Mismatch between sample diluent and eluent: Maintaining integrity of gradient peaks using in silico approaches

Predicting sample injection profiles in liquid chromatography: A modelling approach based on residence time distributions

The pharmaceutical and bio-pharmaceutical industries rely on simulations of liquid chromatographic processes for method development and to reduce experimental cost. The use of incorrect injection profiles as inlet boundary condition for these simulations may, however, lead to inaccurate results. This study presents a novel modelling approach for accurate prediction of injection profiles for liquid chromatographic columns. The model uses the residence time distribution theory and accounts for the residence time of the sample through the injection loop, connecting tubes and heat exchangers that exist upstream of the actual chromatographic column, between the injection point and the column inlet. To validate the model, we compare simulation results with experimental injection profiles taken from the literature for 20 operating conditions. The average errors in the predictions of the mean and variance of the injection profiles result to be 8.98% and 8.52%, respectively. The model, which is based on fundamental equations and actual hardware details, accurately predicts the injection profile for a range of sample volumes and sample loop-filling levels without the need of calibration. The proposed modelling approach can help to improve the quality of in-silico simulation and optimization for analytical chromatography.

Characterization of a high throughput approach for large scale retention measurement in liquid chromatography

Many contemporary challenges in liquid chromatography-such as the need for "smarter" method development tools, and deeper understanding of chromatographic phenomena-could be addressed more efficiently and effectively with larger volumes of experimental retention data than are available. The paucity of publicly accessible, high-quality measurements needed for the development of retention models and simulation tools has largely been due to the high cost in time and resources associated with traditional retention measurement approaches. Recently we described an approach to improve the throughput of such measurements by using very short columns (typically 5 mm), while maintaining measurement accuracy. In this paper we present a perspective on the characteristics of a dataset containing about 13,000 retention measurements obtained using this approach, and describe a different sample introduction method that is better suited to this application than the approach we used in prior work. The dataset comprises results for 35 different small molecules, nine different stationary phases, and several mobile phase compositions for each analyte/phase combination. During the acquisition of these data, we have interspersed repeated measurements of a small number of compounds for quality control purposes. The data from these measurements not only enable detection of outliers but also assessment of the repeatability and reproducibility of retention measurements over time. For retention factors greater than 1, the mean relative standard deviation (RSD) of replicate (typically n=5) measurements is 0.4%, and the standard deviation of RSDs is 0.4%. Most differences between selectivity values measured six months apart for 15 non-ionogenic compounds were in the range of +/- 1%, indicating good reproducibility. A critically important observation from these analyses is that selectivity defined as retention of a given analyte relative to the retention of a reference compound (kx/kref) is a much more consistent measure of retention over a time span of months compared to the retention factor alone. While this work and dataset also highlight the importance of stationary phase stability over time for achieving reliable retention measurements, we are nevertheless optimistic that this approach will enable the compilation of large databases (>> 10,000 measurements) of retention values over long time periods (years), which can in turn be leveraged to address some of the most important contemporary challenges in liquid chromatography. All the data discussed in the manuscript are provided as Supplemental Information.

An approach to high throughput measurement of accurate retention data in liquid chromatography

Efforts to model and simulate various aspects of liquid chromatography (LC) separations (e.g., retention, selectivity, peak capacity, injection breakthrough) depend on experimental retention measurements to use as the basis for the models and simulations. Often these modeling and simulation efforts are limited by datasets that are too small because of the cost (time and money) associated with making the measurements. Other groups have demonstrated improvements in throughput of LC separations by focusing on "overhead" associated with the instrument itself - for example, between-analysis software processing time, and autosampler motions. In this paper we explore the possibility of using columns with small volumes (i.e., 5 mm x 2.1 mm i.d.) compared to conventional columns (e.g., 100 mm x 2.1 mm i.d.) that are typically used for retention measurements. We find that isocratic retention factors calculated for columns with these dimensions are different by about 20%; we attribute this difference - which we interpret as an error in measurements based on data from the 5 mm column - to extra-column volume associated with inlet and outlet frits. Since retention factor is a thermodynamic property of the mobile/stationary phase system under study, it should be independent of the dimensions of the column that is used for the measurement. We propose using ratios of retention factors (i.e., selectivities) to translate retention measurements between columns of different dimensions, so that measurements made using small columns can be used to make predictions for separations that involve conventional columns. We find that this approach reduces the difference in retention factors (5 mm compared to 100 mm columns) from an average of 18% to an average absolute difference of 1.7% (all errors less than 8%). This approach will significantly increase the rate at which high quality retention data can be collected to thousands of measurements per instrument per day, which in turn will likely have a profound impact on the quality of models and simulations that can be developed for many aspects of LC separations.

