Multilinear gradient elution optimization in reversed-phase liquid chromatography based on logarithmic retention models: application to separation of a set of purines, pyrimidines and nucleosides

The analytical solutions of the fundamental equation of the multilinear gradient elution are derived in two cases, when the dependence of the logarithm of the solute retention (lnk) upon the volume fraction of organic modifier (φ) is a three-parameter logarithmic expression, and when a simple linear relationship between lnk and lnφ is adopted. The derived theoretical expressions for retention times under multilinear gradient conditions are embodied to simple algorithms for fitting gradient data and especially for resolution optimization. Their performance was examined by using a mixture of 16 model compounds chosen among purines, pyrimidine and nucleosides in eluting systems modified by acetonitrile. It was found that the accuracy of the predicted gradient retention times is very satisfactory even if the simple logarithmic expression for the retention behavior of solutes, i.e. the linear dependence of lnk upon lnφ, is used.     

Evaluation of the Linear-Elution-Strength Model for the Prediction of Retention and Selectivity in Isothermal Gas Chromatography

Linear-elution strength theory and temperature-programmed gas chromatography is evaluated as a rapid method for predicting isothermal retention factors and column selectivity. Retention times for a wide range of compounds are determined at the program rates of 3 and 12 °C/min for the temperature range 60 to 160 °C on three open-tubular columns (DB-1701, DB-210 and EC-Wax) and used to predict isothermal retention factors for each column over the temperature range 60 to 140 °C. The temperature-program predicted isothermal retention factors are compared with experimental values using linear regression and the solvation parameter model. It is shown that isothermal retention factors predicted by the linear-elution-strength model only approximately represents the experimental data. The model fails to predict the slight curvature that exists in most plots of the experimental retention factor (log k) as a function of temperature. In addition, regression of the temperature-program predicted isothermal retention factors against the experimental values indicates that the slopes and intercepts deviate significantly from their target values of one and zero, respectively, in a manner which is temperature dependent. The temperature-program predicted isothermal retention factors result in system constants for the solvation parameter model that are different to those obtained from the experimental retention factors. These results are interpreted as indicating that linear-elution-strength theory predicts retention factors that fail to accurately model stationary phase interactions over a wide temperature range. It is concluded that temperature-program methods using linear-elution-strength theory are unsuitable for constructing system maps for isothermal separations.     

Optimisation of multilinear gradient elutions in reversed-phase liquid chromatography using ternary solvent mixtures

The multilinear gradient elution theory for binary mobile phases in reversed-phase liquid chromatography presented in [P. Nikitas, A. Pappa-Louisi, A. Papageorgiou, J. Chromatogr. A 1157 (2007) 178] is extended to ternary gradients. For the evaluation of this theory and the performance of the various fitting and optimisation algorithms we used 13 o-phthalaldehyde (OPA) derivatives of amino acids with mobile phases modified by acetonitrile and methanol. It is shown that the theory can lead to high quality predictions of the retention times under gradients elutions and optimisation of ternary gradients provided that we use a six-parameter expression for the logarithm of the retention factor, lnk, and the adjustable parameters of this expression are determined from ternary isocratic data.     

Applicability of linear and nonlinear retention‐time models for reversed‐phase liquid chromatography separations of small molecules,peptides, and intact proteins

The applicability and predictive properties of the linear solvent strength model and two nonlinear retention‐time models, i.e., the quadratic model and the Neue model, were assessed for the separation of small molecules (phenol derivatives), peptides, and intact proteins. Retention‐time measurements were conducted in isocratic mode and gradient mode applying different gradient times and elution‐strength combinations. The quadratic model provided the most accurate retention‐factor predictions for small molecules (average absolute prediction error of 1.5%) and peptides separations (with a prediction error of 2.3%). An advantage of the Neue model is that it can provide accurate predictions based on only three gradient scouting runs, making tedious isocratic retention‐time measurements obsolete. For peptides, the use of gradient scouting runs in combination with the Neue model resulted in better prediction errors (<2.2%) compared to the use of isocratic runs. The applicability of the quadratic model is limited due to a complex combination of error and exponential functions. For protein separations, only a small elution window could be applied, which is due to the strong effect of the content of organic modifier on retention. Hence, the linear retention‐time behavior of intact proteins is well described by the linear solvent strength model. Prediction errors using gradient scouting runs were significantly lower (2.2%) than when using isocratic scouting runs (3.2%).     

