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.

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.

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.

Comparison of core-shell particles and sub-2µm fully porous particles for use as ultrafast second dimension columns in two-dimensional liquid chtomatography.

The peak capacity of small columns packed with 2.7µm core-shell particles and 1.8µm fully porous particles were compared at high temperatures using very steep (fast) gradient conditions and quite high linear velocities using the same instrument configuration as used to transfer first dimension effluent to the second dimension column as done in on-line comprehensive two-dimensional liquid chromatography. The experimental peak capacities of small columns (2.1mm×30mm) packed with both types of particles were measured with fast gradients (9s to 2min) at high temperature (95°C) using both the same flow rate (1.75mL/min) and then at different flow rates at the same pressure (400bar). Equal or slightly better peak capacities were achieved with the core-shell particle columns as compared to the fully porous particle columns at the same backpressure or the same flow rate. However, core-shell particles offer a real advantage over the smaller, fully porous particles because they can be operated at higher flow rates thus gradient mixer flush out and column reequilibration can be done in less time thereby allowing a greater fraction of the second dimension cycle time to be dedicated to the gradient time.

Two dimensional assisted liquid chromatography - a chemometric approach to improve accuracy and precision of quantitation in liquid chromatography using 2D separation, dual detectors, and multivariate curve resolution.

Comprehensive two-dimensional liquid chromatography (LC×LC) is rapidly evolving as the preferred method for the analysis of complex biological samples owing to its much greater resolving power compared to conventional one-dimensional (1D-LC). While its enhanced resolving power makes this method appealing, it has been shown that the precision of quantitation in LC×LC is generally not as good as that obtained with 1D-LC. The poorer quantitative performance of LC×LC is due to several factors including but not limited to the undersampling of the first dimension and the dilution of analytes during transit from the first dimension ((1)D) column to the second dimension ((2)D) column, and the larger relative background signals. A new strategy, 2D assisted liquid chromatography (2DALC), is presented here. 2DALC makes use of a diode array detector placed at the end of each column, producing both multivariate (1)D and two-dimensional (2D) chromatograms. The increased resolution of the analytes provided by the addition of a second dimension of separation enables the determination of analyte absorbance spectra from the (2)D detector signal that are relatively pure and can be used to initiate the treatment of data from the first dimension detector using multivariate curve resolution-alternating least squares (MCR-ALS). In this way, the approach leverages the strengths of both separation methods in a single analysis: the (2)D detector data is used to provide relatively pure analyte spectra to the MCR-ALS algorithm, and the final quantitative results are obtained from the resolved (1)D chromatograms, which has a much higher sampling rate and lower background signal than obtained in conventional single detector LC×LC, to obtain accurate and precise quantitative results. It is shown that 2DALC is superior to both single detector selective or comprehensive LC×LC and 1D-LC for quantitation of compounds that appear as severely overlapped peaks in the (1)D chromatogram - this is especially true in the case of untargeted analyses. We also anticipate that 2DALC will provide superior quantitation in targeted analyses in which unknown interfering compounds overlap with the targeted compound(s). When peaks are significantly overlapped in the first dimension, 2DALC can decrease the error of quantitation (i.e., improve the accuracy by up to 14-fold compared to 1D-LC and up to 3.8-fold compared to LC×LC with a single multivariate detector). The degree of improvement in performance varies depending upon the degree of peak overlap in each dimension and the selectivities of the spectra with respect to one another and the background, as well as the extent of analyte dilution prior to the (2)D column.

Instrument parameters controlling retention precision in gradient elution reversed-phase liquid.

The precision of retention time in RPLC is important for compound identification, for setting peak integration time windows and in fundamental studies of retention. In this work, we studied the effect of temperature (T), initial (ϕo) and final mobile phase (ϕf) composition, gradient time (tG), and flow rate (F) on the retention time precision under gradient elution conditions for various types of low MW solutes. We determined the retention factor in pure water ( [Formula: see text] ) and the solute-dependent solvent strength (S) parameters of Snyder's linear solvent strength theory (LSST) as a function of temperature for three different groups of solutes. The effect of small changes in the chromatographic variables (T, ϕo, ϕf, tG and F) by use of the LSST gradient retention equation were estimated. Peaks at different positions in the chromatogram have different sensitivities to changes in these instrument parameters. In general, absolute fluctuations in retention time are larger at longer gradient times. Drugs showed less sensitivity to changes in temperature compared to relatively less polar solutes, non-ionogenic solutes. Surprisingly we observed that fluctuations in temperature, mobile phase composition and flow rate had less effect on retention time under gradient conditions as compared to isocratic conditions. Overall temperature and the initial mobile phase composition are the most important variables affecting retention reproducibility in gradient elution chromatography.

