Comprehensive Two-dimensional Separations Research Articles

Unwrapping Wrap-around in Gas (or Liquid) Chromatographic Cyclic Ion Mobility-Mass Spectrometry.

Gas chromatography multiplexed with cyclic ion mobility mass spectrometry is a comprehensive two-dimensional separation technique that can resolve compounds that would otherwise coelute in a single-dimension separation. The cyclic geometry of the ion mobility cell enables ions to travel multiple passes, increasing their drift times to the detector and relative separation. However, the quality of the separation may be obfuscated when "wrap-around" occurs, during which speedier ions catch up with slower ion populations when allowed to travel through more than one pass. Consequently, cyclic ion mobility is incorrectly perceived as a targeted approach that requires preselection of ions prior to separation. The present study demonstrates that "wrap-around" can be mitigated by comparing drift times measured during single- and multipass experiments and extrapolating the number of passes experienced by each ion. This straightforward calculation results in the "unwrapping" of cyclic ion mobility data so that the experiments can be interpreted in a nontargeted way while reaping the benefit of peak capacities that rival those achieved using other comprehensive two-dimensional separations.

Bayesian optimization of comprehensive two-dimensional liquid chromatography separations

Comprehensive two-dimensional liquid chromatography (LC×LC), is a powerful, emerging separation technique in analytical chemistry. However, as many instrumental parameters need to be tuned, the technique is troubled by lengthy method development. To speed up this process, we applied a Bayesian optimization algorithm. The algorithm can optimize LC×LC method parameters by maximizing a novel chromatographic response function based on the concept of connected components of a graph. The algorithm was benchmarked against a grid search (11,664 experiments) and a random search algorithm on the optimization of eight gradient parameters for four different samples of 50 compounds. The worst-case performance of the algorithm was investigated by repeating the optimization loop for 100 experiments with random starting experiments and seeds. Given an optimization budget of 100 experiments, the Bayesian optimization algorithm generally outperformed the random search and often improved upon the grid search. Moreover, the Bayesian optimization algorithm offered a considerably more sample-efficient alternative to grid searches, as it found similar optima to the grid search in far fewer experiments (a factor of 16–100 times less). This could likely be further improved by a more informed choice of the initialization experiments, which could be provided by the analyst’s experience or smarter selection procedures. The algorithm allows for expansion to other method parameters (e.g., temperature, flow rate, etc.) and unlocks closed-loop automated method development.

Impact of sample dimensionality on orthogonality metrics in comprehensive two-dimensional separations

Orthogonality is a key parameter in the evaluation of the performance of a 2D chromatography-based separation system. Two different perspectives on orthogonality are determined: the extent of the separation space utilized (global orthogonality) and the uniformity of the coverage of the separation space (local orthogonality). This work aims to elucidate the impact of sample dimensionality (the number of separation processes involved) on orthogonality evaluation through the use of descriptors from seven different algorithms utilizing mutually different properties of a chromatogram: Pearson correlation, conditional entropy, asterisk equations, convex hull, arithmetic mean (AN) and harmonic mean of the nearest neighbor, and geometric surface coverage (SC). Artificial chromatograms generated in silico and real GC × GC separations of diesel, plasma, and urine were used for the evaluation of orthogonality. The sample dimensionality has a deep effect on the orthogonality results of all approaches. The SC algorithm emerged as the best descriptor of local orthogonality samples of both low and high dimensionality, the AN algorithm on the global orthogonality of low-dimensionality samples. However, in the case of samples of high dimensionality, AN consistently indicated just the exploitation of the whole separation space; therefore, only local orthogonality is optimized by means of SC. Since no approach was able to monitor both global and local orthogonality as a single value, a new descriptor, ASCA, was developed. It combines the best global (AN) and local (SC) orthogonality algorithms by averaging, giving the same importance to data spread and crowding. ASCA thus provides the best estimation of orthogonality.

Fraction transfer process in on-line comprehensive two-dimensional liquid-phase separations.

