416 GRADIENT ELUTION changes in run time, resolution, and peak heights for these isocratic separations as column conditions are varied. When changing experimental conditions during method development for iso- cratic elution, it is desirable to first vary conditions that affect values of k and α, so as to optimize selectivity and resolution. If a further improvement in separation is desired, by varying column conditions, the previously optimized values of k and α will not change for isocratic separation. With constant values of k and α,the interpretation of subsequent experiments is also simplified—as only N and run time can change. For gradient elution, the situation is more complicated—as values of k ∗ vary with column length and flow rate (Eq. 9.5). For values of k ∗ and α to remain constant while varying column conditions for gradient elution, it is necessary to hold values of (t G F/L) constant (Eq. 9.5; V m is proportional to column length L, provided that the column diameter is not changed). For changes in column length L or flow rate F, a concomitant change in gradient time t G is the most convenient way of maintaining constant values of k ∗ and α.Foranx-fold change in L,gradient time should be changed by the same factor x.Foranx-fold change in F,gradient time should be changed by 1/x-fold. Just as a change in isocratic values of L or F results in a change in run time, changes in gradient values of L or F result in the same relative change in run time—as long as constant values of k ∗ are maintained by changing gradient time. 10 Time (min) 1 2 3 4 5 1.0 2.0 3.0 Time ( min ) isocratic 100-mm 1.0 mL/min R s = 1.7 isocratic 300-mm 1.0 mL/min R s = 3.0 isocratic 100-mm 3.0 mL / min R s = 1.2 (a) (b) (c) 0 Time (min) 10 300 0 02468 Figure 9.6 Isocratic and gradient elution compared for a regular sample and change in col- umn length or flow rate. Sample and conditions as in Figure 9.4, except for varying column length and flow rate (as indicated in figure); 55% B for isocratic runs (a–c), 0–100% B for gradient runs (d–h). Note that actual peak heights are shown (not normalized to 100% for tallest peak). Chromatograms recreated from data of [8]. 9.2 EXPERIMENTAL CONDITIONS AND THEIR EFFECTS ON SEPARATION 417 10 12 Time (min) 28 30 32 34 36 Time (min) 3.0 3.2 3.4 3.6 3.8 4.0 Time (min) 1 2 3 4 5 (d ) (e) (f ) gradient (0-100% B in 15 min) 100-mm 1.0 mL/min R s = 1.7 45-min gradient 300-mm 1.0 mL/min R s = 3.1 5-min gradient 100-mm 3.0 mL/min R s = 1.2 11 14 16 Time (min) 15-min gradient 300-mm 1.0 mL /min R s = 1.0 15-min gradient 100-mm 3.0 mL /min R s = 2.8 6789 Time ( min ) (g) (h) 13 15 Figure 9.6 (Continued) The gradient separations of Figure 9.6d–f illustrate the effects of the same changes in column length and flow rate as in the isocratic separations of Figure 9.6a–c, while holding k ∗ constant by varying gradient time t G .Forthe ‘‘corresponding’’ separations of Figure 9.6b,e, where column length is increased from 100 to 300 mm (and gradient time in e is increased from 15 to 45 min), there is a similar increase in run time (by a factor of 3) and resolution (R s = 3.0[isocratic] and 3.1 [gradient]). Peak heights are decreased in each run, as a result of an increase in peak width. Likewise for the corresponding separations of Figure 9.6c,f where flow rate is increased from 1.0 to 3.0 mL/min (and gradient time in f is decreased from 15 to 5 min), there is a similar decrease in run time (by a factor of 3) and resolution (R s = 1.2 [isocratic] and 1.2 [gradient]). Peak heights are increased in 418 GRADIENT ELUTION Table 9.1 Contrasting Changes in Separation as Flow Rate F or Column Length L is Changed for Isocratic versus Gradient Elution (Examples of Fig. 9.6) Elution Mode Original Increase L Increase F Separation by 3-fold by 3-fold R s Average Peak R s Average Peak R s Average Peak Height d Height d Height d 1. Isocratic a 1.7 (1.0) 3.0 0.6 1.2 0.8 2. Gradient (t G varies, k ∗ constant) b 1.7 (1.0) 3.1 0.6 1.2 0.7 3. Gradient (t G constant, k ∗ varies) c 1.7 (1.0) 1.0 1.0 2.8 0.3 a Figure 9.6a–c. b Figure 9.6d–f . c Figure 9.6g–h. d Relative