the theory of hplc gradient hplc

The Theory of HPLC

Gradient HPLC

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Contents Page

1 Aims and Objectives 2 2 Isocratic HPLC Analysis 3 3 Gradient HPLC Analysis 4-8 4 Gradient Elution Parameters 9 5 Optimizing Gradient Parameters 10-11 6 Gradient Elution Principles 12-14 7 Peak Shape in Gradient HPLC 15 8 Scouting Gradients 16-18 9 Optimizing Initial Gradient Conditions 19-20 10 Gradient Steepness 21-22 11 Optimizing Gradient Analyses 23-27 12 Practical Gradient HPLC 28-29 13 Changing Method Parameters 30-31 14 Gradient Suitability 32-33 15 Method Transfer Between HPLC Systems 34-35 16 Gradient Method Transfer Calculator 36 17 Non-Linear Gradients 37 18 Segmented Gradients 38-39 19 Isocratic Hold 40-41 20 Peak Capacity 42-43 21 Estimating Gradient Parameters 44 22 Gradient Performance Checks 45-46

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1. Aims and Objectives

To explain the problems that can be encountered when using isocratic HPLC

To demonstrate how these problems can be overcome using gradient HPLC

To define the parameters of gradient elution HPLC

To explain and interactively illustrate how gradient elution HPLC works and how the retention and elution processes differ from isocratic HPLC

To demonstrate why peak shapes in gradient HPLC are more efficient than those obtained from isocratic HPLC

To examine the effects of gradient steepness and show how the various gradient parameters can be practically determined

To interactively illustrate the use of scouting gradients in HPLC method development and optimization

Examine the pitfalls and advantages of gradient elution HPLC in a practical situation

Figure 1: Scouting gradient.

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2. Isocratic HPLC Analysis

When the composition of the mobile phase does not change during an analysis (i.e. the composition is constant), the method is said to be isocratic.

Figure 1: Chromatogram generated from an isocratic HPLC analysis.

Several potential problems are associated with isocratic analysis. These are listed below.

When the range of analyte polarities is broad, some analytes may be poorly retained and resolution is lost with peaks eluting at or near the void volume (t0)

Alternatively, other analyte components may be significantly more hydrophobic and show unacceptably long retention times

Due to the various band broadening processes, these late eluting peaks will be broad and show reduced sensitivity due to reduced peak height

It is possible that some components will be irreversibly adsorbed on the column and cause contamination

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3. Gradient HPLC Analysis

Many of the problems associated with Isocratic HPLC analysis can be overcome using gradient HPLC. In this mode of analysis, the mobile phase composition is altered during the analysis – normally by increasing the amount of organic modifier.

The initial composition is chosen so that the strength is appropriate to retain and resolve early eluting analytes

The elution strength is then increased in a predetermined way to elute compounds with optimum resolution

The final mobile phase composition is chosen to ensure elution of all compounds of interest from the column within a reasonable time

It is possible to increase the organic modifier concentration to wash strongly retained, potentially contaminating components from the column

Gradient elution is best suited to analyses carried out using reversed phase, normal phase separations using bonded stationary phases, and for ion exchange chromatography. Particular pumps are required to carry out gradient HPLC analysis, which allow on-line mixing of the mobile phase components.

Figure 1: Chromatogram generated from a gradient HPLC analysis.

Advantages of Gradient Elution:

Improved resolution Increased sensitivity Ability to separate complex samples Shorter analysis times Decrease in column deterioration due to strongly retained components

Disadvantages of Gradient Elution:

More expensive instrumentation Possible precipitation at solvent interfaces when using multiple proportioning (mixing)

valves

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Re-equilibration time adds to analysis time Instruments vary in their dwell volume (VD), which can cause method transfer problems

Other uses of Gradient Elution:

Column cleaning Scouting runs for method development (more later)

Case Study 1

Figure 2: Gradient HPLC analysis of herbicides.

Column: ZORBAX C18, 4.6 x 150 mm, 5 μm Mobile Phase: A: H2O with 0.1% TFA, pH 2

B: Acetonitrile Flow Rate: 1.0 mL/min Temperature: 35 °C

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Case Study 2

Figure 3: Gradient HPLC analysis of pesticides in drinking water.

Column: ZORBAX SB-C18, 3.0 x 250 mm, 5 μm Gradient: 10%B for 2 min

10-45% B in 70 min Mobile Phase: A: 2 mM sodium acetate pH 6.5 with 5% acetonitrile

B: Acetonitrile Flow Rate: 0.35 mL/min Temperature: 40 °C Sample: Pesticides

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Case Study 3

Figure 4: Gradient HPLC analysis of high molecular weight mixtures. Top - effect of % organic on retention factor, bottom - chromatogram of high molecular weight separation.