Accuracy of retention model parameters obtained from retention data in liquid chromatography

In liquid chromatography (LC), it is often very useful to have an accurate model of the retention factor, k, over a wide range of isocratic elution conditions. In principle, the parameters of a retention model can be obtained by fitting either isocratic or gradient retention factor data. However, in spite of many of our own attempts to accurately predict isocratic k values using retention models trained with gradient retention data, this has not worked in our hands. In the present study we have used synthetic isocratic and gradient retention data for small molecules under reversed-phase LC conditions. This allows us to discover challenges associated with predicting isocratic k's without the confounding influences of experimental issues that are difficult to model or eliminate. The results indicate that it is not currently possible to consistently predict isocratic retention factors for small molecules with accuracies better than 10%, even when using synthetic gradient retention data. Two distinct challenges in fitting gradient retention data were identified: 1) a lack of 'uniqueness' in the parameters; and 2) an inability to find the global optimum fit in a complex fitting landscape. Working with experimental data where measurement noise is unavoidable will only make the accuracy worse. This article is protected by copyright. All rights reserved.

Closed form approximations to predict retention times and peak widths in gradient elution under conditions of sample volume overload and sample solvent mismatch

Closed form expressions for the prediction of retention times and peak widths for gradient liquid chromatography are particularly useful in understanding, rationalizing and optimizing separations. These expressions are obtained by integrating differential equations, in conjunction with a model of the variation of the retention factor as a function of mobile phase composition. Two of these models, the linear solvent strength (LSS) model and the Neue-Kuss (NK) model are explored in the present work. Here, we expand on these closed form expressions to account for effects of sample volume overload and a mismatch between the sample solvent and the initial mobile phase composition for the gradient. We show that there have been errors in expressions reported in the literature, and we have evaluated the accuracy of the predictions from the closed form expressions reported here using a recently developed liquid chromatography simulator. The expressions assume a constant plate height and consider elution across four zones of the gradient profile - elution in the sample solvent, elution in the initial (isocratic) mobile phase caused by the gradient delay volume, elution during a linear gradient, and elution post-gradient at the final (isocratic) mobile phase composition. The expressions generally give reasonably accurate predictions for retention times and peak widths, except for cases where the solute elutes during transitions between the different zones. The average magnitude of the prediction errors for retention time and peak width relative to simulation were 0.093% and 0.40% for the LSS expressions for ten amphetamine solutes at 36 different separation conditions, and 0.22% and 1.8% for the NK expressions for eight alkylbenzene solutes at 36 different separation conditions, respectively.

Detailed numerical study of the peak shapes of neutral analytes injected at high solvent strength in short reversed-phase liquid chromatography columns and comparison with experimental observations

We report on a numerical investigation of the different steps in the development of the spatial concentration profiles developing along the axis of a liquid chromatography column when injecting large relative volumes (>10 to 20% of column volume) of analytes dissolved in a high solvent strength solvent band as can be encountered in the second dimension (²D) column of a two-dimensional liquid chromatography (2D-LC) system. More specifically, we made a detailed study of the different retention and the axial band broadening effects leading to the double-headed peak shapes or strongly fronting peaks that can be experimentally observed under certain conditions in 2D-LC. The establishment of these intricate peak profiles is discussed in all its fine, mechanistic details. The effect of the volume of the column, the volume and the shape of the sample band, the retention properties of the analyte and the band broadening experienced by the analytes and the sample solvent are investigated. A good agreement between the simulations and the experimental observations with caffeine and methylparaben injected in acetonitrile/water (ACN/H₂O) mobile phase with different injection volumes is obtained. Save the difference in dwell volume, key features of experimental and simulated chromatograms agree within a few %. The simulations are also validated against a number of simple mathematical rules of thumb that can be established to predict the occurrence of a breakthrough fraction and estimate the amount of breakthrough.

Recent applications of retention modelling in liquid chromatography

Recent applications of retention modelling in liquid chromatography (2015–2020) are comprehensively reviewed. The fundamentals of the field, which date back much longer, are summarized. Retention modeling is used in retention‐mechanism studies, for determining physical parameters, such as lipophilicity, and for various more‐practical purposes, including method development and optimization, method transfer, and stationary‐phase characterization and comparison. The review focusses on the effects of mobile‐phase composition on retention, but other variables and novel models to describe their effects are also considered. The five most‐common models are addressed in detail, i.e. the log‐linear (linear‐solvent‐strength) model, the quadratic model, the log–log (adsorption) model, the mixed‐mode model, and the Neue–Kuss model. Isocratic and gradient‐elution methods are considered for determining model parameters and the evaluation and validation of fitted models is discussed. Strategies in which retention models are applied for developing and optimizing one‐ and two‐dimensional liquid chromatographic separations are discussed. The review culminates in some overall conclusions and several concrete recommendations.