Retention In Gradient Elution Research Articles

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(ts )), ts 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.

Retention and bandwidths prediction in fast gradient liquid chromatography. Part 2—Core–shell columns

Recently, we confirmed that the well-established theory of gradient elution can be employed for prediction of retention in gradient elution from the isocratic data, method development and optimization in fast gradient chromatography employing short packed fully porous and monolithic columns and gradient times in between 1 and 2min, or even less. In the present work, we extended this study to short core–shell reversed-phase columns. We investigated the effects of the specification of the stationary phase in the core–shell structure on the prediction of gradient retention data. Two simple retention models describing the effects of the mobile phase on the retention by two-parameter equations yield comparable accuracy and can be used for prediction of elution times. The log–log model provides improved prediction of gradient bandwidths, especially for less retained compounds. A more sophisticated three-parameter model did not offer significant improvement of prediction. We compared the efficiency, selectivity and peak capacity of fast gradient separations of alkylbenzenes, phenolic acids and flavones on seven core shell columns with different lengths and chemistry of bonded shell stationary phase. Within the limits dictated by a fixed short separation time, appropriate adjustment of the range of the composition of mobile phase during gradient elution is the most efficient means to optimize the gradient separation. The gradient range affects sample bandwidths equally or even more significantly than the column length. Both 5-cm and 3-cm core–shell columns may provide comparable peak capacity in a fixed short gradient time.

Possibilities of retention prediction in fast gradient liquid chromatography. Part 1: Comparison of separation on packed fully porous, nonporous and monolithic columns

Due to ever increasing importance of short analysis times in modern HPLC practice, fast gradient elution is becoming widely used both in one-dimensional and two-dimensional separations, especially in the second dimension where the speed of separation is of primary importance. For method development and optimization, prediction of retention in gradient elution from the isocratic data is very important. This is principally possible using the well-established theory of gradient elution, especially for reversed-phase separations. Feasibility of these approaches has been proven in conventional liquid chromatography and commercial prediction software is available for this purpose. However, fast gradient chromatography employing short columns and gradient times in between 1 and 2min or even less, impose additional stringent demands on the accuracy of prediction, due to rapid changes in mobile phase composition and increased role of extra-column contributions and instrumental dwell volume on the retention. In the present work, possibilities of prediction of the gradient elution times from the isocratic data measured only at two mobile phase concentrations were investigated in fast chromatography of alkylbenzenes, phenylurea and triazine pesticides on five columns differing in lengths: two monolithic ones and three packed with particles of different size. In the second dimension, gradient times are strongly restricted by the short cycle frequency. The effects of the flow-rate on the elution times, on the accuracy of their prediction and on peak capacity were studied under time constraint conditions. Gradient theory can be useful for the optimization of fast gradients.

From Isocratic Data to a Gradient Elution Retention Model in IC: An Artificial Neural Network Approach

Gradient elution is used in ion chromatography to achieve rapid analysis with reasonable separation. Optimization and prediction of the gradient is clearly a multidimensional problem, however. One approach to prediction of gradient retention behavior is based on isocratic experimentation. In this work, a gradient model for simultaneous prediction of the retention behavior of fluoride, chlorite, chloride, chlorate, nitrate, and sulfate ions, on the basis of isocratic experimental data, is proposed. An artificial neural network was used to predict isocratic results; the network was optimized with regard to the number of data in the training set (25) and number of neurons in the hidden layer (6). A slight systematic error was observed in the isocratic prediction, but this did not effect gradient prediction. Good predictions were achieved for all the anions investigated (average error 1.79%). Deviations were somewhat higher for prediction of sulfate retention than for the other anions, probably because of the higher charge and larger size of sulfate in comparison with the other ions examined.

Influence of Acetyl and Amide Groups on Peptides RP-LC Retention Behavior

Reversed phase liquid chromatography (RP-LC) is still one of the most efficient analytical techniques for separation of complex biologically active analytes, including proteins and peptides. However, the separation of those analytes is not easy to perform in practice. Therefore, the appropriate optimization of the separation conditions is necessary. The aim of the study was to explore the influence of acetyl and amide groups in peptides on their retention in gradient elution reversed phase LC. Moreover, the investigation regards the influence of temperature and gradient time for such peptides. Those results were suggested in view of their usefulness in predictions of peptides RP-LC retention on the basis of quantitative structure retention relationships for proteomic research.

Prediction of Analyte Retention for Ion Chromatography Separations Performed Using Elution Profiles Comprising Multiple Isocratic and Gradient Steps

This study addresses the simulation of ion chromatographic (IC) separations performed under conditions where the elution profile consists of a sequence of isocratic and gradient elution steps (referred to as "complex elution profiles"). First, models for prediction of retention under gradient elution conditions in IC were evaluated using an extensive database of gradient elution retention data. It is shown that one such model is preferred on the basis that it can be used to predict gradient retention times on the basis of isocratic input data. A method is then proposed for using this model for complex elution profiles whereby each step of the elution profile is treated separately and analyte movement through the column is mapped. An empirically based algorithm for predicting peak width under complex elution conditions is also proposed. Evaluation of the suggested approaches was undertaken on a set of 24 analyte anions and 13 analyte cations on 5 different Dionex columns using a range of 5-step complex elution profiles that gave R2 values for correlations between predicted and observed retention times of 0.987 for anions and 0.997 for cations. The simulation of separations of anions and cations using a 3-step complex elution profile is demonstrated, with good correlation between observed and predicted chromatograms. The proposed approach is useful for the rapid development of separations when complex elution profiles are used in IC.

