Simulation of elution profiles in liquid chromatography⿿I: Gradient elution conditions, and with mismatched injection and mobile phase solvents

Abstract

High-performance liquid chromatography (HPLC) simulators are effective method development tools. The goal of the present work was to design and implement a simple algorithm for simulation of liquid chromatographic separations that allows for characterization of the effect of injection solvent mismatch and injection solvent volume overload. The simulations yield full analyte profiles during solute migration and at elution, which enable a thorough physical understanding of the effects of method variables on chromatographic performance. The Craig counter-current distribution model (the plate model) is used as the basis for simulation, where a local retention factor is assigned for each spatial and temporal element within the simulation. The algorithm, which is an adaptation of an approach originally described by Czok and Guiochon (Ref. [10]), is sufficiently flexible to allow the use of either linear (e.g., Linear Solvent Strength Theory) or non-linear models of solute retention (e.g., Neue-Kuss (Ref. [36])). In this study, both types of models were used, one for simulating separations of a homologous series of alkylbenzenes, and the other for separations of selected amphetamines. The simulation program was validated first by comparison of simulated retention times and peak widths for five amphetamines to predictions obtained using linear solvent strength (LSS) theory, and to results from experimental separations of these compounds. The simulated retention times for the amphetamines agreed within 0.02% and 2.5% compared to theory and experiment, respectively. Secondly, the program was evaluated for simulating the case where there is a compositional mismatch between the mobile phase at the column inlet and the injection solvent (i.e., the sample matrix). This work involved alkylbenzenes, and retention time and peak width predictions from simulations were within 1.5 and 6.0% of experimental values, respectively, even without correction for extra-column dispersion. The issues of sample/eluent solvent mismatch and solvent volume overload are especially important when considering the challenges of transferring eluent from the first to the second dimension in comprehensive two-dimensional liquid chromatography.

Recent applications of chemometrics in one‐ and two‐dimensional chromatography

“…These initial conditions are important when transferring compounds from the first to the second dimension, as these conditions influence band broadening. Jeong, Stoll, and others addressed these issues in a series of papers [288,289], with calculations being performed for each time frame. The authors admitted that their algorithms were slower than conventional modeling, but their predictions were thought to be more accurate.…”

“…Simulation of elution profiles in LC: Gradient conditions, and with mismatching injection and mobile phase solvents LC 2016 [288] Data fitting problems encountered in modelling retention behaviour of analytes with dual retention mechanisms LC 2015 [233] Prediction of retention time in high-resolution anti-doping screening data using ANNs LC 2013 [210] Linear gradient prediction algorithm for stationary phase optimized selectivity LC LC 2010 [204] Simulation of elution profiles in LC: Investigation of the injection solvent in the second dimension LC × LC 2017 [289] Sorption of organic compounds on black carbon LFER 2018 [246] Application of hydrogen bonding calculations, LFER LFER 2002 [244] Effect of temperature on retention using RP-LC LFER, van 't Hoff 2019 [247] Optimization of ANNs for modelling impurities retention in micellar LC MLC 2011 [209] Retention modelling in NP-LC and RP-LC -Adsorption model NP-LC, RP-LC 2000 [225] Applications of polyparameter LFER in environmental chemistry Review, LFER 2014 [248] Gradient retention time predictions for suspect screening RP-LC 2016 [217] Improved RP gradient retention modelling, Neue-Kuss model RP-LC 2010 [230] Nonlinear retention relationships in RP-LC, Neue-Kuss model RP-LC 2006 [229] Possibilities of retention modelling and computer-assisted method development in SFC SFC 2015 [238] Peak tracking Title…”

In situ silanization for continuous stationary phase gradients on particle packed LC columns

“…13,14 In contrast to discontinuous gradients, continuous gradients have the added benet of novel selectivities that could arise from neighboring ligand effects, which can occur when two ligands are adjacent on a single chromatographic support. 11,15 Compared to traditional mixed-mode chromatography, which has a xed ratio between the moieties along the length of the column, 16 the ligand ratio on a stationary phase gradient is not constant. Rather, the ligand ratio changes along the length of the column as dictated by the gradient shape or prole.…”

Temperature-assisted solute focusing with sequential trap/release zones in isocratic and gradient capillary liquid chromatography: Simulation and experiment

“…The simulation uses a simple stepwise modeling procedure similar to that of Gilar et al [58, 59]. The Gilar et al approach is simpler than the more rigorously formulated approach based on mass balance [60, 61] but it does not calculate on-column dispersion. In the mass balance case, on-column dispersion must be handled in an ad-hoc fashion because of the Craig-tube-like spreading that occurs naturally in the computation.…”

“…We have combined the approach of Gilar et al in which the front and rear positions of each individual zone are calculated, with a straightforward approach to on-column dispersion. Unlike earlier approaches [58, 60–64] we explicitly include the time and space dependence of retention and dispersion. Thus, this simulation is capable of predicting chromatograms resulting from spatial and temporal temperature programs in combination with isocratic and solvent gradient elution.…”