Detailed analysis of the effective and intra-particle diffusion coefficient of proteins at elevated pressure in columns packed with wide-pore core-shell particles.

To determine the efficiency that can be obtained in a packed-bed liquid-chromatography column for a particular analyte, a correct determination of the molecular and effective diffusion coefficients (Dm and Deff) of the analyte is required. The latter is usually obtained via peak parking experiments wherein the flow is stopped. As a result, the column pressure rapidly dissipates and the measurement is essentially conducted at ambient pressure. This is problematic for analytes whose retention depends on pressure, such as proteins and potentially other large (dipolar) molecules. In that case, a conventional peak parking experiment is expected to lead to large errors in Deff. To obtain a better estimate ofDeff, the present study reports on the use of a set-up enabling peak parking measurements under pressurized conditions. This approach allowed us to report, for the first time, Deff for proteins at elevated pressure under retained conditions. First, Deff was determined at a (average) pressure of about 105 bar for a set of proteins with varying size, namely: bradykinin, insulin, lysozyme, ß-lactoglobulin, and carbonic anhydrase in a column packed with 400 Å core-shell particles. The obtained data were then compared to those of several small analytes: acetophenone, propiophenone, benzophenone, valerophenone, and hexanophenone. A clear trend between Deff and analyte size was observed. The set-up was then used to determine Deff of bradykinin and lysozyme at variable (average) pressures ranging from 28 bar to 430 bar. These experiments showed a decrease in intra-particle and surface diffusion with pressure, which was larger for lysozyme than bradykinin. The data show that pressurized peak parking experiments are vital to correctly determine Deff when the analyte retention varies significantly with pressure.

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.

Chemometric Strategies for Fully Automated Interpretive Method Development in Liquid Chromatography.

The majority of liquid chromatography (LC) methods are still developed in a conventional manner, that is, by analysts who rely on their knowledge and experience to make method development decisions. In this work, a novel, open-source algorithm was developed for automated and interpretive method development of LC(-mass spectrometry) separations ("AutoLC"). A closed-loop workflow was constructed that interacted directly with the LC system and ran unsupervised in an automated fashion. To achieve this, several challenges related to peak tracking, retention modeling, the automated design of candidate gradient profiles, and the simulation of chromatograms were investigated. The algorithm was tested using two newly designed method development strategies. The first utilized retention modeling, whereas the second used a Bayesian-optimization machine learning approach. In both cases, the algorithm could arrive within 4-10 iterations (i.e., sets of method parameters) at an optimum of the objective function, which included resolution and analysis time as measures of performance. Retention modeling was found to be more efficient while depending on peak tracking, whereas Bayesian optimization was more flexible but limited in scalability. We have deliberately designed the algorithm to be modular to facilitate compatibility with previous and future work (e.g., previously published data handling algorithms).

Recycling gradient-elution liquid chromatography for the analysis of chemical-composition distributions of polymers.

Synthetic polymers typically show dispersity in molecular weight and potentially in chemical composition. For the analysis of the chemical-composition distribution (CCD) gradient liquid chromatography may be used. The CCD obtained using this method is often convoluted with an underlying molecular-weight distribution (MWD). In this paper we demonstrate that the influence of the MWD can be reduced using very steep gradients and that such gradients are best realized utilizing recycling gradient liquid chromatography (LC↻LC). This method allows for a more-accurate determination of the CCD and the assessment of (approximate) critical conditions (if these exist), even when high-molecular-weight standards of narrow dispersity are not readily available. The performance and usefulness of the approach is demonstrated for several polystyrene standards, and for the separation of statistical copolymers consisting of styrene/methyl methacrylate and methyl methacrylate/butyl methacrylate. For the latter case, approximate critical compositions of the copolymers were calculated from the critical compositions of two homopolymers and one copolymer of known chemical composition, allowing for a determination of the CCD of unknown samples. Using this approach it is shown that the copolymers elute significantly closer to the predicted critical compositions after recycling of the gradient. This is most clear for the lowest-molecular-weight copolymer (Mw = 4.2 kDa), for which the difference between measured and predicted elution composition decreases from 7.9% without recycling to 1.4% after recycling.

