A study of the precision and accuracy of peak quantification in comprehensive two-dimensional liquid chromatography in time

Simulated chromatographic data were used to determine the precision and accuracy in the estimation of peak volumes (i.e., peak sizes) in comprehensive two-dimensional liquid chromatography in time (LC × LC). Peak volumes were determined both by summing the areas in the second dimension chromatograms and by fitting the second dimension areas to a Gaussian peak. The Gaussian method is better at predicting the peak volume than the moments method provided there are at least three second dimension injections above the limit of detection (LOD). However, when only two of the second dimension signals are substantially above baseline, the accuracy and precision of the Gaussian fit method become quite poor because the results from the fitting algorithm become indeterminate. Based on simulations in which the modulation ratio (M_R = 4¹σ/t_s) and sampling phase (?) were varied, we conclude for well-resolved peaks that the optimum precision in peak volumes in 2D separations will be obtained when the M_R is between two and five, such that there are typically four to ten second dimension peaks recorded over the eight σ width of the first dimension peak. This sampling rate is similar to that suggested by the Murphy–Schure–Foley criterion. This provides an RSD of approximately 2% for the signal-to-noise ratio used in the present simulations. The precision of the peak volume of experimental data was also assessed, and RSD values were in the range of 4–5%. We conclude that the poorer precision found in the LC × LC experimental data as compared to LC may be due to experimental imprecision in sampling the effluent from the first dimension column.     

The impact of sampling time on peak capacity and analysis speed in on-line comprehensive two-dimensional liquid chromatography

Comprehensive two-dimensional liquid chromatography (2DLC) offers a number of practical advantages over optimized one-dimensional LC in peak capacity and thus in resolving power. The traditional “product rule” for overall peak capacity for a 2DLC system significantly overestimates peak capacity because it neglects under-sampling of the first dimension separation. Here we expand on previous work by more closely examining the effects of the first dimension peak capacity and gradient time, and the second dimension cycle times on the overall peak capacity of the 2DLC system. We also examine the effects of re-equilibration time on under-sampling as measured by the under-sampling factor and the influence of molecular type (peptide vs. small molecule) on peak capacity. We show that in fast 2D separations (less than 1 h), the second dimension is more important than the first dimension in determining overall peak capacity and conclude that extreme measures to enhance the first dimension peak capacity are usually unwarranted. We also examine the influence of sample types (small molecules vs. peptides) on second dimension peak capacity and peak capacity production rates, and how the sample type influences optimum second dimension gradient and re-equilibration times.     

Smart templates for peak pattern matching with comprehensive two-dimensional liquid chromatography

Comprehensive two-dimensional liquid chromatography (LCxLC) generates information-rich but complex peak patterns that require automated processing for rapid chemical identification and classification. This paper describes a powerful approach and specific methods for peak pattern matching to identify and classify constituent peaks in data from LCxLC and other multidimensional chemical separations. The approach records a prototypical pattern of peaks with retention times and associated metadata, such as chemical identities and classes, in a template. Then, the template pattern is matched to the detected peaks in subsequent data and the metadata are copied from the template to identify and classify the matched peaks. Smart Templates employ rule-based constraints (e.g., multispectral matching) to increase matching accuracy. Experimental results demonstrate Smart Templates, with the combination of retention-time pattern matching and multispectral constraints, are accurate and robust with respect to changes in peak patterns associated with variable chromatographic conditions.     

Fast, comprehensive two-dimensional liquid chromatography

The absolute need to improve the separating power of liquid chromatography, especially for multi-constituent biological samples, is becoming increasingly evident. In response, over the past few years, there has been a great deal of interest in the development of two-dimensional liquid chromatography (2DLC). Just as 1DLC is preferred to 1DGC based on its compatibility with biological materials we believe that ultimately 2DLC will be preferred to the much more highly developed 2DGC for such samples. The huge advantage of 2D chromatographic techniques over 1D methods is inherent in the tremendous potential increase in peak capacity (resolving power). This is especially true of comprehensive 2D chromatography wherein it is possible, under ideal conditions, to obtain a total peak capacity equal to the product of the peak capacities of the first and second dimension separations. However, the very long timescale (typically several hours to tens of hours) of comprehensive 2DLC is clearly its chief drawback. Recent advances in the use of higher temperatures to speed up isocratic and gradient elution liquid chromatography have been used to decrease the time needed to do the second dimension LC separation of 2DLC to about 20s for a full gradient elution run. Thus, fast, high temperature LC is becoming a very promising technique. Peak capacities of over 2000 and rates of peak capacity production of nearly 1 peak/s have been achieved. In consequence, many real samples showing more than 200 peaks with signal to noise ratios of better than 10:1 have been run in total times of under 30 min. This report is not intended to be a comprehensive review of 2DLC, but is deliberately focused on the issues involved in doing fast 2DLC by means of elevating the column temperature; however, many issues of broader applicability will be discussed.     

