Application of the reversed-phase liquid chromatographic model to describe the retention behaviour of polydisperse macromolecules in gradient and isocratic liquid chromatography

Capacitively coupled contactless conductivity detection to account for system-induced gradient deformation in liquid chromatography

The time required for method development in gradient-elution liquid chromatography (LC) may be reduced by using an empirical modelling approach to describe and predict analyte retention and peak width. However, prediction accuracy is impaired by system-induced gradient deformation, which can be especially prominent for steep gradients. As the deformation is unique to each LC instrument, it needs to be corrected for if retention modelling for optimization and method transfer is to become generally applicable. Such a correction requires knowledge of the actual gradient profile. The latter has been measured using capacitively coupled "contactless" conductivity detection (C⁴D), featuring a low detection volume (approximately 0.05 μL) and compatibility with very high pressures (80 MPa or more). Several different solvent gradients, from water to acetonitrile, water to methanol, and acetonitrile to tetrahydrofuran, could be measured directly without the addition of a tracer component to the mobile phase, exemplifying the universal nature of the approach. Gradient profiles were found to be unique for each solvent combination, flowrate, and gradient duration. The profiles could be described by convoluting the programmed gradient with a weighted sum of two distribution functions. Knowledge of the exact profiles was used to improve the inter-system transferability of retention models for toluene, anthracene, phenol, emodin, sudan-I and several polystyrene standards.

Principles and potential of solvent gradient size-exclusion chromatography for polymer analysis

The properties of a polymeric material are influenced by its underlying molecular distributions, including the molecular-weight (MWD), chemical-composition (CCD), and/or block-length (BLD) distributions. Gradient-elution liquid chromatography (LC) is commonly used to determine the CCD. Due to the limited solubility of polymers, samples are often dissolved in strong solvents. Upon injection of the sample, such solvents may lead to broadened or poorly shaped peaks and, in unfavourable cases, to "breakthrough" phenomena, where a part of the sample travels through the column unretained. To remedy this, a technique called size-exclusion-chromatography gradients or gradient size-exclusion chromatography (gSEC) was developed in 2011. In this work, we aim to further explore the potential of gSEC for the analysis of the CCD, also in comparison with conventional gradient-elution reversed-phase LC, which in this work corresponded to gradient-elution reversed-phase liquid chromatography (RPLC). The influence of the mobile-phase composition, the pore size of the stationary-phase particles, and the column temperature were investigated. The separation of five styrene/ethyl acrylate copolymers was studied with one-dimensional RPLC and gSEC. RPLC was shown to lead to a more-accurate CCD in shorter analysis time. The separation of five styrene/methyl methacrylate copolymers was also explored using comprehensive two-dimensional (2D) LC involving gSEC, i.e. SEC × gSEC and SEC × RPLC. In 2D-LC, the use of gSEC was especially advantageous as no breakthrough could occur.

The 2023 Lifetime Achievement and Emerging Leader in Chromatography Awards

Peter Schoenmakers and Emanuela Gionfriddo are the winners of the 16th annual LCGC Lifetime Achievement and Emerging Leader in Chromatography Awards, respectively. The LCGC Awards honor the work of leading separation scientists for lifetime achievement and emerging potential. The award winners will be honored in an oral symposium at the Pittcon 2023 conference in March 2023 in Philadelphia, Pennsylvania, USA.

Thermal modulation to enhance two-dimensional liquid chromatography separations of polymers

Many materials used in a wide range of fields consist of polymers that feature great structural complexity. One particularly suitable technique for characterising these complex polymers, that often feature correlated distributions in e.g. microstructure, chemical composition, or molecular weight, is comprehensive two-dimensional liquid chromatography (LC × LC). For example, using a combination of reversed-phase LC and size-exclusion chromatography (RPLC × SEC). Efficient and sensitive LC × LC often requires focusing of the analytes between the two stages. For the analysis of large-molecule analytes, such as synthetic polymers, thermal modulation (or cold trapping) may be feasible. This approach is studied for the analysis of a styrene/butadiene "star" block copolymer. Trapping efficiency is evaluated qualitatively by monitoring the effluent of the trap with an evaporative light-scattering detector and quantitatively by determining the recovery of polystyrene standards from RPLC × SEC experiments. The recovery was dependant on the molecular weight and the temperatures of the first-dimension column and of the trap, and ranged from 46% for a molecular weight of 2.78 kDa to 86% (or up to 94.5% using an optimized set-up) for a molecular weight of 29.15 kDa, all at a first-dimension-column temperature of 80 °C and a trap temperature of 5 °C. Additionally a strategy to reduce the pressure pulse from the modulation has been developed, bringing it down from several tens of bars to only a few bar.

