New approach to linear gradient elution used for optimisation in reversed-phase liquid chromatography

A new mathematical treatment concerning the gradient elution in reversed-phase liquid chromatography when the volume fraction psi of an organic modifier in the water-organic mobile phase varies linearly with time is presented. The experimental ln k versus psi curve, where k is the retention factor under isocratic conditions in a binary mobile phase, is subdivided into a finite number of linear portions and the solute gradient retention time tR is calculated by means of an analytical expression arising from the fundamental equation of gradient elution. The validity of the proposed analytical expression and the methodology followed for the calculation of tR was tested using eight catechol-related solutes with mobile phases modified by methanol or acetonitrile. It was found that in all cases the accuracy of the predicted gradient retention times is very satisfactory because it is the same with the accuracy of the retention times predicted under isocratic conditions. Finally, the above method for estimating gradient retention times was used in an optimisation algorithm, which determines the best variation pattern of psi that leads to the optimum separation of a mixture of solutes at different values of the total elution time.     

Prediction of elution bandwidth for purine compounds by a retention model in reversed-phase HPLC with linear-gradient elution

In reversed-phase liquid chromatography, the retention mechanism of solute has been studied under linearly programmed gradient mobile-phase conditions. The separation of a mixture of four purine compounds (purine, theobromine, theophylline, and caffeine) was considered as a practical case in two binary mobile phase systems, water/methanol and water/acetonitrile. The retention model which describes how the retention factor is related to the mobile-phase composition has been developed in various mathematical forms to predict the retention time in both linear and gradient elutions. For a pulse injection of sample, two important factors, the retention time and the bandwidth of solute, might be computable to predict the elution profiles estimated by the distribution function, such as the Gaussian distribution function. In this work, a prediction method based on the analogue of the retention model was proposed to calculate the bandwidth in linear gradient elutions. Band broadening was caused by the different migration velocities of the front and rear ends of the solute band in a chromatographic column. Therefore, the migration behaviors of the front and rear ends of the solute band were explained with the same retention model which had been used to predict the retention time of solute. For the well retained solutes, theophylline and caffeine, the predicted bandwidth and experimentally obtained bandwidth showed good agreement in both isocratic and gradient elutions.     

Application of Multilinear Gradient Elution for Optimization of Separation of Chlorophenols Using Derringer’s Desirability Function

Multilinear gradient elution was applied for the simultaneous optimization of resolution and analysis times of nine chlorophenols separated by HPLC. The first relationship of ln k versus φ was determined using the isocratic retention time for each analyte. For prediction of gradient retention times of analytes, the fundamental equation of gradient elution was numerically solved. Then a grid search program was used to simulate chromatograms under each new condition. Two different chromatographic goals, analysis time and minimum distance between adjacent peaks, were evaluated simultaneously using Derringer’s desirability function for each chromatogram. The sigmoid function was used to transform the optimization criteria to desirability values. Under optimal conditions, a good agreement was observed between predicted and experimental values of the chromatographic response function when analysis time was less than 40 min.     

Study of elution behaviour with gradient voltage in CEC using methacrylate monolithic columns

A theoretical study on the retention behaviour and chromatographic performance of neutral solutes using a lauryl methacrylate‐based monolithic column under voltage gradient mode in CEC was carried out. Through a flexible mathematical function based on a modified Gaussian model, the peak shape of compounds was firstly fitted under constant and gradient voltage. Using the peak shape parameters and retention time, the estimation of global chromatographic performance, efficiency and peak capacity under several voltage conditions was performed. The influence of voltage gradient on the separation efficiency is discussed and simple equations are presented to calculate retention and peak widths under voltage gradient conditions. A comparison in terms of chromatographic performance of a test mixture of neutral solutes under constant and gradient voltage modes was also carried out. The experiments carried out under gradient voltage showed better efficiencies (172 000 plates/m) and lower peak widths than those obtained under constant voltage (52 000 plates/m).     

Multi-linear gradient elution optimization for separation of phenylthiohydantoin amino acids using pareto optimality method

Multi-linear gradient elution was applied for simultaneous optimization of resolution and analysis times for ten phenylthiohydantoin amino acids (PTH-AAs) in liquid chromatography. Relation of lnK upon φ for each analyte was determined using isocratic retention time data, and gradient retention time of analytes was predicted using fundamental equation of gradient elution. Then a grid search program was used to predict retention time of solutes in variable space. Two different chromatographic goals-analysis time and minimum difference between adjacent peaks- were simultaneously evaluated using Pareto optimality method. Gradient program in optimum condition was: initially 24% CH₃OH/Water for 10 min, linear ramp to 34% over 5 min, to 29% over 5 min, and to 70% over 20 min. The average of calculated relative error in the prediction of the retention time in optimal conditions was -1.67% that shows a good agreement between predicted and experimental values of the chromatographic retention time in optimal condition.     