Development of gradient elution retention model in ion chromatography by using radial basis function artificial neural networks

This work focuses on problems regarding empirical retention modeling in gradient elution ion chromatography. Traditionally, retention modeling in ion chromatography requires certain assumptions. On the other hand, the use of artificial neural networks provides a promising alternative. In this work, radial basis function artificial neural network were used to model varied inherent non-linear relationship of inorganic anions retention behavior (fluoride, chloride, nitrite, sulphate, bromide, nitrate, and phosphate) with respect to mobile phase parameters (starting time of gradient elution and slope of linear gradient elution curve). The training algorithm of hidden layers was divided into two phase (radial assignment and radial spread) and separately optimized followed by output layer training algorithm optimization (one- or two-phase training algorithm were used, respectively). 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 work shows that radial basis artificial neural networks are found to be a viable retention modeling tool in gradient elution ion chromatography.

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.

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.

Application of the artificial neural network in quantitative structure–gradient elution retention relationship of phenylthiocarbamyl amino acids derivatives

Quantitative structure–retention relationship(QSRR) method was used to model reversed-phase high-performance liquid chromatography (RP-HPLC) separation of 18 selected amino acids. Retention data for phenylthiocarbamyl (PTC) amino acids derivatives were obtained using gradient elution on ODS column with mobile phase of varying acetonitrile, acetate buffer and containing 0.5 ml/l of triethylamine (TEA). Molecular structure of each amino acid was encoded with 36 calculated molecular descriptors. The correlation between the molecular descriptors and the retention time of the compounds in the calibration set was established using the genetic neural network method. A genetic algorithm (GA) was used to select important molecular descriptors and supervised artificial neural network (ANN) was used to correlate mobile phase composition and selected descriptors with the experimentally derived retention times. Retention time values were used as the network's output and calculated molecular descriptors and mobile phase composition as the inputs. The best model with five input descriptors was chosen, and the significance of the selected descriptors for amino acid separation was examined. Results confirmed the dominant role of the organic modifier in such chromatographic systems in addition to lipophilicity (log P) and molecular size and shape (topological indices) of investigated solutes.

Simultaneous optimisation of gradient time, gradient shape and initial composition of the mobile phase in the high-performance liquid chromatography of homologous and oligomeric series

A general approach for optimisation of non-linear gradient elution in reversed-phase and in normal-phase chromatography was suggested. This should be suitable especially for separations of more complex samples containing compounds with repeat units such as members of homologous or oligomeric series where more or less regular retention increase between the adjacent peaks is observed. The approach is based on predictive calculations of the retention and of the resolution of the individual pairs of compounds in the sample mixture. Isocratic or gradient-elution retention data acquired in a few initial runs under different conditions are employed to determine the parameters of retention equations describing the dependence of the retention factor, k, on the composition of the mobile phase and on the number of repeat structural units in homologous or oligomeric series. The approach allows us to optimise simultaneously the initial composition of the mobile phase, the time (volume) and the shape of the gradient to achieve required resolution for all components of the sample mixture in minimum time. Using non-linear gradients, band spacing and peak capacity in the chromatogram may be improved with respect to the elution with linear gradients. For better practical convenience, optimised curved shape of the gradient can be substituted by corresponding multisegmented linear profile. The approach is illustrated by examples of reversed-phase gradient-elution separation of n-alkyl-3,5-dinitrobenzoates and of normal-phase gradient-elution separation of lower oligostyrenes on a silica gel column.

Optimisation of gradient elution in normal-phase high-performance liquid chromatography

An optimisation approach for linear gradient elution in normal-phase chromatography was suggested. The approach is based on predictive calculations of the retention and of the resolution of the individual pairs of compounds in the sample mixture. Isocratic or gradient-elution retention data, acquired in a few initial runs under different conditions, are employed to determine the parameters of retention equations describing the dependence of the retention factor, k, on the composition of the mobile phase. Unlike earlier procedures, a more complex, three-parameter retention equation can be used as the basis of predictive calculations, if necessary. The approach allows one to use either maximised minimum resolution in the sample mixture or the minimum time necessary to achieve the required resolution as the optimisation criterion. It accounts for the contribution of the initial isocratic elution step induced by the gradient dwell volume, so that it is not necessary to delay the injection with respect to the start of the gradient. Simultaneous optimisation of the gradient slope and of the gradient range is performed, with the gradient volume (time), plate number and other variables as adjustable parameters. The approach is illustrated by examples of gradient-elution separation of phenylurea herbicides on a silica gel and on a bonded nitrile column, with binary gradients of 2-propanol in n-heptane and of dioxane in n-heptane. Dried solvents and the temperature (controlled to ±0.1°C) were used to improve the reproducibility of the retention data.

