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.     

离子色谱线性梯度淋洗分离阴离子的计算机模拟

建立了使用氢氧化钠淋洗液时用计算机模拟离子色谱梯度淋洗分离阴离子的新方法,研究了在线性梯度淋洗过程中不同时间阴离子在色谱柱中的位置及所在位置的淋洗液浓度,得出阴离子在不同时间的容量因子、迁移速度,通过积分得到保留时间。再根据离子色谱峰峰形变化的规律,得到色谱峰峰形的参数。模拟色谱图保留值与实验值的相对误差小于5%,模拟色谱图的色谱峰峰形与实验所得到的色谱图的色谱峰峰形也非常接近。     

A general strategy for performing temperature-programming in high performance liquid chromatography--prediction of segmented temperature gradients

In the present work it is shown that the linear elution strength (LES) model which was adapted from temperature-programming gas chromatography (GC) can also be employed to predict retention times for segmented-temperature gradients based on temperature-gradient input data in liquid chromatography (LC) with high accuracy. The LES model assumes that retention times for isothermal separations can be predicted based on two temperature gradients and is employed to calculate the retention factor of an analyte when changing the start temperature of the temperature gradient. In this study it was investigated whether this approach can also be employed in LC. It was shown that this approximation cannot be transferred to temperature-programmed LC where a temperature range from 60°C up to 180°C is investigated. Major relative errors up to 169.6% were observed for isothermal retention factor predictions. In order to predict retention times for temperature gradients with different start temperatures in LC, another relationship is required to describe the influence of temperature on retention. Therefore, retention times for isothermal separations based on isothermal input runs were predicted using a plot of the natural logarithm of the retention factor vs. the inverse temperature and a plot of the natural logarithm of the retention factor vs. temperature. It could be shown that a plot of lnk vs. T yields more reliable isothermal/isocratic retention time predictions than a plot of lnk vs. 1/T which is usually employed. Hence, in order to predict retention times for temperature-gradients with different start temperatures in LC, two temperature gradient and two isothermal measurements have been employed. In this case, retention times can be predicted with a maximal relative error of 5.5% (average relative error: 2.9%). In comparison, if the start temperature of the simulated temperature gradient is equal to the start temperature of the input data, only two temperature-gradient measurements are required. Under these conditions, retention times can be predicted with a maximal relative error of 4.3% (average relative error: 2.2%). As an example, the systematic method development for an isothermal as well as a temperature gradient separation of selected sulfonamides by means of the adapted LES model is demonstrated using a pure water mobile phase. Both methods are compared and it is shown that the temperature-gradient separation provides some advantages over the isothermal separation in terms of limits of detection and analysis time.     

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.     

Retention time and peak width in the combined pH/organic modifier gradient high performance liquid chromatography

The purpose of this work was to test the applicability of the current theory to predict the peak retention time and the peak width in the combined pH/organic modifier gradient reversed phase high performance liquid chromatography (RP HPLC). A series of 38 isocratic measurements have been conducted for a wide range of pH and methanol contents for ketoprofen (weak acid) and papaverine (weak base). It served to find the model describing dependence of retention factor and the height equivalent of a theoretical plate (HETP) on pH and organic modifier content. The information gathered in the isocratic mode was used to simulate retention times and peak widths for 30 various methanol gradients, 25 pH gradients, and 3 combined pH/methanol gradients. The simulations were compared with the experimental data. We also proposed a simplified version of this model that was parameterized based on 12 initial organic modifier gradients carried out for different pHs and for the 20 min and 60 min gradient development times. The full and the simplified model described the experimental data very well. In conclusion, the proposed modeling approach allowed predicting analyte retention times and peak width for various pH and organic modifier changes. Its simplified version required only 12 initial experiments and seems to be very promising in the optimization RP HPLC separations for complex samples and for conditions providing peak compression.     

Optimisation of the separation of herbicides by linear gradient high performance liquid chromatography utilising artificial neural networks

An artificial neural network (ANN) was employed to model the chromatographic response surface for the linear gradient separation of 10 herbicides that are commonly detected in storm run-off water in agricultural catchments. The herbicides (dicamba, simazine, 2,4-D, MCPA, triclopyr, atrazine, diuron, clomazone, bensulfuron-methyl and metolachlor) were separated using reverse phase high performance liquid chromatography and detected with a photodiode array detector. The ANN was trained using the pH of the mobile phase and the slope of the acetonitrile/water gradient as input variables. A total of nine experiments were required to generate sufficient data to train the ANN to accurately describe the retention times of each of the herbicides within a defined experimental space of mobile phase pH range 3.0-4.8 and linear gradient slope 1-4% acetonitrile/min. The modelled chromatographic response surface was then used to determine the optimum separation within the experimental space. This approach allowed the rapid determination of experimental conditions for baseline resolution of all 10 herbicides. Illustrative examples of determination of these components in Milli-Q water, Sydney mains water and natural water samples spiked at 0.5-1 μg/L are shown. Recoveries were over 70% for solid-phase extraction using Waters Oasis^® HLB 6 cm³ cartridges.     

