Application of the phenomenological model to retention in reversed-phase high-performance liquid chromatography

Mathematical Modelling in Analytical Chromatography: Problems and Solutions

Abstract

Based on an analysis of the results of original research performed in the Laboratory of Sorption Methods of the Vernadsky Institute of Geochemistry and Analytical Chemistry of the Russian Academy of Sciences within the project “Mathematical Chromatograph,” the review covers the aim and strategy of the imitation modeling of high-performance chromatography; associated problems of the theory of intermolecular interactions; classifications of polar stationary phases by their selectivity; descriptions of the kinetics and dynamics of sorption processes, choice of the composition of multicomponent mobile phases in HPLC and ion chromatography using the method of the dynamic map of a chromatographic system; and the development of alternating gradient modes using a mathematical experiment.

Mathematical representation of xanthine oxidase activity in hydro-organic mixtures

A mathematical model is proposed to calculate the enzyme activity in different concentrations of the organic solvent in hydro-organic mixtures. The accuracy and predictability of the model have been evaluated employing experimentally determined xanthine oxidase activity in five hydro-organic mixtures by using absolute percentage mean deviation (APMD). The obtained APMD for correlative and predictive studies were 5.3% and 7.6%, respectively.

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.

Optimization methods in chromatography and capillary electrophoresis

Many methods have been developed in order to optimize the parameters of interest in either chromatography or capillary electrophoresis. In chemometric approaches experimental measurements are performed in such a way that all factors vary together. An objective function is utilized in which the analyst introduces the desired criteria (selectivity, resolution, time of analysis). Simplex methods and overlapping resolution maps are declining. Factorial designs and central composite designs are more and more popular in electrodriven capillary separations since the number of parameters to master is much larger than in either GC or LC. The use of artificial neural networks is increasing. The advantage of chemometrics tools is that no explicit models are required, conversely the number of experiments to perform may be high and boundaries of the domain are not straightforward to draw and the approach does more than is required. When models are available optimization is easier to perform by regression methods. Computer assisted methods in RPLC are readily available and work well but are still in infancy in CE. Linear solvation energy relationships seem a very valuable tool but estimates of coefficients still require many experiments.

Reversed-phase high-performance liquid chromatography of ionogenic compounds: comparison of retention models

Two kinds of retention models describing a behaviour of ionogenic substances in reversed-phase chromatographic systems were compared. Model A utilises a concept of limiting retention factors and is especially suitable for the prediction of retention of compounds co-existing in several forms in mobile phase. An effect of the concentration of organic modifier (e.g., methanol) on the magnitudes of the limiting retention factors and equilibrium constants (dissociation constants of the separated substances) can be expressed with the aid of various, more or less sophisticated, relationships. A stoichiometric displacement model (model B) in its original form simply relates the analyte retention to the content of organic modifier in the mobile phase. In this work, it was modified to also express an effect of the mobile phase pH introducing side equilibria (acid-base) into the model. Both models predict a sigmoidal dependence of the analyte retention factor on the mobile phase pH in accordance with experimental data, and allow, among others, to estimate dissociation constants from those data. Experimental dependencies between the analyte retention and the concentration of methanol in the mobile phase comply well with model A, whereas the stoichiometric displacement model could be used only in a limited range of the methanol concentrations.