Liquid chromatography (LC) is the single largest analytical field in terms of people involved and money spent. LC is crucial for almost all public and private sectors and the technique has seen tremendous technological advancements. Nevertheless, separations are often performed under suboptimal conditions and technological capabilities remain unused. Because expert knowledge and method development time are increasingly scarce, methods are often inefficient. Exploiting the full technological capabilities of liquid-phase separation technology requires deep knowledge and great time investments. Method optimization strategies that can simultaneously optimize the large number of parameters involved are therefore of great interest to chromatographers. This review examines different workflows that have been designed and used to facilitate and/or automate method development. In particular, focus is paid to the implementation of computer-aided workflows for the optimization of kinetic and thermodynamic parameters in LC, as well as on the possibilities to conduct this in a closed-loop fashion. Finally, the opportunities to use machine learning to achieve these goals is addressed.

Decades of research and development have allowed liquid chromatography (LC) to become the reliable and robust technique that we know today. This has paved the way for the development of increasingly advanced two-dimensional LC (2D-LC) methods with increased peak capacities, better use of mass spectrometry (MS), and new opportunities such as in-line reactions (1). For complex samples a 2D-LC method can be much faster than a one-dimensional (1D)-LC counterpart (2,3).

The development of 2D-LC has largely been driven by the growing interest of society and industry in understanding the increasingly complex and diverse samples, each with their own challenges associated.

The need to implement more powerful separation technologies is growing faster than the number of qualified users of multidimensional chromatography. The leading cause hampering further proliferation is the considerable amount of resources required for method development. This task is ever more daunting as method parameters are numerous and often interdependent, increasing the experience required to use all capabilities effectively.

This is illustrated in Figure 1, where the technological complexity (that is, the cost) is sketched against the information density (the benefit). There is a disproportionate increase in resources required to obtain further information. State-of-the-art separation technology such as 2D-LC can only make an impact if it can be efficiently employed.

To facilitate this, researchers worldwide have been designing strategies with software to simplify method development (4–6) These and other method development and optimization strategies capitalize on theoretical understanding to simplify the method development process, as well as maximize its potential similar to the motto “work smarter, not just harder” (7). This review will map the method development process and identify categories of parameters that can be targeted. Different method optimization approaches that simplify or even automate sections of this workflow will then be examined. Finally, the opportunities to use machine learning to achieve in this context will be addressed.

Objectives of Chromatographic Method Development

Chromatographic method development is affected by the aim of the method. The optimization approaches for LC method development can be roughly classified as targeted and untargeted (8). Targeted approaches focus on specific analytes, whereas untargeted methods attempt to characterize the entire sample. This article will focus on untargeted methods, as targeted methods tend to have dedicated goals that cannot easily be generalized.

Generally, an analyst will start method development by using any information available on the sample chemistry, for example, Giddings’ sample dimensions (9), literature, and other resources to select an initial column (often a general-purpose column available in the laboratory) and generic method parameters (a generic linear gradient).

After the initial instrument parameters are established, the method can be evaluated based on its ability to provide the required critical information. When the method does not provide this information, method parameters can be adjusted to improve the method. This process is generally termed 

. In chromatographic literature, the term 

 often represents divergent intentions based on the objective and the stage of the method development process. Indeed, “optimization” can refer to sample preparation (10), kinetic parameters that affect efficiency (11), the selection of a suitable stationary-phase chemistry (12), a reduction in analysis time (8), and so on. The common denominator in each case is that method parameters are adjusted with the aim of obtaining the desired information more effectively. Typically, this is evaluated through metrics that quantify the quality of separation, also known as 

To maximize the ability of a method to characterize a sample, untargeted approaches are often driven by such quality descriptors. For example, in the case where an analyst encounters a chromatogram saturated with peaks, maximization of the peak capacity (that is, the number of peaks that can be separated by the method) can be employed as a quality descriptor.

Untargeted optimization suffers from the vast number of adjustable parameters and the large interdependence between these. It is inherently difficult to predict whether a change in parameters will result in an improved method. Improving one metric (analysis time) may result in worsening another metric (resolution). Computer-aided development of a chromatographic method thus requires a balanced approach.

Resolution to Adjust a Chromatographic Method:

 One useful quality descriptor that quantifies the degree of separation, yet also instructs on possibilities to improve it, is the resolution (equation 1):

Here, the separation between analytes 1 and 2 is expressed with 

 and σ representing the retention time and peak standard deviation. When assuming that both analytes experience a similar column efficiency (that is, 

), we can re-write equation 1 as follows (13):

Now, we have resolution quantified as the product of three contributions: efficiency (

), selectivity (α), and average retention factor (

). Equation 2 demonstrates that the only means to adjust the separation is to change something within either of these three parameters.

At this point, it is important to acknowledge the significance of sample preparation and the crucial effect this has on the method development workflow. Sample preparation tends to be highly sample dependent, and it has been extensively treated elsewhere (14,15). It is outside the scope of this review.