values, versus original separation. the separations of Figure 9.6c,f , as a result of narrower peaks. The examples of Figure 9.6a–f confirm the similarity of gradient and isocratic elution for changes in column conditions, when values of k or k ∗ are held constant. Details of the separations of Figure 9.6 are summarized in Table 9.1. When only column dimensions or flow rate are changed in gradient elution (i.e., gradient time unchanged), changes in k ∗ will also occur (Eq. 9.5; see also Eq. 9.5c on p. 431). Resulting separations may then appear surprising to workers who expect similar results as in isocratic elution (as in Figs. 9.6a–c). This is illustrated in Figure 9.6g,h, for the same changes in column length or flow rate as in Figure 9.6e,f, while holding gradient time constant at 15 min so that k* is no longer constant. For the latter conditions, resolution decreases when column length is increased (Fig. 9.6g, R s = 1.0), and increases when flow rate is increased (Fig. 9.6h, R s = 2.8). In the latter case (Fig. 9.6e,f), the opposite behavior is found for gradient elution when k ∗ is allowed to vary. For this reason, when changing column length or flow rate in gradient elution, gradient time should be changed at the same time so as to maintain values of k* constant and—more important—retain the same relative retention or selectivity. To conclude, ‘‘corresponding’’ separations by isocratic or gradient elution (i.e., with similar values of k and k ∗ ) will generally exhibit similar values of resolution and peak heights. Run times will change to the same extent, when any column condition (or combination of column conditions) is changed for both isocratic and gradient runs, as long as k ∗ (or k) is held constant. 9.2.2 Effects of Changes in the Gradient Changes in the gradient can be made intentionally—or unintentionally as a result of a change in equipment. These changes in the gradient can be summarized as follows: • a change in %B at the start of the gradient (initial-%B; Section 9.2.2.1) • a change in %B at the end of the gradient (final-%B; Section 9.2.2.2) • gradient delay (Section 9.2.2.3) 9.2 EXPERIMENTAL CONDITIONS AND THEIR EFFECTS ON SEPARATION 419 • a change in equipment (dwell-volume, Section 9.2.2.4) • segmented gradients (Section 9.2.2.5) 9.2.2.1 Initial-%B The usual goal of a change in initial-%B is to shorten run time, by removing empty space in the early part of a gradient chromatogram, as illustrated in Figure 9.7. A change in initial-%B (and therefore a change of the gradient range Δφ), without a change in gradient time, would also change values of k ∗ (Eq. 9.5)—which can be undesirable. In the present section we will examine the effects of a change in initial-%B while holding k ∗ constant (by varying gradient time t G in proportion 0-100% B in 50 min 2%B/min 20-100% B in 40 min 2%B/min 40-100% B in 30 min 2%B/min 60-100% B in 20 min 2%B/min 01020 Time (min) 0 10203040 Time (min) (a) (b) (c) (d) 0 102030 Time (min) 0246810 Time (min) 1 2 3 1 2 3 1 2 3 1 2 3 Figure 9.7 Effect of a change in initial %B for the gradient separation of a ‘‘regular’’ sam- ple. Sample: a mixture of herbicides. Conditions; 150 × 4.6-mm (5-μm) C 18 column; ambient temperature; 2.0 mL/min; methanol-water mobile phase; gradient time adjusted to maintain k ∗ = 4. Other conditions indicated in the figure. 420 GRADIENT ELUTION to Δφ), thus holding (Δφ/t G )andk ∗ constant. Keep in mind that if only %B is changed, while holding other conditions constant, resulting changes in separation will represent the combined effect of change in k* and the value of initial-%B.It is much easier to interpret and optimize separation, if k ∗ is held constant when initial-%B (or some other condition) is varied (as in the preceding example of changes in column length or flow rate). Figure 9.7 illustrates the effects of a change in initial-%B for the separation of a ‘‘regular’’ sample. In successive separations, Figure 9.7a–d, the value of %B at the start of the gradient is increased (resulting in a reduction of the gradient range Δφ), while simultaneously shortening gradient time t G so as