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.     

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.     

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.     

The gradient volume principle for fast evaluation of optimum conditions for isocratic analysis

Summary The paper describes by simple experiments in a pragmatical way by easy rules of thumbs gradient optimization. Besides selection of the stationary phase and initial and final conditions the two other important variables are program time and eluent flow rate. It is demonstrated, that when the product of both, the gradient volume, is kept constant, the solutes are always eluted with the same eluent composition at column outlet. At constant gradient volume, peak broadening depends on flow rate and on the eluent properties (viscosity) at which the solutes elute, and on the time the solutes spend in the column. Because peak broadening increases with increasing gradient volume, the peak capacity in gradient elution shows an optimum at gradient volumes around 15 empty column volumes (program times 45 to 60 min at flow rates of 1 ml/min with standard columns).Gradient elution can also be used for fast evaluation of optimum eluent composition for isocratic analysis. This procedure requires a calibration of the equipment for determination of eluent composition at column outlet. The sample is chromatographed in a standard gradient run of 10 to 15 empty column volumes. The eluent composition at which the solute of interest elutes during the gradient is used for isocratic analysis, where the k' value of this solute will then be around 2.Part of Ph. D. Thesis H. Elgass, Saarbrücken, 1978, present address Hewlett-Packard, Waldbronn, FRG. In part presented at Eastern Analytical Symposium, New York, 1982.     

Response surface methodology to optimize gradient ion chromatographic separation of inorganic anions and organic acids in tobacco leaves

The separation optimization of nine organic and inorganic anions in tobacco leaves using gradient ion chromatography by response surface methodology was investigated.In order to achieve this goal the usefulness of the chromatographic response function(CRF) for the evaluation of the two different chromatographic performance goals(resolution and analysis time) was tested. The experiments were performed according to a Box-Behnken design response surface experimental design.     

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.     

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.     

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.     

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.     

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.     

Optimization of stepwise gradient elution in reversed-phase chromatography

Summary Equations describing multi-step gradient elution with a mobile phase of constant composition in each step were derived. These equations useful for calculating the retention volumes in both gradient HPLC and TLC were derived on the basis of the relationship between the isocratic capacity factor and the volume fraction of the organic modifier. The validity of the equations was experimentally verified in a LiChrosorbRP-18-water/methanol system for 11 methyl- and chlorobenzenes and phenols. A satisfactory agreement between the theoretical and experimental k′ values was found.     

Theoretical study of preparative chromatography using closed-loop recycling with an initial gradient

Complementing classical isocratic elution, several more sophisticated operating modes have been proposed and are applied in preparative chromatography in order to improve performance. One such approach is gradient elution, where the solvent strength is altered by varying the fraction of a modifier added to the mobile phase to enhance selectivity and to achieve faster elution. Another useful technique is closed-loop recycling, allowing better peak resolution and increased yields. This study focuses on a modified new scheme which incorporates the advantages of both gradient elution and closed-loop recycling for the separation of a ternary mixture where the intermediately eluting component is the target. A parametric study was carried out using typical adsorption isotherm parameters to elucidate the effects of varying loading factors and parameters specific to the two basic operational modes on production rates and yields. A comparison was also made between the proposed scheme and conventional techniques. It was found that the studied scheme could exploit increased column loadings and offers significantly higher production rates.     

Computational method for modeling of gradient separation in ion-exchange chromatography

A model for the simulation of the gradient separation in ion-exchange chromatography is presented. It is based on discontinuous plate model and simulates the distribution of analytes in the ion-exchange column during the separation process. It enables calculations of chromatograms for the analytes with integer and non-integer effective charges under complex gradient profiles. Equilibrium concentrations of all analytes are calculated using the same mathematical equations and expressions regardless of the effective charge on the analyte. The main parameters required for the simulations have to be determined under isocratic elution. The suitability of the model was tested with different types of gradients. A comparison of retention times and chromatograms shows that reliable predictions for all tested gradients are achieved. The observed average of the absolute values of the relative errors of the retention times obtained for any analyte in the present study from the calculated chromatograms is below 4%, while the average error considering all analytes in the study is below 2%.     

Peak capacity optimization in comprehensive two dimensional liquid chromatography: a practical approach

In this work we develop a practical approach to optimization in comprehensive two dimensional liquid chromatography (LC x LC) which incorporates the important under-sampling correction and is based on the previously developed gradient implementation of the Poppe approach to optimizing peak capacity. The Poppe method allows the determination of the column length, flow rate as well as initial and final eluent compositions that maximize the peak capacity at a given gradient time. It was assumed that gradient elution is applied in both dimensions and that various practical constraints are imposed on both the initial and final mobile phase composition in the first dimension separation. It was convenient to consider four different classes of solute sets differing in their retention properties. The major finding of this study is that the under-sampling effect is very important and causes some unexpected results including the important counter-intuitive observation that under certain conditions the optimum effective LC x LC peak capacity is obtained when the first dimension is deliberately run under sub-optimal conditions. In addition, we found that the optimum sampling rate in this study is rather slower than reported in previous studies and that it increases with longer first dimension gradient times.     

