Development of an inorganic cations retention model in ion chromatography by means of artificial neural networks with different two-phase training algorithms

This paper describes development of artificial neural network (ANN) retention model, which can be used for method development in variety of ion chromatographic applications. By using developed retention model it is possible both to improve performance characteristic of developed method and to speed up new method development by reducing unnecessary experimentation. Multilayered feed forward neural network has been used to model retention behaviour of void peak, lithium, sodium, ammonium, potassium, magnesium, calcium, strontium and barium in relation with the eluent flow rate and concentration of methasulphonic acid (MSA) in eluent. The probability of finding the global minimum and fast convergence at the same time were enhanced by applying a two-phase training procedure. The developed two-phase training procedure consists of both first and second order training. Several training algorithms were applied and compared, namely: back propagation (BP), delta-bar-delta, quick propagation, conjugate gradient, quasi Newton and Levenberg-Marquardt. It is shown that the optimized two-phase training procedure enables fast convergence and avoids problems arisen from the fact that every new weight initialization can be regarded as a new starting position and yield irreproducible neural network if only second order training is applied. Activation function, number of hidden layer neurons and number of experimental data points used for training set were optimized in order to insure good predictive ability with respect to speeding up retention modelling procedure by reducing unnecessary experimental work. The predictive ability of optimized neural networks retention model was tested by using several statistical tests. This study shows that developed artificial neural network are very accurate and fast retention modelling tool applied to model varied inherent non-linear relationship of retention behaviour with respect to mobile phase parameters.     

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.     

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).     

Application of retention modelling to the simulation of separation of organic anions in suppressed ion chromatography

The ion-exchange separation of organic anions of varying molecular mass has been demonstrated using ion chromatography with isocratic, gradient and multi-step eluent profiles on commercially available columns with UV detection. A retention model derived previously for inorganic ions and based solely on electrostatic interactions between the analytes and the stationary phase was applied. This model was found to accurately describe the observed elution of all the anions under isocratic, gradient and multi-step eluent conditions. Hydrophobic interactions, although likely to be present to varying degrees, did not limit the applicability of the ion-exchange retention model. Various instrumental configurations were investigated to overcome problems associated with the use of organic modifiers in the eluent which caused compatibility issues with the electrolytically derived, and subsequently suppressed, eluent. The preferred configuration allowed the organic modifier stream to bypass the eluent generator, followed by subsequent mixing before entering the injection valve and column. Accurate elution prediction was achieved even when using 5-step eluent profiles with errors in retention time generally being less than 1% relative standard deviation (RSD) and all being less than 5% RSD. Peak widths for linear gradient separations were also modelled and showed good agreement with experimentally determined values.     

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.     

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.     

Modelling and prediction of retention in high-performance liquid chromatography by using neural networks

Summary Multi-layer feed-forward neural networks trained with an error back-propagation algorithm have been used to model retention behaviour of liquid chromatography as a function of the composition of the mobile phases. Conventional hydro-organic and micellar mobile phases were considered. Accurate retention modelling and prediction have been achieved using mobile phases defined by two, three and four parameters. With micellar mobile phases, the parameters involved included the concentrations of surfactant and organic modifier, pH and temperature. It is shown that neural networks provide a competitive tool to model varied inherent nonlinear relationships of retention behaviour with respect to the mobile phase parameters. The soft models defined by the weights of the networks are capable of accommodating all types of linear and nonlinear relationships, neural networks being specially useful when the relationships between retention behaviour and the mobile phase parameters are unknown. However, to train neural networks more experimental points than with hard-modelling methods are required, hence the use of the networks is recommended only for those cases where adequate theoretical or empirical models do not exist.     

Optimization of stepwise gradient elution in columns chromatography

Summary A general equation for the final retention of a solute chromatographed under conditions of stepwise gradient elution has been derived. The elution process and the distances travelled by solutes as a function of eluent volume were simulated by computer for the optimization of stepwise gradient prorams from isocratic HPLC data. The validity of the equations was experimentally veritied.     

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.     

Modeling of salt and pH gradient elution in ion‐exchange chromatography

The separation of proteins by internally and externally generated pH gradients in chromatofocusing on ion‐exchange columns is a well‐established analytical method with a large number of applications. In this work, a stoichiometric displacement model was used to describe the retention behavior of lysozyme on SP Sepharose FF and a monoclonal antibody on Fractogel SO₃ (S) in linear salt and pH gradient elution. The pH dependence of the binding charge B in the linear gradient elution model is introduced using a protein net charge model, while the pH dependence of the equilibrium constant is based on a thermodynamic approach. The model parameter and pH dependences are calculated from linear salt gradient elutions at different pH values as well as from linear pH gradient elutions at different fixed salt concentrations. The application of the model for the well‐characterized protein lysozyme resulted in almost identical model parameters based on either linear salt or pH gradient elution data. For the antibody, only the approach based on linear pH gradients is feasible because of the limited pH range useful for salt gradient elution. The application of the model for the separation of an acid variant of the antibody from the major monomeric form is discussed.     