to keep Δφ/t G and k ∗ constant. For an increase in initial-%B from 0 to 20% (Fig. 9.7b), Δφ is shortened by 20%, so a similar 20% shortening of gradient time is required (from 50 to 40 min), in order to maintain k ∗ constant (Eq. 9.5). The separation of Figure 9.7b remains essentially the same as in Figure 9.7a, except that all peaks leave the column 10 minutes earlier—and run time is reduced by 20%. When initial-%B is increased further to 40%B (Fig. 9.7c), a slight change in peaks 1 and 2 is observed: the heights of these peaks have increased a bit, and their resolution has decreased a bit, too (R s = 2.7vs.R s = 4.0inFig.9.7a). However, separation is still acceptable, and run time has been shortened by another 10 minutes. Finally, in Figure 9.7d,the initial-%B is increased to 60%, with a considerable increase in the heights of early peaks, as well as markedly lower resolution for peaks 1 and 2 (R s = 0.9). In this case the shortest run time with acceptable resolution occurs for approximately 40% B at the start of the gradient (Fig. 9.7c). Because early peaks elute fairly late in the 0–100% B gradient of Figure 9.7a, these peaks are strongly retained initially at the column inlet. As a result their values of k ∗ are given by Equation (9.5) (average k ∗ ≈ 3.7). When the initial-%B of the gradient is increased to 20% B (Fig. 9.7b), the initial peaks are still well retained, and k ∗ still equals 3.7. When initial-%B is increased further in Figures 9.7c (40% B) and 9.7d (60% B), peaks at the beginning of the chromatogram leave the column in a still stronger mobile phase, but now with lower values of k ∗ (Eq. 9.5 is strictly applicable only for peaks that are strongly retained at the start of the gradient; for weakly retained peaks, see Eq. 9.5f in following Section 9.2.4.1). This decrease in values of k ∗ for early peaks, when initial%-B is increased sufficiently, results in narrower, higher peaks—usually with reduced resolution. Because values of k ∗ decrease for early peaks when initial-%B is increased enough, changes in relative retention can also result for ‘‘irregular’’ samples. As a result resolution has been observed in some cases to increase when the initial-%B is increased [10], despite the corresponding decrease in k ∗ . See the further discussion of Section 9.2.3 for the gradient separation of ‘‘irregular’’ samples. 9.2.2.2 Final-%B Figure 9.8 illustrates the effect of changing the final-%B for the ‘‘regular’’ sample and separation of Figure 9.7a, with the goal of a reduction in run time. The separation in Figure 9.8a is for a gradient of 0–100% B in 50 minutes. Subsequent changes in the final-%B value are accompanied by changes in gradient time so as to keep (Δφ/t G )andk ∗ constant (as in Fig. 9.7 for changes in initial-%B). Thus, for a 20% shortening of Δφ to a final-%B of 80% in Figure 9.8b, the gradient time is also 9.2 EXPERIMENTAL CONDITIONS AND THEIR EFFECTS ON SEPARATION 421 02040 Time (min) 0 20 Time (min) 7 9 7 9 0-100% B in 50 min 2%B/min 0-80% B in 40 min 2%B/min 0-60% B in 30 min 2%B/min (a) (b) (c) 8 0204060 Time (min) 7 8 9 8 Figure 9.8 Effect of a change in final %B for the gradient separation of the regular sample of Figure 9.7. Conditions as in Figure 9.7; gradient time adjusted to maintain k ∗ = 4. Dashed lines indicate the gradient: values of %B at the column outlet (so as to correspond to peaks in the chromatogram). Arrows mark end of gradient as it leaves the column. Other conditions indicated in the figure. shortened by 20% (from 50 to 40 min). For the separation of Figure 9.8b,thereis no change in separation because the last peak in the sample leaves the column before the gradient has ended (see arrow). A further shortening of the gradient to 0–60% B in 30 minutes (Fig. 9.8c), however, results in elution of peaks 7 through 9 after the end of the gradient, so these peaks leave the column under isocratic conditions. As a result peak width and resolution increase for peaks 7 through 9, as does run time, because of larger values of k ∗ for these peaks (Note that Eq. 9.5 only applies for peaks that are eluted during the