Multilinear gradient elution optimisation in reversed-phase liquid chromatography using genetic algorithms

The treatment presented in a recent paper [P. Nikitas, A. Pappa-Louisi, J. Chromatogr. A, 1068 (2005) 279] is extended to multilinear gradients, i.e. continuous gradients consisting of a certain number of linear portions. Thus, the experimental lnk versus phi curve, where k is the retention factor of a sample solute under isocratic conditions and phi is the volume fraction of the organic modifier in the water-organic mobile phase, is subdivided into a finite number of linear portions resulting in simple analytical expressions for the solute gradient retention time. These expressions of the retention time are directly used in an optimisation technique based on genetic algorithms. This technique involves first the determination of the theoretical dependence of k upon phi by means of gradient measurements, which in turn is used by the genetic algorithm for the prediction of the best gradient profile. The validity of the analytical expressions and the effectiveness of the optimisation technique were tested using fifteen underivatized amino acids and related compounds with mobile phases modified by acetonitrile. It was found that the adopted methodology exhibits significant advantages and it can lead to high quality predictions of the gradient retention times and optimisation results.     

Novel computer-assisted approach to quick prediction and optimization of gradient separation for online enrichment-reversed phase liquid chromatography tandem system

An algorithm capable of predicting and optimizing the gradient separation of LC × LC system was developed in this paper. Two groups of structural analogues, five ginsenosides as well as eight bisphenols,which were difficult to discriminate in routine analysis, were used to verify the effectiveness of the proposed algorithm in fast separation optimization. Average errors of retention times below 1% were found in the retention prediction for all types of gradient programs, implying that the theory...     

In Process Citation

Some problems concerning the efficiency of temperature gradient chromatography as compared to that of isothermal chromatography have been investigated. The following expression has been derived for temperature-gradient chromatography: where beta is the separation coefficient, alpha(1) and alpha(2), are the partition coefficients of two substances to be separated, R(f)(1) is the retardation factor for the substance with alpha(1)v is the volume of the eluent in the column, Deltav is the Supplementary volume of the eluent passing through the column owing to evaporation caused by the temperature-gradient, A(M). is the cross-sectional area of the mobile phase and d is the distance between the mid-points of the spots on the chromatogram. It has been shown that under the influence of the temperature gradient Deltav can be large enough for separation of two substances with an alpha(1)/alpha(2), ratio very close to 1. For this reason temperature-gradient chromatography with an open column is the most efficient means of separation so far known.     

反相液相色谱中溶剂强度规律的研究

 以溶质计量置换保留模型 (SDM R)为依据 ,通过研究 3种正链醇同系物溶剂置换剂对 14种正链醇同系物溶质色谱保留行为的影响 ,发现计量置换参数Z(对应 1mol溶质被吸附时从溶质与固定相接触处释放出的溶剂的总摩尔数 )、lgI(与 1mol溶质对固定相亲和势有关的常数 )和 j(与 1mol溶剂对固定相亲和势有关的常数 )均随着同系物置换剂相对分子质量的增大而减小 ,并呈现出线性变化 ,表明溶剂强度与溶剂分子的大小有关 ,分子愈大 ,溶剂洗脱能力愈强 ,并遵循同系物规律。     

Prediction of the effects of methanol and competing ion concentration on retention in the ion chromatographic separation of anionic and cationic pharmaceutically related compounds

The mixed-mode separation of a selection of anionic and cationic pharmaceutically related compounds is studied using ion-exchange columns and eluents consisting of ionic salts (potassium hydroxide or methanesulfonic acid) and an organic modifier (methanol). All separations were performed using commercially available ion-exchange columns and an ion chromatography instrument modified to allow introduction of methanol into the eluent without introducing compatibility problems with the eluent generation system. Isocratic retention prediction was undertaken over the two-dimensional space defined by the concentration of the competing ion and the percentage of organic modifier in the eluent. Various empirical models describing the observed relationships between analyte retention and both the competing ion concentration and the percentage of methanol were evaluated, with the resultant model being capable of describing the separation, including peak width, over the entire experimental space based on six initial experiments. Average errors in retention time and peak width were less than 6% and 27%, respectively, for runs taken from both inside and outside of the experimental space. Separations performed under methanol gradient conditions (while holding the competing ion concentration constant) were also modelled. The observed effect on retention of varying the methanol composition differed between analytes with several analytes exhibiting increased retention with increased percentage methanol in the eluent. An empirical model was derived based on integration of the observed t_R vs. %methanol plot for each analyte. A combination of the isocratic and gradient models allowed for the prediction of retention time using multi-step methanol gradient profiles with average errors in predicted retention times being less than 4% over 30 different 2- and 3-step gradient profiles for anions and less than 6% over 14 different 2- and 3-step gradient profiles for cations. A modified peak compression model was used to estimate peak widths under these conditions. This provided adequate width prediction with the average error between observed and predicted peak widths being less than 15% for 40 1-, 2- and 3-step gradients for anions and less than 13% over 14 1-, 2- and 3-step gradients for cations.     