Impact of reversed phase column pairs in comprehensive two-dimensional liquid chromatography.

A major issue in optimizing the resolving power of two-dimensional chromatographic separations is the choice of the two phases so as to maximize the distribution of the analytes over the separation space. In this work, we studied the choice of appropriate reversed phases to use in on-line comprehensive two-dimensional liquid chromatography (LC×LC). A set of four chemically different conventional bonded reversed phases was used in the first dimension. The second dimension column was either a conventional bonded C18 phase or a carbon-clad phase (CCP). The LC×LC chromatograms and contour plots were all rather similar indicating that the selectivities of the two phases were also similar regardless of the reverse phase column used in the first dimension. Further, the spatial coverage seen with all four first dimension stationary phases when paired with a second dimension C18 phase were low and the retention times were strongly correlated. However, when the C18 column was replaced with the CCP column much improved separations were observed with higher spatial coverages, greater orthogonalities and significant increases in the number of observed peaks.

"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.

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.

Analysis of the temporal performance of one versus on-line comprehensive two-dimensional liquid chromatography.

Our purpose is to generalize the chief conclusion of earlier studies based on complex maize seed extract samples that indicated that at very short times (less than 5 min) the peak capacity of 1D liquid chromatography was better than that of comprehensive, on-line 2D liquid chromatography (LC × LC), but that the LC × LC method begins to out-perform the 1D method at surprisingly short analysis times of only 5-10 min. We call the analysis time at which the peak capacities of 1D and LC × LC become equal the "crossover time." We quantify the importance of various system parameters such as the 1D peak capacity, the second dimension cycle time and second dimension peak capacity, and fractional coverage of the two-dimensional separation space on the crossover time of 1D versus LC × LC chromatography. For ranges of these parameters used in our earlier experimental studies, we believe that crossover times will generally be between 3 and 8 min under optimized on-line LC × LC conditions.

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.

Optimization of gradient reversed phase chromatographic peak capacity for low molecular weight solutes.

A general protocol for optimizing peak capacity for the separation of low molecular weight molecules under gradient elution conditions has not yet been developed. By studying the effects of gradient time, flow rate, temperature, final eluent composition, and column length on peak capacity, a protocol has been developed for the optimization of a separation of small molecules such as those seen in metabolomic studies. The strategy developed employs the Linear-Solvent-Strength Theory (LSS Theory) to predict retention, building on an approach for the optimization of the peak capacity of large molecules (peptides) in fixed column format separations.

Easy and accurate calculation of programmed temperature gas chromatographic retention times by back-calculation of temperature and hold-up time profiles.

Linear retention indices are commonly used to identify compounds in programmed-temperature gas chromatography (GC), but they are unreliable unless the original experimental conditions used to measure them are stringently reproduced. However, differences in many experimental conditions may be properly taken into account by calculating programmed-temperature retention times of compounds from their measured isothermal retention vs. temperature relationships. We call this approach "retention projection". Until now, retention projection has been impractical because it required very precise, meticulous measurement of the temperature vs. time and hold-up time vs. temperature profiles actually produced by a specific GC instrument to be accurate. Here we present a new, easy-to-use methodology to precisely measure those profiles: we spike a sample with 25 n-alkanes and use their measured, programmed-temperature retention times to precisely back-calculate what the instrument profiles must have been. Then, when we use those back-calculated profiles to project retention times of 63 chemically diverse compounds, we found that the projections are extremely accurate (e.g. to ±0.9 s in a 40 min ramp). They remained accurate with different temperature programs, GC instruments, inlet pressures, flow rates, and with columns taken from different batches of stationary phase while the accuracy of retention indices became worse the more the experimental conditions were changed from the original ones used to measure them. We also developed new, open-source software (http://www.retentionprediction.org/gc) to demonstrate the system.

Effect of background correction on peak detection and quantification in online comprehensive two-dimensional liquid chromatography using diode array detection.

A singular value decomposition-based background correction (SVD-BC) technique is proposed for the reduction of background contributions in online comprehensive two-dimensional liquid chromatography (LC×LC) data. The SVD-BC technique was compared to simply subtracting a blank chromatogram from a sample chromatogram and to a previously reported background correction technique for one dimensional chromatography, which uses an asymmetric weighted least squares (AWLS) approach. AWLS was the only background correction technique to completely remove the background artifacts from the samples as evaluated by visual inspection. However, the SVD-BC technique greatly reduced or eliminated the background artifacts as well and preserved the peak intensity better than AWLS. The loss in peak intensity by AWLS resulted in lower peak counts at the detection thresholds established using standards samples. However, the SVD-BC technique was found to introduce noise which led to detection of false peaks at the lower detection thresholds. As a result, the AWLS technique gave more precise peak counts than the SVD-BC technique, particularly at the lower detection thresholds. While the AWLS technique resulted in more consistent percent residual standard deviation values, a statistical improvement in peak quantification after background correction was not found regardless of the background correction technique used.