gradient; peaks eluting after the gradient will have larger values of k ∗ ). Figure 9.8c, where the value of final-%B is reduced too much, can be compared with Figure 9.7d, where initial-%B is increased too much; in each case the resulting separation is unsatisfactory—either resolution is too low or run time is too long. As long as the last peak leaves the column before the end of the gradient, there is no effect of a change in final-%B on separation (provided that t G /Δφ is held constant), other than to decrease run time for smaller values of final-%B. In most cases it will be advisable to end the gradient as soon as the last peak leaves the column, but not before. The elution of peaks after the gradient wastes run time and leads to undesirable peak broadening (Fig. 9.8c). The effect of final-%B 422 GRADIENT ELUTION on separation is similar for both ‘‘regular’’ and ‘‘irregular’’ samples (no change in relative retention or elution order), as long as late elution of peaks is avoided and (t G /Δφ) is held constant. For some samples the use of a very steep gradient can lead to elution of the last peaks after the gradient, even when the gradient ends with 100% B (and less steep gradients do not result in late elution). However, this situation does not present any special problem; it is only necessary to wait for the last peak to leave the column (by adding an isocratic hold at the end of the gradient; for example, 0/60/60% B in 0/30/60 min for the separation of Fig. 9.8c)before starting the next gradient (although the gradient of Fig. 9.8b is obviously a better choice). From the combined examples of Figures 9.7 and 9.8, it can be concluded that a gradient of 40–80% B in 20 minutes represents a suitable shortening of the original gradient (vs. Fig. 9.7a; 0–100%B in 50 min). This separation is shown in Figure 9.9a; sample resolution is acceptable, with a 60% decrease in run time compared to the separation of Figure 9.7a, and no unacceptable loss in resolution or other problems. 9.2.2.3 Gradient Delay Gradient delay (alsoreferredtoasanisocratic hold) refers to isocratic elution for some period of time prior to the start of the gradient. The effect of a gradient delay is illustrated in Figure 9.9 for the ‘‘regular’’ sample of Figure 9.7. Figure 9.9a shows a chromatogram for a 40–80% B gradient without a gradient delay, where the first peak in the chromatogram does not leave the column until well after the arrival of the gradient at the outlet of the column (the column dead-time t 0 is indicated by the arrow). When a 5-minute gradient delay is added (Fig. 9.9b), the effect is to increase retention times by 2 to 5 minutes, but the two chromatograms of Figures 9.9a and b are otherwise quite similar (there is also a typical, modest increase in resolution for early peaks in Fig. 9.9b). When initial peaks leave the column close to the start of the gradient, a gradient delay can have a more noticeable effect on the separation—especially if early peaks are not well resolved. This is illustrated in the similar examples of Figure 9.9c (no delay) and Figure 9.9d (with delay), for the same sample but different starting gradient conditions. In the separation of Figure 9.9d, peaks 1 through 3 leave the column isocratically during the gradient delay (note the arrow in Fig. 9.9d that marks the arrival of the gradient at the column outlet). As can be seen in these latter two examples, peaks 1 and 2 are poorly separated in Figure 9.9c (R s = 1.1), whereas in Figure 9.9d their separation is much improved (R s = 2.3). The better resolution of early peaks in Figure 9.9d as a result of the gradient delay can be attributed to larger values of k ∗ for these peaks compared to the separation of Figure 9.9c (see later Eq. 9.5g). Peaks 1 through 3 for Figure 9.9d show the expected increase in peak width characteristic of isocratic separation, whereas later peaks, eluted under gradient conditions, exhibit narrower peak widths—typical of gradient separation. When peaks elute near the end of the gradient, the effect of an initial gradient delay is to increase retention time by the same amount as the delay, with no change in relative retention. For example, the last two peaks in Figure 9.9b,d are delayed by 5 minutes relative to Figures 9.9a,c—exactly the amount of the gradient delay. This behavior holds for both regular and irregular samples. 