Two-dimensional liquid-phase separations have gained increasing attention for their ability to separate complex sample mixtures. Among the experimental setups used, an on-line approach is preferred to reduce the probability of sample contamination, for easier automation and high-sample throughput. The interfacing of the separation techniques in the on-line mode brings additional demands on proper optimization of the two-dimensional system. In this review, the possibilities of the on-line coupling of liquid chromatography and liquid chromatography with capillary electrophoresis in two-dimensional systems are discussed. Special attention is paid to the fraction transfer process, which includes an overview of interfaces and experimental setups applied, the compatibility issues of separation systems, and instrumental parameters. The benefits and drawbacks of using electromigration separations in combination with liquid chromatography are presented as well.

Improved Flow Modulator Construction for GC × GC with Quadrupole Mass Spectrometry.

Improvement and testing of a flow modulator for the application in comprehensive two-dimensional gas chromatography separations is the subject of the presented paper. This improved setup constructed from two independent capillary branches each consisting of a pressure regulator, a pressure sensor, a two-way solenoid valve and a microfluidic T-connector, allows an independent and easy settings of the pressures and flow velocities in the modulator and provides system flexibility in an operation without need of any component exchange. The estimated flow rates were 0.4 mL/min in the first column and 3.2 mL/min in the second column. This setup was compared with the commercial Zoex cryogenic modulator for the separation of 17 selected solvents at isothermal conditions. Modulator working conditions were optimized and its separation power was demonstrated on the analysis of a lavender extract under an application of two orthogonal capillary column sets (nonpolar-polar vs. polar-nonpolar) and temperature program. The results were evaluated by two commercial software packages and discussed with respect to the identification compliance.

Automated dual two-dimensional liquid chromatography approach for fast acquisition of three-dimensional data using combinations of zwitterionic polymethacrylate and silica-based monolithic columns

A monolithic sulfobetaine polymethacrylate micro-column BIGDMA-MEDSA designed in our laboratory, shows dual retention mechanism: In acetonitrile-rich mobile phase, hydrophilic interactions control the retention (HILIC system), whereas in more aqueous mobile phases the column shows essentially reversed-phase behavior with major role of hydrophobic interactions. The zwitterionic polymethacrylate micro-column can be used in the first dimension of two-dimensional LC in alternating reversed-phase (RP) and HILIC modes, coupled with an alkyl-bonded core-shell or silica-based monolithic column in the second dimension, for HILIC×RP and RP×RP comprehensive two-dimensional separations. During the HILIC×RP period, a gradient of decreasing acetonitrile gradient is used for separation in the first dimension, so that at the end of the gradient the polymeric monolithic micro-column is equilibrated with a highly aqueous mobile phase and is ready for repeated sample injection, this time for separation under reversed-phase gradient conditions with increasing concentration of acetonitrile in the first dimension. The fast repeating reversed-phase gradients on a short silica-monolithic or core-shell column in the second dimension can be optimized independently of the actual running first-dimension gradient program. As the alternating HILIC and RP separations on the first-dimension zwitterionic methacrylate column are based on complementary retention mechanisms, the instrumental setup essentially represents two coupled two-dimensional systems. It is first time that such an automated dual LCxLC approach is reported. The novel system allows obtaining three-dimensional data in a relatively short time and can be applied not only to multidimensional gradient separations of flavones and related polyphenolic compounds.

