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.     

Characterization and prediction of retention in gradient-elution normal phase HPLC with ternary gradients

Summary Chromatographic behaviour of phenylurea herbicides and phenols on a silica gel column with ternary gradient elution using mobile phases containing dry 2-propanol, n-heptane and dioxane was investigated. With dried solvents and the temperature controlled to ±0.1 °C, the data from repeated experiments measured on the same column after ten months of use were reproducible. Algorithms were suggested for characterization and prediction of retention in ternary gradients at a constant ratio of the two polar solvents (elution strength gradients) and at a constant sum of their concentrations (selectivity gradients). These were based on two- and three-parameter equations describing the dependence of the sample retention factors (isocratic) on the concentration of the polar solvent in binary mobile phases. Presented at the 21^st ISC held in Stuttgart, Germany, 15^th–20^th September, 1996     

Simple algorithms for fitting and optimisation for multilinear gradient elution in reversed-phase liquid chromatography

The theory of the multilinear gradient elution in reversed-phase liquid chromatography (RP-HPLC) presented in [P. Nikitas, A. Pappa-Louisi, P. Agrafiotou, J. Chromatogr. A 1120 (2006) 299] is modified to increase its flexibility. In addition, it is embodied to simple algorithms for fitting gradient data and especially for resolution optimisation under multilinear gradient conditions. In particular, two new algorithms for fitting and one for optimisation are tested and compared with conventional algorithms. Their performance was examined using 13 o-phthalaldehyde (OPA) derivatives of amino acids with mobile phases modified by acetonitrile. It was found that the new proposed algorithms, a repeated application of the Levenberg-Marquardt (LM) method for fitting (R_LM) and a modified descent algorithm for optimisation (RND_D), in combination with the modified theory of the multilinear gradient elution can lead to high quality predictions of the retention times and optimisation results.     

Retention prediction in ternary solvent reversed-phase liquid chromatography systems based on the variation of retention with binary mobile phase composition

An extension of the treatment adopted in a recent paper [P. Nikitas, A. Pappa-Louisi, P. Agrafiotou, J. Chromatogr. A 946 (2002) 33] was used to derive expressions describing the variation of solute retention k with composition in ternary reversed phase liquid chromatography, RP-LC, solvent systems. The equation of the partition model obtained in this way for a ternary mobile phase was identical to that previously derived using the solubility parameter concept. This equation as well as two new expressions of In k versus organic modifiers content were tested in a variety of ternary solvent systems in order to examine the possibility of predicting retention behavior of solutes under ternary solvent mixture elution conditions from known retention characteristics in binary mobile phases. It was demonstrated the superiority of both new equations derived in this paper to that previously proposed and applied to date in ternary solvent mixtures.     

Prediction of Retention in Liquid-Solid Chromatography with Ternary Mobile Phases

The method for the prediction of capacity factors in ternary mobile phases is presented. The adsorption mechanism of retention is considered. The simple theoretical equations are proposed for mobile phases for which the ratio of mole fractions of the weaker solvents remains fixed. The relations between parameters characterizing retention in ternary and binary mobile phases are discussed. The theoretical model is verified for numerous solutes and different mobile phases.     

Adsorption model for retention in normal-phase liquid chromatography with ternary mobile phases

The review gives a link between the theory of adsorption from multicomponent solutions and liquid chromatography. The article surveys the methods developed to describe the retention in normal-phase chromatography with ternary mobile phases with emphasis on the results of the authors. In the model used the driving force for the separation is the difference in adsorption of a solute and all solvents onto the solid surface. The general equation generates a series of simple linear relationships to predict the retention factor in ternary mobile phase for which certain parameters remain fixed. Theoretical concepts are tested by comparison with experimental data. The correlations between parameters characterizing retention in ternary, binary and pure solvents are discussed.     

Adsorption-driven retention in normal-phase chromatography with ternary mobile phases

The model for retention in chromatographic systems using ternary mobile phases is considered. The driving force for the separation is assumed to be only a difference in adsorptive properties of a solute and all solvents. The effects of mobile phase composition are discussed. A series of very simple dependences between parameters characterizing retention in ternary and binary solvents is presented. The linear relationship is proposed to predict the capacity factor in the ternary mobile phase, for which the ratio of mole fractions of two less-polar solvents remains fixed. Theoretical concepts are verified by comparing the calculated values with experimental data measured in the entire concentration region.     