Molecular structure retention relationships in comprehensive two-dimensional gas chromatography

Comprehensive two-dimensional gas chromatography (GC x GC) offers new opportunities to develop relationships between molecular structure and retentions in the two dimensional (2D) separation space defined by the GC x GC retention in each dimension. Whereas single dimension GC provides only one retention property for a solute, and hence the specific relationship between retention and chemical property is not readily apparent or derivable, the 2D presentation of compounds in GC x GC provides a subtle and exquisite correlation of chemical property and retention unlike any other GC experiment. The 'orthogonality' of the two separation dimensions is intimately related to the manner in which different separation mechanisms, available through use of two dissimilar phases, are accessible to the different chemical compounds or classes in a sample mixture, and indeed the specific chemical classes present in the sample. The GC x GC experiment now permits various processes such as chemical decompositions, molecular interconversions, various non-linear chromatography effects, and processes such as slow reversible interactions that may arise with stationary phases or in the injector or column couplings, to be identified and further investigated. Here, we briefly review implementation of the GC x GC method, consider the molecular selectivity of GC x GC, and highlight a selection of molecular processes that can be probed by using GC x GC.     

Evaluation of a retention model in comprehensive two-dimensional gas chromatography

Modeling the retention in comprehensive two-dimensional gas chromatography (GC x GC) was achieved using retention indices obtained in conventional GC. Predicted results were compared with experimental data obtained in the two-dimensional separation of a synthetic hydrocarbon mixture. This proved to be helpful in optimizing the operating conditions of GC x GC separation of a complex petroleum sample and in identifying chemical families.     

Development of an algorithm for peak detection in comprehensive two-dimensional chromatography

A method for peak detection in two-dimensional chromatography is presented. The algorithm applies first the methods developed for peak detection in one-dimensional chromatography to detect peaks in one dimension. In a second step, a decision tree is applied to decide which one-dimensional peaks are originated from the same compound and have to be 'merged' into one two-dimensional peak. To this end, different features of the peaks (second-dimension peak regions and second-dimension retention times) are compared and different criteria (common peak regions, retention time differences, unimodality in the first dimension) are applied. Different options can be used, depending on the nature of the data. The user controls this decision tree by establishing several options and "switches". The algorithm was tested with GCxGC chromatograms obtained for a commercial air-freshener sample, detecting and merging the modulated peaks belonging to the same compound. Recommendations for the set of options and switches are given. A utility that calculates and sums peak areas from merged peaks is added to facilitate automated quantification. Although the algorithm was developed for GCxGC, its application to comprehensive two-dimensional liquid chromatography (LCxLC) data should at most require minor modifications.     

Model for predicting comprehensive two-dimensional gas chromatography retention times

A model for approximating the relative retention of solutes in comprehensive two-dimensional gas chromatography (GCxGC) is presented. The model uses retention data from standard single-column temperature-programmed separations. The one-dimensional retention times are first converted into retention indices and then these indices are combined in a simple manner to generate a retention diagram. A retention diagram is an approximation of the two-dimensional chromatogram that has retention order and spacing in both dimensions similar to that found in the experimental chromatogram. If required, the retention diagram can be scaled to more closely resemble the two-dimensional chromatogram. The model has been tested by using retention time data from single-column gas chromatography-mass spectrometry and valve-based GCxGC. A total of 139 volatile organic compounds (VOCs) were examined. Approximately half of the VOCs had a single functional group and a linear alkyl chain (i.e., compounds with the structure Z-(CH(2))(n)-H). The retention diagrams had primary retention orders that were in excellent agreement with the GCxGC chromatograms. The relative secondary retention order for compounds with similar structures was also accurately predicted by the retention diagram. However, the relative secondary retention for compounds with dissimilar structures, such as acyclic alcohols and multi-substituted alkylbenzenes, were less accurately modeled. This study demonstrates how readily available single-column retention time data can be used to provide an a priori estimate of the relative retention of solutes in a GCxGC chromatogram. Such a capability is useful for screening possible combinations of stationary phases.     

