Optimisation technique for stepwise gradient elution in reversed-phase liquid chromatography

An optimisation technique of reversed-phase liquid chromatographic separations based on gradient elution with a stepwise variation pattern of the volume fraction phi of the organic modifier in the water-organic mobile phase is presented. It uses a non-linear least-squares programme with a Monte-Carlo search for initial estimates in order to determine the best variation pattern that leads to the optimum separation of a mixture of solutes. The validity of the above methodology was tested by separating eight catechol-related solutes with mobile phases modified by methanol or acetonitrile and variation patterns of two, three or four steps in the psi values. It was found in all cases a very satisfactory accuracy of the predicted gradient elution times, which is of the same order with the accuracy of the retention times predicted under isocratic or linear gradient conditions. In addition, it was shown that the proposed optimisation technique is both effective and flexible but well-shaped chromatograms are obtained under electrochemical detection only if steps with increasing psi are used and the change in psi is programmed to occur at the intermediate of the predicted peaks.     

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。     

液相色谱梯度洗脱中的谱带压缩效应

谱带压缩效应是梯度洗脱区别于等度洗脱的重要特征。经典的范德姆特(van Deemter)理论塔板高度方程基于等度洗脱推导得到,因此不能对谱带压缩效应进行描述。在梯度洗脱中,保留因子(k)会随流动相组成(φ)的改变而发生变化,这就使得对梯度洗脱机理的研究要比等度洗脱复杂许多。该文对近10年来谱带压缩效应的研究进展,特别是溶剂强度模型(即描述ln k与φ关系的数学表达式)的非线性特征对谱带压缩因子(G)的影响进行了述评,指出为了更好地认识谱带压缩效应需要将这种非线性因素考虑在内。     

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.     

Interconversion of gradient and isocratic retention data in reversed-phase liquid chromatography: Effect of the uptake of eluent modifier on the retention of analytes

The experimental technique of mass spectrometric tracer pulse chromatography was used to study the effect of the sorption of eluent components by a C₁₈-bonded silica RPLC packing on the retention of a series of test analytes during isocratic and gradient elution experiments. The analytes of interest were a substituted phenol, a substituted nitroaniline, an anti-malaria drug, tetrahydrofuran, and methanol. The eluent used was a mixture of acetonitrile and water. The solutes and isotopically labeled eluent components were injected at fixed time intervals during each gradient run. The mass specific detector allowed the assignment of individual analyte peaks even when there was overlap in the chromatograms from successive injections. Thus, the retention time of each analyte could be determined as a function of gradient slope and initial eluent composition at the time of each injection. Experimental gradient retention time data were then compared with the calculated results from two theoretical models. The first model assumed the velocity of the mobile phase and eluent were equal. The second and most realistic model assumed the velocity of the eluent was less than the velocity of the mobile phase due to the uptake of eluent by the stationary phase. Gradient retention times predicted by the two models were reasonably accurate with the sorption model giving slightly more accurate values. Inverse calculations, i.e., calculation of isocratic retention factors from gradient elution data were also carried out with very similar results. That is, the model allowing for the uptake of eluent was slightly more accurate than the model assuming no eluent-stationary phase interaction.     

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。     

Comparison between the isocratic and gradient retention behaviour of polypeptides in reversed-phase liquid chromatographic environments.

The isocratic and gradient elution behaviour of beta-endorphin and glucagon, two polypeptides known to exist in amphipathic alpha-helical conformations in lipophilic environments, have been examined under reversed-phase high-performance liquid chromatographic (RP-HPLC) conditions with low pH, aquo-acetonitrile mobile phases. The effects of changes in the volume fraction, psi, of the organic solvent modifier and temperature, T, on the magnitudes of the S and log k(o) values of these two polypeptides, obtained from the plots of logarithmic capacity factor (log k') vs. psi using isocratic elution conditions have been determined. These data have then been compared to the corresponding S and log k(o) values, obtained from the plots of logarithmic median capacity factor (log k) versus the median volume fraction of the organic solvent modifier (psi) derived from the linear gradient elution data, using the same n-butyl silica sorbent and related aquo-acetonitrile mobile phase conditions. As apparent from these studies, substantial differences occur in the temperature-dependent trends and magnitudes of the corresponding S and S values, or the log k(o) and log k(o) values, when these parameters are derived from experimental data acquired by these two different elution methods. Moreover, when gradient elution data for beta-endorphin and glucagon are utilised, the extrapolated values of the intercept and slope of the plots of log k vs. 1/T (corresponding to an apparent change in the median enthalpy of association, deltaH(o)assoc, or an apparent change in the median entropy of association, deltaS(o)assoc) substantially deviated from the values obtained for the thermodynamic parameters, deltaH(o)assoc and deltaS(o)assoc, derived from the log k' vs. 1/T plots using the corresponding isocratic data. These findings thus have important implications for biophysical and thermodynamic investigations when gradient elution data are employed to assess the molecular basis of the interaction of polypeptides with non-polar ligates.     