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.     

Automated off-line optimisation of programmed elutions in reversed-phase high-performance liquid chromatography using ternary solvent mixtures

A new system for the unattended optimisation of gradient elutions in reversed-phase high-performance liquid chromatography has been developed. The system is based on the simulation of retention times under conditions of ternary solvent mixtures and ternary gradient programmes. This model is constructed departing from a few experimental data obtained in isocratic elutions and validated against experimental gradient elutions. Once validated, this retention model can be used for the unattended search of an optimum separation. The optimisation process is driven by an evolutionary algorithm (EA), specially developed to map the ternary gradient elutions problem. The development and characteristics of the retention modelling as well as those of the EA and its particularities are discussed and some real world examples of separation presented.     

Obtimization of separation conditions in reversed phase liquid chromatography using complex solvent mixtures

Summary Four different methods of calculation of retention in ternary mobile phases were compared and it was found that the simple calculation based only on two values of the capacity factors (one for each binary system that composes the ternary mobile phase) provides the accuracy of prediction that is, at least, comparable to the other methods of calculation that require a large number of preliminary experiments. The deviations from ideal behaviour in ternary solvent mixtures are discussed; some sources of errors can be avoided, at least partially, using binary systems of adequate compositions for preparation of ternary mobile phases. Several examples show the comparison of calculated and experimental selectivities in ternary solvent systems. A simple calculation can be used for rapid selection of an adequate ternary (or more complex) mobile phase, if it is necessary to achieve the separation of a given sample mixture.Presented at the 14th International Symposium on Chromatography London, September, 1982     

流动相组成对外消旋阿苯达唑亚砜对映体拆分的影响

涂敷直链淀粉-三(3,5-二甲基苯基氨基甲酸酯)(ADMPC)于自制的球形氨丙基硅胶上,制备了一种手性固定相。采用高效液相色谱法(HPLC),在正相条件下用该固定相直接拆分了广谱驱虫药物阿苯达唑的代谢产物阿苯达唑亚砜(albendazole sulfoxide, ABZSO)的外消旋对映体。系统地选用了多种二元及三元流动相体系对样品进行拆分,结果表明,流动相中不同种类的醇改性剂及其含量的不同对样品的保留时间和立体选择性有不同程度的影响,甲醇、乙醇等作改性剂用于拆分样品的效果较好;采用三元流动相体系正己烷-     

Adsorption interaction parameter of polyethers in ternary mobile phases: The critical adsorption line

It is shown that in LC of polymers, the interaction parameter in ternary mobile phases can be described by a plane, which is determined by the dependencies in binary mobile phases. Instead of a critical adsorption point, critical conditions are observed along a straight line of composition between the two critical points in binary mobile phases. Consequently, a separation of block copolymers under critical conditions for one block by an adsorption mechanism for the other block can be achieved in ternary mobile phases of different compositions, which allows an adjustment of the retention of the adsorbing block.     

Theory of retention in reversed phase liquid chromatography with ternary mobile phases

The partition model of retention is developed for reversed phase liquid chromatography with multicomponent mobile phases. Simple equations for the retention and selectivity in ternary mobile phases are derived. For the systems in which the ratio of volume fractions of organic modifiers remains fixed, new linear dependences for retention factor and selectivity are proposed. These equations are successfully used to describe experimental data found in the literature. An influence of the nature of organic solvents and proportion in which they are mixed on retention and selectivity is discussed.     

Optimization of separation in two-dimensional high-performance liquid chromatography by adjusting phase system selectivity and using programmed elution techniques

The overall peak capacity in comprehensive two-dimensional liquid chromatographic (LC x LC) separation can be considerably increased using efficient columns and carefully optimized mobile phases providing large differences in the retention mechanisms and separation selectivity between the first and the second dimension. Gradient-elution operation and fraction-transfer modulation by matching the retention and the elution strength of the mobile phases in the two dimensions are useful means to suppress the band broadening in the second dimension and to increase the number of sample compounds separated in LC x LC. Matching parallel gradients in the first and second dimension eliminate the necessity of second-dimension column re-equilibration after the independent gradient runs for each fraction, increase the use of the available second-dimension separation time and can significantly improve the regularity of the coverage of the available retention space in LC x LC separations, especially with the first- and second-dimension systems showing partial selectivity correlations. Systematic development of an LC x LC method with parallel two-dimensional gradients was applied for separation of phenolic acids and flavone compounds. Several types of bonded C18, amide, phenyl, pentafluorophenyl and poly(ethylene glycol) columns were compared using the linear free energy relationship method to find suitable column combination with low correlation of retention of representative standards. The phase systems were optimized step-by-step to find the mobile phases and gradients providing best separation selectivity for phenolic compounds. The optimization of simultaneous parallel gradients in the first and second dimension resulted in significant improvement in the utilization of the available two-dimensional retention space.     