Achieving high peak capacity production for gas chromatography and comprehensive two-dimensional gas chromatography by minimizing off-column peak broadening

By taking into consideration band broadening theory and using those results to select experimental conditions, and also by reducing the injection pulse width, peak capacity production (i.e., peak capacity per separation time) is substantially improved for one dimensional (1D-GC) and comprehensive two dimensional (GC×GC) gas chromatography. A theoretical framework for determining the optimal linear gas velocity (the linear gas velocity producing the minimum H), from experimental parameters provides an in-depth understanding of the potential for GC separations in the absence of extra-column band broadening. The extra-column band broadening is referred to herein as off-column band broadening since it is additional band broadening not due to the on-column separation processes. The theory provides the basis to experimentally evaluate and improve temperature programmed 1D-GC separations, but in order to do so with a commercial 1D-GC instrument platform, off-column band broadening from injection and detection needed to be significantly reduced. Specifically for injection, a resistively heated transfer line is coupled to a high-speed diaphragm valve to provide a suitable injection pulse width (referred to herein as modified injection). Additionally, flame ionization detection (FID) was modified to provide a data collection rate of 5kHz. The use of long, relatively narrow open tubular capillary columns and a 40°C/min programming rate were explored for 1D-GC, specifically a 40m, 180μm i.d. capillary column operated at or above the optimal average linear gas velocity. Injection using standard auto-injection with a 1:400 split resulted in an average peak width of ～1.5s, hence a peak capacity production of 40peaks/min. In contrast, use of modified injection produced ～500ms peak widths for 1D-GC, i.e., a peak capacity production of 120peaks/min (a 3-fold improvement over standard auto-injection). Implementation of modified injection resulted in retention time, peak width, peak height, and peak area average RSD%'s of 0.006, 0.8, 3.4, and 4.0%, respectively. Modified injection onto the first column of a GC×GC coupled with another high-speed valve injection onto the second column produced an instrument with high peak capacity production (500-800peaks/min), ～5-fold to 8-fold higher than typically reported for GC×GC.     

Factors affecting peak shape in comprehensive two-dimensional gas chromatography with non-focusing modulation

In the case of a non-focusing modulator for comprehensive two-dimensional gas chromatography (GC × GC), the systematic distortions introduced when the modulator loads the second-dimension column give rise to a characteristic peak shape. Depending on the operating conditions this systematic distortion can be the dominant component of the second-dimension elution profiles in the GC × GC peak. The present investigation involved a systematic investigation of peak shape in pulsed-flow modulation (PFM)–GC × GC. It is shown that low flow ratio can lead to significant peak skewing and increasing the flow ratio reduces the magnitude of peak skewing. Validation of the peak shape model is made by comparison with experimental data. The residuals from the fitting process (normalised to the maximum detector response) vary between –1.5% and +2.6% for an isothermal model and between –1.0% and +3.0% for a temperature-programmed model.     

Prediction of retention time of phenols in liquid chromatography

The chromatographic behavior of phenols in reversed-phase mode liquid chromatography differs from that of non-ionic compounds such as alkyl alcohols, alkylbenzenes, halogenated benzenes, polyaromatic hydrocarbons, and aromatic acids. Therefore, the retention times of 61 phenols were measured in a system of an octadecyl bonded silica gel and acetonitrile/water mixtures. The logarithm of the capacity ratio (log k') was found to be a linear function of the hydrophobicity (log P) in acidic acetonitrile/water mixtures. This result was applied to a different octadecyl bonded silica gel. Eight phenols were selected as standard compounds, and their log k' values were measured in 0.05 M phosphoric acid in 10 to 90% acetonitrile/water mixtures. An empirical polynomial relation was obtained between the concentration of acetonitrile and the slope of the log k' vs log P curve. Finally the capacity ratio of all phenols were calculated in given eluents by the equations derived from the measurements of standard compounds and the calculated log P values. The difference between predicted capacity ratios and measured ones was within 10%.     

