Two-Dimensional Liquid Chromatography: A State of the Art Tutorial.

In this tutorial, we discuss the motivations for doing two-dimensional liquid chromatography (2D-LC) and describe the commonly used implementations of the method. We review important guiding principles for method development, discuss the state of the art in 2D-LC performance as measured by peak capacity, and describe example applications from different fields that we hope will inspire new users to adopt 2D-LC for their analytical problems.

Separation Speed and Power in Isocratic Liquid Chromatography: Loss in Performance of Poppe vs Knox-Saleem Optimization.

The best separation possible at a given analysis time and maximum system pressure is achieved by simultaneously optimizing column length, eluent velocity, and particle size. However, this three-parameter optimization is rarely practicable because only a few commercially available particle sizes exist. Practical optimization for systems described by the van Deemter equation therefore proceeds by first selecting an available particle size and then optimizing eluent velocity and column length. This two parameter ("Poppe") optimization must result in poorer performance with respect to both speed and efficiency because one fewer degree of freedom is used. A deeper analysis identifies a distinct point on each pair of "Poppe" curves beyond which the more efficient (and faster) separation is maintained by changing from smaller to larger particles. Here, we present simple equations identifying these "crossover points" in terms of analysis time and plate count thereby allowing a practitioner to rapidly identify the correct particle size for use in tackling a particular separation problem. Additionally, we can now quantitatively compare two-parameter and three-parameter optimization. Surprisingly, we find that for systems well-described by the van Deemter equation there is little separating power lost (only about 11% in the worst case) as a result of the limited availability of different particle sizes in using two-parameter optimization when compared to the ideal three-parameter optimization so long as one changes particle size at the prescribed crossover points. If these crossover times are not used, a great deal of separating power will be needlessly lost.

Improved synthesis of carbon-clad silica stationary phases.

Previously, we described a novel method for cladding elemental carbon onto the surface of catalytically activated silica by a chemical vapor deposition (CVD) method using hexane as the carbon source and its use as a substitute for carbon-clad zirconia.1,2 In that method, we showed that very close to exactly one uniform monolayer of Al (III) was deposited on the silica by a process analogous to precipitation from homogeneous solution in order to preclude pore blockage. The purpose of the Al(III) monolayer is to activate the surface for subsequent CVD of carbon. In this work, we present an improved procedure for preparing the carbon-clad silica (denoted CCSi) phases along with a new column packing process. The new method yields CCSi phases having better efficiency, peak symmetry, and higher retentivity compared to carbon-clad zirconia. The enhancements were achieved by modifying the original procedure in three ways: First, the kinetics of the deposition of Al(III) were more stringently controlled. Second, the CVD chamber was flushed with a mixture of hydrogen and nitrogen gas during the carbon cladding process to minimize generation of polar sites by oxygen incorporation. Third, the fine particles generated during the CVD process were exhaustively removed by flotation in an appropriate solvent.

"Retention projection" enables reliable use of shared gas chromatographic retention data across laboratories, instruments, and methods.

Gas chromatography/mass spectrometry (GC/MS) is a primary tool used to identify compounds in complex samples. Both mass spectra and GC retention times are matched to those of standards; however, it is often impractical to have standards on hand for every compound of interest, so we must rely on shared databases of MS data and GC retention information. Unfortunately, retention databases (e.g., linear retention index libraries) are experimentally restrictive, notoriously unreliable, and strongly instrument dependent, relegating GC retention information to a minor, often negligible role in compound identification despite its potential power. A new methodology called "retention projection" has great potential to overcome the limitations of shared chromatographic databases. In this work, we tested the reliability of the methodology in five independent laboratories. We found that, even when each lab ran nominally the same method, the methodology was 3-fold more accurate than retention indexing because it properly accounted for unintentional differences between the GC/MS systems. When the laboratories used different methods of their own choosing, retention projections were 4- to 165-fold more accurate. More importantly, the distribution of error in the retention projections was predictable across different methods and laboratories, thus enabling automatic calculation of retention time tolerance windows. Tolerance windows at 99% confidence were generally narrower than those widely used even when physical standards are on hand to measure their retention. With its high accuracy and reliability, the new retention projection methodology makes GC retention a reliable, precise tool for compound identification, even when standards are not available to the user.