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k* = gradient retention factor (target value of 5 for average separation) tG = gradient time (min) F = flow rate (mL/min) ΔΦ = change in volume fraction of organic (Final %B – Initial %B) expressed as a decimal Vm = column void volume (mL) S = constant determined by strong solvent and sample compound (small molecules < 500 Da the value is between 2 and 5; a value of 4 is used by convention when the value is not accurately known. Proteins have much higher values, typically between 50-100, and need longer gradient times for separation) Column: ZORBAX 300SB-C3, 4.6 x 150 mm, 5 µm Gradient: 15-35%B in 19 min Mobile Phase: A: 95:5 H2O : acetonitrile with 0.1% TFA

B: 5:95 H2O : acetonitrile with 0.085% TFA Temperature: 35 °C Detection: UV 215 nm Sample: Peptides

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4. Gradient Elution Parameters

The chromatogram shown below is an example of a reversed phase gradient separation of herbicides.

Figure 1: Reversed phase gradient analysis of herbicides.

Column: C8, 4.6 x 150 mm, 5 μm Mobile Phase: A: H2O with 0.1% TFA, pH 2

B: Acetonitrile Flow Rate: 1.0 mL/min Temperature: 35 °C

Typically, two solvents are used, as indicated by solvent reservoirs A and B in the chromatographic conditions shown. Reservoir A usually contains the weaker solvent, in this case, water with 0.1% TFA (pH 2). Solvent reservoir B contains the stronger solvent, acetonitrile.

The elution strength usually increases with time, as shown above, where the gradient starts at 20%B and ends at 60%B over 30 minutes. The gradient shown is a linear gradient that changes at a rate of 1.33% solvent B per min.

The mixing of the mobile phase composition is achieved using the HPLC pump, and two methods of mixing are common. The first is low pressure mixing, in which the solvents are proportioned on the low pressure side of the pump using solenoid valves. The second approach is known as high pressure mixing and occurs when two or more pumps are used to deliver solvents at differing flow rates into a mixing chamber.

To aid with solvent mixing, sometimes solvents are premixed or doped (i.e. solvent A contains 5% solvent B and vice versa).

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5. Optimizing Gradient Parameters

Several parameters are required to be specified and optimized in a gradient HPLC method (Figure 1).

Figure 1: Typical gradient profile.

Initial %B - starting mobile phase composition (described in terms of the % of the strong solvent B).

Isocratic hold - a period within the gradient in which the eluent composition is held at the initial %B. This achieves a degree of analyte focusing but also crucially enables easy transfer of gradients between different instruments based on the specific instrument gradient dwell volume (VD).

Gradient time (tG) - the time during which the eluent composition is changing.

Final %B - final mobile phase composition.

Purging - usually achieved using a short ballistic gradient ramp to high %B in order to elute highly retained components (of no analytical interest) from the column. There may be an isocratic hold at this composition to ensure elution of all analytes and strongly absorbed components of no analytical interest.

Conditioning - returning the system (specifically the column) to the initial gradient composition. In practice, with modern instruments, this step is programmed to occur very rapidly.

Equilibration - the time taken to ensure the whole of the analytical column is returned to initial gradient composition. This is an important step and if not properly considered can lead to retention time and quantitative variability. The equilibration time used is dependent on the column dimensions and flow rate. It is recommend that 10 column volumes (Vm) of eluent at the initial composition are used (calculate the time for the method flow rate and remember to add VD). The re-equilibration time can be reduced empirically; the method should be monitored for any retention time irreproducibility. The eluent flow rate can be increased during re-equilibration BUT ensure stabilization prior to injection of the subsequent sample.

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The rate of change of the mobile phase composition during the gradient can be calculated from equation 1.

∆%B/min =(%Bfinal − %Binitial)

tG (1)

Optimization of the initial and final %B can be carried out using Equation 2 and 3.

Optimized %Binitial = (%Binitial + (ti x ∆%B/min)) − (VD

F x ∆%B/min) − 10%B (2)

Optimized %Bfinal = (%Binitial + (tf x ∆%B/min)) − (VD

F x ∆%B/min) − 10%B (3)

Where:

%Binitial = initial starting %B from scouting gradient

ti = elution time of the initial peak

tf = elution time of the final peak

Δ%B/min = rate of change of the mobile phase composition (Equation 1)

VD = dwell volume

F = flow rate

The re-equilibration time can be calculated using Equation 4:1

Required re − equilibration time =2(VD + Vm)

F

Where:

VD = dwell volume

Vm = column volume

F = flow rate

1. Schellinger, A.P; Stoll, D.R.; Carr, P.W. J. Chromatogr. A 2005, 1064, 143-156.

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6. Gradient Elution Principles

Gradient elution is most useful for reversed phase and ion exchange liquid chromatography.

The gradient is formed by increasing the percentage of organic solvent. Consequently, at the beginning of the analysis, when the mobile phase strength is low, the analyte will be partitioned wholly into the stationary phase (or focused) at the head of the column. (Region A in the movies below)

As the mobile phase strength increases, the analyte will begin to partition into the mobile phase and move along the column. As the mobile phase strength is increasing continuously, the rate at which the analyte moves along the column accelerates. (Region B in the movies below)

At some point within the column elution, the analyte may be wholly partitioned into the mobile phase, and will be moving with the same linear velocity as the mobile phase. (Region C in the movies below)

One cannot assign a fixed retention factor (k) value to a compound when gradient elution is applied, as this value changes during elution.