Transfer-volume effects in two-dimensional chromatography: adsorption-phenomena in second-dimension size-exclusion chromatography

Gradient-elution LC × LC is a valuable technique for the characterization of complex biological samples as well as for synthetic polymers. Breakthrough and viscous fingering may yield misleading information on the sample characteristics or deteriorate separation. In LC × SEC another phenomenon may jeopardize the separation. If the analytes adsorb on the SEC column under the injection-plug conditions, peak splitting may occur. In LC × LC the effluent from the first column is the sample solvent for the analytes injected into the second dimension. If a gradient-elution LC × SEC setup is used (i.e. if reversed-phase gradient-elution LC is coupled to organic SEC and if normal-phase gradient-elution LC is coupled to SEC with a polar solvent), the percentage of weak solvent may be significant, especially at short analysis times. In this case adsorption in the first-dimension-effluent zone on the second-dimension SEC column can become an issue and two peaks--the first eluting in size-exclusion mode and the second undergoing adsorption--can be obtained. The work presented in this paper documents peak splitting in LC × SEC of polymers. The adsorption of the polymer on the size-exclusion column was proven in one-dimensional isocratic runs. The observed effects were modeled and visualized through simulation. Studies on the influence of the transfer volume were carried out. Keeping the transfer volume as small as possible helped to minimize peak splitting due to adsorption.

Analytical Solutions of the Ideal Model for Gradient Liquid Chromatography

The analytical solutions of the ideal model for gradient elution that ignores the influence of the solute concentration on the retention factor (k) were studied by using the method of characteristics for solving partial differential equations. It is found for any gradient profiles and solvent strength models used that the concentration of the solute will be discontinuous where the mobile-phase composition is. On a given characteristic curve, the product of the concentration and the retention factor is kept constant at the point where the concentration is continuous. At the point where the concentration is discontinuous, the product on the left side of this point is equal to that on the right side. We also discussed the basic equations to predict the retention time in gradient elution and introduced the injection time into them. For linear solvent strength stepwise and linear gradient elution, general expressions were proposed for the prediction and they can be used as the basis to derive others for specific gradient modes such as single linear, stepwise, and ladderlike gradients. For these modes, simple expressions to account for the band compression and the concentration change during the elution were also given.

Comparison of retention models for polymers

The suitability of three different retention models to predict the retention times of poly(ethylene glycol)s (PEGs) in gradient and isocratic chromatography was investigated. The models investigated were the linear (LSSM) and the quadratic solvent strength model (QSSM). In addition, a model describing the retention behaviour of polymers was extended to account for gradient elution (PM). It was found that all models are suited to properly predict gradient retention volumes provided the extraction of the analyte specific parameters is performed from gradient experiments as well. The LSSM and QSSM on principle cannot describe retention behaviour under critical or SEC conditions. Since the PM is designed to cover all three modes of polymer chromatography, it is therefore superior to the other models. However, the determination of the analyte specific parameters, which are needed to calibrate the retention behaviour, strongly depend on the suitable selection of initial experiments. A useful strategy for a purposeful selection of these calibration experiments is proposed.

Can the theory of gradient liquid chromatography be useful in solving practical problems?

Advances in the theory of gradient liquid chromatography and their practical impacts are reviewed. Theoretical models describing retention in reversed-phase, normal-phase and ion-exchange modes are compared. Main attention is focused on practically useful models described by two- or three-parameter equations fitting the experimental data in the range of mobile phase composition utilized for sample migration during gradient elution. The applications of theory for gradient method development, optimization and transfer are addressed. The origins and possibilities for overcoming possible pitfalls are discussed, including the effects of the instrumental dwell volume, uptake of mobile phase components on the column and size of the sample molecules. Special attention is focused on gradient separations of large molecules.

Thermodynamic Prediction of Polymer Retention in Temperature-Programmed HPLC

Temperature programming has been used increasingly in liquid chromatography in recent years. In particular, temperature gradient elution has shown great potential in the analysis of complex polymers. In this study, the polymer retention behavior in temperature gradient interaction chromatography is investigated based on thermodynamic consideration of the retention factor. The polymer retention predicted by the model calculation is in good agreement with the experimental results, and the model allows devising a temperature program for designed retention behaviors such as a linear dependence of retention volume on log(molecular weight) of polymers. In addition, the migration behavior of polymeric solute along the separation column can be simulated, which shows strong molecular weight dependence. The migration behavior is also confirmed experimentally by employing different length columns or delayed injection.

