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  The CHROMacademy Essential Guide to Understanding Gradient HPLC

Tony Taylor
Technical Director
Crawford Scientific.

Scott Fletcher
Senior Tutor

Peter Houston
Editorial Director
LCGC Europe
In this session, Scott Fletcher and Tony Taylor (CHROMacademy Technical Director), present a definitive guide to using, optimizing and troubleshooting Gradient HPLC. The session will consider key topics such as the mechanisms of Gradient HPLC versus isocratic elution, developing robust gradient HPLC methods, the dangers of altering column flow or column dimensions without proper gradient scaling and the essentials of troubleshooting gradient issues. A must see for everyone using or developing Gradient HPLC methods.

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The CHROMacademy Essential Guide to Understanding Gradient HPLC

A definitive guide to using, optimizing and troubleshooting Gradient HPLC, all supported by Interactive Multi-Media from The CHROMacademy. The session will consider key topics such as the mechanisms of Gradient HPLC versus isocratic elution, developing robust gradient HPLC methods, the dangers of altering column flow or column dimensions without proper gradient scaling and the essentials of troubleshooting gradient issues.

Scott Fletcher Scott Fletcher
Senior Tutor
Tony Taylor Tony Taylor
Technical Director
Crawford Scientific.


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Isocratic HPLC for reversed phase separations, whilst being both convenient and robust in its nature, has inherent issues, especially when dealing with compounds whose polarity (hydrophobicity) vary widely. Some of the generally accepted problems with isocratic separations include:

  • Poor resolution of early eluting peaks;
  • Increased peak width (potentially resulting in poor resolution and sensitivity) for later eluting analytes due to peak broadening caused diffusion of the analyte band;
  • The inability to cope effectively with analytes having a broad range of hydrophobicity (LogP or LogD), often resulting in unnecessarily long analyses; and
  • Contamination of columns by strongly retained components.

Gradient HPLC can help to overcome some of these issues. Gradients in reversed phase HPLC typically involve the on-line (dynamic) mixing of solvents to achieve a steady increase in the organic solvent (typically methanol or acetonitrile) over the course of the analysis, which serves to increase the elution strength of the eluent over time.

Some advantages and disadvantages of Gradient Elution HPLC are shown in Table 1

Table 1: Advantages and disadvantages of Gradient HPLC
Advantages of Gradient Elution:   Disadvantages of Gradient Elution:   Other uses of Gradient Elution:
  • Improved resolution
  • Increased sensitivity of later eluting analytes
  • Ability to separate complex samples
  • Improved peak shape
  • Shorter analysis times — especially for analytes whose polarity differs widely
  • Reduced column deterioration due to strongly retained components
  • More expensive instrumentation
  • Possible precipitation at interfaces, when using multiple proportioning valves
  • Re-equilibration time adds to analysis time
  • Instruments vary in their dwell volume (VD), which can cause method transfer problems
  • Column cleaning
  • Scouting runs for method development
The advantages of implementing a gradient separation are illustrated in Figure 1.
fig 1
Figure 1: Typical Isocratic and Gradient separations of environmentally persistent pollutants.
It can be clearly seen that the gradient separation provides better peak shape, higher efficiency and resolution, even revealing two peaks that weren’t seen in the isocratic separation. We will see later what might have been done to reduce the elution time of the first peak and how to manipulate the gradient conditions.

Three parameters are required to specify a gradient in reversed phase HPLC, although as we will see there are several other important considerations.
We need to be able to specify:

  • Initial %B;
  • Final %B; and
  • Gradient time (tG) over which the transition in eluotropic strength will be achieved.

In practice, there are several other very important parameters to be considered and these are highlighted in Figure 2.

fig 2

Figure 2: 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) (see later).
  • 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.

We will consider the important topics of the isocratic hold and gradient re-equilibration time shortly.

The ‘big’ questions in gradient HPLC are how to decide upon the initial and final eluent composition and the gradient time (tG) [or steepness (b)]. We have considered these questions several times in past editions of the Resolver, and you can follow THIS LINK to find further information on the technique known as the ‘Gradient Scan’. This technique uses a gradient over a wide range of eluotropic strengths in order to assess the elution behavior of the analytes of interest and then estimate the best values for the critical gradient parameters.

In order to better understand how we can optimize the gradient parameters and troubleshoot problems, we should first understand a little more about how Gradient HPLC works.

It’s interesting to draw a quick but effective analogy between Isocratic and Gradient HPLC.