Retention in liquid chromatography with multicomponent mobile phases: Relationship with binary systems

Summary Using the concept of an effective concentration a method is proposed for predicting retention in liquid chromatography with multicomponent mobile phases based on experiments with corresponding binary ones. The method is verified for normal and reversed-phase systems with ternary mobile phases and agrees closely with experimental data.     

Predictive Optimization of the Separation of Phenylurea Pesticides using Ternary Mobile Phase Gradients in Reversed-Phase HPLC

Abstract

The method for optimization of ternary mobile phase gradients in HPLC developed earlier is illustrated on a practical example of reversed-phase separation of phenylurea pesticides. Predictive calculation methods were used to optimize subsequently “solvent strength”, “selectivity” and “combined solvent strength - selectivity” gradients. The merits of the three types of ternary gradients for this specific separation problem are discussed to elucidate the basic principles of the optimization strategy. The predicted retention data are compared with the experimental results and the limitations of the approach are shown. The present method makes it possible to reduce significantly the number of experiments and calculations necessary to perform the optimization in comparison to a systematic search of the optimized parametr space.     

禾草灵对映体在纤维素-三(3,5-二甲基苯基氨基甲酸酯)手性固定相上的拆分

将纤维素-三(3,5-二甲基苯基氨基甲酸酯)(CDMPC)涂敷于自制的球形氨丙基硅胶上,制备了手性固定相.在正相条件下,用高效液相色谱法在该固定相上直接拆分了农药禾草灵的外消旋体,并系统地选用了多种二元及三元流动相体系对样品进行拆分.实验结果表明,流动相中不同的醇类改性剂及其含量的不同对样品保留时间和立体选择性有不同程度的影响,选用异丙醇改性剂时样品的拆分效果较好,在三元流动相体系正己烷/异丙醇/乙醇中可以实现对禾草灵外消旋体快速有效的拆分.     

A refined physico-chemical model of solute retention in reversed-phase high-performance liquid chromatography with ternary mobile phases

Summary In our previous publication we have introduced a new model of solute retention in RP-HPLC systems with ternary mobile phases of the B+AB₁+AB₂ type (B: acetonitrile or tetrahydrofuran; AB₁: methanol; AB₂: water). That model proposed no stoichiometric differentiation between acetonitrile and tetrahydrofuran, alternatively present in the solvent system; moreover, it made some very rough assumptions only as to the intermolecular interactions among the mobile phase constituents.This paper introduces a significant refinement to the already established retention model, which is based on the simple quantitative relationships between acetonitrile and tetrahydrofuran, and the remaining components of the ternary liquid system. The refined model is tested with same experimental data.     

Evaluation of ternary mobile phases for reversed-phase liquid chromatography: Effect of composition on retention mechanism

The effect of varying mobile phase composition across a ternary space between two binary compositions is examined, on four different reversed-phase stationary phases. Examined stationary phases included endcapped C8 and C18, as well as a phenyl phase and a C18 phase with an embedded polar group (EPG). Mobile phases consisting of 50% water and various fractions of methanol and acetonitrile were evaluated. Retention thermodynamics are assessed via use of the van’t Hoff relationship, and retention mechanism is characterized via LSER analysis, as mobile phase composition was varied from 50/50/0 water/methanol/acetonitrile to 50/0/50 water/methanol acetonitrile. As expected, as the fraction of acetonitrile increases in the mobile phase, retention decreases. In most cases, the driving force for this decrease in retention is a reduction of the enthalpic contribution to retention. The entropic contribution to retention actually increases with acetonitrile content, but not enough to overcome the reduction in the enthalpic contribution. In a similar fashion, as methanol is replaced with acetonitrile, the v, e, and a LSER system constants change to favor elution, while the s and c constants change to favor retention. The b system constant did not show a monotonic change with mobile phase composition. Overall changes in retention across the mobile phase composition range varied, based on the identity of the stationary phase and the composition of the mobile phase.