarly, the last peak (11) leaves at 12.3 minutes in a mobile phase of 42% B. It is recommended to terminate the gradient just after the elution of the last peak. In the example of Figure 9.18e the retention time of the last peak is 12.3 min. If the gradient time is shortened in this way, the final %B in the gradient must be reduced proportionately in order to maintain k ∗ constant (so as to preserve the optimum peak spacing of Fig. 9.18e). That is, t G /Δφ in Equation (9.5) must be held constant; for the present example, t G /Δφ = 30/0.95 = 31.6. The value of φ at the time a peak elutes from the column (φ e ) can also be calculated by φ e = φ 0 + Δφ(t R − t o − t D ) t G (9.19) where φ o is the value of φ at the start of the gradient, and t R is the retention time of the peak. For the last peak in Figure 9.18e, φ e = 0.05 + 0.95(12.3–0.5–0.0)/30 = 0.42 (note that t 0 = 0.5andt D ≈ 0.0 in this example). That is, the new (shortened) gradient should end at 42% B. The new value of Δφ is then 42–5% = 37% or 0.37. As t G /Δφ = 31.6 should remain constant (to avoid changes in relative retention, the new value of t G is 31.6 × 0.37 = 11.7 minutes (i.e., a final gradient of 5–42% B in 11.7 min, with other conditions kept the same as in Fig. 9.18e). This new gradient will result in the same chromatogram but end at 12.2 minutes (equal t G + t 0 ). 9.3 METHOD DEVELOPMENT 445 It is advisable to extend the gradient somewhat beyond the time that the last peak leaves the column because of gradient rounding (Section 3.10.1.2). We might therefore increase the gradient time to 13 minutes, which then requires an increase in final-%B to maintain k ∗ constant. As t G /Δφ = 31.6 for the ‘‘optimized’’ separation of Figure 9.18e, the new value of Δφ = 13/31.6 = 0.41, and the final%-B equals 41 + 5% = 46%; that is, a gradient of 5–46% B in 13 minutes. In principle, the gradient run time could be shortened further by increasing initial-%B (while decreasing t G so as to hold k ∗ constant). In this example, however, resolution became smaller for any increase in initial-%B (due to changes in relative retention for this irregular sample, similar to the example of Fig. 9.13e). Conse- quently the value of initial-%B was left unchanged at 5% B. For other samples, it may be possible to increase initial-%B in order to reduce run time, with no loss in resolution. 9.3.5 Segmented (Nonlinear) Gradients (Step-6 of Table 9.2 continued) The preceding discussion of gradient elution assumes that we are dealing with linear gradients. Various reasons for the possible use of a segmented gradient in place of a linear gradient were summarized in Section 9.2.2.5: (1) to clean the column between sample injections, (2) to shorten run time, or (3) to improve separation by adjusting selectivity for different parts of the chromatogram. Because of the excess resolution between peaks that follow peak 9 in the separation of Figure 9.18e, run time could be shortened by an increase in gradient steepness after peak 9 leaves the column. See the similar example of Figure 9.11c. Keep in mind, however, that gradient rounding may vary between different equipment, which can make segmented gradients less reproducible—as well as require an increase in final %B. Cleaning the column is a common reason for the use of segmented gradients, while shortening run time and improving separation by the use of segmented gradients are less often feasible or desirable. For further details, see Section 9.2.2.5. 9.3.6 Optimizing the Column Plate Number N ∗ (Step 7 of Table 9.2) The column plate number N ≡ N ∗ is affected by column dimensions, particle size, and flow rate (called column conditions, Section 2.5.3), as well as by sample molecular weight (Section 2.4.1.1). Particle size and column diameter are usually selected prior to the start of method development (e.g., as recommended in Table 9.3). An increase in column length usually results in an increase in N ∗ , resolution, and run time (as in Figs. 9.6e vs. Fig. 9.6d). Conversely, run time can be shorted by a decrease in column length and/or an increase in flow rate (as in Fig. 9.6f vs. Fig. 9.6d). After varying conditions for improved selectivity α* (step 5 of Table 9.2), and adjusting gradient range and shape (step 6 of Table 9.2), the resulting separation may exhibit a resolution that is either (1) too low (R s < 2) or (2) greater than needed (R s  2). In either case, a change in column conditions can be used to improve separation; any resulting changes in the pressure drop across the column should be kept in mind (Eq. 2.13). In isocratic elution, changes in column length or flow rate do not affect relative retention or selectivity because values of k and α are not affected when column conditions are varied. When changing column length L or flow rate F in gradient elution, however, a change in either of these two conditions alone will result in . Section 9.2.2.5: (1) to clean the column between sample injections, (2) to shorten run time, or (3) to improve separation by adjusting selectivity for different parts of the chromatogram. Because. will be able to separate all peaks to baseline. If every sample component is of interest, it may be necessary to develop a more powerful separation scheme. Two-dimensional (2D) chromatography (Sections. that the sample may be too nonpolar for separation with the usual RPC conditions. In such cases an acetonitrile/buffer gradient can be replaced by a gradient from acetonitrile to a less-polar solvent