μGC × μGC: Comprehensive Two-Dimensional Gas Chromatographic Separations with Microfabricated Components

The development and characterization of a microanalytical subsystem comprising silicon-micromachined first- and second-dimension separation columns and a silicon-micromachined thermal modulator (μTM) for comprehensive two-dimensional (i.e., μGC × μGC) separations are described. The first dimension consists of two series-coupled 3.1 cm × 3.1 cm μcolumn chips with etched channels 3 m long and 250 μm × 140 μm in cross section, wall-coated with a poly(dimethylsiloxane) (PDMS) stationary phase. The second dimension consists of a 1.2 cm × 1.2 cm μcolumn chip with an etched channel 0.5 m long and 46 μm × 150 μm in cross section wall-coated with either a trigonal tricationic room-temperature ionic liquid (RTIL) or a commercial poly(trifluoropropylmethyl siloxane) (OV-215) stationary phase. The two-stage, cryogen-free μTM consists of a Si chip containing two series-coupled, square spiral channels 4.2 cm and 2.8 cm long and 250 μm × 140 μm in cross section wall-coated with PDMS. Conventional injection methods and flame ionization detection were used. Temperature-ramped separations of a simple alkane mixture using the RTIL-coated second-dimension ((2)D) μcolumn produced reasonably good peak shapes and modulation numbers; however, strong retention of polar compounds on the RTIL-coated (2)D μcolumn led to excessively broad peaks with low (2)D resolution. Substituting OV-215 as the (2)D μcolumn stationary phase markedly improved the performance, and a structured 22 min chromatogram of a 36-component mixture spanning a vapor pressure range of 0.027 to 13 kPa was generated with modulated peak fwhm (full width at half-maximum) values ranging from 90 to 643 ms and modulation numbers of 1-6.

Branched polymers characterized by comprehensive two-dimensional separations with fully orthogonal mechanisms: Molecular-topology fractionation × size-exclusion chromatography

Polymer separations under non-conventional conditions have been explored to obtain a separation of long-chain branched polymers from linear polymers with identical hydrodynamic size. In separation media with flow-through channels of the same order as the size of the analyte molecules in solution, the separation and the elution order of polymers are strongly affected by the flow rate. At low flow rates, the largest polymers are eluted last. At high flow rates, they are eluted first. By tuning the channel size and flow rate, conditions can be found where separation becomes independent of molar mass or size of linear polymers. Long-chain branched polymers did experience lower migration rates under these conditions and can be separated from linear polymers. This type of separation is referred to as molecular-topology fractionation (MTF) at critical conditions. Separation by comprehensive two-dimensional molecular-topology fractionation and size-exclusion chromatography (MTF×SEC) was used to study the retention characteristics of MTF. Branching selectivity was demonstrated for three- and four-arm “star” polystyrenes of 3–5×106g/mol molar mass. Baseline separation could be obtained between linear polymer, Y-shaped molecules, and X-shaped molecules in a single experiment at constant flow rate. For randomly branched polymers, the branching selectivity inevitably results in an envelope of peaks, because it is not possible to fully resolve the huge numbers of different branched and linear polymers of varying molar mass. It was concluded that MTF involves partial deformation of polymer coils in solution. The increased coil density and resistance to deformation can explain the different retention behavior of branched molecules.

A Modeling Approach for Orthogonality of Comprehensive Two-Dimensional Separations

A novel method is developed for orthogonality evaluation of comprehensive two-dimensional separations (C2DS). Utilization of efficiency measures such as peak capacity (n(c)) can be critically evaluated for C2DS analysis to describe an orthogonal separation of the analytes in a 2D plane. Unlike most previous methods focusing on "bin coverage" over 2D space, rather than taking into account the distribution based on accurate peak retention, in the proposed method, the separation orthogonality of C2DS is divided into two parts (i.e., C(pert) and C(peaks)). These correspond to peak coverage percent, and 2D distribution correlation of compounds, respectively. Bin occupation and a simple-linear regression model, on the basis of normalized retention times in 2D separation space ((1)t(R) and (2)t(R)), are further introduced to quantitatively define the two terms. Orthogonality ranges from 0 to 1 correspond to perfectly correlated and orthogonal separations, respectively, which are presented based on both C(pert) and C(peaks) considerations. The advantage of this method is the use of separation properties of C2DS to characterize practical 2D peak distribution and does not rely on assumptions or any imposed limitations. Simulation of comprehensive two-dimensional gas chromatography (GC × GC) was achieved by using the Abraham solvation parameter model, and applied to generate examples for orthogonality assessment. In this work, 225 compounds comprising a range of chemical classes were simulated for separation on two column set pairs comprising low polarity/polar and moderately polar/polar combinations. Results illustrate that the proposed method applied to GC × GC provides a reasonable assessment of 2D separation performance and may be used to derive optimal experimental conditions when used with an experimental design strategy.