Calculating k using the formula k = (tr-t0) / t0 is only correct during isocratic elution.

Figure 1: Gradient elution principles for large biomolecules.

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Figure 2: Gradient elution principles for hydrophobic analytes.

Figure 3: Gradient elution principles for small polar analytes.

The relationship between the gradient retention factor and the mobile phase composition depends upon molecular properties. Band spacing may change as column length is altered.

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Figure 4: Effect of altering column length in gradient elution.

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7. Peak Shape in Gradient HPLC

In isocratic elution the peaks are relatively broad, the peak width increasing with retention time. In gradient elution, the peaks are narrow with almost equal peak widths.

Figure 1: Analyte elution under isocratic conditions.

The main reason for the narrow peak shape is the velocity of the peak as it leaves the column. During gradient elution, all compounds accelerate through the column and thus elute at a high velocity. The retention time difference between compounds is a consequence of the percent organic modifier at which each starts to accelerate. All compounds should have approximately the same speed when they leave the column.

Another reason for peak focusing is the fact that the front and tail of a peak are residing in different concentrations of organic modifier. The tail will experience a higher percentage of organic modifier than the heart of a peak. The velocity of the tail will thus be slightly higher than the heart of the peak and vice versa for the front. This results in peak focusing. Asymmetric peaks are less frequently a problem in gradient elution. In practicality, the narrow peaks obtained in gradient elution provide better detection limits and higher loading capacities.

Figure 2: Analyte elution under gradient conditions.

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8. Scouting Gradients

When developing either gradient or isocratic separations – a scouting gradient analysis is a good starting point.

The scouting gradient is a linear gradient from 5-10%B to 100%B over a set time (20 minutes is standard). The elution strength is held at 100%B for a few minutes to make certain that all sample components have eluted. For reversed phase gradient elution, water (or buffer if there are ionizable analytes) and acetonitrile are typically the eluents of choice. The use of volatile buffers, for example ammonium formate, will result in a method which is LC-MS compatible.

The chromatogram obtained can reveal a lot about the required mobile phase composition for the separation.

If compounds elute more than 25% of the gradient time after the end of the gradient (i.e. after 25 mins. in our example), then a stronger B solvent is required for the analysis – or a less retentive column.

Equation 1 can be used to determine if an isocratic separation is possible - this is always preferred as it increases sample throughput (no re-equilibration time) and simplifies the analysis.

The mobile phase composition, at which the first peak elutes, should be used as the initial mobile phase composition when developing a gradient.

Figure 1: Scouting gradient used to assess viability of performing an isocratic separation and to

calculate the initial %B for a gradient separation.

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Worked Example

Isocratic analysis possible when scouting gradient:

ΔtG < 0.25tG (1)

Where: tG = gradient time

ΔtG = (tf - ti)

For the above scouting gradient:

ti (elution time of initial peak) = 12.8 min.

tf (elution time of final peak) = 21.2 min.

ΔtG = 21.2 - 12.8 = 8.4 min.

0.25tG = 0.25 x 20 = 5 min.

ΔtG > tG therefore, isocratic analysis is NOT POSSIBLE for this analysis.

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Figure 2: Scouting gradient used to calculate the isocratic eluent composition if isocratic elution is

feasible.

If isocratic analysis is found to be possible, the isocratic mobile phase composition can be simply estimated.

From the scouting gradient, calculate the mobile phase composition for the average retention time of the eluted compounds; that is:

tr(avg) = (ti + tf)/2

If isocratic analysis had been possible in this case then:

tr(avg) = (12.8 + 21.2)/2 = 17.0 min.

To calculate the isocratic mobile phase composition, first calculate the rate of change of %B (i.e. Δ%B/min)

Δ%B/min = (%Bfinal - %Binitial)/tG = (100 - 5)/20 = 4.75 %B/min

Then calculate the eluent composition at the average analyte elution time as follows (remember to take into account the initial eluent composition of 5%B):

Isocratic composition = (Δ%B/min x tr(avg)) + %Binitial

Isocratic composition at 17 min = (4.75 x 17) + 5 = 85.75 ≈ 86%B

Therefore, the mobile phase composition that should be used for the isocratic analysis is:

14% water (or buffer at the correct pH and concentration) / 86% acetonitrile.

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9. Optimizing Initial Gradient Conditions

1. Perform a scouting a scouting gradient

Figure 1: Initial scouting gradient.

2. Can the method be carried out isocratically?

∆tG < 0.25tG

∆tG = tf − ti

= 21.142 − 12.786 = 8.536 minutes

0.25tG = 0.25 x 20 = 5 minutes

Where: ti = time of the initial peak (12.786 min in this case) tf = time of the final peak (21.142 min in this case)

ΔtG > 0.25tG therefore, isocratic analysis is NOT possible for this separation.

3. Calculate the rate of change of the mobile phase composition using Equation 1.


tG (1)

=(100 − 5)

20

= 4.75 %B/min

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4. Optimize the initial %B required using Equation 2.