Turbidimetric titration and gradient high-performance liquid chromatography of polystyrene samples

Summary Polystyrene samples of narrow molecular-weight distribution have been eluted according to their molecular weight from columns packed with bare silica Si50, phenyl, or C18 bonded phase by gradients of methanol and tetrahydrofuran (THF) or ofiso-octane and THF. Among the six combinations investigated,iso-octane/THF with a silica column formed a proper normal-phase system whereas methanol/THF with a C18 column formed a proper reversed-phase system. The combinations of C18 column andiso-octane/THF or of Si50 column and methanol/THF gradient did not correspond to the approved polarity rules in high-performance liquid chromatography but were nevertheless effective in separating polystyrene mixtures by molecular weight. Methanol andiso-octane are nonsolvents for polystyrene whereas THF is a solvent. The solubility of polystyrene as a function of molecular weight and concentration was determined by means of turbidimetric titration of solutions in THF with the nonsolvents used in the gradients. The solubility and elution characteristics were almost identical on C18 columns or in methanol/THF combinations. The elution from phenyl bonded phase and Si50 columns usingiso-octane/THF gradients required more THF than the solubility experiments. Information is also given on the occurrence of multimodal elution patterns.     

Isocratic and gradient elution in micellar liquid chromatography with Brij‐35

Polyoxyethylene(23)lauryl ether (known as Brij‐35) is a nonionic surfactant, which has been considered as an alternative to the extensively used in micellar liquid chromatography anionic surfactant sodium lauryl (dodecyl) sulfate, for the analysis of drugs and other types of compounds. Brij‐35 is the most suitable nonionic surfactant for micellar liquid chromatography, owing to its commercial availability, low cost, low toxicity, high cloud temperature, and low background absorbance. However, it has had minor use. In this work, we gather and discuss some results obtained in our laboratory with several β‐blockers, sulfonamides, and flavonoids, concerning the use of Brij‐35 as mobile phase modifier in the isocratic and gradient modes. The chromatographic performance for purely micellar eluents (with only surfactant) and hybrid eluents (with surfactant and acetonitrile) is compared. Brij‐35 increases the polarity of the alkyl‐bonded stationary phase and its polyoxyethylene chain with the hydroxyl end group allows hydrogen‐bond interactions, especially for phenolic compounds. This offers the possibility of using aqueous solutions of Brij‐35 as mobile phases with sufficiently short retention times. The use of gradients of acetonitrile to keep the concentration of Brij‐35 constant is another interesting strategy that yields a significant reduction in the peak widths, which guarantee high resolution.     

The theory of gradient elution under hydrostatic equilibrium in liquid chromatography. Part 3: Using solvents of different densities

Gradient elution under hydrostatic equilibrium is extended to the treatment of the case where the two liquids have different densities. Analytic expressions are derived only for the cases where both mixing chamber and reservoir have constant cross-sectional areas. As in the case where the densities of the liquids are equal, pressigned concentration gradients can be duplicated quite satisfactorily by combining a mixing chamber having a constant cross-sectional area and a reservoir having an area which changes linearly with reservoir height. A numerical example is given to illustrate the use of the derived equations.     

Optimization of two-dimensional gradient liquid chromatography separations

An almost orthogonal comprehensive two-dimensional liquid chromatography was developed for the separation of phenolic and flavone natural antioxidants by using combinations of a polyethylene glycol silica micro-column in the first dimension and a porous-shell fused-core C18 column in the second dimension, both in the reversed-phase mode. System orthogonality was improved using parallel gradients of acetonitrile in buffered mobile phase. A new approach was proposed to optimize matching segmented gradient profiles in the two dimensions. An algorithm was developed for automatic corrections of the shifts in retention in the second dimension induced by the parallel two-dimensional gradient operation technique. Using the porous-shell C18 column in the second dimension at elevated temperature (60 degrees C) and high pressure (480 bar) with optimized segmented profiles of the parallel gradients in the two dimensions, the overall separation time for comprehensive LC x LC was reduced to 30 min.     

Probing the kinetic performance limits for ion chromatography. II. Gradient conditions for small ions

A gradient kinetic plot method is used for theoretical characterisation of the performance of polymeric particulate anion exchange columns for gradient separations of small inorganic anions. The method employed requires only information obtained from a series of isocratic column performance measurements and in silico predictions of retention time and peak width under gradient conditions. Results obtained under practically constrained conditions provide parameters for the generation of high peak capacities and rapid peak production for fast analysis to be determined. Using this prediction method, a maximum theoretical peak capacity of 84 could be used to achieve separation of 26 components using a 120 min gradient (R_s > 1). This approach provides a highly convenient tool for development of both mono- and multidimensional ion chromatography (IC) methodologies as it yields comprehensive understanding of the influence of gradient slope, analysis time, column length and temperature upon kinetically optimised gradient performance.