Equation 2 can be schematically expressed in the context of method development workflows as depicted in Figure 2, which represents a typical case often faced by chromatographers. After having used their experience to select an appropriate column and initial method parameters, chromatographers are recommended to first adjust the method conditions by altering thermodynamic parameters that affect retention and selectivity. For example, they may change the gradient program or—if necessary—adjust the selectivity dramatically by selecting a different column or mobile-phase chemistry. Finally, they may opt to improve the efficiency or analysis time of the method by regarding the kinetic parameters. Different approaches that have been developed to facilitate method development through automated workflows or chemometrics will be reviewed in the following sections.

Improving the efficiency (that is, the theoretical plate number) of the separation provides a clear metric relevant to method optimization as it increases the peak capacity for the separation and decreases the likelihood of coelution. For 1D-LC it is possible to predict how different parameters will affect the efficiency. Another method is the use of kinetic plots (16). However, the square-root dependence of 

 implies a rapidly diminishing return on investment.

In comprehensive two-dimensional liquid chromatography (LC×LC) kinetic optimization schemes can be applied to substantially improve the method. This is attributed to the additional parameters, including the second-dimension (

D) column dimensions, and phenomena such as under-sampling (of the 

D sample-dilution (17). Vivo-Truyols et al. proposed the use of sample-independent Pareto optimization (PO) for LC×LC (18). In this chemometric-driven approach, multiple method parameters (column dimension, flow rates, gradient slope) were varied and the effects thereof were evaluated using (theoretically related) quality descriptors such as peak capacity, analysis time, and dilution factor. The authors demonstrated that optimizing the kinetic parameters can be highly rewarding and that this approach is suited to deal with trade-offs between different objectives. The PO method provided optimal values for a large number of parameters, including 

D particle sizes and column diameters, while taking into account pressure restrictions.

This work was extended by the group of de Villiers (11,19,20), who applied the PO strategy for the chromatographic separation of a phenolic red-wine extract (19), implemented a predictive kinetic-optimization tool for a hydrophilic interaction liquid chromatography×reversed-phase liquid chromatography (HILIC×reversed-phase LC) separation of procyanidins (11), and used the same tool to compare reversed-phase LC×HILIC and HILIC×reversed-phase LC for phenolic analysis (20). In all cases, optimization of kinetic parameters provided higher peak capacities and produced valuable knowledge on the influence of under-sampling, dilution factors, and band broadening.

Selectivity in liquid chromatography is influenced by the thermodynamic parameters related to analyte interactions with the mobile and stationary phases. Changes in mobile phase composition, gradient program, stationary phase chemistry, pH, or temperature can significantly affect the distribution of peaks in a chromatogram. While modifying the mobile phase, pH, or temperature is relatively straightforward in theory, in practice this may not suffice to meet the objectives of the separation. Changing the stationary phase in principle requires a re-optimization of the mobile phase, making it more expensive in terms of effort (apart from the column cost), but generally provides broader changes in selectivity.

Various strategies and workflows have been described to select appropriate chemistries for both the mobile and stationary phases in LC. One such strategy involves optimizing the parameters through a Design-of-Experiments (DoE) workflow, in which sets of parameters (for example, mobile phase, temperature, pH) are varied and an extensive screening is performed, often on multiple columns, to determine the optimum approach. Similar approaches are commonly used in the industry (21). They may be efficient in terms of manpower required, but can be quite inefficient in terms of numbers of measurements, time, solvents and instruments required.

For column selection, stationary phase characterization methods aim to simplify the end user’s choice of stationary phases based on characterizing the physicochemical interactions with small-molecule probes. For an extensive review the reader is referred elsewhere (22). The best-documented example is the hydrophobic subtraction model (HSM) developed by Snyder, Dolan, and co-workers, which may be used to select columns with different selectivity (23).

Recently, workflows have emerged related to selectivity screening for 2D-LC method development. For example, Zhang et al. developed a multiple heart-cut 2D-LC setup for pharmaceutical purity testing that enabled automated screening of the 

D selectivity (24). In other work, Wang et al. (25) used an automated column screening framework for analyzing chiral and achiral impurities, with online multiple heart-cutting 2D-LC; in a similar study, Zhang and co-workers described fast chiral and achiral profiling of compounds with multiple chiral centres by an LC–multicolumn-LC approach (26). Together with automated data acquisition, these workflows constituted a step forwards, but interpretation and processing of the data are still dependent on manual input and user experience.

In an ideal scenario, a method development workflow must be capable of integrating all previously discussed parameters and optimizing these in an automated and interpretive manner. In this context, the word 

 implies that the chromatograms are interpreted as a result of the elution of the individual analytes. In the workflow the peaks should be tracked and simple models may be established for each analyte—all of this in an unsupervised and automated manner. Based on the analyte models, many chromatograms can be simulated and the objective function can be optimized. Such a method development workflow has the potential to minimize manual input and the expertise required for developing complex methods.