9.2 EXPERIMENTAL CONDITIONS AND THEIR EFFECTS ON SEPARATION 423 40-80% B in 20 min 2.0%B/min 02468812141618 Time (min) (a) 40/40/80% B in 0/5/25 min 2.0%B/min 020 Time (min) (b) 50-100% B in 7.5 min 6.7%B/min 024681012 Time (min) (c) 1 2 3 4 50/50/100% B in 0/5/12.5 min 6.7%B/min 0 2 4 6 8 10 12 Time (min) (d) 1 2 3 4 t 0 Figure 9.9 Effect of gradient delay on the gradient separation of the herbicide sam- ple of Figure 9.4. Conditions: 150 × 4.6-mm (5-μm) C 18 column; 30 ◦ C; 2.0 mL/min; methanol-water mobile phase; gradient time adjusted to maintain k ∗ = 4. Peak heights not normalized to 100%; gradient indicated by (- - -), and arrows mark start of the gradient (mea- sured at the column outlet). Other conditions indicated in the figure. A gradient delay is sometimes used to increase the resolution of early peaks in the chromatogram, as in the example of Figure 9.9d compared to that of Figure 9.9c. For separations that start at a higher %B (e.g., Fig. 9.9c), however, resolution can best be improved by simply reducing the initial value of %B in the gradient (compare separations in Fig. 9.7d vs. Fig. 9.7c). On the other hand, when the initial-%B of the gradient is close to zero (and a significant reduction in initial-%B is therefore not feasible), a gradient delay may be the most convenient alternative; still there are other means for increasing k in this situation (Section 6.6.1). Note that relative retention does not change when a gradient delay is used for a ‘‘regular’’ sample, as in Figure 9.9. However, because a gradient delay can affect values of k ∗ for early 424 GRADIENT ELUTION peaks in the chromatogram, changes in relative retention can occur for ‘‘irregular’’ samples (see Section 9.2.2.4, and later Fig. 9.13f vs. Fig. 9.13a). 9.2.2.4 Dwell-Volume Every instrument used for gradient elution will have a certain holdup volume (called the dwell-volume V D ) equal to the volume of the gradient mixer plus that of the mobile-phase flow path between the mixer and the column inlet (Section 3.5.3; Figs. 3.13 and 3.14). Values of V D can vary for different gradient equipment, from a fraction of a mL for modern equipment to several mL for older equipment. The existence of a dwell-volume is equivalent to the intentional use of a gradient delay, so the effects on separation of varying dwell-time t D = V D /F can therefore be inferred from the examples of Figure 9.9 for a gradient delay. The actual gradient entering the column is delayed by a time t D , while the gradient leaving the column is delayed further by the column dead time t 0 (Fig. 9.10). Values of V D for a particular gradient system can be determined as described in Section 3.10.1.2. When a gradient method is transferred from one HPLC system to another, differences in the dwell-volume V D of the two systems can result in changes in separation. Often an HPLC method will be developed on a newer system in an R&D laboratory, while routine assays will be carried out on an older system in a production laboratory. As a result the dwell-volume may be greater for a method in routine operation, compared to the method procedure issued by the R&D laboratory. For a ‘‘regular’’ sample, as in the examples of Figure 9.9, an increase in dwell-volume will cause an increase in retention times for all peaks, possibly with some reduction in peak height and increase in resolution for early peaks in the chromatogram (as in the example of Fig. 9.9d). Relative retention will remain unchanged for different values of V D . When the dwell-volume is changed for ‘‘irregular’’ samples, however, changes in relative retention can occur for early t D t 0 %B Time t G programmed gradient actual gradient at column inlet (shifted by t D ) actual gradient at column outlet (shifted by t D + t 0 ) Figure 9.10 Effect of dwell-volume on the gradient. (____), Programmed gradient selected by the user; (- - -) actual gradient at the column inlet, taking the dwell-volume of the system into account; ( ) actual gradient at the column outlet, assuming a dwell time t D . 