On-line comprehensive two-dimensional separations of charged compounds using reversed-phase high performance liquid chromatography and hydrophilic interaction chromatography. Part I: Orthogonality and practical peak capacity considerations

Comprehensive on-line two-dimensional liquid chromatography is expected to generate impressive peak capacities, which makes it a method of choice for the analysis of complex samples such as pharmaceutical or biological ones. A comparative study of different sets of chromatographic conditions including stationary phase, mobile phase and column temperature was carried out with mixtures of representative solutes in order to find out the best two-dimensional analytical conditions for charged compounds. Our approach focused on ultra-fast gradient runs in second dimension using HT-UHPLC conditions. The choice of volatile buffers was intended for future coupling with mass spectrometry in order to get another relevant dimension. The potential of various pairs of chromatographic systems was examined by means of two-dimensional gradient data. An attempt is made to rationalize the concept of orthogonality and a method is proposed to assess, for a given pair of chromatographic systems, both the degree of orthogonality and the practical peak capacity. It is shown that the degree of orthogonality between both dimensions is a critical factor but it is not sufficient to definitely appreciate the potential of a given pair of systems. The combination of HILIC and RPLC (HILIC×RPLC or RPLC×HILIC), although providing a very high degree of orthogonality, is disappointing due to the poor peak capacities obtained in HILIC especially with peptide samples. RPLC systems offer a large variety of analytical conditions, some of them leading to appropriate degrees of orthogonality when they are combined. More importantly, due to high column efficiencies along with large separation power, some combinations of RPLC systems leads to very high practical peak capacities.

A Review of Chemometrics Applied to Comprehensive Two-dimensional Separations from 2008–2010

This review article covers developments in multidimensional separations combined with chemometrics that were published in 2008 through 2010, specifically for multidimensional gas chromatography, liquid chromatography, and electrophoresis. Although different instrumentation is used to generate multidimensional separations data, many similar data processing options and chemometrics can be applied in order to objectively distill the data into useful knowledge while reducing manual analysis and preserving data integrity. This review article describes the chemometrics employed in the referenced studies in terms of unsupervised, supervised, preprocessing, resolution, and image analysis algorithms. Other factors that affect converting data into useful knowledge are the structure of the data and the format of the data submitted to the analysis methods, so the studies are also described in terms of data dimensionality and data format (i.e., whether peak tables or raw data points were analyzed).

Comprehensive two-dimensional liquid chromatography — practical impacts of theoretical considerations. A review

Abstract A theory of comprehensive two-dimensional separations by liquid chromatographic techniques is overviewed. It includes heart-cutting and comprehensive two-dimensional separation modes, with attention to basic concepts of two-dimensional separations: resolution, peak capacity, efficiency, orthogonality and selectivity. Particular attention is paid to the effects of sample structure on the retention and advantages of a multi-dimensional HPLC for separation of complex samples according to structural correlations. Optimization of 2D separation systems, including correct selection of columns, flow-rate, fraction volumes and mobile phase, is discussed. Benefits of simultaneous programmed elution in both dimensions of LCxLC comprehensive separations are shown. Experimental setup, modulation of the fraction collection and transfer from the first to the second dimension, compatibility of mobile phases in comprehensive LCxLC, 2D asymmetry and shifts in retention under changing second-dimension elution conditions, are addressed. Illustrative practical examples of comprehensive LCxLC separations are shown.