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.

Development of a carbon clad core-shell silica for high speed two-dimensional liquid chromatography.

We recently introduced a new method to deposit carbon on fully porous silicas (5 µm) to address some of the shortcomings of carbon clad zirconia (C/ZrO(2)), which has rather low retention due to its low surface area (20-30 m(2)/g). The method enables the introduction of a thin, homogeneous layer of Al(III) on silica to serve as catalytic sites for carbon deposition without damaging the silica's native pore structure. Subsequent carbon deposition by chemical vapor deposition resulted in chromatographically useful carbon phases as shown by good efficiencies and higher retentivity relative to C/ZrO(2). Herein, we use the above method to develop a novel carbon phase on superficially porous silica (2.7 µm). This small, new form of silica offers better mass transfer properties and higher efficiency with lower column back pressures as compared to sub 2 µm silica packings, which should make it attractive for use as the second dimension in fast two-dimensional LC (LC × LC). After carbon deposition, several studies were conducted to compare the new packing with C/ZrO(2). Consistent with work on 5 µm fully porous silica, the metal cladding did not cause pore blockage. Subsequent carbon deposition maintained the good mass transfer properties as shown by the effect of velocity on HETP. The new packing exhibits efficiencies up to ∼5.6-fold higher than C/ZrO(2) for polar compounds. We observed similar chromatographic selectivity for all carbon phases tested. Consequently, the use of the new packing as the second dimension in fast LC×LC improved the peak capacity of fast LC × LC. The new material gave loading capacities similar to C/ZrO(2), which is rather as expected based on the surface areas of the two phases.

Fractional coverage metrics based on ecological home range for calculation of the effective peak capacity in comprehensive two-dimensional separations.

Optimization of comprehensive two-dimensional separations frequently relies on the assessment of the peak capacity of the system. A correction is required for the fact that many pairs of separation systems are to some degree correlated, and consequently the entire separation space is not chemically accessible to solutes. This correction is essentially a measure of the fraction of separation space area where the solutes may elute. No agreement exists in the literature as to the best form of the spatial coverage factor. In this work, we distinguish between spatial coverage factors that measure the maximum occupiable space, which is characteristic of the separation dimensionality, and the space actually occupied by a particular sample, which is characteristic of the sample dimensionality. It is argued that the former, which we call f(coverage), is important to calculating the peak capacity. We propose five criteria for a good f(coverage) metric and use them to evaluate various area determination methods that are used to measure animal home ranges in ecology. We consider minimum convex hulls, convex hull peels, α-hulls, three variations of local hull methods, and a kernel method and compare the results to the intuitively satisfying but subjective Stoll-Gilar method. The most promising methods are evaluated using two experimental LC×LC data sets, one with fixed separation chemistry but variable gradient times, and a second with variable first dimension column chemistry. For the 12 separations in the first data set, in which f(coverage) is expected to be constant, the minimum convex hull is the most precise method (f(coverage)=0.68±0.04) that gives similar results to the Stoll-Gilar method (f(coverage)=0.67±0.06). The minimum convex hull is proposed as the best method for calculating f(coverage), because it has no adjustable parameters, can be scaled to different retention time normalizations, is easily calculated using available software, and represents the expected area of solute occupation based on a proposed linear free energy formalism.

Silica-based, hyper-crosslinked acid stable stationary phases for high performance liquid chromatography.

A new family of hyper-crosslinked (HC) phases for use under very aggressive acid conditions including those encountered in ultra-fast, high temperature two-dimensional liquid chromatography (2DLC) has been recently introduced. This type of stationary phase shows significantly enhanced acid and thermal stability compared to the most acid stable, commercial RPLC phases. In addition, the use of "orthogonal" chemistry to make surface-confined polymer networks ensures good reproducibility and high efficiency. One of the most interesting features of the HC phases is the ability to derivatize the surface aromatic groups with various functional groups. This has led to the development of a family of hyper-crosslinked phases possessing a wide variety of chromatographic selectivities by attaching hydrophobic (e.g. -C8), ionizable (e.g. -COOH, -SO3H), aromatic (e.g. -toluene) or polar (e.g. -OH) species to the aromatic polymer network. HC reversed phases with various degrees of hydrophobicity and mixed-mode HC phases with added strong and weak cation exchange sites have been synthesized, characterized and applied. These silica-based acid-stable HC phases, with their attractive chromatographic properties, should be very useful in the separation of bases or biological analytes in acidic media, especially at elevated temperatures. This work reviews prior research on HC phases and introduces a novel HC phase made by alternative chemistry.