In Isocratic HPLC, the analytes enter the HPLC column and, depending upon the partition co-efficient of the analyte between the mobile and stationary phase material (governed by many factors including the hydrophobicity of the analyte and its shape), moves at a constant pace along the column, undergoing successive partitioning events into the stationary phase, which controls analyte retention. Retention in Isocratic HPLC is measured using the Retention Factor (k) which is defined as:


fig. 3

Figure 3: Measurement of Retention Factor (k) in Isocratic HPLC.


In Gradient HPLC, things are somewhat different, as is explained below.

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 and will not be moving through the column at all
(Region A in Figure 4).

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 increases continuously, the rate at which the analyte moves along the column subsequently increases and the analyte ‘accelerates’ through the column (Region B).

At some point within the column, the analyte may be wholly partitioned into the mobile phase, and will be moving with the same linear velocity as the mobile phase. The point at which this occurs depends upon the nature of the analyte and its interaction with the stationary phase material (Region C).

  Figure 4: Retention behavior of an
analyte under Gradient HPLC conditions.
As the rate at which the analyte elution changes during Gradient HPLC, the Retention Factor (k) used above for isocratic separations is not applicable. Instead we use an ‘average’ retention value, k*, or the Retention Factor of the analyte as it passes the mid-point of the column. Most analytes will be moving at the same rate as they pass the mid-point of the column and hence the Retention Factors for all analytes in Gradient HPLC are very similar.

The Gradient Retention Factor is defined as follows;

Calculating k* for our gradient in Figure 1 above:

k* = 25 x 2 / (1.15 x 4 x 0.90 x 1.7) = 7.10

0.90 – the change in volume fraction of organic expressed as a decimal. 1.7 – the interstitial volume of the HPLC column (in mL) calculated using
(Π x 2.32 x 150 x 0.68).

The target value for k* for small molecules typically analysed using reversed phase HPLC is around 5 — so our value is in reasonable agreement.

Isocratic Hold
From an instrument perspective, gradients are formed in one of two ways:



The solvents are ‘proportioned’ and mixed using a valve on the low pressure side of the pump prior to passing through the pump heads and being delivered to the system. The percentage of each solvent is proportioned using the timing of the valve system in order to achieve the correct eluent composition. This is known as ‘Low Pressure’ mixing. This instrument type will typically have one (or one set) of pump heads with a separate proportioning valve.


Two solvents are pumped independently and are brought together under high pressure for mixing prior to delivery to the system. The correct composition is achieved by adjusting the speed or stroke volume of each of the two independent pumps within the system. This is known as ‘High Pressure’ mixing


The volume in the system between the points at which the gradients are mixed, to the point at which that composition enters the HPLC column 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. Whilst it may not be intuitively obvious, 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!

fig. 5  

Figure 5: Effect of System Dwell Volume on selectivity and resolution in Gradient HPLC.


Figure 5 clearly illustrates the effects of changing system volume on resolution. System A has a relatively low system dwell volume of 0.5 mL whereas System B has a very large (somewhat over exaggerated!) dwell volume of 5 mL. As well as affecting retention times, it can be seen that the earlier eluting peaks within the chromatogram suffer from a loss of resolution. This is often attributed to the differences in time (after injection) that the gradient profile moves through the column and a degree of isocratic elution that may occur when the gradient is still at the starting composition where dwell volumes are high.

This phenomenon is often the reason why chromatographers find it difficult to successfully transfer gradients from one system to another — especially when changing between high pressure and low pressure mixing systems, as typically High Pressure Mixing (Binary) pump systems have a much lower dwell volume then Low Pressure Mixing (Quaternary) pumps.

These issues can be successfully overcome by inserting an isocratic hold at the beginning of the gradient, which is often set to match the dwell time of the system (see below). In the example in Figure 5, the resolution in the chromatogram from System B may have been preserved if the injection had been delayed for 4.5 min after the gradient was started — effectively the injection is made 0.5 min before the initial change in eluent composition reaches the column, therefore matching System A’s performance characteristics. Similarly, if we were to transfer the method from System B to System A, an isocratic hold of 4.5 min could be added to the start of the gradient — again matching the two systems gradient delivery characteristics. Both of these approaches are possible with modern HPLC pumping equipment.