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.     

色谱累加进样分离实验条件的研究

在采用反相液相色谱或亲和色谱完成蛋白质等大分子分离时,根据溶质保留值随溶剂梯度变化曲线上突变点的差别,可以通过累加进样分离法进行样品制备或直接柱内富集分析,但这一方法并非在任意条件下、对任何样品都适用。该文根据不同形式的保留值方程从理论上探讨了样品保留值与进样时间差、梯度洗脱速率等实验条件之间的关系;结果表明：两次进样的出峰时间差与进样时间间隔成正比关系,也与其在等度情况下的容量因子有关。样品中的两种组分在间隔进样时的流出时间差主要由两组分的容量因子决定,当样品中存在两种以上保留性能相近组分时,若保证指定的分离度,进样时间间隔存在一极大值,超出该范围,分离条件将不能满足     

Migration of neutral solutes by double stepwise gradient elution in capillary electrochromatography

Characteristics of electroosmotic flow (EOF) and the migration of neutral solutes under double stepwise gradient elution in capillary electrochromatography were studied systematically. EOF velocity proved to be the function of operation time changing with the introduction of the second mobile phase. Accordingly, the retention of components also changed. The migration of neutral solutes was studied under the following three situations; A, components eluted when the column was filled only with the first kind of mobile phase; B, solutes eluted still in the first kind of mobile phase while at that time two kinds of mobile phase coexisted in the column and C, samples eluted in the second kind of mobile phase. Equations to describe the retention times of components under these three kinds of conditions were deduced and applied to predict the retention times of 12 aromatic compounds. Relative errors between experimental and calculated values were below 5.0%, which proved the reliability of the equations. In addition, parameters that might affect the retention time of solutes, such as the transferring time of mobile phase vials, the capacity factors of components and EOF velocities two steps were studied systematically.     

Evaluation of a reversed-phase column (supelcosil LC-ABZ) under isocratic and gradient elution conditions for estimating octanol-water partition coefficients

The solvation parameter model is used to identify suitable chromatographic models for estimating the octanol-water partition coefficient for neutral compounds of varied structure by reversed-phase liquid chromatography. The stationary phase Supelcosil LC-ABZ with methanol-water mobile phases affords a series of suitable correlation models for estimating the octanol-water partition coefficient (log KOW) under isocratic and gradient elution conditions. Isocratic separations with mobile phase compositions containing from about 25 to 40% (v/v) methanol provide the most accurate results for log KOW values in the range -0.1 to 4.0. Gradient separations programmed from 5 to 100% (v/v) methanol are suitable for faster separations of compounds with large log KOW values. The standard error in the estimate for the regression models of the predicted log KOW values against literature values are 0.135 log units for the 30% (v/v) methanol-water isocratic system and 0.263 log units for the methanol-water gradient system. Isocratic retention factors predicted from two gradient separations with gradient times of 15 and 45 min afford a poorer fit for the correlation models between log KOW and the estimated retention factors than that of either the above isocratic and gradient models. Plots of the retention factor (log k) as a function of mobile phase composition are generally non-linear. Values of log kw obtained by non-linear extrapolation to a volume fraction of 0% (v/v) methanol do not afford a useful model for estimating log KOW.     