Optimized %Binitial = (%Binitial + (ti x ∆%B/min)) − (VD

F x ∆%B/min) − 10%B (2)

= (5 + (12.786 x 4.75)) − (5.5

2 x 4.75) − 10%B

= 42.67 %B

5. Optimize final %B using Equation 3.

Optimized %Bfinal = (%Binitial + (tf x ∆%B/min)) − (VD

F x ∆%B/min) − 10%B (3)

= (5 + (21.142 x 4.75)) − (5.5

2 x 4.75) − 10

= 82.36 %B

The initial gradient conditions can then be programmed to 42-83 %B in 20 minutes. From this point the gradient can be further optimized to produce the desired separation.

Figure 2: Initial optimization.

Where: %Binitial = initial starting %B from scouting gradient ti = elution time of the initial peak tf = elution time of the final peak Δ%B/min = rate of change of the mobile phase composition (Equation 1) VD = dwell volume F = flow rate

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10. Gradient Steepness

Gradient steepness is controlled by the mobile phase starting and ending composition and the gradient time.

The steepness of the mobile phase gradient can have a significant effect on the separation – below are some examples.

The retention factor (k*) in gradient HPLC is different from isocratic elution. In gradient HPLC the retention factor of each analyte is constantly changing as the eluotropic strength of the mobile phase is altered. k* can be thought of as an average k value throughout the separation.

Values of 2 < k* < 10 are desired. A good starting value for k* is 5. Gradient conditions should always be checked (using the equation for k*) to ensure a reasonable value of k* can be achieved.

Usefully, the equation may be rearranged to obtain an expression that predicts the gradient time, based on a scouting gradient as previously described. Each of the terms in the equation is defined below. All terms in the equation are simply defined which makes the equation particularly useful in practical terms.

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𝑘∗ =tGF

SΔΦVm

Where: k* = target value of 5 for average separation tG = gradient time (minutes) F = flow rate (mL/min) Δφ = change in volume fraction of organic (final %B – initial %B) expressed as a decimal Vm = the interstitial volume of the column (µL)

Vm = π (dc

2)

2

L0.68

Where: dc = column diameter (mm) L = column length (mm) S = shape selectivity factor (5 is a good estimate for small molecules) (Equation 3)

S = 0.25MW0.5 Where: S = shape selectivity factor MW = compound molecular weight

Below is a worked example for the application presented. Gradient times above those estimated by the equation shown are unlikely to produce better resolution.

Theoretical Gradient Time

More gradient time will not considerably improve resolution.

tG =𝑘∗SΔΦVm

F

=5 x 4 x 0.95 x 1.7

2

= 16.15 min

Where: k* = 5 for average separation S = 4 for small molecules Δφ = 5-100% = 95% = 95/100 = 0.95 Vm = 1.7 mL (4.6 x 150 mm column) F = 2 mL/min

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11. Optimizing Gradient Analyses

It is worthwhile taking a further look at the terms in the equation for the gradient retention factor, as there are several ways in which a gradient separation may be improved. Also, the manipulation of the gradient retention factor is counter intuitive from knowledge gained about isocratic HPLC.

𝑘∗ =tGF

SΔΦVm

Where: Δφ = change in volume fraction of organic (final %B – initial %B) expressed as a decimal S = constant determined by strong solvent and sample compound (small molecules < 500 Da the value is between 2 and 5; a value of 4 is used by convention when the value is not accurately known) F = flow rate (mL/min.) tG = gradient time (min.) Vm = column void volume (πr2L x 0.68) 1/k* = gradient steepness

From the equation it follows that in order to INCREASE the gradient retention factor you can:

Use a longer gradient time (shallow gradient)

Use a shorter column

Use a higher flow rate

Use a shorter organic range (Δφ)

The use of shorter columns and higher flow rates to GAIN retention in reversed phase HPLC will be counter intuitive. Here are some of the more important terms with a further explanation on how these changes will increase the gradient retention factor and how they may be usefully manipulated.

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To increase k*:

Use a longer gradient time (tG)

Usually gradient slope is expressed as %B/min.

Gradient slope for a given column dimension is however more correctly given as %B/mL. It is flow and not time that transports a compound through the column. An increase in flow rate consequently means a decrease in gradient slope, i.e. typically an improvement in resolution and vice versa. The change in plate number with flow rate may counteract this. The net effect is case dependent. However, changes in band spacing may occur as with any alteration of a gradient slope.

Analyte elution times are less flow rate sensitive than in isocratic analysis. This is best understood by considering a simplified case: Take a molecule that does not migrate when the organic modifier percentage is below 30% but when it is above 30% it moves at the same velocity as the mobile phase. The gradient reaches 30% at 20 minutes.

At a flow rate of 1 mL/min the compound elutes at 22 minutes, i.e. it does not move for 20 minutes and then it goes through the column in two minutes.

Increasing the flow rate to 2 mL/min will results in an elution volume of 21 minutes - a much less significant change in retention behavior compared to isocratic analysis.