Separation of branched polystyrene by comprehensive two-dimensional liquid chromatography

Branched polystyrenes (PS) featuring a bivariate distribution in the molecular weight and in the number of branches were characterized by comprehensive two-dimensional liquid chromatography (2D-LC). The branched PS were prepared by anionic polymerization using n-butyl Li as an initiator and a subsequent linking reaction with p-(chlorodimethylsilyl)styrene (CDMSS). The n-butyl Li initiator yields polystyryl anions with broad molecular weight distribution (MWD) and the linking reaction with CDMSS yields branched PS with different number of branches. For the first dimension (1st-D) separation, reversed-phase temperature gradient interaction chromatography (RP-TGIC) was employed to separate the branched polymer according to mainly the molecular weight. In the second dimension (2nd-D) separation, the effluents from the RP-TGIC separation are subjected to liquid chromatography at chromatographic critical conditions (LCCC), in which the separation was carried out at the critical condition of linear homo-PS to separate the branched PS in terms of the number of branches. The 2D-LC resolution of RP-TGICxLCCC combination worked better than the common LCCCxsize-exclusion chromatography (SEC) configuration due to the higher resolution of RP-TGIC in molecular weight than SEC. Furthermore, by virtue of using the same eluent in RP-TGIC and LCCC (only the column temperature is different), RP-TGICxLCCC separation is free from possible 'break through' and large system peak problems. This type of 2D-LC separation could be utilized efficiently for the analysis of branched polymers with branching units distinguishable by LC separation.     

Method for reducing the ambiguity of comprehensive two-dimensional chromatography retention times

Comprehensive two-dimensional chromatography generates a two-dimensional chromatogram from a one-dimensional signal array. This process can only be done unambiguously when the range of secondary retention times is less than the modulation period. However, complex samples often produce wider ranges of secondary retention times. Peaks with retention times that exceed the modulation period are said to be "wrapped-around". A simple algorithm has been developed that determines absolute retention times when wrap-around occurs. A sample is first analyzed under standard modulation conditions and then re-analyzed with a modulation period that is increased by an integer fraction of the original modulation period. Retention shifts along the secondary axis are used to determine absolute retention times. A theoretical analysis has been performed to optimize the implementation conditions and characterize the technique limitations. The efficacy of this algorithm has been tested through a series of isothermal GC x GC separations. This method has been found to be particularly useful during the initial stages of method development.     

Retention time locking procedure for comprehensive two-dimensional gas chromatography

In gas chromatography (GC) reproducible retention times are in many cases highly favorable or in some cases even required. In one-dimensional GC, retention time shifts can be eliminated or minimized using a procedure called retention time locking (RTL). This procedure is based on adjusting the (constant) column head pressure. Unfortunately, this RTL procedure cannot be used in comprehensive two-dimensional gas chromatography (GC × GC) given the fact that peaks will shift in both dimensions. Adjusting the column head pressure in GC × GC will only minimize or eliminate the primary retention time shifts. In this paper, a fast and easy to perform, two-step retention time locking procedure for two-dimensional gas chromatography (2D-RTL) is proposed and its feasibility is demonstrated. This 2D-RTL procedure involves adjustment of the column head pressure or constant column flow, followed by the adjustment of the so-called effective secondary column length. The secondary column length is increased or decreased, simply by moving it stepwise through the modulator. It is demonstrated that retention time shifts in both the primary- and secondary-dimension, which may occur after e.g. replacing the column set, can be minimized to less than half peak base width. The proposed 2D-RTL procedure is used successfully for approximately 1 year in our laboratory.     

Optimization of a comprehensive two-dimensional normal-phase and reversed-phase liquid chromatography system

The present investigation is based on the evaluation of the performance of a comprehensive two-dimensional liquid chromatography (LCxLC) system during method optimization. The LCxLC set-up, operated in normal phase (NP) mode (adsorption) in the first dimension (1D) and reversed-phase (RP) mode in the second dimension (2D), is equipped with a 1D microbore silica column and a 2D monolithic C(18) column with a 10-port two position valve as the interface. A photodiode array detector is used after the 2D separation. A possible cause of peak distorsion because of the immiscibility of the mobile phases employed in the two dimensions is resolved. The optimization of the analytical run time and flow rate for both dimensions and the initial gradient in the 2D is carried out with various standard compounds. The potential and versatility of this LCxLC approach is demonstrated through the separation of 11 standard components, most of them allergens. The latter, which are characterized by a scattered distribution on the 2D space plane, underwent separation on both a hydrophobicity and polarity basis.     