Response surface methodology and support vector machine for the optimization of separation in linear gradient elution

Experimental design methodology was used to optimize the linear gradient elution chromatography. The effect of initial mobile phase composition (φ_in), initial isocratic time (t_in), and gradient time (t_G) on the retention times of phenyl thiohydantoin aminoacids (PTH‐amino acids) was investigated. The experiments were performed according to Box–Behnken experimental design to map the chromatographic response surface. Then multiple linear regression and support vector machine (SVM) methods were used to fit the retention times of solutes. Results shows the SVM models have better ability to predict retention time and used for grid search in factor space. The SVM models were verified, as good agreement was observed between the predicted and experimental values of retention time in the optimal condition.     

A new approach to the prediction of RP-HPLC retention times in gradient elution from isocratic data

Summary A general chromatographic model has been set up starting from a set of equations based on the concept of the velocity of a solute along the column. The composition of the mobile phase is taken into account solely as a numerical factor entering into suitable equations and totally independent of the chemical-properties of the constituents. A few isocratic experimental runs are necessary as input data, and subsequently a small amount of computational effort is sufficient to make predictions of retention times under gradient elution conditions for solutes of whatever chemical structure. The prediction errors are dependent on the steepness of the linear gradient chosen but are, in any case, acceptably low.     

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.     

反相高效液相色谱中流动相线性梯度洗脱条件下溶质保留时间预测的新方法

 在计算溶质的梯度保留时间时 ,根据流动相在色谱柱内的分布规律 ,对溶质在色谱柱内的迁移距离和流动相梯度同时进行校正 ,从而建立了一种预测溶质线性梯度洗脱条件下保留时间的新方法。该方法在不同的仪器系统中 ,对于弱保留和强保留溶质在不同线性梯度洗脱条件下保留时间的预测 ,都具有良好的准确度。以 15种氨基酸和 8种苯的同系物为例 ,该方法对于弱保留溶质保留时间的预测 ,相对平均误差分别为 3 70 %和 4 90 % ,远小于文献方法得到的结果 (2 3 6 1%和 31 16 % ) ;对于强保留溶质保留时间的预测 ,相对平均误差分别为 0 2 1%和6 0 1% ,略小于文献 。     

Error analysis and performance of different retention models in the transference of data from/to isocratic/gradient elution

The transferability of retention data among isocratic and gradient RPLC elution modes is studied. For this purpose, 16 beta-blockers were chromatographed under both isocratic and gradient elution with acetonitrile-water mobile phases. Taking into account the elution mode where the experimental data come from, and the mode where the retention should be predicted, the following combinations are possible: isocratic predictions from (i) isocratic or (ii) gradient experimental designs; and gradient predictions from (iii) isocratic or (iv) gradient data. Each of these possibilities was checked using three retention models that relate the logarithm of the retention factor: (a) linearly and (b) quadratically with the volume fraction of organic solvent, and (c) linearly with a normalised mobile phase polarity parameter. The study was carried out under two different perspectives: a straightforward examination of the prediction errors and the analysis of the uncertainties derived from the variance-covariance matrix of the fitted models. The best combinations of prediction mode and model were: (i)-(b), (ii)-(c), (iii)-(b), and (iv)-(a) or (c).     

New uniform algorithm to predict reversed phase retention values under different gradient conditions

A new numerical emulation algorithm was established to calculate retention parameters in RP-HPLC with several retention times under different linear or nonlinear binary gradient elution conditions and further predict the retention time under any other binary gradient conditions. A program was written according to this algorithm and nine solutes were used to test the program. The prediction results were excellent. The maximum relative error of predicted retention time was less than 0.45%.     

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 peptide retention times in normal-phase liquid chromatography with only a single gradient run.

Previous studies of peptide separation by normal-phase liquid chromatography have shown a linear relationship between the logarithm of the capacity factor and the logarithm of the volume fraction of modifier in the mobile phase. This permitted the use of a model to predict isocratic and gradient retention times based on data obtained by two initial gradient runs. In the present study, chromatographic behavior of 25 peptides in normal-phase liquid chromatography with isocratic elution have been studied and a linear relationship between the slope (S) and intercept [log k(0)] was obtained. This relationship was combined with the algorithm of prediction reported in the previous paper. The prediction of peptide retention times with only a single experimental gradient retention data was investigated.