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Use a shorter column (Vm)

This example shows the increase in resolution gained for this separation of proteins and peptides by decreasing Vm, using a shorter column, and therefore increasing the gradient retention term. It is counter intuitive compared to isocratic HPLC and something similar may happen with changes in flow rate. The effect may not improve resolution depending on changes in the efficiency of the separation.

Gradient: 2-75%B in 30 min. Mobile Phase: A = 5:95.MeCN : H2O 0.1% TFA

B = 95:5.MeCN : H2O 0.085% TFA Flow Rate: 1 mL/min. Injection: 10 µL, 2.6 µg each Temperature: 35 °C Detector: UV 215 nm

The tradeoff between flow rate, column length, and time is similar for isocratic and gradient elution. When separation time is a vital issue, use a short column (5-15 cm) and run at high flow rate. When maximum resolution is crucial it is advisable to use a long column (20-30 cm) at normal flow rate.

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Compounds with a very steep velocity curve (e.g. proteins) do not benefit from long columns. These compounds quickly reach (after a few centimeters of acceleration) a k* = 0 i.e. no stationary phase interaction.

When applying steep gradients it is actually counterproductive to use a long column as the compounds reach k = 0 (no partitioning) before leaving the column. The last part of the column then only adds band broadening.

Use a higher flow rate (F)

Increased gradient retention improves resolution of several peak pairs - 1, 2 and 4, 5

In this example the gradient time has been extended, therefore, reducing the gradient steepness. This can affect the gradient retention factor as well as the selectivity of the separation.

1

𝑘∗ ∝ gradient steepness = b =

SΔΦVm

tGF

If b is kept constant from run-to-run peaks will elute in the same relative pattern, but overall analysis time can be shortened.

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In this separation the gradient time and column length have been altered in order to retain the same gradient steepness value. In this case the order of peaks remains constant.

Use a shorter organic range (Δφ)

It should be highlighted that although k* is increasing, this will not necessarily improve the resolution - decreases in efficiency may counteract any benefit. This will depend upon the parameter being altered and the specific application type.

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12. Practical Gradient HPLC

A few practical considerations for running gradient elution chromatography:

Due to long column equilibration times, applications using strongly retained components such as triethylamine are not suitable. For the same reasons, ion pair applications are not suited to gradient elution.

Normal phase HPLC applications utilizing bare silica columns are not suitable either. Long equilibration times lead to retention time imprecision.

Solvents utilized in gradient elution must be pure. Water quality is of particular importance. Impurities are retained on the column while the composition of the mobile phase is weak. As the elution strength is increased, the impurities appear as peaks in the chromatogram. The chromatogram shown is a real-life example of these ghost peaks – the impurities are from the water, which has been inappropriately stored.

To avoid precipitation problems within the instrument, test the buffer to make certain it is soluble in the final mobile phase composition.

Finally, to increase retention time precision, make certain that adequate re-equilibration time is allowed between each chromatographic run. This is usually around 10 column volumes but may vary widely with different columns and applications. To be certain, retention time reproducibility should be verified during the analytical development.

Ghost peaks in gradient analysis can be caused by impurities in the solvents used - water is particularly susceptible to this phenomenon.

Gradient elution may not be suitable for:

Applications utilizing strongly retained additives

Ion pair applications

Normal phase liquid chromatography on bare silica due to water adsorption and irreproducibility

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Column: C18 Gradient: 100% water to 100% acetonitrile in 20 min. Flow Rate: 1 mL/min.

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13. Changing Method Parameters

Increased throughput can be achieved by speeding up gradient analyses. However, when changing any parameter in order to decrease analysis time the effect on the chromatography (retention factor, selectivity etc.) must be taken into account. For example, under isocratic conditions increasing the flow rate will decrease the retention factor (k) resulting in a faster analysis.

Retention factor in isocratic HPLC is determined by Equation 1. An increase in flow rate under isocratic conditions will decrease both tR and t0 by the same factor, hence, k will remain constant.

𝑘 =tR − t0

t0 (1)

Where: tR = retention time t0 = void time

However, if flow rate alone is changed in gradient HPLC the retention factor k* will be altered, which in turn can have an impact on selectivity and resolution, often leading to a change in elution order in the chromatogram. This is unsurprising when the equation for calculating k* is considered (Equation 2).

𝑘∗ =tGF

SΔΦVm (2)

Where: tG = gradient time (minutes) F = flow rate (mL/min) Δφ = fractional change in eluent composition (i.e. 0.4 for a 20 to 60 %B gradient) Vm = the interstitial volume of the column (µL) (Equation 3)

Vm = π (dc

2)

2

L0.68 (3)

S = shape selectivity factor (5 is a good estimate for small molecules) (Equation 4)

S = 0.25MW0.5 (4)

It can be seen from Equation 2 that the retention factor (k*) in gradient HPLC is different from isocratic elution. In gradient HPLC the retention factor of each analyte is constantly changing as the eluotropic strength of the mobile phase is altered. k* can be thought of as an average k value throughout the separation.

The retention factor is dependent upon the eluent flow (F) as well as the interstitial volume within the HPLC column (Vm, and hence the column length and internal diameter). The Fundamental Resolution Equation (Equation 5) shows that altering retention can alter resolution, therefore, the ability to alter retention by changing only flow rate or column dimensions in gradient HPLC has a direct effect, albeit limited, on resolution.

