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%).     

Evaluation of separation in gradient elution ion chromatography by combining several retention models and objective functions

In this work, three different methods for modeling of gradient retention were combined with several optimization objective functions in order to find the most appropriate combination to be applied in ion chromatography method development. The system studied was a set of seven inorganic anions (fluoride, chloride, nitrite, sulfate, bromide, nitrate, and phosphate) with a KOH eluent. The retention modeling methods tested were multilayer perceptron artificial neural network (MLP-ANN), radial-basis function artificial neural network (RBF-ANN), and retention model based on transfer of data from isocratic to gradient elution mode. It was shown that MLP retention model in combination with the objective function based on normalized retention difference product was the most adequate tool for optimization purposes.     

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.     

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.     

梯度液相色谱保留时间公式在梯形梯度洗脱研究中的应用

根据前期得到的梯度液相色谱保留时间计算公式,在不指定溶剂强度模型形式的前提下,探讨了梯形梯度洗脱的一些特点。对于溶质在梯形梯度坡度上流出时的情形,推导得到溶质流出色谱柱所对应的流动相组成(φ_R)随梯度斜率(B)变化的表达式。该公式表明,在该情形中φ_R将会随着B值的增加而增加。对于溶质在梯形梯度最后一个等度区间流出时的情形,如果初始和终止流动相组成保持不变而仅有梯度的斜率发生变化时,从理论上证明了溶质保留时间(t_R)与梯度斜率的倒数(1/B)之间呈线性关系。实验中以C18色谱柱为固定相,甲醇-水为流动相,联苯为样品,测定了不同流动相组成以及梯形梯度条件下的保留时间,所得到的实验值与理论值吻合,从而验证了理论方法的正确性。     

Novel criteria for fast searching for optimal method in gradient ion chromatography: an integrated approach

In this article, an integrated approach for prediction and optimization in ion chromatography (IC) was presented. The approach provides a fast and reliable insight in the elution behavior of an IC system. The predictions are based on a mathematical model that predicts ion retentions (for both isocratic and gradient modes) by using an empirical isocratic model. Other chromatographic values significant for the optimal elution conditions (resolution, peak asymmetry) are calculated quickly and easily from the predicted retention values of characteristic points of a chromatographic peak. Every day, IC users might find this approach a suitable tool for finding optimal IC elution conditions in a given system.     

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.     

Chromatographic behaviour of low molar-mass polyesters in normal-phase high-performance liquid chromatography

Summary The normal-phase chromatographic retention behaviour of polyesters on bare silica and on a polymer-based polyamine (PA) column has been studied with a variely of binary mobile phases under isocratic conditions. The dependence of experimental retention data on the degree of polymerization (p) and on mobile phase composition (φ) was characterized by to an approach developed by Jandera et al. The bulky repeating unit and the relatively highly polar end groups of the polyesters both had a large influence on retention behaviour. The two effects in combination explain the molar-mass-independent retention observed experimentally at a particular mobile phase composition for all the mobile phase—stationary phase combinations investigated. These conditions were found to be independent of the type of end group. End group separation on a silica column improves when the polarity of the less polar solvent is increased. End group separation is better on the PA column because of a greater difference between the adsorption energy of the alcohol and acid end groups. Better prediction of retention data on the PA column was achieved by use of an approach which assumes two different types of adsorption site. Results enabled further understanding of retention behaviour in normalphase gradient polymer-elution chromatography (NPGPEC) and explained both the dependence of the order of elution onp and differences between the end-group selectivity of different systems.     

Retention models for isocratic and gradient elution in reversed-phase liquid chromatography

One- and multi-variable retention models proposed for isocratic and/or gradient elution in reversed-phase liquid chromatography are critically reviewed. The thermodynamic, exo-thermodynamic or empirical arguments adopted for their derivation are presented and discussed. Their connection to the retention mechanism is also indicated and the assumptions and approximations involved in their derivation are stressed. Special attention is devoted to the fitting performance of the various models and its impact on the final predicted error between experimental and calculated retention times. The possibility of using exo-thermodynamic retention models for prediction under gradient elution is considered from a practical point of view. Finally, the use of statistical weights in the fitting procedure of a retention model and its effect on the calculated elution times as well as the transferability of retention data among isocratic and gradient elution modes are also examined and discussed.     

Development of an ion chromatographic gradient retention model from isocratic elution experiments

When facing separation problems in ion chromatography, chromatographers often lack guidelines to decide a priori if isocratic elution will give enough separation in a reasonable analysis time or a gradient elution will be required. This situation may be solved by the prediction of retention in gradient elution mode by using isocratic experimental data. This work describes the development of an ion chromatographic gradient elution retention model for fluoride, chloride, nitrite, bromide, nitrate, sulfate and phosphate by using isocratic experimental data. The isocratic elution retention model was developed by applying a polynomial relation between the logarithm of the retention factor and logarithm of the concentration of competing ions; the gradient elution retention model was based on the stepwise numerical integration of the corresponding differential equation. It was shown that the developed gradient elution retention model was not significantly affected by transferring data form isocratic experiment. The root mean squared prediction error for gradient elution retention model was between 0.0863 for fluoride and 0.7027 for bromide proving a very good predictive ability of developed gradient elution retention model.     