An Advanced, Interactive, High-Performance Liquid Chromatography Simulator and Instructor Resources.

High-Performance Liquid Chromatography (HPLC) simulation software has long been recognized as an effective educational tool, yet we found that existing HPLC simulators are either too expensive, out-dated, or lack many important features we deemed necessary to make them widely useful for educational purposes. Here we describe a free, open-source HPLC simulator we developed that we believe meets this need. The web-based simulator is uniquely sophisticated, yet accessible to a diverse user group with varied expertise in HPLC. It features intuitive controls and indicators for a wide range of experimental conditions, and it displays a graphical chromatogram to provide immediate feedback when conditions are changed. The simulator can be found at hplcsimulator.org. At that website, we also provide a number of example problem sets that can be used by educators to more easily incorporate the simulator into their curriculum. Comments from students who used the simulator in an undergraduate Analytical Chemistry class were very positive.

A simple, robust orthogonal background correction method for two-dimensional liquid chromatography.

Background correction is a very important step that must be performed before peak detection or any quantification procedure. When successful, this step greatly simplifies such procedures and enhances the accuracy of quantification. In the past, much effort has been invested to correct drifting baseline in one-dimensional chromatography. In fast online comprehensive two-dimensional liquid chromatography (LC×LC) coupled with a diode array detector (DAD), the change in the refractive index (RI) of the mobile phase in very fast gradients causes extremely serious baseline disturbances. The method reported here is based on the use of various existing baseline correction methods of one-dimensional (1D) liquid chromatography to correct the two-dimensional (2D) background in LC×LC. When such methods are applied orthogonally to the second dimension ((2)D), background correction is dramatically improved. The method gives an almost zero mean background level and it provides better background correction than does simple subtraction of a blank. Indeed, the method proposed does not require running a blank sample.

Approximate and exact equations for peak capacity in isocratic high-pressure liquid chromatography.

In this letter, we examine an equation that had been published in Analytical Chemistry in a paper entitled "Comprehensive Study on the Optimization of Online Two-Dimensional Liquid Chromatographic Systems Considering Losses in Theoretical Peak Capacity in First- and Second-Dimensions: A Pareto-Optimality Approach" by Vivo-Truyols, G.; van der Wal, Sj.; Schoenmakers, P. J. Anal. Chem. 2010, 82, 8525-8536. In that paper, the authors considered, among many issues, the effects of extra-column and column broadening on isocratic peak capacity. They developed an equation to cover all possible conditions and offered a derivation based on two Taylor-series expansions and a regression. We have found an exact equation that covers all conditions and have compared the results using our equation to the results using their approximation in predicting ratios of peak widths. Their approximation works well, as we show, but we wish to offer the exact equation which is simpler in form than the approximate solution.

Perspectives on recent advances in the speed of high-performance liquid chromatography.

Perhaps the most consistent trend in the development of high-performance liquid chromatography (HPLC) since its inception in the 1960s has been the continuing reach for ever faster analyses. The pioneering work of Knox, Horvath, Halasz, and Guiochon set forth a theoretical framework that was used early on to improve the speed of HPLC, primarily through the commercialization of smaller and smaller particles. Over the past decade, approaches to improving the speed of HPLC have become more diverse, and now practitioners of HPLC are faced with the difficult task of deciding which of these approaches will lead them to the fastest analysis for their application. Digesting the rich literature on the optimization of HPLC is a difficult task in itself, which is further complicated by contradictory marketing messages from competing commercial outlets for HPLC technology. In this perspectives article we provide an overview of the theoretical and practical aspects of the principal modern approaches to improving the speed of HPLC. We present a straightforward theoretical basis, informed by decades of literature on the problem of optimization, that is useful for comparing different technologies for improving the speed of HPLC. Through mindful optimization of conditions, high-performance separations on the subminute timescale are now possible and becoming increasingly common under both isocratic and gradient elution conditions. Certainly the continued development of ultrafast separations will play an important role in the development of two-dimensional HPLC separations. Despite the relatively long history of HPLC as an analytical technique, there is no sign of a slow-down in the development of novel HPLC technologies.