Bos et al. developed the AutoLC approach, in which the mobile phase gradient was optimized in a closed-loop fashion (27). Based on an earlier theoretical LC×LC proof-of-principle study (28), and the pioneering work of Dolan and co-workers (29), Bos et al. designed an algorithm that could accommodate different chemometric optimization strategies. Two examples were presented: one using empirical retention modelling, and one using the machine-learning Bayesian optimization technique. In both cases, the algorithm developed multi-segment gradient programs to optimize the retention and selectivity of separations of a monoclonal antibody digest by LC–MS.

The examples above demonstrate the possibility of including computer-assisted optimization strategies for kinetic and thermodynamic parameters in automated workflows. However, despite the significant progress made, three major challenges remain that need to be addressed to achieve a closed-loop, interpretive algorithm for developing LC methods in a completely unsupervised and automated manner.

The first and arguably most important challenge is to define quality descriptors that can assess the quality of a separation. The success or failure of the optimization process critically depends on the objective function. The latter depends on quality descriptors that, in turn, may depend on chemical and physical parameters. The objective function serves as the primary driving force for every algorithm. Single-number descriptors, known as 

 (CRFs), have been developed to quantify the critical information that the method is intended to provide. Various CRFs have been proposed in the past (30). Although many CRFs exist for 1D-LC, few are available for 2D-LC (31–36). Alvarez-Segura and co-workers recently included peak prominence in their CRF (33,34), Huygens et al. (35) introduced a CRF for 2D-LC based on peak purity, and Boelrijk et al. (36) presented a CRF based on connective components in graph theory to assess both separation quality and time. It has also been demonstrated that the selection of inappropriate quality descriptors can lead to suboptimal separations (27). Therefore, it is crucial to create CRFs that can effectively weigh quality descriptors, while the program provides quantitative information regarding various practical aspects of analytical queries, such as method time and sensitivity.

The second challenge is related to the data processing. The quality of the output of an algorithm relies strongly on the input data and the data processing. Any error in background correction, peak detection, or peak tracking can lead to cascading errors in later iterations (27). While MS provides information to reduce the errors in 1D-LC, data processing remains a significant challenge for LC×LC. This is especially the case for peak tracking, where an algorithm must establish the location of each analyte across multiple signals and account for incorrect clustering of coeluting peaks (37,38). In addition, it is difficult to quantitatively compare the performance of the large number of data processing approaches available (27,39).

The third challenge concerns the computation costs associated with the large number of simulations and the number of parameters that need to be optimized. Improving the performance of the algorithm either requires more measurements or more simulated data that resemble the experiments more closely. The former increases the amount of time and solvent needed, while the latter requires more computation power. Machine learning techniques may be employed to reduce the computation time required.

Interest in machine learning methods is rapidly gaining momentum in the field of chromatography (7). The increasing computation power available, combined with the demand for advanced simulation tools, has led to the exploration of machine learning approaches for accelerated method development (40,41). Machine learning has the potential to enhance various stages of the chromatographic-analysis workflow, including baseline and noise correction (42), retention-time or retention-index prediction (43–45), peak detection (46,47), peak annotation (48), and classification (49). This section will focus on the utilization of machine learning to optimize the gradient program, which frequently relies on several of the aforementioned stages.

One type of machine learning is artificial neural networks (ANNs). The application of neural networks in chromatography has been explored in the past (50–53). In a recent study, Kensert et al. (42) investigated the potential use of reinforcement learning for selecting optimal isocratic scouting runs for retention modelling. The neural network was trained on simulated data using a Q-Learning algorithm and evaluated based on the accuracy of the retention predictions for 57 small-molecule analytes 

 experiments. While the work is promising, the algorithm from this study has only been tested on isocratic data for a specific reversed-phase LC setup with a limited number of simplistic molecules. A downside of the use of artificial neural networks is that they require a large amount of data for training. This can be mitigated with simulated data, but this carries a risk of the model not capturing the actual chromatographic space with sufficient accuracy (46).

Several authors have explored the potential of evolutionary algorithms to optimize gradient profiles (35,54). In particular, Hao et al. (54) used a genetic algorithm to optimize multi-linear gradient profiles for the separation of lignin-degradation products. They validated their simulations by comparison with experimental measurements and found good agreement. Huygens et al. (35) investigated evolutionary strategies for optimizing 

 experiments of a LC×LC separation of 100 experiments. Their genetic algorithm required less than 100 experiments to reach a better CRF than a grid search of 625 experiments. This suggests that evolutionary algorithms have the potential to guide search-based method development, accelerate computational model-based method development, and deal with many parameters simultaneously. However, the authors simplified the experimental conditions by assuming perfect orthogonality, equal concentrations, and perfect Gaussian peaks. This raises concerns over the risk of oversimplification and the underutilization of the full range of variations in chromatographic conditions, as can also occur with neural networks.