System Dwell Volume (VD)
In order to perform Gradient HPLC analysis and to transfer methods between instruments successfully, it is important to know the system Dwell Volume (VD).
This is reasonably straightforward to measure and the procedure is demonstrated in Figure 6.
fig. 6  

Figure 6: Determination of system Dwell Volume


To determine the system Dwell Volume (VD):

  • Remove the column from the system and replace with a restriction capillary
  • Run a gradient of 0–100% B over 20 mins using a UV transparent solvent (such as acetonitrile) as Solvent A and the same solvent doped at 0.1% with a UV active substance (such as Acetone) at a detection wavelength of 254 nm. MS users may want to choose solvents and dopants appropriate to their ionization and mass analysis techniques. Typically flows of 1 or 2 mL/min are used.
  • The gradient profile should resemble that in Figure 6 — use the profile to measure the 50% absorbance (or detector response) position (i.e., half way between the lowest and highest absorbance points in the gradient profile)
  • Note the time at which this 50% absorbance occurred. The system Dwell TIME is this time minus half of the gradient time (in our case ½ tG would be 10 min). The system Dwell Volume is the Dwell Time multiplied by the flow-rate as shown in Figure 6.

Re-equilibration Time

The time required to completely re-equilibrate the analytical column prior to the next injection is dependent upon the column dimensions and the flow-rate used. Most manufacturers recommend passing through ten column volumes of eluent at the gradient starting composition for complete re-equilibration, however this can be determined empirically by shortening or lengthening the re-equilibration time and carefully observing any irreproducibility in retention times on successive injections of a test mixture. Further, the equilibration time may be shortened by increasing the eluent flow-rate (take care not to exceed the maximum system operating pressure) during the equilibration phase, but care must be taken to ensure pressure stabilization at the original flow-rate prior to injection of the next sample.

The column volume may be calculated by using either of the two following approximations:

  • (Π x r2 x h x 0.68)
  • Column length (mm) / 100

For a 150 x 4.6 mm column this would equate to:

  • (Π x 2.32 x 150 x 0.68) = 1.7 mL
  • 150 / 100 = 1.5 mL

Following manufacturers specification will result in a re-equilibration time, at the initial gradient eluent composition, of approximately 15 minutes PLUS the system Dwell Volume at an eluent flow-rate of 1 mL/min.


fig. 7

Figure 7: Illustration of the effects of altering initial %B whilst keeping the gradient slope constant.


The chromatograms above illustrate the effect of increasing initial %B whilst keeping the gradient slope (i.e., the change in %B per minute) constant. As can be seen, the general effect is to ‘compress’ the initial section of the chromatogram first, and on further increasing the %B, the entire chromatogram will ultimately be affected, especially where analytes have similar hydrophobicity.

A reasonable rule of thumb for the initial %B is to note the composition of mobile phase at which the first peak elutes from the column
and reduce this by around 10%.

fig. 8


Figure 8: Illustration of the effects of altering final %B whilst keeping the gradient slope constant.

Figure 8 illustrates the effects of lowering the final %B whilst keeping the gradient slope constant. As can be seen there is little effect on the separation. However, it should be noted that for more highly retained components k*>10, the final %B should be adjusted so as to effectively elute the final components of the mixture. Failure to do so will result in later eluting, broad peaks, similar to those seen with isocratic analysis.


fig. 9


Figure 9: Illustration of the effects of altering gradient steepness (%B / min).

The slope of the gradient (%B / min) has a profound effect on resolution in Gradient HPLC. Generally as the slope of the gradient decreases the resolution increases. This is primarily due to the increase in k* as resolution is linked to Gradient Retention Factor via the usual resolution equation:

Rs = ¼ (N1/2)[α-1/α][k*/(1+k*)]      Equation 2

It should be noted that whilst the general trend is for resolution to improve as the gradient becomes shallower, this trend does not necessarily hold as the gradient becomes very shallow, but instead approaches a limiting value. This behavior is also very similar for Isocratic HPLC where increasing k* values
(above around k* = 10) do not significantly improve resolution.

fig. 10Further, it is also very important to note that for some gradient separations, resolution may be adversely impacted as gradient slope is reduced due to changes in selectivity between the analytes involved. The resolution map in Figure 10 plots minimum resolution (between any critical peak pair), against gradient time [longer gradient time (tG) equates to shallower slope]. It should be noted that resolution can both increase and decrease with increasing gradient time due to changes in analyte retention and selectivity.


Figure 10: Plot of resolution against gradient time for a
separation in which changes in selectivity effect resolution.


When developing gradient methods the gradient slope or time (tG) is an important parameter. We can usefully use Equation 1 to estimate a reasonable gradient time for the separation – by re-arranging in terms of tG as follows:

tG = 1.15 S k* ΔΦ Vm / F       Equation 3

A reasonable value for k* in Gradient HPLC is 5 — which gives good retention characteristics.