Improving peak capacity in fast online comprehensive two-dimensional liquid chromatography with post-first-dimension flow splitting.

The use of flow splitters between the two dimensions in online comprehensive two-dimensional (2D) liquid chromatography (LC × LC) has not received very much attention, in comparison with their use in 2D gas chromatography (GC × GC), where they are quite common. In principle, splitting the flow after the first dimension column and performing online LC × LC on this constant fraction of the first dimension effluent should allow the two dimensions to be optimized almost independently. When there is no flow splitting, any change in the first-dimension flow rate has an immediate impact on the second dimension. With a flow splitter, one could, for example, double the flow rate into the first dimension column and perform a 1:1 flow split without changing the sample loop size or the sampler's collection time. Of course, the sensitivity would be diminished, but this can be partially compensated through the use of a larger injection; this will likely only amount to a small price to pay for this increased resolving power and system flexibility. Among other benefits, we found a 2-fold increase in the corrected 2D peak capacity and the number of observed peaks for a 15-min analysis time, using a post-first-dimension flow splitter. At a fixed analysis time, this improvement results primarily from an increase in the gradient time, resulting from the reduced system re-equilibration time, and, to a smaller extent, it is due to the increased peak capacity achieved by full optimization of the first dimension.

Optimization of the synthesis of a hyper-crosslinked stationary phases: a new generation of highly efficient, acid-stable hyper-crosslinked materials for HPLC.

A new family of hyper-crosslinked (HC) phases was recently developed for use under very aggressive conditions including those encountered in ultra-fast, high-temperature two-dimensional liquid chromatography (2-DLC). This type of stationary phase has improved acid stability compared with the most acid-stable, commercial RPLC phases. Kinetic studies are here reported that allow optimization of reaction time and crosslinking reagent concentrations used to prepare such HC phases. We have determined that the Friedel-Crafts chemistry used to prepare HC phases is nearly complete within about 15 min. Thus, reaction time for each step of the synthesis was greatly reduced from the multihour reactions used previously without sacrificing the stationary phases' acid stability and separation performance. Results from elemental analysis of the finished particles were combined with LC data to provide insights regarding the properties of these HC phases. This new generation of acid stable HC phases, with their attractive chromatographic properties, should be very useful in the separations of bases or biological analytes in acidic media, especially at elevated temperatures.

Closed form approximations to predict retention times and peak widths in gradient elution under conditions of sample volume overload and sample solvent mismatch.

Closed form expressions for the prediction of retention times and peak widths for gradient liquid chromatography are particularly useful in understanding, rationalizing and optimizing separations. These expressions are obtained by integrating differential equations, in conjunction with a model of the variation of the retention factor as a function of mobile phase composition. Two of these models, the linear solvent strength (LSS) model and the Neue-Kuss (NK) model are explored in the present work. Here, we expand on these closed form expressions to account for effects of sample volume overload and a mismatch between the sample solvent and the initial mobile phase composition for the gradient. We show that there have been errors in expressions reported in the literature, and we have evaluated the accuracy of the predictions from the closed form expressions reported here using a recently developed liquid chromatography simulator. The expressions assume a constant plate height and consider elution across four zones of the gradient profile - elution in the sample solvent, elution in the initial (isocratic) mobile phase caused by the gradient delay volume, elution during a linear gradient, and elution post-gradient at the final (isocratic) mobile phase composition. The expressions generally give reasonably accurate predictions for retention times and peak widths, except for cases where the solute elutes during transitions between the different zones. The average magnitude of the prediction errors for retention time and peak width relative to simulation were 0.093% and 0.40% for the LSS expressions for ten amphetamine solutes at 36 different separation conditions, and 0.22% and 1.8% for the NK expressions for eight alkylbenzene solutes at 36 different separation conditions, respectively.