Molar mass distributions by gradient liquid chromatography: predicting and tailoring selectivity

Interactive liquid chromatography (iLC) for polymer analysis is usually applied to the characterisation of distributions other than molar mass. In particular, its use for the determination of chemical-composition, functionality-type and tacticity distributions has been demonstrated. The application of iLC for the determination of molar mass distributions (MMDs), however, has not yet been fully explored. An expanded version of the reversed-phase liquid chromatography model has been developed to describe and predict how the retention behaviour of polydisperse polystyrene samples changes with molar mass. The relationship between molar mass and the parameters of the model has been investigated in some detail and non-linear correlations were found. From the model and the relationships between the model parameters and molar mass, calibration curves (retention time versus molar mass) were constructed to predict changes in chromatographic selectivity across a given molar mass range. These calibration curves were compared to experimentally obtained curves and, in most cases, excellent agreement was found. The dramatic enhancement in selectivity that can be obtained with iLC in comparison to size-exclusion chromatography (SEC) was illustrated by measuring matrix-assisted laser desorption ionisation (MALDI) MS spectra of fractions collected during a gradient-LC separation. In the low-molar mass range, essentially monodisperse fractions were obtained. Calibration curves, predicted by the model and validated experimentally using narrow-dispersity standards and MALDI-MS spectra of fractions, were used to determine the molar mass distribution of some narrowly distributed polystyrene samples. Molar mass distributions for such standards were found to be somewhat lower than the values reported by the manufacturers. The results also deviated from those obtained by MALDI-MS.

Band broadening in size-exclusion chromatography of polydisperse samples

Understanding and controlling the band broadening is essential to obtain accurate molar-mass distributions by size-exclusion chromatography (SEC). In this paper, band broadening in SEC is reviewed from a contemporary perspective. The observed band broadening is due to dispersion inside and outside the chromatographic column (undesirable band broadening) and to the polydispersity of the sample (desirable SEC selectivity). The various contributors to band broadening are discussed. Integrity plots are introduced as a tool to evaluate the performance of specific SEC columns at given experimental conditions. For narrow polymer standards on single SEC columns the observed peak width is dominated by the chromatographic dispersion. MALDI-ToF-MS is demonstrated as an alternative to determine the PDI of narrowly distributed samples. The plate heights encountered at very high reduced velocities are found to be lower than expected. This is advantageous for fast separations by SEC.

Accurate prediction of the retention behaviour of polydisperse macromolecules based on a minimum number of experiments

This study illustrates how retention models can be used to accurately predict the retention behaviour of polydisperse macromolecules in LC separations. It highlights that the number of experiments required can be drastically reduced when the relationship between the model parameters and molecular structure parameters (e.g. molar mass) can be incorporated into one global model. A practical implication of this work is that an appropriate model can then be used for the determination of molar-mass distributions for polydisperse samples. The globalised model can predict retention time as a function of molar mass and gradient slope. Both the original and globalised versions of the model were rigorously validated in terms of the difference between the predicted and experimental retention times. The original model had very low residuals and there was no apparent dependence of the errors on the applied gradient, the molar mass or the retention times. Confidence intervals for the model parameters (S and ln k0) were determined using a bootstrapping analysis of the residual errors in the predicted retention times. Confidence intervals were seen to broaden significantly as the mass of the polymer increased. The parameters were also seen to be highly correlated. For the global model, retention-time residuals remained quite low, even when the number of experiments used to determine the model parameters was reduced from approximately 100 to 10.

Adsorption thin-layer chromatography and viscometry of polystyrenes in solvent mixtures

The effect of the thermodynamic quality of solvent mixtures on the adsorption behavior of macromolecules under dynamic conditions was investigated. The chromatographic behavior of polystyrenes (PSs) in various mixed eluents was studied under conditions of adsorption and size-exclusion thin-layer chromatography as well as at the exclusion-adsorption transition point with silica gel KSKG adsorbent. The thermodynamic quality of the solvent mixtures used in the chromatographic experiments was determined viscometrically. The dependences of the intrinsic viscosity of PSs on solvent composition for solvent-non-solvent, two solvents, and theta-solvent-solvent mixtures were obtained. A correlation was found between Snyder's polarity indices for the solvent mixtures used in polymer chromatography under "critical conditions" and the intrinsic viscosity values of PSs in the same mixtures.

Comprehensive two-dimensional liquid chromatography of polymers

The need for and the emergence of comprehensive two-dimensional liquid chromatographic separations of synthetic polymers are reviewed in this paper. LC x SEC is shown to be a particularly valuable two-dimensional technique in this domain. An improved (symmetrical) configuration based on a single 10-way switching valve is described. The use of LC x SEC to understand and optimize one-dimensional separations is illustrated, as well as the potential of the technique for the separation and characterization of functional polymers and copolymers.