One of the biggest limitations of applying machine learning is the required amount of data. An emerging optimization method that is less dependent on the amount of input data is Bayesian optimization, a type of machine learning tool that can optimize expensive-to-evaluate functions (expensive in terms of computation cost), even when there is a low amount of data available. Due to the compatibility with black box functions, only the score itself needs to be ascertainable, while the underlying mechanics or processes do not necessarily need to be understood or known. Boelrijk et al. investigated the potential use of Bayesian approaches for LC×LC 

 (36); they developed an unsupervised closed-loop algorithm to predict 1D-LC gradient profiles for a complex dyestuff mixture (55) and compared Bayesian optimization to retention modelling for automated method development (27). These studies demonstrated the versatility of Bayesian approaches and highlighted their applicability in method development workflows, with the added benefit of being less reliant on retention models and peak tracking. However, a potential limiting factor for LC×LC is the maximum number of parameters that can be optimized simultaneously. Due to the multivariate nature of the method, the number of necessary measurements for each additional parameter increases exponentially. The authors emphasized that the efficiency of Bayesian optimization is heavily dependent on the accurate definition of the objective function.

Machine learning approaches show tremendous potential to optimize the gradient program, yet the most advanced applications often have limitations that render them unsuitable for widespread use. This is partly due to the fact that these models can only handle scenarios that were present in the training data. Insufficient data can stem from a lack of appropriate standards or from insufficient resources to perform all the necessary measurements. One way to alleviate this issue is by employing simulated data, but this approach only works effectively if the simulated data closely resemble real-world situations, which is frequently not the case. With the rapid advancements in the field of machine learning, the issues currently encountered are expected to be addressed in the near future.

Driven by the ever-increasing need for more information, separation technology is advancing faster than our ability to use it to its full potential. Despite the enormous size and importance of the field, separations are often performed under suboptimal conditions and technical capabilities remain unused. For advancements in LC, such as 2D-LC, to make a significant impact, it is imperative that our community develops tools to fully exploit the current potential.

To this end, the chromatographic community must continue to deepen its understanding of fundamental concepts. This review has underlined the huge benefits and impressive advancements by scientists who have developed tools to streamline method development, focusing on kinetic or thermodynamic parameters—or both. Many of these advances are expressed as improved method development workflows that capture the experience and knowledge of the chromatographer.

However, the chromatographic community cannot do it alone. Indeed, we need the help of computers and information sciences. Automated LC method development workflows are rapidly advancing through the implementation of chemometric and machine learning algorithms. Nevertheless, despite the potential and promise of such algorithms to expedite method development, the challenges are still daunting and require a combined effort by the chromatographic and chemometric communities. Better ways must be found to mathematically express the chromatographic end goals, improve data analysis (peak detection), and invent smart algorithms that can interpret chromatographic data and combine these with fundamental kinetic (kinetic plots) and thermodynamic (retention models) concepts to create better methods. Meanwhile there is also the continuous need for chromatographers to deepen the understanding of physicochemical interactions of analytes inside our columns. The use of machine learning has recently been demonstrated by several groups to show great promise (35,55).

From the above-mentioned strategies it is clear that optimization workflows, especially for selectivity, remain heavily dependent on prior knowledge of the sample dimensionality or a trial-and-error approach. New machine learning algorithms should be able to optimize more parameters without needing unreasonable amounts of data. Other approaches may entail optimizing subsets of parameters at a time to lower the dimensionality of the problem or combining retention modelling with machine learning; in that way aspects that can be well described do not need to be captured in the machine learning models. The practical challenges are mostly on the required number of measurements or computations. Every optimization process is quicker when starting with a good setup. By scanning various columns at the start, a good estimate can be made of which columns show potential and are candidates for orthogonal separation in 2D-LC.

Computer-aided method development for LC has been under development for some four decades and it has failed to become common practice. However, with the rapid advances in LC, the gap between contemporary LC practice and potential has grown to a point where computer-aided method development is becoming a must. This need, in combination with the enormous growth in computation power and the dramatic advances in artificial intelligence, suggests that the time has come for computers to outperform analysts in LC method development.

This publication is part of the project Unleashing the Potential of Separation Technology to Achieve Innovation in Research and Society (UPSTAIRS) (with project number 19173) of the research programme TTW-VENI, which is financed by the Dutch Research Council (NWO).

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This review examines different workflows that have been designed and used to facilitate and/or automate method development in liquid chromatography (LC).

Approaches to Accelerate Liquid Chromatography Method Development in the Laboratory Using Chemometrics and Machine Learning

Many high performance liquid chromatography (HPLC) users are confronted with questions about how to improve upon the performance of an existing or recently developed method. These days, we have many technological options to consider, but how do we choose one (or a few) to try? The variables that are most important for improving the separation of complex samples are quite different from those that are most convenient for improving the resolution of simpler samples. Considering these differences can help avoid wasting time and resources when trying to improve separation performance.