Predictions of comprehensive two-dimensional gas chromatography separations from isothermal data

Two-dimensional retention times and peak widths in temperature programmed comprehensive two-dimensional gas chromatography were predicted using a theoretical model developed from experimental data obtained under isothermal conditions. A Matlab program was written to calculate the following parameters: dead time (tM), elution temperature (Te), retention time (tR), hold-up width (wM) and peak width (wR). The two-dimensional retention times of a sample mixture that contained n-alkanes and polyaromatic hydrocarbons (PAHs) were predicted and were observed to be in excellent agreement with experimentally determined values. The relative deviation between the model and the experimental data was less than 2 and 7% for the primary and secondary retention times, respectively. The relative deviation of peak width was less than 7 and 10% in the primary and secondary dimensions, respectively. The advantage of this model was its simplicity, informed entirely from experimental data, with no reliance on theoretical parameters. This prediction model would be useful for optimizing GC×GC separation conditions and for confirming compound identifications of components that are chromatographically resolved but that have nearly identical mass spectra.

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 fcoverage, is important to calculating the peak capacity. We propose five criteria for a good fcoverage 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 fcoverage is expected to be constant, the minimum convex hull is the most precise method (fcoverage=0.68±0.04) that gives similar results to the Stoll–Gilar method (fcoverage=0.67±0.06). The minimum convex hull is proposed as the best method for calculating fcoverage, 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.

Relationship between selectivity and average resolution in comprehensive two-dimensional separations with spectroscopic detection

The average value of the multivariate selectivity ( SEL) of randomly positioned peaks in a multi-component separation is shown to equal the average fraction of peaks that are singlets, as predicted by statistical-overlap theory (SOT). This equality is the basis for proposing a useful metric, specifically the average minimum resolution of nearest-neighbor peaks, for the performance of comprehensive two-dimensional (2D) separations. Furthermore this metric was computed both without ancillary spectroscopic information and with the assistance of such help, specifically multi-wavelength UV–vis spectra, acquired during the separation. Separations are simulated with randomly positioned peaks over wide ranges of total number of peaks, first- and second-dimension peak capacity, dimensionless first-dimension sampling time, and spectral diversity. The specific version of the general multivariate selectivity concept that is used here – identified as SEL – gives the relative precision of quantification when using the PARAFAC (parallel factor analysis) method, a popular curve resolution algorithm. The SEL values of all peaks were calculated, averaged, and compared to the predictions of SOT. In the absence of auxiliary spectral data, the SEL-based average minimum resolution required to separate two peaks in a 2D separation is 0.256, compared to resolution of 0.5 if no chemometric assistance is available. This was found to be valid over a wide range of conditions and is essentially independent of peak crowding. With the assistance of the spectral data, the requisite minimum resolution substantially improves, that is, it decreases, especially when peak crowding is severe. The requisite minimum resolution decreases even further, up to a limit, as the spectral diversity is increased. In contrast, the SEL-based average under-sampling correction factor is virtually independent of the presence of the additional spectral data, and additionally is about the same as calculated with SOT from the average number of maxima in closely analogous simulations. The use of selectivity greatly increases the fraction of peaks that are singlets, relative to the number of singlet maxima, especially when spectral assistance is added. The insensitivity of the under-sampling correction factor to either the use of selectivity or added spectral data simplifies optimization of the corrected peak capacity in on-line comprehensive 2D separations.

Construction and initial evaluation of an apparatus for spatial comprehensive two-dimensional liquid-phase separations

Spatial comprehensive two-dimensional chromatography is discussed as a potentially alternative to the conventional column-based approach. In “spatial” separations each analyte ends up in a specific location, rather than being eluted at a specific time. Ultimately, higher peak-capacity-production rates (peak capacity per unit time) may be attained by spatial two- and three-dimensional separations. While low-pressure planar chromatography is well developed, the high-pressure equivalent is still in its infancy. We discuss the requirements for a device for high-pressure spatial two-dimensional chromatography and we describe a possible design. A prototype instrument has been constructed in-house. The preparation of a polymer monolithic separation body and a valve configuration that allows manual sample injection are described. Initial tests of this study included the investigation of the homogeneity of the monolith and the flow profile through the separation body. Furthermore, in order to evaluate the current chromatographic performance of the device, a mixture of dyes was separated in one dimension within 30 s.

