In earlier lessons, we have assumed (mostly implicitly) that the mobile-phase composition remains constant throughout an LC run. While this is the defining feature of isocratic elution, in practice most LC separations are performed under gradient elution, where the solvent composition is deliberately varied during the analysis. Gradient elution increases the elution strength over time, enabling the efficient separation of complex mixtures containing analytes with a broad range of retention factors. In this lesson, we examine why gradients are used, the principles governing their operation, and how to design and implement gradient programs effectively. Special attention is given to gradient profiles, dwell volume effects, retention modelling under gradient conditions, and the practical considerations necessary for reproducible, high-quality separations.
Learning Goals #
After this lesson you should be able to
Explain the fundamental differences between isocratic and gradient elution, and identify situations in which gradient elution is advantageous.
Describe how mobile-phase composition changes during a gradient and how this influences retention and peak width.
Explain the influence of dwell volume, gradient deformation, and mixing efficiency on gradient performance.
- Recognize common artefacts and troubleshooting strategies specific to gradient-elution LC.
READ MODULE 3.4
Gradient Elution
1. Introduction #
The immense success of LC has meant that ever-more-complex samples are being analysed. Rather than mixtures of just we few analytes, we are confronted with mixtures containing dozens of analytes or more.
A case in point is the separation of a mixture of 32 peptides that is illustrated in Figure 1. If reversed-phase liquid chromatography (RPLC) experiments are performed with isocratic mobile phases (i.e. mobile phases of constant composition) containing 55, 60, 65, and 75% of methanol in water we obtain quite unsatisfactory results. All chromatogram fall well short of demonstrating a separation of 32 peptides.
Figure 1. Simulated isocratic chromatograms of a mixture of 32 peptides, based on retention data from K. Cohen et al., J. Chromatogr. 316, 1984, 359 [1].
The isocratic chromatograms from Figure 1 can be understood from a plot of retention vs. mobile-phase composition, as shown in Figure 2. The simple log-linear retention model
Equation 3.46b: \ln{k}=\ln{k_0}-S\cdot\phi
is used to summarize the experimental data. Each line denotes the retention behaviour of one of the peptides.
Figure 2. Retention plot of 32 peptides, based on retention data from K. Cohen et al., J. Chromatogr. 316, 1984, 359 [1].
At 55% methanol (\phi = 0.55), a few peptides are seen to elute below \ln{k} = 3 (i.e. k \approx 20), while most peptides are strongly retained (above \ln{k} = 5 or k \approx 150). If we move up to higher methanol contents (to the right in the figure), for example to \phi = 0.6 or \phi = 0.65 more peptides are eluted, while many remain retained beyond the analysis time of the chromatograms. At \phi = 0.7, a bunch of peaks are poorly resolved at very low retention times (below \ln{k} = -1 or k \approx 0.4), followed by a largely empty region. The peptide represented by the white line in Figure 2 corresponds with the isolated peak in the bottom chromatogram of Figure 1. At higher methanol contents (not shown), more peptides are eluted, but also an increasing number end up in the early bunch of poorly (if at all) resolved peptides in the beginning of the chromatogram.
Clearly, there is no isocratic composition that provides a satisfactory separation of the 32 peptides.
As the volume fraction of strong solvent increases (i.e. we are moving to the right in Figure 2), peptide retention factors start coming down and they are being mobilized or “swept up”, one after the other. An example is shown in Figure 3, where a linear gradient has been applied from 40 to 95% methanol in 60 min. Not all 32 peptides are separated, but this is due to overlap and not to peptides eluting unretained or remaining on the column. In the following sections we will discuss gradient elution in greater depth.
Figure 3. Simulated gradient-elution chromatogram of a mixture of 32 peptides, based on retention data from K. Cohen et al., J. Chromatogr. 316, 1984, 359 [1].
EXERCISE 1
Which of the following gradients are sensible and which are fundamentally nonsensical? For the last option, see Section 3.15.1 in the book.
Excellent!
Hint: Sensible gradients run from weak to strong elution conditions.
2. Types of gradients #
There are many different gradient programs, as illustrated in Figure 4. In isocratic elution (top left) the mobile-phase composition (vertical axis) is invariable with time. The other five frames all constitute gradients. Linear gradients, in which the composition varies linearly with time, are most common. They are simple to implemented and near-optimal for RPLC. However, in other cases – and for specific samples – other programs may be more desirable. For example, in ion-exchange chromatography (IEC) a convex gradient is more appropriate (in this case is the concentration of counter ion).
