Distribution-centric 3-parameter thermodynamic models of partition gas chromatography

Relation between characteristic temperature and elution temperature in temperature programmed gas chromatography - Part II: Influence of column properties

The method development process in gas chromatography can be accelerated by suitable computer simulation tools using knowledge about the solute-column interactions described by thermodynamic retention parameters. Since retention parameters usually are determined under isothermal conditions, the presented work offers a step to estimate one of the most important retention parameters, the characteristic temperature Tchar by less laborious temperature programmed measurements. In the first part an empirical multivariate model was introduced describing the correlation between the elution temperature Telu of a solute and its characteristic temperature Tchar. Now in the second part a simulation model of GC and available retention data from a retention database was used to investigate the correlation between Telu and Tchar for an expanded range of heating rates and initial temperatures. In addition to part I, the simulation is used to investigate the influences of different properties of the separation column such as different phase ratios and column geometries like length and diameter or various stationary phases including SLB-5 ms, SPB-50, Stabilwax, Rtx-Dioxin2, Rxi-17Sil MS, Rxi-5Sil MS, ZB-PAH-CT, DB-5 ms, Rxi-5 ms, Rtx5 and FS5ms. The fit model is valid for all investigated stationary phases. The influence of the phase ratio to the correlation could be determined. Therefore, the model was expanded to this parameter. The expanded range of heating rates and the normalization for the system independent dimensionless heating rate required a further modification of the previously presented correlation model. The model now fits also under isothermal conditions. The results were used for estimation of the Tchar of an analyte from the elution temperature in the temperature program. The prediction performance was investigated and evaluated for 20 different temperature program conditions and at two phase ratios (β=125 and β=250). Under best conditions the estimated and the measured Tchar values show relative differences <0.5 %. With this novel model estimations for Tchar are possible at 20 °C above the initial temperature, which expands the prediction range even for low and medium retained analytes compared to earlier approaches.

Simulation of gas chromatographic separations and estimation of distribution-centric retention parameters using linear solvation energy relationships

For method development in gas chromatography, suitable computer simulations can be very helpful during the optimization process. For such computer simulations retention parameters are needed, that describe the interaction of the analytes with the stationary phase during the separation process. There are different approaches to describe such an interaction, e.g. thermodynamic models like Blumberg's distribution-centric 3-parameter model (K-centric model) or models using chemical properties like the Linear Solvation Energy Relationships (LSER). In this work LSER models for a Rxi-17Sil MS and a Rxi-5Sil MS GC column are developed for different temperatures. The influences of the temperature to the LSER system coefficients are shown in a range between 40 and 200 °C and can be described with Clark and Glew's ABC model as fit function. A thermodynamic interpretation of the system constants is given and its contribution to enthalpy and entropy is calculated. An estimation method for the retention parameters of the K-centric model via LSER models were presented. The predicted retention parameters for a selection of 172 various compounds, such as FAMEs, PCBs and PAHs are compared to isothermal determined values. 40 measurements of temperature programmed GC separations are compared to computer simulations using the differently determined or estimated K-centric retention parameters. The mean difference (RSME) between the measured and predicted retention time is less than 8 s for both stationary phases using the isothermal retention parameters. With the LSER predicted parameters the difference is 20 s for the Rxi-5Sil MS and 38 s for the Rxi-17Sil MS. Therefore, the presented estimation method can be recommended for first method development in gas chromatography.

Theoretical modeling and machine learning-based data processing workflows in comprehensive two-dimensional gas chromatography-A review

In recent years, comprehensive two-dimensional gas chromatography (GC × GC) has been gradually gaining prominence as a preferred method for the analysis of complex samples due to its higher peak capacity and resolution power compared to conventional gas chromatography (GC). Nonetheless, to fully benefit from the capabilities of GC × GC, a holistic approach to method development and data processing is essential for a successful and informative analysis. Method development enables the fine-tuning of the chromatographic separation, resulting in high-quality data. While generating such data is pivotal, it does not necessarily guarantee that meaningful information will be extracted from it. To this end, the first part of this manuscript reviews the importance of theoretical modeling in achieving good optimization of the separation conditions, ultimately improving the quality of the chromatographic separation. Multiple theoretical modeling approaches are discussed, with a special focus on thermodynamic-based modeling. The second part of this review highlights the importance of establishing robust data processing workflows, with a special emphasis on the use of advanced data processing tools such as, Machine Learning (ML) algorithms. Three widely used ML algorithms are discussed: Random Forest (RF), Support Vector Machine (SVM), and Partial Least Square-Discriminate Analysis (PLS-DA), highlighting their role in discovery-based analysis.