A critical look at the definition of multidimensional separations

Multidimensional (MD) separations, especially comprehensive two-dimensional (2D) separations such as comprehensive 2D LC (LC × LC), and comprehensive 2D GC (GC × GC), are potentially powerful separation techniques. It is important to have a clear definition of MD techniques to better understand the scope and boundaries of the subject. Widely accepted definitions of MD Separations have their roots in the definition proposed by Giddings. Giddings also added several comments that clarified the scope of his definition. However, some researchers extend Giddings’ definitions beyond their intended scope. Doing so disqualifies such comprehensive 2D techniques as LC × LC, GC × GC and 2D TLC from being considered as 2D techniques. In other instances, extended treatment of Giddings’ definition is used as a basis to justify design-parameters of comprehensive 2D separations despite the fact that these parameters lead to sub-optimal implementations. We believe that the shortcomings in the definition and its popular interpretations are serious enough to warrant attention, especially by those interested in designing optimal instrumentation for MD separations like comprehensive 2D GC. After discussion of the weaknesses in the currently used definitions, we propose to define n-dimensional analysis as one that generates n-dimensional displacement information. We believe that this definition captures the spirit of Giddings’ definition while avoiding the problems associated with its popular interpretations.

Comprehensive two-dimensional liquid chromatography separations of pharmaceutical samples using dual Fused-Core columns in the 2nd dimension

This paper focuses on the application of RPLC×RPLC to pharmaceutical analysis and addresses the specific problem of separating co-eluting impurities/degradation products that maybe “hidden” within the peak envelope of the active pharmaceutical ingredient (API) and thus may escape detection by conventional methods. A comprehensive two-dimensional liquid chromatograph (LC×LC) was constructed from commercially available HPLC equipment. This system utilizes two independently configurable 2nd dimension binary pumping systems to deliver independent flow rates, gradient profiles and mobile phase compositions to dual Fused-Core secondary columns. Very fast gradient separations (30s total cycle time) were achieved at ambient temperature without excessive backpressure and without compromising optimal 1st dimension sampling rates. The operation of the interface is demonstrated for the analysis of a 1mg/ml standard mixture containing 0.05% of a minor component. The practicality of using RPLC×RPLC for the analysis of actual co-eluting pharmaceutical degradation products, by exploiting pH-induced changes in selectivity, is also demonstrated using a three component mixture. This mixture (an API, an oxidation product of the API at 1.0%, w/w, and a photo degradant of the API at 0.5%, w/w) was used to assess the stability indicating nature of an established LC method for analysis of the API.

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.

Comparison of one-dimensional and comprehensive two-dimensional separations by gas chromatography

Comprehensive two-dimensional gas chromatography (GC×GC) can reveal information on the composition of a sample in a way that cannot be done by one-dimensional GC (1D-GC). GC×GC also offers much greater control of chromatographic selectivity based on molecular structure. However, in spite of more than 15 years of claims of the ability of GC×GC to resolve an overwhelmingly larger number of peaks than 1D-GC, and in spite of the theoretically proven potential of GC×GC to have an order of magnitude larger peak capacity than 1D-GC, the peak capacity of currently practiced GC×GC does not generally exceed the peak capacity attainable from 1D-GC with the same analysis time and the same minimal detectable concentration (MDC). The methodology for comparing the peak capacity of GC×GC to 1D-GC is described. The comparison of the performance of GC×GC to 1D-GC shows that the modulator is the key bottleneck limiting the performance of existing GC×GC. To realize the full potential of GC×GC, duration of injection from a modulator into the second-dimension column should be reduced by an order of magnitude or more. Use of powerful data analysis techniques such as peak deconvolution in both dimensions can further increase resolving power of GC×GC.