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.     

Multi-criteria decision making development of ion chromatographic method for determination of inorganic anions in oilfield waters based on artificial neural networks retention model

This paper describes the development of ad hoc methodology for determination of inorganic anions in oilfield water, since their composition often significantly differs from the average (concentration of components and/or matrix). Therefore, fast and reliable method development has to be performed in order to ensure the monitoring of desired properties under new conditions. The method development was based on computer assisted multi-criteria decision making strategy. The used criteria were: maximal value of objective functions used, maximal robustness of the separation method, minimal analysis time, and maximal retention distance between two nearest components. Artificial neural networks were used for modeling of anion retention. The reliability of developed method was extensively tested by the validation of performance characteristics. Based on validation results, the developed method shows satisfactory performance characteristics, proving the successful application of computer assisted methodology in the described case study.     

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。     

Poly(ethylene oxide)-bonded stationary phase for capillary ion chromatography

Methyl-capped poly(ethylene oxide) moieties were chemically bonded to silica gel using an amine-reactive modification reagent and evaluated as the stationary phase for ion chromatography. In this work, primary amino groups of an aminopropylsilica packing material were reacted with methyl-PEO₁₂-NHS ester (succinimidyl-{[N-methyl]-dodecaethyleneglycol} ester) in phosphate buffer (pH 7.0) at room temperature. The prepared poly(ethylene oxide)-bonded stationary was evaluated for the separation of inorganic anions, and the retention behavior of inorganic anions on the prepared stationary phase was examined. The elution order of the investigated anions was the same as that observed in common ion chromatography. Both cations and anions of the eluent affected the retention of the analyte anions. Ion exchange was involved for the retention of analyte anions, although the present stationary phase does not possess any discrete ion-exchange sites. The stationary phase was applied to the separation of trace anions contained in tap water and a rock salt.     

Optimization of artificial neural networks used for retention modelling in ion chromatography

The aim of this work is the development of an artificial neural network model, which can be generalized and used in a variety of applications for retention modelling in ion chromatography. Influences of eluent flow-rate and concentration of eluent anion (OH-) on separation of seven inorganic anions (fluoride, chloride, nitrite, sulfate, bromide, nitrate, and phosphate) were investigated. Parallel prediction of retention times of seven inorganic anions by using one artificial neural network was applied. MATLAB Neural Networks ToolBox was not adequate for application to retention modelling in this particular case. Therefore the authors adopted it for retention modelling by programming in MATLAB metalanguage. The following routines were written; the division of experimental data set on training and test set; selection of data for training and test set; Dixon's outlier test; retraining procedure routine; calculations of relative error. A three-layer feed forward neural network trained with a Levenberg-Marquardt batch error back propagation algorithm has been used to model ion chromatographic retention mechanisms. The advantage of applied batch training methodology is the significant increase in speed of calculation of algorithms in comparison with delta rule training methodology. The technique of experimental data selection for training set was used allowing improvement of artificial neural network prediction power. Experimental design space was divided into 8-32 subspaces depending on number of experimental data points used for training set. The number of hidden layer nodes, the number of iteration steps and the number of experimental data points used for training set were optimized. This study presents the very fast (300 iteration steps) and very accurate (relative error of 0.88%) retention model, obtained by using a small amount of experimental data (16 experimental data points in training set). This indicates that the method of choice for retention modelling in ion chromatography is the artificial neural network.     

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).     

Some insights on the description of gradient elution in reversed‐phase liquid chromatography

The so‐called “fundamental equation for gradient elution” has been used for modeling the retention in gradient elution. In this approach, the instantaneous retention factor (k) is expressed as a function of the change in the modifier content (φ(t_s)), t_s being the time the solute has spent in the stationary phase. This approach can only be applied at constant flow rate and with gradients where the elution strength depends on the column length following a f(t?l/u) function, u being the linear mobile phase flow rate, and l the distance from the column inlet to the location where the solute is at time t measured from the beginning of the gradient. These limitations can be solved by using the here called “general equation for gradient elution”, where k is expressed as a function of φ(t,l). However, this approach is more complex. In this work, a method that facilitates the integration of the “general equation” is described, which allows an approximate analytical solution with the quadratic retention model, improving the predictions offered by the “linear solvent strength model.” It also offers direct information about the changes in the instantaneous modifier content and retention factor, and gives a meaning to the gradient retention factor.     

Statistical scanning method for the optimization of gradient elution high performance liquid chromatography

Summary A computer-assisted method is presented for the optimization of separation in gradient elution reversed-phase HPLC. The method is based on a polynomial estimation from nine preliminary experiments according to a two-factor (initial solvent composition C and gradient time T) rectangular design. This is followed by a two-dimension computer scanning technique. Resolution is used as the selection criterion. Good agreement was obtained between predicted data and experimental results.