In the April 2023 instalment of “LC Troubleshooting”, I kicked off a series of articles aimed at addressing the general question, “How do I improve my separation?” Given the diversity of analytical challenges that are addressed using high performance liquid chromatography (HPLC), there are several variants of the general question. In the first part of the series (1), I reviewed some basic and foundational concepts that are relevant to these discussions. In Part 2 (2), I first discussed the idea of sample complexity, the likelihood of fully resolving samples with different numbers of constituents, and different approaches to improving resolution of simple mixtures (primarily thermodynamic adjustments), including changes to the mobile and stationary phases. In this third part in the series, I will address the other end of the spectrum, focusing on complex sample mixtures and options for improving resolution with these samples. As with the other parts of this series, building up knowledge of how different factors affect resolving power from a theoretical point of view, as well as what changes are possible within practical constraints, is powerful when we are confronted with a separation that needs to be improved, or when an existing separation is not performing as expected.

How Do We Define a “Complex Mixture”?

as a sample containing less than five compounds, and a 

as any sample containing more than 100 compounds. These numbers are somewhat arbitrary, but they at least give us a concrete basis for discussion, and we will continue with them here. Thus, the remainder of this instalment is focused on considerations relevant to samples containing more than 100 compounds, but many of the ideas are also applicable to samples of intermediate complexity, in the range of 5 to 100 compounds in the sample.

What Are My Chances of Separating the Mixture I Have?

In Part 2 of this series, I wrote about how the statistical theory of peak overlap (SOT) developed by Davis and Giddings can be used to quantify the likelihood of fully resolving simple mixtures (3). The same framework can be used to quantify the likelihood of separation for complex samples as well, but, in this case, the likelihood of fully resolving all the components of the sample is so low that it is not very informative, and we need a different performance metric to help us understand the impact of changes we might make. One option is to calculate the fraction (

) that are observed in a chromatogram as singlet, or “pure” peaks (

) (that is, no coelution). The number of singlets is given by equation 1, thus the fraction 

(on a percent scale) for different combinations of sample complexity (

) offered by the separation method. The vast majority of separations of complex mixtures involve gradient elution conditions due to the large range in analyte properties encountered with the mixture. Under these conditions, peak capacities on the order of 100 to 200 are readily achieved using conventional LC with analysis times less than one hour for most types of analytes. Achieving peak capacities much higher than this usually requires special measures (for example, high pressures, high temperatures, or very long analysis times), and is typically only possible with certain analyte types, such as peptides, but values in the range of 200 to 400 are still possible using a single column. Moving even further, beyond a peak capacity of 400, usually requires two-dimensional separation (see below for further discussion). In Figure 1, we see just how bad the prospects are for fully resolving complex mixtures (4). Even with a peak capacity of 400 (green line), only about 50% of the compounds in the sample will be resolved as “pure peaks” when the sample contains 150 compounds (follow blue dashed lines). Significantly increasing the fraction of compounds in the mixture that are really separated from everything else in the sample requires a dramatic increase in the peak capacity.

Figure 2 shows simulated separations of a 100-component mixture, in 30 min, with peak capacities of 100 (panels 2[a] and 2[b]) or 400 (panel 2[c]). The widths of pure peaks are all the same (as is approximately observed in many gradient elution separations), the height of each pure peak is assigned a value of 1, and retention times are randomly distributed. This makes it easy to visualize which peaks in the chromatogram are nominally pure (peak apex at 2 units on the 

-axis), and where there are areas of moderate to severe overlap. When two compounds are perfectly coeluted, the peak apex of the two-component peak occurs at 3 units, if three compounds are perfectly coeluted, the peak apex occurs at 4, and so on, as the peak heights are additive. In panel 2(a), we see that there are only about 15 peaks (out of 100 components in the sample) with a height of exactly 1, which is consistent with Figure 1 that provides estimates of the percentage of components in the sample that will be observed as pure peaks.

In Part 2 of this series, I emphasized the importance of changing the stationary phase chemistry as a means of adjusting separation selectivity when working with simple mixtures, and giving ourselves a chance to significantly improve the resolution of a pair of compounds that are not well separated using the original column. So, one might reasonably ask if the same game can be played here, when dealing with more complex samples. Figure 2(b) shows another simulated chromatogram using all the same parameters as in panel 2(a) (that is, analysis time, peak capacity, and number of components in the sample), except that the retention times of the peaks have been re-distributed using a new set of random numbers to mimic a change in stationary phase chemistry. As we can see from the appearance of the new chromatogram in panel 2(b), the areas of overlap have changed, but the degree of overlap (that is, the number of pure peaks, and the number of areas of severe overlap) is nominally unchanged. And so this is the disappointing answer when working with complex mixtures—that changing the selectivity of the separation (through changes in mobile or stationary phase chemistry) can impact the resolution of specific compounds, but, on average, it will not improve the overall separation much. This is because adjusting the retention times of the compounds by changing the selectivity merely rearranges which compounds are resolved, and which ones are overlapped.

Readers interested in a thorough, contemporary discussion of the concept of peak capacity and the influence of different chromatographic variables on the production of peak capacity are referred to a recent book chapter (5). Here, I summarize the most influential relationships that dictate the peak capacities that are achievable under practically relevant conditions, and the major levers that are within reach in routine method development.