Gradient high‐performance liquid chromatography of statistical and block copolymers of styrene and t‐butyl methacrylate

AbstractCopolymers of styrene (S) and tert‐butyl methacrylate (TBMA) containing 24–92 mass % of the latter monomer were investigated using a silica column with isooctane/tetrahydrofuran (THF) gradients and on a phenyl bonded‐phase column by methanol (MeOH)/THF gradients using UV detection. In both cases, retention decreased with increasing TBMA content of the sample. This is in contrast to the behavior of copolymers of S and methyl methacrylate (MMA) whose retention in gradient elution on silica columns increases with MMA content due to the polarity of this unit. The inversion of elution order is a result of the bulky TBMA residues shielding the polar groups of the ester units. For copolymers of varying composition, the gradation in retention on retention on silica is quite sufficient for separating S/MMA but not for S/TBMA mixtures. The latter could be separated by composition on phenyl packings through MeOH/THF gradient elution. Block copolymers containing 80 or 92% TBMA could be baseline‐separated. It was also possible to separate these samples from admixed PTBMA or PS homopolymers. Under the conditions used, the retention of a given block copolymer was somewhat higher than that of a statistical copolymer having the same composition. A block copolymer containing 80% TBMA was converted by transesterification into a S/MMA block copolymer. The elution of the latter fitted well in the sequence of S/MMA copolymers on silica column.

Relationship between isocratic and gradient retention times in the high-performance ion-exchange chromatography of proteins : Theory and experiment

Using isocratic retention parameters, the gradient elution retention time for several proteins has been calculated. The gradient retention time calculation is based on fitting the isocratic retention data to an equation of the form: log k′  m log (1/[Ca 2+]) + log K and on applying well-established principles of gradient elution. A good correlation between the observed and calculated retention times for several test proteins was obtained at various total gradient times and column flow-rates. Conversely, isocratic retention parameters characterizing protein retention can be calculated from gradient elution retention data. However, even with retention data of high quality, small errors are amplified by the log—log nature of the ion-exchange isocratic retention model employed. Based on the close correlation between predicted and observed gradient retention times, no evidence for protein denaturation resulting from immobilization of the protein at high initial k′ values at or near the column inlet was observed.

Salt-mediated retention of proteins in hydrophobic-interaction chromatography : Application of solvophobic theory

Retention behavior in hydrophobic-interaction chromatography was examined within the framework of the solvophobic theory. The principal parameters which determine the effect of salt on the retention are salt molality and the molal surface tension increment of the salt. According to the theory, in the absence of special binding effects, increase in salt molality in the mobile phase or change of salt to one of greater molal surface tension increment will result in increased retention of proteins in hydrophobic chromatography. The theory is expanded to treat retention in gradient elution with linear decrease in salt concentration that is equivalent to linear increase in eluent strength. The results of the simple model lead to an expression with two parameters: the adjusted isocratic retention volume of the eluite with the gradient former and the slope of plot of logarithmic adjusted elution volume against salt molality,λ. The latter parameter is linearly dependent on molal surface tensio increment if no specific interactions between the eluite and the stationary phase and/or salt are present. In practice, deviations are to be expected from the predicted behavior due to such effects. The results of calculations are consistent with experimental results obtained with several proteins as the eluites and various salts in the eluent. Although unique values of the critical parameter λ could not be obtained from the data, the trends showed that λ is strongly correlated with the value of the molal surface tension increment. The prediction that increase in salt concentration in the initial eluent leads to increase in retention volume was found to be generally true, even when the isocratic retention volumes obtained with the use of eluent having low salt concentration were small. Use of NaClO 4 in the starting eluent led in some cases to decrease in retention volume with increase in the salt concentration at the beginning of the gradient elution. This effect may be due to specific binding effects.

Measurement and use of retention data from high-performance gradient elution : Correction for “non-ideal” processes originating within the column

Under “ideal” conditions it is possible to model retention in gradient elution so as to be able to calculate retention times, t g, as a function of isocratic retention in corresponding liquid chromatographic systems. In this paper we consider various “non-ideal” processes that lead to errors in calculated values of t g. The more important of these are solvent demixing due to uptake of one mobile phase component by the column packing, non-linear plots of log k′ vs. gradient time or mobile phase composition and changes in column dead-time, t 0, due to changes in mobile phase composition and flow-rate. Expressions are derived to correct for these various “non-ideal” effects, including equipment limitations discussed in the preceding paper. Calculated values of t g for reversed-phase gradient elution systems then agree with experimental values to within ± 1 % (1 standard deviation) of the total gradient time, t G. These results should prove useful in (a) improving the precision of retention in gradient elution (which should be comparable to that in isocratic elution), (b) using gradient elution for more efficient method development in isocratic procedures and (c) better understanding gradient separations of macromolecules such as proteins.