In Figure 5 some essential parameters associated with a gradient-elution experiment are indicated. The upward diagonal line is the actual linear gradient, with a duration t_{\text{G}}. The initial and final compositions, \phi_{\text{init}} = 0.5 and \phi_{\text{final}} = 0.7 can be found on the vertical axis. The line indicates the expected mobile-phase composition at the column exit. This is different from the gradient program, which starts at t = 0. As mentioned above, it takes a time for changes in the mobile-phase composition at the column inlet to take effect at the column outlet. In addition, the program may start with an initial hold period (t_{\text{init}}). Finally, there is an instrumental dwell, that expires before a signal to the instrument to change the composition actually results in changes at the start of the column. This dwell time (t_{\text{D}}) is determined by the flow rate (F) and the dwell volume (V_{\text{D}}) of the instrument through t_{\text{D}}=V_{\text{D}}/F. Here, V_{\text{D}} is an instrumental constant, whereas t_{\text{D}} is variable.
Figure 4. Important parameters in a gradient-elution experiment. The pink arrows indicate the composition at the column exit as a function of time.
At the end of the linear segment a final hold (duration t_{\text{final}}) may be programmed. It can be seen that peaks eluting in the linear segments remain narrow, while peaks that elute under isocratic conditions during t_{\text{final}} become increasingly broad.
Finally, it is prudent (with an eye on column lifetime) to program a reverse gradient in a short, well defined time, rather than an abrupt return to the initial composition, as indicated by the dashed pink line. The re-equilibration time (t_{\text{eq}}) prior to the next injecton should also be well defined, on ensure repeatability of the separation and the baseline.
EXERCISE 2
Your company has been running LC separations for many years and the technique has yielded reliable gradient-elution data all this time. However, your instrument was getting old, spare parts became difficult to find, and its lack of compatibility with the laboratory computer system became a frustration. Finally, your manager has agreed with the purchase of a high-efficiency binary pump system. You measure a reference analyte mixture. You obtain the following data.
The results shock you. To exclude as many factors as possible, you program exactly the same gradient, use the same solvents in the same reservoirs, and you make a run with the same column in both instruments.
3. Equilibria in the column #
All chromatographic experiments are based on a thermodynamic distribution of the analytes between the mobile phase and the stationary phase. In the context of gradient elution, it is important to realize that there is also an equilibrium between the mobile phase and the stationary phase. The actual composition of the stationary phase is determined by that of the mobile phase, so that the composition of both phases is subject to changes during the run.
Table 1. Summary of the effects of the mobile-phase composition on the stationary phase in various forms of liquid chromatography.
| Mode | Mobile-phase induced changes to stationary phase |
|---|---|
|
RPLC |
Alkyl chains at the surface are preferentially solvated by the organic modifier in the mobile phase. This causes an excess concentration of modifier in the stationary phase. |
|
HILIC |
A low concentration of water (typically a few percent) in an organic solvent, such as acetonitrile, causes an absorbed water layer on the stationary surface. |
|
NPLC |
Adsorption sites are covered by mobile-phase components, depending on their nature and concentration. Small amounts of water strongly affect the chromatographic behaviour of the stationary phase. |
|
IEC |
Association of ion-exchange groups at the surface with counterions depends on the mobile-phase composition.
The capacity of weak ion exchangers depends on the pH of the mobile phase.
|
|
IPC |
In ion-pair chromatography the ion-exchange character of the stationary phase is determined by the nature and concentration of the ion-pair reagent, and by the overall composition of the mobile phase (e.g. nature and concentration of organic modifier) |
To ensure that subsequent measurements are conducted under the same conditions it is crucial that the stationary phase is equilibrated. As gradients inherently involves changing mobile-phase conditions, gradient elution requires column equilibration time (t_{\text{eq}} in Figure 4).
READ SECTION 3.3.1
Hardware for LC
4. Instrumentation #
The performance of any liquid chromatographic separation is critically dependent on the quality and configuration of its instrumentation. In gradient elution, in particular, the precise delivery and mixing of mobile-phase components determine whether the programmed gradient matches the effective gradient experienced by the column. Even small deviations can alter retention behaviour, selectivity, and peak shape. This is thus a good excuse for us to take a look at the instrumentation used in LC.
Figure 5. Schematic animation of the flow paths of a binary pump system. The yellow marked area indicates the dwell volume. See text for further explanation. Note that the pump design can be different for different manufacturers.
4.1. Pump #
As with any chromatographic system, the delivery of the mobile phase is of critical importance. A pressure-driven pump is used to achieve this. Different blends of mobile-phase compositions can be delivered using different pump formats as shown in Figure 6.
ISOCRATIC
Single Solvent-
Delivers a single solvent.
-
Requires no mixer.
-
Suitable for separations with constant mobile-phase composition (e.g. size-exclusion chromatography and isocratic RPLC).
BINARY
Two Solvents-
Delivers (varying mixtures of) two solvents.
-
Allows accurate formation of gradients.