Relation between characteristic temperature and elution temperature in temperature programmed gas chromatography - part I: Influence of initial temperature and heating rate

The development of new analytical methods can save resources, time and costs if there are prediction tools like computer simulation which support the optimization process. In GC the distribution-centric 3-parameter model (K-centric model) is well established for prediction of retention factors k and retention times but laborious isothermal measurements for determination of the characteristic parameters are needed. For the most important parameter, the characteristic temperature Tchar, the search for simpler determination methods or even estimates is an interesting research topic. In this work the elution temperatures for 37 fatty acid methyl esters, 6 BTEXs and 40 other volatile substances are determined by measurements under variable heating rates, initial temperatures, constant pressure mode and constant flow mode. The relationship between the measured elution temperature and the characteristic temperature was investigated. The novel multivariate curve fit model presented in this study describes accurately the relation between the characteristic temperature Tchar and elution temperatures Telu under variable heating rates RT, respectively, and initial temperature Tinit conditions. The novel model shows good accordance to earlier estimation models and expands the prediction range, especially for high volatile compounds. The model is suitable for determination of Tchar by estimated Telu and vice versa. Predictions of retention times of simple temperature programs were also possible by using the model with relative deviations < 5% compared to measurements.

Retention Database for Prediction, Simulation, and Optimization of GC Separations

This work presents an open source database with suitable retention parameters for prediction and simulation of GC separations and gives a short introduction to three common retention models. Useful computer simulations play an important role to save resources and time in method development in GC. Thermodynamic retention parameters for the ABC model and the K-centric model are determined by isothermal measurements. This standardized procedure of measurements and calculations, presented in this work, have a useful benefit for all chromatographers, analytical chemists, and method developers because it can be used in their own laboratories to simplify the method development. The main benefits as simulations of temperature-programed GC separations are demonstrated and compared to measurements. The observed deviations of predicted retention times are in most cases less than 1%. The database includes more than 900 entries with a large range of compounds such as VOCs, PAHs, FAMEs, PCBs, or allergenic fragrances over 20 different GC columns.

Estimation of retention parameters from temperature programmed gas chromatography

A fast and reliable method is presented to evaluate retention parameters of the distribution-centric 3-parameter model from temperature programed gas chromatographic measurements. Based on a fully differentiable model of the migration of solutes in a gas chromatographic (GC) system, Newton's method with a trust region is used to determine the three parameters, respectively the three parameters and the column diameter, of several solutes as the minima of the difference between measured and calculated retention times. The determined retention parameters can then be used in method development, using the simulation of GC separation. The results of the retention parameters are compared to the parameters determined using isothermal GC measurements and show good agreement, with deviations of less than 0.5% (1.8 K) for the most important parameter of characteristic temperature T_char. Using the estimated retention parameters, additional GC separations are simulated and compared with measurements. Retention times in additional temperature programmed measurements could be predicted with less than 0.7% deviation. Four to five different temperature programs are enough to determine reliable retention parameters. Unless the column diameter and the column length are exactly known, it is preferable to also estimate the diameter (more precisely the L/d-ratio) together with the retention parameters.