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.     

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.     

Prediction of Retention Time of Solutes under Linear Gradient Elution Conditions in RP-HPLC

A model for prediding retention time of solutes undeir linear gradient elulioa conditions has been established. In this model,the theorelkal expressions under different eluflon modes were derived and tested with the retention behaviors of p-hydroxy-benzaldehyde, vanilUn, biphenyl, phenanthrene in gradient elution. With halting into account the dwell time of the instrumeatal system, the theoretically predicted retention times agreewell with those experimentally determined.     

人参皂甙的反相高效液相色谱多台阶梯度优化方法

建立了一种反相高效液相色谱多台阶梯度分离人参皂甙的方法.该方法以乙腈-水溶液为流动相,通过一系列等度实验,获得了8种人参皂甙Rg1,Re,Rf,Rg2,Rb1,Rc,Rb2和Rd的色谱保留参数,发现两参数保留方程不适合用于人参皂甙这种天然产物的分离条件的优化,而三参数保留方程的高精度才可满足预测的要求.在三参数保留方程的基础上,通过计算确定了8种人参皂甙(包括3台阶梯度)的液相色谱分离条件.通过实验对此优化条件进行了验证,实验结果显示了较好的预测精度和分离度.将本方法用于分离人参皂甙,分析时间短且分离度高,显示了等度台阶梯度优化方法对确定色谱分离条件的优越性.     

反相高效液相三元流动相台阶梯度分离条件的快速优化方法

 根据溶质在柱内的迁移规律 ,建立了一种利用线性梯度实验快速获得溶质保留值方程系数 ,然后以串行响应函数为优化指标进行多台阶梯度分离条件优化的方法。与利用等度实验获得保留值方程的方法相比 ,该法可以大大缩短优化时间。通过该方法对芳香胺和衍生化氨基酸样品进行了分离 ,获得了满意的分离度 ,表明该方法的预测精度很好。     

Automated off-line optimisation of programmed elutions in reversed-phase high-performance liquid chromatography using ternary solvent mixtures

A new system for the unattended optimisation of gradient elutions in reversed-phase high-performance liquid chromatography has been developed. The system is based on the simulation of retention times under conditions of ternary solvent mixtures and ternary gradient programmes. This model is constructed departing from a few experimental data obtained in isocratic elutions and validated against experimental gradient elutions. Once validated, this retention model can be used for the unattended search of an optimum separation. The optimisation process is driven by an evolutionary algorithm (EA), specially developed to map the ternary gradient elutions problem. The development and characteristics of the retention modelling as well as those of the EA and its particularities are discussed and some real world examples of separation presented.     

HPLC analysis of PCBs on porous graphitic carbon: Retention behavior and gradient elution

Summary The fractionation of PCB congeners into classes according to their planarity (i.e. amount of ortho substitution) by HPLC on porous graphitic carbon (PGC) as stationary phase has been investigated as a preliminary step before GC analysis, indispensable for a complete separation of PCB congeners. A systematic study of retention behavior on PGC eluted with different n-hexane-dichloromethane mixtures made it possible to design a linear binary gradient which separated PCB congeners in a reasonable time and with good performance. Relationships were obtained between retention behavior and the molecular structure of the PCB congeners. The beneficial effects of elevated temperature on separation efficiency were also investigated. The analysis conditions selected, i.e. continuous gradient separation at 40°C, were successfully used for fractionation of technical PCB formulations, e.g. Aroclor 1242.     

Evaluation of the retention dependence on the physicochemical properties of solutes in reversed-phase liquid chromatographic linear gradient elution based on linear solvation energy relationships

This paper describes the results of the evaluation of retention dependence on the physicochemical properties of solutes in linear gradient elution by reversed-phase liquid chromatography (RPLC) based on linear solvation energy relationships (LSERs). Retention time data on Inertsil ODS(3) column by linear gradient elution were collected for both acetonitrile-water and methanol-water binary mobile phases under various gradient steepness. Based on the LSERs, the retention times were linearly correlated with the physicochemical properties (size, dipolarity, and hydrogen bond donor-acceptor acidity and basicity) of solutes. As predicted by LSERs, very acceptable linear relationships are observed for both mobile phases. While the magnitudes of the coefficients are modified by the gradient steepness, their signs are consistent with those obtained by isocratic elution. As obtained for isocratic elution, the dominant factors to retention in linear gradient elution of RPLC are the solutes' size and hydrogen bond acceptor basicity. The conclusions of the study allow us to predict retention in chromatographic method development by gradient elution.     