-
Typically features very efficient mixers to achieve a low dwell volume whilst maintaining a homogenous mobile phase.
-
Preferred for any high-resolution separation involving gradient elution.
QUATERNARY
Four Solvents-
Identical to an isocratic pump with a proportioning valve to draw from up to four solvent lines.
-
Greater flexibility of mobile phase composition.
-
Large mixers required for achieving a homogenous mobile phase yield a large dwell volume.
Figure 6. Overview of different pump systems and their main features.
Figure 6 shows that the binary (Figure 5) and quaternary (Figure 7) pump both allow gradient elution. Where the binary pump offers high efficiency mixing and low dwell volumes, the quaternary pump sacrifices this to benefit from greater mobile-phase flexibility.
Figure 7. Schematic animation of the flow paths of a quaternary pump system. The yellow marked area indicates the dwell volume. See text for further explanation. Note that the pump design can be different for different manufacturers.
Figures 5 and 7 show that the pump comprises of several components that have various critical functions. Figure 8 investigates these in more detail.
Figure 8. Clarification of several components of a pump.
At very high pressures it is easy to imagine that the flow will try to opt for the path of least resistance and flow backwards. To prevent this, pumps typically employ check valves. Check valves function similar to our own heart valves, but instead employ balls. This is depicted in Figure 9.
Figure 9. Animation depicting the function of check valves.
4.2. Injector #
A basic injector introduces a volume of sample identical to the sample loop volume into the mobile phase stream. A simple schematic is shown in Figure 10. It can be seen that a valve is used to achieve the repositioning of port connections. The autosampler introduces a precisely measured volume of sample automatically from different sample vials of choice. This automated robot is discussed in more detail in Section 3.3.1.4.
Key components of an autosampler include:
Needle and needle seat for sample aspiration and injection.
Sample loop for defined injection volume.
Waste ports for cleaning and rinsing to minimise carryover.
Figure 10. Schematic overview of a valve (A) and a basic injector (B). See the book for more elaborate configurations used in autosamplers.
Fast, reproducible injections are essential to minimise pre-column band broadening.
4.3. Column oven #
The column oven controls temperature to enhance reproducibility and sometimes selectivity. Stable thermal conditions also prevent retention time drift. In temperature-sensitive separations, precise oven control is vital. Column ovens may feature heat exchangers that pre-heat the incoming mobile phase prior to entering the column.
5. Gradient deformation #
In the previous section we have seen that adequate mixing of the different mobile-phase components is crucial for performing good gradient-elution LC experiments. We have seen that any volumes (mixers, capillaries, and possibly pump heads in case of low-pressure mixing) between the point where the mobile-phase components are brought together and the top of the column add to the dwell volume (V_{\text{D}}).
Figure 11. Gradient deformation for two different systems with respect to the programmed gradient.
Equally important is their contribution to deformation of the gradient. While short, narrow capillaries may contribute little band broadening in a chromatographic system, any dead spaces may be detrimental to the chromatographic efficiency and peak shape. For example, poor connections may easily lead to excessive peak tailing.
Analyte peaks do not pass through the dwell volume, but the gradient does. Every small fraction of the gradient is experiencing band broadening in the system. The requirements to achieve adequate mixing and to deliver perfect gradients are at odds. Greater mixing volumes result in greater deformation of the gradient, as illustrated in Figure 11 (Left).
The extent of gradient deformation can be characterized through a response function (Figure 11, right). The observed gradient is the convolution integral of the programmed gradient and the response function. Actual gradient profile can be measured, using for example a capacitively coupled contactless conductivity detector (C4D) [2].
Concluding remarks #
Gradient elution is a cornerstone technique in modern LC, allowing the separation of complex mixtures that would be poorly resolved under isocratic conditions. By progressively increasing mobile-phase strength, gradients maintain analytes within an optimal retention window, resulting in sharper peaks and improved separation efficiency. Successful implementation requires careful consideration of gradient shape, instrument dwell volume, and mixing performance, as well as an understanding of how retention models predict analyte behaviour during the run. When properly optimized, gradient programs not only enhance resolution but also reduce analysis time, improve reproducibility, and expand the applicability of LC to a wider range of analytical challenges.
References #
[1] K.A. Cohen, J.W. Dolan, S.A. Grillo, J.Chromatogr. 316, 1984, 359, DOI: 10.1016/S0021-9673(00)96165-X
[2] Capacitively coupled contactless conductivity detection to account for system-induced gradient deformation in liquid chromatography, L.E. Niezen, T.S. Bos, P.J. Schoenmakers, G.W. Somsen, B.W.J. Pirok, Anal. Chim. Acta., 2023, 1271, 341466, DOI: 10.1016/j.aca.2023.341466