Temperature programmed retention indices: Calculation from isothermal data. Part 1: Theory

Direct conversion of isothermal to temperature programmed indices is not possible. In this work it is shown that linear temperature programmed retention indices can only be calculated from isothermal retention data if the temperature dependence of both the distribution coefficients and the column dead time are taken into account. Procedures are described which allow calculation of retention temperatures and from these, accurate programmed retention indices. Within certain limits the initial oven temperature and programming rate can be chosen freely. The prerequisite for this calculation is the availability of reliable isothermal retention data (retention times, retention factors, relative retention times, or retention indices) at two different temperatures for one column. The use of compiled isothermal retention indices at two different temperatures for the calculation of retention temperatures and thus temperature programmed indices is demonstrated. For the column for which programmed retention indices have to be determined, the isothermal retention times of the n-alkanes and the column dead time as a function of temperature have to be known in addition to the compiled data for a given stationary phase. Once the programmed retention indices have been calculated for a given column the concept allows the calculation of temperature programmed indices for columns with different specifications. The characteristics which can be varied are: column length, column inner diameter, phase-ratio, initial oven temperature, and programming rate.     

Generic approach to the method development of intact protein separations using hydrophobic interaction chromatography

We describe a liquid chromatography method development approach for the separation of intact proteins using hydrophobic interaction chromatography. First, protein retention was determined as function of the salt concentration by isocratic measurements and modeled using linear regression. The error between measured and predicted retention factors was studied while varying gradient time (between 15 and 120 min) and gradient starting conditions, and ranged between 2 and 15%. To reduce the time needed to develop optimized gradient methods for hydrophobic interaction chromatography separations, retention‐time estimations were also assessed based on two gradient scouting runs, resulting in significantly improved retention‐time predictions (average error < 2.5%) when varying gradient time. When starting the scouting gradient at lower salt concentrations (stronger eluent), retention time prediction became inaccurate in contrast to predictions based on isocratic runs. Application of three scouting runs and a nonlinear model, incorporating the effects of gradient duration and mobile‐phase composition at the start of the gradient, provides accurate results (improved fitting compared to the linear solvent‐strength model) with an average error of 1.0% and maximum deviation of –8.3%. Finally, gradient scouting runs and retention‐time modeling have been applied for the optimization of a critical‐pair protein isoform separation encountered in a biotechnological sample.     

The impact of column inner diameter on chromatographic performance in temperature gradient liquid chromatography

The impact of column inner diameter on chromatographic performance in temperature gradient liquid chromatography has been investigated in the present study. Columns with inner diameters of 0.32, 0.53, 3.2 and 4.6 mm were compared with respect to retention and efficiency characteristics using temperature gradients from 30 to 90 degrees C with temperature ramps of 1, 5, 10 and 20 degrees C min(-1). The columns were all of 15 cm length and were packed with 3 microm Hypersil ODS particles. Alkylbenzenes served as model compounds, and the mobile phase consisted of acetonitrile-water (50:50, v/v). The study revealed that the column ID is not a critical limiting factor when performing temperature programming in LC, at least for columns narrower than 4.6 mm inner diameter in the temperature interval 30-90 degrees C. The retention times for all components on all columns were highly comparable, with similar peak profiles without any signs of peak splitting. The use of mobile phase pre-heating when using the larger bore columns was avoided by starting the temperature gradients close to ambient. However, the relative apparent efficiency was inversely proportional to column inner diameter, making the capillary columns generally more functional towards temperature gradients than the larger bore columns with respect to chromatographic efficiency. In addition, the capillary columns possessed higher robustness towards temperature programming than the conventional columns.     