To a good approximation, peak capacity is proportional to the square root of chromatographic efficiency:

This means that anything we can do to increase 

, but with a weak half-power dependence. Moreover, the relationships between 

and important variables such as analysis time (

. In 2022, Ken Broeckhoven and I wrote a series of “LC Troubleshooting” articles aimed at explaining the concept of kinetic plots and how they can be used to both develop and troubleshoot LC methods (6–8). One of the important concepts in the kinetic plot framework for optimizing chromatographic efficiency is the so-called 

(KSL). The KSL describes conditions where the particle size is chosen to maximize the efficiency for a particular analysis time by working with the longest possible column that allows one to work at the van Deemter optimum flow rate without exceeding the maximum system pressure. As the name suggests, these conditions enable the absolute maximum efficiency (

) that can be obtained at that analysis time (and a certain temperature, operating pressure, and molecule type). It is physically impossible to do better than the 

 number that is calculated at the KSL, and this framework yields a set of surprisingly simple, yet instructive relationships that are useful in setting our expectations with respect to peak capacity. At the KSL:

These relationships show us that, under KSL conditions, increasing the analysis time will lead to an increase in the peak capacity. However, the dependence of peak capacity on analysis time is very weak (one quarter power), and we should be careful to manage our expectations about how helpful simply increasing the analysis time can be. For example, doubling the peak capacity requires a 16-fold increase in the analysis time!

These relationships again show that increasing the system operating pressure has the potential to increase the achievable peak capacity, but the dependence is also quite weak. Again, this relationship is very helpful for managing our expectations. The prospect of increasing peak capacity by 50% by working at higher pressures is realistic, but the idea that we could increase peak capacity fivefold by working at higher pressures is not.

Whatever means we use to achieve higher peak capacities, the comparison of chromatograms in panels (b) (

 = 400) of Figure 2 provides a qualitative sense for the potential impact of the increased peak capacity because the only difference here is in the peak widths; the retention times in the two cases are exactly the same. The major difference we observe is that there are fewer instances of severe peak overlap as indicated by fewer peaks with signals greater than 2. This, in turn, carries a variety of benefits, including greater quantitative accuracy, and reduction of matrix effects (for example, ionization suppression when using electrospray ionization with mass spectrometric detection). Increasing the peak capacity fourfold has not completely eliminated overlap, but it has made overlap less frequent. Completely eliminating overlap requires peak capacities that greatly exceed the number of components in the sample.

As stated above, the upper limit of the peak capacity that can be achieved with current technology under practically relevant conditions and a single LC column is about 400 for most samples. Significantly increasing the peak capacity beyond this requires a move to multidimensional separation, where there is the potential to increase peak capacity several times without significantly increasing the analysis time. Readers interested in this possibility, and how this is accomplished in practice, are referred to recently published guidance (9). Figure 3 shows an example of what is possible, both in terms of the increase in peak capacity upon moving to a two-dimensional LC (2D-LC) separation, and the impact of this increase on the resolution of a complex sample (peptides). In this case, the 2D separation provides a 20-fold increase in peak capacity without increasing the analysis time. Whereas the chromatogram is very crowded in the 1D separation, which undoubtedly involves severe peak overlap, in the 2D case compounds are generally much better separated, with large areas of unoccupied baseline between neighbouring peaks.

Many HPLC users are confronted with questions about how to improve upon the performance of an existing method. In this instalment, I have discussed options to consider when confronted with the need to improve the separation of a complex sample (defined here as more than 100 components). Unlike the case of improving the resolution of simple samples, making adjustments to the selectivity of the separation (through changes in mobile or stationary phase chemistry) does not help much when dealing with complex samples, as changing the selectivity merely moves peaks around without affecting the average resolutions for pairs of peaks. More impactful for complex samples are changes that increase peak capacity of the separation, including increasing analysis time and increasing the pressure used to drive the separation (along with accompanying changes in particle size, flow rate, and column length). These changes have the potential to increase peak capacity by a factor of two or three, but typically not much more than that. Substantially increasing the peak capacity (more than fivefold) usually requires a move to multidimensional separation.

(1) Stoll, D. R. What Are My Options to Improve My Separation? Part 1: Foundational Concepts. 

(2) Stoll, D. R. What Are Options to Improve My Separation? Part 2: Likelihood of Separation, Adjusting Selectivity for Simple Mixtures. 

(3) Davis, J. M.; Giddings, J. C. Statistical Theory of Component Overlap in Multicomponent Chromatograms. 

(4) Stoll, D. R.; Carr, P. W. Two-Dimensional Liquid Chromatography: A State of the Art Tutorial. 

(5) Carr, P. W.; Stoll, D., R. Speed and Performance in Liquid Chromatography. In 

(6) Broeckhoven, K.; Stoll, D. R. But Why Doesn’t It Get Better? Kinetic Plots for Liquid Chromatography, Part 1: Basic Concepts. 

(7) Broeckhoven, K.; Stoll, D. R. But Why Doesn’t It Get Better? Kinetic Plots for Liquid Chromatography, Part 2: Making and Interpreting the Plots. 