Top-Down Approach to Retention Time Prediction in Comprehensive Two-Dimensional Gas Chromatography-Mass Spectrometry

In this contribution, we describe a novel modeling approach to predicting retention times (t_r) in comprehensive two-dimensional gas chromatography coupled to time-of-flight mass spectrometry (GC × GC-ToF-MS) with a particular emphasis on the second-dimension (²D) retention time predictions (²t_r). This approach is referred to as a "top-down" approach in that it breaks down the complete GC × GC separation into two independent one-dimensional gas chromatography separations (1D-GC). In this regard, both dimensions, that is, first dimension (¹D) and second dimension (²D) are treated separately, and the cryogenic modulator is simply considered as a second consecutive injection device. Separate 1D-GC t_r predictions are performed on both dimensions using the same flow rate as the one deployed in the conventional GC × GC system. The separate t_r predictions are then combined to account for the two-dimensional separation. This model was applied to 24 analytes from 2 standard mixtures (Grob Test Mix and Fragrance Materials Test Mix) and assessed across 9 GC × GC chromatographic conditions. The experimental and predicted chromatographic retention space occupations were assessed by using the convex hull approach defined by the Delaunay triangulation. The predicted percentage of space occupation corresponded favorably with the experimental values. Furthermore, the top-down approach enabled an accurate prediction of the ²t_r of all investigated analytes, providing an average ²t_r modeling error of 0.26 ± 0.01 s.

Optimal heating rate in constant pressure and constant flow gas chromatography

Optimal heating rate is the one resulting in the shortest analysis time for achieving a required separation performance of a column. The previously recommended default heating rate (R_T,Def ) was optimal for temperature-programmed gas chromatography analyses in constant pressure mode. It has been shown herein that the same recommendation can be extended to constant flow mode with fixed heating rate (R_T ). The numerical value of R_T,Def has been herein rescaled from previous 10 ∘ C / t M (10°C per void time) where t_M was measured at 50°C, to 12 ∘ C / t M with t_M measured at 150°C-a round number in the middle of the gas chromatography temperature range, chosen as a reference temperature for numerical values of all temperature-dependent gas chromatography parameters. It has been experimentally found based on theory developed herein that R T , Def = 12 ∘ C / t M is optimal for columns with φ = 0.001 ( φ = d f / d is dimensionless film thickness, d and d_f  are the column internal diameter and film thickness, respectively) in constant pressure mode and constant flow mode with fixed R_T . Theory shows that, for arbitrary φ, R T , Def = 12 ( 1000 φ ) 0.09 ∘ C / t M . The theory also shows that the fixed R_T is optimal for constant pressure mode. In constant flow mode, however, the optimal R_T should gradually increase with increasing temperature (T). The optimal theoretical curves R_T (T), different for different flow rates, were found. However, only the optimization of the fixed R_T was experimentally evaluated due to limited capability of existing gas chromatography instrumentation and resources. It has been shown that the separation-time tradeoff in constant pressure mode is slightly better than that in constant flow mode. The experimental data are compiled in the Supporting information.

Modeling approaches for temperature-programmed gas chromatographic retention times under vacuum outlet conditions

This contribution evaluates the performance of two predictive approaches in calculating temperature-programmed gas chromatographic retention times under vacuum outlet conditions. In the first approach, the predictions are performed according to a thermodynamic-based model, while in the second approach the predictions are conducted by using the temperature-programmed retention time equation. These modeling approaches were evaluated on 47 test compounds belonging to different chemical classes, under different experimental conditions, namely, two modes of gas flow regulation (i.e., constant inlet pressure and constant flow rate), and different temperature programs (i.e., 7 °C/min, 5 °C/min, and 3 °C/min). Both modeling approaches gave satisfactory results and were able to accurately predict the elution profiles of the studied test compounds. The thermodynamic-based model provided more satisfying results under constant flow rate mode, with average modeling errors of 0.43%, 0.33%, and 0.15% across all the studied temperature programs. Nevertheless, under constant inlet pressure mode, lower modeling errors were achieved when using the temperature-programmed retention time equation, with average modeling errors of 0.18%, 0.18%, and 0.31% across the used temperature programs.