RS =√N

4

α − 1

α

k

k + 1 (5)

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Equation 2 also allows gradient separations to be modified in order to decrease analysis time, without incurring changes in analyte selectivity. In order to maintain selectivity the gradient steepness 1/k* (often termed ‘b’) must be maintained (Equation 6).

b =SΔΦVm

tGF (6)

This can be achieved as follows:

Change in flow rate - alter tG to keep b constant

Change in column length - alter tG or F to keep b constant

Change in column internal diameter - alter tG or F to keep b constant

Most modern applications of fast gradient HPLC arise when moving from traditional HPLC to UHPLC formats. This usually involves a change in column dimensions and gradient time as well as alterations to the flow rate.

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14. Gradient Suitability

Ideally for any method retention factors (k*) of between 2 and 10 are desirable for method robustness. The use of UHPLC instrumentation and columns does allow these limits to be altered to 0.5 < k* < 5. If k* is too low there is a risk of interference from other sample components or analytes, and if k* is too high the analysis time will be unnecessarily long. The suitability of a method can be determined using Equation 1.

𝑘∗ =tGF

SΔΦVm (1)

Where: tG = gradient time (minutes) F = flow rate (mL/min) Δφ = fractional change in eluent composition (i.e. 0.4 for a 20 to 60 %B gradient) Vm = the interstitial volume of the column (µL) (Equation 2)

Vm = π (dc

2)

2

L0.68 (2)

S = shape selectivity factor (5 is a good estimate for small molecules) (Equation 3)

S = 0.25MW0.5 (3)

Example Calculations

Traditional HPLC Method Column: C18 150 x 4.6 mm, 5 µm Flow: 1.5 mL/min Gradient: 20-65% acetonitrile (0.1% formic acid) in 7 minutes

Vm = π (dc

2)

2

L0.68

= π (4.6

2)

2

x 150 x 0.68

= 1695 μL = 1.7 mL

𝑘∗ =tGF

SΔΦVm

=7 x 1.5

5 x 0.45 x 1.7

= 2.75

A k* value of above 2 indicates that this method will be suitable.

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Fast HPLC Method Column: C18 50 x 2.1 mm, 1.8 µm Flow: 0.9 mL/min Gradient: 20-65% acetonitrile (0.1% formic acid) in 2 minutes

Vm = π (dc

2)

2

L0.68

= π (2.1

2)

2

x 50 x 0.68

= 118 μL = 0.12 mL

𝑘∗ =tGF

SΔΦVm

=2 x 0.9

5 x 0.45 x 0.12

= 6.67

A k* value of above 6 indicates that this method will be suitable, although, the method could be run a little faster without loss of robustness.

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15. Method Transfer Between HPLC Systems

One of the most common problems encountered when transferring a gradient HPLC method between instruments are irreproducible gradients and, therefore, inconsistent chromatographic results.

One cause of irreproducible gradients is that instruments will have different dwell volumes. The dwell volume is the volume between the point at which the gradient is mixed, to the point at which that composition enters the HPLC column; this will differ depending on how the gradient is formed (high or low pressure mixing), the tubing volume, internal volume of the autosampler and loop etc.

Differences in this system dwell volume (VD) can make large differences to not only the retention in gradient HPLC but also to selectivity and, hence, resolution. In order to account for dwell volume differences an isocratic hold can be included in the method or an injection delay can be used.

See the following CHROMacademy pages for determining dwell volume:

http://www.chromacademy.com/frameset-chromacademy.html?fChannel=0&fCourse=1&fSco=29&fPath=sco29/hplc_3_2_13.asp

Even though the system dwell volume has been catered for by altering the gradient start time (either starting the gradient prior to injection or inserting an isocratic hold at the start of the gradient), there can still be problems with irreproducible separation selectivity.

This problem results from differences in the way that gradients are formed and delivered and the inherent pump volumes associated with solvent mixing. It is important to note that this problem can be seen when transferring methods between different quaternary HPLC systems and is not only associated with method transfer between high and low pressure mixing systems.

UHPLC systems have markedly different technologies to mix the required gradient composition online and, as well as having different gradient composition delay characteristics, there will be differences in the slope and wash out characteristics of the gradient delivery profiles as shown in Figure 1.

Figure 1: Gradient profile determination for two UHPLC systems.



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Unless one can compensate for the differences in the gradient delivery characteristics, then successful method translation may be difficult. Whilst some UHPLC systems are equipped with software which can simulate differences from certain manufacturer’s equipment, not all systems are similarly equipped.

The following approximation can be used to adjust the gradient profile between systems, once the gradient slope or wash out volume (wash out time x flow rate) has been characterized:

New segment time = Original segment time ×Original system wash out volume

New system wash out volume

Adjusting the gradient segment times as outlined above will adjust the slope of the gradient delivered by the new system. When combined with a similar adjustment to account for dwell volume differences at the beginning of the analysis, this can help to more closely match the solvent composition at the head of the analytical column at any given time within the gradient.