Critical comparison of background correction algorithms used in chromatography.

The objective of the present work was to make a quantitative and critical comparison of a number of drift and noise-removal algorithms, which were proven useful by other researchers, but which had never been compared on an equal basis. To make a rigorous and fair comparison, a data generation tool is developed in this work, which utilizes a library of experimental backgrounds, as well as peak shapes obtained from curve fitting on experimental data. Several different distribution functions are used, such as the log-normal, bi-Gaussian, exponentially convoluted Gaussian, exponentially modified Gaussian and modified Pearson VII distributions. The tool was used to create a set of hybrid (part experimental, part simulated) data, in which the background and all peak profiles and areas are known. This large data set (500 chromatograms) was analysed using seven different drift-correction and five different noise-removal algorithms (35 combinations). Root-mean square errors and absolute errors in peak area were determined and it was shown that in most cases the combination of sparsity-assisted signal smoothing and asymmetrically reweighted penalized least-squares resulted in the smallest errors for relatively low-noise signals. However, for noisier signals the combination of sparsity-assisted signal smoothing and a local minimum value approach to background correction resulted in lower absolute errors in peak area. The performance of correction algorithms was studied as a function of the density and coverage of peaks in the chromatogram, shape of the background signal, and noise levels. The developed data-generation tool is published along with this article, so as to allow similar studies with other simulated data sets and possibly other algorithms. The rigorous assessment of correction algorithms in this work may facilitate further automation of data-analysis workflows.

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.

Reducing the influence of geometry-induced gradient deformation in liquid chromatographic retention modelling.

Rapid optimization of gradient liquid chromatographic (LC) separations often utilizes analyte retention modelling to predict retention times as function of eluent composition. However, due to the dwell volume and technical imperfections, the actual gradient may deviate from the set gradient in a fashion unique to the employed instrument. This makes accurate retention modelling for gradient LC challenging, in particular when very fast separations are pursued. Although gradient deformation has been addressed in method-transfer situations, it is rarely taken into account when reporting analyte retention parameters obtained from gradient LC data, hampering the comparison of data from various sources. In this study, a response-function-based algorithm was developed to determine analyte retention parameters corrected for geometry-induced deformations by specific LC instruments. Out of a number of mathematical distributions investigated as response-functions, the so-called "stable function" was found to describe the formed gradient most accurately. The four parameters describing the model resemble the statistical moments of the distribution and are related to chromatographic parameters, such as dwell volume and flow rate. The instrument-specific response function can then be used to predict the actual shape of any other gradient programmed on that instrument. To incorporate the predicted gradient in the retention modelling of the analytes, the model was extended to facilitate an unlimited number of linear gradient steps to solve the equations numerically. The significance and impact of distinct gradient deformation for fast gradients was demonstrated using three different LC instruments. As a proof of principle, the algorithm and retention parameters obtained on a specific instrument were used to predict the retention times on different instruments. The relative error in the predicted retention times went down from an average of 9.8% and 12.2% on the two other instruments when using only a dwell-volume correction to 2.1% and 6.5%, respectively, when using the proposed algorithm. The corrected retention parameters are less dependent on geometry-induced instrument effects.

Recent applications of chemometrics in one- and two-dimensional chromatography.

The proliferation of increasingly more sophisticated analytical separation systems, often incorporating increasingly more powerful detection techniques, such as high-resolution mass spectrometry, causes an urgent need for highly efficient data-analysis and optimization strategies. This is especially true for comprehensive two-dimensional chromatography applied to the separation of very complex samples. In this contribution, the requirement for chemometric tools is explained and the latest developments in approaches for (pre-)processing and analyzing data arising from one- and two-dimensional chromatography systems are reviewed. The final part of this review focuses on the application of chemometrics for method development and optimization.