Simulation of the effects of negative thermal gradients on separation performance of gas chromatography

The effect of a gradient of solute velocity on the chromatographic separation of closely spaced solutes is investigated by usage of a simulation. The concept of the ideal basic separation (IBS), introduced by Blumberg, is used to determine the theoretical limit of a separation without any natural or artificial gradients of features of the chromatographic medium. The IBS is the best achievable separation and can therefore be used as a baseline to which other separations can be compared to. An addition of a negative velocity gradient cannot improve the separation of closely spaced solutes. The velocity gradient is realized by adding a temperature gradient to a GC separation. The simulation confirms this theoretical limit for a range of differently strong retained solutes. In a second part controlled deviations from IBS are used to show, that a velocity gradient can be beneficial in realistic, non-IBS. The addition of a negative velocity gradient can improve e.g. the separation of broad injected solute zones or counteract a positive gradient of the mobile phase velocity caused by gas decompression along the GC column. However, the improved separation cannot exceed that of a corresponding ideal basic separation. The resolution of broadly injected solutes can be increased by up to 45% of the corresponding IBS resolution by adding a negative velocity gradient. A positive velocity gradient due to gas decompression reduces the separation by up to 6%. The added negative velocity gradient, realized by a linear temperature gradient, can compensate this resolution loss by up to 2%.

Retention time prediction of hydrocarbons in cryogenically modulated comprehensive two-dimensional gas chromatography: A method development and translation application

Thermodynamic modeling of GC × GC separations provides a tool for rapid method evaluation and optimization. Separations of 95 hydrocarbons on two cryogenically modulated GC × GC systems (atmospheric outlet and vacuum outlet) are modeled, displaying average second dimension retention time modeling absolute errors of 0.17 s and 0.12 s respectively, and generating modeled chromatograms which sufficiently represent experimental data. A web-based GC × GC modeling routine is presented which allows users to model separations, currently focused on hydrocarbons, with full control over all system parameters. The method translation capabilities of the application are further demonstrated by replicating Piotrowski et al.'s GC × GC-HRT temporal distribution plots of hydraulic fracturing flowback fluid hydrocarbons [28].

Thermodynamics-based modelling of gas chromatography separations across column geometries and systems, including the prediction of peak widths

Thermodynamics-based models have been demonstrated to be useful for predicting retention time and peak widths in gas chromatography and two-dimensional gas chromatography separations. However, the collection of data to train the models can be time consuming, which lessens the practical utility of the method. In this contribution, a method for obtaining thermodynamic-based data to predict peak widths in temperature-programmed gas chromatography is presented. Experimental work to collect data for peak width prediction is identical to that required to collect data for retention time prediction using approaches that we have presented previously. Using this combined approach, chromatograms including retention times and peak widths are predicted with very high accuracy. Typical errors in retention time are < 0.5%, while errors in peak width are typically < 5% as demonstrated using polycycic aromatic hydrocarbons and a mixture containing compounds with aldehyde, ketone, alkene, alkane, alcohol, and ester functionalities.

Migration and elution equations in gradient liquid chromatography

What is known in the literature as the fundamental equation for gradient elution (FEGE) was previously proven only for conventional gradient LC - uniform (the same at any distance from the inlet) static (fixed in time) solvent velocity (u_m) in a column of uniform and static internal structure, cross-section and thermodynamic properties. A published alternative to the FEGE - the general migration equation - is valid for any column-based linear chromatography (GC, LC, SFC etc.). It allows one to theoretically or numerically predict a solute migration time to any location along the column. Starting from that general equation, several migration equations in gradient LC under different operational conditions including non-uniform non-static u_m, Neue-Kuss retention model and others have been developed in this report. It has been shown that the conditions of validity of the FEGE can be expanded to include non-uniform u_m. On the other hand, the FEGE is not valid for other unconventional operations of LC including gradient LC with dynamic (changing in time) u_m. This implies that FEGE cannot be applied to, e.g., gradient LC operating at constant pressure where, due to the change in solvent composition, the solvent viscosity changes causing the change in u_m with time. Applications of newly developed equations to other unconventional operations of gradient LC were also considered. Several new time parameters of the mobile phase flow were identified, interpreted, and evaluated.