Comprehensive feature analysis for sample classification with comprehensive two-dimensional LC.

Comprehensive two-dimensional LC (LC x LC) is a powerful tool for analysis of complex biological samples. With its multidimensional separation power and increased peak capacity, LC x LC generates information-rich, but complex, chromatograms, which require advanced data analysis to produce useful information. An important analytical challenge is to classify samples on the basis of chromatographic features, e.g., to extract and utilize biomarkers indicative of health conditions, such as disease or response to therapy. This study presents a new approach to extract comprehensive non-target chromatographic features from a set of LC x LC chromatograms for sample classification. Experimental results with urine samples indicate that the chromatographic features generated by this approach can be used to effectively classify samples. Based on the extracted features, a support vector machine successfully classified urine samples by individual, before/after procedure, and concentration with leave-one-out and replicate K-fold cross-validation. The new method for comprehensive chromatographic feature analysis of LC x LC separations provides a potentially powerful tool for classifying complex biological samples.

Effective saturation: a more informative metric for comparing peak separation in one- and two-dimensional separations.

A theoretical comparison is made of the numbers of observed peaks in one-dimensional (1D) and two-dimensional (2D) separations having the same peak capacity, as calculated from the traditional metric of resolution. The shortcoming of the average minimum resolution of statistical overlap theory (SOT) for this comparison is described. A new metric called the "effective saturation" is introduced to ameliorate the shortcoming. Unlike the "saturation", which is the usual metric of peak crowding in SOT, the effective saturation is independent of the average minimum resolution and can be determined using traditional values of resolution and peak capacity. Our most important finding is that, under a wide range of practical conditions, 1D and 2D separations of the same mixture produce almost equal numbers of observed peaks when the traditional peak capacities of the separations are the same, provided that the effective saturation and not the usual saturation is used as the measure of crowding. This is the case when peak distributions are random and when edge effects are minor. The numerical results supporting this finding can be described by empirical functions of the effective saturation, including one for the traditional peak capacity needed to separate a given fraction of mixture constituents as observed peaks. The near equality of the number of observed peaks in 1D and 2D separations based on the effective saturation is confirmed by simulations. However, this equality is compromised in 2D separations when edge effects are large. The new finding does not contradict previous predictions by SOT of differences between 1D and 2D separations at equal saturation. Indeed, the simulations reaffirm their validity. Rather, the usual metric, i.e., the saturation, is just not as simple a metric for comparing 1D and 2D separations as is the new metric, i.e., the effective saturation. We strongly recommend use of the new metric for its great simplifying effect.

Equation for peak capacity estimation in two-dimensional liquid chromatography.

Two-dimensional liquid chromatography (2DLC) is a very powerful way to greatly increase the resolving power and overall peak capacity of liquid chromatography. The traditional "product rule" for peak capacity usually overestimates the true resolving power due to neglect of the often quite severe under-sampling effect and thus provides poor guidance for optimizing the separation and biases comparisons to optimized one-dimensional gradient liquid chromatography. Here we derive a simple yet accurate equation for the effective two-dimensional peak capacity that incorporates a correction for under-sampling of the first dimension. The results show that not only is the speed of the second dimension separation important for reducing the overall analysis time, but it plays a vital role in determining the overall peak capacity when the first dimension is under-sampled. A surprising subsidiary finding is that for relatively short 2DLC separations (much less than a couple of hours), the first dimension peak capacity is far less important than is commonly believed and need not be highly optimized, for example, through use of long columns or very small particles.

Effect of pressure, particle size, and time on optimizing performance in liquid chromatography.