(8) Broeckhoven, K.; Gunnarson, C.; Stoll, D. R. But Why Doesn’t It Get Better? Kinetic Plots for Liquid Chromatography, Part 3: Pulling It All Together. 

is the editor of “LC Troubleshooting”. Stoll is a professor and the co-chair of chemistry at Gustavus Adolphus College in St. Peter, Minnesota, USA. His primary research focus is on the development of 2D-LC for both targeted and untargeted analyses. He has authored or coauthored more than 75 peer-reviewed publications and four book chapters in separation science and more than 100 conference presentations. He is also a member of 

’s editorial advisory board. Direct correspondence to: 

Building up knowledge of how different factors affect resolving power from a theoretical point of view, as well as what changes are possible within practical constraints, is powerful when we are confronted with a separation that needs to be improved, or when an existing separation is not performing as expected.

What Are Options to Improve My Separation? Part 3: Options to Consider to Improve Resolution of Complex Mixtures

Metal-analyte interaction is a type of nonspecific adsorption (NSA) that occurs mainly between acidic analytes and active adsorptive sites present in the metal surfaces of the fluidic path of any chromatographic system. NSA represents a chromatographic challenge since it may lead to poor peak shape, low recovery, and poor performance from the high performance liquid chromatography (HPLC) system. As a result, many solutions that circumvent and mitigate this type of secondary interaction have been published or commercialized in the last few years. Such solutions encompass swapping stainless steel components for non-reactive polymers, “biocompatible” metals or alloys, the addition of additives into the mobile phase, pretreating the system with large amounts of sample or strong acids, and the use of coated stainless steel materials. This article will explore these solutions in more detail, particularly the recent adaptation and benefits of coated metal surfaces in LC.

Stainless steel has been the preferred material to manufacture HPLC columns due to its ease of fabrication and mechanical resistance to pressure. Specifically, 316 stainless steel, which contains up to 3% molybdenum, has been implemented in instrument and column hardware due to its superior resistance to chemical corrodents, such as brine solutions and sulphuric acid. However, 316 stainless steel is still subject to corrosion and rust under certain conditions. The American Society for Testing and Materials International (ASTM International) official standard A967 has been the official protocol since 1996 describing the chemical treatment for stainless steel parts via nitric acid, citric acid, and electrochemical treatment. ASTM A967 also describes several tests to confirm the effectiveness of passivation, particularly concerning the removal of free iron. Furthermore, an “LCGC Troubleshooting” article, published soon after the ASTM A967 dossier, described the passivation and practical recommendations to keep a well-passivated high performance liquid chromatography (HPLC) instrument by using a 50% nitric acid solution as the last resource when stainless steel parts replacement is not a viable option (1).

Twenty-three years have passed since the issue of passivation was addressed in the LCGC article above, and, although only a handful of LC users would feel comfortable flushing 50% nitric acid solution through their system, new enabling and milder technologies have been reported in the literature (or even commercialized) to tackle stainless steel passivation from a chromatographic standpoint. However, now more than ever, stainless steel adsorption still represents a technical challenge that leads to poor recovery, poor peak shape, and even undetected analytes (2).

There are two proposed mechanisms for surface metal-analyte interaction. The first consists of trace metal impurities that are adsorbed by active sites within the fluidic flow path of the LC system, where they exhibit cation-exchange properties (3,4). The second is the electrostatic attraction of the negatively charged analytes to the electropositive metal surface (5). It is these strong interactions that lead to the chromatographic challenges and particularly for molecules prone to complexation and Coulombic interactions, such as phosphorylated compounds (for example, oligonucleotides), catecholamines (apomorphine), beta-hydroxy ketones (tetracyclines), and beta-hydroxy amines (salmeterol), among others (6).

This article will survey numerous passivating solutions, and their respective advantages and drawbacks, including leaching data from stainless-steel alternatives. It is worth mentioning that solutions labelled as “bioinert”, “biocompatible”, and “metal-free” are interchangeably (yet wrongly) used within the chromatography field. In general, the term “bioinert” refers to a surface that impedes adsorption, while the term “biocompatible” is used to define a corrosion-resistant material (7). Nevertheless, the LC user should be aware of such terminology when choosing some of the recent column technologies designed to mitigate nonspecific adsorption (8).

Table 1 summarizes the current solutions that have been developed by both academia and industry. As described in the previous section, acid treatment has been an established protocol for the passivation of stainless steel for many years. Nitric acid, citric acid, and phosphoric acid have mainly been the chemicals of choice, since they not only clean the surface by flushing out metal ions and other particulates but also improve the corrosion resistance by leaving a thin layer of chromium oxide on the surface of stainless steel (9). The goal is to achieve a higher ratio of chromium atoms to iron on the surface of the metal, rendering the surface passivated. Nevertheless, acid passivation is a temporary solution, as the corrosion process can and will start again once water, organic solvents, and salt additives are introduced into the system (10). Furthermore, proper care should be taken when performing acid passivation to make sure that all the strong acids are flushed out with water by performing a pH test, but also by making sure that all the parts of the HPLC systems are compatible with the strong acids, such as column compartments (LC phases) and detectors (flow cell or mass spectrometer). Improper system flushing and reconditioning with the mobile phase can lead to analyte suppression or damage to the instrument.