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.     

Theoretical background of monolithic short layer ion-exchange chromatography for separation of charged large biomolecules or bioparticles

The retention and peak spreading in linear gradient elution of charged large biomolecules were investigated by using numerical simulations. Oligo-DNA separation by monolithic anion-exchange chromatography was chosen as a model system. The peak width and the retention were well predicted by using the parameters obtained by gradient elution experiments at different gradient slopes. As the distribution coefficient at the peak retention volume K_R decreases with increasing molecular size, the peak became sharper for larger DNAs. This is due to very large effective charge (binding site) values of large DNAs (20–60). The peak width was well correlated with K_R based on the model equation developed for linear gradient elution of proteins. It was shown that the monolithic disk is best suited for very large charged biomolecule separations at high flow velocities with shallow gradients slopes.     

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 protein retention at gradient elution conditions in ion-exchange chromatography.

This work presents a prediction procedure for protein retention in ion-exchange chromatography, where two linear gradient experiments of different length give the protein retention time at other linear gradients. The procedure predicts the retention time of early and late eluting proteins with similar precision and predictions by extrapolation deviate approximately 3% or less from the experimental retention times. By using the ionic strength, this procedure predicts protein retention times obtained with divalent ions in the eluent more accurately than a well-established procedure that uses the protein co-ion concentration.     

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.     

Application of artificial neural networks for gradient elution retention modelling in ion chromatography

Gradient elution in ion chromatography (IC) offers several advantages: total analysis time can be significantly reduced, overall resolution of a mixture can be increased, peak shape can be improved (less tailing) and effective sensitivity can be increased (because there is little variation in peak shape). More importantly, it provides the maximum resolution per time unit. The aim of this work was the development of a suitable artificial neural network (ANN) gradient elution retention model that can be used in a variety of applications for method development and retention modelling of inorganic anions in IC. Multilayer perceptron ANNs were used to model the retention behaviour of fluoride, chloride, nitrite, sulphate, bromide, nitrate and phosphate in relation to the starting time of gradient elution and the slope of the linear gradient elution curve. The advantage of the developed model is the application of an optimized two-phase training algorithm that enables the researcher to make use of the advantages of first- and second-order training algorithms in one training procedure. This results in better predictive ability, with less time required for the calculations. The number of hidden layer neurons and experimental data points used for the training set were optimized in terms of obtaining a precise and accurate retention model with respect to minimization of unnecessary experimentation and time needed for the calculation procedures. This study shows that developed, ANNs are the method of first choice for retention modelling of inorganic anions in IC.     

Methodology for porting retention prediction data from old to new columns and from conventional-scale to miniaturised ion chromatography systems

Several procedures are available for simulating and optimising separations in ion chromatography (IC), based on the application of retention models to an extensive database of analyte retention times on a wide range of columns. These procedures are subject to errors arising from batch-to-batch variability in the synthesis of stationary phases, or when using a column having a different diameter to that used when the database was acquired originally. Approaches are described in which the retention database can be recalibrated to accommodate changes in the stationary phase (ion-exchange selectivity coefficient and ion-exchange capacity) or in the column diameter which lead to changes in phase ratio. The entire database can be recalibrated for all analytes on a particular column by performing three isocratic separations with two analyte ions. The retention data so obtained are then used to derive a "porting" equation which is employed to generate the required simulated separation. Accurate prediction of retention times is demonstrated for both anions and cations on 2mm and 0.4mm diameter columns under elution conditions which consist of up to five sequential isocratic or linear gradient elution steps. The proposed approach gives average errors in retention time prediction of less than 3% and the correlation coefficient was 0.9849 between predicted and observed retention times for 344 data points comprising 33 anionic or cationic analytes, 5 column internal diameters and 8 complex elution profiles.     