9.2 EXPERIMENTAL CONDITIONS AND THEIR EFFECTS ON SEPARATION 425 peaks, and this can lead to a change in the resolution of early peaks (see the later example of Fig. 9.13f vs. Fig. 9.13a)—sometimes unacceptably. These and other problems relating to equipment dwell-volume are discussed in Section 9.3.8.2. A similar situation can arise when the column size (and dead-volume V m )is changed because the effect of the dwell-volume on relative retention for early peaks is determined by the ratio V D /V m . When changes are made in the column-volume, it may be necessary to adjust the dwell-volume in proportion to column volume, in order to maintain the same relative retention and resolution for early peaks in the chromatogram. For example, if column diameter d c is reduced for use with LC-MS, the dwell volume should be reduced in proportion to d 2 c . (A reduction in dwell volume by the user usually is possible with high-pressure-mixing systems, but not with low-pressure-mixing systems.) If column diameter is increased for scaling up a preparative separation, a similar increase in dwell-volume may be necessary—although this can be duplicated more conveniently by the addition of an isocratic hold at the start of the gradient. See [11, 12] and Section 3.5.3 of [2] for further details. When a test gradient is carried out as in Section 3.10.1.2, some distortion is normally observed at each end of the gradient (Fig. 3.26). This gradient rounding results from dispersion of the A- and B-solvents as the mobile phase flows into the gradient mixer and on to the column inlet; gradient rounding is more pronounced for low-pressure-mixing gradient systems. The extent of gradient rounding increases for larger values of V D and can be described quantitatively in terms of the equipment mixing volume V M (V M ≈ V D ). Gradient rounding has little effect on separation, unless the value of V M becomes comparable to that of the gradient volume V G = t G F. For a further discussion of the effect of mixing volume on gradient shape and separation, see Section 17.4.6.1 and pp. 394–396 of [2]. 9.2.2.5 Segmented Gradients Segmented gradients, as in Figure 9.2d, are used for different purposes: • to clean the column between sample injections • to shorten run time • to increase resolution by adjusting selectivity for different parts of the chromatogram (for ‘‘irregular’’ samples only) Segmented or step gradients for cleaning the column are often employed when separating environmental or biological samples because the presence of extraneous, strongly retained sample components (non-analytes) can foul the column. When separating samples of this kind, and where the gradient required to elute all peaks of interest ends short of 100% B, it is customary to follow the initial gradient with a steep gradient segment or step that ends at or near 100% B. Figure 9.11a shows the linear gradient separation of a mixture of peptides from a tryptic digest of recombinant human growth hormone (rh-GH). Nineteen peptides are baseline-separated in 50 minutes. In Figure 9.11b the separation of Figure 9.11a is followed by a gradient step from 40% B to 100% B in one minute, in order to purge the column of any sample components that are not eluted by the gradient of Figure 9.11a. This increase in steepness at the end of the gradient is usually followed . reduced too much, can be compared with Figure 9.7d, where initial-%B is increased too much; in each case the resulting separation is unsatisfactory—either resolution is too low or run time is too. different purposes: • to clean the column between sample injections • to shorten run time • to increase resolution by adjusting selectivity for different parts of the chromatogram (for ‘‘irregular’’. column-volume, it may be necessary to adjust the dwell-volume in proportion to column volume, in order to maintain the same relative retention and resolution for early peaks in the chromatogram. For example,