An alternate method to acid passivation is sample saturation of the surface’s active sites. This approach uses several injections of the analytes until a stable and reproducible signal is observed. The effectiveness of this temporary solution is dependent on the analyte’s affinity towards the oxide layer of stainless steel, the pH of the mobile phases, the isoelectric point of both the metal or alloy used and the molecule of interest, the overall surface area of the system’s wetted flow path, and concentration of the analyte. Hansen and associates determined the adsorption isotherms of 3,4-dihydroxybenzoic acid and compared it to that of the bovine serum albumin (BSA) and poly-L-Lysine. He concluded that BSA had the highest affinity towards stainless steel, an affinity of three orders of magnitude higher than the small molecule and just a bit higher than the oligopeptide (11). These determining factors ultimately impact the number of analyte injections required to obtain a reproducible signal, since these interactions are reversible and affected by other competing species within the sample or matrix.

Sometimes acid or sample passivation may not guarantee suitable chromatography, especially when dealing with trace metal ions constantly leaching from HPLC componentry or when the sample matrix is contaminated with metals. In such cases, metal chelators, either spiked into the sample or as part of the mobile phase, have been employed to sequester such metal ions flowing through the system. For example, citric acid and ethylenediaminetetraacetic acid (EDTA) are well-known metal chelators that are effective in improving the peak shape of many metal-sensitive analytes in both reversed-phase and normal-phase separations (12–14).

In recent years, medronic acid has been implemented for many liquid chromatography–mass spectrometry (LC–MS) analyses, including metal-sensitive applications, such as phosphorylated peptides and polar pesticide assays (15,16). Apart from solubility issues, the major drawback of such metal chelators is the propensity to interfere with signal sensitivity. In addition, metal-complexing acids can lead to signal suppression if used in high concentrations, since they could also be retained by the system, causing them to persist in future injections. However, when used correctly, medronic acid has shown minimal interference in metabolite-related applications and is commercialized as a mobile phase additive (17).

Polyetheretherketone (PEEK) polymer is a high-temperature thermoplastic that offers a unique combination of exceptional performance characteristics. It has been adapted in chromatography primarily as connecting tubing due to its chemical inertness, flexibility, easy-to-cut to any desired length, and ease of identification (colour coding). In addition, it can be finger tightened, economical, and is compatible with conventional HPLC pressures. On the other hand, PEEK’s most significant limitation comes from its inability to withstand ultrahigh-pressure liquid chromatography (UHPLC) pressures (18). From a manufacturing standpoint, internal diameters of PEEK tubing have shown vast variability in the past, which may result in retention and efficiency inconsistencies (19). Furthermore, PEEK may swell in the presence of chlorinated solvents, tetrahydrofuran (THF), and dimethyl sulfoxide.

PEEK tubing with stainless steel cladding offers a pressure advantage that the polymer alone cannot. It allows the polymer to withstand up to 18,000 psi pressures while covering the metal surface and preventing it from coming into contact with the flow path. However, to our knowledge, such a reinforcing technique only applies to tubing formats, leaving many other PEEK accessories, such as frits, unavailable. Figure 1 summarizes an internal study showing the theoretical plates per metre of several commercially available columns with similar particle technology and diameter. The stainless-steel clad columns have about 20–30% lower theoretical plates than the conventional columns. The lower performance could be attributed to PEEK’s internal diameter variability along the column length and the possible use of PEEK frits incompatible with highpressure column packing protocols. Although these drawbacks could be detrimental in specific cases, there is still merit in using PEEK hardware as a low-adsorptive and chemically inert solution for many HPLC applications (20).

Titanium and other biocompatible alloys have also been adopted as a solution for nonspecific adsorption. Many HPLC systems have been commercialized, with titanium pump heads and stators that guarantee excellent corrosion resistance against high salt concentrations and a wide pH range for biological applications. These instruments also come with many low adsorptive features, including ceramic needles, PEEK plumbing, stainless steel-cladding PEEK capillaries, and other metal alloys to maximize the benefits of the biocompatible metal. Several solutions are readily available in the column hardware field, including titanium filters, frits, and lining of the stainless-steel column tubing. Frits are particularly interesting since they are usually a high source of sample adsorption, due to their extensive surface area compared to the rest of the LC system (21,22).

Nonspecific adsorption leads to poor peak shapes and poor performance from HPLC systems, but coating-enabling technologies can serve as a potential solution. We explain how.

June 2023 | LCGC Europe

Approaches to Accelerate Liquid Chromatography Method Development in the Laboratory Using Chemometrics and Machine Learning

What Are Options to Improve My Separation? Part 3: Options to Consider to Improve Resolution of Complex Mixtures

Methods for the Passivation of High Performance LC Instruments and Columns

Functional Copolymers Analysis Using Liquid Chromatography—Sort It Out