Introduction to Modern Liquid Chromatography, Third Edition part 47 pps

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∗andα.. Table 9.1Contrasting Changes

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∗andα 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∗andα For an x-fold change in L, gradient

time should be changed by the same factor x For an x-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

5

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)

0

0

Figure9.6 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 colcol-umn

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]

10 12 Time (min)

Time (min)

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

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

Time (min)

(g)

(h)

13 15

Figure9.6 (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 For the

‘‘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

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)

R s Average Peak R s Average Peak R s Average Peak Heightd Heightd Heightd

1 Isocratica 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.

dRelative 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)

• 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

Time (min)

Time (min)

(a)

(b)

(c)

(d)

Time (min)

Time (min)

1 2 3

1 2

3

1 2 3

1 2 3

Figure9.7 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) C18column; ambient temperature; 2.0 mL/min; methanol-water mobile phase; gradient time adjusted to maintain

k∗= 4 Other conditions indicated in the figure

to Δφ), thus holding (Δφ/t G ) and k∗ 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 keepΔφ/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 = 2.7 vs R s = 4.0 in Fig 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 ) and k∗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

0 20 40

Time (min)

Time (min)

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

Time (min)

7

8

Figure9.8 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, there is

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

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 (also referred to as an isocratic 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 t0is 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

40-80% B in 20 min

2.0%B/min

Time (min)

(a)

40/40/80% B in 0/5/25 min

2.0%B/min

Time (min)

(b)

50-100% B in 7.5 min 6.7%B/min

Time (min)

(c)

1 2

3 4

50/50/100% B in 0/5/12.5 min

6.7%B/min

Time (min)

(d )

1 2

t 0

Figure9.9 Effect of gradient delay on the gradient separation of the herbicide

sam-ple of Figure 9.4 Conditions: 150× 4.6-mm (5-μm) C18column; 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

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 t0(Fig 9.10) Values of V Dfor 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

t0

%B

Time

t G

programmed gradient

actual gradient at

column inlet (shifted by t D)

actual gradient at

column outlet (shifted by t D + t0 )

Figure9.10 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

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 d2

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