Retention models for programmed gas chromatography

The models proposed by many authors for the prediction of retention times and temperatures, peak widths, retention indices and separation numbers in programmed temperature and pressure gas chromatography by starting from preliminary measurements of the retention in isothermal and isobaric conditions are reviewed. Several articles showing the correlation between retention data and thermodynamic parameters and the determination of the optimum programming rate are reported. The columns of different polarity used for the experimental measurement and the main equations, mathematical models and calculation procedures are listed. An empirical approach was used in the early models, followed by the application of thermodynamic considerations, iterative calculation procedures and statistical methods, based on increased computing power now available. Multiple column arrangements, simultaneous temperature and pressure programming, applications of two-dimensional and fast chromatography are summarised.     

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).     

Retention process in reversed phase TLC systems with polar bonded stationary phases

The retention of a solute in RP chromatography is a very complex process which depends on many factors. Therefore, the study of the influence of a mobile phase modifier concentration on the retention in different reversed phase chromatographic systems is very important for understanding the rules governing retention and mechanisms of substance separation in a chromatographic process. Composition changes and the nature of mobile phases enable tuning of the separated analytes' retention over a wide range of retention parameters and optimization of the chromatographic process as well. Optimization of the chromatographic process can be achieved by several different methods; one of them is the so-called interpretative strategy. The key approach adopted in this strategy is the implementation of adequate retention models that couple the retention of solute with the composition of a mixed mobile phase. The use of chemically bonded stationary phases composed of partially non-bonded silica matrix and organic ligands bonded to its surface in everyday chromatography practice leads to questions of the correct definition of the retention model and the dominant retention mechanism in such chromatographic systems. The retention model for an accurate prediction of retention factor as a function of modifier concentration and the heterogeneity of the adsorbent surface should be taken into consideration. In this work the influence of mobile-phase composition on the retention of sixteen model substances such as phenols, quinolines, and anilines used as test analytes in different RP-TLC systems with CN-, NH2-, and Diol-silica polar bonded stationary phases has been studied. The aim of this study is to compare the performance of three valuable retention models assumed as the partition, adsorption/partition, and adsorption mechanism of retention. All the models were verified for different RP-TLC systems by three statistical criteria. The results of investigations presented in this work demonstrate that the best agreement between the experimental and calculated Rf values was obtained by the use of new-generation retention models, which assume heterogeneity of adsorbent surface. The results reported here show that heterogeneity of the adsorbent surface may be important in analysis of the elution process in liquid chromatography. Consideration of the goodness of fit for the experimental data to the examined retention models is in conformity with the adsorption mechanism of retention on all polar bonded stationary phases in most eluent systems for most investigated compounds.     

Phenomenon of dual‐ and single‐retention behaviors of solutes and its validation by computational simulation in linear programmed temperature gas chromatography

The current theory of programmed temperature gas chromatography considers that solutes are focused by the stationary phase at the column head completely and does not explicitly recognize the different effects of initial temperature (T_o) and heating rate (r_T) on the retention time or temperature of a homologue series. In the present study, n‐alkanes, 1‐alkenes, 1‐alkyl alcohols, alkyl benzenes, and fatty acid methyl esters standards were used as model chemicals and were separated on two nonpolar columns, one moderately polar column and one polar column. Effects of T_o and r_T on the retention of nonstationary phase focusing solutes can be explicitly described with isothermal and cubic equation models, respectively. When the solutes were in the stationary phase focusing status, the single‐retention behavior of solutes was observed. It is simple, dependent upon r_T only and can be well described by the cubic equation model that was visualized through four sequential slope analyses. These observed dual‐ and single‐retention behaviors of solutes were validated by various experimental data, physical properties, and computational simulation.     