Probability of failure of the watershed algorithm for peak detection in comprehensive two-dimensional chromatography

The watershed algorithm is the most common method used for peak detection and integration in two-dimensional chromatography. However, the retention time variability in the second dimension may render the algorithm to fail. A study calculating the probabilities of failure of the watershed algorithm was performed. The main objective was to calculate the maximum second-dimension retention time variability, Δ²t_R,crit, above which the algorithm fails. Several models to calculate Δ²t_R,crit were developed and evaluated: (a) exact model; (b) simplified model and (c) simple-modified model. Model (c) gave the best performance and allowed to deduce an analytical expression for the probability of failure of the watershed algorithm as a function of experimental Δ²t_R, modulation time and peak width in the first and second dimensions. It could be demonstrated that the probability of failure of the watershed algorithm under normal conditions in GC × GC is around 15–20%. Small changes of Δ²t_R, modulation time and/or peak width in the first and second dimension could induce subtle changes in the probability of failure of the watershed algorithm. Theoretical equations were verified with experimental results from a diesel sample injected in GC × GC and were found to be in good agreement with the experiments.     

Effects of pressure drop on absolute retention matching in comprehensive two-dimensional gas chromatography

Comprehensive two-dimensional gas chromatography (GC x GC) analysis has the capability to resolve many more components of complex mixtures than traditional single column GC analysis. There is an increasing need to provide reliable identification of these separated components; time-of-flight mass spectrometry (TOFMS) is the most appropriate technology to achieve this task. Rather than require MS for all GC x GC separations, it is desirable to assign peak identities to specific peak positions in the GC x GC separation space, and this necessitates matching peak retentions in the two experiments - GC x GC-FID and GC x GC-TOFMS. The atmospheric vs. vacuum outlet conditions confound this task. It is shown here that by employing a supplementary gas supply, provided to a T-union between the column outlet and the MS interface, it is possible to generate 2D chromatograms for GC x GC-FID and GC x GC-TOFMS that are essentially exactly matched. There is no degradation in separation performance or efficiency in the second column in the system interfaced to the T-union. Since the GC x GC-FID experiment uses hydrogen for maximum efficiency, and GC x GC-TOFMS uses helium carrier, translation of (conditions/retentions) must account for the different viscosities of the carrier gases. Translation of conditions is based on well-known principles established in single column analysis. Tabulated data illustrate that retention reproducibility was of the order of better than 4 s for the average first dimension retention difference, and about 40 ms for the average second dimension retention difference when comparing GC x GC-FID and GC x GC-TOFMS results. This should provide considerable support for identification in routine GC x GC-FID analysis of specific sample types, once the peaks in 2D separation space have been assigned identities through GC x GC-TOFMS analysis.     

Prediction of peak shape as a function of retention in reversed-phase liquid chromatography

Optimisation of the resolution of multicomponent samples in HPLC is usually carried out by changing the elution conditions and considering the variation in retention of the analytes, to which a standard peak shape is assigned. However, the change in peak shape with the composition of the mobile phase can ruin the optimisation process, yielding unexpected overlaps in the experimental chromatograms for the predicted optimum, especially for complex mixtures. The possibility of modelling peak shape, in addition to peak position, is therefore attractive. A simple modified-Gaussian model with a parabolic variance, which is a function of conventional experimental parameters: retention time (tR), peak height (H0), standard deviation at the peak maximum (sigma0), and left (A) and right (B) halfwidths, is proposed. The model is a simplification of a previous equation proposed in our laboratory. Linear and parabolic relationships were found between the peak shape parameters (sigma0), A and B) and tR, with a mean relative error of 1-5% in most cases. This error was partially due to variations in peak position and shape among injections, which in some cases were above 2%. Correlations between (sigma0, A and B) and the retention time, which is easily modelled as a function of mobile phase composition, allowed a simple and reliable prediction of chromatographic peaks. A parameter that depends on the slopes of the linear relationships for A and B versus tR is also proposed to evaluate column efficiency. The modified-Gaussian model was used to describe the peaks of six diuretics of diverse acid-base behaviour and polarity, which were eluted with 15 mobile phases where the composition was varied between 30 and 50% (v/v) acetonitrile and the pH between 3 and 7.