Retention profiles and mechanism of anion separation on latex-based pellicular ion exchanger in ion chromatography

A retention model based on stoichiometric approach has been developed in order to describe analyte retention of anions on latex-based pellicular ion exchanger. The chromatographic process entails two stepwise and complex equilibria, first is ion-pair forming of analyte or eluent ion with ion-exchange sites under the effect of electrostatic forces due to the sulfonic layer behind the aminated functional groups of stationary phase. Second component is the ion-exchange between the analyte and eluent ions. As a new parameter of the fractional electrostatic coefficient of the ion exchange capacity was introduced to develop retention profiles of anions. Analysis of the dependence of the capacity factors on the eluent concentrations at different values of fractional coefficient shed light on the possible complex mechanism. Extensive experimental retention data were obtained for 14 anions (formate, acetate, propionate, pyruvate, lactate, chloride, nitrate, oxalate, malonate, succinate, tartarate, fumarate, maleate, sulphate) using hydroxide eluents of varying concentration. The ion-pair formation and ion-exchange selectivity constants for analyte and eluent species are determined using derived retention equation from experimental data by nonlinear iterative calculation. The model was utilized to predict retention data under elution conditions of practical importance. The predicted and obtained retention factors are in good agreement, which confirms the predictive power of the model.     

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.     

Limits of multi-linear gradient optimisation in reversed-phase liquid chromatography

The concept of limiting peak purity was applied to quantify the degree of completion of the separation capability of a chromatographic system using multi-linear gradients. The objective was to check whether the complexity of a gradient program deserves be increased to enhance resolution by inserting more linear segments, or on the contrary, no significant improvements can be expected under more complex gradients. A set of 19 isoindole derivatives of primary amino acids was selected to test the performance of isocratic, single linear and multi-linear gradients. Accurate simulated chromatograms were obtained via numerical integration of the general equation of gradient elution, using pre-established start and end conditions of the gradient program. The overall peak purity was selected as objective function. Good--although not baseline--resolution was achieved with an optimal trilinear gradient. Excellent agreement between experimental and predicted optimal chromatograms was found. With the proposed approach, a degree of completion of the separation capability of the chromatographic system of 21.2, 49.7, 81.5 and 88.5% was accomplished with optimal gradients with one, two, three and four segments, respectively. More complex gradients did not enhance the latter figure significantly. Also, multi-linear gradients gave rise to more benefits than complementary gradients.     

Simultaneous determination of inorganic anions and cations in explosive residues by ion chromatography

A non-suppressed ion chromatographic method by connecting anion-exchange and cation-exchange columns directly was developed for the separation and determination of five inorganic anions (sulfate, nitrate, chloride, nitrite, and chlorate) and three cations (sodium, ammonium, and potassium) simultaneously in explosive residues. The mobile phase was composed of 3.5mM phthalic acid with 2% acetonitrile and water at flow rate of 0.2 mL/min. Under the optimal conditions, the eight inorganic ions were completely separated and detected simultaneously within 16 min. The limits of detection (S/N=3) of the anions and cations were in the range of 50-100 microg/L and 150-320 microg/L, respectively, the linear correlation coefficients were 0.9941-0.9996, and the R.S.D. of retention time and peak area were 0.10-0.29% and 5.65-8.12%, respectively. The method was applied successfully to the analysis of the explosive samples with satisfactory results.     

Fast ion chromatography using short anion exchange columns

A fast ion chromatographic system is described which uses shorter column lengths and compares various eluent profiles in order to maximise the performance without sacrificing the chromatographic resolution. Both isocratic and gradient elution profiles were considered to find the most efficient mode of separation. The separation and determination of seven target anions (chloride, chlorate, nitrate, chromate, sulfate, thiocyanate and perchlorate) was achieved using a short (4 mm ID, 50 mm long) column packed with Dionex AS20 high-capacity anion exchange material. A hydroxide eluent was used at an initial concentration of 25 mM (at a flow-rate of 1.0 mL/min) and two performance maxima were found. The maximum efficiency occurred at a normalised gradient ramp rate of 5 mM/t₀, resulting in a peak capacity of 16, while the fastest separation (<3 min) occurred at a normalised ramp rate of 30 mM/t₀. The retention time, peak width and resolution using the different eluent profiles on varying column lengths is also compared. Further investigations in this study determined that the highest peak capacity separation under gradient conditions could be approximated using an isocratic separation. The advantage of using this novel approach to approximate the maximum efficiency separation removes the need for column re-equilibration that is required for gradient elution resulting in faster analyses and enhanced sample throughput, with benefits in particular for multidimensional chromatography.