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

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

A New Equation for Solute Retention in Liquid Chromatography

In consideration of the adsorption of solvent, diluent and solute molecules on the surface of a stationaryphase, a new equation for solute retention in liquid chromatography is presented. This equation includesthree parameters: the displacement equilibrium constant (Ksd) between the solvent and diluent molecules onthe surface of the stationary phase, the total number(N) of the solvent and diluent molecules released fromthe stationary phase after one solute molecule being adsorbed, and the parameter (I) related to the thermody-namic equilibrium constant for the solute adsorption on the stationary phase. Over the whole concentrationrange of the solvent in the mobile phase, the experimental retention data can be well described by this equa-tion, parameters K~, N and I can be obtained by the regression analysis of the experimental retention data,and consequently the number of the solvent and the diluent molecules displaced by one solute molecule fromthe stationary phase can also be derived at different solvent concentrations in the mobile phase,     

Simple models for the effect of aliphatic alcohol additives on the retention in reversed-phase liquid chromatography

Four retention models for the effect of aliphatic alcohol additives on the retention of analytes in reversed-phase liquid chromatography have been developed following either a semi-thermodynamic treatment or an empirical approach. Their performance was tested using the experimental retention times of six non-polar analytes (alkylbenzenes) and ten o-phthalaldehyde derivatives of amino acids under different isocratic chromatographic runs when a small amount of ethanol, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol or 1-heptanol was added to methanol/water mixtures containing a constant amount of methanol. It was shown that for the structurally simple alkylbenzenes all the models can be adopted for retention prediction with good results. In contrast, just one out of four models, that with the fewest approximations, predicts satisfactorily the retention properties of amino acids derivatives. However, the most interesting feature is that this model can predict the effect of an alcohol-additive on the retention properties of solutes, even if this additive was not used in chromatographic runs done for the fitting procedure, provided that it belongs to the same homologous series of alkanols. This feature is also observed in all models described the retention of alkylbenzenes.     

Heteroscedasticity of retention factor and adequate modeling in micellar liquid chromatography

The two concepts of micelle formation (pseudo-phase and mass-action) could be the basis of retention models in micellar liquid chromatography (MLC). The separation of 4-hydroxybenzoic acid esters and seven polyaromatic hydrocarbons were performed to study the repeatability of retention factor in MLC. The full two factor experimental design was used for studying the dependence of retention factor variance on mobile phase composition (sodium dodecylsulfate, 1-butanol). The experimentally observed heteroscedasticity and perturbations after linearization were taken into account by using statistical weights obtained on the basis of errors propagation law and the modeling of retention by non-weighted and weighted least squares method was performed. The mechanistical retention models based on pseudo-phase and mass-action concepts of micelle formation were compared by fitting quality and prediction capability and high robustness of bilogarithmic dependence was observed. The significance of retention factor heteroscedasticity for retention hydrophobicity relationships was shown.     

Retention in SFC at high density

The elucidation of the detailed mechanism of retention in supercritical fluid chromatography (SFC) is a complex problem, especially for high-density supercritical fluid mobile phases. Martire and Boehm developed a theory of SFC retention based on a statistical thermodynamic treatment, and introduced a density-squared equation for retention in SFC: In k = a + b/T + cρ + dρ/T + eρ²/T. In this paper the systems n-alkane-polydimethylsiloxane-CO₂ and n-carboxylic acid methyl ester-polydimethylsiloxane-CO₂ have been treated using the method introduced by Martire and Boehm. In the ranges of reduced temperature from 1.079 to 1.293 and reduced SF mobile phase density from 0.705 to 1.632, two problems were discovered in the treatment of SFC retention behavior by the method of Martire and Boehm: (1) the experimental value of the site of CO₂ in the lattice field, r_a, of the two systems was ca 0.9, which is obviously different from the theoretical values of 3.6 or 5.4; and (2) the difference between experimental and calculated retention values increased with increasing SF mobile phase density. The minimum in SFC retention predicted by Martire and Boehm was not observed. On the basis of some assumptions and the experimental data, the following retention equation was derived: In k = a + b/T + cρ + dρ/T + eρ²/T + fρ³/T + gρ⁴/T. This equation was consistent with the experimental data and can conveniently be used to explain other SFC retention behavior.     

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.     