Measuring Wash Out Volume

The wash out volume is the volume required for the instrument to wash out the strong solvent channel and can be as much or more than the dwell volume. This can affect both method transfer and re-equilibration time i.e. re-equilibration cannot occur until the initial eluent conditions are reached. An estimate of the wash out volume is when the eluent at the column inlet contains 3% of the final eluent (i.e. 97% flushed).

The wash out volume can be measured using a step change from 100%B to 100%A. B is water with 0.1% acetone and A is water (monitor at 254 nm).

Figure 2: Wash out profile of a conventional instrument at 1.0 mL/min.

1. Schellinger, A.P; Stoll, D.R.; Carr, P.W. J. Chromatogr. A 2005, 1064, 143-156.

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16. Gradient Method Transfer Calculator

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17. Non-Linear Gradients

Most gradient elution methods use linear gradients as has been shown previously, however, the use of non-linear gradients may provide modest improvements for some separations. In the early days of gradient HPLC with online solvent mixing, curved gradient profiles were popular and various manufacturers offered the possibility of forming gradients of the type shown in Figure 1.

Figure 1: Curved gradient profiles.

In practice, curved gradients are difficult to reproduce on a consistent basis and are especially difficult to transfer between different instruments/laboratories, and for that reason they are now much less popular.

In modern gradient HPLC, the approach is to use multi-segment linear gradients to achieve optimum resolution for more difficult separations. Generally this involves changes in gradient slope or the insertion of isocratic segments into the gradient profile. Non-linear gradients can be applied to separations of homologous or oligomeric samples, which exhibit a decrease in resolution with an increase in molecular weight.

Separations which produce chromatograms with bunched, overlapping, or widely separated peaks within different areas of the chromatogram, or where analytes will show alternate selectivity for gradients of different slopes at varying points in the chromatogram.1

1. Snyder, L. R.; Kirkland, J. J.; Glajch, J. L. Practical HPLC Method Development 2nd Ed. John Wiley & Sons Inc., 2011.

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18. Segmented Gradients

Segmented gradients can be applied to chromatograms which exhibit critical pairs (or groups) of peaks that are widely spaced within the initial chromatogram.

The chromatogram shown in Figure 1 (top) has critical peak pairs at points 1 and 2. The issue is that they are widely spaced in the gradient and a universal reduction in gradient slope will not solve both problems. Generally, poorly resolved peaks require a change in the slope of the gradient.

Usually this will involve lowering the slope of the gradient profile, however, in some cases a steeper gradient may force one peak to move through the other and solve the issue. There are no hard and fast rules regarding the time (or gradient composition) at which the slopes should be altered and the use of simple chromatographic optimization software can help enormously to visualize gradient slope changes and their effect on the resulting chromatogram. Segmenting the gradient will enable independent control over the early and later portions of the chromatogram resulting in the satisfactory separation of both critical pairs.

Figure 1: Original gradient profile (top) and segmented gradient (bottom).

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Optimization of Segmented Gradients

From the initial gradient the slope can be segmented in an infinite number of ways. As shown in Figure 2, starting from the initial gradient and overlaying a grid (4x8 grid in this case) at possible break points in the gradient can result in 19 possible alternative gradient profiles.1 If a more complex grid were used then the number of possible gradients would increase. Therefore, it can be seen that the use of computer software to visualize each of these gradients and the effect on the chromatography can be invaluable.

Figure 2: Optimization of a segmented gradient profile.

Solid blue line = initial gradient profile, dashed lines = alternative gradient profiles.

1. Jupille, T.; Snyder, L.; Molnar, I. LCGC Europe 2002, 2-6.

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19. Isocratic Hold

When separation problems occur at the midpoint of the chromatogram, an isocratic hold is useful to help increase resolution. As a rule of thumb, the gradient steepness should be retained from the original method.

The isocratic composition is calculated by subtracting 10%B from the elution composition of the first peak in the problematic region of the original chromatogram (52% as indicated in Figure 1). If the isocratic eluent composition is not satisfactory, the eluent composition should be reduced in steps of 10%B.

The length of the isocratic hold is typically matched to the duration of the problematic region in the original chromatogram. This of course can be lengthened if required. The gradient steepness after the isocratic hold should once again be matched to the original method.

Once again, the separation can be empirically optimized and computer optimization can assist enormously.

Figure 1: Original gradient profile (top) and gradient profile with isocratic hold (bottom).

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Example Calculation

The following equations can be used to calculate the composition of the isocratic hold required to resolve a critical peak pair in a gradient HPLC method.

Method Gradient: 5-100 %B tG = 30.48 minutes Flow rate = 2 mL/min VD = 1.7 mL Critical pair at 9.25 minutes

The rate of change of the mobile phase composition during the gradient can be calculated from equation 1.


tG (1)

=(100 − 5)

30.48= 3.117 %B/min

Optimization of the %B used in the isocratic hold can be carried out using Equation 2.