Therefore, in terms of our original gradient method from Figure 1 this would correspond to

tG = 1.15 x 4 x 5 x 0.9 x 1.7 / 2 = 17.6 min

In practice we might use an 18 min gradient for this separation.

FIG. 11

Figure 11: Effects of eluent flow-rate on critical pair resolution in Gradient HPLC.


The results in Figure 11 may come as somewhat of a surprise to some readers. Essentially we demonstrate that altering flow-rate in Gradient HPLC may lead to a change in analyte resolution. This is not due to changes in the efficiency with flow-rate, (as we see in Isocratic HPLC), but due to changes in selectivity within the separation.

In reality, we shouldn’t be too surprised when we consider Equation 1:

k* = tG F / 1.15 S ΔΦ VM

We can see that the retention factor in Gradient HPLC 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. Equation 2 showed the relationship between retention factor and resolution — therefore in Gradient HPLC, we can directly affect resolution by altering the eluent flow-rate or column dimensions — this is very different to Isocratic HPLC!

However, Equation 1 also helps us to rationalize how to avoid selectivity changes when a change in eluent flow or column dimensions is required. To avoid selectivity changes we merely need to keep 1/ k* (the gradient steepness often termed ‘b’) constant — this is usually achieved in the following ways:

Gradient steepness (b) = ΔΦ VM / tG F   (Equation 4)

  • Change in flow-rate – alter tG to keep k* constant
  • Change in column length - alter tG or F to keep k* constant
  • Change in column internal diameter - alter tG or F to keep k* constant

In the example in Figure 11, the flow-rate was scaled from 0.5 to 5.0 mL/min. The most convenient way to ‘balance’ the change in flow is to alter tG in order to achieve a constant value for k* — in this case the gradient time (tG) might have been scaled down from 60 to 6.0 min in order to maintain separation selectivity.

Most modern applications of Gradient Scaling arise when moving from traditional to ‘Faster’ HPLC formats. This usually involves a change in column dimension as well as alterations to the flow-rate.

fig. 12
Figure 12: Transferring traditional methods to higher throughput column dimensions.


tG in the original gradient method:

tG = 1.15 S k* ΔΦ Vm / F

tG = 1.15 x 4 x 5 x 0.55 x 1.7 / 1 = 21.5 min

To transfer to the higher throughput method we can use a derivation of Equation 1 as follows:

tG2 = tG1 x (VM2 / VM1) x (F1 / F2)   (Equation 5)

tG2 = 21.5 x (0.353 / 1.7) x (1000 / 600) = 7.5 min

Altering column length can result in even more drastic changes in selectivity within the chromatogram. Peaks may merge or swap elution order (known as peak inversion) — the principle behind this phenomenon is illustrated below:



Figure 13: Principles leading to peak inversion in Gradient HPLC.



In this example, because of the relationship between %B and Gradient Retention Factor, using a 10 cm column will result in Compound A eluting first. However, when a 25 cm column is used, the retention factors dictate that Compound B has enough distance to ‘overtake’ compound A and so elutes first.

It is also important to note that although the column length is more than doubled, the retention times of the peaks has not increased by this factor due to the nature of the way in which peaks migrate through the column under the influence of the changing gradient conditions.

In isocratic elution, peaks are relatively broad, the peak width increasing with retention time, due to increased diffusion of the analyte band. In gradient elution, the peaks are narrow with almost equal peak widths.

The main reason for the narrow peak shape in Gradient HPLC 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.


Figure 14: Principles governing peak shape in Gradient HPLC.



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


Figure 15: Peak focusing under Gradient HPLC conditions.



In the early days of Gradient HPLC with online solvent mixing, curvilinear gradient profiles were popular and various manufacturers offered the possibility of forming gradients of the type shown in Figure 16.

fig. 16   
Figure 16: Typical curvilinear gradient profiles.

In practice, curvilinear 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.

Some recommendations on when to use these techniques and their practical implementation are included below.

fig. 17

Figure 17: Illustration of the effect of changing gradient slope where critical pairs occur early and late in the chromatogram.

Figure 17 illustrates a possible approach to gradient optimization when critical pairs of peaks are widely separated within the gradient, that is, when there are separation issues at the beginning and end of the chromatogram. Generally, poorly resolved peaks require a change in 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.

fig. 18

Figure 18: Use of an isocratic hold to improve resolution in the mid-section of a gradient elution chromatogram.


Where the 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 18). 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.

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