Although the principles of optimization of high-performance liquid chromatography (HPLC) have a long history starting with the work of Giddings in the 1960s and continuing with work by Knox and Guiochon extending into the 1990s we continue to see statements that flatly contradict theory. A prominent example is the notion that optimum "performance", as measured by plate count, is always obtained by operating conventional length columns (e.g., 5-15 cm) at eluent velocities corresponding to the minimum plate height in the van Deemter curve. In the past decade the introduction of "Poppe plots" by Poppe and "kinetic plots" by Desmet and others has simplified the selection of "optimum" conditions, but it is evident that many workers are not entirely comfortable with this framework. Here we derive a set of simple, yet accurate, equations that allow rapid calculation of the column length and eluent velocity that will give either the maximum plate count in a given time or a given plate count in the shortest time. Equations are developed for the optimum column length, eluent velocity, and thus plate count for both the cases when particle size is preselected and when particle size is optimized along with eluent velocity and column length. Although both of these situations have been previously considered the implications of the resulting equations have not been previously made explicit. Lack of full understanding of the consequences of the differences between these two cases is very important and responsible for many erroneous conclusions. The simple closed-form equations that result from this work complement the graphical, iterative approaches of Poppe and Desmet; the resulting compact framework allows practitioners to rapidly and effectively find the operating parameters needed to achieve a specific separation goal in the shortest time and to compare emerging technologies (e.g., high pressure, high temperature, and different particle types) in terms of their impact on achievable plate counts and speeds in HPLC. A Web-based calculator based on the equations presented here is now available (http://homepages.gac.edu/ approximately dstoll/calculators/optimize.html).

Column selection for comprehensive two-dimensional liquid chromatography using the hydrophobic subtraction model.

Two-dimensional (2D) liquid chromatography (2DLC) methods have grown in popularity due to their enhanced peak capacity that allows for resolving complex samples. Given the large number of commercially available column types, one of the major challenges in implementing 2DLC methods is the selection of suitable column pairs. Column selection is typically informed by chemical intuition with subsequent experimental optimization. In this work a computational screening method for 2DLC is proposed whereby virtual 2D chromatograms are calculated utilizing the Snyder-Dolan hydrophobic subtraction model (HSM) for reversed-phase column selectivity. Towards this end, 319 225 column pairs resulting from the combination of 565 columns and 100 sets of 1000 diverse analytes are examined. Compared to other screening approaches, the present method is highly predictive for column pairs that are able to resolve the largest number of analytes. This approach shows a strong sensitivity to the choice of the second dimension column (having a shorter operating time) and a preference for those with embedded polar moieties, whereas a relatively weak preference for C18 and phenyl columns is found for the first dimension.

Dependence of effective peak capacity in comprehensive two-dimensional separations on the distribution of peak capacity between the two dimensions.

One of the basic tenets of comprehensive two-dimensional chromatography is that the total peak capacity is simply the product of the first- and second-dimension peak capacities. As formulated, the total peak capacity does not depend on the relative values of the individual dimensions but only on the product of the two. This concept is tested here for the experimentally realistic situation wherein the first-dimension separation is undersampled. We first propose that a relationship exists between the number of observed peaks in a two-dimensional separation and the effective peak capacity. We then show here for a range of reasonable total peak capacities (500-4000) and various contributions of peak capacity in each dimension (10-150) that the number of observed peaks is only slightly dependent on the relative contributions over a reasonable and realistic range in sampling times (equal to the first-dimension peak standard deviation, multiplied by 0.2-16). Most of this work was carried out under the assumption of totally uncorrelated retention times. For uncorrelated separations, the small deviations from the product rule are due to the "edge effect" of statistical overlap theory and a recently introduced factor that corrects for the broadening of first-dimension peaks by undersampling them. They predict that relatively more peaks will be observed when the ratio of the first- to the second-dimension peak capacity is much less than unity. Additional complications are observed when first- and second-dimension retention times show some correlation, but again the effects are small. In both cases, deviations from the product rule are measured by the relative standard deviations of the number of observed peaks, which are typically 10 or less. Thus, although the basic tenet of two-dimensional chromatography is not exact when the first dimension is undersampled, the deviations from the product rule are sufficiently small as to be unimportant in practical work. Our results show that practitioners have a high degree of flexibility in designing and optimizing experimental comprehensive two-dimensional separations.