Optimized %Biso = (%Binitial + (ti x ∆%B/min)) − (VD

F x ∆%B/min) − 10%B (2)

= (5 + (9.25 x 3.117)) − (1.7

2 x 3.117) − 10%B

= 21.18 %B

Therefore, the isocratic hold would be added into the method at 21%B and held until the peak pair was resolved before continuing the gradient at the same gradient steepness as the original method.

Where: %Binitial = initial starting %B from scouting gradient ti = elution time of the initial peak Δ%B/min = rate if change of the mobile phase composition (Equation 1) VD = dwell volume F = flow rate

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20. Peak Capacity

The separation efficiency of columns under isocratic elution conditions is measured in theoretical plates. Peak capacity is used to describe the separation efficiency for gradient elution. Peak capacity describes the maximum theoretical number of components that can be successfully separated with a given column and set of analytical conditions with Rs =1 (Figure 1 and Equation 1).1-2

Equation 1 can be used to give an approximation of the number of components that can be separated under a specific set of conditions, if this number is lower than the number of components in a sample then the method will not produce a chromatogram with resolved peaks.

P ≈ 1 +tG

w (1)

Where: tG = gradient time w = average peak width at 4σ (13.4% of peak height)

Note: This is an approximation but a good guide. The average peak width can be calculated by adding the peak widths of the first and last peaks and dividing by 2.

Figure 1: Calculation of peak capacity.

Peak capacity is a function of gradient time, flow rate, column length, and particle size. Increasing column length while keeping particle size and gradient time constant results in a maximum value of peak capacity being reached, and in fact, for longer columns the value of peak capacity may decrease (Figure 2).

Improving peak capacity using particle size seems to give more promising results, with the decrease in particle size giving higher peak capacity values. Increasing the gradient duration will increase the peak capacity; however, for longer gradients the increase in peak capacity with time becomes small as a maximum will be reached.

Peak capacity can be optimized using the flow rate at a fixed gradient time (tG). Peak capacity will increase proportionally to the square root of column efficiency (Equation 2); therefore, doubling column efficiency will increase peak capacity, but only by 40%.

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P = 1 +√N

4

B∆C

B∆Ct0tG

+ 1 (2)

Where: N = efficiency B = slope of the function ln k (k is the retention factor) versus solvent composition C ΔC = change in solvent composition t0 = breakthrough time tG = gradient time

Figure 2: Plot of tG/t0 vs. P giving the optimal peak capacity for a separation.

1. Gilar, M.; Daly, A. E.; Kele, M.; Neue, U. D.; Gebler, J. C. J. Chromatogr. A 2004, 1061, 183-192.

2. Wang, X.; Stoll, D. R.; Schellinger, A. P.; Carr, P. W. Anal. Chem. 2006, 78, 3406–3416.

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21. Estimating Gradient Parameters

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22. Gradient Performance Checks

To proportion and mix a reliable gradient the components of the HPLC pump must be functioning correctly. Carrying out regular gradient performance checks on equipment can be used to:

Test the solvent delivery system (highlight malfunctioning check valves, leaks etc.)

Test gradient performance (indicate failures with low pressure valves, electronic control of pumps etc.)

Test proper mixing of high salt buffer gradients used in biochemical applications

Test the linearity and influence of stray light on detectors

Gradient performance checks can be carried out using a simple generic step gradient, or under the analytical conditions which are to be used. For biological applications where systems are required to mix high salt buffers using the analytical conditions can be advantageous to ensure proper gradient formation.1

A gradient performance check (on high or low pressure systems) can be carried out as follows:

Remove the column and replace with a restriction (1 m x 0.125 mm)

Solvent A and B are water/water*, MeOH/MeOH*, MeCN/MeCN* (*solvent B spiked with UV active compound) or the mobile phases which will be used for the specific application

For most applications use 0.025% benzoyl alcohol as the UV active compound and monitor at 254 nm. For applications that use high salt buffers benzyl alcohol will not be suitable due to poor solubility; in this case acetone, uracil, or another appropriate UV active compound can be used

Program a step gradient from 0-100 %B in 10% steps

Run the gradient over a range of flow rates to ensure correct mixing at all possible flow rates that may be used. The steps for the gradient produced by the HPLC system should be flat with a slight rounding at the edge of the step (Figure 1). The step size for each step should be calculated and should be within 1% of the theoretical (programmed) value2

Figure 1: Step gradient.

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Gradient proportioning valves on low pressure mixing systems can also be tested as follows:2

1. Remove the column and replace with a restriction (1 m x 0.125 mm). 2. Water is placed in reservoir A and inlet lines A and C are placed in this reservoir. 3. Water and 0.1% acetone are placed in reservoir B and inlet lines B and D are placed in this

reservoir. 4. The UV absorbance of acetone is measured at 265 nm. 5. Flow rate is set to 2 mL/min. 6. 1-2 minute steps are programmed as per Figure 2. 7. A properly functioning system should have the plateau heights within 1-2% of each other.

Figure 2: Gradient proportioning valve check.

1. Marten, S.; Knöfel, A.; Földi, P. LCGC Europe, 2008. 2. Gilroy, J. J.; Dolan, J. W. LCGC Europe, 2004, 566-572.

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