Combined effect of temperature and organic modifier concentration on the retention under single mode gradient conditions in reversed-phase HPLC

The combined effect of temperature, T, and organic modifier concentration, phi, on the retention under gradient conditions in RPLC is studied by considering, both theoretically and experimentally gradients, of phi at constant T and gradients of T at constant phi. Two approaches are examined: in the first approach the prediction of the elution time of a sample solute is based on the isocratic/isothermal properties of this solute. The second approach is based on a direct fitting procedure of a proper retention model to 2-D isocratic/T-gradient or isothermal/phi-gradient retention data. These approaches were tested using alkylbenzes in eluting systems modified by ACN. We found that both approaches can give excellent predictions under certain prerequisites. However, the first approach exhibits the notable advantage that it can be used effectively to predict retention times under any kind of phi-gradients at constant T or T-gradients at constant phi. The second approach has the advantage that it is relatively simple but its applicability is very restricted since its predictions are satisfactory only if the gradients are of the same kind with those used in the fitting procedure and the conditions lie within those used for fitting.     

Use of literature values of temperature programmed retention indexes in qualitative analysis by isothermal gas chromatography

Numerous reports have appeared on the determination of temperature programmed retention indexes in gas chromatography and although chromatographic variables should be completely consistent with published data if such indexes are to be of use, the reproduction of such rigorous parameters is quite difficult. This report presents an approximate method for using published values of temperature programmed retention indexes in isothermal chromatography. In general, the temperature dependence of the isothermal retention indexes of a number of compounds can be expressed as a series of oblique lines on a plot with retention index as the abscissa and temperature as the ordinate; the elution order of the compounds at a given, isothermal, temperature is then indicated by the points at which the compounds' oblique lines cut the horizontal line corresponding to the temperature of interest. In linear temperature programmed chromatography, the horizontal line representing isothermal operation becomes, to a first approximation, a sloping line with a gradient corresponding to the programming rate: this has been verified experimentally and may be valid over a wide range of temperatures. This line can be used to predict isothermal retention indexes for use in qualitative analysis.     

糖类化合物亲水作用色谱保留行为评价

以糖类化合物为研究对象,系统评价了其在亲水模式下的色谱保留行为。分别考察了流动相、固定相和缓冲盐等对糖类化合物保留的影响,建立了糖类化合物在亲水模式下的保留方程。结果表明,糖类化合物随着流动相中乙腈比例的降低,保留时间减小;随着缓冲盐浓度的增加,保留时间增加;同时,糖类化合物的保留行为还会受到有机溶剂种类和固定相类型的影响;其保留行为可使用顶替吸附-液相相互作用模型定量描述。将该模型进一步用于实际样品中糖类化合物保留行为的预测,获得了较好的实验结果,预测保留时间与实测保留时间的相对误差小于0.3%。对糖类化合物亲水模式下的保留行为进行了系统的评价和定量描述,该研究结果将有助于糖类化合物亲水作用色谱分离方法的发展。     

Correct identification of polychlorinated biphenyls in temperature-programmed GC with ECD detection

A method has been developed for peak identification of PCBs in GC with ECD detection under different temperature programs and isothermal conditions on two commonly used columns (DB-5 and DB-1701). This was achieved by means of accurate calibration of retention times based on the concept of the relative retention index P (i) and retention times of the selected PCB internal standards. The P (i) was calculated from the predicted retention times with the database of the retention parameters (A, B) and the migration equations. Through comparison of the calibrated and experimental retention times of PCBs in technical samples, it was shown that the developed method was effective for correct PCB comprehensive, quantitative, congener-specific (CQCS) analyses.     

Predictions of Reversed-Phase Gradient Elution LC Separations Supported by QSRR

Previous studies demonstrated that quantitative structure-retention relationships (QSRR) combined with the linear solvent strength (LSS) model allow for prediction of gradient reversed-phase liquid chromatography retention time for any analyte of a known molecular structure under defined LC conditions. A QSRR model derived at the selected gradient time and at the same gradient time was tested. The aim the present study was to evaluate the accuracy of QSRR predictions used during the predictions of LC gradient retention times with variable gradient times. For this purpose, predictions of retention times at two gradient times were used to find the optimal, different gradient times. In the first step, experimental retention data for the model set of analytes were used to derive appropriate QSRR models at two gradient times. These QSRR models were further used to predict gradient retention times for another set of testing analytes at the two selected above gradient times. Then, applying linear solvent-strength (LSS) theory, the predicted retention times for test analytes were used to find other optimal gradient times for those analytes. Satisfactory predictions of gradient retention times for test analytes were obtained at gradient times different from those applied for model analytes.     