High-speed gradient elution reversed-phase liquid chromatography of bases in buffered eluents. Part I. Retention repeatability and column re-equilibration.

We studied the run-to-run repeatability of the retention times of both non-ionizable and basic compounds chromatographed using buffered eluents. The effect of flow rate, organic modifier and other additives, buffer type/concentration, stationary phase type, batch-to-batch preparation of the initial eluent, gradient time, sample type and intra-day changes on retention repeatability were examined. We also assessed the effect of column storage solvent conditions on the inter-day repeatability. Although retention repeatability is strongly influenced by many parameters (flow rate, solvent compressibility compensation, precision of temperature control, and buffer/stationary phase type), our primary finding is that with a reasonable size column (15cmx4.6mm (i.d.)) two column volumes of re-equilibration with initial eluent suffices to provide acceptable repeatability (no worse than 0.004min) for both non-ionizable and basic analytes under a wide variety of conditions. Under ideal conditions (e.g. the right buffer, flow rate, etc.) it is possible to obtain truly extraordinary repeatability often as good as 0.0004min. These absolute fluctuations in retention translate to worst case changes in resolution of 0.2 units and average changes of only 0.02 units.

Synthesis and characterization of silica-based hyper-crosslinked sulfonate-modified reversed stationary phases.

A novel type of silica-based sulfonate-modified reversed phase ((-)SO3-HC-C8) has been synthesized; it is based on a newly developed acid stable "hyper-crosslinked" C8 derivatized reversed phase, denoted HC-C8. The (-)SO3-HC-C8 phases containing controlled amounts of sulfonyl groups were made by sulfonating the aromatic hyper-crosslinked network of the HC-C(8) phase at different temperatures. The (-)SO3-HC-C8 phases are only slightly less hydrophobic than the parent HC-C8 phase. The added sulfonyl groups provide a unique strong cation-exchange selectivity to the hydrophobic hyper-crosslinked substrate as indicated by the very large C coefficient as shown through Snyder's hydrophobic subtraction reversed-phase characterization method. This cation-exchange activity clearly distinguishes the sulfonated phase from all other reversed phases as confirmed by the very high values of Snyder's column comparison function F(s). In addition, as was found in previous studies of silica-based and zirconia-based reversed phases, a strong correlation between the cation-exchange interaction and hydrophobic interaction was observed for these sulfonated phases in studies of the retention of cationic solutes. The overall chromatographic selectivity of these (-)SO3-HC-C8 phases is greatly enhanced by its high hydrophobicity through a "hydrophobically assisted" ion-exchange retention process.

High speed gradient elution reversed phase liquid chromatography of bases in buffered eluents. Part II. Full equilibrium.

In this work we determined when the state of thermodynamic (full) equilibrium, i.e. time-invariate solute retention, was achieved in gradient elution reversed-phase chromatography. We investigated the effects of flow rate, temperature, organic modifier, buffer type/concentration, stationary phase type, n-butanol as eluent additive, and pore size. We also measured how selectivity varied with reequilibration time. Stationary phase wetting and the ability of the stationary phase to resist changes in pH strongly affect the time needed to reach full equilibrium. For example, full equilibrium is realized with many endcapped stationary phases after flushing with only two column volumes of acetonitrile-water containing 1% (v/v) n-butanol and 0.1% (v/v) trifluoroacetic acid. Trends in retention time (<0.010min) and selectivity become quite small after only five column volumes of reequilibration. We give practical guidelines that provide fast full equilibrium for basic compounds when chromatographed in buffered eluents.