Prediction of the chromatographic signal in gradient elution ion chromatography

This study describes the development of a signal prediction model in gradient elution ion chromatography. The proposed model is based on a retention model and generalized logistic peak shape function which guarantees simplicity of the model and its easy implementation in method development process. Extensive analysis of the model predictive ability has been performed for ion chromatographic determination of bromate, nitrite, bromide, iodide, and perchlorate, using KOH solutions as eluent. The developed model shows good predictive ability (average relative error of gradient predictions 1.94%). The developed model offers short calculation times as well as low experimental effort (only nine isocratic runs are used for modeling).     

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。     

Characterization of hybrid organo-silica monoliths for possible application in the gradient elution of peptides

We characterized thermally polymerized organo-silica hybrid monolithic capillaries to test their applicability in the gradient elution of peptides. We have used a single-pot approach utilizing 3-(methacryloyloxy)propyltrimethoxysilane (MPTMS), ethylene dimethacrylate (EDMA), and n-octadecyl methacrylate (ODM) as functional monomers. The organo-silica monolith containing MPTMS and EDMA was compared with the stationary phase prepared by adding ODM to the original polymerization mixture. Column prepared using a three-monomer system provided a lower accessible volume of flow-through pores, a higher proportion of mesopores, and higher efficiency. We utilized isocratic and gradient elution data to predict peak widths in gradient elution. Both protocols provided comparable results and can be used for peptide peak width prediction. However, applying gradient elution data for peak width prediction seems simpler. Finally, we tested the effect of gradient time on achievable peak capacity in the gradient elution of peptides with a column prepared with a three-monomer system providing a higher peak capacity. However, the performance of hybrid organo-silica monolithic stationary phases in gradient elution of peptides must be improved compared to other monolithic stationary phases. The limiting factor is column efficiency in highly aqueous mobile phases, which needs to be focused on.     

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.     

Retention Behavior of Anti-Arrhythmic Drugs on the Chromolith Performance RP 18 Column. Liquid Chromatographic Determination of Mexiletine Hydrochloride

The retention behavior in liquid chromatography of a series of anti-arrhythmic drugs is described. Chromatographic analysis was performed on a Chromolith Performance ODS column with acetonitrile–phosphate buffer mixtures as mobile phases. The effects of the proportion of organic solvent (from 20 to 90%), phosphate buffer pH (from 2.73 to 7.5), flow rate (from 1 to 6 mL min^–1), and isocratic or gradient elution on the retention of the compounds was studied. Mexiletine hydrochloride was determined in the pure substance and in capsules by isocratic liquid chromatography with 20:80 (v/v) acetonitrile–0.007 M phosphate buffer, pH 3.0, as mobile phase at 2 mL min^–1. Methanol was found to be a suitable solvent for extraction of the active substance from capsules. The calibration plot was linear (r=0.9999) in the concentration range 1.0 to 6.0 g mL^–1. The proposed method is selective, precise (RSD=0.37%), and accurate (recovery=100.08%).Revised: 28 January and 2 March 2004     

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。     

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.     

Modeling of overloaded gradient elution of nociceptin/orphanin FQ in reversed-phase liquid chromatography

The Reversed-phase (RP) gradient elution chromatography of nociceptin/orphanin FQ (N/OFQ), a neuropeptide with many biological effects, has been modeled under linear and non-linear conditions. In order to do this, the chromatographic behavior has been studied under both linear and nonliner conditions under isocratic mode at different mobile phase compositions--ranging from 16 to 19% (v/v) acetonitrile (ACN) in aqueous trifluoracetic acid (TFA) 0.1% (v/v)-on a C-8 column. Although the range of mobile phase compositions investigated was quite narrow, the retention factor of this relatively small polypeptide (N/OFQ is a heptadecapeptide) has been found to change by more than 400%. In these conditions, gradient operation resulted thus to be the optimum approach for non-linear elution. As the available amount of N/OFQ was extremely reduced (only a few milligrams), the adsorption isotherms of the peptide, at the different mobile phase compositions examined, have been measured through the so-called inverse method (IM) on a 5 cm long column. The adsorption data at different mobile phase compositions have been fitted to several models of adsorption. The dependence of the isotherm parameters on the mobile phase composition was modeled by using the linear solvent strength (LSS) model and a generalized Langmuir isotherm that includes the mobile phase composition dependence. The overloaded gradient separation of N/OFQ has been modeled by numerically solving the equilibrium-dispersive (ED) model of chromatography under a selected gradient elution mode, on the basis of the previously determined generalized Langmuir isotherm. The agreement between theoretical calculations and experimental overloaded band profiles appeared reasonably accurate.