利用HCI程序确定儿茶酚化合物的反相高效液相色谱最佳分离条件

有效地确定了反相高效液相色谱分离儿茶酚化合物的最佳条件。在水和甲醇的二元流动相里分别加入乙酸缓冲液,利用基于ln k=ln kw +SF, k=A+B/F, ln k=L+MF+NF2 (F是流动相中有机物甲醇的体积分数)等保留因子的一次或二次方程式的塔板理论得到色谱分离结果;利用保留原理得到等度和梯度洗脱的最佳条件。得出最佳初始流动相是含0.1%乙酸的水和含0.1%乙酸的甲醇(体积比为75∶25)的混合溶液;梯度洗脱条件：初始流动相保持15 min,然后用10 min的时间将上述二元流动相的体积比线性变换成50∶50,直到完成全部分离。通过实验证实该计算结果与实验值相近。     

Monolithic capillary columns synthesized from a single phosphate-containing dimethacrylate monomer for cation-exchange chromatography of peptides and proteins

Monoliths containing phosphoric acid functional groups were synthesized from only one monomer, bis[2-(methacryloyloxy)ethyl] phosphate (BMEP), in 75-μm i.d. UV transparent fused-silica capillaries by photo-initiated polymerization for cation exchange chromatography of peptides and proteins. Various synthetic conditions, including porogen solvents, monomer concentration, and polymerization time, were studied. The hydrophobicities of the resulting monoliths were evaluated using propyl paraben under reversed-phase conditions and synthetic peptides under ion-exchange conditions. These monoliths exhibited low hydrophobicities and relatively low porosities due to their highly cross-linked structures. A dynamic binding capacity (lysozyme) of 73 mg/mL of column volume was measured using the best performing monolith. Synthetic peptides were eluted in approximately 30 min without addition of acetonitrile to the mobile phase, yielding a peak capacity of 28. Efficiencies of 52,900 plates/m for peptides and 71,000 plates/m for proteins were obtained under isocratic conditions. The effects of separation conditions, i.e., mobile phase pH and salt gradient rate, were studied. Good run-to-run reproducibility was achieved with a relative standard deviation (RSD) less than 1.5% for retention times of proteins. The column-to-column retention time reproducibility for peptides was less than 3.5% RSD. A monolithic column was used to follow the deamidation of ribonuclease A. The kinetics of deamidation were founded to be first order with a half life of 195 h. A cytochrome C digest was also separated using a linear gradient of sodium chloride.     

Retention prediction of a set of amino acids under gradient elution conditions in hydrophilic interaction liquid chromatography

The analysis of amino acids presents significant challenges to contemporary analytical separations. The present paper investigates the possibility of retention prediction in hydrophilic interaction chromatography (HILIC) gradient elution based on the analytical solution of the fundamental equation of the multilinear gradient elution derived for reversed‐phase systems. A simple linear dependence of the logarithm of the solute retention (ln k) upon the volume fraction of organic modifier (φ) in a binary aqueous‐organic mobile is adopted. Utility of the developed methodology was tested on the separation of a mixture of 21 amino acids carried out with 14 different gradient elution programs (from simple linear to multilinear and curved shaped) using ternary eluents in which a mixture of methanol and water (1:1, v/v) was the strong eluting member and acetonitrile was the weak solvent. Starting from at least two gradient runs, the prediction of solute retention obtained under all the rest gradients was excellent, even when curved gradient profiles were used. Development of such methodologies can be of great interest for a wide range of applications.     

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.     

Simultaneous chromatographic identification of a few components in mixtures based on a correlation between their absolute or relative retention times under different conditions

A correlation was established between the absolute and relative retention parameters of various compounds under different conditions of chromatographic analysis (isothermal and temperature programming conditions in gas chromatography or isocratic and gradient elution in high-performance liquid chromatography). This correlation is described by the linear regression equations t _R (II) = = at _R (I) + b with a high degree of accuracy. This property of chromatographic retention parameters allowed us not only to recalculate the values of these parameters determined under different conditions, but also to propose an algorithm for the simultaneous identification of a few components in complex mixtures with the use of published data on retention parameters found under other conditions (even presented as the drawings of chromatograms).     

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...