Alternating iterative regression method for dead time estimation from experimental designs

An indirect method for dead time (t ₀) estimation in reversed-phase liquid chromatography, based on a relationship between retention time and organic solvent content, is proposed. The method processes the retention data obtained in experimental designs. In order to get more general validity and enhance the accuracy, the information from several compounds is used altogether in an alternating regression fashion. The method was applied to nitrosamines, alkylbenzenes, phenols, benzene derivatives, polycyclic aromatic hydrocarbons and β-blockers, among other compounds, chromatographed in a cyano and several C18 columns. A comprehensive validation was carried out by comparing the results with those provided by the injection of markers, the observation of the solvent front and the homologous series method. It was also found that different groups of compounds yielded the same t ₀ value with the same column, which was verified in different solvent composition windows. The method allows improved models useful for optimisation or for other purposes, since t ₀ can be estimated with the retention data of the target solutes.       

iMatch: a retention index tool for analysis of gas chromatography-mass spectrometry data

A method was developed to employ National Institute of Standards and Technology (NIST) 2008 retention index database information for molecular retention matching via constructing a set of empirical distribution functions (DFs) of the absolute retention index deviation to its mean value. The effects of different experimental parameters on the molecules' retention indices were first assessed. The column class, the column type, and the data type have significant effects on the retention index values acquired on capillary columns. However, the normal alkane retention index (I(norm)) with the ramp condition is similar to the linear retention index (I(T)), while the I(norm) with the isothermal condition is similar to the Kováts retention index (I). As for the I(norm) with the complex condition, these data should be treated as an additional group, because the mean I(norm) value of the polar column is significantly different from the I(T). Based on this analysis, nine DFs were generated from the grouped retention index data. The DF information was further implemented into a software program called iMatch. The performance of iMatch was evaluated using experimental data of a mixture of standards and metabolite extract of rat plasma with spiked-in standards. About 19% of the molecules identified by ChromaTOF were filtered out by iMatch from the identification list of electron ionization (EI) mass spectral matching, while all of the spiked-in standards were preserved. The analysis results demonstrate that using the retention index values, via constructing a set of DFs, can improve the spectral matching-based identifications by reducing a significant portion of false-positives.     

Influence of surface modification on protein retention in ion-exchange chromatography: Evaluation using different retention models

A large number of different stationary phases for ion-exchange chromatography (IEC) from different manufacturers are available, which vary significantly in a number of chemical and physical properties. As a consequence, binding mechanisms may be different as well. In the work reported here, the retention data of model proteins (α-lactalbumin, β-lactoglobulin A, bovine serum albumin and alcohol dehydrogenase) were determined for three anion-exchange adsorbents based on synthetic copolymer beads with differences in the functional group chemistry. Fractogel EMD DEAE and Fractoprep DEAE consist of functional groups bound to the surface via “tentacles”, ToyopearlDEAE by a short linker. Three models which describe chromatographic retention were used to analyse the characteristic parameters of the protein/stationary-phase interactions. The number of electrostatic interaction between the stationary phase and the model proteins, the protein specific surface charge densities and the interacting surface of the proteins with the adsorptive layer of the chromatographic media depend on the surface modification as well as on the molecular mass of the model proteins. In general, protein retention of the model proteins on the weak anion exchangers was found to be greater if the stationary phase carries tentacles and protein mass is above 60 kDa.     

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.     

Retention in coupled capillary column supercritical fluid chromatography with lipids as model compounds

Summary We have investigated to which extent retention data, acquired on single capillary columns, can be used for predicting retention factors in a coupled column system. For this purpose we utilized a model mixture of 18 lipid components with widely different vapor pressures and polarities. The sample was chromatographed on two columns, SB-biphenyl-30 (70% methyl-30% biphenylpolysiloxane) and SB-cyanopropyl-50 (50% methyl-50% cyanopropylsiloxane). Experimental retention factors, acquired in coupled column systems with two columns connected in different order, were thus compared with values calculated from runs on each single column. The agreement between calculated and experimental values generally was better than 5% without any pressure drop correction.To study the possibility of predicting retention behavior in a wide pressure range from a limited number of experiments, we also investigated the relation between solute retention and mobile phase density. We found that all data could be fitted to second order equations, which gives the possibility to optimize the resolution with respect to pressure from a limited number of runs at different pressures.