Easy and accurate high-performance liquid chromatography retention prediction with different gradients, flow rates, and instruments by back-calculation of gradient and flow rate profiles

Isocratic retention data should make a suitable foundation for an accurate, cross-instrument LC retention prediction system. Our previous work suggested that in order to accurately calculate (or "project") gradient retention times on a wide range of HPLC systems using a single set of isocratic retention data, the precise shape of both the gradient and flow rate profiles produced by each instrument must be properly taken into account. However, accurate measurement of these system properties is difficult and time-consuming. In this work, we describe an approach that uses the measured gradient retention times of a set of standard solutes spiked into the sample along with their known isocratic retention vs. eluent composition relationships to determine the effective gradient and flow rate profiles by back-calculation. Retention "projections" of 20 other solutes using these back-calculated profiles, under various chromatographic conditions typical of metabolomics experiments, were remarkably accurate (as good as 0.23% of the gradient time, R2 up to 0.99996), being very near the level of retention reproducibility. Our calculations suggest that this level of accuracy will allow a quadrupole MS to identify 38-fold more compounds out of a simulated mixture of 7307; it would allow an FTICR-MS to improve its identification rate nearly two-fold with the same mixture. Moreover, very little effort is required of the user. This approach provides a simple way to correct for all instrument-related factors affecting retention, allowing dramatically streamlined and improved retention projection across gradients, flow rates, and HPLC instruments.     

Kinetic performance limits of constant pressure versus constant flow rate gradient elution separations. Part I: theory

We report on a general theoretical assessment of the potential kinetic advantages of running LC gradient elution separations in the constant-pressure mode instead of in the customarily used constant-flow rate mode. Analytical calculations as well as numerical simulation results are presented. It is shown that, provided both modes are run with the same volume-based gradient program, the constant-pressure mode can potentially offer an identical separation selectivity (except from some small differences induced by the difference in pressure and viscous heating trajectory), but in a significantly shorter time. For a gradient running between 5 and 95% of organic modifier, the decrease in analysis time can be expected to be of the order of some 20% for both water–methanol and water–acetonitrile gradients, and only weakly depending on the value of V_G/V₀ (or equivalently t_G/t₀). Obviously, the gain will be smaller when the start and end composition lie closer to the viscosity maximum of the considered water-organic modifier system. The assumptions underlying the obtained results (no effects of pressure and temperature on the viscosity or retention coefficient) are critically reviewed, and can be inferred to only have a small effect on the general conclusions. It is also shown that, under the adopted assumptions, the kinetic plot theory also holds for operations where the flow rate varies with the time, as is the case for constant-pressure operation. Comparing both operation modes in a kinetic plot representing the maximal peak capacity versus time, it is theoretically predicted here that both modes can be expected to perform equally well in the fully C-term dominated regime (where H varies linearly with the flow rate), while the constant pressure mode is advantageous for all lower flow rates. Near the optimal flow rate, and for linear gradients running from 5 to 95% organic modifier, time gains of the order of some 20% can be expected (or 25–30% when accounting for the fact that the constant pressure mode can be run without having to leave a pressure safety margin of 5–10% as is needed in the constant flow rate mode).     

Prediction of retention times for anions in linear gradient elution ion chromatography with hydroxide eluents using artificial neural networks

The feasibility of using an artificial neural network (ANN) to predict the retention times of anions when eluted from a Dionex AS11 column with linear hydroxide gradients of varying slope was investigated. The purpose of this study was to determine whether an ANN could be used as the basis of a computer-assisted optimisation method for the selection of optimal gradient conditions for anion separations. Using an ANN with a (1, 10, 19) architecture and a training set comprising retention data obtained with three gradient slopes (1.67, 2.50 and 4.00 mM/min) between starting and finishing conditions of 0.5 and 40.0 mM hydroxide, respectively, retention times for 19 analyte anions were predicted for four different gradient slopes. Predicted and experimental retention times for 133 data points agreed to within 0.08 min and percentage normalised differences between the predicted and experimental data averaged 0.29% with a standard deviation of 0.29%. ANNs appear to be a rapid and accurate method for predicting retention times in ion chromatography using linear hydroxide gradients.